A Primer on Engineering Design of Biomedical Devices [2 ed.]

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A Primer on Engineering Design of Biomedical Devices Carl A. Nelson, PhD University of Nebraska

A Primer on Engineering Design of Biomedical Devices Second e-book edition © 2013 by Carl A. Nelson All rights reserved No part of this book may be copied or distributed without written permission of the author.

Table of Contents Unit 1: Understanding Biomedical Systems and Devices Chapter 1: Introduction to Biomedical Device Design ........................................................1 1.1 – The FDA and Device Design .................................................................................1 1.2 – Topics for Thought and Discussion ......................................................................4 1.3 – Problems ................................................................................................................5 1.4 – References for Further Study ................................................................................5 Chapter 2: Defining the Intended Function of a Device ......................................................6 2.1 – Viscoelastic Tissues: Their Properties and Behaviors ...........................................6 2.2 – The Body’s Fluid Systems ...................................................................................17 2.3 – Summary and Relation to Device Design ............................................................23 2.3 – Topics for Thought and Discussion .....................................................................24 2.4 – Problems ..............................................................................................................24 2.5 – References for Further Study...............................................................................26 Chapter 3: Introduction to Biocompatibility ......................................................................28 3.1 – The Bio-Environment ..........................................................................................28 3.2 – Stability and Degradation ....................................................................................29 3.3 – Surfaces and Biocompatibility.............................................................................29 3.4 – Topics for Thought and Discussion .....................................................................31 3.5 – Problems ..............................................................................................................31 3.6 – References for Further Study...............................................................................32 Chapter 4: Introduction to Metals as Biomaterials ............................................................33 4.1 – Corrosion .............................................................................................................33 4.2 – Stainless Steels ....................................................................................................34 4.3 – Cobalt-Chromium Alloys ....................................................................................35 4.4 – Titanium...............................................................................................................35 4.5 – Other Alloys ........................................................................................................36 4.6 – Topics for Thought and Discussion .....................................................................37 4.7 – Problems ..............................................................................................................37 4.8 – References for Further Study...............................................................................38 Chapter 5: Introduction to Ceramics and Composites as Biomaterials .............................39 5.1 – Alumina ...............................................................................................................40 5.2 – Zirconia ................................................................................................................40 5.3 – Calcium Phosphates .............................................................................................40 5.4 – Glass ....................................................................................................................40 5.5 – Carbon .................................................................................................................41 5.6 – Ceramics Overview .............................................................................................41 5.7 – Composites ..........................................................................................................41 5.8 – Topics for Thought and Discussion .....................................................................43 5.9 – Problems ..............................................................................................................44 5.10 – References for Further Study .............................................................................44 Chapter 6: Introduction to Polymers as Biomaterials ........................................................45 6.1 – Types of Polymers and Their Properties .............................................................45 6.2 – Elastomers ...........................................................................................................47 6.3 – Hydrogels.............................................................................................................48

6.4 – Molecular Weight Distributions ..........................................................................48 6.5 – Biodegradation and Hydrolysis ...........................................................................49 6.6 – Topics for Thought and Discussion .....................................................................50 6.7 – Problems ..............................................................................................................51 6.8 – References for Further Study...............................................................................51 Unit 2: Designing Biomedical Devices Chapter 7: Choosing Biomaterials using Performance Indices .........................................52 7.1 – General Guidelines for Choice of Biomaterials ..................................................52 7.2 – Performance Indices for Material Selection ........................................................53 7.3 – Topics for Thought and Discussion .....................................................................55 7.4 – Problems ..............................................................................................................55 7.5 – References for Further Study...............................................................................56 Chapter 8: Defining and Meeting Product Requirements ..................................................57 8.1 – Screening Matrix .................................................................................................57 8.2 – Functional Decomposition...................................................................................58 8.3 – Concept Generation: Morphological Chart .........................................................60 8.4 – Concept Evaluation: Pugh Decision Matrix ........................................................60 8.5 – Axiomatic Design ................................................................................................62 8.6 – Quality .................................................................................................................63 8.7 – Topics for Thought and Discussion .....................................................................66 8.8 – Problems ..............................................................................................................67 8.9 – References for Further Study...............................................................................67 Chapter 9: Techniques for Detailed Design of Devices.....................................................69 9.1 – Design for Manufacture .......................................................................................69 9.2 – Design for Assembly ...........................................................................................71 9.3 – Practical Considerations Relevant to Medical Devices .......................................73 9.3 – Topics for Thought and Discussion .....................................................................74 9.4 – Problems ..............................................................................................................74 9.5 – References for Further Study...............................................................................75 Chapter 10: Failure Analysis and Prevention ....................................................................76 10.1 – Failure and Reliability .......................................................................................76 10.2 – Failure Modes and Effects Analysis (FMEA) ...................................................77 10.3 – Sensitivity Analysis ...........................................................................................79 10.4 – Robust Design....................................................................................................80 10.5 – Topics for Thought and Discussion ...................................................................82 10.6 – Problems ............................................................................................................83 10.7 – References for Further Study .............................................................................83 Appendix A: Table of some polymer properties and typical uses Appendix B: Sample QFD chart for a surgical tool design problem Appendix C: Sample DFA evaluation table Appendix D: Sample FMEA template

Chapter 1: Introduction to Biomedical Device Design The purpose of this text is to introduce concepts of design methodology in the context of biomedical engineering and medical devices in particular. The desired result is that the reader will develop an understanding of the entire process of medical device development, from problem definition through concept generation and refinement to the final product. To some extent, this requires one to become familiar with some aspects of various engineering and science disciplines, including biology, mechanics, kinematics, chemistry, etc. To gain the correct perspective for this study, it is necessary to understand the importance of the various steps that are involved in the design of medical devices and related technologies. Therefore, we will begin by describing the motivation for following a rigorous procedure in design. This will be followed by an introduction to select modeling techniques and other basic information related to the human body, or the environment in which biomedical devices are designed to operate. Material selection, an important step in the design process, will then be discussed. Finally, a variety of techniques and methodologies for design will be presented. 1.1

The FDA and Device Design

The US Food and Drug Administration (FDA) was created in 1906 with the mission of ensuring that products are both effective and safe for consumers. In 1938, the FDA was granted power to enforce its mission. As its name implies, the FDA has jurisdiction over the safety and effectiveness of food products, drugs, and medical devices. We will concern ourselves here only with medical devices. A key to understanding the FDA is to know that it does not regulate the practice of medicine. Rather, it regulates commerce and marketing of products within its jurisdiction. For instance, if a surgeon decides to design a new tool, build a prototype in his garage, and use it on a patient, the FDA has no authority to prohibit this. If he then decides to produce and sell this new tool, he must then abide by the FDA’s regulations. The FDA defines a medical device as a non-drug material intended for use in diagnosis, cure, prevention, or treatment of disease, or one created with the intent to affect the structure or function of the body. An important aspect of any medical device is which structure or function of the body it is intended to affect. Therefore, no device is approved for general use; devices are only approved for specific uses. The process of gaining approval for a medical device from the FDA can involve several steps depending on the type of device. These can include a Pre-Market Notification application, a Pre-Market Approval application, and an Investigational Device Exemption application. For many devices, the minimum basic requirements are to file a Pre-Market Notification, register any business involved in production, marketing, or sale, list the

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device officially with the FDA, follow so-called good manufacturing practices, and maintain detailed records. 1.1.1 Registration and Listing The FDA requires that any company involved in the manufacture, labeling, packaging, or distribution of medical devices register their business with the FDA. These companies must also provide to the FDA a list of all medical devices that they have a part in marketing or producing. 1.1.2 Pre-Market Notification The Pre-Market Notification application is commonly referred to as the 510(k). The goal of this application is to establish that the device in question is “substantially equivalent” to an existing approved device. Substantial equivalence means that the device has the same or similar technological characteristics and is intended for the same use. Existing approved devices are called predicate devices, and a 510(k) application may refer to many predicate devices. Equivalence is claimed by comparing and contrasting features of the new device and the predicates. If the characteristics or functions are different, one must indicate why this does not affect the safety or efficacy of the device. Generally, the 510(k) application also includes samples of labeling, indicating the intended use and function of the device. Data from laboratory evaluations are usually included, but clinical tests are not required. 1.1.3

Clinical Research and Institutional Review Boards

Any entity performing clinical research (on human subjects) must have an Institutional Review Board (IRB). This group of individuals is charged with determining whether the risk to the subjects is equitable, the selection of subjects is equitable, their informed consent is sought and documented, and that their privacy and confidentiality are maintained. The IRB also ensures that test data are monitored to ensure the safety of the subjects. 1.1.4 Investigational Device Exemption Investigational Device Exemption (IDE) applications enable medical devices to be shipped or transported for purposes of clinical trials prior to the device receiving clearance to be sold on the open market. These applications include reports of prior investigations, descriptions of methods, facilities, and controls used, and so forth. They also include samples of agreements between the researchers or investigators, lists of involved IRBs, copies of informed consent forms, samples of labeling, etc.

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1.1.5 Pre-Market Approval The Pre-Market Approval application (PMMA) is a lot like the 510(k) application but is more involved. Generally, clinical research is involved in this step, so an IDE has already been filed. The PMMA includes a detailed description of the device, performance standards used in its evaluation, results of clinical and laboratory testing, and an assessment of the device’s environmental impact. Samples of proposed labeling are also included, as well as samples of the device itself. 1.1.6 Device Classification The FDA classifies devices based on their intended function and the level of risk which may be associated with their use. Class I devices are not life-sustaining, and their failure poses no risk to a person’s life. Therefore, there is no need for performance standards for such devices. In fact, simpler Class I devices can even be exempt from the basic requirements of a 510(k) application. Class II devices are not life-sustaining, but their failure can post some risk of harm. Therefore, these devices must meet specific controls or performance standards. Class III devices are life-sustaining, and/or their failure could pose a serious risk to life or health. Generally, Class III devices require a full PMMA process, which can take years in the current system. In short, the determining factor which decides the device classification is the potential for risk to life and health. Risk can depend on direct effects of device failure, systemic or secondary effects, duration of device contact with the human body, and even the degree of difficulty of failure detection. For devices intended to help restore proper functionalities in the body, one must consider the change in a person’s health relative to the “diseased” state, not necessarily from the fully healthy state, when considering the effects of device failure. Many examples of medical devices and their FDA classification can be found at: http://www.accessdata.fda.gov/scripts/cdrh/cfdocs/cfpcd/classification.cfm 1.1.7 Good Lab and Manufacturing Practices During the device development and testing phase, the FDA requires that so-called Good Lab Practices (GLP) be followed. These include internal audits and inspections, mechanisms for approval of study protocols, and detailed reports of data to support any information provided to the FDA. During the manufacturing phase, Good Manufacturing Practices (GMP) must be followed. The GMP are a list of rules providing a minimum standard of safety throughout the manufacturing process. In short, the GMP stipulate that the design process and manufacturing controls must be documented in detail. Also included in the GMP is compliance with the ISO 9001 industry standard related to quality management.

