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An Introduction to the Physics of Nuclear Medicine

An Introduction to the Physics of Nuclear Medicine Laura Harkness-Brennan University of Liverpool

Morgan & Claypool Publishers

Copyright ª 2018 Morgan & Claypool Publishers All rights reserved. No part of this publication may be reproduced, stored in a retrieval system or transmitted in any form or by any means, electronic, mechanical, photocopying, recording or otherwise, without the prior permission of the publisher, or as expressly permitted by law or under terms agreed with the appropriate rights organization. Multiple copying is permitted in accordance with the terms of licences issued by the Copyright Licensing Agency, the Copyright Clearance Centre and other reproduction rights organisations. Rights & Permissions To obtain permission to re-use copyrighted material from Morgan & Claypool Publishers, please contact [email protected]. ISBN ISBN ISBN

978-1-6432-7034-0 (ebook) 978-1-6432-7031-9 (print) 978‑1‑64327‑032‑6 (mobi)

DOI 10.1088/978-1-6432-7034-0 Version: 20180601 IOP Concise Physics ISSN 2053-2571 (online) ISSN 2054-7307 (print) A Morgan & Claypool publication as part of IOP Concise Physics Published by Morgan & Claypool Publishers, 1210 Fifth Avenue, Suite 250, San Rafael, CA, 94901, USA IOP Publishing, Temple Circus, Temple Way, Bristol BS1 6HG, UK

I dedicate this book to mum and Rachel.

Contents Preface

ix

Acknowledgments

x

Author biography

xi

1

Introduction

1-1

1.1 1.2 1.3

Building blocks of matter Fundamental forces Overview of nuclear medicine

1-1 1-2 1-3

2

A brief history of nuclear medicine

2-1

2.1 2.2 2.3

Radioactivity Production of radionuclides for medicine Diagnostic imaging

2-1 2-3 2-5

3

Radioactivity

3-1

3.1 3.2

3.3

Nuclear stability Radioactive decay processes 3.2.1 Alpha decay 3.2.2 Beta decay 3.2.3 Gamma decay Radioactive decay law

3-1 3-2 3-2 3-3 3-5 3-6

4

Radionuclide production

4-1

4.1 4.2 4.3 4.4 4.5 4.6

Radionuclide selection Cyclotrons Nuclear reactors Radionuclide generators Production yield Emerging radiopharmaceuticals

5

Radiation interactions with matter

5-1

5.1

Gamma-ray interaction mechanisms 5.1.1 Photoelectric absorption 5.1.2 Compton scattering

5-1 5-3 5-4

4-1 4-2 4-4 4-8 4-11 4-12

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5.2

Charged particle interaction mechanisms 5.2.1 Collisional Coulomb energy loss 5.2.2 Radiative energy loss 5.2.3 Charged particle range

5-5 5-6 5-6 5-7

6

Radiation detection

6-1

6.1

6.2 6.3 6.4

Gas detectors 6.1.1 Region A: recombination 6.1.2 Region B: ionisation 6.1.3 Region C: proportional 6.1.4 Region D: limited proportional 6.1.5 Region E: Geiger–Müller 6.1.6 Region F: continuous discharge Semiconductor detectors Scintillation detectors Performance of radiation detectors

7

Imaging

7-1

7.1 7.2 7.3

Gamma camera Single photon emission computed tomography Positron emission tomography

7-1 7-5 7-9

8

Radionuclide therapy

8-1

8.1 8.2

Principles of radiotherapy Medical internal radiation dosimetry (MIRD)

8-1 8-4

6-1 6-2 6-3 6-3 6-4 6-4 6-4 6-5 6-7 6-12

9-1

Appendix A

viii

Preface The complexity and vulnerability of the human body has driven the development of a diverse range of diagnostic and therapeutic techniques in modern medicine. The nuclear medicine procedures of positron emission tomography (PET), single photon emission computed tomography (SPECT) and radionuclide therapy are wellestablished in clinical practice and are founded upon the principles of radiation physics. This book will offer an insight into the physics of nuclear medicine by explaining the principles of radioactivity, how radionuclides are produced and administered as radiopharmaceuticals to the body and how radiation can be detected and used to produce images for diagnosis. The treatment of diseases such as thyroid cancer, hyperthyroidism and lymphoma by radionuclide therapy will also be explored.

ix

Acknowledgements I would like to thank Morgan & Claypool Publishers and the Institute of Physics for the opportunity to write a book on the topic that inspired me to become a physicist. I hope it can in some way inspire others. I would also like to thank those who provided images: The University of Manchester; DOE Photography; The Regents of the University of California, through the Lawrence Berkeley National Laboratory; University of Birmingham; Eckert & Ziegler; MEDICIS, CERN; Capintec, Inc.; Ludlum Measurements, Inc.; Saint-Gobain Ceramics & Plastics, Inc.; Hamamatsu Photonics, UK; SensL; the University of Liverpool; Philips Healthcare; Spectrum Dynamics Medical; GE Healthcare and Siemens Healthineers. I would like to thank Dr Bradley Cheal and Dr Daniel Judson for their support in the preparation of this book. To all my colleagues and students at the University of Liverpool, I have the warmest appreciation for your continued support and guidance. Finally, I would like to thank my family, for without you, nothing is possible.

x

Author biography Laura Harkness-Brennan Dr Laura Harkness-Brennan is a Senior Lecturer in the Department of Physics at the University of Liverpool. She completed her PhD in 2010, which was a design study of the ProSPECTus Compton camera for nuclear medicine. In the same year, she also received the Shell and Institute of Physics Women in Physics Very Early Career Award. She now leads a team of researchers developing novel radiation detection and imaging techniques for medical physics and nuclear structure physics experiments. She has been a principal or co-investigator on over £5.3 million of external grant funding for this research. Laura teaches undergraduate and postgraduate courses in medical physics and nuclear instrumentation. She is a member of the Institute of Physics and a fellow of the Higher Education Academy. She is passionate about contributing to the public understanding of physics by engaging in outreach activities such as public lectures and family science days.

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An Introduction to the Physics of Nuclear Medicine Laura Harkness-Brennan

Chapter 1 Introduction

Procedures that involve the production and administration of radionuclides to the body for either diagnostic or therapeutic purposes fall under the remit of nuclear medicine. This chapter will provide a revision of the building blocks of matter and their interactions, which is necessary to understand the topics discussed in later chapters. A brief overview of nuclear medicine will also be given.

1.1 Building blocks of matter The building blocks of matter are illustrated in figure 1.1. Understanding the characteristics of these is important because the physical and chemical properties of all types of matter are determined by its constituents. All substances are made of elements, such as oxygen, sodium and lithium. The periodic table of the elements is shown in figure 1.2. Example elements that are of particular interest in nuclear medicine have been highlighted in yellow and will be referred to using their chemical symbols throughout the book. A list of these chemical elements and their symbols can be found in Appendix A. An atom is the smallest amount of the element to retain its chemical properties. The diameter of an atom is approximately 0.1 nm (1 × 10−10 m), which is a million times smaller than a single grain of fine sand. When at least two atoms of at least one element are present, they may be chemically bound together as molecules. One of the most essential molecules found on Earth is water, for which each molecule contains two hydrogen atoms and one oxygen atom, H2O. Biological molecules of interest in nuclear medicine are usually constructed from various combinations of hydrogen, carbon and oxygen atoms. An atom is composed of a positively charged nucleus and negatively charged electrons. The nucleus is formed from protons and neutrons, which together are known as nucleons. The total atomic and nuclear composition can be described by A ZX N , where the mass number, A, is the total number of nucleons and the atomic number, Z, is given by the number of protons. The atomic number defines the type of chemical element, X. Nucleons are each composed of three quarks, which are the doi:10.1088/978-1-6432-7034-0ch1

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Figure 1.1. Illustration of the building blocks of matter.

Figure 1.2. Periodic table of the elements, ordered by atomic number and grouped according to chemical properties. Example elements that have radioisotopes used in nuclear medicine are highlighted in yellow.

fundamental constituents. One of the most important particles in nuclear medicine is the positron, as it is released by radionuclides used in the diagnostic imaging procedure positron emission tomography. A positron is the anti-particle of an electron and as such has the same mass but an equal and opposite charge. A particle and antiparticle pair have the important property that they annihilate each other, producing energy. This is an example of matter-to-energy conversion, which is described by one of the most famous equations in physics, Einstein’s equation, E = mc2. In the annihilation of an electron and positron, 1.64 × 10−13 Joules of energy is released. This energy can be more conveniently expressed as 1.022 MeV. The properties of protons, neutrons, electrons and positrons are given in table 1.1. As can be seen in the table, mass may be expressed in units of MeV c−2, courtesy of E = mc2.

1.2 Fundamental forces Nature is governed by the four fundamental forces: strong; electromagnetic; weak and gravitational. Although all forces will play a role in nuclear medicine, it is the 1-2

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Table 1.1 Properties of particles relevant to nuclear medicine.

Name

Symbol

Charge (C)

Mass (kg)

Mass (MeV c−2)

Proton Neutron Electron Positron

p n e− e+

+ 1.6 × 10−19 0 − 1.6 × 10−19 + 1.6 × 10−19

1.6726 × 10−27 1.6749 × 10−27 9.1094 × 10−31 9.1094 × 10−31

938.28 939.57 0.511 0.511

first three that will be the most important, particularly in the discussion of radioactive decay processes: Strong force: acts only on particles that are made from quarks, such as protons and neutrons. It is known as the strong nuclear force because it is responsible for binding together the nucleons within a nucleus. It is the strongest of the four forces (a relative strength of 1 in what follows) but acts only over a short range. Electromagnetic force: acts on all electrically charged particles, with infinite range. It has a relative strength ≈ 10−2. Weak force: acts on all particles but with an extremely short range. It has a relative strength ≈ 10−5. It is responsible for beta decay, which is an important radioactive decay process in nuclear medicine. Gravitational force: acts on all particles, with infinite range. At the atomic scale, it is the weakest interaction, with a relative strength ≈ 10−39. It is important for large masses and is responsible for binding together the solar system.

1.3 Overview of nuclear medicine Nuclear medicine is exclusively dedicated to administering radionuclides to patients for the purpose of diagnosis or therapy. In these procedures, radioisotopes are attached to a biological compound, which together form a radiopharmaceutical that accumulates in the body depending on its biokinetic response. This relies on the dedicated production of radionuclides for medicine, since naturally occurring radioactive materials do not undergo radioactive decay quickly enough. The imaging methods used for diagnosis are single photon emission computed tomography (SPECT) and positron emission tomography (PET). The methods used to produce the images are slightly different but the underlying principles are the same. Photons are emitted, either directly from the radiopharmaceutical (SPECT), or following positron annihilation with an electron (PET) in the organ of interest. The photons interact in a radiation detector system surrounding the patient, which is used to locate and visualise the distribution of the radiopharmaceutical. The generated images are used to elucidate disease status, particularly in oncology, neurology and cardiology. The treatment of diseases such as hyperthyroidism, neuroendocrine tumours and non-Hodgkin lymphoma by radionuclide therapy using radioactive sources is also an important aspect of nuclear medicine. This employs the same principle of the uptake

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Figure 1.3. Overview of the foundations of nuclear medicine.

of the radiopharmaceutical to regions of interest in the body, such as within a highlymetabolic tumour. However, the objective of radionuclide therapy is to deliver lethal radiation doses to targeted tissue whilst minimising the dose to the surrounding tissue. This is achieved by using radionuclides that emit charged particles, since they will only travel up to a few millimetres in the tissue, which confines the region over which dose is delivered. The physical principles of these diagnostic and therapeutic procedures will be discussed in detail in this book. However, the foundations will first be provided, which are an introduction to radioactivity, methods used to synthesise radionuclides, radiation interactions with matter and the detection of radiation. Understanding all of these topics is essential to appreciate the clinical application, as indicated by figure 1.3. We will begin with a short history of nuclear medicine.

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An Introduction to the Physics of Nuclear Medicine Laura Harkness-Brennan

Chapter 2 A brief history of nuclear medicine

This chapter will outline the major discoveries and developments relevant to the field of nuclear medicine. We will start with the discovery of radioactivity and then learn about the development of methods to produce medical radionuclides, detect their emissions and use this information to either diagnose or treat a patient.

2.1 Radioactivity Nuclear medicine is founded upon our understanding of radioactivity, in which charged particles and photons are released from an unstable nucleus. Radioactivity was discovered by Henri Becquerel when he was conducting experiments in 1896 to investigate the phosphorescence of materials. The aim of his experiment was to demonstrate that some materials release light after they have been exposed to sunlight. His plan was to expose uranium salts to sunlight and then position them in front of a metal object placed on a photographic plate. If the uranium salts fluoresce, then an image of the object would be observed on the plate. By chance, Becquerel could not carry out the experiment due to overcast weather, so he stored the uranium salts and photographic plates together. A few days later when he wished to conduct his experiment, he noticed an image on the plate. This was a rather surprising observation, since the salts and plate had been shielded from sunlight. He attributed the phenomenon to the emission of some other type of ray from the uranium salts. The experiment was inspired by the work of Wilhelm Röentgen, who used the same method in 1895 to discover x-rays. Following further investigation, Becquerel determined that the rays emitted from the uranium salts must be different to x-rays since they could be deflected by electric and magnetic fields, which would not be possible for uncharged x-rays. He had in fact observed spontaneous radioactivity. The term radioactivity was first used by Marie Curie and Pierre Curie, who together discovered the elements radium and polonium in their search for radioactive materials other than uranium. These three pioneers shared the 1903 Nobel Prize for Physics in recognition of their discoveries. The decay rate of radioactive doi:10.1088/978-1-6432-7034-0ch2

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material is described by its activity, the units of which are the Becquerel (Bq) and Curie (Ci), in honour of their contributions. Many important discoveries pertaining to radioactivity were made over the next few years. In 1898, Ernest Rutherford identified two different types of emissions in radioactive decay and called them alpha, α, and beta, β. He would also later name the gamma-ray, γ-ray. He conducted many experiments at the Cavendish Laboratory in Cambridge to characterise α and β properties, including studying how readily stopped they are in materials. This method can still be used today to discriminate α and β particles emitted in radioactive decay. Rutherford moved to McGill University in Canada, where he worked alongside Frederick Soddy to develop the theory of atomic disintegration, which was the first to attribute radioactive processes to the spontaneous disintegration of atoms. They studied how radioactive samples decayed over time and found that radioactive materials have a characteristic decay period. They described this relationship using the concept of half-life, which is the time taken for half the nuclei in a radioactive sample to decay. Rutherford was awarded the 1908 Nobel Prize in Chemistry for these contributions. Soddy would have to wait until 1921 to be awarded his Nobel Prize. Rutherford moved to the University of Manchester in 1907, where he inherited a research assistant, Hans Geiger. They are photographed working together in figure 2.1. Rutherfordʼs talented research assistant developed a method to detect α particles using gas. This would later become known as a Geiger–Müller counter, a variant of which is still used widely in radiation detection today. Rutherford and his team conducted a series of experiments from 1908 to 1913, in which they were able to show that an atom consists of electrons orbiting a nucleus. In the famous Rutherford scattering experiment, a beam of α particles emitted from polonium was directed towards a thin gold foil target. A schematic illustration of the experimental setup is shown in figure 2.2. The path of the particles could be deduced because a zinc sulphide screen surrounded the setup and when struck by an α particle would produce visible light. It was the task of Geiger and undergraduate student Ernest Marsden to count the flashes of light at various angles using a microscope. The team observed that about 99% of the particles passed straight through the foil, whilst the others were deflected through small angles or even backscattered from the

Figure 2.1. Photograph of Ernest Rutherford (right) and Hans Geiger (left) working together at the University of Manchester in 1908. Courtesy of the University of Manchester.

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An Introduction to the Physics of Nuclear Medicine

Figure 2.2. Illustration of the Rutherford scattering experiment.

foil. Since most travelled straight through the foil, Rutherford correctly deduced that the atom is mostly empty space. He proposed that the particles that backscattered from the gold foil must have struck a small but concentrated positively charged part of the atom, which he named the nucleus. Scientific progress in this field was put on hold during World War I (1914–1918). However, some scientists would continue to make important contributions, including Marie Curie who developed compact x-ray systems called petite Curies. These systems could be taken onto battlefields to diagnose the injuries of soldiers. Shortly after the end of the war, Rutherford discovered the proton, but it was not until 1932 that the other component of the nucleus, the neutron, was discovered by James Chadwick at the Cavendish Laboratory. Three years later Chadwick was awarded the Nobel Prize in physics for this discovery, whilst working at the University of Liverpool. The pioneering work of these scientists in nuclear physics paved the way for the production and use of synthetic radionuclides for medical purposes.

2.2 Production of radionuclides for medicine Frédéric Joliot and Iréne Joliot-Curie (daughter of Marie and Pierre Curie) were the first scientists to synthesise a radioactive material. They achieved this in 1934 by irradiating an aluminium target with α-particles to create radioactive phosphorous, 30 P, which can be described by: 27

Al + α →

30

P + n.

(2.1)

After this success, more radioactive materials were made through nuclear reactions, including the production of 32P, by irradiating a sulphur target with neutrons. This radionuclide can be administered to patients since (stable) phosphorus is naturally abundant in biology. John Lawrence realised the potential clinical benefit of 32P and used it to treat a patient with leukaemia. This was a major milestone in the history of nuclear medicine, since it was the first reported use of a synthetic radionuclide for the 2-3

An Introduction to the Physics of Nuclear Medicine

treatment of a patient. In parallel, John’s brother, Ernest Lawrence, was investigating new methods to produce radionuclides by bombarding stable materials with high-energy particles. In 1934 whilst working at the University of California, Berkeley, he patented an invention called a cyclotron. This is a type of particle accelerator still used widely in medical radionuclide production today. The original design by Lawrence can be seen in the patent illustration of figure 2.3. The aim of a cyclotron is to increase the speed, and therefore energy, of particles so that they can induce nuclear reactions. The principles of their operation will be discussed in chapter 4. In 1937, the first cyclotron-produced radionuclide was used for medicine (59Fe for studies of haemoglobin in the blood). This work was undertaken by John Livingood, Fred Fairbrother and Glenn Seaborg, the latter of whom discovered many of the radionuclides that are used in modern nuclear medicine. Two years later, Ernest Lawrence won the Nobel Prize in physics for his development of the cyclotron to produce artificial radionuclides. Today, cyclotrons and nuclear reactors are the main production source of radionuclides for medicine. Nuclear reactors are underpinned by the process of nuclear fission, in which a uranium nucleus bombarded by a neutron is split into smaller fragments. This phenomenon was discovered in 1938 by Lise Meitner, Otto Hann and Fritz Strassmann. Just one year later, it was found that this process also released neutrons that could then be used to sustain a nuclear chain reaction. This discovery came the same year that World War II commenced, which gave birth to the Manhattan project, the aim of which was to produce nuclear weapons. There was therefore considerable development in nuclear fission reactor technologies throughout the remainder of World War II. The world’s first operational nuclear reactor, the graphite reactor, was developed at Oak Ridge National Laboratory (ORNL). Following World War II, the reactor was used for peaceful purposes. Radionuclides were first produced for medical use by ORNL in 1946. The radionuclide was 14C, and was used by Barnard Free Skin and Cancer Hospital in St.

