Laser Doppler Vibrometry for Non-Contact Diagnostics [1st ed.] 9783030466909, 9783030466916

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Bioanalysis Series Editor: Tuan Vo-Dinh

Kristian Kroschel   Editor

Laser Doppler Vibrometry for Non-Contact Diagnostics

Bioanalysis Advanced Materials, Methods, and Devices Volume 9

Series Editor Tuan Vo-Dinh, Fitzpatrick Institute for Photonics, Duke University, Durham, NC, USA

The book series on BIOANALYSIS: Advanced Materials, Methods, and Devices is intended to serve as an authoritative reference source for a broad, interdisciplinary audience involved in the research, teaching, learning, and practice of bioanalytical science and technology. Bioanalysis has experienced explosive growth due to the dramatic convergence of advanced technologies and molecular biology research, which has led to the development of entirely new ways to probe biomolecular and cellular processes as well as biological responses to implanted biomaterials and engineered tissues. Novel optical techniques using a wide variety of reporter gene assays, ion channel probes, and fluorescent probes have provided powerful bioanalytical tools for cell-based assays. Fluorescent reporters allow the development of live cell assays with the ability for in vivo sensing of individual biological responses across cell populations, tracking the transport of biological species within intracellular environments, and monitoring multiple responses from the same cell. Novel classes of labels using inorganic fluorophors based on quantum dots or surface-enhanced Raman scattering labels provide unique possibilities for multiplex bioanalyses. Laser-based technologies are important in the development of ultrasensitive bioanalytical techniques. Lasers are now used as excitation light sources in a wide variety of molecular bioassays. Today, single-molecule detection techniques using laser excitation provide the ultimate tools to elucidate cellular processes. The possibility of fabricating nanoscale materials and components has recently led to the development of devices and techniques that can measure fundamental parameters at the molecular level. With “optical tweezer” techniques, for example, small particles may be trapped by radiation pressure in the focal volume of a high-intensity, focused laser beam. Ingenious optical trapping systems have also been used to measure the force exerted by individual motor proteins. Whereas the laser has provided a new technology for excitation, the miniaturization and mass production of sensor devices and their associated electronic circuitry has radically transformed the ways detection and imaging of biological species can be performed in vivo and ex vivo. Sensor miniaturization has enabled significant advances in imaging technologies over the last decade in such areas as microarrays and biochips for bioanalysis of a wide variety of species. The miniaturization of high-density optical sensor arrays has also led to the development of advanced high-resolution imaging methods at the cellular or molecular scales. With powerful microscopic tools using near-field optics, scientists are now able to image the biochemical processes and sub-microscopic structures of living cells at unprecedented resolutions. Recently, nanotechnology, which involves research on and development of materials and species at length scales between 1 to 100 nanometers, has been revolutionizing important areas in bioanalysis at the molecular and cellular level. The combination of molecular nanotechnology and various sensing modalities (optical, electrochemical, etc) opens the possibility of detecting and manipulating atoms and molecules using nano-devices, which have the potential for a wide variety of bioanalyses at the cellular level. These new bioanalytical tools are capable of probing the nanometer world and will make it possible to characterize the chemical and mechanical properties of biomolecules and cells, discover novel phenomena and processes, and provide science with a wide range of tools, materials, devices, and systems with unique characteristics. This book series will present the most recent scientific and technological advances in materials, methods and instrumentation of interest to researchers, students, and manufacturers. The goal is to provide a comprehensive forum to integrate the contributions of biophysicists, biomedical engineers, materials scientists, chemists, chemical engineers, biologists, and others involved in the science and technology revolution reshaping molecular biology and biomedicine. More information about this series at http://www.springer.com/series/8091

Kristian Kroschel Editor

Laser Doppler Vibrometry for Non-Contact Diagnostics

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Editor Kristian Kroschel VID Fraunhofer Institute of Optronics, System Technologies and Image Exploitation IOSB Karlsruhe, Baden-Württemberg, Germany

ISSN 2364-1118 ISSN 2364-1126 (electronic) Bioanalysis ISBN 978-3-030-46690-9 ISBN 978-3-030-46691-6 (eBook) https://doi.org/10.1007/978-3-030-46691-6 © Springer Nature Switzerland AG 2020 This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publisher, the authors and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, express or implied, with respect to the material contained herein or for any errors or omissions that may have been made. The publisher remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. This Springer imprint is published by the registered company Springer Nature Switzerland AG The registered company address is: Gewerbestrasse 11, 6330 Cham, Switzerland

Preface

Cardiovascular diseases are with 40% the most frequent death reason followed by cancer. Many patients realize that they are suffering from heart-circulation diseases in a late state when there is no chance to overcome the disease anymore. An example is atrial fibrillation, which leads to tiredness and lack of activation which mostly is not assumed to be caused by heart disease but by other less dangerous reasons. Therefore, the idea came up to check the heart functionality every day in the morning and evening when people brush their teeth and stand in front of the mirror in the bathroom. A small box beside the mirror observes the client and measures her or his heart activity by acquiring vibration signals picked up from the human body with a small-size Laser Doppler Vibrometer (vibrocardiogram). If there are no hints for a malfunction of the heart, no message is sent to a health center from where the patient would get help if this is required. The main advantage of this approach is that the patient does not realize that data are picked up, since in contrast to the well-established electrocardiogram the vibrocardiogram is picked up contactless. Another aspect is that the patient will behave as if no measurement would take place. So she or he is not anxious, stressed, or nervous knowing that data are picked up. To realize this setting, besides the small-size laser Doppler vibrometer a detection system is required to decide whether a person is in front of the system or not. Furthermore, a pan-tilt unit has to track the optimal position for measurement. Since the patient might wear a bathing gown, the best position for measurement might not be a region on the thorax closest to the heart but the neck or throat which is not covered by the gown. Last but not least, the price has to be affordable for mass consumption. The new device has despite the advantage of contactless measurement to compete in its price with today's available systems for the measurement of the electrocardiogram. This is a quite ambitious challenge for a laser Doppler vibrometer! Karlsruhe, Germany October 2019

Kristian Kroschel

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Acknowledgements

To write a book is not a project that can be done in only a few days. It was back in early 2018 during the SPIE conference in Strasbourg when Malwina Strenkowska asked me if I would like to write a book for the Springer Nature series on remote sensing of vital parameters of humans using a laser Doppler vibrometer, which was more or less the topic of my presentation in Strasbourg. Inspired by the presentations of other participants during the conference, I agreed. I was further motivated by initial, very promising results from my student, Laura Mignanelli, who had worked on data which she acquired from the municipal hospital in Karlsruhe. Thanks to the initiative of Christian Rembe, at that time responsible for optics development at Polytec, a well-known manufacturer of laser Doppler vibrometers, a grant was given by the BMBF, the German Ministry of Education and Research, for the Tricorder project under the number 13N13725. Within this framework, the companies Polytec and Getemed along with three hospitals (Städtisches Klinikum Karlsruhe, University Clinic Mannheim, Charité Berlin) and the Fraunhofer Institute IOSB in Karlsruhe cooperated to develop both, a laser doppler vibrometer for the application mentioned in the foreword and the corresponding software to extract vital parameters including heart rate, heart sounds, and respiration information. The authors would like to thank the engineers from Polytec, mainly Marco Wolfer, Robert Downes from Getemed who took over the management of the consortium, all employees at the three hospitals involved in data acquisition and Martin Ruckhäberle from the Fraunhofer IOSB, who solved the tedious task of synchronizing measurements and transforming the data into a format for further processing. Deborah Kaska from Santa Barbara, California, also deserves many thanks for her help to improve the writing in English. Last but not least, we would like to thank Smith Chae and his team who transformed the manuscript into this book which is now on the market. We hope all our readers enjoy reading it and that it enhances their research efforts throughout their professional lives. Karlsruhe, Germany October 2019

The editor and the authors

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Contents

1 Non-contact Health Monitoring with LDV . . . . . . . . . . . . . . . . . . . . Laura Mignanelli and Christian Rembe

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2 Introduction to Laser-Doppler Vibrometry . . . . . . . . . . . . . . . . . . . . Christian Rembe and Laura Mignanelli

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3 Data Acquisition and Processing . . . . . . . . . . . . . . . . . . . . . . . . . . . . Kristian Kroschel

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4 Parameters of Respiration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Kristian Kroschel and Süha Demirakca

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5 Vital Parameters of the Heart . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Kristian Kroschel and Armin Luik

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6 VCG Signals on the Thorax and Detection of the PR-Interval . . . . . 155 Laura Mignanelli and Christian Rembe 7 Distant Pulse Oximetry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 167 Christian Herrmann and Jürgen Metzler Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 179

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About the Editor

Kristian Kroschel is a member of the electrical engineering and communication technology department of the Karlsruhe Institute of Technology. Currently, he is with the Fraunhofer Institute of Optronics, System Technologies and Image Exploitation IOSB and does research in signal processing. He is author of many publications and book chapters on “Laser Doppler vibrometry” and digital signal treatment.

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Chapter 1

Non-contact Health Monitoring with LDV Laura Mignanelli and Christian Rembe

Abstract In the last years, non-contact health monitoring has become a research topic in biomedicine. It delivers several advantages in applications such as intensive care, home health care, rehabilitation, nursing of elderly, monitoring of physical efforts, measuring the stress of drivers and human–machine interaction. In literature, different methods for the detection of important vital signs can be found. Among them the Laser Doppler Vibrometry presents metrologic properties suitable for the detection of vital signs. Laser Doppler Vibrometry has been adopted in several biomedical fields. The application of interest in this book is restricted to the monitoring of cardiovascular and respiratory signals. This chapter reports a brief introduction of the available contactless methods for health monitoring. Consequently, the current state of laser Doppler vibrometry as a non-contact detection tool and its application for cardiac and respiration monitoring are described.

1.1 Non-contact Health Monitoring Techniques Non-contact detection of human health conditions is beneficial in different monitoring applications. For example, premature neonatal infants in an intensive care unit (NICU) are monitored with several contact instruments which represent a huge load to their tiny body and their sensitive skin. A non-contact monitoring method would be very helpful to avoid lesions and infection to the baby [1, 14, 23, 24]. Measuring the health condition with an instrument fixed on the ceiling could be very advantageous for applications like home health care, rehabilitation, or nursing of elderly. With a tracking system it could be possible to recognize the patient and successively perform a measurement of the vital signs every time when it is needed without efforts. L. Mignanelli (B) · C. Rembe Institute for Electrical Information Technology, TU Clausthal, Leibnizstr. 28, Clausthal-Zellerfeld, Germany e-mail: [email protected] © Springer Nature Switzerland AG 2020 K. Kroschel (ed.), Laser Doppler Vibrometry for Non-Contact Diagnostics, Bioanalysis 9, https://doi.org/10.1007/978-3-030-46691-6_1

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Cables or sensors (which traditionally are attached to the body) do not restrict the movements for non-contact measurements [1, 14, 24]. This would open the possibility to monitor the vital functions of an athlete during competitions and thus, to recognize if the athlete is in a proper health condition for high physical loads. Another application field is offered from the increasing networking and digitization of our industrial society which provide more human–machine interactions. The willingness of the human and its ability to assume or maintain control should be reliably assessed before transferring it to a machine or conversely. For this task in real use, it is first necessary to detect some medical parameters contactless with which a willingness to take over control in critical work steps can be identified. The standard health monitoring techniques require mainly contact with the patients which in some occasions is inconvenient or difficult to apply on peculiar groups of patients [1, 14, 24]. Cardiovascular (CV) diseases are known to be one of the most spread death causes in the developed states. Most of its monitoring techniques provide contact with the patient. For example the electrocardiogram (ECG) delivers information about the heart rate (HR) and heart rate variability (HRV) which are primary vital signs that are used to detect arrhythmia, heart block, and other heart diseases. It measures the electrical signals that trigger the movements of the heart muscles by placing electrodes in standard positions. Misplacing the electrodes may lead to erroneous measurements, thus it requires trained personnel. Electrodes can be used only one time and they can be very uncomfortable for long term and everyday measurements especially for subjects with very sensible skin like preterm infants or burned subjects. The required cables can also limit the patient’s mobility and comfort [24]. Moreover, in the case of infants, the cable may represent a potential risk of strangulation. An alternative to ECG for the analysis of HRV is photoplethysmography (PPG). PPG is a non-invasive optical measuring technique where a small sensor placed in the earlobe or fingertip measures the peripheral pulse. The skin is illuminated with a dedicated light source. The reflected or transmitted light is measured. The light absorption depends on the hemoglobin, which is related to the pressure level. This method provides a quick indication of the cardiac rhythm [14]. PPG sensors are not only non-invasive but also simple and low cost. For these reasons, they are used in wearable sensors for the monitoring of the heart rate. However, PPG showed to be less accurate, more vulnerable to motion artifacts and less reliable for long-term recording with respect to the ECG [14]. The use of a non-contact technique for the detection of the ECG allows to overcome the limitations mentioned above and it would also reduce the risk of exposure of medical personnel to toxic material and biochemical hazard conditions. The ECG has limitations in combination with magnetic resonance imaging. A non-contact technique could overcome this problem too [19]. The blood pressure (BP) is another parameter that has to be monitored at home or in an ambulance and it provides information regarding the functionality of the cardiovascular system. In particular, the measure of the continuous pressure waveform in real time is possible with intra-arterial pressure catheter, which is an invasive technique and it is not suitable for daily practice [25].

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A non-invasive alternative technique is tonometry. Tonometry allows to measure the pressure wave but still with contact to the patient. This method has adverse aspects like the compression of the artery against the bone. The measure of the undisturbed pulse is not possible since the artery is flattened because of the presence of the sensor. There are also difficulties for measuring obese subjects and a specialized personnel is required [25]. Arterial stiffness is also a parameter related to CV risk. The arterial stiffness can be calculated by the measure of the pulse wave velocity (PWV) with applanation tonometry. This method consists of placing a piezoelectric contact sensor on the carotid artery and on the groin. The measure of the PWV is performed by knowing the distance of the two measurement locations and by calculating the time delay of the pulse wave arriving at the position of the sensors. With this technique it is necessary to be undressed. Its drawbacks are the same as those mentioned for the case of using tonometry for measuring the pressure wave. Moreover, because the position of the sensor is identified by palpation this can be uncomfortable for the subject since one of the measurement points is on the groin. Another invasive measurement is the monitoring of peculiar respiratory events of infants to prevent their death. The standard device to measure breathing parameters is the spirometer. It is not only invasive but it also requires the cooperation of the patient. Therefore, this application on infants is very difficult to achieve [16, 26]. In all these cases and many others, too, a non-contact technique would be convenient and recommended. Several research groups investigated in the last years different techniques for noncontact monitoring of health. As reported in [1, 14, 24], these non-contact methods are based on different working principles. The main categories are as follows: • electromagnetic-based monitoring system, • laser-based monitoring system, • image-based monitoring system. Electromagnetic- and laser-based methods exploit the Doppler effect. In particular, the electromagnetic methods includes continuous wave, frequency modulated, or ultra-wide band pulsed radar. An antenna is used to transmit electromagnetic radiation, the radiation irradiates the target and the reflected signal is detected by the antenna. The phase difference between the transmitted and received signal is proportional to the movement of the target according to the Doppler effect. The target is in this case a measurement point on the human body which vibrates because of vital signs like respiration, blood flow, and muscle contraction. The principle of operation of laser-based monitoring systems is the same as the electromagnetic ones but they use laser light instead of a radar. This technique was used to extract several medical parameters and is based on a laser Doppler vibrometer (LDV) [22]. It is named optical vibrocardiography (VCG) [19]. The image-based monitoring can be classified in thermal, color and motion imaging methods. The thermal imaging method detects the heat variations caused by the pulsatile blood flow or by the respiration from the human body at certain locations. The color-based technique utilizes the principle of PPG. The skin is illuminated with

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dedicated light or ambient light. Depending on the blood volume variation, the optical properties of the skin change and so the reflected light. The reflected light is detected with a camera and by signal processing biomedical information is extracted. The motion-based system investigates video and images acquired by a camera to detect small skin movements related to cardiorespiratory activity. Other methods are also present in literature. An alternative application proposes the use of magnetic induction. Investigations which exploit the capacitive coupling method and ultrasonic sensing are also carried out. Another study shows that it is possible to detect the activities of the heart from human speech [14]. In the Refs. [1, 14, 23, 24] a detailed description of the abovementioned techniques is found together with a comparison of their advantages and disadvantages in terms of costs, measurement duration, reliability, data processing complexity, detection range, and other parameters. According with [1, 14, 24], the LDV presented the highest accuracy and signalto-noise ratio among the described methods. Other advantages using the LDV as non-contact method for measuring the cardiac activity are the immunity to acoustic, electrical and radio-frequency noise, simplicity of data processing, long-distance measurements, and high bandwidth. The main disadvantages are the high cost, the complex optical interface and the possibility to measure only one subject at a time. However, actual researches are focused on the realization of a miniaturized, lowcost LDV [17, 32] and, recently, appeared on the market a multipoint laser Doppler vibrometer with 48 channels that allows the simultaneous measurement of 48 sites with a working distance up to 5 m [21], thus the monitoring of more than one subject at time is also possible.

1.2 Application of Laser Doppler Vibrometry in the Biomedical Field Laser Doppler vibrometry (LDV) is an interferometric technique which is widely used in several engineering applications. The LDV is suitable for biomedical application. Vibrations originating from the human body itself are in the velocity range up to mm/s and displacement range up to mm. The resolution of the LDV allows the detection of vibrations smaller by a factor 103 at least. The description of the principle of the LDV and its resolution limits are discussed in the next chapter. Tabatabai et al. in 2013 [31] presented a review of the application of the LDV for medical imaging. These research fields are as follows: • • • • • • •

hearing, dentistry, biometrics, monitoring of cardiovascular activity, monitoring of respiratory activity, monitoring of muscular activity, detection of aortic aneurysms,

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• integration of implants non invasively, • heart valve testing. The focus of this book is the optical vibrocardiography for the monitoring of the cardiovascular and respiration activity. Details about the other above mentioned applications can be found in Ref. [31]. One of the first investigations on the detection of CV parameters with LDV was presented in Ref. [20]. The authors performed preliminary tests for the registration of the pressure pulse on the carotid artery. Several studies followed to assess the possibility to detect CV parameters based on the fact that vascular movements propagate through the tissue generating skin motion, which can be detected with LDV. The studies were focused on the detection of the heart rate (HR) and heart rate variability (HRV) by measuring the vibration on the thorax and on the carotid artery. In these studies, the parameter extracted from the VCG and from a simultaneously recorded ECG were compared. The results showed that the two methods are comparable to monitor the cardiac rate [19, 27]. Simultaneously recording of the vibrations generated by arteries at different locations delivers information about the propagation of the pulse waveform. The change of its characteristics is related to obstruction or arterial condition. Many studies are focused on the assessment of arterial stiffness by measuring the pulse transit time (PTT) and pulse wave velocity (PWV) with the LDV. In Ref. [9] the authors showed that the PPT in young healthy volunteers measured with the LDV and the arterial applanation tonometry are equivalent. Similar results were reported by the experiments carried out by Campo et al. [3]. Campo et al. measured also with a multichannel LDV phantom arteries mimicking real-life conditions [4, 5]. The authors stated that the PWV parameter measured from LDV signals in elastic vessels is conform with the theoretically expected values. The blood pressure waveform is obtainable by integrating the LDV-velocity signal acquired on the tissue overlying arteries. The recorded waveform cannot be directly related to the pressure value, but a calibration is needed [11]. In [7], the authors tested this possibility. They calibrated the VCG signal by means of brachial diastolic and mean blood pressure values measured via the oscillometric method, using an exponential model. They observed that the LDV allows to detect mechanical events of the carotid artery related to hemodynamics with a very high sensitivity, but there are contributions of reflection phenomena, which may be not related to the investigated vessel. In [25] the calibration of the LDV signals was made with a tonometer measuring on the radial artery. The results showed that the systolic blood pressure measured with LDV have a mean deviation of 8 mmHg with respect to the tonometric data. The authors identified the uncertainty due to the integration process. It resulted in 15% which is not negligible, but it is comparable to the standard blood pressure measuring devices. Reference [6] presents also the LDV as an indirect method for the non-contact measurement of the carotid blood pressure. The authors performed a comparison of the LDV traces with the photoplethysmogram (PPG) for the assessment of the left ventricular ejection time at carotid level. The study showed comparable results with a deviation lower than 10% between the two techniques.

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The detection of respiration activity with the LDV was also a topic. The work of Sirevaag et al. [30] focuses on the change of cardiovascular activity over a respiration cycle. LDV measurements on the thorax or on the abdomen were carried out to determine the respiration rate (RP) [16, 28, 29]. To have a reference, a spirometer measurement is performed simultaneously. These measurements were carried out for both, adults and infants in a neonatal intensive care unit. The two techniques showed a strong agreement. In Refs. [16, 28, 29], the monitoring of infants in a NICU with the LDV allowed to detect irregular inspiration/expiration acts, hiccups, and apnea precisely. The monitoring of the respiration and the cardiovascular activity without contact for infants in a NICU is very advantageous. The VCG was also used for the identification of some cardiac mechanic events. A preliminary study [10] compared VCG signals acquired on the thorax with digital phonocardiography to identify cardiac events. According with the authors, the VCG traces allow the recognition of heart sounds relative to the closure of the mitral valve and the closure of the aortic and pulmonary valve. The filling time, which is a critical parameter for the cardiac functionality could be also measured. In [12, 13] LDV was compared to another auscultation devices, such as the stethoscope. The authors found out that certain morphological features could be identified as unique for specific heart murmurs. Measurements on the thorax of healthy subjects and subjects affected by CV diseases showed differences in the pattern. It is also demonstrated that AV-blocks can be identified. It was possible to distinguish the vibration pattern generated by the contraction of the atria and the contraction of the ventricles. This allows the detection of the PR-interval, the interval between the two contractions, which is a very important parameter for a cardiologist [15]. One aspect that was also investigated is the reliability of the measurement point by means of a scanning vibrometer and a multipoint vibrometer [4, 15, 18]. Scanning measurements on the carotid were performed [2] to find evidence for the local operation of the carotid artery. This investigation highlights the importance of precise targeting and the spatial distribution of the signal strength can be used as a targeting criterion itself. Multichannel measurements performed on the thorax of one subject revealed a large area where the typical pattern can be detected [15]. Researches are also focused on the algorithm and filtering techniques to extrapolate the desired parameters like in Ref. [8].