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1.1.8 Industry Standards Standards are guidelines representing the common viewpoint of manufacturers, users, consumers, and regulators. Compliance with standards is generally voluntary, and in the case of medical devices compliance is not enforceable unless specifically stipulated by the FDA. There are many bodies which publish standards related to medical devices, including AAMI, ASTM, ANSI, and ISO. Most of these standards are published with annual revisions. There are two standards with the highest relevance to biomedical devices. The first of these is ASTM volume 13.01 – Medical Devices. This standard primarily addresses the use of biomaterials in device design. It covers manufacture, chemical requirements, mechanical requirements, test methods and best practices, special tests, and certification. The other important standard related to medical devices is ISO 10993. This is a standard for evaluation of medical devices. Part 1 of the standard helps to decide which types of tests are necessary, and the rest of the standard describes how to perform these tests. Much of Part 1 is summarized in a table at: http://www.ethoxint.com/laboratory/tox-table.htm As in FDA device classification, factors influencing the tests and other recommendations contained in these standards include duration of tissue-device contact and type of contact (e.g., skin-contact devices vs. implanted devices). 1.1.9 Summary As has become evident, the process of bringing a biomedical device to market can be long and involved. Rather than focus on the details of the approval process, let us simply summarize by saying that detailed documentation is the key to FDA compliance. Furthermore, detailed documentation of the steps in the design process can also be used as a tool for achieving effective and high-quality designs. This premise is a primary motivation for the remainder of this text. 1.2

Topics for Thought and Discussion

1) Why is it important to understand the regulations that govern medical devices before starting the design process? 2) Can you summarize the pathways to FDA approval for different classes of medical devices? 3) What is the importance of predicate devices in the FDA classification process? 4) How would you succinctly state the FDA’s mission? What is the most important implication of this for product engineers?

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1.3

Problems

1) Without looking at the FDA database, classify the following devices (I, II, or III). Give an explanation (a few words) of your reasoning for each. Then verify your answers by checking the database. If your assessment is different from what you find in the database, state what assumptions you may have made that caused the difference. Based on information in the database, list the 7-digit regulation numbers, submission type (describing the device approval pathway), and any recognized consensus standard. a) Umbilical clamp/cutter for newborn babies b) Operating room shoe cover c) Surgical knife/scalpel d) Silicone breast implant e) Laser for use in dental soft tissue ablation f) Infusion pump g) Metal orthodontic bracket h) Prosthetic mechanical “hook” limb component i) External cardiac compressor 2) Research and provide a more detailed description of GLP and GMP. 3) Research any specific relevant standard contained in ISO 10993 or ASTM 13.01, and give a detailed description of what it outlines. 4) Visit your IRB’s website, and summarize its particular mission and any interesting information you found there. 1.4

References for Further Study

1) Ethox Intl. Inc., 2013. Toxicology Table, online at http://www.ethoxint.com/laboratory/tox-table.htm. 2) King, P. H. and Fries, R. C. (eds.), 2003. Design of Biomedical Devices and Systems, Dekker. 3) Fries, R. C., 2013. Reliable Design of Medical Devices, 3rd ed., CRC Press. 4) US Food and Drug Administration, 2013. Device Classification Database, online at http://www.accessdata.fda.gov/scripts/cdrh/cfdocs/cfpcd/classification.cfm.

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Chapter 2: Defining the Intended Function of a Device Successfully bringing a medical product to market hinges on FDA approval (or other regulatory bodies, outside the United States). As pointed out in the previous chapter, the approval process is first concerned with identification of the intended function of the device and comparison with devices having similar function. Not coincidentally, analysis of the function of a device is an important part of the design process as well. Systematically identifying the intended device function(s) can sometimes lead to an improved understanding of how those functions might be accomplished. It is important, especially early in the design process, that one distinguish between function (what the device should do) and form (how the function is accomplished). The process of rigorously identifying the functions of a product is called functional decomposition. Typically, one begins by stating the overall function, and then creating descriptions of subfunctions. With the subfunctions arranged logically, the process is repeated (subfunctions are refined) until single actions are obtained. Each low-level subfunction should be stated as a verb, with a possible object (e.g., circulate blood). We will return to the topic of functional decomposition in greater detail in a later chapter. Because medical devices include those which attempt to affect the function of the body, it is important to start with an understanding of how the body works. This knowledge provides a basis from which to design medical devices starting with the definition of intended function. Therefore, the remainder of this chapter is devoted to providing an overview of some characteristics of tissues, organs, and systems in the body, with an emphasis on the engineering perspective, including mathematical modeling. This will aid in determining device function and identifying engineering specifications for devices. 2.1

Viscoelastic Tissues: Their Properties and Behavior

On a very basic level, human tissue is a composite material. The soft tissues of the body are largely made up of two components called elastin and collagen. Simply summarized, elastin gives tissues their compliance, and collagen gives them strength and toughness. 2.1.1 Elastin A long, cross-linked molecule called elastin is the most linearly elastic biosolid known. In terms of mechanical properties (Young’s modulus in particular), elastin (E = 0.6 MPa) can be compared to lightly vulcanized rubber (E = 1.4 MPa).

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2.1.2 Resilin and Abductin Resilin is a protein found in arthropods. Like elastin, it is a long, cross-linked molecule. Its mechanical properties (E = 1.8 MPa, UTS = 3 MPa) are comparable to those of elastin. Another similar material is abductin (E = 1-4 MPa). 2.1.3

Examples of Elastic Tissues

Examples of tissues made up primarily of elastin, resilin, and abductin are manifold in nature. Horses have a large ligament supporting their neck which is made almost entirely from elastin. This special ligament is different from most other ligaments because it does not damp or impede stretch in the ligament; in other words, there is very little energy loss (this is important to the dynamics of galloping). This lack of viscous damping is an inherited property of elastin. Resilin can be found in the wing joints of insects and the leg joints of locusts; this allows them to move without expending as much energy. For example, jumping insects contract their leg muscles to store energy in resilin “springs,” which allows them to release that stored energy very quickly and efficiently simply by relaxing their muscles. Scallops have prestressed hinges made of abductin; a muscle in the scallop keeps the shell closed, and when the muscle is relaxed, the abductin hinge springs the shell open. These are just a few instances of elastic soft tissue in the natural world. 2.1.4 Collagen Collagen is a triple-helix protein whose molecules are arranged in tiny fibrils; these fibrils combine to form fibers. Collagenous fibers are the main load-carrying element in most tissues. For example, most ligaments are almost entirely made of collagen. (This is in contrast to the ligament in the horse’s neck, which is made almost entirely of elastin.) Another example of a collagenous tissue is skin, which is roughly 75% collagen and 4% elastin by dry weight. Collagen (E = 1 GPa, UTS = 50-100 MPa) imparts special properties to tissues. In addition to being much stiffer and stronger, it exhibits nonlinear stress-strain behavior. Under cyclic loading, hysteresis can also be observed in its stress-strain curve. Under constant strain, collagenous tissues relax (stress level drops), and under constant stress, creep behavior is observed. These are all features of a viscoelastic material. 2.1.5 Bone Bone is essentially calcified cartilage. The organic component is mostly collagen, and the inorganic component is called hydroxyapatite (HA). HA is a stiff inorganic crystal (E = 165 GPa) and constitutes roughly two thirds of the bone’s makeup by weight (or one half by volume). Overall, the long load-bearing bones of the body have stiffness in 7

between those of the two component materials (femur in tension: E = 18 GPa). However, the composite material that we call bone is stronger than either HA or collagen alone, attesting to the body’s ability to optimize its performance. Bone’s microstructure is also modulated by stress levels in the bone. When stress is too low, the bone becomes less stiff and less strong; when stress is too high, the bone tissue is resorbed, or broken down. In between these two extremes is a region in which bone is considered healthy. Bone is a “trajectorial” material: more (and stronger) bone tissue is found in areas of high load. This is another evidence of the body’s ability to selfoptimize. The shaft of the long bones is called the diaphysis, and the ends are called the metaphyses. At the surface of the metaphysis is a growth area called the epiphysis. Through its cross-section, the bone can be divided into the medullar cavity (where the marrow is stored), the cortex (where the more dense cortical bone is located), and the periosteum (the outer growth area). This is shown in Figure 2.1.

epiphysis (growth area)

metaphyses

diaphysis

medullar cavity (marrow) cortex (dense) periosteum (growth layer)

Figure 2.1. Anatomy of the long bones. The mechanical properties of bone vary depending on which bone is considered, whether the loading is tensile or compressive, the direction of the loading, etc. For example, bones are typically three times stiffer in tension than in compression. Poisson’s ratio is approximately 0.4 under axial loading and approximately 0.62 under transverse loading. Although both tensile and compressive strength vary with bone specimen, compressive strength appears to vary less. When moisture is removed from bone, it retains its stiffness but becomes brittle, failing near 0.4% strain vs. 1.2% strain for wet bone. Various properties of bone are summarized in Table 2.1. For comparison, consider two other materials: oak (E = 10 GPa, UTS = 100 MPa) and common steel (E = 200 GPa, UTS = 500 MPa).

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Table 2.1. Human bone (adapted from [Yamada 1970]). UTS % E (tension) UCS % (MPa) elong. (GPa) (MPa) contr. Femur 124 1.41 17.6 170 1.85 Femur ~50 ~10 ~125 (transverse) Tibia 174 1.5 18.4 Humerus 125 1.43 17.5 Radius 152 1.5 18.9 ~ Data compiled from [Reilly 1975].

Shear str. (MPa) 54 ~65

G (GPa) 3.2 ~3.3

2.1.6 Cartilage Cartilage is a porous and fluid-filled tissue used to perform load-carrying, joint lubrication, and other functions in the body. Articular cartilage is found in the joints and is slightly stiffer (E = 8-15 MPa) than other cartilage (E = 5-10 MPa). Poisson’s ratio for cartilage is approximately 0.45, indicating that cartilage can be considered nearly incompressible. 3.0 2.7

static load saline

static load synovial fluid

2.4 2.1 1.8 1.5 1.2 dynamic load saline

0.9 0.6

dynamic load synovial fluid

0.3

400

800

1200

1600

2000

Normal stress, kPa

Figure 2.2. Coefficient of friction in joints with cartilage (adapted from [Malcolm 1976]).