Figure 2.3. Illustration of the cyclotron, as designed by Ernest Lawrence. Extracted from US patent 1948384.

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Louis, USA. A photograph of the ORNL director, Eugene Wigner, delivering the first shipment of 14C to the hospital is shown in figure 2.4. In the late 1930s and 1940s several papers were published on the medical use of 14C, 131I, 89Sr, 125I, 32P, and 24Na. These radionuclides remain in use today. The most commonly used radionuclide in modern nuclear medicine is 99mTc,1 which is a decay product of 99Mo. Emilio Segrè and Glenn Seaborg discovered 99mTc at Berkeley in 1938. However, it was not until 1958 that a piece of equipment called a radionuclide generator was developed at Brookhaven National Laboratory to allow easy chemical separation of 99mTc from the 99Mo. Scientists at this time recognised the suitability of using 99mTc for diagnosis in nuclear medicine and that 99 Mo can be readily sourced from a nuclear fission reactor. New diagnostic imaging cameras being developed in parallel, were therefore optimised for use with 99mTc.

2.3 Diagnostic imaging In 1948, Joseph Rotblat and George Ansell administered radioactive iodine to patients and then used a collimated Geiger counter to produce images of the uptake of the iodine in the thyroid gland. This work was undertaken in Liverpool for patients who had enlarged thyroids and is reported to be the first diagnostic image in clinical nuclear medicine. At this time, the Geiger counter was the only commercially available γ-ray detector. Just a few years later, this diagnostic imaging technique was revolutionised by Hal Anger, who at Berkeley developed the Gamma camera, which is also known as the Anger camera. The first generation of the Anger camera was revealed in 1952. The configuration was a pinhole collimator placed in front of a scintillator (sodium-iodide, NaI) crystal, which had a photographic film directly beneath. A collimator is necessary in this configuration to determine the angle of incidence of a γ-ray, so that the radiation distribution can be

Figure 2.4. Photograph by Ed Westcott: Eugene Wigner delivering the first shipment of 14C from ORNL to the director of the Barnard Free Skin and Cancer Hospital, St. Louis. Courtesy of DOE Photography. The ‘m’ denotes a metastable nuclear state, where the nucleus temporarily possesses a higher energy than its most stable configuration. When it loses this excess energy, a gamma-ray is emitted, which can be detected for diagnostic purposes. 1

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visualised. When γ-rays emitted from the radionuclide passed through the collimator and interacted in the scintillation detector, flashes of light were produced that exposed the photographic film. The design of the camera evolved during the 1950s as the photographic film was replaced by seven photomultiplier tubes (PMTs) that could convert the flashes of scintillation light to an electrical signal. Anger logic was used to calculate the position of each γ-ray interaction within the scintillation crystal. In 1958, Anger published a paper on this design in which he highlighted the use of the camera for visualising the thyroid gland with 131I. A photograph of Hal Anger with one of his cameras is shown in figure 2.5. The camera can be seen pointing towards the thyroid, which is in the neck. Example thyroid iodine uptake images produced by Anger are shown in figure 2.6. The butterfly shape characteristic of the thyroid is clearly visible. The technology showed excellent promise, since the pinhole collimator allowed the uptake of the radionuclide to be visualised. However, the counting times were over an hour long and it therefore took until 1962 for the first commercial system to be marketed. As the technology evolved, through the deployment of more sensitive collimator geometries, the counting time for patient studies became more practical. Throughout the 1960s, several pioneers rotated the gamma camera (or patient) to produce three-dimensional images using a technique called tomography that will be described in chapter 7. In 1978, these systems became commercially available for single photon emission computed tomography, SPECT, and are now prevalent in nuclear medicine. One of the fundamental limitations of a gamma camera is that a collimator is required to determine the angle of incidence of a γ-ray, so that the radiation distribution can be visualised. Other methods of producing an image of the radionuclide uptake were therefore investigated. Frank Wrenn, Myron Good and Philip Handler working at Duke University were the first known proposers of the detection of e+e− annihilation radiation from positron emitting radionuclides in medicine. This negates the use of a collimator system and therefore improves the counting time and image quality. The team used NaI scintillation counters read out

Figure 2.5. Photograph of Hal Anger with an Anger camera, taken in 1959. © 2010 The Regents of the University of California, through the Lawrence Berkeley National Laboratory.

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Figure 2.6. Anger camera images of the thyroid, acquired 1961. © 2010 The Regents of the University of California, through the Lawrence Berkeley National Laboratory.

by PMTs to detect pairs of 511 keV photons produced due to e+e− annihilation. Pairs of photons could be correlated by their time, since the two photons in a pair are produced at the time of annihilation. The radionuclide source was 64Cu, which is a positron emitter that was readily available from ORNL at the time. The source was placed both within air and a brain. There were no images presented in the 1951 publication reporting on this work but the data were presented as count profiles at different detector positions. This laid the foundations for the development of the first positron emission tomography, PET, system two years later by Gordon Brownell and William Sweet at Massachusetts General Hospital. They produced a threedimensional image of a tumour administered with 74As by operating two NaI scintillation crystals to detect pairs of annihilation photons and scanning the crystals across different positions mechanically. There was growing excitement about this technique for use in brain imaging, however the use of only two scintillation detectors minimised the sensitivity. In 1962, Seymour Rankowitz and his team at Brookhaven National Laboratory proposed that the sensitivity could be vastly improved by using a single plane ring of 32 scintillation detectors packed together. These would capture many more annihilation photons and therefore decrease the counting time for imaging brain tumours. Over the next few years there were advancements in imaging outside nuclear medicine, in particular the development of computerised x-ray computed tomography (CT) scans and techniques to reconstruct tomographic data. These techniques would directly impact on PET performance.

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Michel Ter-Pogossian, Michael Phelps and Edward Hoffman are credited with developing the first automated PET scanners in the early 1970s. Their PET-II system used a hexagonal array of 24 NaI detectors on a computer-controlled mount to produce Fourier-based tomographic images. This system was used for patient studies at Washington University as PET-III, which had twice as many NaI detectors in a hexagonal array and now also included eight along the side, to allow data to be acquired in linear and rotational directions. Since then, the performance of PET systems have been drastically improved by the use of more sensitive scintillation detectors such as bismuth germanium oxide (BGO), which became the standard PET detector material. In 1991, David Townsend and Ronald Nutt proposed the combination of PET and x-ray CT technologies into a single integrated system. This was a major milestone in nuclear medicine as it would seed the development of systems that provide images depicting both the physiological function from PET and anatomical detail from CT. An added benefit is that x-ray CT images are also used to calculate attenuation corrections for the 511 keV photons traversing the tissue. A fully integrated system offers improved accuracy in fusion of the PET and CT images, in comparison to if the patient has to be moved between systems. The first prototype PET/CT scanner was used to image cancer patients from 1998 and shortly after, the three major commercial providers of nuclear medical imaging systems, GE Healthcare, Siemens Medical Solutions and Philips Healthcare placed the Discovery LS, Biograph and Gemini PET/CT systems, respectively, on the market. The technology was so revolutionary that by 2006 it was no longer possible to purchase standalone PET systems. Another major development in PET was that of time of flight (TOF) PET, in which the difference in the time of arrival of the annihilation photons in the detectors is calculated to help improve the quality of the image. This technique will be discussed in detail later. Although the pioneers in 1970s PET technology were well aware of the potential benefits of TOF-PET, no scintillation detector had yet been developed with the required performance characteristics, which are fast timing (of the scintillation material and PMT) and high sensitivity. Some early systems were developed based on caesium fluoride (CsF), but they did not compete with the conventional BGO-based detector systems. It was not until 2006 that the first modern commercial TOF-PET scanner was introduced, by Philips Medical Systems. The GEMINI TF used the latest in fast-scintillation detector technology, lutetium oxyorthosilicate with yttrium impurity, LYSO. These detectors offer very fast timing and high light output, which are ideal characteristics of TOF-PET scintillation detectors.

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An Introduction to the Physics of Nuclear Medicine Laura Harkness-Brennan

Chapter 3 Radioactivity

Radioactivity is the emission of particles or photons when an unstable nucleus decays. A nucleus will always tend towards its lowest possible energy. Therefore, a nucleus that has excess energy from an unstable balance of neutrons and protons or nuclear excitation can spontaneously emit radiation to achieve a more energetically favourable nuclear configuration. The particles and photons emitted from radionuclides administered to patients in nuclear medicine are used in the diagnosis and treatment of diseases. This chapter will introduce the principles of radioactivity, including nuclear stability, radioactive decay processes and the decay law.

3.1 Nuclear stability The majority of nuclides found naturally on Earth today are stable but many more have been experimentally synthesised using accelerator and reactor facilities. Of the >3300 nuclides studied, approximately 250 are stable, 90 are naturally occurring radionuclides and the others are artificially generated radionuclides. Figure 3.1 shows the stable nuclides plotted according to their proton (Z) and neutron (N) number. This distribution is known as the line of stability. It can be seen from the plot that the low-Z stable nuclides are distributed around N = Z (illustrated as a blue line on the graph). This is because the nuclear force acts between neutrons and protons equally. However, as more protons and neutrons are added, the line of stability will bend away from N = Z. This happens because the Coulomb force acts to repel the positively charged protons from each other, whilst the neutral neutrons do not experience this force. Additional neutrons up to N = 1.5 × Z are required to balance the forces in the nucleus, to achieve stability. Radionuclides lie in the regions outside the line of stability and are said to be neutron rich or proton rich if they lie beneath or above it, respectively. The term rich is used here to indicate an excess of those particular nucleons in the unstable nucleus. A change in the ratio of proton and neutron number for an unstable nucleus can improve its stability. The radioactive nucleus undergoing disintegration is referred to as the parent and the

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140 120

Proton Number, Z

N=Z 100 80 60 Stable nuclides 40 20 0 0

20

40

60

80

100

120

140

Neutron Number, N

Figure 3.1. Plot of stable nuclides according to neutron number, N, and proton number, Z. The N = Z line is also shown.

by-product as the daughter, which may also be radioactive. The nuclei can undergo a single or multiple step decay, the latter of which is known as a decay chain.

3.2 Radioactive decay processes When a nucleus spontaneously decays, radiation can be emitted in the form of charged particles or photons. The three primary decay modes are named according to the emitted particle or photon. These are alpha (α), beta (β) and gamma (γ) decay. There are also three types of β decay, which are β−, β+ and electron capture (EC). Radionuclides that emit γ-rays and β+ particles are commonly used for medical diagnosis in SPECT and PET imaging, respectively, whilst α and β− emitters are used in the treatment of diseases by radionuclide therapy (RNT). 3.2.1 Alpha decay Alpha (α) decay is the spontaneous emission of an α particle from an unstable nucleus. The α particle is a 42 He nucleus, which consists of two protons and two neutrons and is a stable, tightly bound system. The decay occurs due to instability in the nucleus arising from Coulomb repulsion of the protons, a force that increases as Z2. The decay process is therefore more probable for heavy (high-Z) unstable nuclei and is an efficient method of reducing their mass. When a nucleus decays by α emission, the daughter nucleus, Y, will be a different element to the parent, X, and will therefore have different chemical properties: A ZX

→

A−4 Z−2Y

+ α.

(3.1)

The α decay process is illustrated in figure 3.2. Energy is released in the decay (the Q-value), which can be calculated as the difference in mass energy between the parent nucleus and final products, which is typically several MeV. The α particle 3-2

An Introduction to the Physics of Nuclear Medicine

Figure 3.2. Illustration of alpha decay.

takes most of this as kinetic energy and the remainder is the recoil energy of the daughter nucleus, AZ −− 42 Y . Radionuclides that decay by α emission are used in radionuclide therapy. The α particles deposit the radiation dose locally to a tumour site (within 0.1 mm), sparing the surrounding healthy tissue. One such example is 223 Ra , which decays to 219 Rn : 223 88 Ra

→ 219 86 Rn + α .

(3.2)

Radium has similar chemical properties to calcium and so will be readily uptaken in bones. This is one of the reasons why 223 Ra is used in nuclear medicine for the treatment of metastatic bone cancer. 3.2.2 Beta decay As mentioned previously, there are three types of beta decay, β−, β+ and EC. These processes are characterised by the conversion of a neutron in the nucleus to a proton (β−), a proton in the nucleus to a neutron (β+), or the capture of an inner atomic electron by the nucleus (EC). As with α emission, the process results in a daughter nucleus, Y, that is a different chemical element to the parent, X. The three beta decay modes are depicted in figure 3.3. Radionuclides that decay towards stability by the emission of β− particles are neutron rich and therefore lie in the region beneath the line of stability shown in figure 3.1. When these nuclei β decay, they move diagonally towards the line of stability, conserving A. In β− decay, an electron and antineutrino, ν¯ , are emitted from the nucleus to conserve charge, energy and momentum. The β− particle is now known to be the electron, which is produced by this particular decay mode. This process is illustrated in figure 3.3 and can be described by: A ZX

→

A Z + 1Y

+ β− + ν.

(3.3)

Following the same laws of conservation, a positron (β+) and neutrino (ν) are emitted in β+ decay. The β+ decay process occurs for proton rich nuclei and is given by: A ZX

→

A Z − 1Y

+ β + + ν.

(3.4)

The energy released in β−(β+) decay is shared between the daughter nucleus, the e−(e+) and the ν (ν ). For any given radionuclide sample, the kinetic energy of the 3-3

An Introduction to the Physics of Nuclear Medicine

Figure 3.3. Illustrations of (a) β− decay, (b) β+ decay and (c) electron capture.

emitted β particles is within a continuous range up to the endpoint energy, Emax, as illustrated in figure 3.4. The endpoint energy is achieved when no kinetic energy is given to the (anti)neutrino and can therefore be calculated from the mass difference of the parent and daughter nuclei. However, this particular distribution of energies between the particles is not very likely to occur. The average kinetic energy of the β particle is weighted towards lower energies, which is approximately 0.33 × Emax. The β particle energy spectrum determines the distance travelled by the particles in human tissue. When β-emitting radionuclides are used in nuclear medicine, it is always desirable for the distance travelled to be short. For example, the short distance travelled by β− particles concentrates the delivery of the radiation dose over a small volume of tissue, which makes them a good choice for use in radionuclide therapy.

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Number of Beta particles emitted

An Introduction to the Physics of Nuclear Medicine

0

Eavg

Emax

Beta particle kinetic energy Figure 3.4. Illustrative example of the number of β particles emitted as a function of energy.

Nuclei can decay via more than one process. One example of this is the decay of F, which is one of the most commonly used radionuclides in PET. 18F decays to 18 O by the emission of a positron 97% of the time:

18

18 9F

→ 188O + β + + ν .

(3.5)

In the remaining 3% of the time, 18F will decay by EC. This is the process by which an unstable parent nucleus ZAX captures an electron from an inner orbital shell of the parent atom. The electron will combine with a proton to produce a neutron, as described by: A ZX

+ e−→Z −A1Y + ν .

(3.6)

The vacancy left in the inner orbital shell will subsequently be populated by an electron from a higher-energy shell. This results in the emission of either characteristic x-rays or an Auger electron, which is an electron ejected from an outer orbital shell. 3.2.3 Gamma decay Gamma rays are emitted when an unstable nucleus, ZAY *, decays from an excited nuclear state to a lower state, typically following an α or β decay. The γ decay is usually much faster than the preceding α or β decay, although it can sometimes be longer lived and is then known as a metastable state. This is denoted as such by the * ‘m’ in Am Z Y . Gamma rays are electromagnetic radiation and thus have no charge or mass. There is, therefore, no change in the atomic number or mass of a nucleus when undergoing γ decay, so it remains the same chemical element and does not move the nucleus towards the line of stability: A * ZY

→ ZAY + γ .

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(3.7)

An Introduction to the Physics of Nuclear Medicine

The energy, Eγ, of the γ-ray emitted from the nucleus, is equal to the energy difference between the initial, Ei, and final, Ef, nuclear states:

E γ = E i − Ef .

(3.8)

Nuclear energy states are attributed to a nuclear species and the energy difference will therefore be a characteristic signature of the specific decaying nucleus. These can be thought of as its nuclear fingerprint. Since there are typically several nuclear energy states, it is possible for the unstable nucleus to decay through different combinations of states and therefore multiple γ-ray energies can be observed. The emission probability, Pγ, is the likelihood a particular γ-ray is emitted per decay of a radionuclide sample. A Pγ of 50% would represent the scenario that the corresponding γ-ray would on average be emitted in 50% of the decays. Gamma-ray spectroscopy is dedicated to the measurement of these energies from unstable nuclear species. This technique is used in nuclear medicine to select or reject events to be used in the production of diagnostic images. Most radionuclides selected for diagnosis in nuclear medicine emit γ-rays with energy less than 511 keV because these γ-rays can travel from inside to outside the body without significant absorption and still be readily stopped by radiation detectors surrounding the body. An example is the medical radionuclide 123I, which has a dominant γ-ray at 159 keV (Pγ = 83.3%) and a number of other higher energy but less probable emissions.

3.3 Radioactive decay law Radioactive decay of a single nucleus is a random process, so it is not possible to predict the precise time it would decay. Radioactivity is therefore described statistically by observing the decays of a large number of nuclei in a sample and using mathematical relationships to calculate the probability of decay. The average decay rate can be estimated for a sample of N radioactive nuclei using:

dN = −λN, dt

(3.9)

where λ is the decay constant, which represents the probability per second that a given radioactive nucleus will decay. It is possible that a nucleus can decay by i different processes and the weighting of each is given by the branching ratio, λi/λ. The decay constant of each of the possible decay processes contributes to λ as:

λ = λ1 + λ2 + ⋯ + λi .