1.3 Summary and Conclusions To summarize, the LDV is suitable for the detection of cardiovascular and respiration parameters from vibration signals. Its miniaturization and its consequent cost accessibility will probably lead in the future to a compact LDV for daily use at home and in clinical practice.

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References 1. Al-Nji, A., Gibson, K., Lee, S-H., Chahl, J.: Monitoring of cardiorespiratory signal. Principles of remote measurements and review of methods. IEEE Access 5, 15776–15790 (2017) 2. Casaccia, S., Sirevaag, E.J., Richter, E.J., Casacanditella, L., Scalise, L., Rohrbaugh, J.W.: LDV arterial pulse signal: evidence for local generation of carotid. In: AIP Conference Proceedings, vol. 1740, p. 050008 (2016) 3. Campo, A., Segers, P., Dirckx, J.: Laser Doppler vibrometry for in vivo assessment of of arterial stiffness. In: IEEE International Workshop on Medical Measurements and Applications Proceedings, pp. 119–121 (2011) 4. Campo, A., Dirckx, J.: Dual-beam laser Doppler vibrometer for measurement of pulse wave velocity in elastic vessels. In: 22nd Congress of the International Commission for Optics: Light for the Development of the World. SPIE Proceedings, p. 80118Y (2011) 5. Campo, A., Waz, A., Dudzik, G., Dirckx, J., Abramski, K.: Application of four-channel vibrometer system for detection of arterial stiffness. In: AIP Conference Proceedings, vol. 1740, p. 050004 (2016) 6. Casacanditella, L., Cosoli, G., Casaccia, S., Tomasini, E.P., Scalise, L.: Indirect measurement of the carotid arterial pressure from vibrocardiographic signal: calibration of the waveform and comparison with photoplethymographic signal. In: 38th Annual International Conference of the IEEE Engineering in Medicine and Biology Society (EMBC), pp. 3568–3571 (2016) 7. Casacanditella, L., Cosoli, G., Casaccia, S., Scalise, L., Tomasini, E.P.: Derived non-contact continuous recording of blood pressure pulse waveform by means of vibrocardiography. In: Ando, B., Baldini, F., Di Natale, C., Marrazza, G., Siciliano, P. (eds.) Sensors, vol. 431, pp. 365–372. Springer, Berlin (2018) 8. Cosoli, G., Casacanditella, L., Pietroni, F., Calvaresi, A., Revel, G.M., Scalise, L.: A novel approach for features extraction in physiological signals. In: IEEE International Symposium on Medical Measurements and Applications (MMA). pp. 380–385 (2015) 9. De Melis, M., Morbiducci, U., Scalise, L., Tomasini, E.P., Delbeke, D., van Baets, R., Bortel, L.M., Segers, P.: A noncontact approach for the evaluation of large artery stiffness: a preliminary study. Am. J. Hypertens. 12(21), 1280–1283 (2008) 10. De Melis, M., Morbiducci, U., Scalise, L.: Identification of cardiac events by optical vibrocardiography: comparison with phonocardiography. In: 29th Annual International Conference of IEEE Engineering in Medicine and Biology Society, pp. 2956–2959 (2007) 11. Desjasrdins, C.L., Antonelli, L.T., Soares, E.: A remote and non-contact method for obtaining the blood-pulse waveform with a laser Doppler vibrometer. In: Proceedings of SPIE, vol. 6430. Advanced Biomedical and Clinical Diagnostic Systems, V. p. 64301C (2007) 12. Koegelenberg, S., Scheffer, C., Blanckenberg, M.M., Doubell, A.F.: Application of laser Doppler vibrometry for human heart auscultation. In: Annual International Conference of the IEEE Engineering in Medicine and Biology Society, pp. 4479–4482 (2014) 13. Koegelenberg, S.: Application of laser Doppler vibrocardiography for human heart auscultation. Master thesis, Department of Mechanical and Mechatronic Engineering, University of Stellenbosch. https://scholar.sun.ac.za/handle10019.1/86649 14. Kranjec, J., Begus, S., Garsak, G., Drnovasek, J.: Non-contact heart rate and heart rate variability measurements: a review. Biomed. Signal Process. Control 13, 102–112 (2014) 15. Luik, A., Mignanelli, L., Kroschel, K., Schmitt, C., Rembe, C., Scalise, L.: Laser Doppler vibrometry as a noncontact method to detect various degrees of atrioventricular block: a feasibility study. Futur. Cardiol. 12(3), 269–279 (2016) 16. Marchionni, P., Scalise, L., Ercoli, I., Tomasini, E.P.: An optical measurement method for the simultaneous assessement of respiration and heart rates in preterm infants. Rev. Sci. Instrum. 84, 121705 (2012) 17. Medtronic: Cardis - Early stage CARdio Vascular Disease Detection with Integrated Silicon Photonics (2015). http://www.cardis-h2020.eu/ Cited 26 Aug 2019

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18. Mignanelli, L., Rembe, C., Kroschel, K., Luik, A., Castellini, P., Scalise, L.: Medical diagnosis of the cardiovascular system on the carotid artery with IR laser Doppler vibrometer. In: AIP Conference Proceedings, vol. 1600, pp. 313–322 (2014) 19. Morbiducci, U., Scalise, L., De Melis, M., Grigioni, M.: Optical vibrocardiography: a novel tool for the optical monitoring of cardiac activity. Ann. Biomed. Eng. 35, 45–58 (2007) 20. Pinotti, M., Paone, N., Santos, F.A., Tomasini, E.P.: Carotid artery pulse wave measured by a laser vibrometer. In: SPIE Proceedings, pp. 611–616 (1998) 21. Rembe, C., Würtge, M. Dräbenstedt, A., Braun, T.: Optisches Interferometer und Vibrometer mit solch einem optischen Interferometer. Europaeische Patentschrift EP 2 808 644 B1 (2017) 22. Rembe, C., Siegmund, G., Steger, H., Wörtge, M.: Measuring MEMs in motion laser Doppler vibrometry. In: Osten, W. (ed.) Optical Inspection of Microsystems, pp. 297–347. CRC Press, Boca Raton (2019) 23. Rohrbaugh, J.W.,: Ambulatory and non-contact recording methods. In: Caccioppo, J.T., Tassinary, L.G., Berntson, G.G. (eds.) Handbook of Psychphysiology, 4th edn. ch 14. Cambridge University Press, United Kingdom (2019) 24. Scalise, L.: Non contact heart monitoring. In: Millis, R.M. (ed.) Advances in Electrocardiograms, ch. 4. IntechOpen, Rijeka (2012) 25. Scalise, L., Cosoli, G., Casacanditella, L., Casccia, S. Rohrbaugh, J.W.: The measurement of blood pressure without contact: an LDV-based technique. In: IEEE International Symposium on Medical Measurements and Applications (MMA), pp. 245–250 (2017) 26. Scalise, L., Marchionni, P., Ercoli, I., Tomasini, E.P.: simultaneous measurement of respiration and cardiac period in preterm infants by laser Doppler vibrometry. In: AIP Conference Proceedings, vol. 1457, pp. 275–281 (2012) 27. Scalise, L., Morbiducci, U.: Non-contact cardiac monitoring from carotid artery using optical vibrocardiography. Med. Eng. Phys. 304, 490–497 (2008) 28. Scalise, L., Marchionni, P., Ercoli, I., Tomasini, E.P.: simultaneous measurement of respiration and cardiac period in preterm infants by laser Doppler vibrometry. In: AIP Comference Proceedings, vol. 1457, pp. 275–281 (2012) 29. Scalise, L., Marchionni, P., Ercoli, I., Tomasini, E.P.: Laser measurement of respiration activity in preterm infants: monitorng of peculiar events. In: AIP Conference Proceedings, pp. 63–68 (2012) 30. Sirevaag, E.J., Casaccia, S., Richter, E.A., O’Sullivan, J.A., Scalise, L., Rohrbaugh, J.W.: Cardiorespiratory interactions: noncontact assessment using Doppler vibrometry. Psychphysiology 6(53), 847–867 (2016) 31. Tabatabai, H., Oliver, D., Rohrbaugh, J.W., Papadopoulos, C.: Noval application of laser Doppler vibration measurements to medical imagings. Sens. Imaging. Int. J. 14, 13–28 (2013) 32. Wolfer, M.: Optischer Interferometrischer Recorder für die Vitalfunktionen (Tricorder) (2015). https://www.photonikforschung.de/lebenswissenshaften/pdf/TRICORDER-Vor-OrtAnalytik-Projektsteck-korr2019-08-bf-C1.pdf. Cited 26 Aug 2019

Chapter 2

Introduction to Laser-Doppler Vibrometry Christian Rembe and Laura Mignanelli

Abstract Laser-Doppler vibrometry (LDVy) is especially interesting for applications where a vibration measurement could not be obtained with an accelerometer or any other surface-contacting sensor. In contrast to tactile sensors, a laser-Doppler vibrometer (LDV) measures without contact over a distance that could vary from millimeters to kilometers depending on the focusing optics of the measurement laser beam. Typical specimens, where it is impossible or impractical to measure tactilely, are hot, rotating, tiny, lightweight, or fragile. A specific problem of tactile sensors is the coupling of sound or vibrations to the sensor element. On the other hand, the optical pathlength varies between an LDV and a specimen without coupling issues if enough scattered light is detected. Therefore, it is not surprising that laser-Doppler vibrometry has gained an enormous importance in a wide range of applications. This chapter discusses the technology behind LDVy and explores the physical limits of the technique. Especially the high dynamic of the detected light power for an eyesafe infrared LDV of more than 150 dB as well as the displacement resolution in the picometer regime make LDVy a promising tool for medical applications.

2.1 Introduction Laser-Doppler techniques were explored shortly after the first demonstration of the LASER in 1960 by Maiman [13]. Yeh and Cummins investigated flow fields and introduced the laser-Doppler technique in 1964 [20] to measure velocities of moving microscopic monodispersed polystyrene spheres by the frequency shift of scattered laser light. These frequency shifts are generally called Doppler shifts [3] named after the Austrian physicist who first considered the phenomenon in 1842. The detection C. Rembe (B) · L. Mignanelli Institute of Electrical Information Technology, Clausthal University of Technology, Leibnizstr. 28, 38678 Clausthal-Zellerfeld, Germany e-mail: [email protected] © Springer Nature Switzerland AG 2020 K. Kroschel (ed.), Laser Doppler Vibrometry for Non-Contact Diagnostics, Bioanalysis 9, https://doi.org/10.1007/978-3-030-46691-6_2

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of flow became known as Doppler anemometry which was the most popular application of laser-Doppler technique in the 1960s. Laser-Doppler vibrometry as it is still applied today to study vibration behavior was introduced in the year 1968 when G. A. Massey first presented a heterodyne laser-Doppler system with scanning capability for measurement and analysis of vibrating surfaces [14]. The first researchers who carried out extensive research on LDV were F. J. Eberhardt and F. A. Andrews [6]. The experimental analysis of vibrating surfaces with laser-Doppler technique became known as laser-Doppler vibrometry and inventions continued during the 1980s with important developments like the fiber-based vibrometer [10] the torsional-vibrations measuring vibrometer [9] or the in-plane vibrometer [11]. In the 90s, LDVy became commercially available and especially scanning LDV was established as standard tool for the experimental investigation of vibration behavior of technical systems [16, 17, 21]. Here, the measurement beam is scanned pointwise over the surface and the LDV captures the vibration with a phase relation to the other measurements of the scan. Usually, a reference signal is required to establish the phase relation. Displaying phase and amplitude at a certain frequency reveals the operational deflection shape (ODS), which is an important output to allocate vibration modes. However, scanning LDV is not applicable to measure an ODS for transient vibration phenomena as they are present in self-excited vibrations in the human body. Here, parallel measurements with a multi-point LDV [2, 7, 8, 12, 19] are required. The first really suitable multi-point LDV was introduced recently [15] and can measure at 48 points in 1D or at 16 points in 3D simultaneously. Today laser-Doppler vibrometers measure vibrations in all kinds of applications [1, 16–18, 21]. Several book chapters and books give a detailed representation of the laser-Doppler technique for vibration measurements [1, 4, 16]. Doppler frequency shifts generated by moving technical surfaces are rather small, for example, a velocity of 10 meters per second will shift infrared laser light at 1550 nm of about 13.9 MHz. This corresponds just to 7 parts in 108 at a light frequency of 1.9 · 1014 Hz. Heterodyning or beating two signals with two frequencies by a mixer and a low-pass filter allows to mix down a modulated signal to a lower carrier frequency. Heterodyning is applied to measure small shifts at such high frequencies which can not be detected directly with a photodetector. The photodetector transforms optical power linearly into current and, therefore, provides a nonlinearity for the sum of the electrical fields of the measurement and reference beams because the light power is proportional to the square of the electrical field amplitude. The output of the detector is a modulated carrier signal and the carrier frequency corresponds to the heterodyne frequency. The instantaneous velocity or displacement signal is finally obtained from the heterodyne signal by using electronic decoders. From the beginning, laser-Doppler vibrometry was especially interesting for applications with sensitive surfaces which are not well suited for a surface-contacting sensor. Such an application is the vibration measurement on the human body. In order to avoid glaring of the patient and to benefit from the relatively high laser power of 10 mW for a laser-class I sensor the preferable laser wavelength for measuring on human skin is 1550 nm. High-performance optical and optoelectronic components are available at this wavelength because 1550 nm is the standard wavelength for opti-

2 Introduction to Laser-Doppler Vibrometry

11

cal telecommunication and, consequently, the most powerful, eye-safe LDV can be realized at 1550 nm wavelength [5]. The medical applications of LDV are broadly discussed in the other chapters of this book.

2.2 Laser-Doppler-Effect Light is an electromagnetic wave at a frequency in the order of 1014 Hz and at a propagation speed in vacuum of c = 299.792.458 m/s. A refractive index of a medium n alters the speed of light to cn =

c . n

(2.1)

The light transmission is defined by the wave propagation of the electromagnetic field. Since the magnetic field is always perpendicular to the electrical field in the absence of charges and currents, as it can be assumed for air, the electric field vector E of length E defines the wave propagation of light 2 ∂ 2E 2 d E = c · . n ∂t 2 dx2

(2.2)

In air the polarization is maintained and, therefore, it is sufficient to consider in the following the wave propagation as scalar field E(t) = E 0 · cos(ωt − kn · ss (t)) .

(2.3)

Here, E 0 is the amplitude of the electrical field, ω is the angular frequency, kn = ω = 2π = 2π·n is the wavenumber with wavelength λn = λn , and ss (t) is the distance cn λn λ between the LDV and the specimen surface. Usually the propagation distance ss (t) = 2 · (s0 + s(t)) consists of a constant working distance s0 and a displacement s(t) with s0 >> s(t)|max . The LDV is sensitive to the surface displacement s(t). With reflectance r of the target the electrical field at the photodetector results in      √ 2s0 + sd ˜ + φ0 r · E 0 · cos ωt − kn · 2 · s t − cn √ = r · E˜ 0 · cos(ωt − 2 · kn · s(t) + φ0 ) ,

E˜ m (t) =

(2.4)

d ≈ 0, where sd is a constant distance in the sensor (see Fig. 2.1) and φ0 for 2 s0c+s n the initial phase of the interference signal. The power of the measurement light is divided by a factor 2 through the beam splitter that superimposes measurement and reference light. Therefore, the electrical field impinging on the detector E˜ m (t) = E√ m (t) is reduced in respect to the amplitude reflected at the specimen surface. 2

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Finally, the phase of the electrical field at the photodetector results in ϕ(t) = φ0 − 2 · k · n · s(t) .

(2.5)

The derivative of ϕ(t) results in ϕ(t) ˙ = −2 · km · s˙ (t) = −2 · kn · v(t)

(2.6)

with the velocity v(t). The quantity fD =

v(t) ϕ(t) ˙ = −2 · 2π λn

(2.7)

is known as Doppler frequency shift. The negative sign complies to the situation that a shift toward the LDV reduces the distance between sensor and specimen. Therefore, a movement toward the LDV with a negative sign increases the frequency of the measurement light due to the negative sign in Eq. (2.7).

2.3 Interferometric Measurement of the Light Phase 2.3.1 Detection of Light Photodiodes convert light power P to a photo current i P in a certain detector bandwidth B, for example, within B = 100 MHz i P = KP · P = KP · Z 0 · < E 2 (t) > with the impedance of free space Z 0 =



μ0 0

(2.8)

≈ 376,73 and the sensitivity of the

photo diode KP . < E > is the low-pass-filtered signal within the bandwidth B. Typical values for KP is KP ≈ 0,5 A/mW in the visible wavelength regime or KP is KP ≈ 1 A/mW at a wavelength of λ = 1550 nm. 2

2.3.2 Interferometric Detection The variation of the electrical field amplitude cannot be measured directly. Thus, optical beating of the measurement light with a reference beam together with the lowpass-limited detection with a photodiode provides down conversion to a frequency band that can be measured with a fast photodetector. An interferometer superimposes one light beam with another reference light beam and, thus, the resulting light beam consists of the sum of the electrical fields of

2 Introduction to Laser-Doppler Vibrometry

13

measurement (E m ) and reference beam (Er ) ˜ E(t) = E˜ m (t) + E˜ r (t) =

√ r · E˜ m,0 cos(ωt + ϕ(t)) + E˜ r ,0 · cos(ωt)

(2.9)

with E˜ r = √Er2 the amplitude of the reference light after the beam splitter that superimposes measurement and reference light. The square of the low-pass filtered electrical field at the photodetector results in 2 +2· < E˜ 2 (t) >= r · E˜ m,0

√ r · η · E˜ m,0 · E˜ r ,0 · cos(ϕ(t)) + E˜ r2,0 ,

(2.10)

where η is introduced to take signal degradation by wavefront aberrations between measurement and reference beam into account. For example, a sinusoidal vibration of s0 · cos(Ωt) generates a modulation of the electrical field of the measurement light and with a phase ϕ(t) = M · sin(Ωt) (2.11) 0 . with the modulation index M = − 4π·s λ

2.3.3 Heterodyne Interferometers The generation of a quadrature signal is important to obtain the direction of displacement. This can be realized optically in the baseband [1, 16]. However, it has advantages to use a carrier signal and to down-convert it to a quadrature signal in the digital domain. Advantages of such a heterodyne approach are the minimization of technical noise in the detector and the option to suppress harmonic distortion in the detector with suited filters. A possible setup for such an heterodyne interferometer is shown in Fig. 2.1.

Fig. 2.1 Optical setup of a heterodyne interferometer with balanced detector

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Heterodyning is achieved by shifting the measurement light frequency in respect to the reference light frequency by the carrier frequency ωc √ r · E˜ m,0 cos(ωt + ωc t + ϕ(t)) + E˜ r ,0 · cos(ωt) . (2.12) The photocurrent is transferred to a voltage signal u TIA with a transimpedance amplifier (TIA) with a transimpedance RTIA . Thus, the detector signal is ˜ E(t) = E˜ m (t) + E˜ r (t) =

u TIA, f ull (t) = RTIA · K P · Z 0 · < E˜ 2 >

(2.13)

with the square of the electric field 2 · cos2 (ωt + ωc t + ϕ(t)) E˜ 2 = r · E˜ m,0 √ +2 · r · η · E˜ m,0 · E˜ r ,0 · cos((ωc + ω)t + ϕ(t)) · cos(ωt) + E˜ r2,0 · cos2 (ωt) .

(2.14)

As mentioned before, the photodetector averages the square of the electric field < E 2 > within the bandwidth B of the detector. Usually the detector bandwidth B is designed to be B = 2 · ωc . In addition, the offset is usually electronically removed (ac-coupled). The best way to remove the offset is balanced detection (see Fig. 2.1) [18] because it suppresses amplitude modulation and obtains twice the signalpower. Thus, the detector signal results with 2 · E˜ m · E˜ r = E m · Er in √ r · η · E m,0 · Er ,0 · Z 0 · cos(ωc t + ϕ(t))   √ = 2 · RTIA · K P · r · η · Pm · Pr · cos(ωc t + M · sin(Ωt)) (2.15)

u TIA,B (t) = 2 · RTIA · K P ·

for a sinusoidal vibration and with the power of the reference beam Pr and the power of the measurement beam Pm . In this case, the modulation term can be developed in a sum of Bessel functions Ji of first kind and first order at frequencies separated by the modulation frequency Ω. First the equation for the detector signal is converted by the angle transformation formulae to u TIA, f ull (t) = uˆ · (cos(ωc t) · cos(M · sin(Ωt)) − sin(ωc t) · sin(M · sin(Ωt)) (2.16)

√ √ √ with the voltage amplitude uˆ = 2 · RTIA · K P · r · η · Pm · Pr . This expression can be developed by the Jacobi–Anger expansion   ∞  i u TIA, f ull (t) = uˆ · cos(ωc t) · J0 (M) + 2 (−1) · J2i · cos(2 · i · Ω · t)  − sin(ωc t) · −2

i=1

∞  i=1



. (−1)i · J2i−1 (M) · cos((2i − 1) · Ωt) (2.17)

2 Introduction to Laser-Doppler Vibrometry

15

The modulation index can be estimated by the Bessel lines M=

2i · Ji Ji+1 + Ji−1

(2.18)

which can be simplified for small modulation indices (M m and coefficients aν and bμ is descibed by the transfer function [2] m

μ=0

bμ z −μ

ν=0

aν a −ν

H (z) = n

(3.4)

and the FIR filter of order m and coefficients bμ by the transfer function H (z) =

m 

bμ z −μ

(3.5)

μ=0

with z = e j2π f / fs the complex frequency corresponding with the real-valued frequency f . Therefore the transfer functions are complex valued with H ( f ) = |H ( f )| · e−ϕ( f ) ,

(3.6)

i.e., they can be described by their magnitude |H ( f )| and angle or phase ϕ( f ). To reduce distortion, the magnitude should be constant and the phase linear within the frequency band of interest [2]. Instead of the phase ϕ( f ), the group delay τg ( f ) can be used which is the derivative of the phase ϕ(t). To avoid distortion, the group delay should be constant so that all frequency components of the signal at the input of the filter are delayed by the same time at the output of the filter. Recursive filters with the transfer function given in Eq. (3.4) never have a linear phase or constant group delay, but a low order n. With bμ = b(m − μ) non-recursive filters with the transfer function given in Eq. (3.5) have a linear phase and thus have no phase distortion. Choosing the filter order m appropriately high, the distortion in the pass-band can be reduced. A high order m of the filter implies a delay of the signal by Δt = 2·mfs . For recursive filters the pass-band can be approximated by a Butterworth, Chebyshev, and elliptic or Cauer characteristic [2]. They differ from each other with respect to their magnitude |H ( f )| and group delay τg ( f ). The Cauer filter is the one with the largest distortion and will not be taken into further account. For all types of filters the magnitude and group delay are shown in Fig. 3.3. The design parameters of the filters are the attenuation in the stop-band a = 60 dB and the cutoff frequency of the pass-band at f = 0.5 Hz. As order of the IIR filters n = 6 has been chosen. Since the linear-phase FIR filter can be implemented very efficiently, the order m = 32 is equivalent to the IIR filter of order n = 6.