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In articular cartilage, the two main functions are load-carrying and lubrication. The cartilage accomplishes these in a fascinating way. Hydrophilic proteoglycans in the cartilage draw synovial fluid into the tissue, swelling the tissue and pretensioning the collagen fibers. In this way, the hydrostatic pressure helps to support loads in the tissue while reducing stress in the tissue. Through viscous effects, fluid is drawn out into the joint interface where sliding contact occurs, providing natural lubrication. This effect is heightened under dynamic loading (such as in the knee joint during walking). The coefficient of friction in the articulated joints is dependent upon maintaining the correct level of normal stress so that a layer of lubricating fluid is kept in the contact area. This is shown in Figure 2.2. 2.1.7 Muscle The body contains three basic types of muscle: heart muscle, smooth muscle, and skeletal muscle. There are two main factors which distinguish these three muscle types: their contractile behavior and their microstructure. Heart and skeletal muscle are striated, meaning that they have a microstructure composed of aligned fibers. As might be expected, the orientation of these fibers dictates the contractile direction of the muscle force. Smooth muscle, as its name indicates, is not striated. It undergoes involuntary rhythmic contractions and is responsible for such functions as moving nutrients through the digestive tract. Heart muscle receives isolated electrical stimuli, causing the pulsed contraction that we are familiar with. Because the length changes in the heart muscle are relatively small, resting tension in the tissue is important. In contrast, skeletal muscle generally undergoes large deformation when it contracts, so resting tension does not have a very important effect on the tissue function. 100/s 40/s Fcontr 10/s

100

200

300

400

t (ms)

Figure 2.3. Muscle tetanization due to electrical impulses. 10

Both skeletal and smooth muscle tetanize; that is, individual electrical stimuli add at high frequency until an apparent constant force is achieved. This is illustrated in Figure 2.3. Hill’s equation can be used to model what happens when tetanized muscle is suddenly released: (v + b)(F + a) = b(Fmax + a) where F = force, v = contraction velocity, Fmax = force generated at initial muscle length, and a and b are constants. An alternate expression is: v = b(Fmax – F)/(F + a)  vmax = bFmax/a This can also be expressed in a dimensionless way as: (v/vmax) = [1 - (F/Fmax)]/[1 + c(F/Fmax)] or (F/Fmax) = [1 - (v/vmax)]/[1 + c(v/vmax)] Typically, 1.2 < (c = Fmax/a) < 4. The characteristic shape of the force-velocity curve given by Hill’s model is shown in Figure 2.4. The main limitation of this model is that it only describes one aspect of muscle behavior (contraction velocity and tensile force based on sudden release of tetanized muscle). Nevertheless, it is a widely used and widely accepted model for muscle.

v

F

Figure 2.4. Force-velocity curve according to Hill’s model. 2.1.8 Musculoskeletal overview The tissues that make up the body’s frame are optimized for their intended functions. For example, bone remodels itself in response to its mechanical environment; this also applies in a lesser degree to ligaments, tendons, and other tissues. Ligaments and tendons strain to about 2-5% under normal operating conditions and fail at 10-15% strain. Tendons are roughly twice as strong as the muscles to which they are connected; this is why tears often occur at the interface between tendon and muscle and not through the middle of the tendon. Figure 2.5 shows the approximate composition of the various components of the musculoskeletal system. It is clear to see that collagen plays a very important role in the organic portion of each of these tissues. In fact, any high-collagen tissue will behave much like tendon once stretched; skin is a good example of this. 11

Bone

Articular cartilage

Ligament

30

22

Tendon 35

40

Water Inorganic matrix

9 69

70

65

Organic matrix

60

Weight percent 8 2

20

10 2.5 2.5

25 10

90

70

Elastin Glycoproteins/other

5 5 65 Percent of organic matrix

Proteoglycans 85

Collagen

Figure 2.5. Composition of bone, cartilage, ligament, and tendon. Due in large part to collagen, all these tissues exhibit a viscoelastic sensitivity to strain rate. This is even true of bone – stress triples and fracture strain halves when going from very low to very high strain rates. Collagen’s viscoelastic behavior can be explained by considering its fibrous structure. The fibers are not perfectly aligned initially. Then, as the tissue is stressed, the fibers align and begin to take the load. This is why some tissue models incorporate many discrete springs that “activate” at different stretch ratios (this is like creating a nonlinear curve from many piecewise linear segments). These characteristics can also be used to avoid or treat injury or illness. For example, because tissues remodel, relax, and creep with loading history, disorders such as scoliosis (deformity of the spine) can be treated through load-based therapy (like a form of weight training). We also take advantage of an understanding of the viscoelastic nature of tissue when we stretch prior to engaging in exercise. This helps the tissue to relax (stretch out) and avoids heightened stress levels during physical exertion. 2.1.9 Modeling Viscoelastic Behavior There are a variety of ways to model viscoelasticity, and each has its advantages and disadvantages. The simplest models use a small number of discrete springs and dampers to represent the continuum of viscoelastic material. For example, the Maxwell model (named after the great James Clerk Maxwell) uses a spring and damper connected in series. The Kelvin-Voigt model (think Lord Kelvin) consists of a spring and damper arranged in parallel. The Maxwell model is good at predicting relaxation behavior (reduction in stress over time when subjected to a constant displacement), and the KelvinVoigt model is good at predicting creep behavior (elongation over time when subjected to a constant stress). A composite of these two is called the Kelvin body or standard linear

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viscoelastic solid. It is composed of a spring and damper in series, with another spring in parallel, as shown in Figure 2.6. c

k

F

F kR

Figure 2.6. The Kelvin body or standard linear solid. Letting x represent the overall displacement in spring kR, and y and z representing the displacements in spring k and damper c respectively, we have: ̇ ̇ ̇ By applying Newton’s third law to the interconnection between the spring and damper, ̇ and by summing forces, ky  kR x  F

Substitution yields ̇ and rearranging the sum of forces, we obtain ( ̇ ̇

̇)

Expressing the damper velocity as the difference of the spring velocities gives ̇ ( ̇ ̇) which can be written as a 1st-order input-output differential equation: ̇

(

) ̇

Defining characteristic time constants c k c  k     1  R  kR  k 

 

the model can be rewritten as subject to the boundary condition

̇

(

̇)

  F (0)  kR  x(0)

The time constant  is the relaxation time for constant stress (which characterizes the rate of decay of displacement), and is the relaxation time for constant strain (which characterizes the rate of decay of force).

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The creep function describes how a material behaves under unit-step force input. To derive the creep function, we assign F = 1 and apply Laplace-domain techniques to obtain the displacement response. F 1    s   x  k R    k R s 

1  1 s  A B X    s  kR    kR s  s kR    kR s

with s being the Laplace variable. Using the technique of partial fractions, the unknown parameters can be found to be A

1 kR

B   

Therefore, the creep displacement function can be expressed in the Laplace domain as 1 X ( s) 

kR  s



1

  kR  kR s 1



and in the time domain (through taking the inverse Laplace transform) as x(t ) 

1 kR

     t /  1  1   e    

  

The characteristic shape of the displacement response curve under a pulsed step input is shown in Figure 2.7. The creep function describes this response during the time period when the pulse is applied.

x

t F t

Figure 2.7. Creep response of a standard linear solid under square-pulse force input. The relaxation function describes how a material behaves under unit-step displacement input. To derive the relaxation function, we assign x = 1 and apply Laplace-domain solution techniques to obtain the force in the body as a function of time. 1  k  k s  A B F   R  R   s  1 s  s 1 s

Using the technique of partial fractions, the unknown parameters can be found to be A  kR

B  kR      

Therefore, the relaxation function can be expressed in the Laplace domain as 14

kR

F ( s) 

      kR    s s 1 

and in the time domain (through taking the inverse Laplace transform) as    F (t )  kR 1  1      

 t /  e 

  

Based on the form of the relaxation function, kR is referred to as the relaxed elastic modulus. The characteristic shape of the force response curve under a step displacement input is shown in Figure 2.8.

F

t x t

Figure 2.8. Relaxation response of a standard linear solid under step displacement input. Creep and relaxation are two special-case behaviors. Even more interesting information is obtained by finding the response of the viscoelastic material to dynamic (periodic) input rather than constant input. To do this, we can again use Laplace-domain techniques. Realizing that the steady-state response of a linear system given periodic input will be a periodic function with the same frequency, we can write the force and displacement as F (t )  eit x(t )  Aeit

where A is an amplification factor or gain, i is equal to the square root of -1, and  is the frequency of the applied force. The purpose in expressing these sinusoidal functions as complex exponentials is so that we notice that differentiation simply results in a multiplication by i. Therefore, for purposes of analyzing the steady-state frequency response problem, the system model can be written as F 1  i    kR x 1  i  

So the force-displacement relation is of the form F  Gx

where G is a function of frequency and is called the complex modulus. The imaginary part describes energy dissipation through viscous damping, and the real part describes elastic energy storage.

15

 1  i   G( )  kR    1  i  

The magnitude of this complex quantity, for any given value of frequency, is called the dynamic modulus: 1   2  2 1   2  2

G  kR

As frequency approaches zero, the dynamic modulus approaches the relaxed elastic modulus, which we can think of as a scaled version of Young’s modulus. Complex modulus G can also be rationalized:  1  i   1  i   G ( )  k R     1  i   1  i    1   2     i         kR    1   2  2  

This is helpful in determining the phase of the steady-state response:           2  1     

  tan 1 

The phase of the response is also indicative of energy dissipation, and tan is called internal friction. Dynamic modulus and internal friction are related in that the fastest rise in dynamic modulus coincides with the peak in internal friction, as shown in Figure 2.9. This occurs at a characteristic frequency of  = ()-1/2.

|G|

tan

.01

.1

1

10

100



Figure 2.9. Dynamic modulus and internal friction of a standard linear solid. 2.1.10 Generalized Viscoelastic Models The basic linear solid model does not always accurately represent the behavior of tissues or materials. This is because a lumped model can never completely capture the behavior of a continuum. When this is the case, it can be advantageous to use a model which is more complex. Such a model can be constructed by adding spring and damper elements to the system. The generalized nth-order model consists of a spring (to represent the relaxed stiffness) arranged in parallel with n Maxwell bodies. Each of the Maxwell bodies contributes a characteristic time constant to the system; as a result, the creep and 16

relaxation functions each contain n exponential terms, the dynamic modulus exhibits n “stair steps” (or a gradual rise if the characteristic frequencies are close together), and the internal friction has n peaks (or a single broad, flat peak if the frequencies are close together). 2.1.11 An Empirically-Based Approach to Viscoelastic Modeling One of the observed behaviors of many tissues is that they stiffen as stress increases. If a linear relationship between stress and stiffness is assumed (reflecting the concept of a uniform distribution of collagen fiber recruitment), then a two-parameter model for stress and strain can be derived. E

d  a   b  d

The solution to this differential equation is   b  cea

From the boundary condition that stress and strain both equal zero simultaneously, we can see that b = c, so the model is   b  bea

The typical procedure is to plot d/d (stiffness) versus  from experimental data and use a linear curve-fit to find the parameter values a and b. Because this model does not account for stiffening due to strain rate, the parameters must be tabulated for various strain rates (to capture the effect of the imaginary component of dynamic modulus). A similar method also typically works for the case of sinusoidal strain profiles; in this case, the parameters are tabulated by frequency. This approach has its limitations. Because of tissues’ viscoelastic nature, hysteresis is observed in cyclic loading. Therefore, different parameters are valid for loading and unloading. Furthermore, the linear relationship between stress and stiffness may not be valid for the entire range of stress, so a piecewise-linear relation may be needed. If this is the case, the various stress ranges can be identified by the intersection of the linear curvefits. 2.2

The Body’s Fluid Systems

2.2.1 The Vascular System Blood vessels are composed of three layers. As shown in Figure 2.10, the inner layer is called the intima, the middle layer is called the media, and the outer layer is called the adventitia. Mechanical properties of blood vessels vary quite a bit throughout the circulatory system. Under small strains, linear elastic behavior is observed. For larger strains, the mechanical behavior becomes nonlinear. As an example of how the mechanical properties of blood vessels can vary even within the same vessel, a few data points are shown in Table 2.2.