(3.10)

The negative term in equation (3.9) indicates a loss of radioactive nuclei from the radionuclide sample over time. Integration of this equation shows that the number of radioactive nuclei, N, decreases exponentially as a function of time, t:

Nt = N0e−λt ,

(3.11)

where N0 represents the initial number of radioactive nuclei. The fraction of radioactive nuclei that remain in the sample at any given time is termed the decay factor (DF). This can be calculated using the relationship: 3-6

An Introduction to the Physics of Nuclear Medicine

DF =

Nt = e − λt . N0

(3.12)

Figure 3.5 shows a graph of the decay factor as a function of time. The exponential decay of the sample can clearly be seen. The time taken for half of the radioactive nuclei to decay is highlighted by the red dashed lines on the graph. This time is known as the half-life, T1/2, of the radionuclide. Just like the energy of emitted γ-rays, the half-life is a characteristic property of the radionuclide and another component of its nuclear fingerprint. It is an important property in nuclear medicine, since it will impact the retention duration of an administered radionuclide in a patient and how long the corresponding imaging or therapeutic procedures will last. By substituting Nt = N0/2 into equation (3.11), it can be seen that T1/2 is inversely proportional to λ:

T1/2 =

ln 2 . λ

(3.13)

The half-life (and therefore decay constant) can be determined by experimentally observing the decay rate of a sample as a function of time. The average decay rate dN ∣ dt ∣ of a sample is known as its activity, At. Two units of activity are widely adopted in nuclear medicine: 1. Becquerel (Bq): average decay rate per second. 2. Curie (Ci): 3.7 × 1010 disintegrations per second, which corresponds to the approximate activity of 1 g of 226Ra. As discussed in chapter 2, these units are named in honour of Antoine Henri Becquerel, Marie Curie and Pierre Curie, for their pioneering work in the discovery

1

Decay Factor

0.8

0.6

0.4

0.2

0 0

T 1/2

2T 1/2

3T 1/2

4T 1/2

5T 1/2

6T 1/2

Time (half-lives)

Figure 3.5. Decay factor as a function of time (half-lives).

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7T 1/2

8T 1/2

An Introduction to the Physics of Nuclear Medicine

and study of radioactivity. The number of radioactive nuclei, Nt, that must be present in a sample to produce a given activity is determined by its characteristic λ:

At = Ntλ .

(3.14)

Example 1. Calculate the number of radioactive nuclei present in a 37 MBq activity sample, at time t, for the following radionuclides: (a) 99m Tc , which has T1/2 = 6.00 hours (b) 131I, which has T1/2 = 8.02 days ln 2 At and T1/2 = . λ λ AT Convert T1/2 to seconds and input to: Nt = t 1/2 ln 2 3.7 × 107 × 21 600 (a) Nt = = 1.15 × 1012 ln 2 3.7 × 107 × 692 928 (b) Nt = = 3.7 × 1013 ln 2

Solution 1. Use Nt =

For samples with the same activity there are approximately 32 times more radioactive nuclei present in 131I than in 99mTc. The specific activity of a radionuclide sample, which is the activity (Bq) per unit mass (g), can be calculated using:

A=

λNA , m

(3.15)

where NA is Avogadro’s constant (6.022 × 1023 mol−1) and m is the mass number. This relationship can be derived because the mass of the radionuclide sample is represented by:

Nt [mol] × m [g mol]−1. NA

(3.16)

It is advantageous to ensure the mass of radiopharmaceuticals administered to patients is as low as possible, which corresponds to samples with a high specific activity. If a sample is 100% composed of the radionuclide of interest, it is known as a carrier free sample. This is a desirable property of radionuclides that are to be administered to patients. The methods used to produce such samples will be described in the next chapter. In nuclear medicine, radionuclides with a T1/2 between minutes and a few days are selected so that they can be readily transported from their production site, administered to the patient with sufficient activity for the procedure but decay relatively quickly after the procedure. The sample will be delivered with a known activity as measured at a specific time, typically in a bulk solution. The samples may be used hours or days after delivery and small volumes for administration may need

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An Introduction to the Physics of Nuclear Medicine

to be extracted from a larger volume. An important role for physicists in nuclear medicine departments is therefore the calculation of sample activities at various points in time. Substitution of A = λN into equation (3.11) allows the activity of a ln 2 ) is known: sample to be calculated, if the decay constant (or half-life since T1/2 = λ

At = A0 e−λt .

(3.17)

Example 2. At 9 am a 99mTc sample of 37 MBq and T1/2 of 6 hours is prepared for a diagnostic SPECT scan. What will be the activity of the sample when it is administered to the patient at 11 am? Solution 2. Use equations (3.13) and (3.17) to calculate the activity of the sample after 2 hours:

At = A0 e

− ln 2 × t T1/2 ln 2 × 2

At = 37 × e− 6 At = 29.4 MBq

It is common for a sample to contain a mixture of radionuclides that are not in the same decay chain. The total activity, ATotal (t), at time t, of such a mixed sample is the sum of the individual activities, Ai (t), of each radionuclide:

ATotal(t) = A1(0)e−λ1t + A2(0) e−λ2t + ⋯ + Ai (0) e−λi t .

(3.18)

Example activity–time curves for a mixed sample are illustrated in figure 3.6. In this particular example, there are two radionuclides. The red distribution corresponds to a radionuclide with 30 MBq initial activity and T1/2 = 2 days, whilst the blue represents a radionuclide of 7 MBq initial activity and T1/2 = 10 days. It can be seen that for the initial 5 days, the total activity is dominated by the first radionuclide, whilst the second dominates after this time. The time of extraction of a radionuclide of interest is therefore extremely important in nuclear medicine. Until now, the discussion of half-life has focussed on that of physical radioactive decays. However, when a sample is administered to a patient, the radionuclide will also be ejected from the body by biological processes, such as breathing and urination. The rate of removal of the radionuclide sample by biological processes is difficult to predict or determine because it can depend on the type of excretion and the age or weight of the patient. These biological excretion processes are therefore often approximated to follow an exponential decay. The effective half-life, T1/2eff, considers the excretion of the sample by physical and biological means. As with summing together the contributions of two different decay modes, the total will be

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An Introduction to the Physics of Nuclear Medicine

40 35

Activity (Bq)

30 25 20 15 10 5 0 0

1

2

3

4

5

6

7

8

9

10

Time (days) Figure 3.6. Activity as a function of time for a mixed sample containing a radionuclide (dashed red line) of 30 MBq initial activity and T1/2 = 2 days and a radionuclide from another decay chain (dotted blue line) of 7 MBq initial activity and T1/2 = 10 days. The total activity curve of the mixed sample is illustrated by the solid black line.

the summation of the decay constants. Since T1/2 = calculated using the reciprocals:

1 1 1 = + . T1/2eff T1/2 T1/2bio

ln 2 , the effective half-life can be λ

(3.19)

The effective half-life can be used to calculate the activity of a sample at various times after administration to a patient. In the next chapter, the methods employed to produce radionuclides of suitable half-life for use in nuclear medicine will be discussed, along with specific examples of radionuclides that are used.

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IOP Concise Physics

An Introduction to the Physics of Nuclear Medicine Laura Harkness-Brennan

Chapter 4 Radionuclide production

The physical half-life of naturally occurring radioactive material is too long to be useful in nuclear medicine. Radionuclides with suitable half-life must therefore be produced in nuclear reactions by irradiating target nuclei with particles within a nuclear reactor, or from a particle accelerator (cyclotron). This chapter will outline the properties of medical radionuclides and how they can be synthesised using cyclotrons, nuclear reactors and generators.

4.1 Radionuclide selection Radionuclides are commonly used in nuclear medicine for: • The diagnosis and monitoring of coronary artery disease, thyroid cancer, bone cancer and other diseases (SPECT). • The diagnosis and monitoring of lung cancer, Alzheimer’s disease and other diseases (PET). • The treatment of hyperthyroidism, non-Hodgkin’s lymphoma, liver cancer and other diseases (RNT). The radionuclides selected for these procedures can be administered to a patient either directly or after chemical binding to a biological compound, as a radiopharmaceutical. Upon administration, the radiopharmaceutical will be processed according to the biokinetics of the patient, which means that the radionuclide will be taken to the treatment or imaging site. An example would be tagging a glucose compound with a radionuclide to visualise a tumour. Since cancerous cells are highly metabolic, the compound would be preferentially uptaken to the tumour. When the imaging modalities SPECT and PET are used to diagnose disease using radioactive materials, it is important to ensure the radiation dose received by the patient is minimised. The ideal radioactive decay mode for SPECT is γ-ray emission with a high branching ratio and energy of 100–350 keV. This energy range is suitable because the γ-rays will have sufficient energy to escape the body for imaging but not too much that it is difficult to stop them in the imaging system. In PET, the decay doi:10.1088/978-1-6432-7034-0ch4

4-1

ª Morgan & Claypool Publishers 2018

An Introduction to the Physics of Nuclear Medicine

mode should be β+, after which the positron will annihilate with an electron in the tissue, resulting in the emission of energy as two 511 keV photons (as a reminder, E = mc2). Additional radioactive decay modes would contribute to the radiation dose without benefiting the diagnosis. In RNT, radionuclides are selected to deliver a high radiation dose to biologically targeted areas, such as tumours. These radionuclides should decay by charged particle emission, either α or β. Aside from these important differences, radionuclides in SPECT, PET and RNT should ideally be simple and relatively cheap to produce, non-toxic and have a high specific activity. The physical half-life, T1/2, also needs to be sufficiently long for the radionuclide to be transported from the production site to the clinic so it has the required activity for the procedure but short enough that it decays away quickly after completion and to allow for easy disposal of the remaining sample. Table 4.1 shows some radionuclides that are used in nuclear medicine and example clinical uses. It can be seen that radionuclides are used to study and treat many physiological functions and associated diseases.

4.2 Cyclotrons Particle accelerators are used to produce radionuclides for medicine by directing charged particles onto stable target nuclei, to induce nuclear reactions. Acceleration of the particles is required so they have sufficient energy to overcome Coulomb repulsion, which would otherwise prevent the nuclear reaction from taking place. The most commonly used accelerator in medical radionuclide production is the cyclotron, the operation of which is illustrated in figure 4.1. At the centre of the cyclotron is an ion source that injects charged particles of mass, m, and charge, q, into one of two Dees. These are hollow semi-circular copper electrodes, which are named due to their similarity in shape to the letter D. The Dees are positioned between the North and South poles of an electromagnet. The magnetic field, B, produced by the electromagnet causes the injected charged particles to travel through the Dee with a velocity, v, along a circular path of radius, R, according to: mv . R= (4.1) qB Table 4.1. Example radionuclides used in nuclear medicine.

SPECT

Radionuclide

T1/2

Clinical use

99m

6.00 h 13.22 h 3.04 d 20.33 m 9.97 m 2.03 m 109.73 m 8.02 d

Bone imaging Thyroid imaging Cardiac imaging Prostate cancer Myocardial blood flow Cerebral blood flow Alzheimer’s disease Hyperthyroidism

Tc I 201 Tl 11 C 13 N 15 O 18 F 131 I 123

PET

RNT

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An Introduction to the Physics of Nuclear Medicine

Figure 4.1. Schematic diagram of a cyclotron, illustrating the irradiation of an external target by a beam of accelerated protons.

The Dees are operated under vacuum at a pressure of approximately 10−3 Pa, to avoid charged particles being deflected from their orbital path. A high frequency alternating voltage is applied across the gap between the Dees. When the charged particles enter this gap, they will be given a kick across it due to the potential difference between the Dees. The acceleration increases the kinetic energy, KE, of the charged particles, which also increases the orbital radius. This can be calculated using the relationship:

KE =

mv 2 (qBR )2 . = 2 2m

(4.2)

Since the orbital distance travelled by the particle within each Dee will increase as velocity increases (equation (4.1)), the orbital frequency remains the same. The particle therefore arrives back at the gap exactly in phase with the alternating voltage. This process is repeated as the particle spirals through the cyclotron, until a maximum kinetic energy is reached. The magnetic field strength and diameter of the cyclotron are the limiting factors in the final energy of the accelerated particles. These properties determine the production rate or yield, to be discussed later. Example 1. The University of Birmingham MC40 cyclotron pictured in figure 4.2 is used to produce positron-emitting radionuclides for positron emission tomography. The cyclotron has a Dee radius of 53 cm and a magnetic field strength of 1.8 T. Calculate the maximum kinetic energy of a proton exiting the cyclotron given that the mass of a proton is 1.672 × 10−27 kg and its charge is 1.6 × 10−19 C. Solution 1. Use KE =

(qBR )2 : 2m

(1.6−19 × 1.8 × 0.53)2 2 × 1.67 × 10−27 KE = 6.97 × 10−12J KE = 43.5 MeV KE =

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An Introduction to the Physics of Nuclear Medicine

Figure 4.2. Photograph of a magnet pole from the University of Birmingham MC40 Cyclotron. Courtesy, University of Birmingham.

Charged particles that have been accelerated to sufficient kinetic energy can be used to irradiate a target material and induce nuclear reactions. The target can be placed directly in the path of the charged particles or the beam can be deflected by a charged plate onto a target outside the cyclotron. The radionuclides produced in the target are usually proton-rich and will therefore decay to stability by β+ emission or electron capture. The properties of some radionuclides produced for nuclear medicine by cyclotrons are shown in table 4.2. The nuclear reactions that take place in these examples are all induced by accelerated protons and lead to the production of a radioactive nucleus, accompanied by either α particles or neutrons. It is the particles or photons emitted in the decay of these radioactive nuclei that are of use in nuclear medicine, rather than the particles output from the production reaction. These illustrative reactions produce radioactive nuclei that are a different chemical element to the stable target nuclei, such that the produced sample is carrierfree and can be readily separated from the target. PET using 11C, 13N and 15O can only be undertaken at hospitals that have an on-site cyclotron because the half-life of these radionuclides is so short. 18F has a longer half-life of 110 min, which permits transport from cyclotrons that serve hospitals within geographical regions of several 100 miles. 18F is therefore a more widely used radionuclide in PET. The SPECT radionuclides 67Ga and 123I have a longer half-life, of hours, and the γ-rays emitted following electron capture to excited nuclear states can be used for imaging.

4.3 Nuclear reactors Radionuclides for medicine can be produced in a nuclear reactor directly by fission or by using the intense neutron flux within the reactor to irradiate target materials. Since World War II, nuclear reactors have been widely commissioned for power generation and the production of medical radionuclides has been a secondary, albeit important, benefit. A nuclear fission reactor generates power by harnessing the 4-4

An Introduction to the Physics of Nuclear Medicine

Table 4.2. Properties of example medical radionuclides produced by cyclotrons.

Radionuclide 11

C N 15 O 18 F 67 Ga 123 I 13

T1/2 20.33 m 9.97 m 2.03 m 109.73 m 3.26 d 13.22 h

Relevant decay mode +

β , EC β+ β+ β+, EC EC, γ EC, γ

Reaction

Clinical use

N(p, α) C C(p, n)13N 15 N(p, n)15O 18 O(p, n)18F 68 Zn(p, 2n)67Ga 124 Te(p, 2n)123I 14

13

11

PET PET PET PET SPECT SPECT

Figure 4.3. Illustration of fission induced by neutron irradiation of a target 235U nucleus. The two fission products in this example are 144Xe and 90Sr, along with two neutrons that can induce further fissions.

energy released when a neutron induces the fission of a heavy nucleus. In this process, the heavy nucleus splits into lighter fragments and neutrons. The fissionable material is in the form of a fuel rod and is most commonly composed of natural uranium that has been enriched with 235U. Natural uranium consists of approximately 99.3% 238U and 0.7% 235U, which is not an ideal composition since the probability of fission occurring for 238U is lower than for 235U. The level of enrichment varies according to the type of reactor but 4% 235U and 96% 238U is a typical grade of low-enriched uranium. When a neutron irradiates one of the 235U target nuclei in the fuel, a highly unstable 236U* nucleus is formed: 235

U+n→

236

U*.

(4.3)

The 236U* nucleus will subsequently fission into lighter nuclei and neutrons, as illustrated by the example in figure 4.3. Many radionuclides of different chemical elements can be produced in fission, some of which can be extracted for use in nuclear medicine, for example 99Mo, 131I and 133Xe, whilst others will be treated as nuclear waste at the facility. The fission fragment yield as a function of fragment mass

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An Introduction to the Physics of Nuclear Medicine

10 2

10 0

Fission Yield (%)

99 10

-2

10

-4

10

-6

10

-8

60

80

Mo

100

120

140

160

180

Fission Fragment Mass Number

Figure 4.4. The fission fragment yield as a function of fragment mass number, for fission induced by neutron irradiation of 235U. Data from the JAEA Nuclear Data Centre.

Figure 4.5. Schematic illustration of a fission reactor core.

number, for fission induced by neutron irradiation of 235U is plotted in figure 4.4. It can be seen that most of the time a fission fragment will be produced with a mass number of 90–105, accompanied by a heavier fragment of mass number 130–145. The uranium fuel rods are surrounded by a moderator in the core of the reactor, as illustrated in figure 4.5. Neutrons emitted in fission processes begin a chainreaction of nuclear fissions. The moderator acts to slow down the neutrons until they 4-6

An Introduction to the Physics of Nuclear Medicine

have the ideal energy to keep the chain reaction going. The moderating material is typically graphite or water. Neutron-absorbing control rods can be moved into the regions between the fuel rods to reduce, and therefore control, the rate of nuclear reactions. These control rods are commonly made of boron or cadmium because they readily absorb neutrons. Although radionuclides for nuclear medicine can be synthesised directly in a reactor as the products of nuclear fission, the yield is relatively low as many other radionuclides are generated in the reactor and it is difficult and expensive to chemically extract them from the other waste products. Another production method is to place a stable target material in the reactor so that it is irradiated with neutrons produced from the fission events. In the process of neutron activation, the target nucleus captures a neutron, producing a product nucleus along with either a γ-ray or a proton. The most common type of neutron activation leads to emission of a γ-ray, in which the target and product nuclei are different isotopes of the same chemical element. When a proton is emitted instead, the target and product nuclei are not the same chemical element, which makes it easier to extract the radioactive nuclei from the sample for administration to a patient. Note, the γ-ray and proton produced in the activation are of no further use in nuclear medicine, it is the radionuclide produced that is of interest. A variety of medical radionuclides can be produced by neutron activation in a reactor including 51Cr, which is used to label red blood cells: 50

Cr + n →

51

Cr + γ .

(4.4)

The most important radionuclide produced in a reactor is 99Mo, which can be produced directly as a fission product, with a yield of 6.1% or as a daughter in a β− decay chain from the fission product 99Y: β − 99 β − 99 β − 99 99 Y → Zr → Nb → 39 40 41 42Mo.

(4.5)

Reactor-produced 99Mo is the parent of 99mTc, which is used in more than 80% of all diagnostic studies in nuclear medicine. Samples of 99mTc can be chemically separated from 99Mo locally in a hospital, a process that has made 99mTc so widely used in nuclear medicine. This technique will be discussed in the next section. There are several large-scale producers of 99Mo. In 2009, a global shortage of this radionuclide was caused by the closure of two fission reactors for repair, the high flux reactor in the Netherlands and the National Research universal reactor in Chalk River, Canada. At that time, these two reactors would have otherwise accounted for 70% of the worldwide supply of 99Mo. The global shortage caused many researchers to join the effort in investigating alternative methods to produce 99mTc. Three methods under development include: building new small-scale reactors; using electron accelerators to induce 238U fission and irradiating 100Mo targets with accelerated electrons, to produce 99Mo and a neutron. As of 2018, these novel techniques are still in their infancy and for the foreseeable future 99Mo will be produced using a few large-scale reactors.