30

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Fig. 3.3 Magnitude (left) and group delay (right). IIR filter: Butterworth (top), Chebychev (center), FIR filter (bottom)

All three filters have a constant magnitude in the interval 0 Hz ≤ f ≤ 0.5 Hz. They differ significantly in the transition between pass-band and stop-band. The attenuation of a = 60 dB is reached by the Butterworth filter at f = 1.6 Hz, by the Chebychev at f = 0.8 Hz and by the FIR filter at f = 7.3 Hz. The attenuation of a = 60 dB would be reached at a lower frequency by choosing a higher order n and m, respectively.

3 Data Acquisition and Processing

31 3500

2

3000 2500

| X(f)|

x(t)

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Fig. 3.4 Test signal (left), magnitude of the spectrum (right)

The group delay of the IIR filters is not constant in the pass-band and shows a more or less steep peak at the transition between the pass-band and stop-band. In contrast to this, the group delay of the FIR filter is constant and therefore no source of distortion. To investigate the behavior of the filters with respect to their distortion the synthetic signal shown in Fig. 3.4 together with the magnitude of its spectrum is filtered by the three filters. The task is to remove the two small spectral groups around f = 0.7 Hz and f = 1.3 Hz and to keep the central part of the spectrum more or less unchanged. The result of the filtering is given in Fig. 3.5 with the output signal and the magnitude of its spectrum. In fact, the unwanted spectral components are more or less removed by all filters. Some small residual parts are visible at the output of the Butterworth and FIR filter. The suppression by the Chebychev filter is the best. On the other hand, the distortion visible in the time domain is most dramatic using the Chebychev filter. The smoothing of the amplitude is maximal for the Butterworth filter. The best result is given by the FIR filter because the variations of the amplitude are still visible and equivalently the distortion of the magnitude of the spectrum in its central part is low. Therefore, it is the best choice and the output signal might even be improved by choosing a higher order m of the filter. Its implementation is easily done by efficient use of the FFT [2]. The spectra in Fig. 3.1 have been calculated from all N = 14400 samples with a sampling time ts = 1/ f s = 8.33 ms, i.e., the length of the processed signals is Δt = 120 s. The frequency of the breathing and heartbeat might change during this time interval because both are not stationary processes. This is the reason for the demand that every second an actual value of the extracted parameter of interest is available. On the other hand, neither the heartbeat frequency f h nor the lower breathing frequency f b can be estimated reliably within one second. Thus an appropriate averaging time is required. The calculation of the spectrum from which the frequency is extracted might be based on the FFT given in Eq. (3.3) which requires N samples and is thus a block-based operation. The question is how many samples v[k] or which signal length Δt should be taken? The more samples are used, the higher is the frequency resolution but the more the extracted frequency is averaged and might differ from the instantaneous frequency.

32

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Fig. 3.5 Filtered signal (left), magnitude of the spectrum (right). Butterworth filter (top), Chebychev filter (center), FIR filter (bottom)

A compromise is found by cutting the data stream into overlapping data blocks the length of which depends on the frequency to be estimated. The data blocks should be as short as possible. For a good estimate of the frequency at least five periods of the signal are required. In case of breathing with the typical frequency f b = 0.25 Hz and heartbeat with the typical frequency f h = 1 Hz these five periods fill a data block of length Δtb = 20 s and Δth = 5 s, respectively. This is equivalent to Nb = 2400 samples for the estimation of the breathing frequency and Nh = 600 samples for the estimation of the heartbeat frequency. To generate every second a new estimate, the data blocks (BLK) n − 1 and n are shifted by Nd = 120 samples as shown in Fig. 3.6. From each data block, parameters of interest like the frequency of breathing and heartbeat are estimated. It is an estimate because the vibrometer signal is the sample function of a non-stationary process and only a limited number of samples is available.

3 Data Acquisition and Processing

33 Nd = 120

@ @BLK n @

DATA

BLK n − 1

Fig. 3.6 Cutting data into overlapping blocks

3.5 Frequency Estimation The breathing and the heartbeat signal are periodical signals. For both of them their frequency is of interest. This frequency is not constant but might change over the time of observation. In case of breathing this frequency is under the command of the person under observation. This is not true for the heartbeat frequency: the person under observation cannot stop the heartbeat even for a very short time. The processes breathing and heartbeat are non-stationary processes [4] which has to be taken into account when a method for frequency measurement is looked for, i.e., the calculation of the frequency requires an estimation procedure. Principally four methods for frequency estimation can be used: • the spectral peak is extracted using the FFT method • from the distance between two maxima of the autocorrelation function the frequency is estimated with the ACF method • within the data block the average of the zero-crossings delivers the frequency if the BZC method is used • in contrast to the BZC method the zero-crossings are not averaged but three consecutive zero-crossings are used for frequency estimation if the CZC method is applied. The first three methods are based on block operation and thus deliver averages of the extracted frequency whereas the last one is much closer to the instantaneous frequency. To introduce these methods, a synthetic sinusoidal signal x(t) with sinusoidal variations of the amplitude and the frequency will be investigated. Of course, the sinusoidal variations of the amplitude and the frequency are quite arbitrary and more or less far from the true vibrometer signal but give an impression of how the frequency estimation methods handle the variation of the frequency and the corruption by noise. The amplitude a(t) oscillates with the frequency f = 1/120 Hz weighted by c = 0.1. The mean value of the frequency f (t) is f = 0.3 Hz which is oscillating with the frequency f = 0.02 Hz weighted by c = 0.005. With these parameters the synthetic signal is given by

34

K. Kroschel 0.025

2 1.5

0.02

0.5

hX(x)

x(t)

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−0.5 −1

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−0.5

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t [s] 2 1.5 1

x(t)

0.5 0 −0.5 −1 −1.5 −2

50

55

60

65

70

t [s]

Fig. 3.7 Synthetic signal: full length (top left), histogram (top right), section (bottom)

x(t) = a(t) · sin(2π · f (t) · t) 1 a(t) = 1 + 0.1 · sin(2π · Hz · t) 120 f (t) = 0.3 + 0.005 · sin(2π · 0.02 Hz · t) .

(3.7)

This test signal x(t) of length Δt = 120 s is shown together with its histogram h X (x) and a section of length Δt = 20 s in Fig. 3.7. The variations in the amplitude and frequency are visible in the time domain representation whereas the histogram displays the amplitude variations only. The two symmetric spikes and the minimum in the center are typical for a sinusoidal signal: very often the signal reaches the maximum and passes x(t) = 0 rarely. As mentioned in the last section, the variability of the frequency over time requires signal processing block by block. The length of the block was chosen in such a way that at least five periods fit into the block. For the test signal with a mean frequency of f = 0.3Hz the block length of Δt = 20 s has been chosen so that N = 20 s/(8.33 ms) = 2400 samples can be used for the estimation of the frequency either in the frequency or in the time domain. The building blocks for the methods FFT, ACF, BZC, and CZC are shown in Fig. 3.8. Due to its efficient algorithm, the FFT defined in Eq. (3.3) is the first choice for frequency estimation. It is an estimation since in principle a data block of infinite length is required to calculate the true spectrum of a signal with a constant

3 Data Acquisition and Processing

35 0.5

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(τ)

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t [s]

Fig. 3.8 Signal section: FFT (top left), correlation function (top right), zero-crossing (bottom)

frequency. The result of this estimation is not the instantaneous frequency but the true spectrum weighted by the sin(x)/x function [2] sampled at discrete frequencies f = n · 120/N Hz. The FFT spectrum of the data block shown on the bottom in Fig. 3.7 is given in Fig. 3.8 on the top left. According to the sampling frequency f s = 120 Hz the spectrum up to the Nyquist frequency f s /2 = 60 Hz would have been available. In Fig. 3.8 only the section up to f = 5 Hz is shown since above this frequency there is almost no signal power. The frequency peak is at f = 0.305 Hz. The frequency resolution for N = 2400 samples and the sampling frequency f s = 120 Hz is Δf = Nfs = 0.05 Hz so that the true frequency is found in the interval 0.3 Hz ≤ f ≤ 0.31 Hz. To improve the resolution, the number N of samples has to be enlarged. An extended data block implies an increased averaging so that the result deviates from the instantaneous frequency. An alternative is zero-padding [2]. To the measured N samples a multifs . tude of L = (M − 1) · N zeros are added so that the resolution becomes Δf = M·N The FFT with zero-padding is an expansion of the FFT given in Eq. (3.3) for the N samples x[k] X [n] =

N ·M  k=0

x[k] · e− j2πkn/(N ·M) =

N 

x[k] · e− j2πkn/(N ·M) , 0 ≤ n ≤ N · M .

k=0

(3.8)

K. Kroschel 40

40

30

30

f f(t) [1/min]

f f(t) [1/min]

36

20 10 0 20

20 10

40

60

80

100

t [s]

120

0

20

40

60

80

100

120

t [s]

Fig. 3.9 Estimated frequency measured in 1/min using the FFT (left). FFT with zero-padding by M = 2 (right)

An application of the FFT with zero-padding is shown in Fig. 3.9 to estimate the frequency with N = 2400 samples and L = 4800 samples, i.e., M = 2 holds so that the resolution is Δf = 0.025 Hz. The frequency is not given in Hz but in 1/min because this is used in medical applications. Even the resolution for M = 2 might not be sufficient. If the resolution of approximately 2% is required for the frequency f = 0.3 Hz then Δf = 6 · 10−3 Hz holds which requires 120 fs = ≈ 8.3 , (3.9) M= Δf · N 0.006 · 2400 i.e., roughly a zero-padding factor of M = 8. The frequency estimate with the FFT method for M = 8 is shown in Fig. 3.11 on the top left. The second method or ACF method to estimate the frequency is based on the autocorrelation function for which a sample is shown in Fig. 3.8. Due to the limited number N of available data, only an estimate can be calculated. The unbiased estimate of the autocorrelation function in data block n consisting of N samples is given by [4] c X X,n [κ] =

1 N − |κ|

Nb  −|κ|−1

(x[κ] · x[k + κ]), 0 ≤ κ ≤ N − 1

(3.10)

k=0

for discrete time data x[k]. The continuous time parameters t and τ which are used in the figures are the product of k and κ with the sampling time ts = 8.33 ms. For the N = 2400 data of the data block shown in Fig. 3.7 on the bottom the correlation function c X X (τ ) is given in Fig. 3.8 on the top right. The decay of the amplitudes is due to the finite length with N samples of the data block. The distance between the main maximum at τ = 0 s and the maximum closest to the main maximum is τ = τmax1 = 3.07 s. From this value follows the frequency f = 1/τmax1 = 0.325 Hz. The frequency resolution of the correlation method depends on the sampling time ts = 1/ f s = 8.33 ms because the maximum might be positioned between two sampling instants.

3 Data Acquisition and Processing

37

Δ f(f) [Hz]

Fig. 3.10 Frequency resolution of the time domain methods

0.1

0.05

0

1

0

3

2

4

5

f [Hz]

If the maximum of the correlation function calculated from the sampled data x[k] is at τmax1 , the true maximum of the correlation function calculated from the continuous data might differ by ±t/2 so that it is found at τ = τmax1 + ts /2. From these time instances the corresponding frequencies f 1 = 1/τmax1 and f 2 = 1/(τmax1 + ts /2) are calculated. The difference of these frequencies is the resolution given by Δf ( f ) = =

1 τmax1

−

1 τmax1 +

ts 2 1 f2

+

1 f

·

ts 2

=

ts 2

=

ts 2

τmax1 · (τmax1 + t2s )

· f2 1 + t2s · f ts 2

(3.11)

and shown in Fig. 3.10 for frequencies in the range 0.1 Hz ≤ f ≤ 5 Hz. The disadvantage of this method is that the resolution depends on the frequency to be estimated. A typical breathing frequency at f b = 0.3 Hz delivers a frequency resolution of Δf b = 3.74 · 10−4 Hz and the corresponding value for a typical heartbeat frequency at f h = 1 Hz is Δf h = 4.15 · 10−3 Hz. These values are much better than the corresponding values of the FFT method with Δf b = 0.05 Hz for the breathing with blocks of N = 2400 samples and Δf h = 0.2 Hz for the heartbeat frequency estimation with blocks of N = 600 samples if no zero-padding is applied. The resolution does not depend on f b and f h , respectively, but on the length of the data block. Another aspect for the selection of a frequency estimation method is that with the correlation method the peak of the maximum closest to the main maximum of the correlation function has to be found. Since there is more than one maximum of comparable magnitude, a search region for the maximum of interest has to be known. This is a condition which might not be easy to be fulfilled since this region for reasonable frequencies depends on many parameters like the age of the patient, the physical constitution, and others. The result of the frequency estimation is shown in Fig. 3.11 on the top right. There is no quantization of the estimated frequency visible as with the FFT method. This complies with the much better frequency resolution known from Eq. (3.11).

38

K. Kroschel 40

40

35 30

f (t) [1/min]

20

c

f f(t) [1/min]

30

10

25 20 15 10 5

0 20

40

60

80

100

0 20

120

35

30

30

f (t) [1/min]

25 20

z

fz(t) [1/min]

40

35

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20 15 10

5

5 40

60

80

t [s]

120

25

10

20

100

t [s]

40

0

80

60

40

t [s]

100

120

0

20

40

60

t [s]

80

100

120

Fig. 3.11 Frequency estimation methods: FFT (top left), ACF (top right), BZC (bottom left), CZC (bottom right)

The third method or BZC method is based on determining the zero-crossings of the signal within a data block. This is shown on the bottom in Fig. 3.8. The times tz (i) of zero-crossings are marked by the change of polarity of the rectangular signal and are calculated in the first processing step. If there are Nn zero-crossings in the nth data block with the first zero-crossing at tz,n (1) and the last at tz,n (Nn ) the average time between zero-crossings in the nth block is given by Δtz,n =

1 (tz,n (Nn ) − tz,n (1)) . Nn − 1

(3.12)

Since the period of a sinusoidal signal is equal to the distance between three consecutive zero-crossings, the average period of the signal in the nth block is equal to tn, p = 2 · Δtz,n . From this period follows the average frequency in the nth block f z,n =

1 Nn − 1 . = 2 · Δtz,n 2 · (tz,n (Nn ) − tz,n (1))

(3.13)

The block index n is identical with the time instant t = n s since at every second a new block is generated and the frequency is calculated from the Nn zero-crossings in this block. The result of the frequency calculation is given in Fig. 3.11 on the bottom left.

3 Data Acquisition and Processing

39

Applying the fourth method or CZC method, again the times tz (i) of zero-crossings are determined sequentially and not restricted to a data block. Since the period of a sine wave is identical with the distance of two zero-crossings with another one between them, the instantaneous frequency is given by f z (i · ts ) =

1 tz (i) − tz (i − 2)

(3.14)

which is a very simple method. The result could be used as a reference since there is no degradation by averaging. The frequency of the synthetic signal given in Eq. (3.7) calculated with the CZC method is shown in Fig. 3.11 on the bottom right. In comparison with the ACF and BZC methods the maxima are higher and the minima are marginally lower. This is caused by the fact that no block processing has been applied. Block processing can be seen as a blockwise integration which smooths the extremal values. This becomes specifically clear at the end of the plot at t = 120 s. Here the frequency is much smaller than in the plots of the ACF and BZC methods. These methods do not follow immediately the trend of the frequency downwards whereas the CZC method does. From every three consecutive zero-crossings the frequency is calculated. This has the advantage that with a delay of only two zero-crossings or roughly Δt = 6.7 s for a frequency of f = 0.3 Hz an estimate is calculated. Therefore Fig. 3.11 shows the frequency estimated with the CZC method in the interval 5 s ≤ t ≤ 120 s, i.e., Δt = 15 s earlier than the block-based methods. Nevertheless, the course of the frequency resembles those of the other time domain methods. The differences are the earlier beginning and at the end at t = 120 s the lower amplitude. This is due to the averaging: the decline of the frequency is not very noticable by using the block-based methods because in the past the frequency was ascending. Comparing the estimates of the frequency, similarities and differences are visible. Despite the zero-padding by M = 8, the quantization of the FFT estimate is still visible. The estimates of the ACF and BZC methods are very similar to each other even if their fundamental ideas are different. The CZC method shows a different behavior because the estimate is not based on an average but is close to the instantaneous frequency. Another approach to extract the instantaneous frequency could be to detect the maxima of the signal in Fig. 3.7 instead of the zero-crossings and to derive from them the instantaneous frequency. In fact, this would be a good approach in case of the estimation of the heartbeat frequency from the ECG because the ECG is characterized by steep peaks, the so-called R-peaks. But this does not apply for the VCG in general because there is a lack of distinct maxima so that this approach is not studied here in detail. To compare the shape of amplitudes of the estimated frequencies their histograms are shown in Fig. 3.12. The quantization of the FFT method is clearly visible in the histogram at top left. The range from the smallest frequency to the largest is similar in all three methods, FFT, ACF, and BZC. This is in contrast to the CZC method with a wider range and due to the fact that averaging is not inherent in the CZC method.

40

K. Kroschel

0.1

hF (fc )

0.1 c

f

hF (ff )

0.15

0.05

0 10

15

20

0.05

0 10

25

15

0.1

25

hF (fzl )

0.1

z

z

hF (fz )

20

fc [1/min]

f f [1/min]

0.05

0 10

20

15

25

0.05

0 10

15

fz [1/min]

20

25

fzl [1/min]

Fig. 3.12 Histograms of the estimated frequency: FFT (top left), ACF (top right), BZC (bottom left), CZC (bottom right)

The histogram of the ACF method given on the top right shows many more bars than in the case of the FFT method. These 25 bars given do not reflect the quantization but are controlled by the parameter for the calculation of the histogram. The lower limit at some more than f = 15 1/min and the upper limit at some more than f = 20 1/min with high amplitudes are caused by the relative long time within which the frequency stays at these values. This also applies for the histogram of the CZC method on the bottom right. Since there is no ground truth available the question arises how to compare the results with each other. At first glance all estimated frequencies are close together. But in detail there are differences which can be expressed by the histograms of the estimates and their comparison with each other. For comparison, either the Kullback– Leibler [5] divergence or one of the histogram distance measures [11] can be used. Here the absolute value of the difference of the histograms dH =

NH 1  |h f1 (i) − h f2 (i)| 2 · N H i=0

(3.15)

with h f j (i) the samples of the two compared histograms will be used. If there is no overlap of the histograms compared with each other the distance is d H = 1, whereas in case of identity of both histograms the distance is d H = 0. The results of all comparisons are summarized in Table 3.1.

3 Data Acquisition and Processing

41

Table 3.1 Histogram differences of the four methods for frequency estimation FFT ACF BZC CZC FFT ACF BZC

0

0.40 0

0.42 0.18 0

0.46 0.21 0.23

From the figures given in Table 3.1, it follows that the FFT method is the least comparable method with the other methods AFC, BZC, and CZC since the corresponding values d H of comparison are the largest ones. One reason for this result is the quantization of the FFT method. The ACF and BZC methods are very close together and significantly different from the CZC method. This was also evident by comparing the histograms in Fig. 3.12. The CZC method on the other hand differs from the ACF and BCF methods as far as the figure of comparison d H is concerned. This difference is mainly caused by the broader width of the histogram shown in Fig. 3.12 in comparison with the histograms allocated to the AFC and BZC method. Summarizing all arguments for the decision in favor of one of the frequency estimation methods, the CZC method would be preferred. No block processing is required so that the course of the frequency is not smoothed and the frequency is not calculated at the end of the block but at the time instant at which a zero-crossing occurs. Furthermore, the calculation load is minimum. All these arguments apply if the vibrometer signal is not corrupted by noise which is true in case of the synthetic signals given in Eq. (3.7). A vibrometer signal picked up at the surface of the skin of a patient would be influenced not only by the breathing and heartbeat activity but also by corruptions originating from the movement of the patient, coughing, etc.