17

intima media adventitia

Figure 2.10. Structure of blood vessels. Table 2.2. Pig aorta under small strains – E in kPa. thoracic ascending intima-media 43 448 adventitia 5 112

descending 248 69

As shown in Figure 2.11, the heart circulates more than 5 liters of blood per minute in the average adult. All of the blood becomes oxygenated as it visits the lungs after exiting the right ventricle. Considerable amounts of blood flow to the head, liver, and kidneys, and to the gastrointestinal tract, and so forth, to perform the body’s vital functions. Head

0.75 L/min

Arms Lungs Venae Cavae

RA LA RV LV

5.25 L/min

Aorta 0.25 L/min

Coronary

1.1 L/min

Liver

GI Tract Spleen

0.5 L/min

Kidneys

0.55 L/min

Legs

0.55 L/min

Figure 2.11. Blood flow throughout the body. 2.2.2 Blood Flow Blood is essentially a biphasic fluid consisting of plasma and cells. The plasma is about 90% water. The cells are almost all red cells (erythrocytes), with a relatively small amount of white cells. The red cells typically compose about half of the blood volume. This volume fraction of red cells is called hematocrit (H). 18

The red blood cells exhibit some very interesting behavior. First of all, they have a special biconcave disc shape, kind of like a torus (donut) with a membrane covering its hole. Because of this special shape, the cells can deform easily without stretching the cell membrane. Stretching of the membrane would mean an increase in local energy density and would be observed as heightened viscosity. As a counter-example, a spherical droplet is optimized to have the lowest possible surface area; any deformation of that droplet stretches its surface. The biconcave disc shape allows the cells to deform into an ellipsoidal shape and align with the flow streamlines. Within the blood vessels, the red cells aggregate to form loosely knit structures called rouleaux. Due to velocity gradients in the flow, the rouleaux tumble as they flow, causing disturbances in the flow; the resulting energy expenditure is observed as viscosity. At higher flow velocities, the rouleaux break up. There is also a wall layer effect. Due to higher shear stress along the wall of the vessel, the faster flow occurs in the middle of the flow field. Cells migrate towards this faster flow area, leaving a plasma-rich area near the wall, as shown in Figure 2.12. As smaller vessels branch off of larger ones, the blood flowing into those smaller vessels has lower hematocrit. Therefore, the blood with lowest hematocrit is found in the capillaries. This is necessary since the size of the cells approaches the capillary diameter. The combined outcome of the wall layer effect and the special shape of the red cells produces a remarkable ability to circulate large numbers of red cells throughout the body, oxygenating the tissues.

higher H

flow

lower H

Figure 2.12. The wall layer effect in blood flow. Because of the rouleaux phenomenon, the most basic engineering models for fluid flow do not generally apply to blood. For high shear rates (d/dt > 10 s-1), with the rouleaux largely broken down, blood can be considered a Newtonian fluid with constant viscosity, so  = (d/dt) where  is shear stress,  is shear strain, and  is viscosity. For lower shear rates, Casson’s equation can be used: √ ̇ √ √ where  is viscosity and y is a “yield stress” (finite pressure difference needed to initiate fluid flow). For blood, y = .05 dyn/cm2 = .005 Pa, and  = 3-4 cP = .003-.004 Ns/m2. (Here we use both  and  for viscosity only to differentiate between the two models 19

used.) One can combine the Newtonian and Casson models to obtain a 1-dimensional flow model involving an effective viscosity dependent on strain rate: (√

̇)

√ ̇



r

p1

R

rc

p2

x, u



x, u

Figure 2.13. Flow in a cylindrical tube. Now let us consider Figure 2.13 and take a closer look at the flow problem. For a small cylindrical flow element, the force balance can be written as 2 r   r 2

dp dx

(with the pressure gradient being negative), so the shear stress is  

r dp 2 dx

Substitution into the Casson model gives √





̇

We can define a critical point in the flow field at which the shear stress is equal to the fluid’s yield stress:  rc dp 2 dx 2 y rc  dp dx

y 

From the vessel wall down to this critical radius, the slope of the velocity profile can be expressed as ̇

(√

√ )

with a flat profile as shown in Figure 2.13 inside the critical radius (resembling plug flow). Integration gives u

1 dp  2 2 8  rc  R3 / 2  r 3 / 2   2rc  R  r   for rc  r  R R r  4 dx  3 

and this can be used to calculate the volume flow rate: ̇

̇



( )

( ) As expected, this reduces to Poiseuille flow when the critical radius is zero. 20

This is a laminar flow model. It should be noted that this is quite often not a valid model in much of the vascular system, since in the larger vessels the flow can be very turbulent. The geometry of the vessel is also idealized in this model. 2.2.3 The Respiratory System An average adult takes about 15 breaths per minute, exchanging half a liter of air with each breath. This quantity of 0.5 L is called the tidal air volume, meaning that it is a net value (the difference between the lung volume after inhaling and the lung volume after exhaling). This 7.5 L/min total flow should not be thought of as a local flow rate; the local flow rates are dependent on flow velocity and cross-sectional area in the individual passages of the respiratory system. Within the lungs, small sacs called alveoli are expanded during inhalation, and this is where the oxygen exchange takes place. Only about 5.25 L/min of the total 7.5 L/min actually serves to expand the alveoli. In Figure 2.14, it can be seen that pressure in the lungs is higher during inflation as compared to deflation. This is because of surface tension in the alveoli – they are a bit “sticky.” Gage pressures in the lungs can range in the interval of ±30 mm H2O (±294 Pa) during the inflation/deflation cycle. The shaded volume within the pressure-volume curve represents the work done in breathing. 2

1

10 20 Pressure (mm water)

Figure 2.14. Hysteresis in an isolated dog lung (adapted from [Mead 1957]). The respiratory system is often modeled as a “generational” system. As shown in Figure 2.15, this means that it is a series combination of flow resistances, where each generation of flow resistances includes the effects of multiple parallel airways. A suitable analogy is to think of the system as a tree divided into sections by height, with the higher branches labeled as a higher generation and the trunk as generation 0.

21

trachea

n=0 n=1

main bronchus

n=2 etc.

Figure 2.15. Generational airway model. Using this model, the pressure drop across the nth generation of the respiratory system can be expressed as pn = Rn(dV/dt) Typical values for Rn can be around 20 Pa-s/L, but ultimately the pressure drop is dependent on the geometry of the airways as well as the volume flow rate. This important information is displayed in Table 2.3. Table 2.3. Airway generational properties (adapted from [Weibel 1963]). n dn Ln An Vn generation name diameter length area volume (cm) (cm) (cm2) (cm3) 0 Trachea 1.80 12.00 2.54 30.50 1 Main 1.22 4.76 2.33 11.25 bronchus 2 Lobar .83 1.90 2.13 3.97 bronchus 3 Segmental .56 1.76 2.00 1.52 bronchus 4 Subsegmental .45 1.27 2.48 3.46 bronchus 5 Small .35 1.07 3.11 3.30 bronchus 10 Small .13 .46 13.40 6.21 bronchus 16 Terminal .06 .17 180 29.70 bronchiole 17 Respiratory .054 .141 300 41.80 bronchiole 20 Alveolar duct .045 .083 1600 139.50 23 Alveolar sac .041 .050 11800 591.00 The average air velocity at generation n is un = (dV/dt)/An and the Reynolds number can be computed as Ren = undn/

22

Ren (at dV/dt = 0.5 L/s) 2362 1745 1299 933 605 375 32 1.11 .60 .09 .01

where = 1.2 kg/m3 is the density of air, and  =  = 0.15 cm2/s is the kinematic viscosity of air. One can notice that because cross-sectional areas increase very quickly with generation, Reynolds numbers plummet. The total pressure drop can be attributed to kinetic energy and frictional effects: p = pk + pf where pk is dynamic pressure, and pf is frictional loss. To quantify the losses, one can use an air drag model, where a friction coefficient influences the amount of pressure lost in friction effects: Cf = pf/(½ u2) Without going into excessive detail, we may say that there are different flow regimes, and one must be careful to use formulas for the friction coefficient which are consistent with the type of flow present. Here we consider two different types of laminar flow: Poiseuille flow, which is fully developed, and entrance flow, which is not fully developed (typical of short flow channels). We also consider two different types of turbulent flow, depending on the characteristics of the wall surface. Each of these cases is presented as follows. Poiseuille flow: Cf = 64(L/d)Re-1 Entrance flow: Cf = 6(L/d)1/2Re-1/2 Turbulent flow (Re > 2300), smooth wall: Cf = 0.32(L/d)Re-1/4 Turbulent flow (Re > 2300), rough wall: Cf = kL/d (k = 0.04 typically) So to calculate the frictional pressure losses in a given generation of the airways, one first calculates the flow velocity and Reynolds number based on the volume flow rate. The friction coefficient can then be computed and the pressure drop calculated. Some general observations can be made regarding which flow regimes produce the highest losses. For lower overall flow rates (350 < Re0 < 500), Poiseuille effects tend to dominate. Entrance effects dominate for intermediate flow rates (500 < Re0 < 4000), and rough-walled turbulent effects dominate for 4000 < Re0 < 30000. Moreover, it can be observed that most of the pressure losses occur in the larger airways (0 < n < 8), so dn < 2 mm is considered the “silent zone” where there is not enough sound generated by the friction phenomenon to be easily detected using a stethoscope. 2.3

Summary and Relation to Device Design

The topics discussed in this chapter are intended to provide an overview of some of the common tissues and systems of the human body and to give a perspective based on engineering principles and mathematical modeling. This will facilitate more accurate identification of biomedical device requirements and specifications, which is an important early step in device design.

23

2.4

Topics for Thought and Discussion

1) What are some examples of highly elastic tissues? What are some highly viscous tissues? What substances give each of these their special properties? How might this information influence selection of materials for medical devices? 2) What does it mean that bone is called a trajectorial material? What kinds of devices might interface with bone in a way which could affect this trajectorial property? 3) What substances and properties give cartilage its special characteristics? 4) What causes muscle tetanization? What factors might affect this phenomenon? 5) Can you summarize the mathematical approaches available for modeling viscoelasticity in biologic materials? How might these approaches be useful in designing biomedical devices? 6) What properties and phenomena give blood its special flow characteristics? 7) How does knowing about the geometry and layout of the respiratory system help us to understand potential medical respiratory problems and their possible solutions? 8) In what ways does the adage “form follows function” apply when looking at the tissues and systems discussed in this chapter? 2.5

Problems

1) Stiffness and strength of bone were discussed in this chapter. Find data on 3 other properties of bone and cite your sources. (These could include hardness, dynamic properties, chemical characteristics, etc.) 2) Find two non-wood materials whose stiffness and/or strength is comparable to that of bone. Give specific property values and cite your sources. Give your opinion on their suitability for biomedical applications (either specific applications or in general). 3) You are attempting to lift an object of 10 kg. Your arm is in the quasi-static position shown. The object slips from your hand, freeing your tetanized biceps muscle to contract. Use Hill’s equation to model the angular velocity between your upper and lower arm (initially at 90 deg) as a function of time. Neglect your arm’s inertia, the action of other muscles, or other effects and assume your upper arm to remain motionless. Assume b = 0.5 m/s and a = 1000 N. Plot the arm’s angular speed for a relevant period of time. [Hint: you will need to solve for the initial force in the muscle, and you will need to use the law of cosines to develop a relation between contraction velocity and arm

24

angular speed.]