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4.4 Radionuclide generators A radionuclide generator, which is known as a cow, allows a short-lived daughter radionuclide to be separated and extracted from a longer lived parent radionuclide that would have been produced using an accelerator or nuclear reactor. The radionuclides can be extracted for procedures on-site at a hospital. Since there is no transport required from the production site to the hospital, it is a very effective and efficient method of producing radionuclides of very short half-life (hours or less) that would otherwise have undergone significant radioactive decay before administration to the patient. The first radionuclide generator was developed at Brookhaven National Laboratory, which produced 99mTc from 99Mo. Although other radionuclides can be produced by generators, the most widely used today is still the 99Mo/99mTc generator. Within the generator, the parent 99Mo decays to 99m Tc by β− emission. The 99mTc produced in the generator is in a metastable state and will decay by γ-ray emission with a T1/2 of 6 h to 99Tc. These γ-rays are used in the generation of diagnostic SPECT images. This decay chain is described by: 42

γ

−

99m β Mo T c⃗ 43

99

43

99

Tc.

(4.6)

A schematic illustration of a typical 99Mo/99mTc generator is shown in figure 4.6. At the core of the generator is a glass column, which is filled with alumina (Al2O3). The parent 99Mo, which typically has an initial activity of 75 GBq, is bound to the alumina at the top of the column and decays to the daughter, 99mTc. A porous glass disk is fitted to the bottom of the column, to retain the alumina. A saline (milking) solution is passed through the column and chemically reacts with any 99mTc that has been produced. The eluted 99mTc can then be extracted from the generator for administration to patients. The core components of the generator are encased in a lead shield, to reduce the radiation exposure to those operating it.

Figure 4.6. Schematic illustration of a

4-8

99

Mo/99mTc generator.

An Introduction to the Physics of Nuclear Medicine

The fundamental physical principle of the radionuclide generator is that immediately after 99mTc is extracted, the 99mTc radioactivity starts to build up again until it becomes in equilibrium with production from the parent 99Mo. The activity, Ad, of the daughter radionuclide 99mTc, with decay constant λd, can be calculated using the Bateman equation:

Ad =

λd × Ap(0) × (e−λ pt − e−λ dt ), λd − λp

(4.7)

where Ap and λp are the activity and decay constant of the parent radionuclide 99Mo. In a 99Mo/99mTc generator, the T1/2 of the parent nucleus is 67 h, which is (not significantly) greater than that of the daughter, 6 h. In this case, a special type of equilibrium is established, called transient equilibrium. This means that as the parent decays, the daughter activity will increase to a maximum and then effectively decay according to the decay constant λp. As a result, equation (4.7) can be simplified for transient equilibrium as the term e−λdt becomes negligible:

Ad =

λd × Ap(0) × (e−λ pt ). λd − λp

(4.8)

Since Ap(t) = Ap(0) × (e−λ pt), equation (4.8) can be further simplified to:

Ad =

λd × Ap(t) . λd − λp

(4.9)

Figure 4.7 illustrates the decay of 99Mo and 99mTc as a function of time, where t = 0 is the time at which the activity of the generator has been calibrated to be Ap(0) = 74 GBq. The timescale shown of 120 hours is representative of the typical 80 70

Activity (GBq)

60 50 40 30 20 10 0 0

20

40

60

80

100

120

Time Since Calibration (hours)

Figure 4.7. Activity as a function of time for a 99Mo/99mTc radionuclide generator. The solid black curve shows the decay of 99Mo, the dashed curves show the build up and decay of 99mTc, if no extraction takes place (red) and following extraction every 24 hours (blue).

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Table 4.3. Properties of example parent–daughter radionuclides used in generators.

Parent 68

Ge Rb 82 Sr 99 Mo 81

T1/2

Daughter

T1/2

Clinical use

270.95 d 4.58 h 25.36 d 2.75 d

68

67.71 m 13.10 s 1.27 m 6.00 h

PET SPECT PET SPECT

Ga Kr 82 Rb 99m Tc 81m

Figure 4.8. GalliaPharmⓇ Ge-68/Ga-68 generator. Courtesy of Eckert & Ziegler.

5 days of use from when the radionuclide generator arrives at the hospital. The build up and decay of 99mTc is shown for a generator in which no elution takes place (red dashed curve). It can be seen in this case that the activities of the two radionuclides are very similar after approximately 24 hours. This corresponds to the time at which transient equilibrium is reached. It is therefore efficient to extract the 99mTc in a 24 hour cycle (blue dashed curve), when its activity reaches that of the 99Mo. A variety of radionuclides can be produced using generators, some of which are shown in table 4.3. The first of these is the positron emitter 68Ga, which can be produced from 68Ge, and subsequently used in PET imaging of tumours. Production of PET radionuclides such as 68Ga and 82Rb by a generator alleviates the requirement of the hospital hosting an on-site or local cyclotron. A photograph of an Eckert & Ziegler GalliaPharmⓇ Ge-68/Ga-68 Generator is shown in figure 4.8. 68Ga is continuously produced by decay of its radioactive parent 68Ge. An eluent (sterile ultrapure 0.1 mol/l hydrochloric acid), which is seen in the bag suspended above the generator, rinses the TiO2 column, on which 68Ge is adsorbed. The eluate can then 4-10

An Introduction to the Physics of Nuclear Medicine

250

Cross section (mb)

200

150

100

50

0 0

5

10

15

20

25

30

Proton energy (MeV)

Figure 4.9. Cross-section as a function of proton energy for the reaction p + 14 N → 11C + α . Produced using data taken from Takacs et al 2003 Validation and upgrading of the recommended cross-section data of charged particle reactions used for production of PET radioisotopes NIM B 211 2.

be used for direct or indirect labelling of SomaKit TOC or other compounds for PET imaging.

4.5 Production yield It is desirable and cost-effective to maximise the output of medical radionuclides being produced by nuclear reactors or accelerators. The probability that a given nuclear reaction will occur is represented by the cross-section σ, which depends on the energy and type of incident particle, the type of reaction and the target nucleus. The unit of cross-section that is most typically used in medical radionuclide production is barns (b), where 1 b = 10−28 m2. Figure 4.9 illustrates the crosssection as a function of proton energy for the reaction:

(4.10) p + 14 N → 11C + α . 14 In this example, a N nucleus is irradiated by an accelerated proton, p, which leads to the production of a 11C nucleus and an α particle. The 11C radionuclide can then be used for on-site PET studies. The energy to which the proton is accelerated will be chosen to maximise the yield based upon maximising the cross-section, information that can be extracted from figure 4.9. The rate at which radionuclides are produced (gram per second) by a particular nuclear reaction Ri, can be calculated for a beam of particles with flux ϕ (particles per cm2 per second) irradiating a target material of atomic weight AW: Ri =

ϕσiNA , AW

(4.11)

where σi is the cross-section for that particular reaction (cm2) and NA is Avogadro’s constant. This equation assumes that the nuclei are uniformly distributed within the target material and that the cross-section is independent of energy (or that the irradiating particles have a fixed energy). The production rates are usually less than 4-11

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calculated, since the particles will lose energy as they travel through the material, which changes the cross-section, and the target is not usually 100% pure. Example 2. Calculate the production rate per gram, Ri, of 11C produced when a 100% pure 14N target of AW = 14 is bombarded by a 7.5 MeV beam of 1.2 × 1011 protons per cm2 per second. Use the data in figure 4.9 to extract an approximate value for σi. Solution 2. From figure 4.9, σi = 240 mb = 2.4 × 10−25 cm2 for 7.5 MeV protons. Use equation (4.11):

Ri = 1.24 × 109

1.2 × 1011 × 2.4 × 10−25 × 6.022 × 10 23 ϕσiNA = = 1.24 × 109 AW 14

11

C nuclei are produced per gram per second.

4.6 Emerging radiopharmaceuticals There is a growing demand for radiopharmaceuticals due to the increased prevalence of cancer and cardiovascular disease in an ageing global population. There are two major strands of ongoing research activity aiming to address this challenge. The first is the investigation of methods to sustain the supply of conventional radiopharmaceuticals, through more efficient or robust production mechanisms, and the second is the development of novel radiopharmaceuticals. In 2009, the global shortfall of reactorsynthesised 99Mo triggered several research programmes aiming to develop alternative production methods for this radionuclide. It also encouraged researchers to consider other types of radionuclides that could be used for the same clinical studies. The PET and SPECT detector systems used in diagnosis have also become more advanced and are often coupled to other imaging modalities such as computed tomography (CT) or magnetic resonance imaging (MRI). The performance of these hybrid systems permits the imaging of radionuclides that would traditionally not have been feasible. In parallel, many novel therapeutic applications using α emitting radionuclides have emerged. The clinical impact associated with these radionuclides has driven the market significantly. However, it takes many years to introduce a new radiopharmaceutical into a clinical environment following intensive stages of testing. One exciting and growing field is the development of radionuclides for theranostics. This term is used to describe the administration of a radiopharmaceutical to a patient for both diagnosis and therapy. One example is the use of radioactive copper ions, 64Cu, for targeting prostate tumours. These can be produced by irradiating an enriched 64Ni target with protons in a state-of-the-art cyclotron. The 64Cu will decay with a half-life of 12.7 hours through electron capture and the emission of γ-rays, β+ and β−particles. Imaging of the radionuclide distribution using PET (via the β+ decay) would therefore be possible during treatment. An ongoing project at the ISOLDE facility in CERN aims to provide accelerator produced radioisotopes for hospitals and research centres for delivery across Europe. One of 4-12

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Figure 4.10. Photograph of the robot used for handling radionuclides at the MEDICIS facility. Courtesy of MEDICIS, CERN.

the main objectives of the MEDICIS (MEDical Isotopes Collected from ISolde) facility is to enable the study of radioisotopes that are candidates for theranostics in oncology. The radioisotopes are produced by irradiating a secondary target behind the main ISOLDE target1 with a high-intensity 1.4 GeV proton beam. Since more than 80% of the protons will not be stopped in the main ISOLDE target, the number of protons striking the MEDICIS target will be very high. The produced sample is transported to the MEDICIS facility for extraction through offline mass separation. This extraction technique is an alternative to chemical separation of the radionuclide from the irradiated target, ensuring high specific activity. The radionuclides are handled by the MEDICIS robot, which is shown in figure 4.10. They are then implanted in a metallic foil for delivery to hospitals and research centres. One of the theranostics candidates in MEDICIS is 149Tb, which could be used for PET and radionuclide therapy through its emission of β+ and α particles. Chemical separation of 149Tb from a proton-irradiated target is not feasible, however the MEDICIS mass separation technique could provide a suitable solution. The ultimate goal is to be able to produce 149Tb with high specific activity using a commercial cyclotron to irradiate a 154Gd target with 70 MeV protons and then use the CERN-MEDICIS mass separation technology to extract it for administration to patients. In 2017, the MEDICIS facility produced its first radionuclide, 155Tb, which is a candidate radionuclide for use in prostate cancer diagnosis. 155Tb has a T1/2 of 5.3 days and decays by electron capture and the emission of γ-rays. The 86 keV and 105 keV energy of the γ-rays can be imaged using SPECT, to provide dosimetry. This technique will be discussed later. The 155Tb was produced by proton-induced spallation of tantalum foil targets. The next chapter will discuss how the charged particles and γ-rays emitted from medical radionuclides interact with matter. Knowledge of the physical principles of these interactions is important when considering the passage of radiation through tissue and radiation detection systems. 1

The main ISOLDE target is used for experimental studies of the properties of nuclei.

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An Introduction to the Physics of Nuclear Medicine Laura Harkness-Brennan

Chapter 5 Radiation interactions with matter

Radionuclides administered to patients will undergo radioactive decay by emitting photons or charged particles. The interaction of this radiation with matter is fundamental to achieving the diagnostic and therapeutic aims of nuclear medicine. Producing diagnostic PET and SPECT images relies on the interaction of electromagnetic radiation in detector systems surrounding the patient. In therapy, the interactions of charged particle radiation from administered radionuclides in a patient’s body impart the prescribed RNT radiation dose. This chapter will discuss the ways in which radiation interacts with matter, in the context of these procedures.

5.1 Gamma-ray interaction mechanisms Radionuclides used in diagnostic nuclear medicine emit γ-rays with energies up to 511 keV. Interactions can occur as the γ-rays travel from the volume of interest, through the patient and into the surrounding detector systems. In this energy regime, the γ-rays can interact with materials by either photoelectric absorption (PA) or Compton scattering (CS)1. These interactions result in either the total or partial transfer of energy to the material. As a beam of γ-rays passes through a material, they can either be absorbed or scattered away from the beam. The number of γ-rays in the beam will therefore reduce as a function of depth in the material. This is known as attenuation. In PET and SPECT, attenuation of γ-rays in tissue is undesirable because the number of γ-rays that can be detected and subsequently used for imaging is reduced. Conversely, attenuation in the radiation detectors is essential to allow the γ-rays to be captured for imaging. The intensity, I, of a

1 The γ-ray interaction mechanism of pair production will not be described here because it is only possible for γ-rays that have an energy higher than 1.022 MeV, which is beyond the energy regime of nuclear medicine.

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An Introduction to the Physics of Nuclear Medicine

collimated monoenergetic (single energy) γ-ray beam after travelling a distance, d, through an absorbing medium decreases according to:

I = I0e−μ T d ,

(5.1)

where I0 is the intensity of the γ-ray beam before it enters the absorbing material. The total linear attenuation coefficient, μT, represents the total probability that a γ-ray is removed per unit length by any of the possible interaction mechanisms and is given by:

μT = μPA + μCS .

(5.2)

These are important relationships when calculating the attenuation of γ-rays in a patient, radiation detector or shielding material. Example 1. The 141 keV γ-rays from a sample of 99mTc are collimated into a beam. Calculate the thickness of lead shielding required to reduce the intensity of the beam by 99%. The linear attenuation coefficient for 141 keV γ-rays in lead is 2.71 cm−1. Solution 1. The reduction of beam intensity by 99% is given by equation (5.1):

I I0

= 0.01. Input to

0.01 = e−2.71×d ln(0.01) = − 2.71 × d ln(0.01) d =− = 1.7 cm 2.71 The thickness of lead shielding required to attenuate the γ-ray beam by 99% is 1.7 cm. 1 0.9

Transmission Intensity

0.8 0.7 0.6 0.5 0.4 511keV -rays

0.3 0.2

141keV -rays

0.1 0 0

5

10

15

20

25

30

35

40

Depth (mm)

Figure 5.1. Transmission intensity of a beam of 141 keV (red) and 511 keV (blue) γ-rays travelling through soft tissue, as a function of depth.

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100

Atomic Number, Z

80

Photoelectric absorption dominant

60

40 Compton scattering dominant 20

0 0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

Energy (MeV) Figure 5.2. Relative probabilities of photoelectric absorption and Compton scattering interactions as a function of absorber atomic number and γ-ray energy. The blue dotted line indicates when these interactions are equally probable. The regions in which photoelectric absorption and Compton scattering dominate are highlighted in dark and light grey, respectively. Produced using data from https://www.nist.gov/.

Figure 5.1 shows the transmission intensity, II , as a function of depth for beams of 0 141 keV and 511 keV γ-rays travelling through soft tissue (average Z = 7.4). It can be seen that both distributions follow an exponential decay. The total interaction probability decreases with γ-ray energy, Eγ, therefore the higher energy γ-rays are more penetrating. The relative probability of photoelectric absorption and Compton scattering depends on the atomic number, Z, of the absorbing material and Eγ, as shown in figure 5.2. The atomic number of materials encountered in nuclear medicine varies from approximately (average) Z = 7.4 in soft tissue to Z = 82 in lead components of the imaging systems. The data in figure 5.2 shows that for nuclear medicine (Eγ ⩽ 511 keV), Compton scattering will dominate in tissue and all other materials with Z < 65. For higher Z materials, photoelectric absorption will dominate. The following two sections will discuss these interaction mechanisms. 5.1.1 Photoelectric absorption Photoelectric absorption is the process in which a γ-ray transfers all of its energy to a bound atomic electron, as depicted in figure 5.3. The photoelectron is emitted with kinetic energy, Ee−, which depends on the energy of the incident γ-ray, Eγ, and binding energy of the electron, Eb, as given by:

E e− = E γ − E b.

(5.3)

The electron is most likely to be removed from the most bound shell, which is the K shell. For the elements of interest in nuclear medicine, the binding energy of electrons in the K shell can vary from about Eb = 0.5 keV for oxygen to Eb = 88 keV in lead. The removal of the electron leaves the atom in an ionised state. Since the atom will 5-3

An Introduction to the Physics of Nuclear Medicine

Figure 5.3. Illustration of a γ-ray interacting by photoelectric absorption.

tend towards its most bound configuration, higher state orbital electrons (e.g. from the L or M shell) will rearrange in order to fill the K shell vacancy left behind by the ejected electron. An x-ray will subsequently be emitted, with an energy equal to the difference in energy of the two electron shells. The x-ray can be reabsorbed close to the interaction site but may escape from the material. The x-ray is more likely to escape if the process occurs close to the surface of the absorbing material, or if that material has low-Z. The probability that a γ-ray will interact by photoelectric absorption is given by the cross-section, σPA:

σPA ∝

Zn , E γ3.5

(5.4)

where n varies between 4 and 5 depending on the energy of the incident γ-ray. Photoelectric absorption is therefore dominant for high-Z, low-Eγ interactions, as shown in figure 5.2. If photoelectric absorption is the only interaction a particular γ-ray undergoes in a radiation detector, then the measured energy is equal to that of the incident γ-ray and it will be selected for inclusion in the resulting medical image. Detector materials with high Z are therefore desired in nuclear imaging systems. 5.1.2 Compton scattering Compton scattering is the mechanism illustrated in figure 5.4, in which a γ-ray transfers a fraction of its energy to a weakly bound atomic electron. This process causes the γ-ray to be deflected from its incident path by a scattering angle, θ. The energy carried away by the scattered γ-ray, Eγ′, is related to θ and the remaining energy transferred to the recoil electron, E e−, of rest mass energy, mc 2 = 511 keV , through the following equation:

E γ′ =

Eγ Eγ 1+ (1 − cos θ ) mc 2

.