3.5.1 Influence of Noise on the Frequency Estimation Since measurements mostly are corrupted by noise, the four methods have been tested with additive, zero mean white Gaussian noise. This is not a very realistic case because the raw vibrometer signal will be filtered to extract the breathing and the heartbeat signal, respectively. Thus white noise is the worst case which is used to get general arguments to evaluate the four estimation methods. In Fig. 3.13 a sample function of the white noise process is given as a data block of length Δt = 20 s and another one with length Δt = 1 s and the power spectral density calculated by the Welch method [2]. In the time domain, the frequent zero-crossings are typical together with the constant power density in the frequency band 0 Hz ≤ f ≤ 60 Hz, i.e., up to the Nyquist frequency or half of the sampling frequency fs = 120 Hz. The power spectral

K. Kroschel 4

4

3

3

2

2

1

1

w

n (t)

n (t) w

42

0

0 −1

−1 −2

−2

−3

−3

−4

0

5

−4

20

15

10

5

5.2

5.4

5.6

5.8

6

t [s]

t [s] −1

N

ww

(f) [dB]

−2 −3 −4 −5 −6 −7 −8 −9

0

10

20

30

40

50

60

f [Hz]

Fig. 3.13 White noise: sample function (top left), section of it (top right), power spectral density (bottom)

density does not show a constant line because a limited number of samples of the noise signal is available and the averaging by the Welch method was limited. For the test of the influence of noise on the synthetic signal the signal-to-noise ratio was chosen to be S/N = 30 dB. The corrupted signal with length Δt = 120 s, the histogram of the signal, a section of the signal of length Δt = 20 s and a section with the environment around zero-crossing are depicted in Fig. 3.14. The comparison with Fig. 3.7 shows only few differences. The difference is most visible in the histogram since the edges close to x(t) = ±1 are no longer sharp and the spread of the amplitude is slightly larger. In the section of the signal shown on bottom left, small deviations of the amplitude from the uncorrupted case are visible. The most important difference is seen in Fig. 3.14 on the bottom right: there is no straight line crossing the zero line but additional zero-crossings are visible caused by the additive white noise. It is of interest how these small deviations influence the estimation methods for the frequency. The results for the four methods are shown in Fig. 3.15. There is almost no deviation from the noise-free case found for the FFT method and the correlation or ACF method if Fig. 3.15 is compared with Fig. 3.11. The result of the zero-crossing method with block averaging BZC is far from tracing the true course of the frequency. Finally, the CZC method is rarely in the range of the true frequency and otherwise shows extreme outliers. The reason for these differences in the case of the zero-crossing methods is that there are more zerocrossings caused by the noise around the zero-crossing of the uncorrupted signal.

3 Data Acquisition and Processing

43

2

0.025

1.5

0.02

0.5

h (x)

0

0.01

−0.5 −1

0.005

−1.5 −2

0.015

X

x(t)

1

0

20

40

60

80

100

0 −1.5

120

−1

−0.5

0

t [s]

0.5

1

1.5

x 0.1

2 1.5

0.05

x(t)

x(t)

1 0.5 0

0

−0.5 −0.05

−1 −1.5 −2

65

60

55

50

−0.1 4.5

70

5.5

5

t [s]

t [s]

Fig. 3.14 Influence of additive noise: signal full length (top left), histogram (top right), section (bottom left), zero-crossings (bottom right) 40

40

35

35 30

f (t) [1/min]

25 20 15

c

ff(t) [1/min]

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t [s]

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25 20

z

z

f (t) [1/min]

t [s]

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30 25 20 15 10

10 5

5

0 20

0

40

80

60

t [s]

100

120

20

40

60

80

100

120

t [s]

Fig. 3.15 Influence of noise on frequency estimation: FFT (top left), ACF (top right), BZC (bottom left), CTZ (bottom right)

44

K. Kroschel 0.16 0.14 0.1

0.1

F

0.08

c

c

h (f )

f

h (f ) F f

0.12

0.06

0.05

0.04 0.02 0 10

15

20

25

0 10

15

20

25

f [1/min]

f [1/min]

c

f

Fig. 3.16 Influence of noise on frequency histograms: FFT (left), ACF (right) Table 3.2 Histogram differences of the four methods for frequency estimation from noisy signals FFT ACF BZC CZC FFT ACF BZC

0

0.38 0

0.41 0.32 0

0.95 0.82 0.89

Obviously the additional zero-crossings do not cancel each other so that an erroneous frequency is estimated. On the other hand, with the FFT method and the correlation method ACF, the influence of the additive noise cancels out due to the inherent averaging. This averaging process is expressed by the summation in Eq. (3.3) in the frequency domain and by the summation in Eq. (3.10) in the time domain. The noise robustness of the FFT and ACF method is visible also in their histograms as shown in Fig. 3.16. The histogram difference for all methods calculated with the measure in Eq. (3.15) is given in Table 3.2. This is almost unchanged compared to the noise-free case for the methods FFT, ACF, and BZC as can be read from the data given in Table 3.1. The CZC method is much worse and therefore not discussed further. Comparing these data it has to be taken into account that the result in the noisy case depends on the sample function of the white noise, i.e., it may change over the time. The histograms of the BZC and CZC methods are not shown since they would be dominated by outliers. Summarizing the results given for white noise corruption, it is obvious that the zero-crossing methods BZC and CZC are not applicable. For the investigation of the influence of noise on the synthetic signal, additive white noise with a signal-to-noise ratio of S/N = 30 dB was used. Of course the signal-to-noise ratio influences the result significantly. For S/N = 60 dB the frequency estimation by the zero-crossing methods delivers useful results which is not surprising. The question is therefore how the influence of noise can be reduced. The zero-crossings depicted in Fig. 3.14 at the bottom right show within 1 s three zerocrossings where only one is expected in the noiseless case. This expectation is based on the fact that the distance between two zero-crossings of a sinusoidal signal with the frequency f = 0.3 Hz is roughly Δt = 1.7 s. This increase of the number of zero-

3 Data Acquisition and Processing

45

0.3

0.05 0

nf (t)

0.1

f

n (t)

0.2

−0.05

0 −0.1

−0.1 −0.2

0

5

10

15

−0.15

20

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5.2

5.4

t [s]

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5.8

6

t [s] 0

Nnn(f) [dB]

−10 −20 −30 −40 −50 −60

0

1

3

2

4

5

f [Hz]

Fig. 3.17 Filtered white noise: sample function (top left), section of it (top right), power density spectrum (bottom)

crossings within Δt = 1 s complies with the increased number of zero-crossings of the white process shown in Fig. 3.13 on the top right. As stated earlier, it is not realistic to assume corruption by white noise since the raw vibrometer signal will be filtered to separate the breathing signal and the heartbeat signal. The synthetic signal is narrow band with a center frequency at f = 0.3 Hz which is in the range of the breathing frequency. Under the assumption that the frequency of interest is not larger than f c = 0.6 Hz a low-pass filter can be used to suppress all spectral components beyond this frequency. Therefore the corrupted signal is filtered by a low-pass filter with the cutoff frequency f c = 0.6 Hz. The filtered white noise signal, a section of it and the power spectral density are shown in Fig. 3.17. The reduction of the bandwidth of the power spectrum is clearly visible. Because of this reduction, the number of zero-crossings is reduced as seen in the Fig. 3.17 on the upper right graph with only one zero-crossing within Δt = 1 s. This lowpass filtered noise n f (t) is added to the synthetic signal x(t) given in Eq. (3.7) and weighted so that the signal-to-noise ratio is equal to S/N = 10 dB. This is only 1% of the signal-to-noise ratio S/N = 30 dB used in the previous examples with white noise. In case of S/N = 30 dB almost no influence on the estimation of frequency would follow. Therefore the signal-to-noise ratio is reduced to S/N = 10 dB. The resulting corrupted signal, a section of it and the histogram are given in Fig. 3.18.

46

K. Kroschel 2

0.02

1.5 1

0.015

hX(x)

x(t)

0.5 0

0.01

−0.5 −1

0.005

−1.5 −2

0

20

40

60

80

100

0 −2

120

−1

t [s]

0

1

2

x 2 1.5

x(t)

1 0.5 0 −0.5 −1 −1.5 −2

50

55

60

65

70

t [s]

Fig. 3.18 Signal with filtered noise: sample function (top left), histogram (top right), section (bottom)

The influence of noise is clearly visible, not in an augmented number of zerocrossings but in a variation of the amplitude since the signal-to-noise ratio is lower by a factor of 100. What is the influence on the estimated frequency? The result for the four methods FFT, ACF, BZC, and CZC is shown in Fig. 3.19. As expected, the FFT and the ACF method are still almost unaffected by the noise. Even the block averaged zero-crossing or BZC method delivers a good result as can be drawn from the comparison with Fig. 3.11. The frequency estimated with the continuous zero-crossing or CZC method follows the trend of the true frequency but shows significant errors. The conclusion is that the FFT and ACF methods are the most reliable ones if the input signal is corrupted by noise. The block averaging zero-crossing BZC method is less noise resistant and can be applied in a low noise environment. The continuous zero-crossing or CZC method is applicable only under very low noise conditions. This is underlined by the histograms of the four methods shown in Fig. 3.20: with moderate noise the FFT, ACF, and BZC methods deliver comparable results. The CZC method is characterized by a high variance of the estimated frequency values caused by the missing averaging implemented in the other methods. To compare the results of frequency estimation with and without noise, Table 3.3 shows the histogram differences d H calculated with Eq. (3.15). There is considerable change in the differences given in Table 3.3 in comparison with those given in Table 3.1. The difference between the ACF and BZC methods is

47

40

40

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fc(t) [1/min]

ff(t) [1/min]

3 Data Acquisition and Processing

25 20 15 10

30 25 20 15 10

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5

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0 20

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60

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120

t [s]

t [s]

Fig. 3.19 Methods for frequency estimation: FFT (top left), ACF (top right), BZC (bottom left), CZC (bottom right) 0.12

hF (fc )

0.06

0.1

c

f

hF (ff )

0.1 0.08

0.04

0.05

0.02 0

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15

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15

hF (fzl )

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F

z

z

z

h (f )

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fc [1/min]

ff [1/min]

0.05

0.05

0

10

15

20

fz [1/min]

25

0

10

15

20

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fzl [1/min]

Fig. 3.20 Influence of filtered noise on the histograms: FFT (top left), ACF (top right), BZC (bottom left), CZC (bottom right)

48

K. Kroschel

Table 3.3 Histogram differences of the four methods for frequency estimation with bandlimited noise FFT ACF BZC CZC FFT ACF BZC

0

0.37 0

0.42 0.3 0

2

1.5

# 10 -3

1

v f(t)

1

e(t)

0.43 0.32 0.33

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-2 0

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t [s]

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10

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t [s]

Fig. 3.21 The ECG (left) and the corresponding VCG (right) of a patient without diagnostic findings

larger because of the influence of noise. Furthermore, the smoothness of the courses of the frequency estimated with the ACF and BZC methods is much higher without noise than with noise as can be seen from Figs. 3.11 and 3.15, respectively. The CZC method is still the most noise dependent and shows large fluctuations in the course of the estimated frequency. An alternative to estimate the instantaneous frequency is to observe the peaks of a signal instead of the zero-crossings. To visualize this approach, Fig. 3.21 shows a section of the ECG of a patient without diagnostic findings together with the filtered vibrometer signal which is called vibrocardiogram or VCG. In the ECG, the periodic spikes corresponding with the so-called R-peaks are clearly visible: their amplitude is much larger than the rest of the signal amplitudes. Therefore the detection of the spikes is unambiguous and the heartbeat rate can be determined from three consecutive maxima following Eq. (3.14). In contrast to the ECG, the maxima are not that unique with the VCG: close to the local maxima are other spikes with large amplitudes. Since the heartbeat rate varies with time, the relevant maxima will also vary with time and amplitude so that adjacent maxima are not separable unambiguously from each other. The result of the estimation of the instantaneous heartbeat rate is given for the ECG and VCG together with the histograms in Fig. 3.22. The estimation of the heartbeat rate measured in 1/min delivers good results for the ECG. There are no outliers visible except the higher rate around t = 80 s. The same is found in the VCG so that it might not be an outlier but the true heartbeat rate. But besides this conspicuous feature there are significant deviations of the VCG in comparison to the ECG. These deviations look like extreme low heartbeat rates and

3 Data Acquisition and Processing

49

110

100

100

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are therefore identified as outliers. The histograms of the ECG and VCG are very similar to each other if the outliers are not taken into account. The most frequent heartbeat rate is in the histogram of the ECG f e = 61.9 1/min with the mean f¯e = 62.7 1/min and the standard deviation of σe = 5.5 1/min. The corresponding values for the VCG are f v = 62.4 1/min with the mean f¯v = 60.3 1/min and the standard deviation of σv = 9.0 1/min. These means are close together and the difference is caused by the outliers which can be read primarily from the larger standard deviation and the lower mean value for the VCG because the outliers are all negative. These results depend on the parameters—the minimum distance between peaks, etc.—set for the detection of the maxima. With a different selection of these parameters and a better adjustment with respect to the peak structure of the VCG the results might be better. This underlines that this method is not very robust. In the chapter on heartbeat this topic will be picked up again.

3.5.2 Influence of the Measurement Point on the Frequency Estimation To evaluate the measured signals with respect to their reliability to carry the information of interest such as the respiration or heartbeat rate, an appropriate measure would be helpful. It might also be used to find the best point for measurement on the

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Fig. 3.23 Possible locations for measurements on the neck

surface of the skin. An example are the nine measuring points on the neck shown in Fig. 3.23. In the chapters on the breathing signal and the heartbeat signal, the ability for extraction of reliable data from these measuring points will be discussed in detail. An appropriate reliability measure can be derived from the autocorrelation function defined in Eq. (3.10) and is calculated at the end of the data block with index n r (t) =

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Instead of the discrete time κ the continuous time τ is used and the time parameter t denotes the running time at which the reliability measure r (t) is calculated. This time t is discrete because every second a new data block with Nb samples is generated from which the correlation function c X X,n (τ ) is calculated. The main maximum of c X X,n (τ ) is at τ = 0 and τmax1 is the time instant of the first maximum closest to the main maximum at τ = 0. From the definition in Eq. (3.16) follows r (t) ≤ 1. The closer r (t) to r (t) = 1 the more the signal x(t) resembles a periodic signal like the sinusoidal signal. For the ideal sinusoidal signal the correlation function is a sinusoidal signal, too, with constant maximum amplitudes. The reliability functions of the cases with white noise and the signal-to-noise ratio S N R = 30 dB and with filtered noise and S N R = 10 dB are shown in Fig. 3.24. Obviously the case with S N R = 30 dB and white noise is more reliable than the case with S N R = 10 dB and filtered noise even if the difference is not large. An explanation might be that the noise is concentrated in the same frequency band as the test signal. This results in larger shifts of the maximum c X X,n (τmax1 ) than in the white noise case. In fact, the frequency estimated with the ACF method in Fig. 3.15 is smoother than that in Fig. 3.19. In general the reliability is high in these cases since the signal of interest, the test signal, is very close to a sinusoidal signal. The difference is that the periodicity is not fixed and the maximal amplitude varies very slowly with

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time. But anyway, the reliability is only locally close to r (tn ) = 1 whereas a pure sinusoid signal would display for all times r (t) = 1. The reliability of the estimated frequency depends on the measuring point as given in Fig. 3.23 and on the incident angle between the laser beam and the surface of the skin. Tests have been executed with three angles: a very flat angle close to ϕ = 0◦ , an angle around ϕ = 45◦ and an angle close to ϕ = 90◦ . The raw laser signal was filtered with a linear-phase FIR filter of length n = 512 and pass-band 0.75 Hz ≤ f ≤ 20 Hz from which the section 0 Hz ≤ f ≤ 10 Hz is shown in Fig. 3.25. Furthermore, the 1.5

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reliability measure given in Eq. (3.16) is shown and the estimate of the heartbeat rate measured by the FFT method with zero-padding with M = 8. In the following figures the results for the low incident angle, the medium incident angle, and the angle close to ϕ = 90◦ are shown. The block length for the estimation of the heartbeat rate was chosen to be Δt = 5 s so that the first estimate is available at t = 5 s and the last one at t = 15 s. Since every second an estimate is calculated, only 11 estimates are extracted from the filtered signal. The measurement with the low incident angle delivers low-quality results. This can be seen from the filtered signal with its unstable amplitude and the spectrum with a high power concentration around f = 3 Hz, i.e., outside the frequency interval where the heartbeat activity is expected. In the time domain signal some more than Δt = 2 s at the beginning of the signal are close to zero because of the group delay of the filter with order n = 512 and the sampling frequency of f s = 120 Hz. The spectrum has no components in the section 0 Hz ≤ f ≤ 0.75 Hz because this has been suppressed by the filter to cutoff the influence of breathing. For the reliability function 0.4 ≤ r (t) ≤ 0.7 applies with an average around r (t) = 0.5. Because the spectral line of the heartbeat around f = 1 Hz is not strong in contrast to the other spectral components the estimate of the heartbeat with the FFT method would fail totally. Therefore, the search region for the spectral maximum has been restricted to 0 Hz ≤ f ≤ 2 Hz. An alternative would be to restrict the upper cutoff frequency of the FIR filter to f = 2 Hz. Since not only the heartbeat rate but also details of the filtered signal which is the equivalent of the electrocardiogram or ECG are of interest, only the search region for the largest spectral line has been restricted. But even then strong outliers are visible. The heartbeat rate is given in the unit 1/min because this is used in medicine. The ACF method delivers a better result thanks to its inherent averaging, but this is not given here. For the medium incident angle around ϕ = 45◦ the corresponding results are given in Fig. 3.26. It has to be mentioned that the incident angle was not precisely fixed despite the fact that the laser vibrometer was mounted on a tripod. The patient was asked not to move but small movements cannot be excluded since the patient was not fixed. But since the measuring time was only some more than Δt = 15 s long, this influence was not too high. In the spectrum with the incident angle ϕ = 45◦ the spectral line which can be allocated to the heartbeat rate is much more dominant against the other spectral lines as in the spectrum with the incident angle close to ϕ = 0◦ . The filtered signal is much more regular with clearly visible periodic spikes. But still dominant spectral components are close to the frequency range where the influence of the heartbeat is expected. The reliability measure is not much better than in the previous case but more uniform. The FFT estimate of the heartbeat rate still shows outliers with values above the expected heartbeat rate. They are caused by the spectral components around f = 2 Hz which corresponds with the estimates of the heartbeat rate up to more than f = 100 1/min. The results for the largest incident angle are shown in Fig. 3.27. This is the best result available. The filtered signal is clearly periodic which is also seen in the spectrum with its concentration of spectral energy around multiples of the heartbeat

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at f = 1 Hz or f = 60 1/min. The reliability function is largest compared to the other cases with local values larger than r (t) = 0.8. The estimated heartbeat rate is more or less constant around f = 60 1/min. The results of these investigations on the influence of the point of measurement and the incident angle on the estimation result is that there are significant influences. Since the laser beam was directed on the neck it can be assumed that the locations close to the carotid artery are the best and that the incident angle should be as steep as possible. This makes sense since the influence of scattering is lowest if the incident angle is steepest. This was also a result from clinical tests which will come into focus in subsequent chapters. Obviously, the quality of the estimated frequency depends significantly on the location where the vibrometer signal is picked up and the orientation of the laser beam with respect to the measuring point. Thick clothes are improper and the distance to the source of the vibrations on the skin, the heart, influences the quality of the measurement. To find an appropriate measuring point, tracking by a pan-tilt unit is required. To control the tracking process the reliability measure r (t) given in Eq. (3.16) can be used. It is calculated in the post-processing unit in the system introduced in Fig. 3.2 and fed into the vibrometer with the pan-tilt unit via the feedback path on the bottom of Fig. 3.2. The implementation of the feedback control is not a part of this project.

3.6 Summary Criteria to evaluate methods of frequency estimation are the frequency resolution and the sensitivity with respect to noise. The FFT method delivers the lowest resolution and requires therefore zero-padding but is very robust with respect to additive noise. The calculation effort is low thanks to the efficient FFT algorithm. No parameters are required since normally only one dominant spectral line is found. Despite positive characteristics, the FFT method is not favored for frequency estimation. An improvement might be seen in the zero-padding approach. The correlation or ACF method requires low computational load if the correlation function is efficiently calculated using the FFT [2]. Since at least two FFT calculations are required the load is roughly two times higher than for the FFT method. This load might be reduced by exploiting the fact that the FFT can be applied to complex valued signals. By allocation of one data block to the real part and the next one to the imaginary part of the input of the FFT algorithm, the computational load can be reduced further [2]. The price for it is an increased delay of the estimated frequency. The correlation method is noise resistant thanks to the internal averaging. The frequency resolution is significantly better than that of the FFT method. The zero-crossing method requires the least computational load and, like the ACF method, uses averaging over a data block and is therefore called BZC method. The frequency resolution is as high as with the correlation method. It has been proved to be noise resistant but less than the ACF method.

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The instantaneous frequency can be calculated using the CZC method. The name CZC points out that the frequency is estimated continuously and not block by block. The main drawback is its sensitivity with respect to additional noise. Even low levels of noise corrupt the estimation result dramatically. Thus the zero-crossing method can be applied only if no or very low additive noise is present. If a low-pass filter is used the influence of noise can be reduced. To evaluate the reliability of the measured signal, a figure of reliability based on the autocorrelation function might be used. It serves also for the search of the most appropriate measuring point for the vibrometer signal.