30cm

muscle

4cm

36cm

load

4) Repeat the previous problem when the initial angle of the forearm is 20 degrees from horizontal, the upper arm is vertical (fixed), and the muscle parameters are b = 0.4 m/s and a = 800 N. 5) Using the given knee diagram, estimate the amount of torque needed to actuate the knee near 0° flexion (standing position) based on friction in the knee joint for a person of (a) 50 kg, (b) 75 kg, (c) 100 kg. Do this assuming both static loading (standing relatively still) and dynamic loading (walking), and comment on the differences. The effective cartilage cross-section area is 10 cm2. [Hint: find the normal stress in the cartilage to help determine the friction level.] femur r = 2.5cm cartilage tibia

6) Repeat the previous problem assuming a smaller individual (r = 2cm, A = 8cm2) for masses of (a) 50 kg, (b) 60 kg, (c) 70 kg. 7) Find and read a research paper that discusses viscoelastic behavior of tissues. You may find online databases available through your library website helpful for finding a relevant article. Give the citation of the paper and list two things that you learned from your reading that the class might find interesting and relevant. Describe how this information might be useful in designing biomedical devices. 8) Find and read a research paper that discusses any of the biomechanics topics addressed in this chapter. You may find online databases available through your library website helpful for finding a relevant article. Give the citation of the paper and list two things that you learned from your reading that the class might find interesting and relevant. Describe how this information might be useful in designing biomedical devices. 9) You are designing a device to circulate the proper amount of blood to a patient’s head. Assuming you plan to use a pulsatile-type pump having a chamber volume of 2.5 cubic centimeters, specify the speed (rpm) at which to operate the pump. Search 25

existing available products to find a small pump which may be suitable for this application, and report on the size, cost, power requirements, etc. of the candidate you find. Also list any perceived inadequacies. 10) You are testing a viscoelastic tissue. You fit a curve to its creep response data, and this function is x(t) = 2(1 + 2e-t/2). You fit a curve to its relaxation response data, and this function is f(t) = 0.5(1 + e-t). Under frequency response, you notice that its internal friction is maximum near  = 0.5 rad/s. In what ways does this material fit or not fit the standard Kelvin model? 11) Repeat the previous problem for creep and relaxation functions of x(t) = 2.5(1 + e-t/3) and f(t) = 0.5(1 + e-t) respectively, and maximum internal friction near  = 0.5 rad/s. 12) A known standard Kelvin tissue material has relaxation response f(t) = 2(1 – 0.5e-t/3). Find its dynamic modulus |G| under sinusoidal input when  = 2 rad/s. 13) Repeat the previous problem for a known creep response of x(t) = 1.5(1 + e-t/4) and  = 5 rad/s. 14) Blood is flowing in a vessel of radius R = 0.5 cm with a pressure differential of |dp/dx| = 10 Pa/m. Find the critical flow radius and the flow rate, and plot the velocity profile (either by hand or using a computer). 15) Repeat the previous problem for R = 1 cm and |dp/dx| = 16 Pa/m. At what value of |dp/dx| does the flow theoretically become plug flow? 16) Find some data on blood flow turbulence (e.g., Reynolds number) in various parts of the circulatory system (cite your source(s)), and use it to make some comments about the flow model derived in this chapter. 17) Find the frictional pressure losses in generations 0-2 of the lungs, assuming an instantaneous volume flow rate of 45 L/min, and rough walls in generation 0 only. Consider tubes to be “short” if the ratio of length to diameter is less than 5. Assuming this is a peak flow rate corresponding to a typical peak inflation pressure of 300 Pa, what is the percentage contribution of these 3 generations to the total frictional losses? 18) Repeat the previous problem for generations 2-4 and a flow rate of 20 L/min, with rough walls only in generation 2. 2.6

References for Further Study

1) Bronzino, J. D. (ed.), 2006. Biomedical Engineering Fundamentals (The Biomedical Engineering Handbook, 3rd ed.), Taylor & Francis. 2) Fung, Y.C., 1981. Biomechanics – Mechanical Properties of Living Tissues, Springer-Verlag. 3) Kutz, M., 2002. Standard Handbook of Biomedical Engineering & Design, McGrawHill. 4) Malcom, L.L., 1976. An Experimental Investigation of the Frictional and Deformational Response of Articular Cartilage Interfaces to Static and Dynamic Loading, PhD thesis, University of California, San Diego. 5) Mead, J., Whittenberger, J. L., Radford, E. P. Jr., 1957. “Surface Tension as a Factor in Pulmonary Volume-Pressure Hysteresis,” Journal of Applied Physiology 10:191196. 26

6) Reilly, D. T., Burstein, A. H., 1975. “The Elastic and Ultimate Properties of Compact Bone Tissue,” Journal of Biomechanics 8(6):393-405. 7) Weibel, E. R., 1963. Morphometry of the Human Lung, Academic Press. 8) Yamada, H. and Evans, F. G., 1970. Strength of Biological Materials, Williams and Wilkins.

27

Chapter 3: Introduction to Biocompatibility Biocompatibility can be defined as the capacity of a device or material to function in close proximity to tissue without eliciting an adverse reaction. For implanted materials, an adverse reaction means that the body treats the implant as a foreign body. When this happens, the body tries to isolate itself from the foreign material. In some cases, the body attempts to extrude the foreign material, or physically force it out of the body. Sometimes a protective wall is built around the foreign material. For small enough foreign particles, so-called giant cells ingest the foreign material and break it down. A biomaterial can be defined as either a synthetic or treated biological material which is used to replace or augment the natural function of tissue. Engineered plastics and ceramics are common examples of synthetic biomaterials, and certain processed graft materials derived from tissue are one example of biologically derived biomaterials. In the context of biomedical device design, the definition of biocompatibility can be extended slightly. Thinking in terms of the functional requirements of a device, one might state that device biocompatibility is the capacity to function in close proximity to tissue without eliciting an adverse reaction, while promoting desirable interactions between tissues and biomaterials, so that tissue function is restored or enhanced. 3.1

The Bio-Environment

Medical devices often need to function in challenging environments. For example, some devices are exposed to extremes in pH, temperature, or stress, or to long-term cyclical demands. As an illustration, a small amount of data is presented in Table 3.1, showing some of the conditions in which medical devices may operate. Table 3.1. Conditions in the typical human-body environment. pH T Stress (°C) (MPa) Gastric 1.0 Core 37 Cortical 0-4 bone Urinary 5.25 Core 20Muscle 4 (disease) 42.5 (peak) Intracellular 6.8 Skin 28 Tendon 40 (peak) Interstitial 7.0 Skin 0Ligament 80 (extreme) 45 (peak) Blood 7.25 Aortic 0.1 valve Mitral 0.15 valve

28

Annual cycles Swallowing 3M Heart contraction Walking

Tens of M 1M

Finger joint motion

1M

3.2

Stability and Degradation

Biocompatibility is sometimes classified by the extent of immune response. An inert material is recognized by the body as foreign, but causes little or no host response. A viable material is treated by the host as normal tissue; it is then resorbed or remodeled. Replant material is native tissue which is harvested, cultured in vitro, and subsequently reimplanted. Immune responses to replant materials can vary. Interactive materials are those which are designed to elicit specific desired responses. These are not necessarily immune responses, but can involve behavior such as restructuring of tissues, for example. Biocompatibility is sometimes quantified by the level of stability of the material or whether it degrades. Biostability can be defined as the capacity to remain in close proximity to tissue without experiencing degradation of properties. (Which properties one measures is dependent on the intended function of the device.) Many biomaterials, especially plastics, are considered biodegradable, meaning that they break down or degrade in biological environments. There are four general categories of biodegradation behavior, and they are not necessarily mutually exclusive. Bioabsorption primarily applies to plastics; it refers to a product dissolving without degradation of individual polymer chains. Bioresorption refers to degraded products being dissolved and metabolized or excreted. Biodegradation is primarily enzymatic degradation. Bioerosion is a less specific term and refers to degradation by any known mechanism. 3.3

Surfaces and Biocompatibility

There are many factors which influence biocompatibility. Especially when one considers the intended function of a device when considering its degree of biocompatibility, these factors may include shape, surface finish, size, mechanical stability, density, stiffness, etc. When focusing on the body’s immune response in particular, biocompatibility is dominated by surface interactions. That is to say, the surface of a biomaterial has much more influence on how biocompatible the material is than what lies underneath. There are two general ways to get desired surface properties in a biomaterial. The first is to choose bulk materials having the desired properties. As this is not always feasible, the second approach is to use surface modifications to increase biocompatibility. There are number of chemical modifications which can be made on surfaces. These generally involve deposition of material on the surface or chemical reactions at the surface. For example, synthetic materials such as polymers can be applied. Coatings of biological materials, such as proteins, can also be applied. Similar techniques also exist for active agents, such as drugs, to be either applied as coatings or embedded in degradable materials. There are also plating processes for creating thin films of metal or oxides on surfaces.

29

Physical modifications, which involve changes in geometry, often at very small length scales, are also important. Polishing and etching are two good examples. Common goals for pursuing these types of treatments include controlling texture or porosity. Sometimes these are achieved through chemical means as well. 3.3.1 Surface Properties There are a number of properties specifically attributed to surfaces which can be important in the bio-environment. These include lubricity, wear resistance, and blood or tissue compatibility. Surfaces can also be made to deliver drugs or to have antimicrobial properties. Lubricity refers to the slipperiness of a substance. This is a property which can be desirable for minimizing local trauma when relative motion between tissues and a device occur. Lubricity can be achieved by reducing surface roughness (e.g., by polishing), keeping a liquid film at the surface interface (remember the hydrophilic proteoglycans in cartilage! – this can be replicated with certain polymer coatings), or otherwise reducing stick-slip behavior. Antimicrobial coatings prevent formation of biofilms, which are common immune responses in the presence of microbes or bacteria. These biofilms can often hinder the correct functioning of medical devices by preventing direct tissue contact. An antimicrobial material will impede attachment of bacteria and will kill those that do attach to the device. A common antimicrobial treatment is to use silver microparticles. In small amounts, the human body tolerates them, but they are toxic to bacteria. Wear resistance is another important property which is often desirable. It is easy to forget that when wear occurs at the surface of a device, tiny particles break off, which are then treated as foreign bodies by the immune system. Wear resistance serves to minimize inflammation and embolization (clotting) that can result from wear. Techniques for improving wear resistance include hardening the surface through chemical or mechanical means, reducing friction, or otherwise reducing the formation of particulates. Blood compatibility refers to reducing adhesion or activation of proteins and blood cells which would normally not occur. There are both chemical and physical approaches to achieving blood compatibility. Heparin is a very common anticoagulant, administered as a drug and also used in medical devices. Another chemical technique is called albumin binding; this refers to recruitment of blood’s natural protection against clotting by binding or attracting the albumin to the device. Physical approaches typically involve preventing adhesion of blood. This can be done by a technique called surface passivation, which refers to coating a surface with hydrophilic polymers, such as hydrogels, in order to keep a liquid layer on the surface. One commonly used hydrophilic coating agent is called phosphorycholine. Tissue compatibility, similar to blood compatibility, involves proper porosity and adhesion or growth factors. The details