(5.5)

This relationship is derived from the conservation of energy and momentum, assuming the electron is unbound and at rest before the interaction takes place. The scattering angle θ can be any value between 0° and 180°, which results in a 5-4

An Introduction to the Physics of Nuclear Medicine

Figure 5.4. Illustration of a γ-ray interacting by Compton scattering.

distribution of energies Eγ′ and E e−. The probability of Compton scattering increases linearly as the number of target electrons, Z, increases. Compton scattering of γ-rays in the patient and detector system can degrade image quality in nuclear medicine, the impact of which is discussed in chapter 7. Example 2. Calculate the energy transferred to the recoil electron when a 364 keV γ-ray from 131I interacts by Compton scattering in tissue, if the scattering angle is 45°. Solution 2. The energy transferred to the recoil electron is E e− = Eγ − Eγ′, where Eγ′ can be calculated using equation (5.5):

E e− = E γ −

Eγ Eγ 1+ (1 − cos θ ) mc 2

364

= 364 − 1+

364 (1 − cos 45) 511

= 63 keV.

5.2 Charged particle interaction mechanisms As discussed in chapter 3, radioactive nuclei can emit charged particles through the processes of α and β decay. As a reminder, the α particle is a 42 He nucleus and the β particle is either a positron (β+) or an electron (β−). Unlike γ-rays that transfer their energy in only a few interactions, charged particles lose their energy over many interactions and over a much shorter distance as they pass through a material. In the energy range of interest in nuclear medicine, charged particles primarily transfer their energy to the material by collisions that cause ionisation and excitation of the absorber atoms. These collisions are as a result of the Coulomb force between the incident charged particle and charged components of the material, for example the positive charge of an α particle and the negative charge of an atomic electron. It is also possible that energy can be lost via the emission of bremsstrahlung radiation, 5-5

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Figure 5.5. Illustrations of a charged particle exciting an electron to a higher atomic shell and the subsequent emission of a characteristic x-ray.

although this radiative loss only becomes significant at particle energies beyond those observed in nuclear medicine so shall only be discussed briefly here. 5.2.1 Collisional Coulomb energy loss When a charged particle interacts via the Coulomb force with an orbital electron in an absorbing material, energy is transferred that can either promote the electron into a higher orbital shell (excitation) or liberate it from the atom (ionisation). The process of excitation is shown in figure 5.5. It should be noted that the incident charged particle only has to approach close to the electron in the absorber material, it does not have to be a direct hit. Since the Coulomb force has infinite range, the incident charged particle can also interact simultaneously with many orbital electrons in the material. In excitation, only a relatively small amount of energy is transferred and so the charged particle does not deviate significantly from its original trajectory. When the electron is promoted into a higher shell, it leaves the atom in an unstable configuration. The electron will therefore subsequently return to its stable position, resulting in the emission of a characteristic x-ray. The process of ionisation is illustrated in figure 5.6. In this interaction, energy is transferred from the incident charged particle to an atomic electron and the atom becomes a positively charged ion. The electron will be emitted with a kinetic energy equal to the difference in transferred energy and the binding energy. The ejected electron may have sufficient energy to induce secondary ionisation and excitation, if so, it is named a delta-ray. These secondary ionisations must be included in any calculation of the radiation dose received by a patient and therefore awareness of them is particularly important in radiotherapy treatment planning and verification. This concept will be explored further in chapter 8. Since the amount of energy transferred in ionisation is greater than in excitation, the charged particle is deflected more significantly from its path. 5.2.2 Radiative energy loss As high energy charged particles pass close to the Coulomb field of the nucleus, they can decelerate and suffer a significant deflection, resulting in the emission of 5-6

An Introduction to the Physics of Nuclear Medicine

Figure 5.6. Illustration of a charged particle transferring its energy to an atomic electron, resulting in ionisation.

Figure 5.7. Schematic illustration of a charged particle interacting with the Coulomb field of an atomic nucleus, resulting in the emission of bremsstrahlung radiation.

bremsstrahlung radiation. This is known as radiative energy loss and is shown in figure 5.7. In this interaction, energy is transferred from the charged particles to a continuous spectrum of emitted bremsstrahlung photons, which can either be reabsorbed within or escape from the material. Radiative losses are inversely proportional to the charged particle mass and are therefore more important for β particles than α particles. These losses are also more probable for energetic charged particles interacting in a high-Z absorbing material. For the types of materials and energies of charged particles encountered in nuclear medicine, radiative energy loss is therefore much less significant than collisional energy loss. 5.2.3 Charged particle range Knowledge of the distance travelled by, or range of, a charged particle is important in various aspects of nuclear medicine. When α and β particles interact in materials, their relative mass and velocity results in quite different particle paths, as illustrated

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Figure 5.8. Example particle paths (not to scale) of three α particles of the same initial energy and three β particles of the same initial energy. The variation in β particle paths results in range straggling.

by the examples in figure 5.8. An α particle has a mass approximately 7400 times greater than an atomic electron and therefore its trajectory is not significantly changed in any one collision. To provide a simple illustration, this would be similar to throwing a heavy bowling ball into a target of table tennis balls (the mass of the bowling ball is approximately 2500 heavier than the tennis table ball). For an α particle of initial Eα energy Eα, the maximum energy lost per collision is approximately 1800 , which corresponds to a head-on collision between the α particle and an atomic electron. In practice, less than the maximum energy is transferred in most of the interactions. The α particle must therefore undergo many collisions in order to transfer all of its initial energy and it will follow a nearly straight path, as illustrated in figure 5.8. When a β particle travels through a material, it will be moving at close to the speed of light. It therefore does not spend a long time in the vicinity of the atomic electron, which reduces the probability of interaction. This increases the separation distance between interactions, when compared to α particles. However, the mass of the β particle is equal to that of an atomic electron, so it will be deflected significantly at each collision, transferring relatively large amounts of energy. The result is a collection of haphazard β particle paths that are difficult to predict. In figure 5.8, the example paths of three β particles with the same initial energy are shown. Since the particles undertake different and haphazard paths through the material, the net penetration depth, or range, of these particles will be different. This variation in penetration depth is known as range straggling and has important consequences in dose deposition in radionuclide therapy, which will be discussed in chapter 8. Figure 5.9 shows the transmission intensity ( II ) for beams of α and β particles of a 0 given initial energy passing through soft tissue. It can be seen that the distributions do not follow the exponential attenuation that would be observed for a beam of γ-rays (as per figure 5.1). Since α particles of a given energy will all follow a similar path, the transmission intensity is approximately 1 whilst all the particles have energy remaining to travel through the tissue. There will then be a sharp reduction in intensity to 0, corresponding to when all the α particles have stopped in the tissue. This can be seen in the top panel of figure 5.9. In this example, the mean range, Rm, of the α particles in soft tissue is close to 60 μ m, where Rm is the depth at which the 5-8

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1

0.5

particle 0 0

0.01

0.02

0.03

0.04

0.05

0.06

0.07

5

6

7

Transmission Intensity

Range (mm) 1

0.5

particle 0 0

1

2

3

4

Range (mm) Figure 5.9. Transmission intensity of a beam of α particles (top panel) and β particles (bottom panel) travelling through soft tissue as a function of depth.

transmission intensity is reduced to 0.5. There is only a small amount of range straggling, in other words nearly all of these α particles stop at the same depth. The bottom panel of figure 5.9 shows the equivalent distribution for β particles. It can be seen that the shape of the distribution reflects the haphazard nature of β particle paths. The difference in the mean and maximum penetration depth for β particles is much larger than for α particles so it becomes necessary to define a new term, the extrapolated range, Re. This can be calculated by extrapolating the linear component at the end of the distribution. The extrapolated range for β particles can be up to a factor of 100 higher than for α particles (typically up to 8 mm). The range of a charged particle is determined by how much energy is transferred per unit length, ⎛ dE ⎞ which is given by the total stopping power, ⎜ ⎟ : ⎝ dx ⎠t

⎛ dE ⎞ ⎛ dE ⎞ ⎛ dE ⎞ ⎜ ⎟ =⎜ ⎟ +⎜ ⎟, ⎝ dx ⎠t ⎝ dx ⎠c ⎝ dx ⎠r

(5.6)

⎛ dE ⎞ ⎛ dE ⎞ where ⎜ ⎟ and ⎜ ⎟ are the contributions from collisional and radiative losses, ⎝ dx ⎠r ⎝ dx ⎠c respectively. The higher the stopping power, the lower the range of the charged particle will be. The mass stopping power (MeV cm2 g−1) is commonly used in nuclear medicine, as it accounts for the density, ρ, of the absorbing material:

S=

(dE dx )t . ρ

5-9

(5.7)

An Introduction to the Physics of Nuclear Medicine

Mass Stopping Power (MeVcm2/g)

10

2

10 1 Soft Tissue Collisional BGO Collisional 10 0

10 -1 BGO Radiative

10

-2

10 -3 -2 10

Soft Tissue Radiative

10

-1

10

0

10

1

Electron Energy (MeV)

Figure 5.10. Stopping power as a function of energy for electrons interacting in soft tissue (blue) and bismuth germanium oxide, BGO (red). The contribution due to collisional and radiative losses are indicated by the solid and dashed lines, respectively. Data from https://physics.nist.gov/.

Figure 5.10 shows the mass stopping power for collisional and radiative losses as a function of energy for an electron (β−particle) interacting in soft tissue and a material known as BGO (bismuth germanium oxide). The latter is a common radiation detector material, the operation of which will be discussed in the next chapter. The mass stopping power due to collisional energy losses dominates over radiative energy losses in both materials across the energy range shown, 10 keV to 10 MeV. However, the collisional losses are shown to become less significant at higher energies, as the contribution from radiative losses increases. The contribution to mass stopping power from radiative energy losses is more significant for BGO than soft tissue because the effective atomic number of BGO (Z = 74) is ten times that of soft tissue (average Z = 7.4). The next chapter will describe how materials such as BGO can be used in radiation detectors for nuclear medicine.

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An Introduction to the Physics of Nuclear Medicine Laura Harkness-Brennan

Chapter 6 Radiation detection

Nuclear medicine procedures are underpinned by the use of devices to measure the presence and properties of radioactive samples. These are known as radiation detectors and are essential components in SPECT and PET imaging systems, activity calibrators and dosimeters. A wide range of detectors are available, which can be categorised as gas detectors, semiconductor detectors and scintillation detectors. A detector is selected for a particular application based on its functionality and performance. The focus of this chapter will be to outline the operational principles of radiation detectors and their performance characteristics.

6.1 Gas detectors The most fundamental task of a radiation detector is to identify the presence of radiation. This is achieved by collecting and measuring the charge produced when radiation interacts in the detector material. Gas detectors specifically measure the ionisation produced as radiation interacts in a volume of gas, such as air or argon. These devices can be used for α, β and γ detection, although the probability of γ-ray interactions in gas is low due to its relatively low density. The types of gas detectors encountered in nuclear medicine are ionisation chambers, proportional counters and Geiger–Müller tubes. These devices are all gas-filled volumes with a positively charged electrode, anode, and a negatively charged electrode, cathode. The principle of operation of a basic gas detector is illustrated in figure 6.1. As radiation passes through the detector, it ionises the gas, producing electrons and positive ions. Approximately 25–35 eV of energy deposited by the incident radiation is required to generate one ion pair, therefore many are produced. Application of a voltage across the detector pulls the negative and positive charges to the anode and cathode, respectively. This flow of charge generates a small electrical current, which can be read out from the detector. The amplitude of voltage applied to a gas detector determines the strength of the electric field and therefore how the device collects ion pairs. Figure 6.2 shows the relationship between the number of ion pairs collected (amplitude of the current doi:10.1088/978-1-6432-7034-0ch6

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An Introduction to the Physics of Nuclear Medicine

Figure 6.1. Schematic illustration of a simple gas detector. The interactions of radiation ionises the gas, producing electrons and positive ions that are swept to the anode and cathode, respectively. 10 14 10 12

Ion Pairs Collected

10

A

B

C

D

E

F

10

10

8

10 6 10 4

10

2

10

0

10 -2

Applied Voltage

Figure 6.2. Relationship between the number of ion pairs collected (amplitude of the current signal) and the voltage applied to a gas detector. The solid blue and red dashed lines correspond to the detection of α particles and β particles, respectively.

signal) and the applied voltage. Six regions of interest have been highlighted in the plot: 6.1.1 Region A: recombination In this region of the plot, a low voltage is applied between the anode and cathode. When ion pairs are produced following an interaction, the electric field strength is insufficient to allow for full collection of the ion pairs at their respective electrodes. The negatively charged electrons and positively charged ions that do not reach the electrodes will therefore recombine to form a neutral state in the gas. Since most of the ion pairs are not measured at the electrodes, it is not useful to operate a radiation detector in this region.

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Figure 6.3. Photograph of a Capintec CRCⓇ 55tr dose calibrator. Courtesy of Capintec, Inc.

6.1.2 Region B: ionisation The higher voltage applied to the detector in this region produces a stronger electric field that is now sufficient to overcome the effects of recombination. Therefore, nearly all the ion pairs produced in interactions of radiation with the gas will be collected. Increasing the voltage in this region does not further improve the charge collection, therefore the amplitude of the electrical signal is proportional to the amount of ion pairs produced and thus also the energy deposited. The signal will be larger for α particles than β particles because more ion pairs are produced per unit length. Gas detectors operated in this region are known as ionisation chambers. Air or argon-filled dose calibrators and radiation exposure meters are common applications of ionisation chambers in nuclear medicine. Figure 6.3 shows a photograph of a Capintec CRCⓇ 55tr dose calibrator. This argon-filled ionisation chamber can be calibrated to the specific response of different radionuclides used in nuclear medicine by using sources of known activity. Radionuclide samples of unknown activity can then be placed into the chamber and the activity reported on the display. 6.1.3 Region C: proportional As the voltage is increased further, the ion pairs will be accelerated due to the increased electric field strength. This causes up to 105 secondary ions to be generated per original ion pair, an effect known as the Townsend avalanche. The total (primary and secondary) charge produced is fully collected at the electrodes and the current amplitude will be proportional to the applied voltage. Detectors operated in this region are therefore known as proportional counters. The collection time for the electrons is a few microseconds, so the detector can be used to count individual radiation events as long as the rates are lower than 106 s−1, and to measure the energy deposited by the radiation.

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6.1.4 Region D: limited proportional Detectors are not operated in this region because non-linear effects are observed due to a distorted electric field. 6.1.5 Region E: Geiger–Müller The voltage is increased further until secondary Townsend avalanches are induced. At this point, it is no longer possible to measure the energy deposited by the radiation, only the number of particles that have interacted in the detector. Geiger counters are operated in this voltage region to survey the amount of radiation present. Figure 6.4 shows a photograph of a Geiger–Müller detector that can be used for α, β and γ-ray detection. It has a thin entrance window, which allows for transmission of the α particles, which would otherwise be readily stopped. Figure 6.5 shows a digital survey meter that contains an internal Geiger–Müller counter for the detection of γ-rays. These types of meters are primarily of use in radiation protection for nuclear medicine but can also be used directly in surveying the radiation emitted from radiopharmaceuticals within a patient. As a reminder, these were the first type of detector used in measuring the uptake of radionuclides in the patient. 6.1.6 Region F: continuous discharge Beyond the Geiger–Müller region, the increased voltage causes the gas to break down so it can no longer be used for radiation detection. Although gas detectors are commonly used in nuclear medicine for dosimetry and radiation protection, they are not used in PET and SPECT systems. This is primarily due to the low interaction probability of γ-rays in gas. These diagnostic imaging systems rely instead on solid-state materials, which are most commonly scintillation detectors but can also be semiconductor detectors.

Figure 6.4. Photograph of a Ludlum model 44-7 halogen-quenched Geiger–Müller detector for α, β and γ-ray survey. Courtesy of Ludlum Measurements, Inc.

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Figure 6.5. Photograph of a Ludlum model 3005 digital survey meter with internal energy-compensated Geiger–Müller for γ-ray detection. Courtesy of Ludlum Measurements, Inc.

6.2 Semiconductor detectors Solid materials can be grouped into three categories according to their conductivity: insulators, semiconductors and conductors. This behaviour is characterised by the band structure of permitted electron energies. The energy band structure can be simplified to the conduction band, valence band and the bandgap between them. The size of the bandgap determines whether a material is an insulator or semiconductor, typically >5 eV and ∼1 eV, respectively. If energy is transferred to the electrons in the valence band that is sufficient for them to cross the bandgap to the conduction band, there will be a flow of current. When electrons are excited out of the valence band, a vacancy is left which is known as a hole. The liberated valence electron and hole are collectively known as an electron–hole pair, which are the charge carriers for a semiconductor detector. Some semiconductor materials can be operated such that the transfer of energy by radiation interactions is sufficient to liberate electrons from the valence band. Following the transfer of energy from interactions of incident radiation in a semiconductor material, a large number of excitations and ionisations take place as the electron comes to rest in the detector. This occurs over a small volume in the detector, called the charge cloud. The number of electron–hole pairs, N, that are

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created in the charge cloud is dependent on the energy of the incident radiation, Eincident, and the ionisation energy, Epair of the absorbing material:

N=

E incident . E pair

(6.1)

The electrons and holes, which are the charge carriers, diffuse away from their initial sites in a random motion as a function of time and will eventually recombine. However, under the application of a potential difference which produces an electric field ε, the electrons and holes will migrate in opposite directions, parallel to the direction of the electric field. Each hole acts as a point positive charge and thus the holes move in the same direction as the electric field. Semiconductor detectors can therefore be considered as solid-state ionisation chambers. Semiconductor detectors are typically employed in situations in which precise measurement of the energy deposited by incident radiation is required. Such precision arises due to the large number of charge carriers produced for each incident radiation event in comparison to scintillation detectors. The most commonly used semiconductor materials in radiation detection are silicon, germanium and a compound of cadmium, zinc and tellurium (CZT). A summary of their most important physical properties is shown in table 6.1. Germanium detectors offer the most precise measurement of energy due to the low ionisation energy of 2.96 eV, resulting in the production of a large number of electron–hole pairs for each incident radiation event. However, germanium is not commonly deployed in nuclear medicine systems because it is expensive, has a lower atomic number than many scintillation detectors and it must be cooled during operation using liquid nitrogen temperatures, which adds complexity and cost. These detectors are therefore usually only important when precise energy measurement is required to characterise complex γ-ray sources, for example in radiation protection or as auxiliary detection systems to monitor radionuclide production. CZT is a room temperature semiconductor which has a high density and atomic number and therefore excellent stopping power. However, they can suffer from poor charge collection properties due to trapping and recombination, in comparison to other semiconductor materials, which limits their precision in measuring energy. These detectors have been deployed in some commercially available nuclear medicine imaging systems, examples of which will be discussed later. Silicon is the most widely used

Table 6.1. Properties of intrinsic silicon, intrinsic germanium and cadmium–zinc–telluride.