References 1. Jeliffe, R.W.: Fundamentals of Electrocardiography. Springer, Heidelberg (1990) 2. Kammeyer, K.-D., Kroschel, K.: Digitale Signalverarbeitung. Springer-Vieweg, Wiesbaden (2018) 3. Klinke, R., Silbernagl, S. (eds.): Lehrbuch der Physiologie, 3rd. ed. Thieme , Stuttgart (2001) 4. Kroschel, K., Rigoll, G., Schuller, B.: Statistische Informationstechnik. Springer, Heidelberg (2011) 5. Kullbach, S.: Information Theory and Statistics. Wiley, Hoboken (1969) 6. Luik, A., Mignanelli, L., Kroschel, K., Schmitt, C., Rembe, C., Scalise, L.: Laser Doppler vibrometry for non-contact identification and classification of AV-blocks. Futur. Cardiol. 12, 269–279 (2016). https://doi.org/10.1063/1.4879597 7. Mignanelli, L., Luik, A., Kroschel, K., Scalise, L., Rembe, C.: Auswertung von Vibrometersignalen zur Bestimmung kardiovaskulärer Parameter. tm - Technisches Messen, vol. 83, pp. 462–473 (2016). https://doi.org/10.1515/teme-2015-0113 8. Morbiducci, U., Scalise, L., De Melis, M., Grigioni, M.: Optical vibrocardiography: a novel tool for the optical monitoring of cardiac activity. Ann. Biomed. Eng. 35(1), 45–58 (2007) 9. Polytec GmbH: RSV-150 (2018). www.polytec.com/de/vibrometrie/produkte/spezialvibrometer/rsv-150-remote-sensing-vibrometer 10. Polytec GmbH: PDV-100 (2018). www.polytec.com/de/vibrometrie/produkte/einpunktvibrometer/pdv-100-portable-digital-vibrometer 11. Smith, M.A., Chen, T.: Handbook of Image and Video Processing, 2nd edn. Elsevier, Amsterdam 12. Tabatabai, H., Oliver, D.E., Rohrbough, J.W., Papadopoulos, C.: Novel applications of laser Doppler vibration measurement to medical imaging. Sens Imaging 14, 13–28 (2005; 2013)

Chapter 4

Parameters of Respiration Kristian Kroschel and Süha Demirakca

Abstract Breathing or external respiration is based on the expansion and contraction of the lungs. This mechanical activity can be picked up at appropriate locations on the surface of the skin by a laser Doppler vibrometer. To extract the breathing signal from the raw vibrometer signal, a low-pass filter is required since the bandwidth of the breathing signal is limited to an upper frequency which is below the range of the heartbeat activity. Because of its low distortion, a liner-phase FIR filter is used with an order high enough to suppress the influence of the heartbeat. There are several possibilities to calculate the breathing frequency on the basis of the lowpass filtered vibrometer signal in the frequency and time domain, respectively. The filtered signal is cut into data blocks of fixed length within which the estimation of the breathing frequency is executed. Customarily this frequency with the unit Hz which is identical with the respiration frequency measured in the unit breaths per minute or bpm. Thanks to the overlapping of the processed data blocks every second a new value of the respiration rate is calculated. To achieve a high resolution and a parameter independent implementation, the averaged zero-crossing method and the FFT method with zero-padding is preferred. But also the estimation based on the autocorrelation function is investigated because of its noise resistance based on the inherent averaging. Besides the respiration signal, the ventilation, i.e., the inhalation and exhalation is of interest which can be derived from the route signal of the measurement point. The route signal is the integral of the vibrometer signal which is a speed signal. The breathing can be measured on the thorax, i.e., closest to the lungs, but also at the neck or at other appropriate locations. This has the advantage that the neck normally is not covered by clothes since the laser signal penetrates only just a thin cover of cloth. The new approach is finally evaluated under the aspect of clinical applicability and the need for further investigations. K. Kroschel (B) VID, Fraunhofer Institute of Optronics, System Technologies and Image Exploitation IOSB, Karlsruhe, Germany e-mail: [email protected] S. Demirakca Children‘s Hospital, Clinic of Neonatology and Pediatric Intensive Care, Mannheim, Germany e-mail: [email protected] University of Heidelberg, Heidelberg, Germany © Springer Nature Switzerland AG 2020 K. Kroschel (ed.), Laser Doppler Vibrometry for Non-Contact Diagnostics, Bioanalysis 9, https://doi.org/10.1007/978-3-030-46691-6_4

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4.1 Introduction Breathing is a mechanical process based on the expansion and contraction of the lungs. This is the prerequisite for the respiration, i.e., the exchange of oxygen and carbon dioxide in the somatic cells: in the inspiration phase oxygen is flowing into the lungs and in the expiration phase carbon dioxide is flowing out of the lungs. The mechanical activity can be picked up at appropriate locations on the surface of the skin by a laser Doppler vibrometer. Besides the chest breathing, there is the abdominal breathing with movement of the abdomen. All this counts under the external respiration in contrast to internal respiration based on the blood flow and the consumption of oxygen in the tissue and production of carbon dioxide. In this chapter only the external respiration is of interest. Parameters to evaluate the quality of breathing are the respiration rate, rhythm, and regularity and irregularity, respectively. The respiration rate depends on the age, size, and weight of the patient. Furthermore the gender, the position, i.e., lying in a supine position, sitting or standing, physical activity, diseases, and psychological factors influence the respiration rate. As far as age is concerned, typical values of the respiration rate [6] measured in breaths per minute (bpm) are given in Table 4.1. All these measurements have been taken from patients without any diseases, laying in a supine position at rest with a calm and regular respiration without pauses. A respiration rate below 10 bpm is called bradypnoea and above 25 bpm tachypnoea. The respiration rate can be derived from the ECG [1] since the maximal peaks, the so-called R-peaks, have an amplitude modulation with the modulation frequency equivalent to the respiration rate. Another method is based on the measurement of the expansion and contraction of the chest which is measured by an elastic belt around the chest. The spirometer which measures the volume of the airflow inside and outside the lungs can also be used for the measurement of the respiration rate. All these methods require a direct contact with the patient which might not be possible because the patient is trapped in a car after an accident or the contact might transmit a disease from the patient with an infection to the medical staff. Table 4.1 Dependance of the breathing rate from the age

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Besides the normal periodic breathing there are three typical deviations: the Biot breathing [12] with interruptions of the periodic part named apnea, the Kussmaul breathing with a larger amplitude named hyperpnea and the Cheyne–Stokes breathing with interruptions—apnea—and modulation—gradual hyperpnea and hypopnea— as shown schematically in Fig. 4.1. The difference between the Kussmaul and the normal or normopnea respiration is an increased amplitude. Since the respiration rate is of interest, the autocorrelation function is calculated. From the chapter on data and signal processing, it is known that the frequency of the signal from which the correlation function is calculated is the same as the frequency of the signal itself. This is shown in Fig. 4.2. There is a reduction and variation of the amplitude but the frequency is unaffected which becomes obvious by observing the zero-crossings. In contrast to the schematic representation, the respiration rate will not be constant, i.e., breathing is not a stationary process [5]. Therefore the segment for the analysis of the breathing signal is restricted in time. The longer the observed time period of the breathing signal, the more precise the extracted respiration rate will be but the instantaneous rate is biased. In the sequel, it is assumed that for the sampling frequency f s = 120 Hz the duration of the observed interval is Δt = 20 s long and that the consecutive data blocks are overlapping by Δt = 19 s so that every second a new value of the respiration rate is calculated. The block processing with its inherent averaging serves as a means to suppress artifacts caused by movements, cough, etc. of the patient. Furthermore, typically five periods of the breathing cycle fit into one data block.

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Most of the available input data are those from the Karlsruhe hospital picked up from patients with and without diseases. The measurement time is Δt = 120 s and the sampling frequency is f s = 120 Hz, i.e., the Nyquist frequency is f s/2 = 60 Hz. In a first processing step the mean is suppressed. The spectra of a sample vibrometer signal in the full range 0 Hz ≤ f ≤ 60 Hz and the reduced range 0 Hz ≤ f ≤ 10 Hz are shown in Fig. 4.3.

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In the sequel, the rate will be measured in the unit bpm whereas the unit of the frequency will be Hz. The first spectral spike appears at f = 0.259 Hz which is equal to f = 15.54 bpm and the second at f = 1.07 Hz or f = 64.2 bpm. At multiples of this fundamental frequency f = 1.07 Hz further spikes of lower amplitude are visible. Obviously, the first spike can be allocated to the respiration rate f b = 15.54 bpm and the second spike to the heart rate f h = 64.2 bpm. Since almost no harmonics of the first spike are visible the breathing signal is very much like a sinusoidal signal whereas the harmonics of the second spike are a hint that the heartbeat signal is harmonic but not sinusoidal. To extract the components allocated to breathing from the preprocessed vibrometer signal, a low-pass filter is required. First, the parameters cut-off frequency f c , the type of the filter approximating the given tolerance scheme and the filter order n have to be selected appropriately.

4.2 The Low-Pass Filter From the magnitude of the spectrum shown in Fig. 4.3 it follows that the cut-off frequency of the low-pass filter should be in the range 0.259 Hz ≤ f c ≤ 1.07 Hz because at f = 0.259 Hz the spectral line of the breathing signal is seen and at f = 1.07 Hz the spectral line of the heartbeat. Thus fc = 0.6 Hz would be appropriate because f b = 36 bpm is within the tachypnoea region for an adult in a relaxed state. In case of young children, an adaptation might be required which can be implemented by manual adjustment. The ideal filter characteristic would be a constant attenuation of a p = 0 dB in the pass-band and a given attenuation of as = 60 dB, e.g., in the stop-band. Since this is not realizable with a filter of finite order n the ideal scheme has to be approximated. In the Chap. 3 on data acquisition and processing three types of filters have been investigated. The one with minimal distortion was the linear-phase FIR filter which can be efficiently implemented using the FFT. In the pass-band the magnitude of the transfer function should be |H ( f )| = 1 ± 0.001 and in the stop-band |H ( f )| ≤ 0.001 which is equivalent with an attenuation of as = 60 dB. By this the tolerance scheme of the transfer function together with the cut-off frequency at f c = 0.6 Hz is defined. The approximation of this tolerance scheme should be in the minimum mean square sense. The question is which filter order n has to be chosen to fulfill the requirement that the influence of the heartbeat is suppressed. This is an important question since the transition width between the pass-band and the stop-band depends mainly on the filter order n. To decide on the size of the order of the filter, Fig. 4.4 shows the spectra of the vibrometer signal filtered by FIR filters of order n = 32, n = 128, and n = 512. They all have a constant group delay which is with τg = n/(2 · f s ) proportional to the filter order [4]. The filter of order n = 512 is required to suppress the spectrum of the heartbeat. The high filter order might imply high efforts for realization. But linear-phase FIR

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filters are implemented very efficiently by the FFT [4]. The magnitude of the transfer function, the group delay and the impulse response of the filter are shown in Fig. 4.5 which approximates the transfer function |H ( f )| with the parameters given above: in the pass-band 0 Hz ≤ f ≤ 0.6 Hz the tolerance 0.999 ≤ |H ( f )| ≤ 1.001 is fulfilled which cannot be verified in Fig. 4.5 due to the chosen scale but the fulfillment of the condition |H ( f )| ≤ 60 dB in the stop-band 0.6 Hz ≤ f ≤ 60 Hz is clearly visible. For better representation only the frequency scale up to f = 12 Hz and f = 5 Hz, respectively, are shown. The group delay τg = 2·nfs = 2.01 s with the order n = 512 of the filter and the sampling frequency f s = 120 Hz is constant for all frequencies and thus the filter is free of phase distortion, i.e., the relation of the frequency components at the input of the filter remains the same at the output. The length of the impulse response is τ = nfs = 4.02 s. This is quite long but the only drawback in comparison with other filter realizations. The output of the filter which is fed by the preprocessed vibrometer signal is the breathing signal b(t). Two examples are shown in Fig. 4.6. Both breathing signals are not at all pure sinusoidal signals. The amplitude is in both cases not constant and the histograms differ from the one known from sinusoidal signals. In the upper case, the amplitude stays more often in the negative domain compared to the positive domain. Nevertheless, there are more similarities with a sinusoidal signal in the upper case than in the case shown on the bottom. In the upper

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Fig. 4.6 Breathing signal b(t) at the output of the FIR filter: full length (top left), histogram (top right), the same for a patient with atrial fibrillation (bottom)

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Fig. 4.7 Magnitudes of the spectra of the preprocessed vibrometer signal. Patient with low diagnostic findings (left) and with significant findings (bottom)

case two maxima with different amplitudes are visible at the negative and positive edges of the histogram. Furthermore, minimal values are reached close to amplitudes at zero which underlines the similarity with a sinusoidal signal. This breathing signal was measured on the thorax of a patient with low-level hypertonia. In contrast Fig. 4.6 shows at the bottom an erratic course of the breathing signal. The amplitude is lower, the respiration frequency higher. The histogram does not show the typical parameters of a sinusoidal signal with maxima at the edges and the minimum in the center. This is a first hint that the patient might suffer from a disease. For further investigations, the spectra of the preprocessed vibrometer signals v(t) of length Δt = 120 s are calculated and shown in Fig. 4.7. The magnitude of the spectrum on the left side of Fig. 4.7 shows a dominant peak roughly at f = 1.07 Hz and another one below this dominant peak at f = 0.27 Hz. The first large peak can be identified as the heartbeat frequency and the other smaller one is caused by breathing. The periodic spectral lines with multiples of f = 1.07 Hz are harmonics and indicate that the heartbeat is periodical but not sinusoidal. From this structure no disease can be derived. This is in contrast to the magnitude of the spectrum on the right side. Here a dominant peak is visible at f = 4.88 Hz which indicates a non-regular operation of the heart. Whereas the heart rate of the patient with the spectrum on the left side is 64, 2 bpm and thus in the normal range, the rate of the other patient with the spectrum on the right is f = 292.8 bpm which is in the range of atrial fibrillation. For diagnostic reasons, it is helpful to have a measure which informs about the similarity of the breathing signal, i.e., the filtered vibrometer signal, with a sinusoidal signal. Of course, the observation of the breathing signal itself or the histogram informs about similarity or dissimilarity, respectively. But a figure is much simpler to express the similarity of the breathing signal with a sinusoidal signal which has been discussed in the Chap. 3 on data acquisition and processing. There a figure of reliability has been introduced which is repeated here for convenience. This reliability measure is based on the extracted correlation function of the breathing signal b(t) and given by c B B (τmax1 , t) (4.1) rb (t) = c B B (0, t)

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with c B B (τ ) the autocorrelation function of the data block at time instant t and τ = τmax 1 , the time instant of the first maximum of the autocorrelation function c B B (τ, t) closest to the main maximum at τ = 0. For the reliability measure rb (t) ≤ 1 the maximum value rb (t) = 1 holds for a pure sinusoid. Sections of two breathing signals together with their reliability measures of the whole observation time of Δt = 120 s are shown in Fig. 4.8. The mean of the reliability shown on top of Fig. 4.8 is roughly rb (t) = 0.8 except for two sections around t = 65 s and around t = 85 s. The mean on the bottom is roughly rb (t) = 0.4 which complies with the irregularity of the corresponding block of the breathing signal b(t).

4.3 Estimation of the Respiration Rate In the Chap. 3 on data acquisition and processing three methods based on block processing, the FFT, ACF, and BCZ method have been introduced. The length of the block should be as short as possible to avoid long averaging so that the result differs too much from the instantaneous frequency. Since frequencies of periodic signals are estimated, the number of periods within the data block should be at least five and not more than eight. For adults, the range 17 bpm ≤ f ≤ 23 bpm of the

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respiration rate is given in Table 4.1. For the respiration rate f = 17 bpm the length of one period is Δt = 3.52 s and for f = 23 bpm the length is Δt = 6.61 s so that into a data block of length Δt = 20 s fit 5.7 or 7.7 periods, respectively. This complies with the condition that in a data block between five and eight periods should be contained and used for the estimation of the frequency. Again, the data blocks are overlapping so that every second a new estimate is calculated. By reducing the sampling frequency f s = 480 Hz of the raw vibrometer signal to f s = 120 Hz the data blocks will contain N = 20 · 120 = 2400 samples and are overlapping by 2280 samples because one second is equivalent to 120 samples. 120 Hz = 0.05 Hz Under this condition the spectral resolution of the FFT is Δ f = 2400 which is too coarse for practical use. Since the average respiration rate of adults is, according to Table 4.1, f = 20 bpm or f = 13 Hz the relative error would be 15% which is much too large. With zero-padding by the factor M = 8 the resolution is Δf = 6.25 · 10−3 Hz which corresponds with a relative error of only 2%. In contrast, the resolution of the time domain based methods ACF and BZC is Δf = 4.53 · 10−4 Hz which follows from the resolution formula given in the Chap. 3 on data acquisition and processing. The advantage of the FFT method is its high noise resistance, efficient implementation, and independence of parameters in contrast to the ACF method. The fourth method, the CZC method, is the least noise resistant approach because it implies no averaging. Instead, from every three consecutive zero-crossings the instantaneous frequency is calculated. These methods are now applied to the two cases discussed in the previous section. The result for the patient with hypertonia is given in Fig. 4.9. In the following figures, the range 10 bpm ≤ f b (t) ≤ 25 bpm has been marked because frequencies below f b = 10 bpm are allocated to bradyponea and above f = 25 bpm to tachypnoea. All four methods are comparable with each other as far as their resolution is concerned. An outlier is dominating the estimation result of the CZC method at 46 s ≤ t ≤ 55 s. This outlier is not seen in the results for the other methods which might be caused by their implicit averaging. Due to its high resolution and the averaging the ACF method delivers the smoothest course followed by the FFT method with its visible quantization. Within a data block of length Δt = 20 s almost seven periods of breathing are contained so that roughly 13 zero-crossings will occur. The distance between them is averaged and from this average the respiration frequency is calculated. The low number of zero-crossings yields the rough course of the frequency estimated with the BZC method. This roughness is increased by the CZC method because no averaging is applied. Furthermore, within Δt = 120 s the average respiration rate of f = 20 bpm will cause about 80 zero-crossings which is equivalent to the number of estimated frequencies. In contrast, the BZC method delivers every second an estimate, i.e., 120 estimates within Δt = 120 s. To compare the four methods the histograms of the estimated respiration rates are plotted in Fig. 4.10. For the calculation of the histograms, the quantization Δf = 0.25 bpm was used in the interval 0 bpm ≤ f ≤ 40 bpm. The FFT, ACF, and BZC method deliver as the most frequent rate f = 15 bpm. With the CZC a marginally higher value is found. The difference between the highest

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Fig. 4.9 Respiration rate of the patient with hypertonia: FFT method (top left), ACF method (top right), BZC method (bottom left), CZC method (bottom right) 0.2

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Table 4.2 Comparison of histograms by d H . Patient with hypertonia FFT ACF BZC FFT AFC BZC

0

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and lowest rate is more or less the same if the FFT, ACF method and the BZC method are applied with quite a bit larger span of the BZC method. This span is even wider with the CZC method because there is no averaging to smooth extrema. On the other hand, this method delivers a strong outlier around f = 35 bpm which is also visible in the plot of the respiration rate depicted in Fig. 4.9. None of the frequency values passes the barriers to tachypnoea and bradypnoea. Under the aspect of normality for adults given in Table 4.1 the values are quite low. For comparison of the histograms the difference between the histograms, which was introduced in the Chap. 3 on data acquisition and processing, is repeated here for convenience: NH 1  |h f1 (i) − h f2 (i)|. (4.2) dH = 2 · N H i=0 The histograms to be compared with each other are denoted by h i . The closer d H is to zero the better the histograms fit together. A comparison of the investigated methods for the patient with hypertonia is given in Table 4.2. From Table 4.2 it follows that the methods FFT and ACF have the best fit followed by BZC with CZC. The worst fit is between FFT and BZC. But all values are not too far from each other. Furthermore, it has to be taken into account that the histograms have been calculated from around 100 samples which is a very low figure. On the other hand, it is not surprising that the methods with averaging, FFT and ACF, fit better together than with estimates based on zero-crossing, i.e., BCZ and CZC. On the other hand, these methods are close together. The estimated respiration rates for the patient with atrial fibrillation are shown in Fig. 4.11. As expected from the observation of the time domain representation b(t), very divergent results are obtained. None of the estimates is satisfying. The most consistency is found where the figure of reliability rb (t) defined in Eq. (4.1) is maximum. This applies in Fig. 4.8 in the interval around t = 60 s, t = 90 s and t = 115 s In fact, the FFT method delivers around t = 60 s and t = 115 s, the ACF and BZC methods around t = 60 s respiration rates which fit into the standard interval of the respiration rate of adults. In general, the rates estimated by the BZC method are larger than expected. Again, the least appropriate estimates are delivered by the CZC method. The estimates of the ACF method are limited to 9 bpm ≤ f ≤ 24 bpm because this is the search interval within which the maximum of the correlation function closest to the main maximum at t = 0 is looked for. As mentioned

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Fig. 4.11 Respiration rate of the patient with atrial fibrillation: FFT method (top left), ACF method (top right), BZC method (bottom left), CZC (bottom right)

earlier, this limitation of the search interval is based on the fact that for adults without disease the respiration rate is expected to be found within this interval. The histograms belonging to the respiration rates shown in Fig. 4.11 are depicted in Fig. 4.12. For comparison, the same resolution and range of the respiration rate as in Fig. 4.10 has been chosen. To compare the histograms, again the measure given in Eq. (4.2) is used. For the patient with atrial fibrillation the figures are given in Table 4.3. From the figures given in Table 4.3 it seems that the estimates of the patient with atrial fibrillation fit better together than those of the patient with hypertonia in Table 4.2. But this is a false conclusion. All histograms have a broad range with low amplitudes or occurrences so that broad regions with low amplitudes overlap and thus cancel each other according to the measure given in Eq. (4.2). The wide spread of the histograms in Fig. 4.12 is a hint that the underlying statistic is very weak. Furthermore, the results gained by the ACF method are severely influenced by the limitation of the search interval which explains the concentration at f b = 9 bpm and at f b = 24 bpm. The fluctuations of the respiration rate estimated by the CZC method can be explained by the irregular zero-crossings in Fig. 4.8 on the bottom left where zero-crossings with a low distance are followed by those with larger distances. This is the reason for the flat structure of the histogram in Fig. 4.12. Obviously, all the methods do not deliver reliable results of the estimated respiration rate if the patient suffers from atrial fibrillation. Since the true value of the

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Fig. 4.12 The histograms of the respiration rate estimated by the four methods: FFT method (top left), ACF method (top right), BZC method (bottom left), CZC (bottom right) Table 4.3 Comparison of histograms by d H . Patient with atrial fibrillation FFT ACF BZC FFT AFC BZC

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respiration rate is not known only the course of the frequency and the corresponding histogram are the basis for the interpretation of the measurement result. To avoid misinterpretation it is therefore recommended to display only those estimates f b (t) of the respiration rate with a high value rb (t) of the reliability measure. The drawback of this solution is that a threshold has to be set which influences the displayed result.