30

of the desired characteristics vary with tissue types. Chemical coatings are often used to achieve this. Surface treatments are often used in drug delivery. The goal is to promote healing or enhance device performance through targeting treatment to a localized area. Coatings containing drugs can be applied to device surfaces for this purpose. The drug release rate of such a coating is often the key indicator of its performance. Degradation of polymers, addressed in a later chapter, is a common way to control drug release. 3.3.2 Carcinogenicity When speaking of surfaces and biocompatibility, it is worthwhile to mention carcinogenicity, or the tendency to induce cancer. Carcinogenicity is influenced both by chemical constituents and by physical form. For example, asbestos is considered carcinogenic as a substance, but the danger it poses is dependent on the physical form of the asbestos to which the human body is exposed. Generally, the risk due to carcinogenicity is inversely proportional to the ratio of exposed surface area to volume of the material. Therefore, fibers and fabrics are less carcinogenic than sheets of material, and powders are considered best. When considering asbestos as an example, this may seem counterintuitive, since inhalation of asbestos dust is the key vehicle by which asbestos-related cancer is caused. The explanation for this is that inhalation of the dust is really the only way to get asbestos inside the body; rest assured that implantation of a sheet of asbestos would cause cancer or at least as quickly as inhalation of an equal amount of asbestos dust. Of course, it is always wise to choose materials in view of their basic level of carcinogenicity, and then to decide on a physical form which maximizes the surface area to volume ratio if a cancer risk is identified. 3.4 1) 2) 3) 4) 5) 6)

3.5

Topics for Thought and Discussion What are the various issues covered by the term “biocompatibility”? What are the differences between the various types of material degradation? How do surfaces and surface properties play a role in biocompatibility? What are some important surface properties in biomedical devices? What factors influence the degree to which a material is carcinogenic? What are the relations between the notion of biocompatibility, the ASTM/ISO standards, and the FDA regulations? Problems

1) Research and provide a 1-paragraph explanation of any one of the biocompatibilityenhancing surface treatments mentioned in this chapter. (In other words, fill in the details of how, why, and on what types of devices this treatment is typically performed.) Cite your source(s). 31

2) For each of the following cases, give two specific types of surface treatment that you consider beneficial or appropriate. Start by identifying a method of device/system failure and then indicating a way (surface treatment) to avoid that failure. a) Bearing surface in a knee replacement b) Permanent attachment of a stent within an artery c) Prevention of blood flow blockage during introduction of an arterial catheter d) Implanted drug delivery device e) Adhesive bandage for minor cuts f) Dental implant 3.6

References for Further Study

1) Batchelor, A. W., Chandrasekaran, M., 2004. Service Characteristics of Biomedical Materials and Implants (Series on Biomaterials and Bioengineering, Vol. 3), Imperial College Press. 2) Bronzino, J. D. (ed.), 2006. Biomedical Engineering Fundamentals (The Biomedical Engineering Handbook, 3rd ed.), Taylor & Francis. 3) Ethox Intl. Inc., 2013. Toxicology Table, online at http://www.ethoxint.com/laboratory/tox-table.htm. 4) King, P. H. and Fries, R. C. (eds.), 2003. Design of Biomedical Devices and Systems, Dekker. 5) Kutz, M., 2002. Standard Handbook of Biomedical Engineering & Design, McGrawHill. 6) Ratner, B. D., Hoffman, A. S., Schoen, F. J., and Lemons, J. E., 2004. Biomaterials Science: An Introduction to Materials in Medicine, 2nd ed., Elsevier.

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Chapter 4: Introduction to Metals as Biomaterials Metals are an important class of biomaterials. Metals and alloys are typified by the socalled metallic bond, which consists of an electron cloud shared between positive ion cores. This is a non-directional bond which allows electrons to flow easily without compromising the crystal structure. Because of this electron mobility, metals and alloys are typically good conductors of heat and electricity. Another property imparted by this more flexible bond type is ductility, or the ability of the lattice to shift and deform easily, as shown in Figure 4.1. + + + +

+ + + +

+ + + +

+ + + +

+ + + +

+ + + +

+ + + +

+ + + +

Figure 4.1. Shifting of the crystal lattice due to flexibility of the metallic bond. Alloys form when solute atoms replace solvent atoms (the primary constituent) occasionally, either at lattice points in the crystal structure or interstitially (between those lattice points). Strain in the lattice due to atomic size differences can interfere with deformation, and the result is that alloys tend to have higher strength and/or stiffness as compared to their respective pure metals. Some alloys commonly used as biomaterials include stainless steels, cobalt-chromium alloys, and titanium alloys. 4.1

Corrosion

Corrosion generally refers to an unfavorable reaction of metals with nonmetals, often with oxygen. Oxides are the most stable reaction products of corrosion, and a small amount of oxidation, especially on surfaces, can be a good protection against major chemical damage. Corrosion rates depend on the materials involved, the temperature, other environmental conditions, and the amount of exposed surface area. Galvanic corrosion refers to a so-called battery effect in which two metals in close proximity will corrode due to differences in their electronegativities. When this occurs, one of the two metals will typically corrode more than the other. As an example, it has been found that galvanic corrosion occurs in hip implants when the stem is made of a titanium alloy and the head is made of a cobalt-chromium alloy. Pure elements’ electronegativities can be found tabulated as well as listed on periodic tables of the elements (e.g., Ti: 1.54; Cr: 1.66; Cu: 1.90). Alloys also exhibit effective electronegativity values (e.g., Co-Cr: 1.7-1.8; stainless steels: ~1.8). There are various types of corrosion. Pitting corrosion refers to tiny chunks of metal breaking off from the bulk material. Stainless steels are typically susceptible to this type of problem, but the use of molybdenum as an alloying element can inhibit this. Fretting is a type of corrosion in which wear between surfaces removes the stable oxide layer which would normally protect against corrosion. Crevice corrosion can happen when 33

self-repair (oxide formation) of initial corrosion is limited due to resultant changes in pH which are accentuated in crevices. Fretting and crevice corrosion are often coupled. Corrosion can be enhanced by mechanical stress. Deformation of a material increases its local energy, and this higher energy translates into higher corrosion potential. This is a good motivation for careful handling of metal implants before and during the implantation process so as to minimize the possibility of residual surface stresses from mishandling. Most metal biomaterials form a passive oxide layer, which helps protect against further corrosion. For stainless steels and cobalt alloys, chromium oxide is the protective substance, and titanium oxide forms on titanium alloys. These passive oxide layers are chemically stable, good barriers against the release of metal ions, adherent to the metal surface, hard and abrasion resistant, and self-repairing. Passivation is a process by which a thick oxide layer is intentionally created on a finished part. This is accomplished by a hot acid dip (often nitric or citric acid) followed by a thorough rinse. The duration, temperature, and composition of the acid dip influence the characteristics of the oxide layer. This process can dissolve and remove embedded iron, heat scale, weld tint, etc. in addition to forming the desirable oxide film. 4.2

Stainless Steels

The most common grades of stainless steel used in biomedical applications are AISI 316 and 316L (ASTM F138 and F1350). Most grades have stiffness near 200 GPa. A number of different alloying elements (along with the base element of iron) contribute to the properties of stainless steels. Chromium is the primary constituent which makes stainless steel “stainless.” When alloyed at a minimum of 12%, it forms a passive chromium oxide layer. Nickel is used to increase toughness, and carbon increases strength. Molybdenum is used to help reduce pitting corrosion in saline environments. Trace amounts of manganese and silicon facilitate manufacturing by making the steel easier to form and machine. Nitrogen is used interstitially in F1314, F1586, and F2229 steels to improve strength and pitting corrosion resistance. A common way to increase the strength of stainless steels is through strain hardening (cold working). Heat treatment is commonly used to reduce residual stresses after the strain hardening process, and to restore toughness. Stainless steels cannot be hardened by heat treatment alone, as some other alloys can. Common biomedical uses of stainless steels include fracture fixation (plates, pins), wires, screws, and stents.

34

Table 4.1. Some mechanical properties of various stainless steels. ASTM Material UTS (MPa) YS (MPa) F138 F1314 F1586 F2229

4.3

1015 1350 1140-1240 1340

790 1080 1050-1170 1180

Elongation (%) 25 19 15-19 35

Cobalt-Chromium Alloys

Cobalt-chromium alloys, which also have a stiffness value near 200 GPa, exhibit very good corrosion resistance and have the best wear resistance of common alloys in biomedical applications. Common uses include rods, screws, hip/knee implant components, heart valve rings/struts, etc. Many of the alloying elements used with Co-Cr function just like in stainless steels. Chromium is used to create the passive chromium oxide layer. Molybdenum gives corrosion resistance, and tungsten and nickel are both used to improve wear resistance and toughness. Carbon also helps form carbides, which increase wear resistance. Newer processes for manufacturing Co-Cr components use a technique similar to sintering called hot isostatic pressing (HIP), in which high heat and pressure are applied, to achieve near-net-shape parts. This reduces the need for finishing operations and reduces waste, which is important due to the high cost of these alloys. Table 4.2. Some mechanical properties of various Co-Cr alloys. ASTM Material UTS (MPa) YS (MPa) F75 (cast) 730 560 F75 (HIP) 750 510 F562 790-1790 240-1586 F1537 (low-high C) 1320-1350 900-960 4.4

Elongation (%) 9 16 50-8 26-22

Titanium

Pure titanium and Ti-6Al-4V (titanium alloyed with aluminum and vanadium) are the most common titanium variants in biomedical use. These substances have good corrosion resistance in saline environments and great biocompatibility overall. Their stiffness is generally near 100 GPa, which is half that of stainless steels or Co-Cr. This can be advantageous because is reduces the severity of a phenomenon known as stress shielding. Stress shielding refers to an imbalance in the way load is carried, particularly in bones. When two materials with different stiffness are subjected to the same displacement, as can often be the case when using alloys structurally in the body (e.g., in fracture repair), the stiffer material carries more load and experiences higher stress. If the less stiff material is bone, the bone structure can weaken in response to its reduced loading. Due to titanium’s lower stiffness, the adverse effects of stress shielding are generally less when using titanium structurally in the body. (Refer also to section 2.1.5.) 35

Titanium alloys have their drawbacks. They generally have poor wear resistance and are sensitive to notch fatigue. They are also subject to galling, which is when the protective oxide layer breaks off in tiny chunks. However, titanium is an MRI-compatible material (as are some stainless steels), which is one additional advantage of its use. Common uses include fracture fixation, screws, hip implant stems, etc. Table 4.3. Some mechanical properties of various titanium alloys. ASTM Material UTS (MPa) YS (MPa) F67 (pure) 890 725 F136 (Ti-6Al-4V) 1025 830 F1813* 1060-1100 1000-1060 F1713* 550-1035 345-930 * newer lower-modulus alloys 4.5

Elongation (%) 15 14 18-22 8-15

Other Alloys

4.5.1 Tantalum Tantalum (otherwise known as ASTM 560) exhibits good biocompatibility and excellent corrosion resistance. Its strength and stiffness are lower than those of other alloys generally used in biomedical applications. A key advantage of tantalum is the ability to form porous structures using chemical vapor deposition (CVD) processes for encouraging bone ingrowth, particularly on the bone-contacting side of artificial joint components. 4.5.2 NiTiNOL and Nickel-Titanium NiTiNOL (more commonly known as Nitinol or ASTM 2063) is a superelastic, highly resilient shape memory alloy. This means that it can undergo very large deformations and still return to its original shape. It is considered to have acceptable biocompatibility and corrosion resistance. Its stiffness is fairly low (28-41 GPa). Other nickel-titanium alloys are similar to Nitinol in many ways. They are very resilient and elastic. Common uses of both of these substances include orthodontic wires, catheter guide wires, and stents. 4.5.3 Gold Gold is fairly unique as a pure metal with very good biocompatibility. This, combined with its durability, make it well suited for dental applications, in which it has been used for quite a long time.