Property

Si

Ge

Cd0.9Zn0.1Te

Atomic number Density (g cm−3) Ionisation energy (300 K) (eV) Ionisation energy (77 K) (eV)

14 2.33 3.62 3.76

32 5.33 N/A 2.96

48, 30, 52 5.78 4.64 N/A

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semiconductor material in electronic devices. In radiation detection, it can be used in α, β and γ-ray detection. Silicon is playing an increasingly important role in clinical nuclear medicine systems as a device to read out the signal from a scintillator detector, such that the silicon is not being used as the radiation-sensitive component. This will be discussed in the next section. For a complete description of the principles of operation of semiconductor detectors, the reader is referred to Knoll G 2010 Radiation Detection and Measurement 4th edn (Wiley).

6.3 Scintillation detectors The most common use of scintillation detectors in nuclear medicine is for the detection of γ-rays emitted from radionuclides in SPECT and PET. A schematic illustration of a scintillation detector configured with a photomultiplier tube (PMT) is shown in figure 6.6. When radiation interacts in the scintillation material, the transferred energy causes electronic transitions to excited states, which decay by the emission of scintillation photons (visible light). This process is known as fluorescence. The number of scintillation photons produced, Nphotons, is proportional to the amount of energy that has been transferred in the interaction of radiation with the material, which for nuclear medicine can be up to several thousand photons. The scintillation photons are subsequently converted to an electrical signal by the PMT. Several types of scintillation material are used in nuclear medicine. An ideal scintillation material would efficiently and linearly convert energy deposited by radiation interactions into scintillation photons. It would also ideally be dense, provide fast timing and precise measurement of energy. In practice, the choice of scintillation material is a compromise between these desired characteristics. Table 6.2 displays the properties of scintillation materials that are commonly used for radiation detection in nuclear medicine. Due to excellent light yield (38 photons per keV) and short decay time (230 ns), thallium-doped sodium iodide, NaI(Tl), is widely used as the detection medium in gamma camera systems for planar imaging and SPECT. Figure 6.7 shows a photograph of NaI detectors, configured with photomultiplier tubes. These detectors have been manufactured by Saint-Gobain

Figure 6.6. Schematic illustration of a scintillation detector configured with a photomultiplier tube.

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Table 6.2. Properties of scintillator materials commonly used for radiation detection in nuclear medicine. The absorption of 141 keV γ-rays is not included because it is greater than 95% for all these scintillators.

Material

Density (g cm−3)

Emission max (nm)

Refractive Decay index time (ns)

Photon yield per keV

Absorption of 511 keV γ-rays for 1″ thick crystal (%)

NaI(Tl) CsI(Tl) LaBr3(Ce) LYSO:Ce BGO

3.67 4.51 5.29 7.10 7.13

415 550 370 420 480

1.85 1.80 2.08 1.81 2.15

38 65 63 33 8

55 65 68 85 90

230 ⩽3300 25 36 300

Figure 6.7. Photograph of various NaI scintillation detectors configured with photomultiplier tubes. Courtesy of Saint-Gobain Crystals, a division of Saint-Gobain Ceramics & Plastics, Inc.

Crystals. Although it is one of the less efficient scintillation detectors available for 511 keV γ-rays, just 1 inch of NaI(Tl) is sufficient to stop more than 95% of 141 keV photons. This makes it ideally suited for gamma cameras because 141 keV γ-rays are emitted from 99mTc, which is the most commonly used radionuclide in SPECT. Bismuth germanium oxide (BGO), which has the highest density (7.13 g cm−3) of the materials in table 6.2, was the most widely used scintillation material in PET for decades due to its absorption efficiency of 90% for 511 keV PET photons. A photograph of a 2D pixellated BGO crystal array manufactured by Saint-Gobain Crystals is shown in figure 6.8. When coupled to a position sensitive photomultiplier tube, such an array can provide the spatial coordinates of the interaction position, corresponding to the (X, Y) pixels. Many state-of-the-art commercial PET systems now use dense, fast scintillators such as lutetium yttrium orthosilicate (LYSO) to

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Figure 6.8. Photograph of a 2D pixellated BGO crystal array. Courtesy of Saint-Gobain Crystals, a division of Saint-Gobain Ceramics & Plastics, Inc.

facilitate a technique called time-of-flight PET. This technique, which relies on precise timing, revolutionised PET and will be discussed in the next chapter. To measure the energy deposited in a scintillation material, the light needs to be converted into an electrical signal. This task is most commonly undertaken by PMTs, such as the examples manufactured by Hamamatsu Photonics, shown in figure 6.9. The choice of PMT will be determined primarily by the type of scintillation material, since they will be optimised for the detection of light with particular wavelengths. The shape and size of the detector also influences the PMT selection. The first stage in producing an electrical signal is directing scintillation photons towards a photocathode using a reflective coating and optical guides. The photons are then converted to Ne− electrons by a photocathode through the process of photoemission, if there is sufficient energy to overcome the work function. The quantum efficiency (QE) of the photocathode quantifies its ability to produce electrons:

QE =

Ne− Nphotons

.

(6.2)

Typically, only a few hundred electrons are produced in the photocathode following a radiation interaction in the scintillation material, due to a limited QE of up to 30%. Since the electrical signal at this stage is very small, it is amplified by a factor of approximately 107 using a set of dynodes. Signal amplification is achieved by using a potential of several hundred volts to accelerate the electrons produced from the photocathode towards the surface of the first dynode. Each accelerated electron has

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Figure 6.9. Photograph of photomultiplier tubes. Courtesy of Hamamatsu Photonics UK.

sufficient energy to ionise several hundred atoms in the dynode material, producing hundreds of secondary electrons. The multiplication factor δ for a single dynode is the ratio of the number of electrons emitted to the energy of the incident electron. As the electron passes through the PMT, its energy when incident on the next dynode will be greater than when it was incident on the previous dynode. There is further amplification between each of the N dynodes, which have an increasing potential difference. As the electrons arrive at the anode at the end of the PMT, the total amplification, Atotal, of the signal is given by:

Atotal = Fe− δ N ,

(6.3)

where Fe− is the fraction of all photoelectrons collected by the photomultiplier. Example 1. A NaI scintillation material is coupled to a PMT that has 12 dynodes. When a 500 eV electron strikes a dynode in the PMT, approximately 3000 secondary electrons will be emitted. Calculate the total amplification of the signal in the PMT, assuming that 98% of photoelectrons are collected by the PMT. Solution 1. Use equation (6.3):

Atotal = Fe− δ N 3000 12 500 Atotal = 5.93 × 107 Atotal = 0.98 ×

Although PMTs have been the traditional method of converting scintillation light into an electrical signal, they are limited by their low quantum efficiency, poor spatial resolution and large size. Semiconductor photodiodes have become an

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important competitor to these conventional PMTs. These devices, which are usually silicon, directly convert the light photons produced in the scintillation events to an electrical signal. They have several advantages including a higher QE of up to 75%, the ability to function in the strong magnetic fields used in magnetic resonance imaging (MRI) and high granularity that facilitates excellent position information. A multi-pixel photon counter (MPPC) or silicon photomultiplier (SiPM) uses multiple photodiode pixels that operate in a Geiger mode, in other words through self-triggered avalanches. A single photodiode operating in Geiger mode is not particularly useful in nuclear medicine, since there is no proportional relationship between the signal produced and the number of scintillation photons interacting in the photodiode. However, arrays of photodiodes can be used to count scintillation photons. This is only made possible if the probability that more than one scintillation photon will interact if an individual photodiode is low. This can be achieved if the surface area of the photodiode is very small. The sum of the photodiodes in the array will produce a signal that is proportional to the number of scintillation photons. Figure 6.10 shows photographs of 16 channel (4 × 4) and 64 channel (8 × 8) MPPC arrays manufactured by Hamamatsu Photonics. There are 3584 individual photodiodes of 50 × 50 μm in each of the channels, which are 3 × 3 mm surface area. The device is sensitive to scintillation photons of wavelength 320–900 nm (optimum at 450 nm), with a gain of 1.7 × 106. Figure 6.11 shows photographs of four example SiPM arrays manufactured by SensL. The smallest and largest arrays shown are 6 × 6 mm pixels in a 2 × 2 and 8 × 8 configuration, respectively. The photodiodes are 35 × 35 μm. The other two arrays are 3 × 3 mm pixels in a 4 × 4 and 8 × 8 configuration, respectively. Their optimum sensitivity is for scintillation photons of wavelength 420 nm, although they can be used to detect photons in the range 200–900 nm. Example 2. Identify the two scintillation materials in table 6.2 to be best read out by: (a) Hamamatsu 513361-3060 series array. (b) Sensl J-Series array.

Figure 6.10. Photograph of Hamamatsu Photonics MPPC arrays, which are part of the 513361-3060 series. Arrays of 16 channel (4 × 4) and 64 channel (8 × 8) arrays are shown. Courtesy of Hamamatsu Photonics UK.

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Figure 6.11. Photograph of four Sensl J-Series SiPM arrays. One 4 pixel array of 6 mm pitch, one 16 pixel array of 3 mm pitch and two 64 pixel arrays with 3 mm and 6 mm pitch are shown. Courtesy of SensL.

Solution 2. All of the scintillation materials produce photons with a wavelength that can be detected by the two arrays. Selecting the two scintillation materials that produce photons with a wavelength closest to the peak sensitivity for detection: (a) Peak sensitivity of array is at 450 nm: LYSO (420 nm) and BGO (480 nm). (b) Peak sensitivity of array is at 420 nm: LYSO (420 nm) and NaI(Tl) (415 nm).

6.4 Performance of radiation detectors In nuclear medicine, a radiation detector is often used to quantify the activity or radiation dose. Quantification relies on knowledge of the detector efficiency, which can be described using intrinsic efficiency and absolute efficiency. The intrinsic efficiency relates the number of detected radiation events, Ndetected, to the number of particles or photons incident on the detector, Nincident:

εint =

Ndetected . Nincident

(6.4)

The intrinsic efficiency of most α and β detectors is 100%, which means that all particles incident on the detector will be detected. This is because these charged particles are highly ionising and have a range that is shorter than the detector thickness. For γ-ray detection, the intrinsic efficiency depends on the γ-ray interaction cross-section in the detector material, which varies as a function of γ-ray energy. Perhaps a more useful metric is the absolute efficiency, which is defined as:

εabs =

Ndetected . Nemitted

(6.5)

The εabs will nearly always be less than εint because most sources of radiation in nuclear medicine are isotropic, which means that radiation is emitted in all directions. The number of particles or photons that are directed towards the detector 6-12

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will be given by the solid angle coverage, which is determined by the source to detector distance and the size and shape of the detector. The higher the efficiency, the lower the counting time can be. It is therefore usually desirable to employ a detector with high efficiency in nuclear medicine, so as to reduce the time of clinical procedures. Efficiency is not the only property used to define detector performance. If the energy of the radiation is to be measured then the precision with which it can be determined is also important. This is known as the energy resolution. In PET and SPECT, measuring the energy deposited by γ-rays in the detectors is vital because it allows only those which have deposited all of their incident energy to be selected. All the other γ-rays could have lost some energy through scattering in the patient, and inclusion of these in the image would degrade its quality. There are a number of factors which contribute to the total energy resolution ΔET, of a detector:

(ΔE T )2 = (ΔES)2 + (ΔEX )2 + (ΔEE )2 ,

(6.6)

where ΔEX represents signal losses in the detector such as incomplete charge collection in semiconductor detectors and light loss in scintillation detectors. The contribution of ΔEE is due to noise from the electronics. The inherent contribution of ΔES arises from statistical fluctuations in the number of charge carriers produced per interaction event, Npair, given by,

(ΔES)2 =

(2.35)2 F , Npair

(6.7)

where F is the Fano factor. The experimentally observed statistical fluctuation of the number of charge carrier pairs produced deviates from pure Poisson statistics. The Fano factor is used to correct this discrepancy. Equation (6.7) illustrates that materials which produce a large number of charge carriers due to radiation interactions, for example germanium, provide precise measurement of energy. The timing and spatial resolution of a detector are also important properties of detectors used in nuclear medicine. These correspond to the precision in measuring the radiation interaction time and position, respectively. When radiation detectors are used in imaging systems, such as PET and SPECT, reconstruction of the photon paths is required and therefore this information is essential. Finally, the ability of a detector to process a large number of interaction events without significant event loss is known as good count-rate performance or low dead-time. If the fraction of interactions lost due to dead-time, FD, is known then this loss can be corrected. For example, FD = 0.3 would correspond to 30% of the radiation interaction events being lost due to dead-time. The correction can be applied by modifying the simple conversion of Ndetected to Nefficiency in equation (6.5) to:

Nemitted =

Ndetected εabs (1 − FD)

(6.8)

The important role of radiation detectors in diagnostic imaging systems will be explored in the next chapter.

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An Introduction to the Physics of Nuclear Medicine Laura Harkness-Brennan

Chapter 7 Imaging

Nuclear medical imaging uses radiopharmaceuticals to investigate physiological functions of the body. The radiopharmaceutical accumulates in the body depending on its biological behaviour, which can elucidate disease status. If photons are emitted directly from the radiopharmaceutical, a gamma camera can be used to ascertain the location from which the radiation originated. If the gamma camera is rotated around the patient, the imaging technique is called SPECT, otherwise it is known as scintigraphy. If the radiopharmaceutical decays by positron emission, pairs of photons are produced following the annihilation of the positron with an electron. In this case, PET is used to determine the distribution of the radiopharmaceutical in the body. This chapter will outline these three imaging techniques.

7.1 Gamma camera Gamma cameras are composed of a collimator in conjunction with a scintillation detection system, as illustrated in figure 7.1. The collimator is a thick perforated sheet of dense material that is used to project the spatial distribution of the radiopharmaceutical in the patient, onto the scintillation detectors. For an ideal collimator, only those γ-rays that pass through the perforations will reach the scintillation detector, whilst all other γ-rays will be absorbed by the collimator septa1. This will provide an image with contrasting hot and cold spots, which illustrates the radiation distribution. This technique is similar to producing a shadow image with objects in a beam of light. Gamma cameras are used to generate twodimensional images for planar scintigraphy or to produce three-dimensional images for SPECT. The fundamental difference in these two techniques is that the gamma camera acquires data at a single position for planar scintigraphy, whereas in SPECT the camera is rotated around the patient so that data can be acquired at multiple positions for reconstruction into a 3D image. 1

The collimator septa are defined as the columns of absorbing material between the perforations.

doi:10.1088/978-1-6432-7034-0ch7

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Figure 7.1. Schematic diagram of a gamma camera configured with a parallel-hole collimator. An example 2D image is shown above the camera.

The material and geometry of the collimator is selected to provide a high level of attenuation for the γ-rays emitted from the radionuclide. Lead is a common choice of material due to its high atomic number (Z = 82) and high density (ρ = 11.3 g cm−3), although other heavy metal alloys can be used. There are various collimation geometries available for gamma cameras, the most simple of which is a parallelhole collimator. As the name suggests, the apertures in this configuration are parallel so that ideally only γ-rays that enter a perforation in a direction perpendicular to the collimator will pass through to the scintillation detector. The image produced is a direct projection of the radiation distribution, with no magnification or reduction. The size of the collimator will therefore determine the area of the body that can be imaged at a single gamma camera position, this is known as its field of view (FOV). Figure 7.2 illustrates the operation of a parallel-hole collimator, showing how γ-rays passing through the collimator apertures are projected into the image, whilst wide angle γ-rays are absorbed. Several standard geometries of parallel-hole collimators are available, including: (i) low-energy high-resolution (LEHR); (ii) low-energy general-purpose (LEGP); (iii) low-energy high-sensitivity (LEHS); (iv) mediumenergy high-sensitivity (MEHS) and (v) high-energy general-purpose (HEGP). Lowenergy collimators are designed for use with pharmaceuticals labelled with the radionuclides 99mTc (Eγ = 141 keV), 123I (Eγ = 159 keV) or 201Tl (Eγ = 70 keV and 167 keV). Radionuclides that are imaged using medium-energy collimators include 67Ga (Eγ = 185 keV) and 111In (Eγ = 172 keV and 247 keV). As the energy of the γ-rays increase further, it becomes more difficult to attenuate them. A gamma camera configured with a high-energy collimator can be used to image the spatial distributions of radionuclides such as 131I (Eγ = 364 keV and 637 keV). However, the quality of these images is usually quite poor because the attenuation performance of the collimator degrades, which allows γ-rays to pass through the septa without absorption. This is known as septal penetration. A major disadvantage of using a collimator to project the radiation distribution onto an image is that it is inherently very inefficient. The reasons for this are twofold. Firstly, since the radiation will be emitted in all directions, most of it will never be incident onto the gamma camera. Secondly, even when these γ-rays are incident onto the collimator, most of them will not pass through the apertures and will therefore

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Figure 7.2. Schematic diagram of a parallel-hole collimator, highlighting its length, L, septal thickness, t, and aperture diameter, d. Example γ-ray paths are shown. The two γ-rays that pass through the collimator apertures will contribute to the image.

not interact in the detector system. As a result, most of the decays of the radionuclide administered to the patient do not contribute to the image, which results in low sensitivity, S. The sensitivity (cps/Bq) of a gamma camera is defined as the number of counts per second (cps) detected per unit administered activity (Bq). Maximising the sensitivity of a gamma camera enables either less activity having to be administered to the patient, or the scan to be undertaken more quickly. The sensitivity of parallelhole collimators varies due to geometrical differences in the perforation length, L, the perforation diameter, d and the septal thickness, t. These parameters determine the probability that a γ-ray can pass through the apertures. The collimator transmission efficiency, g, is calculated using:

⎛ Kd 2 ⎞2 g≈⎜ ⎟ , ⎝ L (d + t ) ⎠

(7.1)

where K is a constant that is dependent upon the perforation shape. The most common type of perforation shape is hexagonal, which is more efficient than circular or square holes. For hexagonal holes, K = 0.26. Transmission efficiency can be maximised by increasing the diameter of the apertures, decreasing the length of the apertures or decreasing the septa thickness. However, this will increase the angular acceptance range so that more events originating off axis will undesirably pass through the collimator. These parameters therefore directly influence the quality of the image produced and thus the ability to perform diagnosis. The image quality can be described by spatial resolution, which is the minimum distance at which it is possible to distinguish two points in the image. The spatial resolution of a parallelhole collimator, Rc, depends on L, d and the source to collimator distance, s, according to:

Rc ≅

d (L + s ) . L

(7.2)

It is an inherent compromise of using a collimator that any improvements in spatial resolution are at the expense of efficiency loss. The collimator configuration is therefore chosen for specific clinical studies in order to optimise the trade-off 7-3

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between sensitivity and spatial resolution. The specifications of a few example collimators used with a Philips BrightView gamma camera are given in table 7.1. The LEHR collimator can be used to image 99mTc with a good spatial resolution of 7.4 mm but at the expense of sensitivity. This is achieved by long (27.0 mm), narrow (1.2 mm) apertures, which reduce the angular range about the perpendicular direction. An LEGP collimator that offers a 65% gain in sensitivity over the LEHR collimator can be used if a poorer image resolution of 8.9 mm is acceptable. This will be determined based upon the given clinical study. The MEGP and HEGP collimators both have much longer (58.4 mm) and thicker (3.4 mm and 3.8 mm, respectively) septa. These parameters are required so that the higher energy γ-rays can be more effectively attenuated, however, they result in a degraded image resolution of 10.9 mm. Example 1. Calculate the spatial resolution, Rc, and transmission efficiency, g, of a collimator configured with 2 mm diameter hexagonal apertures, septal thickness 0.3 mm and length 2.4 cm. Assume the source-to-collimator distance is 12 cm. Solution 1. Use equation (7.2) to calculate the spatial resolution:

Rc ≅

d (L + s ) 2(24 + 120) ≅ ≅ 12.0 mm L 24

Use equation (7.1) to calculate the transmission efficiency:

⎛ Kd 2 ⎞2 ⎛ 0.26 × 22 ⎞2 g≈⎜ ⎟ ≈⎜ ⎟ ≈ 3.55 × 10−4 ≈ 0.0355% ⎝ L (d + t ) ⎠ ⎝ 24(2 + 0.3) ⎠ In addition to sensitivity and spatial resolution, the collimator determines the FOV of the gamma camera. The FOV defines the observable imaging landscape, such that any γ-rays originating from outside the FOV will not be able to pass through the apertures. The FOV is determined by the size and type of collimator. The most common types of non-parallel-hole collimator, diverging, converging and pinhole are shown in figure 7.3. Diverging and converging collimators are configured

Table 7.1. Properties of Philips BrightView parallel-hole collimators with hexagonal holes of diameter, d, and septa of thickness, t. The values are quoted for a γ-ray source situated 10 cm from the collimator. Data extracted from Philips BrightView specifications.