4.3.1 Reliability Controlled Respiration Rate Estimation From the reliability functions in Fig. 4.8 on the right side the difference between the breathing signals b(t) picked up from the patient with hypertonia and the one with atrial fibrillation is obvious: whereas the reliability function of the patient with

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Fig. 4.13 Estimates of the respiration rate with threshold tr = 0.61 for the patient without disease (left), tr = 0.35 for the patient with atrial fibrillation (right). FFT method (top), ACF method (center), BZC method (bottom)

hypertonia has an average value rb (t) = 0.82, the mean of the reliability function of the patient with atrial fibrillation is around rb (t) = 0.35, which is significantly lower. To visualize the influence of reliability on the estimated respiration rates only the estimates with a reliability above a threshold set to the mean of the reliability measure is displayed. For the two patients the estimates passing this threshold are shown in Fig. 4.13 for the FFT, ACF, and BZC method. The CZC method is not included because the missing averaging delivers too many outliers. Between the two cases are significant differences. For the patient with hypertonia the results of the three methods are close together. Especially the FFT method and the ACF method deliver similar results. For the BZC method the deviation is larger.

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This is different for the patient with atrial fibrillation. Here the FFT and BZC method are closer together and the ACF method shows noticeable deviations. The reliability function for the patient with atrial fibrillation shown in Fig. 4.8 passes the mean value of r¯b (t) around the times t = 60 s, t = 95 s and t = 115 s. At these times the estimates of the FFT and BZC methods are closest together whereas the ACF method deviates from the result of the other methods at t = 115 s. This might be caused by the fact that the search interval of the AFC method is restricted so that the estimated frequency is too low. Furthermore the averaging might be a reason for this deviation. The threshold has been set equal to the mean of the reliablity measure. Experiments with other values did not yield divergent results. Furthermore, the choice of the threshold has not much influence on the estimation result if the threshold is not too far away from the mean. Assuming that the changes in the reliability measure are not too fast, an adaptation over the time might be an improved version. Then the mean of the threshold is calculated from past values of the reliability in a sliding window and applied at the current time instant. Unfortunately, the results of the application of the reliability measure are not so convincing that further investigations are motivated. It might be sufficient to mark sections which are less reliable. The result of this investigation is that if there is no congruence of the estimates based on the FFT method, the ACF method, and the BZC method this is a hint that the patient suffers from a disease.

4.4 Ventilation The breathing signal b(t) discussed up to now is the filtered vibrometer laser Doppler signal v(t) which is the speed with which the measuring point on the surface of the skin of the patient comes closer to the vibrometer at a fixed position and departs again. To calculate the route s(t) of this movement, the breathing signal b(t) has to be integrated. The simplest form of integration is the running sum of the samples b[k] of b(t) multiplied by the time distance or sampling time 1/ f s . A very simple model to describe the ventilation process is given by a cylinder in which a piston moves up and down. The movement of the piston is described by the route s(t). If the breathing signal b(t), which is a speed signal, is positive the measuring point on the surface of the skin comes closer to the vibrometer, for negative values it departs. Figure 4.14 shows the breathing signal and the route of the measuring point for a patient without any findings together with a section of these signals. Both signals, the speed and route signal, are very similar. Due to integration there is a delay which is known from the sine and cosine functions which are also a pair of signals gained from each other by integration or differentiation. The ventilation consists of two phases, the inhalation and the exhalation. Both can be extracted from the route signal s(t) since the positive branch describes the inhalation and the negative branch the exhalation. Between both phases, there will be a residual volume of air which will not be taken into account in the sequel. Instead

4 Parameters of Respiration

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both phases will be separated and start at zero so that positive values are allocated to inhalation and negative values to exhalation. The result is shown in Fig. 4.15 for the patient without findings. Since the inhalation is coupled with a similar exhalation section the residual volume of air in the lungs will be more or less constant. This is not the case for patients with diagnostic findings. As examples, a patient with hypertonia and another with atrial fibrillation are presented. The route signal and the ventilation signal of the patient with hypertonia are shown in Fig. 4.16

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Significant differences between the patient without findings and the patient with hypertonia are visible: up to t = 50 s the exhalation is larger than the inhalation so that the residual volume of air goes down. After this phase the inhalation dominates so that the residual volume will increase. Since only a section of about Δt = 120 s is available, it is open whether this is a periodic process or a singular event. It has to be remembered that the patients are in a supine position and without any physical or psychological stress. The same is true for the second patient with atrial fibrillation. The results of the route signal s(t) and the ventilation signal sio (t) are shown in Fig. 4.17. Again, the differences between the patient without findings and the patient with atrial fibrillation are significant. The route signal s(t) can be separated in sections with more or less constant levels of the route signal. Within these sections, the dynamics of inhalation and exhalation are constant besides a few outliers which might be caused by corruptions originating from movements, coughing, etc.

4.5 The Influence of the Measuring Point So far the vibrometer signals have been picked up on the thorax of patients in a supine position. With only thin clothes covering the thorax appropriate results of the measurement are gained. An alternative area to measure the breathing activity is the

4 Parameters of Respiration

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Fig. 4.17 Patient with atrial fibrillation. The route signal s(t) with a section (top), the ventialtion signal sio (t) with a section (bottom)

neck because the expansion and contraction of the lungs influences the movement of the surface of the skin at this location, too. Furthermore, the neck is mostly not covered which is a benefit for practical applications. Alternative locations would be the larynx or the forehead. On the neck nine measuring points have been chosen which have been introduced in the Chap. 3 on data acquisition and processing in Fig. 3.23. They are more or less equidistant and cover the major part of the neck. The measuring results of four of these points will be discussed in the sequel. These points are located at the top left, bottom left, top right, and bottom right. The measurements have been taken from a patient with no diagnostic findings. He was sitting upright on a chair and was neither physically nor mentally loaded. The aorta is located close to the measuring points at the right which will generate the strongest movements on the surface of the skin. But these movements are caused by the heartbeat and suppressed by filtering, so that they do not influence the breathing signal b(t). In Fig. 4.18, the figure of reliability rb (t) at the four measuring points is shown. The measurements have not been taken in parallel, but sequentially. Therefore, artifacts influencing the measurements are not identical in the sense of their temporal appearance or intensity. There are significant differences in the figure of reliability at the different measuring points: the reliability on the right is higher than on the left side. Furthermore, the reliability at the measuring point on the bottom right is on average the largest. The value of rb (t) is comparable with the value of the patient with hypertonia in a

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supine position known from Fig. 4.8 on the top right. Here the breathing signal was picked up on the uncovered thorax. This underlines the fact that breathing can be measured at other locations than the thorax. The lowest reliability is found at the position on the bottom left. The other locations deliver a low level of the reliability rb (t) in the interval 100 s ≤ t ≤ 120 s despite the fact that the measurements have not been taken in parallel. Sections of the breathing signal b(t) of length Δt = 20 s extracted from the vibrometer signal by filtering are shown in Fig. 4.19. The amplitude of the breathing signal b(t), i.e., the speed of the movement at the surface of the skin is more or less the same at the four locations. There are a few outliers, at t = 0 in the signal on the top left, e.g., the signals differ significantly with respect to their regularity. The signal on the bottom left is the least regular one and the signal on the bottom right is the most regular one. The latter is a section of the breathing signal shown in Fig. 4.14 on the top left. By this, it is underlined that the regularity is not restricted to the section shown in Fig. 4.19 on the bottom right but is typical for the whole signal. This can also be seen when observing the respiration rate shown in Fig. 4.20 which was calculated with the BZC method. The FFT method with zero-padding delivers similar results but is more dependent on the measuring point. Since the patient is not fixed the measuring point has to be tracked in practical applications. Since this tracking never will perform perfectly, the lower sensitivity is preferable under this aspect.

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The range of the respiration rate is more or less the same at the four measuring points. The smoothest one is measured at the bottom right. Since the figure of reliability is largest at this position this result would be chosen as the most reliable. Derived from this experience, the measuring point should be chosen based on the figure of reliability and the tracking of this point should be based on this figure. Further vibrometer signals have been picked up at the larynx and the forehead and the low-pass component has been extracted. The results are not useable as breathing signals which is not surprising since the distance to the source is very large in comparison to the thorax and the neck. Furthermore, the larynx consists of cartilage and the bones at the forehead are covered by a thin layer of tissue so that the breathing signal is strongly attenuated. The figures of reliability are in the range of rb (t) ≈ 0.2 and thus not reliable enough.

4.6 Clinical Considerations on Parameters of Respiration 4.6.1 Estimation of the Respiratory Rate The respiratory rate is a vital component of clinical assessment and monitoring. It is considered as the most sensitive marker of a deteriorating patient and the first observation to indicate a respiratory problem. Abnormalities in respiratory rate predict serious adverse events including cardio-respiratory decompensation and the need for intensive care unit monitoring and therapy. Poor clinical monitoring plays an important role as a principal contributor to avoidable mortality [3] in hospitals. Due to its clinical importance, the respiratory rate is an integral component of multiple clinical assessment systems such as Early Warning Systems, sepsis or the Systemic Inflammatory Response Syndrome, and the assessment of acute asthma or chronic obstructive pulmonary disease. Respiratory rate measurement has multiple clinical applications including gaining a baseline for comparison, monitoring fluctuations, recognizing acute changes in a patient’s condition, detecting signs of deterioration, monitoring effectiveness of response to treatment, and recognition of need for escalation. Importantly, multiple healthcare workers with various clinical educational backgrounds make assessments during a patients hospital stay, increasing the importance of standardized, accurate methods of assessment. The various uses of respiratory rate recordings facilitate appropriate responses to a patient’s condition. Subsequently, assessments must be accurate and inaccuracies may delay responses or even misguide clinical care. Emergency department triage nurses’ assessments have low sensitivity in detecting bradypnoea and tachypnoea, and show poor agreement with criterion standard measurements [7] by researchers. Furthermore, a recent study showed clinical staff have low levels of confidence in the accuracy of respiratory rate measurements in observation charts, believing rates are estimated, or even fabricated, and not formally assessed using recommended methods. Staff also reported using spot assessments of the respiratory rate, in which they estimated the

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rate by looking at the patient. Though using spot assessments appears to be common practice for some clinical staff, which definitely is an [10] inaccurate method. In neonatology, respiratory rate assessment plays an important role in the monitoring of apnoea of prematurity. It plays obviously a key role in the recognition of sudden infant death syndrome of infants. In children, serious respiratory diseases, in particular pneumonia, account for the majority of emergencies and critical illness states, therefore, require early recognition and treatment in order to minimize morbidity and mortality. In pediatric respiratory failure, acute decompensation is a typical pattern and respiratory rate plays an important role to detect such situations. The accurate measurement of vital signs is a key step in the [2] determination of overall severity of illness in the initial assessment of emergency settings in pediatrics. Respiratory rate in particular is recognized as an important vital sign and is usually estimated by nursing staff counting chest wall movements of children for 15 or 30 s. It is predictive of lower respiratory infections or pneumonia, admission to hospital and death. However, only a minority of general practitioners systematically measure the respiratory rate during their initial assessment of children less than 5 years of age. This may be due to the inaccuracy of manual counting or to the lack of appropriate devices. Current technology for directly measuring the respiratory rate is not practical [11] in many emergency or primary care settings, as it involves attaching electrodes to the chest or the use of nasal thermistors. In so-called occupational settings, technological development is driving an increasing interest in the monitoring of workers during their activities, with the aim to improve health, well-being, and safety. Monitoring the respiratory rate during working activities is of great value because the respiratory rate is sensitive to cognitive load, emotional stress, environmental challenges, pain, and discomfort, among other factors. Specifically, it has been proposed as a sensitive marker of cognitive load, with important implications for workers exposed to highly demanding tasks and weighty responsibilities, including pilots, soldiers, and surgeons. Nicolò et al. [9] have recently reviewed the importance of measuring the respiratory rate during sports and exercise. The authors make a point for respiratory rate being a better marker of physical effort compared to traditional monitoring of physiological variables such as oxygen uptake, blood lactate, and heart rate. Unlike these variables, the respiratory rate is closely associated with perceived exertion in a variety of exercise conditions and experimental interventions, and responds very rapidly to abrupt changes in work rate, which occur during [9] intermittent exercise. Measuring respiratory rate during exercise is not only relevant for athletes but also for other populations. For instance, it is associated with exercise-induced dyspnoea and is a marker of exercise tolerance in patients with chronic obstructive pulmonary disease and asthma. However, the measure of the respiratory rate during exercise has not been established so far. Yet, different exercise modalities may introduce diverse methodological challenges that need to be faced, with motion artifacts being a typical example. Laser Doppler vibrometry is a promising method to measure and monitor respiratory rate in various clinical and non-clinical healthcare environments as described above. The key property is the ability to measure without skin contact to the patient

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or subject and the potential to miniaturize the device. In the following, the measurement characteristics of laser Doppler vibrometry together with future directions to be studied are discussed in detail.

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Metrological Properties Like Sensitivity and Accuracy in the Clinical Setting

In the first clinical studies at the Karlsruhe hospital patients with cardiac diseases and normal subjects were studied with the focus on cardiac vital signs. The respiratory rate was not investigated with respect to a reference method. Marchionni et al. measured respiratory rate with laser Doppler vibrometry compared to values obtained from measurements with a flow-sensor of a mechanical ventilator (reference method) in 55 mechanically ventilated preterm infants during their stay in the neonatal intensive care unit. They reported respiratory rate assessment differences being less than 3% with respect to the flow-sensor data with a high correlation (Pearsons r = 0.99 and respiratory cycle uncertainty of 37 ms). The Bland–Altman plot comparing respiratory periods obtained from the ventilator flow-sensor versus laser Doppler vibrometer showed a mean difference of 0.00 s and a 95% confidence interval of ±0.07 s, which can be interpreted as a high accuracy. The presence of an incubator had no influence on the [8] measured values. Influence of the breathing frequency on measurement accuracy and sensitivity: neonates and infants can increase their respiratory rate to values exceeding 80 breaths per minute, which corresponds to a respiratory cycle period of less than 0.75 s. Marchionni included patients of this measurement range in his study and did not report any difference to patients with a lower breathing rate. So further studies to analyze the effect of very high respiratory rates on the accuracy [8] of laser Doppler vibrometry measurements are warranted. The extend of thoracic and abdominal wall movement during breathing, which can be different by age and severity of respiratory disease may also play a role with respect to sensitivity and accuracy, which should be considered in further investigations.

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Sensor Characteristics to be Usable in the Clinical Setting

The size and cost of laser Doppler vibrometry cannot be assessed at the current stage of development. Miniaturization is the basic requirement for usability in the clinical setting as described above. Further important usability issues are real-time monitoring with the ability to record the respiratory signal together with the pattern of the curves in real time. Important is the measurement intrusiveness, which means how the sensor or the measuring technique limits the subject’s activity. Other aspects are the movements and the sensitivity to body motion artifacts and the sensitivity of a measuring technique to movements and motions which are not related to breathing that negatively affect the output signal. Influence of environmental factors which have to be taken into account: temperature, humidity, external strains, and

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other environmental factors that can affect sensor measurement and consequently the sensor output. Presence of tubes, wires, and connections needed to supply the sensors, and/or register and transfer the data for processing. All these issues have to be addressed in further studies with respect to their fitting in a clinical setting. The reliability function shown in Fig. 4.18 may play an important role to define signal quality under clinical conditions. Taking the existing measurement at current state, the reliability functions are too divers to find out a unique threshold of reliability for the different filtering, especially the FFT, ACF, and BZC methods. So further clinical studies to determine signal quality thresholds with respect to different filtering are warranted. The influence of sensor characteristics and environmental factors described above should be addressed in these future investigations.

4.6.2 Evaluation of the Ventilation The integration of the breathing signal represents a ventilation signal as described in Sect. 4.4. The physiologic definition of ventilation is the movement of air into the lungs via inhalation and exhalation in order to facilitate gas exchange. Inhalation is caused by active expansion of the thorax by the contraction of the diaphragm and the respiratory muscles of the chest. In contrast, exhalation is facilitated by the relaxation of the diaphragm and respiratory muscles, so that the lungs can passively deflate, due to their elastic recoil forces and thoracoabdominal chest wall movement. Therefore inhalation as an active movement has a faster kinetic and different flow pattern than exhalation. These differences have been recorded in Figs. 4.15 and 4.16. For diagnostic purposes to find out typical flow patterns of respiratory diseases and to evaluate their severity this type of recording is not sufficient. A better alternative, which is established in mechanical ventilation monitoring, is to plot the flow against the expanding volume, which is the breathing speed against the expansion of thorax in laser Doppler vibrometry measurements. Figure 4.21 describes an example of this type of recording giving a typical example of the flow pattern of an obstructive respiratory disease compared to a normal flow-volume loop and how this could be translated into a laser Doppler vibrometry measurement. This type of evaluation will allow diagnostic considerations addressing the type and severity of respiratory pathology. Moreover, another potential pulmonologic examination may be derived from lung function testing of spontaneously breathing patients by spirometry. Here the recording of the flow-volume curve is performed during a forced vital capacity manoeuvre. This allows a more detailed evaluation mainly of the exhalation part of the curve. To translate the exhalation flow pattern into numbers, flow readings are made at predefined points represented by the quartiles of exhaled volume. Laser Doppler vibrometry will allow performing the forced vital capacity manoeuvre less invasively as it will not require exhaling in a pneumotachometer via a mouthpiece, which is known to be difficult for older patients and young children. Future studies will have to evaluate whether laser Doppler vibrometry can reflect a comparable type of information given by spirometry.

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Another feature of breathing pattern not readily addressed yet, is the abdominal wall movement during breathing. Main contributor of abdominal movement is the diaphragm, whereas intercostal and neck muscles provide additional effort for the thoracic movement. So far, only chest wall movements are recorded by laser Doppler vibrometry. To examine the complete tidal volume of breathing, the sum of simultaneously recorded data of chest wall and abdominal wall movements have to be assessed. This may have contributed to the difference between in- and exhalation in Fig. 4.21 on the bottom. A comparable method addressing this type of breathing assessment in clinical use is respiratory inductance plethysmography. In this method, bands are placed around the chest wall and the abdominal wall, so that breathing values can be recorded simultaneously. Thoracoabdominal synchrony versus asynchrony incorporates additional information on the work of breathing. In neonates, infants and small children thoracoabdominal asynchrony is a typical sign for severe respiratory distress, due to the higher compliance of their thorax, which can lead to a complete paradoxical breathing pattern in extreme situations with maximum work of breathing.

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4.6.3 The Influence of the Measuring Point The first measurement series of laser Doppler vibrometry are located at the thorax. Thin clothes did not have a relevant impact on the measurement. Additionally tested locations of measurement, which are not covered by clothes, are the larynx, the forehead, and the neck. Within these points, only the neck region could be identified to provide results with acceptable reliability (Fig. 4.18). Therefore, this location is the region of interest when it comes to measurements of subjects in an occupational setting, in sports and exercise or in triage at first contact in an emergency healthcare setting. Any setting outside the intensive care unit could benefit from the opportunity to be able to measure in a region of the skin, which is not covered by clothes. Consequently, the neck region as a measurement location should be further evaluated in studies comparing reliability and accuracy with the optimal thoracic measuring region. The comparison of the chest quadrants addressing reliability, breathing signal amplitude, and respiratory rate count is visualized in Figs. 4.18, 4.19, and 4.20. All three types of measurement confirm consistently that the right side is better than the left side, the left lower quadrant is not usable, and the right lower quadrant may be the optimal region for laser Doppler vibrometry measurement. This might be due to the fact that the right lower quadrant of the lungs incorporates the largest volume with the largest amplitude of inflation and deflation. Whereas the difference between right upper and lower quadrant seems to be very small, so that further studies to evaluate these two regions are warranted. Measurements at the left lower part of the lung reveal clinically relevant differences in reliability, breathing signal amplitude, and in respiratory rate assessment. This measurement region is located nearby the heart and is directly exposed to heart beat so that filtering of the heartbeat signal may have not been enough to eliminate all influences. This has to be taken into account when measurements are done primarily at the right lower region in the case of patients with dextrocardia and may be addressed and confirmed in further studies. Overall, the sequential measurements demonstrate the feasibility and repeatability of the breathing signal and respiratory rate assessment. Nevertheless specifically designed studies with respect to repeated respiratory assessment at predefined locations have to verify these first results. In this context measurement region tracking is still an open question, which has not been addressed yet and should be a subject of further investigations. As mentioned above, simultaneous measurements on thorax and abdominal skin may provide additional information about tidal volume and work of breathing, which will be especially important in an emergency and critical care setting. To implement this context, further studies should also aim to find out the optimum location to register abdominal movements.

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4.7 Summary It has been shown that the breathing signal can be extracted from the vibrometer signal by filtering. To reduce the distortion to a minimum a linear-phase FIR filter with an upper cut-off frequency at f c = 0.6 Hz is used to separate the breathing from the heartbeat activity. From the filtered signal, the respiration frequency can be extracted using the FFT method with zero-padding by M = 8 to gain an appropriate resolution. The data block contains between five to eight breathing cycles so that the data block has the length Δt = 20 s. Alternatives are the ACF method with a very high resolution and noise immunity based on averaging. The same holds for the BZC method with a lower resolution. The CZC method degrades due to outliers caused by movements of the patient. The vibrometer signal measures the speed with which the surface of the skin approaches or departs from the vibrometer. Integration of this speed signal delivers the route of the measured point on the surface of the skin. If the mean of the speed is zero this route is zero in the mean, too. If there are differences between inhalation and exhalation the mean of the route can be different from zero for some time. This can also be observed by the ventilation, the separate registration of inhalation and exhalation. Finally, the measuring point has an influence on the quality of the extracted breathing signal. This quality is given numerically by the measure of reliability. On the basis of this measure an appropriate measuring point can be found. Besides the thorax, some locations on the neck are good measuring points whereas the larynx or the forehead delivers no useful results. The new measuring technique based on laser vibrometry opens new possibilities for clinical applications. Before they can be used more investigations are required which include a significantly increased number of patients. Furthermore, the technical apparatus designed for this special purpose are not yet availabe. Their development is on the way but far from the introduction into the market.