36

4.5.4 Amalgam Amalgam is a composite of mercury, silver, and tin. Its primary use has been in dental fillings. Due to concern over long-term presence of mercury in the body, other materials have begun to replace amalgam in dental applications, including ultraviolet-curing polymeric materials. 4.5.5 Platinum Platinum is a metal with fairly good biocompatibility and is most often used in electrodes and leads, where other good electrical conductors such as silver would not be ideal due to problems with biocompatibility. 4.6

Topics for Thought and Discussion

1) How does the atomic-level bonding in metals influence their properties? 2) What are some of the types of corrosion? What can be done to prevent the adverse effects of corrosion in biomedical devices? 3) Describe the composition and typical properties of stainless steels used in biomedical applications. 4) Describe the composition and typical properties of cobalt-chromium alloys used in biomedical applications. 5) Describe the composition and typical properties of titanium alloys used in biomedical applications. 6) What are some other biocompatible metals or alloys and their uses? 4.7

Problems

1) Find a research paper describing biocompatibility of a specific metal or alloy. Write 1 short paragraph summarizing the application being described and the methods used. Write another short paragraph summarizing the findings relating to material biocompatibility and indicating your own ideas for other biomedical applications in which this material could successfully be used. Cite your source. 2) Rank the following material combinations from highest to lowest risk of galvanic corrosion. (Show your reasoning – no random guessing here.) a) Copper with iron b) Titanium with tantalum c) Cobalt with gold d) Cobalt with titanium e) Chromium with tantalum f) Titanium with stainless steel

37

4.8

References for Further Study

1) Batchelor, A. W., Chandrasekaran, M., 2004. Service Characteristics of Biomedical Materials and Implants (Series on Biomaterials and Bioengineering, Vol. 3), Imperial College Press. 2) Bronzino, J. D. (ed.), 2006. Biomedical Engineering Fundamentals (The Biomedical Engineering Handbook, 3rd ed.), Taylor & Francis. 3) Kambic, H. E., Yokobori, A. T. Jr. (eds.), 1994. Biomaterials’ Mechanical Properties, ASTM. 4) King, P. H. and Fries, R. C. (eds.), 2003. Design of Biomedical Devices and Systems, Dekker. 5) Kutz, M., 2002. Standard Handbook of Biomedical Engineering & Design, McGrawHill. 6) Ratner, B. D., Hoffman, A. S., Schoen, F. J., and Lemons, J. E., 2004. Biomaterials Science: An Introduction to Materials in Medicine, 2nd ed., Elsevier.

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Chapter 5: Introduction to Ceramics and Composites as Biomaterials Ceramics are defined as a chemically bonded combination of a metal and a nonmetal. The attraction which holds ceramics together is the ionic bond. Because this bond type involves directed affinity between specific anions and cations, the electron mobility in ceramics is low. Due to this low electron mobility, one can explain many of the properties of ceramics in general. They tend to have high melting points, low thermal and electrical conductivity, and minimal viscoelastic behavior. They are hard, stiff, brittle materials with low fracture toughness, and they are also very chemically stable or inert. One might also guess that the ionic bond makes ceramics strong. However, the fact is that the strength of ceramics depends much more heavily on the size and distribution of defects in the material than the bond strength (this is due to their brittleness). Figure 5.1 gives a qualitative impression of the stiffness, strength, and toughness of ceramics as compared to metals and polymers. It is easily observed that their stress-strain behavior is very linear and that they tend to be stiffer than the other classes of materials, but their fracture strain is so much lower that they are not considered tough materials. 

ceramic

metal

polymer



Figure 5.1. Comparative stress-strain qualities of ceramics, metals, and polymers. There are several ways to strengthen ceramic materials. Because the defects in the material have such an important influence on its strength, increased strength can either be gained by altering the defects to make them less severe or by introducing counteracting effects that help prevent material failure even in the presence of the defects. Two examples of the former are chemical etching and fire polishing. The goal of these treatments is to round the tips of the cracks that exist at the material surface, so that the stresses are reduced and the cracks are less likely to propagate. An example of the latter approach is to heat treat the ceramic material in such a way that there are residual

39

compressive surface stresses. These help to prevent crack propagation, since tensile stress is most likely to cause cracks to grow. 5.1

Alumina

Alumina is a common name for aluminum oxide (Al2O3, or ASTM F603). This is a very inert, very hard ceramic with good biocompatibility and excellent corrosion resistance. It is also a very strong material which exhibits high wear resistance. There are a number of processing techniques that are commonly used with alumina. It can be sintered from an initial state of finely ground particles. Hot isostatic pressing (HIP) is one approach to fabricating components with alumina. Grinding and polishing are common finishing operations to bring parts to their final form. The most common bio-applications in which one finds alumina being used include tooth implants and bearing surfaces in hip and knee implants. This is due to the hardness and wear resistance of this material. 5.2

Zirconia

Zirconia is a common name for zirconium oxide (ZrO2). When combined with Yttria, it can be called by its ASTM designation, F1873. Zirconia is very similar to alumina in its properties. However, it has somewhat lower stiffness and higher strength. 5.3

Calcium phosphates

Calcium phosphates are a class of ceramic materials that includes hydroxylapatite (HA, or ASTM F1185) and tricalcium phosphate (TCP). These are very biocompatible ceramics which are resorbable, making them uniquely suited to certain bio-applications. Because they occur naturally in the mineral phase of bone and teeth, they can form direct chemical bonds with these tissues, which can be used to great advantage. Hydroxyapatite is often used in powder or fiber form for creating composites. It is usually used for implants which experience relatively low loads. It also sees use as a coating material, as well as for bone scaffolds and grafts. However, as a coating, it carries with it a couple of drawbacks. First, because of its low strength, it is susceptible to flaking. Second, because it is so highly crystalline, its absorption rate is low. 5.4

Glass

Glass (ASTM F1538) is actually an important biomaterial. Unlike many of the ceramics discussed to this point, is has an amorphous rather than a crystalline structure. Although 40

glass is brittle and has low strength, so-called bio-glass can be made which develops an adherent interface with tissues and can sustain loading at that interface. Glass is most commonly used as a biomaterial in coatings, in implants which experience low loads, and as a filler in composites (fiberglass). 5.5

Carbon

There are many forms of carbon which can be used as biomaterials. Although carbon is not technically a ceramic, it tends to be classified alongside true ceramics due to its properties and the fact that it is a nonmetal. In fiber form, it is very stiff. So-called pyrolytic carbon is used as a surface coating in cardiovascular applications (to help prevent thrombosis or clotting). As the density of the particular forms of carbon increases, so the mechanical properties (stiffness and strength) are typically increased. 5.6

Ceramics Overview

The following table lists various mechanical properties of some of the materials just discussed. It can be seen that ceramics provide a rather wide range of properties and so can be useful in a number of biomedical applications. Table 5.1. Comparison of various ceramics’ properties. Alumina Zirconia HA E (GPa) 380 190 80-110 Bending 0.4 1 0.147 strength (GPa) Compressive 2100 1500-2000 294 strength (MPa) Hardness 9 6.5 5 (Mohs) Density (g/cc) 3.8 6 3.2 5.7

Pyrolytic Carbon 28 0.4-0.5 517 7 1.7

Composites

The classic composite material is a combination of a tough matrix (often polymeric) and strong fibers. While the matrix is weak and the fibers are brittle in comparison to the matrix, the overall combination is a strong, tough material, embodying the best properties of the matrix and fibers. The strength of the composite is affected by various fiber properties. These include the shape and size of the fibers, their type or composition, their volume fraction in the overall composite material, and the quality of the interface between the fibers and matrix.

41

The behavior of such a composite material in tension (along the fiber direction) can be described based on an isostrain assumption (the elongations of the fibers and of the surrounding matrix are equal). comp = matvmat + fibvfib Ecomp = Ematvmat + Efibvfib where comp is the bulk stress in the composite material, Emat is the stiffness of the matrix, vfib is the volume fraction of fibers in the material, and so forth. Generally, fiber volume fractions of up to 0.6-0.7 are the attainable limit since poor bonding between the matrix and fiber can occur as the amount of matrix material is reduced beyond this point. The sum of vfib and vmat must equal 1. The transverse behavior of the composite (across the fiber direction in compression) can be described based on an isostress assumption (the matrix and fibers are subjected to equal stress). comp = matvmat + fibvfib /Ecomp = vmat/Emat + vfib/Efib Ecomp 

Emat E fib 1  vmat v fib vmat E fib  v fib Emat  Emat E fib

It is sometimes helpful to think of these two cases as if the fiber and matrix components were springs. When load is applied along the fiber direction, the springs are in parallel, and accordingly the overall material stiffness is a linear combination of the component stiffnesses. In the transverse loading case, the springs are in series, and there is a nonlinear relation dictating the overall material stiffness (see Figure 5.2). One can observe that the equation for transverse stiffness resembles equations for equivalent stiffness of series springs or equivalent resistance of parallel resistors in an electrical circuit. E

Et Ec

Emat

0.2

0.4

0.6

0.8

vfib

Figure 5.2. Characteristic shape of stiffness curves (t = tensile [longitudinal] along the fiber direction; c = compressive [transverse] across the fiber direction) as a function of fiber volume fraction. 42

Composite materials bring with them their own set of issues. There are various ways in which these materials can fail in delamination mode. Under tensile loads, the fibers can break or the matrix can crack. If tension is not uniformly distributed throughout the material, debonding of fibers can cause delamination. Under compressive loading, especially along the fiber direction, buckling of the fibers is a common outcome. Furthermore, compressive loads along the fiber directions can induce transverse tensile loads due to the Poisson effect, causing delamination. As should now be apparent, care must be taken when using composite materials to carry loads. Three-dimensional loading situations can be disastrous for an oriented-fiber composite material, as just pointed out, although one of the key strengths of composites is their superior blend of mechanical properties when loaded appropriately to their structural characteristics. Another scenario to be aware of is that fibers in composite materials can tend to wick moisture into the material, leading to an increase in surface area exposed to the bio-fluid environment. This can in some cases lead to increased rates of degradation in polymeric matrices. There are many uses for composites as biomaterials. For absorbable matrix composites, these include fracture repair and tissue scaffolds. Some typical combinations of this type include PLA, PGA, or PDA polymers as the matrix, and PLA, PGA, or bioglass as the fiber. Considerations when using absorbable composites include the resorption rate and the effects of any byproducts that may be produced as resorption occurs. For non-absorbable matrix composites, applications include total joint replacements, dental applications, and so forth. Common materials for this type of composite include polysulfone, PEEK, carbon fiber, glass fiber, and Kevlar. In dental applications, the interfaces between the matrix and fiber and between the composite and the tissue are critical. Materials common to dental applications include organic resins, methacrylate, or urethane ethylene glycol dimethacrylate as the matrix, and quartz, glass, or silica as the fiber. Actually, in this case the term “fiber” is not quite accurate since particulates rather than fibers are generally used as fillers in dental composites. Fillers in composite materials, whether in powder, particulate, or fiber form, tend to increase stiffness, strength, dimensional stability, toughness, and hardness. They also tend to reduce viscous damping effects, decrease the amount of shrinkage encountered, and lower the coefficient of thermal expansion, all while lowering the overall cost of the material. 5.8