Collimator

d (mm) t (mm) L (mm) S (Cpm/μCi) Rc (mm)

Low-energy high-resolution (LEHR) Low-energy general-purpose (LEGP) Medium-energy general-purpose (MEGP) High-energy general-purpose (HEGP)

1.2 1.4 3.4 3.8

7-4

0.15 0.18 0.86 1.73

27.0 27.4 58.4 58.4

168 277 212 212

(99mTc) (99mTc) (67Ga) (131I)

7.4 8.9 10.9 10.9

An Introduction to the Physics of Nuclear Medicine

Figure 7.3. Schematic diagrams of different types of gamma camera collimator, showing a (a) diverging collimator, (b) converging collimator and (c) pinhole collimator.

with tapered holes that reduce or magnify the object size in the image, respectively. Diverging collimators are useful when a gamma camera is used to image the whole body. If a parallel-hole gamma camera were to be used for whole-body imaging, it would need to be moved along the full length of the patient, which would be an inefficient process. Converging collimators are used when magnification of the object in the image is useful, for example when imaging small organs such as the thyroid or brain. The sensitivity of a converging collimator increases with depth but the spatial resolution will degrade significantly. Pinhole collimators are a conical structure that operate in the same way as an optical pinhole camera, using a single hole that magnifies and inverts the image. The size of the hole is usually between 3 and 6 mm. In contrast to a converging collimator, the sensitivity of a pinhole collimator decreases with depth. Pinhole collimators are most commonly used in imaging small organs such as the thyroid, when magnification provides more complete use of the scintillation detector array. As discussed earlier, lead is the most commonly employed collimator material for gamma cameras. Recently, there has been a drive to manufacture ultra high resolution collimators made of tungsten alloys. Machining dense materials such as tungsten with the very small apertures required for ultra high resolution performance using traditional methods is very challenging. Production of these has only been made possible recently due to advanced additive manufacturing techniques. Figure 7.4 shows a photograph of a small FOV tungsten collimator with 0.6 mm diameter perforations. Producing this collimator with traditional machining would have been extremely costly and time consuming. Instead, an additive manufacturing process was employed in which a high-powered laser fused successive tungsten layers until the collimator was produced. This precision manufacturing technique opens exciting new possibilities in advancing imaging performance with complex collimator geometries. An application of this type of collimator in producing images during radionuclide therapy will be discussed in detail within the next chapter.

7.2 Single photon emission computed tomography A limitation of using a gamma camera to acquire a 2D planar image of a 3D radiopharmaceutical distribution is that radiation emitted from different depths in the patient is superimposed. SPECT is a technique that provides a 3D image by 7-5

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Figure 7.4. A photograph of an ultra high resolution gamma camera collimator manufactured using additive printing. Courtesy of the University of Liverpool.

rotating a gamma camera around a patient and collecting multiple 2D images at various angles, as illustrated in figure 7.5. The information collected as a 2D image produced at each angle must then be reconstructed to show the volumetric distribution of radiation in the 3D object. This is the same principle as x-ray computed tomography. SPECT offers significantly improved image contrast over planar gamma camera imaging and therefore is commonly used in the measurement of cerebral blood flow and glucose metabolism. This can be used to provide diagnosis and staging of Alzheimer’s disease, Parkinson’s disease and brain tumours. The radionuclides used in SPECT are similar to those used in planar gamma camera imaging or scintigraphy, therefore the same types of collimators can be used. SPECT systems can be configured with a single or multi-headed gamma camera, such as dual-head or triple-head gamma cameras, in which the two (or three) cameras are mounted on a rotating gantry at a default position of 180° (or 120°) from each other. Their relative positions can be changed to maximise the sensitivity for particular scans, for example in cardiac SPECT. For example, figure 7.5 shows a dual-head system with the two gamma cameras positioned at 90° from each other. Multiple-headed gamma camera systems allow for faster acquisition of data from the patient. The 2D images that are acquired at every step of rotation are known as projections. These projections are formed on a 2D image, typically represented by a grid of (64 × 64) or (128 × 128) pixels. Each pixel contains the number of γ-rays absorbed in the scintillation detector, after successfully passing through the patient and traversing the collimator, for that particular position. The relative number of counts in each pixel therefore provides information about the location of radiation distributed within the patient. Computer-based algorithms are used to combine the 2D projections into a 3D SPECT image. The SPECT slices can then be viewed in cross-sectional planes or as a 3D representation of the volume of interest.

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Figure 7.5. Illustration of single photon emission computed tomography (SPECT) using a dual-head gamma camera system. The two cameras are rotated around the object to produce a three-dimensional image.

There are many reconstruction methods that can be used to generate SPECT images, which can be grouped into analytical and iterative algorithms. The most common type of analytical method is filtered back projection (FBP). Analytical methods are computationally efficient, however, they often produce inferior image quality as they do not account for experimental characteristics such as the properties of the gamma camera. Iterative methods can be used that are based on a system matrix2, which estimates the source distribution and considers the experimental characteristics of the imaging device. These statistical based methods are used because they often provide superior image resolution, however, they can be computationally expensive. Figure 7.6 shows a photograph of a Philips BrightView XCT system, which is an integrated SPECT/CT system configured with a dual-head variable angle gamma camera. Each gamma camera head contains a single crystal NaI scintillation detector read out by 59 photomultiplier tubes. The two gamma cameras can be configured at either 90° or 180° from each other and then can be rotated around the patient together in steps ranging between 1.4° to 90°. The gamma cameras can be set up close to the patient in this particular system, using Philips CloseUp technologies, to acquire cardiac SPECT images. As a reminder, this close configuration will facilitate excellent spatial resolution according to equation (7.2). The CT system can provide images that allow the SPECT data to be corrected for photon attenuation, which corresponds to the scattering and absorption of photons as they pass through the patient before entering the gamma camera. The CT image effectively provides an attenuation coefficient map to allow a correction to be applied. It also provides 2 The system matrix is a grid of 2D pixels that describes the probability that a γ-ray will be detected in a given pixel.

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Figure 7.6. Photograph of a Philips BrightView XCT SPECT/CT system configured for cardiac SPECT. Reproduced with permission of Philips Ⓒ.

Figure 7.7. SPECT/CT images of the thyroid in a female adult patient. Produced using a Philips BrightView XCT SPECT/CT system. Reproduced with permission of Philips Ⓒ .

anatomical context with excellent spatial resolution. An example set of SPECT/CT images acquired using the Philips BrightView XCT are shown in figure 7.7. The images were acquired for studies of the thyroid of a female adult patient. The coloured regions correspond to SPECT images that illustrate the distribution of the radiopharmaceutical in the body, showing preferential uptake in the thyroid. These SPECT images are overlaid on the CT images, which provide anatomical context. Although NaI scintillation detectors are the most commonly used type of radiation sensor in gamma camera and SPECT systems, there is a growing market for room temperature semiconductor detectors, such as cadmium zinc telluride (CZT), which can offer improved sensitivity and energy resolution. The photograph in figure 7.8 shows the Spectrum Dynamics D-SPECTⓇ Cardiac Imaging system, which uses CZT detectors and a tungsten collimator. The device has been designed for one of the most common applications of SPECT, nuclear cardiology. Figure 7.9 shows an example of the system being used to image the injection of 99mTc-Sestamibi as it passes through the left ventricle of the heart. This allows the coronary flow reserve (CFR) by the coronary artery to be calculated. This is achieved through Gated SPECT, in which an electrocardiogram (ECG) is used to time-align data acquisition with blood flowing through the heart.

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Figure 7.8. Photograph of the D-SPECTⓇ Cardiac Imaging System. Courtesy of Spectrum Dynamics Medical.

Figure 7.9. Dynamic cardiac images produced by measuring the flow of 99mTc-Sestamibi using the D-SPECTⓇ Cardiac Imaging system. Courtesy of Spectrum Dynamics Medical.

7.3 Positron emission tomography Positron Emission Tomography (PET) is used to diagnose physiological conditions by mapping the biological uptake of radiopharmaceuticals labelled with positronemitting radionuclides. Typical radionuclides used in PET include 11C, 13N, 15O and 18 F, which are produced using a cyclotron located at or close to the hospital. Due to 7-9

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Figure 7.10. Illustration of the annihilation of a positron emitted in the decay of 18F, with an atomic electron. The rest mass energy of the particles is converted into two 511 keV photons, which are emitted in opposite directions.

the short half-life of these radionuclides (between 2 and 110 minutes), they are administered as soon as possible to the patient by injection, inhalation or ingestion. The radiopharmaceutical is then allowed time to accumulate in the organs of interest, prior to imaging. The time to accumulate will depend on the physiological function being studied but could be as long as 90 min if 18F is being used. When the radionuclide decays, positrons are emitted with a range of energies up to the endpoint energy Emax, as shown in figure 3.4. As a reminder, the positron travels through the tissue, losing its energy in inelastic scattering interactions until it binds with an electron in the tissue to form the short-lived state positronium. After approximately 10−10 seconds, the positron and electron will annihilate, in which the 511 keV rest mass of each particle is converted into energy in the form of photons. To conserve momentum and energy before and after the annihilation, two photons of 511 keV energy are emitted in opposite directions. An example annihilation of an atomic electron with a positron emitted in the decay of 18F to 18O is illustrated in figure 7.10. The radiopharmaceutical 18F-FDG is used in PET to measure metabolic activity by quantitatively mapping glucose uptake. The data acquired enables early detection of cancerous cells, due to their high metabolism. The principle of PET is illustrated in figure 7.11. If two annihilation photons pass through the body without any scattering and can be detected by a γ-ray detection system within a short time window, then it can be inferred that the annihilation point occurred somewhere along the line that joins the two detection points. This is known as the formation of a line of response (LOR). The detection of many annihilation photon pairs allows many LORs to be computed. Regions of significant LOR overlap represent the distribution of the radiopharmaceutical in the body. The LORs are formed only when two photons are detected within a given time window, known as a coincidence window. The coincidence detection efficiency ε2 depends on the efficiency of detecting a single 511 keV annihilation photon ε:

ε = ϕ(1 − e−μd )

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(7.3)

An Introduction to the Physics of Nuclear Medicine

Figure 7.11. Illustration of the formation of a PET line of response following the detection of two 511 keV annihilation photons in a scintillation detector ring.

Figure 7.12. Illustration of the formation of a PET line of response following a true coincidence event, a false coincidence event due to scattering and a false coincidence event due to randoms.

where ϕ is the fraction of detected events that are selected by the energy window and μ is the linear attenuation coefficient of the detector material, which has a thickness d. The width of the coincidence time window is typically set between a few hundred picoseconds to 10 ns and the selection impacts the image quality. Ideally, the coincidence window would be set with a width that ensures that only those pairs of photons arising from the same annihilation event are correlated. There are two ways in which incorrect or false LORs can be produced, as shown in figure 7.12. The first of these is false scattered, which can account for more than 50% of all LORs. If at least one of the 511 keV photons undergoes Compton scattering within the patient, it will change direction such that the line between the two detection points does not overlay with the annihilation position, producing a false LOR. Some of these events can be successfully removed by applying an energy gate, since the photon will have an energy less than 511 keV if it has undergone Compton scattering. This technique relies on the γ-ray detectors having adequate energy resolution to discriminate these types of events. A more difficult situation is when two annihilation events occur at approximately the same time, so that four annihilation photons are detected within the same coincidence time window. It is not possible to always correctly correlate the sets of photons, which can result in the formation of false random LORs. The number of false random LORs produced will be proportional to the width of the coincidence time window. The impact of 7-11

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introducing false LORs into an image is degradation of the signal-to-noise, which can hinder diagnosis. The accuracy and efficiency of LOR generation relies on the type of γ-ray detectors used to capture the 511 keV photons. As discussed in earlier chapters, the first clinical PET systems used NaI scintillation crystals individually coupled to photomultiplier tubes, since they offer high light output. However, they have limited efficiency for the detection of 511 keV photons due to relatively low density (3.67 g cm−3) and relatively low effective atomic number (Z = 50.8). Blocks of pixellated BGO detectors with large photomultiplier tubes were developed in the 1970s and became the standard choice for PET. The high density (7.13 g cm−3) of BGO increases the detection probability for 511 keV photons (90% absorption for 1 inch BGO, in comparison to 55% absorption for 1 inch NaI). However, BGO detectors are limited by poor energy resolution, which leads to increased correlation of false scattered LORs, and poor time resolution, which require large coincidence windows and therefore increased false random LORs. In recent years, PET has been revolutionised through the development of fast scintillation crystals such as LSO, LYSO and LaBr3, coupled with fast photomultipliers or photodiodes to offer significantly improved timing performance. Figure 7.13 shows a photograph of a GE Discovery MITM PET/CT system, which implements these latest technologies. The GE Discovery MITM employs GE LightBurst digital detectors, which combine a lutetium-based scintillation detector and SiPMs, as a replacement for the conventional PET scintillation detectors with PMTs. A comparison of the conventional and GE LightBurst digital detector technologies are both shown in figure 7.14. Example images produced using PET systems configured with the LightBurst and conventional PET detectors can be seen in figure 7.15. The patient has been administered with 18F-FDG, which has been uptaken in regions of high metabolic activity. It can be seen in this example that the imaging performance of the GE LightBurst digital detector system is superior to a conventional PET/CT system, since the small lesions highlighted within the blue circle can be observed more clearly. This imaging performance is particularly important in patients undergoing a whole-body evaluation of metastases. The availability of fast scintillators have allowed the time of flight PET (TOFPET) technique to reach widespread clinical use, since the first system became

Figure 7.13. Photograph of a GE Discovery MITMPET/CT system. Ⓒ GE Healthcare. All rights reserved.

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Figure 7.14. Photographs of a conventional PET detector, composed of a scintillation detector and PMT (left) and a GE LightBurst Digital Detector configured with a scintillation detector and SiPM (right). © GE Healthcare. All rights reserved.

Figure 7.15. PET/CT image of a patient administered with 18F-FDG acquired with a GE Discovery MI configured with LightBurst Digital detectors (left) and a PET/CT system with conventional PMT technology. The 18F-FDG has been uptaken in regions of high metabolic activity, which allows the small lesions indicated within the blue circle to be seen the left image. © GE Healthcare. All rights reserved.

commercially available in 2006. The aim of TOF-PET is to measure the point of annihilation along the LOR, by calculating the time difference in the detection of the two 511 keV photons. Since the annihilation photons travel at the speed of light, (c = 3 × 10 8 m s−1), and the radius of a whole-body PET scintillation ring is typically 35 cm, the time taken for photons to reach the detectors from a central annihilation point is approximately 1 ns. The detectors must therefore have a coincidence time resolution of the order of a few 100 ps, to measure differences in the time of arrival, a feat that has only been made possible by the development of fast scintillation detectors. Figure 7.16 illustrates the difference in the formation of a LOR using standard PET (no TOF) and TOF-PET, indicating the probability of annihilation having occurred at each position along the line. The standard PET LOR shows

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Figure 7.16. Illustration of the formation of a PET line of response using a standard PET system (without TOF functionality) and using TOF-PET, for photons that are detected at times t1 and t2 after the annihilation event.

equal probability along the length of the line because there is no information available to constrain the annihilation position. The TOF-PET LOR shows a spread in probabilities along the length of the line, where the maximum is centred at the true annihilation position. The width of the probability distribution around the annihilation position is determined by the coincidence time resolution. The correction from the mid-point position is given by:

Δx =

(t2 − t1)c , 2

(7.4)

where t1 and t2 are the interaction times after the annihilation event, as illustrated in figure 7.16. The performance of a PET system is often described by its spatial resolution and sensitivity. As with SPECT systems, the spatial resolution drives image quality and thus the ability to perform accurate diagnosis. The sensitivity will determine how long it takes to acquire data during the scan, which will influence the choice of administered radionuclide activity and/or how many patients can be scanned in a day. The spatial resolution of PET is ultimately limited by the positron range and non-collinearity of the 511 keV annihilation photons. Positrons have different kinetic energies when they are emitted from different radionuclides. The positron range therefore varies according to the radionuclide (∼1 mm for 18F and ∼4 mm for 15 O), therefore the spatial resolution due to positron range, Rrange, depends on the radionuclide being imaged. The total spatial resolution of a PET system, RPET, can be calculated using:

RPET ≈

2 2 R int + R nc2 + R range ,

(7.5)

where Rint is the intrinsic detector spatial resolution and Rnc is the contribution to spatial resolution from non-collinearity of the photons. Using PET radionuclides with low positron range and detectors with good spatial resolution will provide the best possible system spatial resolution. PET sensitivity is defined as the number of events detected per unit of activity (cps per Bq per ml). It depends on the coincidence detection efficiency, ε2, solid angle 7-14

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coverage of the detectors, ω, the packing of the detectors, φ, (ratio of the radiation sensitive detector area to the total surface area including dead space) and the event selection criteria, i.e. the coincidence timing and energy windows used. The sensitivity of a PET system, SPET, for a single point source at the centre of a single PET ring can be calculated using:

SPET(%) = 100 ×

ε 2 φΩ . 4π

(7.6)

It can be seen that the sensitivity of a PET system is maximised by using efficient detectors, packed with minimum dead space into a ring that has large solid angle coverage. The solid angle coverage, Ω, for a PET ring of diameter D, can be calculated by:

⎡ ⎛ A ⎞⎤ Ω = 4π sin ⎢tan−1 ⎜ ⎟⎥ , ⎝ D ⎠⎦ ⎣

(7.7)

where A is the height of the detector in the axial direction. The solid angle coverage is better for PET rings that have a small diameter and are configured with scintillation crystals that cover a large sensitive area. Example 2. Calculate the sensitivity SPET (%) of a PET system consisting of a 76 cm diameter ring of BGO detectors of linear attenuation coefficient 0.96 cm−1. The sensitive volume of each detector crystal is (6 × 6 × 28) mm and they are configured with a packing fraction φ of 0.7. Assume that 85% of events are selected in the energy window of 350–650 keV. Solution 2. First, calculate the efficiency ε, and solid angle coverage Ω:

ε = ϕ(1 − e−μd ) = 0.85 × (1 − e−0.96 × 2.8) = 0.792 ⎡ ⎡ ⎛ 0.6 ⎞⎤ ⎛ A ⎞⎤ ⎟⎥ = 0.099 Ω = 4π sin ⎢tan−1 ⎜ ⎟⎥ = 4π sin ⎢tan−1 ⎜ ⎝ D ⎠⎦ ⎝ 76 ⎠⎦ ⎣ ⎣ Then calculate the total sensitivity SPET:

SPET (%) = 100 ×

0.7922 × 0.7 × 0.099 ε 2 φΩ = 100 × = 0.347% 4π 4π

The technologies used in PET systems are still evolving. As recently as 2011, Siemens Healthineers released the world’s first commercially available fully integrated whole-body PET/magnetic resonance imaging (MRI) scanner, the Biograph mMR. Combining PET with MRI offers improved soft tissue contrast over CT, whilst MRI has the added advantage of using no ionising radiation. However, PET/MRI is more expensive than PET/CT and is technically very challenging

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Figure 7.17. Photograph of a Siemens Biograph mMR system. Ⓒ Siemens Healthineers.

because the large magnetic fields and radiofrequency signals from the MRI system can interfere with conventional PET detectors and electronics. A photograph of the Siemens Biograph mMR is shown in figure 7.17. The MRI system is configured with a 3 T superconducting magnet. The PET detector uses LSO crystals that are read out by avalanche photodiodes (APDs). The system offers excellent performance for imaging in neurology, oncology and cardiology.