References 1. Carlton, P., Birrenkott, D.A., Bonnici, T., Pimentel, M.A., Johnson, A.E., Alastruey, J., Tarassenco, L., Watkinson, P.J., Beale, R., Clifton, D.A.: Breating rate estimation from the electrocardiogram and photoplephysmogram: a review. IEEE Rev. Biom. Eng. 1 (2018). https:// doi.org/10.1109/rbme.2017.276281 2. Demirakca, S.: Respiratory emergergencies and airway management in children. Med. Klin. Intensivmed. Notfallmed. 110(5), 328–337 (2015) 3. Hogan, H., Healey, F., Neale, G., et al.: Preventable deaths due to problems in care in English acute hospitals: a retrospective case record review study. BMJ Qual. Saf. 22(2), 182 (2013) 4. Kammeyer, K.-D., Kroschel, K.: Digitale Signalverarbeitung. Springer, Wiesbaden (2018) 5. Kroschel, K., Rigoll, G., Schuller, B.: Statistische Informationstechnik. Springer, Heidelberg (2011)

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6. Lindh, W.Q., Pooler, M., Tamparo, C., Dahl, B.M.: Delmar’s comprehensive medical assisting: administrative and clinical competencies. Cengage Learning, p. 573, ISBN 978-1-4354-1914-8 (2009) 7. Lovett, P.B., Buchwald, J.M., Sturmann, K., Bijur, P.: The vexatious vital: neither clinical measurements by nurses nor an electronic monitor provides accurate measurements of respiratory rate in triage. Ann. Emerg. Med. 45, 68–76 (2005) 8. Marchionni, P., Scalise, L., Ercoli, I., Tomasini, E.P.: An optical measurement method for the simultaneous assessment of respiration and heart rates in preterm infants. Rev. Sci. Instrum. 84(12), 121705 (2013) 9. Nicolò, A., Massaroni, C., Passfield, L.: Respirattory frequency dring exercise: the neglected physiological measure. Front. Physiol. 8, 922 (2017) 10. Philip, K.E., Pack, E., Cambiano, V., Rollmann, H., Weil, S., O’Beirne, J.: The accuracy of resiratory rate assessment by doctors in a London teaching hospital: a cross-sectional study. J. Clin. Monit. Comput. 29(4), 455–460 (2015) 11. Shah, S.A., Fleming, S., Thompson, M., Tarassenko, L.: Respiratory rate estimation during triage of children in hospitals. Med. Eng. Technol. 39(8), 514–524 (2015) 12. Wijdicks, E.F.: Biots’s breathing. J. Neurol. Psychiatr. 76(5), 512–513 (2007). https://doi.org/ 10.1163/jnnp.2006.104919

Chapter 5

Vital Parameters of the Heart Kristian Kroschel and Armin Luik

Abstract In cases when the activity of the heart has to be observed without contact, the electrocardiogram or ECG is replaced by the vibrocardiogram or VCG. The VCG is gained by filtering the output signal of a laser Doppler vibrometer. Whereas the ECG describes the electrical operation of the heart, the VCG originates from its mechanical operation. Since it is not possible to transform one signal into the other the equivalence of both has to be shown by comparison of the spectra, the histograms, and typical vital parameters like the heart rate extracted from both signals. The reference for the heartbeat operation is the ECG, the gold standard to describe the heartbeat operation. Therefore both signals have been documented in parallel and synchronized. A transversal filter with linear phase to reduce distortion is used to extract the VCG from the raw vibrometer signal. The estimates for the frequency known from the Chap. 3 on data acquisition and processing are used to extract the heartbeat for both, the ECG and the VCG. On this basis diseases like atrial fibrillation can be diagnosed. The vibrometer signals can be picked up at many measuring points on the surface of the skin of the patient. The most appropriate is the thorax. But also the neck or other locations can be of interest. Corruptions of the VCG are caused by several mechanical influences like the movement of the patient, coughing, or utterance. Therefore, a criterion of reliability is required to decide whether the filtered vibrometer signal is corrupted by these influences or not. To simplify the decision whether the VCG is corrupted by the utterance of the patient, specialized filters for the extraction of the heartbeat or other details of the heartbeat operation are used. Finally, the heart sounds are extracted from the vibrometer signal after appropriate filtering to control for the activity of the heart valves.

K. Kroschel (B) VID, Fraunhofer Institute of Optronics, System Technologies and Image Exploitation IOSB, Karlsruhe, Germany e-mail: [email protected] A. Luik Klinikum Karlsruhe, Karlsruhe, Germany e-mail: [email protected] © Springer Nature Switzerland AG 2020 K. Kroschel (ed.), Laser Doppler Vibrometry for Non-Contact Diagnostics, Bioanalysis 9, https://doi.org/10.1007/978-3-030-46691-6_5

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5.1 Introduction The most frequent cause of death in Germany is the malfunction of the cardiovascular system [2]. This applies for female patients with 44% and for male patients with 36%. The second most frequent cause is cancer with 22% for women and with 29% for men [10]. Therefore the frequent observation of the proper operation of the heart is of importance. The gold standard to monitor the heart rhythm is the electrocardiogram or ECG. This will therefore be the reference or ground truth with which the results extracted from the vibrometer signal are compared. The ECG and the vibrocardiogram were recorded simultaneously from the same person. The laser Doppler vibrometer [18, 19] was a general purpose instrument for industrial applications with measurement distances up to 100 m. From the ECG the heart rate can be extracted. This rate depends on many parameters: the age of the patient, the health state, physical and psychological stress, etc. Typical values in beats per minute (bpm) are given in Table 5.1. The heart rate of adults below f = 50 bpm is allocated to bradycardia and above f = 100 bpm to tachycardia [5]. For the following investigations, 50 patients with various diseases were monitored in a supine position in a standard clinical environment. The vibrometer was mounted on a tripod and the distance between the device and the surface of the thorax or the point of measurement in general was roughly 2 m.

5.2 Electrocardiogram and Vibrocardiogram The goal of this section is to show similarities between the electrocardiogram or ECG [7] and the vibrocardiogram or VCG [12, 20]. Whereas the ECG is an electrical tension measured in Volts the vibrometer signal is the speed of the movement of the surface of the skin with respect to the position of the vibrometer measured in Table 5.1 Heart rate as a function of age

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contrast to r¯v = 0.469 for the broad-band filter. Therefore it is not appropriate to choose the threshold tr = 0.5 but tr = 0.615 following from Eq. 5.4. The extracted heartbeat frequency based on this threshold is shown in Fig. 5.46 together with the resulting histogram. In the sections where for the figure of reliability rv (t) < tr = 0.615 holds, the heartbeat frequency is set to f v (t) = 45 bpm and results in the bar at f = 45 bpm in the histogram. In the section with utterance the estimate of the heart rate is higher and reaches f = 70 bpm which follows from the comparison of the histograms in Figs. 5.41 and 5.46.

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5.7.2 An Example To test the procedure to extract sections of the VCG signal with heartbeat activity only, the numerals from zero to nine with length Δt = 10 s and with pauses between them uttered by a male speaker have been used. The preprocessed and filtered signal including the speech pauses is shown in Fig. 5.47 together with the extracted heartbeat frequency. The heartbeat is less powerful than the utterance. For example, using a section of length Δt = 5 s with heartbeat alone and heartbeat plus utterance, respectively, a distance of 10.25 dB has been calculated. It is obvious that the shown heart rate cannot be used since it is not reliable enough. Therefore the figure of reliability has been calculated and the threshold tr = 0.5 was used to separate reliable and unreliable sections from each other. Furthermore, the heartbeat frequency has been extracted from the reliable sections. The result is shown in Fig. 5.48.

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In fact, all speech pauses have been found. Obviously, the speaker was speaking so fast that no pauses within his utterance have been found. But the short pauses between the numerals have been sufficient to extract the heart rate. In all relevant publications on the application of vibrocardiograms to extract vital parameters of the heart, the patients are asked not to speak. This is acceptable since the measurements are executed in cooperation with the patient. To avoid the influence of the patients attitude on this measurement she or he should not realize that a measurement goes on. But then it cannot be excluded that the patient speaks and the utterance influences the measurement significantly. With the previous experiments, it is shown that this can be overcome by excluding the sections with utterance. To detect time sections with utterance a figure of reliability is used and compared with the fixed threshold tr = 0.5. By this reliable sections are identified and within them the heart rate is estimated.

5.8 Heart Sounds Extracted from the Laser Doppler Signal The venous bloodstream passes from the body through the heart in its right half into the lungs. The arterial bloodstream saturated with oxygen passes from the lungs through the left half of the heart into the body [9]. To avoid the blood streaming back when the atrial and ventricular chambers are contracting, four valves close and open the transmission path between the atrium and the ventricle on the one hand, and the ventricle and the vein and aorta, respectively, on the other hand. The venous blood passes from the right atrium to the right ventricle through the tricuspid valve and through the pulmonary valve from the right ventricle to the lungs. Similarly, the arterial blood passes from the atrium to the ventricle through the mitral or bicuspid valve to the ventricle and from there through the aortic valve into the body. The valves between the atria and ventricles are called atriovascular valves

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and the valves from the ventricles to the lungs and aorta, respectively, are called semilunar valves. The streaming blood and especially the opening and closing of the valves is the source of sounds. The most important sounds are the S1 and the S2 sound. The heart cycle is divided into the systolic and diastolic section [3]. At the contraction of the ventricle, the systole starts which is marked in the ECG with the R-peak. The systole ends at the T-peak where the diastole starts. The S1 sound marks the start of the systole and the S2 sound marks the start of the diastole when the ventricle relaxes. Generally, the sounds can be heard using a stethoscope which is pressed on the thorax close to the locations beneath which the valves are located. This is called auscultation. The quality of the sounds picked up by the stethoscope depends therefore on the location where the stethoscope is positioned. Furthermore, the pressure with which the stethoscope is pressed on the skin influences the quality. For documentation and detailed analysis, the sounds can be digitized, stored and explored by signal processing. Since the transmission path from the source to the point of measurement is like a low-pass filter the sounds are distorted. The vibration on the skin originating from the movements of the valves generates the sound picked up by the stethoscope. The same can be done using a laser Doppler vibrometer [1, 15]. An alternative is the use of radar signals [22]. From the literature [4], it is known that the heart sounds cover the frequency range 15 Hz ≤ f ≤ 150 Hz and heart murmurs, gallop rhythms and others up to f =800 Hz. For the following investigations, Doppler vibrometer signals picked up from patients without any disease and the sampling frequency f s = 960 Hz have been used. The point of measurement was located on the thorax without a documented precise position. Figure 5.49 shows the ECG of the patient together with the VCG as a filtered version of the laser Doppler signal and the magnitude of its spectrum. A linear-phase transversal filter of length n = 512 and a pass-band of 0.75 Hz ≤ f ≤ 40 Hz has been used to extract the VCG from the vibrometer signal. The ECG is regular with a constant heart rate in the displayed section. The same is true for the VCG without any visible degradations by movement of the patient or similar influences. The magnitude of the spectrum covers the range according to the filter up to the upper cut-off frequency at f c = 40 Hz. As already said, from f = 15 Hz on the spectrum might be influenced by heart sounds. Therefore the laser Doppler signal has been filtered by another liner-phase FIR filter of order n = 512 with the pass-band 15 Hz ≤ f ≤ 150 Hz. The magnitude of the spectrum is shown in Fig. 5.50 together with the filtered laser Doppler signal. In fact, the spectrum is structured with a concentration of signal energy in the range of 15 Hz ≤ f ≤ 75 Hz. Above this range only low-power white noise can be assumed. The time domain signal represents the heart sounds with two periodic sections, one with a larger amplitude and the other with a smaller amplitude. The first one can be identified with the S1 sound and the second one with the S2 sound. The sounds S1 and S2 mark the transition between the systole and the diastole as shown in Fig. 5.51. During the diastole, the ventricles are filled with blood and during the systole the ventricles contract and the blood streams into the aorta and to the lungs, respectively.

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It is difficult to define the duration of the sounds. If only the large amplitudes are taken into account then the duration of S1 is roughly Δt1 = 0.14 s and the shorter duration of S2 is Δt2 = 0.12 s. This complies with parameters previously reported [22]. The frequency of the two sounds can be read from the length of one period. As mentioned in the literature, the frequency of S1 is lower than the frequency of S2 . From Fig. 5.50 on the right side follows f 1 = 20 Hz for S1 and f 2 = 21.6 Hz for S2 which is significantly lower than the figures given in [21]. Since the zero-crossings are not equidistant the calculation of the frequency is not unambiguous. The distance between the sounds S1 and S2 can be read from Fig. 5.50 and is Δt12 = 0.33 s which is equivalent to the duration of the systole according to Fig. 5.51. To verify this value, the ECG and VCG are shown in Fig. 5.52 together with the sounds filtered from the laser Doppler signal. For better visibility, the ECG is shifted by one unit to the top and the VCG by 1.5 units to the top. The filtered sound signal is shifted by one unit to the bottom. There is an offset between the ECG and the sound signal which is caused by the time delay of the FIR filter. It could easily be compensated by an appropriate delay of the ECG. The VCG and the sound signal are synchronous because they are results of filtering

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the laser Doppler signal with a linear-phase FIR filter of the same order n = 512. From the literature [22] it is known that the S1 sound is associated with the R-peak which is the largest peak of the ECG and that the S2 sound is associated with the end of the T-wave which is the last peak in the ECG at the end of the systole section. This distance can be read from Fig. 5.49 on top and measures Δt = 0.24 s which nicely fits with the result extracted from the sound signal on the bottom of Fig. 5.52. This investigation has shown that the heart sounds can be extracted from the laser Doppler signal by appropriate filtering. Since the laser Doppler signal is highly sensitive in respect of corruptions depending on movements of the patient, coughing, speaking, etc., the filter might be redesigned to suppress the spectral components with higher frequencies shown in Fig. 5.50 on the left side. Besides the S1 and the S2 sounds there might be also the S3 and the S4 sound in the case of a heart disease of the patient. This will not be discussed here. Instead, the case of atrial fibrillation will be considered. The ECG and VCG of a patient with atrial fibrillation are shown in Fig. 5.53. The irregular course is visible in both, the ECG and VCG. In the ECG the distance between the main peaks or R-peaks is not constant, in the VCG the individual beats are difficult to separate. To extract the heart sounds the laser Doppler signal is filtered with the same FIR filter with the pass-band 15 Hz ≤ f ≤ 150 Hz as before and the result is shown in Fig. 5.54 together with the magnitude of the spectrum. The filter output is the heart sound signal which changes from beat to beat. In contrast to the patient without a disease, the spectrum does not decay beyond f = 75 Hz to a low noise floor as in Fig. 5.50 but contributes significant signal energy. The magnitude is still of constant height and thus is white noise. Since the white noise does not carry relevant information, the upper cut-off frequency of the filter might be limited to f = 75 Hz. The difference between the case without and with atrial fibrillation is also visible by comparing the ECG and VCG, respectively, with the sound signal of the filtered laser Doppler signal as shown in Fig. 5.55.

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In contrast to the case without atrial fibrillation, the two sounds S1 and S2 are not separable. Furthermore, the sound changes from beat to beat significantly as can be seen from the sections on the bottom of Fig. 5.55. It has been mentioned that a reduced bandwidth of the filter which extracts the heart sound from the laser Doppler signal is recommended since above f = 75 Hz only white noise is found. A reduced bandwidth has the advantage that the influence of movements of the patient and other disturbances is reduced. For comparison Fig. 5.56 shows the filtered laser Doppler signal with the cut-off frequency f = 150 Hz and f = 75 Hz, respectively. There is almost no difference visible since the white noise above f = 75 Hz has only a very low influence. The higher cut-off frequency was the first choice based on results found in the literature [3]. But due to the minimal influence of the reduced bandwidth on the filtered signal the reduction is recommended.

5.8.1 Extraction of the Heart Rate from the Heart Sound The occurrence of the heart sounds is identical with the heart rate. Therefore it is possible to derive the heart rate from the occurrence of the heart sounds. In addition, the heart rate variability will be extracted from the histogram of the heart rate. In contrast to the previously discussed methods to estimate the heart rate, no averaging to suppress the influence of noise will be applied. The data of the ECG and the vibrometer signal have been picked up synchronously from patients with various diseases like cardiac infarction, atrial fibrillation, vascular disease, defect at the mitral valve, etc. Samples have been picked up from four patients at locations on the thorax. For one of the patients, three locations for measurement on the thorax have been chosen. These locations are the second, the third, and the

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fourth intercostal space. For the other three patients, the measurements are taken from the second intercostal space. The sampling frequency for both, the ECG and the vibrometer signal, was f s = 480 Hz. As previously the measured signals have been downsampled to f s = 120 Hz and the mean was suppressed. The time delay originating from the filtering applied to the vibrometer signal was compensated for the ECG signal in the preprocessing step. Since one dominant peak is visible in each beat of the ECG signal the heart rate can be extracted directly from the distance of these peaks. In contrast, this can not be done for the vibrometer signal as can be seen from Fig. 5.57 on the top. This signal has been picked up from a patient with a vascular disease. The periodicity of the raw vibrometer signal is almost not visible. As in previous discussions, the raw vibrometer signal can be filtered to extract a signal which is equivalent to the ECG and is therefore named VCG. To avoid phase distortion and to reduce the amplitude distortion, a linear-phase FIR filter of order n = 512 with the pass-band 0.75 Hz ≤ f ≤ 15 Hz is used. The filtered vibrometer signal is shown in Fig. 5.57 on the bottom left. This signal resembles much more the ECG than the raw vibrometer signal. But still there is more than one dominant peak within one

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heartbeat interval. Therefore the filter is replaced by another one which can be used to extract the heart sounds and has the pass-band 15 Hz ≤ f ≤ 40 Hz. The upper cut-off frequency is further reduced compared to f u = 150 Hz or f u = 75 Hz as shown in Fig. 5.56 when the heart sounds have been of interest. This reduction is required to avoid aliasing because the sampling frequency is f s = 120 Hz and thus the Nyquist frequency is f s /2 = 60 Hz. The filtered signal is called vibrometer sound signal and is shown in Fig. 5.57 on the bottom right. In each heartbeat a large peak for the S1 sound and a smaller one for the S2 sound is visible. To calculate the heart rate one peak per beat has to be extracted. For the calculation of the heart rate either the largest positive or negative peak within one beat can be used. To become independent of the polarity, both signals, the ECG and the vibrometer sound signal, are passing a half-wave rectifier and are then filtered by a linear-phase low-pass FIR filter of order n = 512 and cut-off frequency f c = 2 Hz. The results are shown in Fig. 5.58. Besides the large main peak, additional smaller maxima are visible within each heartbeat interval. To extract the largest peak within one beat interval, a data-driven peak detector is used which is parameterized by the mean and the spread of the histogram of the peaks. By this approach, the distance of the extracted peaks has fit into an interval with the minimum given by the mean minus the standard deviation and the maximum given by the mean plus the standard deviation. The heart rate is finally calculated from inverse of the distance of the peaks and shown together with the histogram of the heart rate in Fig. 5.59. The heart rate is not constant which can be seen observing Fig. 5.59 on the top left. The variation is in the interval 37.6 bpm ≤ f e (t) ≤ 60 bpm as can be read from the histogram shown in Fig. 5.59. These figures apply for both methods, the one based on the ECG and the other one based on the vibrometer sound signal. The latter differs from the ECG method by an outlier at around t = 110 s when the patient moved his head. On the other hand, the statistical parameters of both signals are quite close

5 Vital Parameters of the Heart

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Fig. 5.59 The heart rate (left) and the histogram (right). ECG (top), vibrometer sound signal (bottom). Measurement at the 2nd intercostal space Table 5.6 Parameters of the heart rates ICS ECG μ (bpm) σ (bpm) 2nd 3rd 4th

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together as can be seen from Table 5.6 in the second row. The criteria for comparison are mainly the mean μ and the standard deviation σ . Besides the second intercostal space also the third and fourth intercostal space has been chosen as the location for the measurement. The results for the third intercostal space are shown in Fig. 5.60. The heart rates extracted from the ECG and the vibrometer sound signal, respectively, are again very close together except at t = 83 s and t = 101 s where the heart rate extracted from the vibrometer sound signal does not show the small values around f e (t) = 22 bpm visible in the heart rate extracted from the ECG. A reason

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for this difference cannot be given. Again, the statistical parameters of both methods show significant similarities as can be seen from Table 5.6 in the third row. Finally, the fourth intercostal space has been chosen as the location for measurement. The results are shown in Fig. 5.61. The heart rate extracted from the vibrometer sound signal shows a large outlier at t = 58 s and major differences compared to the heart rate calculated from the ECG

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in the interval 90 ≤ t ≤ 100 s. Nevertheless, there is still a significant concordance of the results gained from the ECG and the vibrometer sound signal as can be seen in Table 5.6 in the fourth row. For comparison of the results from the three measurement locations the mean μ and the standard deviation σ of the heart rate are calculated for the ECG and the vibrometer sound signal together with the mean square error E{( f e (t) − f v (t))2 } between the heart rates and the histogram difference d H defined in the Chap. 3 on data acquisition and processing. The result is given in Table 5.6. The results of the first two locations of measurement are quite close together whereas the fourth intercostal space delivers a result further apart from those of the other locations. For the interpretation of these results, it has to be taken into account that the measurements have not been picked up in parallel but sequentially. From the ECG signals on top left in Figs. 5.57, 5.60 and 5.61 follows that their shape is very similar and their difference lies in the irregularity of the heart rate. The rate measured at the third intercostal space is the most regular one followed by the measurement at the second intercostal space and the least regular heart rate is found at the fourth intercostal space. Another difference can be seen in the shape of the heart sounds. At the second intercostal space, the two sounds are clearly distinct from each other whereas this is not the case at the other measurement locations. From this investigation follows that the ECG and the vibrometer sound signal picked up at the second intercostal space deliver heart rates with the best fit. To conclude this investigation the results of three other patients are given. The location of measurement is the second intercostal space because it is the most appropriate one. The results gained from the first patient are shown in Figs. 5.57 and 5.59, respectively. The corresponding result for the second patient suffering from atrial fibrillation is shown in Fig. 5.62. The ECG signal is characterized by large spikes followed by three smaller spikes. This pattern repeats roughly every Δt = 2.6 s. The distance between the large spike and the first smaller spike is roughly Δt = 0.8 s followed by two other spikes in a shorter distance. The heart rate is oscillating between f e (t) = 60 bpm and f e (t) = 100 bpm. This is coarsely reproduced by the heart rate based on the vibrometer sound signal. Around the two frequencies at f e (t) = 60 bpm and f e (t) = 100 bpm clusters are visible as if the crisp information would be smeared over the frequency axis. In contrast to the ECG with its regular sequence of spikes, the vibrometer sound signal looks very noisy. From this follows that the more or less clearly structured histogram based on the ECG is replaced by the less concentrated clusters derived from the vibrometer sound signal. The results for the third patient with minor cardiac problems are given in Fig. 5.63. The ECG is very regular and thus closer to the first patient than to the second patient. The heart rate variability is even lower as can be read from the data given in Table 5.7. The heart rate derived from the vibrometer sound signal seems to be the sum of the heart rate derived from the ECG plus an oscillating disturbance. Finally, the results of the fourth patient with severe cardiac problems concerning the mitral valve, atrial fibrillation, and others are shown in Fig. 5.64 which are similar to those of the second patient.