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IOP Concise Physics

An Introduction to the Physics of Nuclear Medicine Laura Harkness-Brennan

Chapter 8 Radionuclide therapy

Radionuclide therapy (RNT) is an established technique used to treat cancerous and non-cancerous diseases. Radiotherapy treatments using external beams of radiation do not fall under the remit of nuclear medicine, but RNT does because unsealed radiation sources are administered to patients. This chapter will introduce the general principles of radiotherapy, and specifically of RNT. The application of medical internal radiation dosimetry (MIRD) in planning and verification of RNT treatments will also be discussed.

8.1 Principles of radiotherapy Radiotherapy is used to deliver a lethal radiation dose to a target volume with the aim of stopping or slowing the progression of disease. The most fundamental definition of radiation dose is absorbed dose, D, which is the mean energy, dE˜ , transferred to matter by ionising radiation, per unit mass, dm:

D=

dE˜ . dm

(8.1)

The unit of absorbed dose is the Gray (Gy), where 1 Gy = 1 J kg−1. The calculation of dose and its importance in treatment planning and verification will be discussed in the next section. For now, it is sufficient to note that it is the energy deposited in radiation interactions with tissue that induces cell damage and thus knowledge of how the dose is deposited in a patient is important. The most common application of radiotherapy is in the treatment of cancer, which is a disease caused by the uncontrolled division of abnormal cells. There are several treatment options for cancer but around 50% of cancer patients will undergo radiotherapy that targets these abnormal cells. The most common type of radiotherapy is external beam radiotherapy (EBRT), which uses beams of high-energy photons or accelerated charged particles directed from outside the patient to deliver a radiation dose to the target tissue. A highly simplified EBRT scenario of two doi:10.1088/978-1-6432-7034-0ch8

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ª Morgan & Claypool Publishers 2018

An Introduction to the Physics of Nuclear Medicine

Figure 8.1. An illustration of radionuclide therapy (RNT) and external beam radiotherapy (EBRT). A simplified representation of the primary path of the radiation is shown in orange, to highlight the difference in the two therapies.

beams irradiating a patient is illustrated in figure 8.1. The dose delivered to the target volumes using EBRT can be accurately planned using medical images produced by computed tomography (CT), magnetic resonance imaging (MRI), PET or SPECT. The aim of using these images is to ascertain the location of the target, for example, a tumour, and any organs at risk (OARs). A dose delivered by radiotherapy to an OAR should always be minimised, where possible. The timedependent delivery of the dose from EBRT is highly controlled, since it is possible to switch the beam on and off. This control is advantageous and unique to this type of radiotherapy. However, EBRT is not a technique without risks because as the beams pass through the patient they will ionise the tissue, causing dose deposition along the whole beam path. This will include regions outside the target volume and even OARs if it is not possible to avoid them. A number of techniques can be employed to reduce the dose deposition to healthy tissue and OARs, including irradiation of the target volume by multiple beams passing through the patient at different angles, with variable energy or weighting. Collimator systems and adaptive systems are also usually employed. Since EBRT is outside the remit of nuclear medicine, the reader is referred to Cherry and Duxbury 2009 Practical Radiotherapy: Physics and Equipment 2nd edn (Wiley-Blackwell) for detailed information. Internal radiotherapy uses unsealed radiation sources in radionuclide therapy (RNT), as illustrated in figure 8.1, or sealed radiation sources in brachytherapy. The term sealed applies to encapsulated radiation sources, such as radioactive implants. In brachytherapy these implants are placed directly into the target tissue, whereas unsealed sources are uptaken according to biological processes. The radiobiological principles and treatment objectives of EBRT, RNT and brachytherapy are the same. The main differences arise from how the radiation is administered to the body, which includes the location of the radiation source, the type and energy of particles used, irradiation time and rates, all of which impact the clinical outcome. In RNT 8-2

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and brachytherapy, radionuclides that decay by the emission of charged particles are administered to patients. Charged particles will ionise the tissue over a short range (relative to EBRT photons or accelerated charged particles), resulting in the delivery of lethal radiation doses to the targeted tissue and minimal damage to the surrounding healthy tissue and OARs. RNT relies on knowledge of the physiological function of the body being targeted, for example the tumour biology. This vital information can be determined using SPECT and PET, prior to treatment. As with radionuclides used in SPECT and PET, the important characteristics of RNT radionuclides include the type of decay, the half-life and the production method. They also must be readily uptaken and retained in tissues of interest and have minimum uptake in healthy tissue. Table 8.1 shows example radionuclides used in RNT and their properties. These example radionuclides all decay by either α or β emission. These particles have mean ranges up to 0.1 mm and 3.9 mm, which facilitates localised dose deposition. The half-life of these radionuclides is of the order of days, which is ideal to allow time for uptake and delivery of the dose during its retention in the target volume. The β-emitting radionuclide 131I has been used successfully in RNT since its first deployment in 1946, because it is naturally uptaken by the thyroid. It is used in the treatment of benign (non-cancerous) diseases, such as hyperthyroidism. For cancer patients, 131I can also be used to deliver a high radiation dose to the thyroid after surgery to remove any cancerous cells that were not extracted. One of the many advantages of using 131I is that it emits γ-rays in addition to β particles, which can be imaged before and after therapy to visualise the distribution of the radionuclide in the patient, for treatment planning and dosimetry. There are some challenges to this, which will be discussed in the next section. Bone metastases can grow due to primary tumours located in the prostate, breasts and lungs. The radionuclides 89Sr, 153Sm, and 223Ra can be used for palliative treatment of these bone metastases, the aim of which is to ease the pain experienced by the patient. The β-emitting radionuclide 89Sr has been used for this purpose in the UK and USA since its approval in 1989 and 1993, respectively. It has similar chemical properties to calcium so will be readily uptaken into bone. A disadvantage of using the β-emitting radionuclides 89Sr and 153Sm in this treatment is that they can degrade bone marrow. This is less problematic for 223Ra, which

Table 8.1. Properties of RNT radionuclides, highlighting the decay mode, physical half-life, mean range of the charged particle in soft tissue and example medical use.

Radionuclide

Decay mode

T1/2 (d)

Rm (mm)

Medical use

89

β− β− β− β− β− α

50.5 2.7 8.0 2.0 6.7 11.5

2.4 3.9 0.4 0.6 0.23 0.1

Bone metastases Non-Hodgkin lymphoma Thyroid disease Bone metastases Neuroendocrine tumours Bone metastases

Sr Y 131 I 153 Sm 177 Lu 223 Ra 90

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emits α particles that have a much shorter range. Coupled with the similar chemical properties to calcium, this makes 223Ra a favourable radionuclide for treatment of bone metastases. Neuroendocrine tumours can be targeted by 177Lu, which emits β particles with very short range and γ-rays that can provide visualisation of the uptake. Finally, monoclonal murine antibodies labelled with either 90Y or 131I can be used to treat a type of cancer known as non-Hodgkin lymphoma. The physiological mechanisms govern the uptake and distribution of the radiopharmaceutical in the body. As the radionuclide accumulates in an organ that has preferential biochemical uptake of the radiopharmaceutical, the activity in that organ will increase. However, as the radiopharmaceutical undergoes radioactive decay and is excreted by biological processes, the total activity in the patient will decrease. The absorbed dose rate in each organ will therefore change as a function of time and there is no way to ‘switch off’ the radiation, as is possible with EBRT. It is therefore challenging to calculate the absorbed dose delivered to target organs and OARs in RNT. Treatment planning for patients usually follows a generic protocol, in which radionuclides are administered with standardised activity, which may be scaled to account for the patient weight. However, it is known that for the same initial activity, the absorbed dose can vary significantly between patients. The next section discusses how to calculate the dose to target organs from the uptake of the radiopharmaceutical.

8.2 Medical internal radiation dosimetry (MIRD) In radiotherapy treatment planning and verification, it is necessary to determine how the dose will be, or has been, deposited in a patient. The calculation of the radiation dose is known as dosimetry. As discussed previously, this is particularly challenging in RNT because the radiopharmaceutical will be uptaken in the body according to the biological processing of the compound, of which the time and spatial distribution can vary between patients. The total activity of the radionuclide will also be decreasing over time, due to radioactive decay and excretion through biological processes, which together govern the effective half-life. Dosimetry specific to RNT is the medical internal radiation dosimetry (MIRD) scheme. In this technique, the complex physical structures of the body are simplified to a set of source organs, s, and target organs, t. The source organs are those in which there is preferential uptake of the radionuclide, which results in significant activity there. Although these organs will primarily be self-irradiating, they will also irradiate nearby organs, since the emitted β particles can travel up to approximately 8 mm in soft tissue. All the organs for which the dose is to be calculated are known as target organs, not necessarily just those in which the treatment is aiming to deliver maximum radiation dose. The absorbed dose Dt←s to a target organ from a source organ is directly proportional to the cumulated activity A˜s in the source organ. The cumulated activity can be calculated using:

A˜s =

∞

∫0

As (t ) dt .

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(8.2)

An Introduction to the Physics of Nuclear Medicine

The cumulated activity is determined by generation of a time activity curve (TAC). This can be produced either by using computer models to predict the theoretical response or by quantifying the activity experimentally at various time intervals subsequent to administration of the radiopharmaceutical. If pharmacokinetic modelling is used, it is usually based upon one of the following assumptions and depends on the radiopharmaceutical used: • Instantaneous uptake of the radionuclide in the organ, with excretion by biological processes and physical decay. • Instantaneous uptake of the radionuclide in the organ, with no excretion by biological processes. • Instantaneous uptake of the radionuclide in the organ, with excretion by biological processes only. • Uptake is not instantaneous. A TAC can be produced experimentally by using a simple Geiger counter to determine the total activity or by using an activity-calibrated gamma camera to image the spatial distribution of the radionuclide, if the radionuclide emits γ-rays. The latter method is preferred and would allow for personalised dose verification. However, there are limitations in the operational performance of gamma cameras when imaging such high activity radionuclides. Figure 8.2 shows an illustrative example of the uptake and decay of a radionuclide in a source organ (blue), and two TACs generated using data acquired at three different times post administration, for each curve (green and red). It can be seen that when only a small number of measurement points are used, the curve is not well-formed and may not accurately represent the true uptake and decay. Since the cumulated activity is calculated as the area under the curve, the errors will therefore be large. The curve could be improved by increasing the number of data points but this would require significant time on the gamma camera, which is costly and time-consuming. It is also not desirable for

True Activity TAC 1

Measured Activity

TAC 2

Time Post Administration

Figure 8.2. Example time activity curves (TACs) generated using data acquired at different time points (green and red) for a given activity in the source organ (blue).

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patients to return frequently to the hospital. In practice, the entire shape of the TAC will be estimated using the experimental data points and a relationship based upon the theoretical uptake and retention of the radiopharmaceutical. However, it is not always correct because it relies upon patient-dependent biological processes. A further challenge for the generation of experimental TACs is that the radionuclides administered in RNT are of much higher activity than those used in diagnostic imaging (since the primary mechanism of successful therapy is DNA damage with high radiation doses). Gamma cameras are therefore not optimised to work at high count rates and also the energy of the γ-ray emitted by the therapeutic radionuclide is often outside the conventional range used in diagnostic SPECT. This can lead to inaccuracies in activity quantification, in terms of the amount of activity and how it is distributed spatially. There are a number of methods being investigated to tackle these problems, one being the development of custom imaging systems for RNT dosimetry and verification. An example system under development is DEPICT (dosimetric imaging with CZT), which uses a pixellated CZT detector and an ultra high resolution, 3D printed parallel hole collimator to provide accurate activity quantification and improved spatial resolution for 131I thyroid treatments. A conceptual drawing of the DEPICT system is shown in figure 8.3. Other methods include combining the experimental data with kinetic modelling to extrapolate some of the information lost in the experimental measurement. The absorbed dose, Dt←s , to a target organ of mass m t , from uptake of a radionuclide with cumulated activity A˜s in a source organ is given by:

Dt←s = A˜s St←s

(8.3)

where the MIRD S factor represents the mean dose to the target organ from the source organ, per unit cumulated activity. The S factors depend on the radionuclide and organ properties. They are tabulated for different source to target combinations in standard phantoms representing a standard man, pregnant woman and children of various ages. Table 8.2 shows example MIRD S factors tabulated in MIRD pamphlet no. 15 (Bouchet et al 1999 Radionuclide S values in a revised dosimetric

Figure 8.3. Conceptual diagram of a device for dosimetry in RNT. Courtesy of the University of Liverpool.

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Table 8.2. MIRD S factors for various target organs, which are irradiated by 123I and 131I accumulated in the thyroid as the source organ. Extracted from: MIRD pamphlet no. 15. Bouchet et al 1999 Radionuclide S values in a revised dosimetric model of the adult head and brain J. Nucl. Med. 40 62S–101S.

S factor (mGy MBq−1 s−1) Target organ

123

131

Brain Eyes Skin Spinal cord Thyroid

1.27 × 10−7 1.47 × 10−7 5.05 × 10−7 1.27 × 10−6 2.91 × 10−4

I

I

3.45 × 10−7 4.61 × 10−7 1.04 × 10−6 2.92 × 10−6 1.61 × 10−3

model of the adult head and brain J. Nucl. Med. 40 62S–101S) corresponding to target organs irradiated by 123I and 131I accumulated in the thyroid, which is the source organ. It can be seen that the S factors are higher for 131I than 123I, and that in both cases the mean dose per unit cumulated activity is highest for the thyroid, in which there is self-irradiation. Example 1. A patient is administered with 74 MBq of 131I for the treatment of hyperthyroidism, 65% of which is instantly uptaken by the thyroid. 131I decays with a physical half-life of 8.02 days and is excreted with a biological half-life of 13.25 days. Using the information from table 8.2, calculate the dose from the thyroid to the: (a) thyroid, (b) brain. Solution 1. Calculate the effective half-life for

1 T1/2eff 1 T1/2eff T1/2eff

131

I using equation (3.19):

1 1 + T1/2 T1/2bio 1 1 = + 8.02 13.25 = 5.00 days = 4.32 × 105 s =

Use equations (8.2) and (8.3) to calculate the absorbed dose: ∞

Dt←s =

∫0

Dt←s =

∫0

Dt←s =

A0 t1/2eff × St←s ln 2

As (t )dt × St←s

∞

A0 e

−ln 2 × t t1/2eff dt

8-7

× St←s

An Introduction to the Physics of Nuclear Medicine

(a) Dt←s = (b) Dt←s =

0.65 × 74 × 4.32 × 105 ln 2 0.65 × 74 × 4.32 × 105 ln 2

× (1.61 × 10−3) = 48.26 × 103 mGy, or 48.26 Gy. × (3.45 × 10−7) = 10.34 mGy.

The dose from the thyroid to the brain is approximately 4660 times less than to the thyroid. When tabulated S factors based on standardised phantoms are used to calculate the dose distributions in a patient, the treatment plan is undesirably generic. A further limitation is that it is assumed that the radioactivity is uniformly distributed in the source organ and the mean dose is therefore reported. In reality, the uptake of radioactivity will vary throughout the organ, particularly if there is presence of disease, and it would be more useful to be able to calculate the maximum and minimum dose in the organs of interest. An expanding research field in RNT is the development of computer simulations based on particle transport Monte Carlo. These calculate the theoretical transport of the particles emitted in radioactive decay and track them through the patient, if personalised CT images are available. They depend on knowledge of the physical interaction processes and their relative probabilities for different materials and radiation energies. Although these programs are time-intensive, this makes an important positive step towards personalised treatment in radionuclide therapy.

8-8

IOP Concise Physics

An Introduction to the Physics of Nuclear Medicine Laura Harkness-Brennan

Appendix A Chemical symbols

C N O F Na P Cr Fe Ni Cu Ga Ge As Kr Rb Sr Y Tc In Sn I Xe Re Tl Ra Sm Gd Tb Er Lu U

carbon nitrogen oxygen fluorine sodium phosphorus chromium iron nickel copper gallium germanium arsenic krypton rubidium strontium yttrium technetium indium tin iodine xenon rhenium thallium radium samarium gadolinium terbium erbium lutetium uranium

doi:10.1088/978-1-6432-7034-0ch9

A-1

ª Morgan & Claypool Publishers 2018