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In contrast to the second patient, no regularity can be found in the ECG. Instead, the heart rate seems to change randomly between a lower limit at roughly f e (t) = 50 bpm and an upper limit at roughly fe (t) = 100 bpm. The histogram shows a higher concentration close to the upper limit. Due to this randomness, the vibrometer sound signal does not show a clear distinction between the sounds S1 and S2 . From this follows that the extracted heart rate is more or less randomly distributed in the interval 40 bpm ≤ f e (t) ≤ 100 bpm.

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Table 5.7 Parameters of the heart rates of four patients Patient ECG VCG μ (bpm) σ (bpm) μ (bpm) σ (bpm) 1 2 3 4

41.2 74.9 80.4 76.8

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The similarities of the second and the fourth patient can be expressed by the parameters given in Table 5.7 in the third and fifth row, respectively: the mean and the standard deviation of the heart rate are almost the same for both patients even if the structure of the ECG is different in both cases. The differences between the heart rate extracted from the ECG and the vibrometer sound signal of the first and the third patient are the smallest. But even in the other two cases with larger differences, the character of the heart rate is the same. This becomes most evident by the observation of the histograms. The results given in Tables 5.6 and 5.7, respectively, depend on the data-driven parameters used for peak detection from the rectified and filtered signals shown in Fig. 5.58. A further improvement might be possible by development of a more sophisticated algorithm for the calculation of these parameters. The advantage of the algorithm used here is its simplicity.

5.9 Clinical Considerations of the Heart Rhythm The monitoring of the heart rhythm is one of the central diagnostic methods in medicine. Disorders of the heart rhythm are varied and range from harmless deviations to sudden cardiac death. The heart consists mainly of muscles and forms four different heart cavities. The main function of the heart is to supply the body and organs with oxygenated blood and to supply blood to the lungs for oxygenation. Like every other muscle in the body, the heart needs an electrical impulse to contract. This impulse is predominantly formed in the sinus node and is subject to vagal and hormonal influences. Starting from the sinus node, the excitation wavefront continues via the atria to the atrioventricular node (AV-node). From there it will be forwarded via fast neural pathways. This causes a conduction delay from the atria to the ventricles and thus optimizes the heart work. Under resting conditions, an adult’s heart rate is usually 50–100 beats per minute. About the autonomic nervous system, which in turn affects the sinus node, the pulse rate, however, changes depending on physical or mental stress. At maximum conditions, heart rates of up to 200 bpm can be achieved.

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A cardiac arrhythmia is an irregular or disturbed sequence of the heartbeat. These may be due to the occurrence of extra beats, delays of the conduction system and by reentry tachycardia in the atria or ventricles. Basically, deviations of the heart rhythm are subdivided into “too slow” (bradycardia) and “too fast” (tachycardia). Clinically, cardiac arrhythmias present with symptoms such as palpitations, dizziness, limited exercise capacity, dyspnea, or anxiety. It can also cause serious symptoms such as a syncope, stroke or sudden cardiac death. The risk to die of a sudden cardiac death is dependent on the tachycardia’s origin. Ventricular arrhythmia are more dangerous than atrial arrhythmia. The most common cardiac arrhythmia is atrial fibrillation. Patients suffering from atrial fibrillation often do not claim very severe symptomes, but it carries a high risk of stroke. Therapeutically, a permanent anticoagulation to the blood is of major importance. Cardiac arrhythmias may be persistent or paroxysmal. Especially the latter makes diagnosis more difficult. The Electrocardiogram (ECG) is the standard diagnostic procedure for the registration of cardiac activity. In this case, voltages are measured between two points. Therefore electrodes have to be attached to the skin. Usually, these electrodes are connected to the ECG via a cable. The standard ECG takes a few seconds and consists of twelve leads. Analyzing the different leads can detect many cardiac diseases, even die diagnosis of genetic disorders of ion channel are possible. Intermittent cardiac arrhythmias can rarely be diagnosed with standard ECG. For this, longer recordings of the heart rhythm are required. Usually, if longer recording periods are required, an ECG with one to three leads is recorded over 24 h. Meanwhile, even longer ECG recordings, up to 14–30 days, are available (Holter ECGs). If necessary, heart rhythm monitors can be implanted by surgery and are then able to record the heart rhythm over 3 years. In recent years, new smartphone-based technologies have come on the market, which are able to record a one lead ECG. The ECG rhythm is recorded and the software can distinguish between normal sinus rhythm and atrial fibrillation. All techniques have in common that electrodes must be applied to the skin, which then transmits the recordings to a recording device either by wire or wireless. Irritations of the skin are a common side effect, especially if recordings were acquired over several days. Another limitation is that only the electrical activity can be recorded and no conclusions about an actual mechanical contraction of the heart can be drawn. Additional cardiac diagnostics as the echocardiography, computerized tomography (CT scans), and magnetic resonance imaging (MRI) enable the assessment of the mechanical function of the heart. These investigation techniques have in common that they are associated with greater technical effort. The LDV is a noncontact interferometric technique, which allows noncontact registrations of vibration patterns less than the diameter of an atom. If the laser beam is aimed at the thorax, the heart action can be detected. The main difference to the ECG is that die VCG registers mechanical contraction of the heart. Recordings can be done without contact over arbitrary distances. During the first studies, the respiratory rate, heart rate, and heart rate variability could be extracted from the recording signal. The high resolution of the laser interferometer enables to differentiate between the contraction of the atria and the ventricles. In a multichannel recording, conduction

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delays between the right and left side could be observed [14]. Thus, it may be possible to analyze intracardiac conduction delays (AV-blocks, femoral blocks). In summary, the vibrocardiogram is the only technology available that allows noncontact registration of the heartbeat. Respiration rate, heart rate, heart rate variability could be extracted from the recording signal. It might also be possible that the signal contains even more information about the presence of conduction blocks, valvular heart diseases and other hemodynamic parameters. The major advantage of this technique is the noncontact aspect and the possibility to record signals over arbitrary distances. This might be of special importance in the rescue of persons in difficult terrains, in burnt patients and infants.

5.10 Summary There are many similarities between the ECG and the VCG. The VCG as the equivalent of the ECG is extracted from the Doppler vibrometer signal by filtering with a linear-phase FIR filter with a pass-band of 0.75 Hz ≤ f ≤ 40 Hz which can be reduced if only the heart rate is of interest. The lower frequency components are suppressed because they are allocated to respiration. The higher frequency components originate from the heart sounds S1 and S2 emitted from the heart valves. There are much more variations in the VCG than in the ECG because the VCG as a mechanical signal is influenced by the movement of the patient under observation, by utterance, coughing, etc. By selection of an appropriate filter, these influences can be suppressed depending on the physiological parameters which have to be extracted. Four methods were used for the estimation of the heart rate: the FFT method with zero-padding, the ACF method based on the autocorrelation function, the BZC method counting and averaging the zero-crossings in a data block, and the CZC method of continuous measurement of the zero-crossings. The latter method does not include data processing in blocks which helps to reduce the influence of interference. All the other methods are based on processing of data blocks of length Δt = 5 s which contain between five and eight periods of the heart rate. If the CZC method is of interest, the bandwidth of the filter is reduced to 0.75 Hz ≤ f ≤ 2 Hz. Utterance of the patient disturbs the VCG so much that the measurement of the heart rate is not possible. But by reducing the bandwidth and cutting off unreliable data segments the measurement of the heart rate is partially possible. For the detection of reliable data segments, a measure of reliability is used which is based on the autocorrelation function calculated from the actual data block. Finally, the heart sounds S1 and S2 can be extracted from the vibrometer signal. For this purpose, a high-pass filter is used to extract the structure-borne sounds which are of lower frequency than the airborne sounds. On the basis of the heart sounds, the heart rate can be calculated without averaging. On this basis, the variability of the heart rate from beat to beat can be extracted. It has been shown that a high similarity exists between the heartbeat rate extracted from the ECG and the vibrometer signal.

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References 1. Bai, J., Sileshi, G., Nordehn, G., Burns, S., Wittmers, L.: Development of laser-based heart sound detection system. J. Biomed. Sci. Eng. 5, 34–37 (2012) 2. Bauer, A.W.: Kardiovaskuläre Erkrankungen. In. Geradek, W.E. (ed.) Enzyklopädie Medizingeschichte, pp. 722–728. Walter de Gruyter, Berlin (2005). ISBN 3-11-0157144-4 3. Hall, J.E.: Guyton and Hall Textbook of Medical physiology. Elsevier, Philadelphia (2016) 4. Hoth, M., Wischmeyer, E.: Herzötne und Herzgeräusche. In: Behrends, J.C. (ed.) Duale Reihe Physiologie. Georg Thieme Verlag, Stuttgart (2010). ISBN 978-3-13138-411-9 5. Hottenrott, K., Haas, G., Esperer, H.H. (ed.): Herzfrequenzvariabilität, Trainingssteuerung, Biofeedback. Schriftenreihe der deutschen Vereinigung fr Sportwissenschaft, vol. 214. Czwalina Feldbauer Verlag, Hamburg (2011). ISBN 978-3-88020-570-3 6. International Telecommunication Union: ITU-T Recommendation R.52. Blue Book (1993) 7. Jeliffe, R.W.: Fundamentals of Electrocardiography. Springer, Heidelberg (1990) 8. Kammeyer, K.-D., Kroschel, K.: Digitale Signalverarbeitung. Springer-Vieweg, Wiesbaden (2018) 9. Klinke, R., Silbernagl, S. (eds.): Lehrbuch der Physiologie, 3rd edn. Thieme, Stuttgart (2001) 10. Krebs in Deutschland 2013/14: Häufigkeit und Trends. Robert Koch Institut, Gesellschaft der epidemiologischen Krebsregister in Deutschland e.V. 11th edn. (2017) 11. Kroschel, K., Rigoll, G., Schuller, B.: Statistische Informationstechnik. Springer, Heidelberg (2011) 12. Kroschel, K., Luik, A.: Laser-based remote measurement of vital parameters of the heart. Proceedings of the SPIE, vol. 10680, Strasbourg, pp. 1068000-2–1068000-8 (2018) 13. Kroschel, K., Metzler, J.: Lokalisation des optimalen Messorts zur berührungslosen Bestimmung von Puls- und Atemfrequenzen. 28th Konferenz Elektronische Sprachsignalverarbeitung, Saarbrücken, pp. 300–387 (2017) 14. Luik, A., Mignanelli, L., Kroschel, K., Schmitt, C., Rembe, C., Scalise, L.: Laser Doppler vibrometry for non-contact identification and classification of AV-blocks. Future Cardiol. 12, 269–279 (2016). https://doi.org/10.1063/1.4879597 15. De Melis, M., Morbiducci, U., Scalise, L.: Identification of cardiac events by Optical Vibrometry: comparison with Phonocardiography. In: Proceedings of the 29th Annual International Conference of the IEEE EMBS, pp. 2956–2959 (2007) 16. Mignanelli, L., Luik, A., Kroschel, K., Scalise, L., Rembe, C.: Auswertung von Vibrometersignalen zur Bestimmung kardiovaskulärer Parameter. In: tm - Technisches Messen, vol. 83, pp. 462-473 (2016). https://doi.org/10.1515/teme-2015-0113 17. Morbiducci, U., Scalise, L., De Melis, M., Grigioni, M.: Optical vibrocardiography: a novel tool for the optical monitoring of cardiac activity. Ann. Biomed. Eng. 35(1), 45–58 (2007) 18. Polytec GmbH: RSV-150. www.polytec.com/de/vibrometrie/produkte/spezial-vibrometer/ rsv-150-remote-sensing-vibrometer (2018) 19. Polytec GmbH: PDV-100. www.polytec.com/de/vibrometrie/produkte/einpunkt-vibrometer/ pdv-100-portable-digital-vibrometer (2018) 20. Tabatabai, H., Oliver, D.E., J.W. Rohrbough, J.W., Papadopoulos, C.: Novel applications of laser doppler vibration measurement to medical imaging. Sens Imaging, 14, pp. 13-28 (2013) 21. von Westphalen, G., Antwerpes, F., Steigenberger, P., Harig, K.: Herzton. https://flexicon. dochseck.com/de/Herzton (2019). Accessed 12 June 2019 22. Will, C., Shi, K., Schellenberger, S., Steigleder, T., Michler, F., Fuchs, J., Weigel, R., Ostgathe, C., Koelpin, A.: Radar-Based heart sound detection. Scientific Reports 8, (2018). https://doi. org/10.1038/s41598-018-29984-5

Chapter 6

VCG Signals on the Thorax and Detection of the PR-Interval Laura Mignanelli and Christian Rembe

Abstract Vibration measurements on the thorax deliver characteristic patterns in the time domain. It was demonstrated that they contain relevant information on the heart rhythm. In particular, it was possible to measure the time interval corresponding to the PR-time in the ECG. The PR-time is very important for cardiologists because its variation from normal values is associated with various cardiac diseases. In this chapter, the typical VCG signal acquired on the thorax is introduced and the reliability of the detection of the PR-time in the VCG is analyzed. A method to determine the uncertainties is shown and the uncertainty contribution due to setup features is analyzed.

6.1 Introduction Measurements on the thorax not only allow the detection of the heart rate (HR) and of the heart rate variability (HRV) but also the detection of the time interval corresponding to the PR-interval in the ECG (Fig. 6.1) [4]. The PR-interval or PRtime in the ECG is one of the most important parameters for the diagnosis of cardiovascular diseases. It is defined as the time period delimited by the start of the P-wave to the beginning of the QRS-complex and it represents the time between the onset of the atrial depolarization and the onset of ventricular depolarization. From its duration, it is possible to discern between healthy patients and patients affected by different types of heart rhythm diseases. Normal values for the PR-interval in the ECG are between 120–200 ms. Narrower intervals may indicate the presence of illnesses. A prolongation over 200 ms can be a symptom of a first-degree atrioventricular

L. Mignanelli (B) · C. Rembe Institute for Electrical Information technology, TU Clausthal, Leibnizstrasse 28, Clausthal-Zellerfeld, Germany e-mail: [email protected] © Springer Nature Switzerland AG 2020 K. Kroschel (ed.), Laser Doppler Vibrometry for Non-Contact Diagnostics, Bioanalysis 9, https://doi.org/10.1007/978-3-030-46691-6_6

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(AV) block. However, well-conditioned athletes may present an asymptomatic PR prolongation. Since the first-degree AV-block is associated with an increased risk of atrial fibrillation, pacemaker implantation and all-cause mortality, anomalies of the PR-time of at least 20 ms need to be detected. In fact, increments of 20 ms of the PR-interval are associated with an adjusted hazard ratio of 1.11 for atrial fibrillation, 1.22 for pacemaker implantation and 1.08 for all-cause mortality [4, 8]. A time-varying PR-interval, together with beat drops, may be associated with the other types of AV-blocks. A dropped beat happens when the contraction of the atria is not followed by the contraction of the ventricles, i.e., the electrical impulse does not succeed in traveling in the normal conduction pathway, causing the delay or the absence of ventricular depolarization [3]. In Ref. [4] LDV measurements on healthy subjects and subjects affected by an AVblock of third degree were reported. The measurements were performed on the thorax in the third intercostal space, in correspondence to the left atrium. A simultaneous ECG is performed to have a reference signal. The sampling frequency was 960 Hz. While the acquisition on healthy subjects had an acquisition time of 64 s, for the sick patients it was reduced to 5–15 s. The measurements on sick subjects were performed during the routine follow-up. The pacemakers were inhibited for several seconds and the ECG and VCG were simultaneously obtained. The inhibition time was dependent on the symptoms of the patient. The VCG-velocity signals of a heartbeat acquired on the thorax of healthy subjects showed to be reproducible. In the structure of a typical VCG beat, three main segments can be identified (Fig. 6.1). The first segment is the PV -wave. It consists of a sequence of positive/negative/positive deflections in the VCG pattern delineated by the points PV and PN . They represent the vibration generated by the electrical activation of the atria. The second is the RV -wave which contains a negative peak, the RV -peak. This pattern is caused by the electrical activation of the ventricles. The RV -peak can be used as a fiducial point for the detection of the HR and HRV in the time domain. By localizing the PV -wave and the RV -point in healthy subjects, it is possible to measure on VCG signals the time interval corresponding to the PRinterval in the ECG. The third segment consists of the two prominent waves which determine the end of a beat. The maximum of the first prominence is identified with the letter C and the second with the letter D. While the PV -wave and the RV -wave were related directly to the ECG, the prominence of the third segment which comes up at the end of the ventricle relaxation may be correlated to the venous back-flow of the blood. Further studies need to be carried out to verify this assumption [4]. The measurements performed on patients with AV-block of third degree allowed to detect the vibrations generated by a dropped beat, i.e. the pattern delivered by isolated P-waves could be detected. The positive/negative/positive deflections of the PV wave were traceable also in this measurement during sinus rhythm and fusion beats. The second heartbeat of Fig. 6.2 displays the signature of an isolated P-wave. The positive/negative/positive deflection continues in its sequence, since it is interrupted by the vibrations due to the activation of the ventricles. The third beat shows a fusion of the PV - and RV -wave. Even in this case, the PV -wave can be recognized. This

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allows to conclude that a reliable beat to beat detection of the PV RV -interval is feasible. After the filtering of artifacts and the breathing component, a first possibility for the detection of the PR-time in the VCG is performed with a peak detection algorithm for the point RV and a maximum search algorithm for PV for each cycle. Then, by subtracting the time point of RV and PV , the PV RV -interval is calculated. However, since the reference points for the PR-time in the ECG are the onset of the P-wave and the onset of the QRS-complex (and not their maximum) a calibration is required. In Ref. [4] a calibration factor was calculated for the case that the measuring direction is perpendicular to the thorax surface of the patient. References [6, 7] present first attempts to automatically detect the PV RV -interval. A second possibility is the detection of the starting point PS of the PV -wave. Once PS is identified, the RV -point is detected as mentioned before and the time interval PS RV can be calculated. The time calibration factor must be adapted to this case. Reference [7] presents a method for the detection of the PS -point. However, it has been noticed that the PS -point is not always clearly recognizable since, sometimes, interferences from other vibration sources occur.

6.2 Reliability of the Detection of the PR-Interval LDV signals are mechanical signals and they are stronger influenced by the peculiarity of each subject with respect to the ECG signal. In fact, the electrical pulse (measured with ECG), which is different from person to person, causes the contraction of the heart, then vibrations are originated and they propagate through different tissue layers. Finally, they are detected on the skin with the LDV. Therefore, vibration signals are more complex than electrical signals. The factors which influence the vibration signals are the time and amplitude characteristics of the electrical pulse, the mechanical response of the heart, the damping due to the tissue stratification, and the interference with other biological vibrations (like breathing or blood pressure wave through the vessels). All of these factors depend on the specific characteristics of each subject as the body mass index (BMI), heart rate, diseases, sport activity, etc. They influence the shape, the amplitude, and the time duration of the typical waves. In addition to these features, there are other external interfering factors which influence the shape of the VCG signals, no matter where the signals are acquired. These disturbances are, for example, noise or vibrations that contain not needed information and have to be removed like involuntary movements. The respiration is also considered as a disturbance if the aim of the measurement is to extract heart or blood flow signals. Setup features as the metrological properties of the measuring instrument, the measurement point, and the measuring direction can also alter the measurement. A contribution to the uncertainties is also given by the filtering techniques and the algorithms chosen for the post processing. Usually, only the uncertainties of the post processing are calculated [9], while the uncertainty of the measuring condition

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is considered mostly as ideal. However, considering the measuring condition as ideal could lead to uncertainties in the determination of the extracted cardiovascular parameter.

6.2.1 Accuracy of the PV RV -Interval Clinical data implicate that a measurement accuracy of