Topics for Thought and Discussion

1) How does the atomic-level bonding of ceramics influence their properties? 2) What are some ways to “improve” the properties of ceramics for biomedical device applications? 43

3) What are some of the common ceramic materials used in biomedical devices? What are some of their typical properties? 4) How does orientation of loading and/or fibers affect bulk properties of composites? 5) How do filler materials affect bulk properties of composites? 5.9

Problems

1) You are creating a composite material using a polyethylene matrix with bio-glass fibers. Estimate the stiffness of this material, in both the fiber direction and the transverse direction, when the volume fraction of fibers is 0.2, 0.4, and 0.6. Plot these values on a diagram like Figure 5.2. 2) Repeat the previous problem for the case of a composite of polyethylene with glass fibers. 3) Repeat the previous problem for the case of a composite of polycarbonate with glass fibers. 4) Repeat the previous problem for the case of a composite of polycarbonate with carbon fibers. 5) Find a research paper describing the use of a composite and/or ceramic biomaterial. Write a paragraph summarizing the application in which it was used, the reasons for its use, and some of the issues (e.g., biocompatibility considerations) which had to be addressed. Cite your source. 5.10

References for Further Study

1) Batchelor, A. W., Chandrasekaran, M., 2004. Service Characteristics of Biomedical Materials and Implants (Series on Biomaterials and Bioengineering, Vol. 3), Imperial College Press. 2) Kambic, H. E., Yokobori, A. T. Jr. (eds.), 1994. Biomaterials’ Mechanical Properties, ASTM. 3) Ramakrishna, S., et al., 2004. An Introduction to Biocomposites, Imperial College Press. 4) Ratner, B. D., Hoffman, A. S., Schoen, F. J., and Lemons, J. E., 2004. Biomaterials Science: An Introduction to Materials in Medicine, 2nd ed., Elsevier.

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Chapter 6: Introduction to Polymers as Biomaterials Polymers are perhaps the most versatile class of biomaterials. According to one estimate, about 70% of biomaterials in use are polymeric. By definition, a polymer is a long chain macromolecule with repeating units (called monomers). Polymers are often named for their monomer, following the pattern: polymonomer (e.g., polyester, polypropylene). 6.1

Types of Polymers and their Properties

As shown in Figure 6.1, polymers can be classified according to the number of different monomers they contain or the presence of patterns in the ordering of the monomers. For example, a copolymer contains two different monomers, which can be arranged randomly, alternating, or in blocks. Proteins are essentially very complex polymers with lots of different monomer components. Monomer Polymer Alternating copolymer Random copolymer Block copolymer Terpolymer Protein (many monomers)

Figure 6.1. Classification of polymers by the number and arrangement of monomer units.

Graft on substrate

Graft copolymer

Polymer blend

Ladder copolymer

Figure 6.2. Graft, ladder, and blended polymer structures. As shown in Figure 6.2, polymers can also be classified by their physical structure. This can include graft- and ladder-type structures as well as blended polymers (which are not 45

true copolymers). In Figure 6.3, several important structure types are highlighted. Linear polymers can be crystalline, meaning that the individual polymer chains tend to align and stack together, or amorphous, meaning that the arrangement of polymer chains is much more random. Crosslinked polymers form highly interconnected networks of chains. Note that this is fundamentally different from linear amorphous polymers, which do not form bonds between the various polymer chains where they may come into contact. Linear Branched

Star or dendritic

Linear crystalline

Linear amorphous

Crosslinked network

Figure 6.3. Types of polymer networks. Another important designation regarding graft-type polymer structures is whether the side chains have a preferred orientation. Isotactic polymers have side chains which all face in the same direction, syndiotactic polymers have alternating side chains, and the side chains of atactic polymers have no preferred orientation. The simpler and more regular a polymer’s structure, the more crystalline its behavior will be. That is, its bulk properties will include higher stiffness, strength, and hardness as compared to less regularly structured polymers in general. Atactic versions of a given polymer have less crystalline natures than isotactic or syndiotactic versions of the same polymer. Crystallinity is also affected by thermal history. Quenching treatments create more amorphous structures, and annealing gives more regularity and crystallinity. Isotactic

Syndiotactic

Atactic

Figure 6.4. Isotactic, syndiotactic, and atactic graft polymer structures.

46

Although there are many different ways to classify polymers, there are two basic types. Thermoplastics melt with heat repeatably, regardless of their thermal history. Thermosets cure with initial application of heat, and then decompose if further cycles of high heat are applied. Because of the many and varied properties of polymers, they are often classified into a number of descriptive categories. These include:  Elastomers (highly elastic, generally highly crosslinked)  Hydrogels (hydrophilic)  Interpenetrating networks (self-explanatory)  Dendrimers (star-like or highly branched structures)  Phase change (smart) polymers (can be tailored for precise changes in phase)  Bioinspired polymers (e.g., engineered proteins, see also natural polymers)  Block- and graft-copolymers (see Figures 6.1 and 6.2)  Biodegradable polymers (self-explanatory)  Conductive polymers (self-explanatory)  Polymer blends (not true copolymers)  Organic-inorganic (e.g., sol-gel)  Polymeric composites (composites as in chapter 5, made of different polymers)  Plasticizers/additives (to help in processing other polymers)  Natural polymers (DNA, structural proteins, polysaccharides, collagen, elastin) Polymers can have a variety of special qualities. Their molecular weight distributions can be tuned to yield different versions of the same polymer having different bulk properties. They generally exhibit viscoelastic behavior. They can have special or unusual transitions between the solid and liquid phases (a glassy region). Because their structure is so different compared to metals or ceramics, their characteristic behavior can follow different trends; for example, polymers generally contract when heated rather than expanding like crystalline or other bulk materials. Polymers, again due to their longmolecule structure, tend to dissolve into solution slowly and with difficulty. Because they can exhibit special chemical properties, they often require unique methods for processing and handling. Here it is worth mentioning a couple of specific polymer types with similarities to soft tissues in the human body. 6.2

Elastomers

Elastomers are a class of polymers which are very flexible and can achieve very high strains before failing. They are generally amorphous in structure and lightly crosslinked, which gives them their particular mechanical properties.

47

6.3

Hydrogels

Hydrogels are a group of hydrophilic polymers. They can be made with a wide range of properties, including their swelling ratio (change in volume due to water intake). They are favored in many biomedical applications due to their similarities to soft tissue: high water content, low strength, etc. Because of the way that they interact with water, they can be used for carrying and delivering drugs. 6.4

Molecular Weight Distributions

The molecular weight of a polymer chain is equal to its monomer weight times the number of monomers present in the chain. In any polymer material, there is a distribution of chain lengths. Therefore, the bulk property of molecular weight can be defined in more than one way. The number-average molecular weight is defined as Mn 

1   nx M x N x 1

where N is the total number of molecules in the sample, nx is the number of molecules having x monomers, and Mx is the weight of a single molecule having x monomers (or m·x, if m is the monomer weight). Similarly, the weight-average molecular weight is defined as Mw 

1 W



w M x 1

x

x



1 W



n M x 1

x

2 x

where W = N·Mn is the total weight of the sample and wx is the weight of the molecules with x monomers (or nx·m·x). The difference between these two approaches to molecular weight distribution is shown in Figure 6.5.

Mn - count number in each bin

Mw - weigh contents of each bin

Figure 6.5. Distribution of molecular weights in any polymer sample leads to two different methods for calculating bulk molecular weight. The molecular weight of a polymer has important effects on its properties, as shown in Figure 6.6. Viscosity of the liquid phase, and various measures of strength, increase with polymer weight. The increase in viscosity is due to the increased physical contact between the molecules, and the increase in strength can be similarly explained.

48

commercial range

melt viscosity tensile strength

impact strength

molecular weight

Figure 6.6. Effect of molecular weight on bulk properties. The polydispersity index (PI or PDI) is a measure of the distribution of molecular weights in a polymer. It is defined as PI = Mw/Mn The value of PI is always greater than 1, and usually between 1.5 and 5. This first fact can be observed from the formulas for Mn and Mw just presented, in that Mw is always the greater of the two, as shown in Figure 6.7. The greater the PI, the more irregular the polymer in the size of its molecules. This can correlate strongly with the material’s bulk properties. The more uniform the weight distribution (smaller PI), the more crystalline the bulk mechanical properties will be, in general. Mw Mn # of molecules

molecular weight

Figure 6.7. Histogram-type distribution of molecular weights. 6.5

Biodegradation and Hydrolysis

Various polymers can undergo the one or more of the four types of degradation discussed in chapter 3. They can also experience hydrolysis. Hydrolysis is interaction between water and the chemical groups of a polymer, causing the polymer chains to break apart. Types of polymer groups which are susceptible to hydrolysis include anhydrides, esters, amides, and urethanes. Resistant types include hydrocarbons, halocarbons, and siloxanes. Hydrolysis can be catalyzed by acids, bases, or enzymes. Its products can include acids and amines, resulting in changes in pH. 49

Many different factors can influence rates of hydrolysis. Hydrolysis rate increases with the number of susceptible groups, the hydrophilicity of the polymer, the surface area to volume ratio, and application of mechanical stress, and decreases with crosslinking and crystalline structures. Whether by hydrolysis or more classic biodegradation, there are two principal ways in which the breakdown occurs. In bulk degradation, the initial loss of mechanical properties is followed by loss of mass. An appropriate analogy is the way a sugar cube dissolves in water; it first becomes mushy and then breaks apart. The second mechanism is called surface erosion. This term describes degradation which happens at the surface or polymer/water interface. A bar of soap floating in the bathtub is a reasonable analogy; whereas the surface of the soap is becoming soft and rinsing away, the center of the bar is solid and intact. Copolymerization can affect degradation rates. For example, PGA/PLA copolymer has a lower half-life (faster degradation rate) than either PGA or PLA. Fitting with our analogy, the half-life curve has a bathtub shape when plotted against the copolymerization percentage, as shown in Figure 6.8.

50

100

% PGA

Figure 6.8. “Bathtub curve” describing half-life of PGA/PLA copolymers. It should be clear at this point that there are quite a few factors that influence whether a given polymeric material is suitable for a specific biomedical application. As an aid in beginning evaluation of polymers as biomaterials, a table summarizing some properties and typical uses of a number of polymers is included as Appendix A. 6.6

Topics for Thought and Discussion

1) What are some different types or classes of polymers? How and why do their properties differ? 2) How does molecular weight affect polymer properties? Why is it an important engineering measurement in this context? 3) What types of degradation are typical of polymers? How does the bio-environment influence this? What are some effects of degradation in terms of biomedical device functionality? 50

6.7

Problems

1) You are working with a polymeric material; its composition is as follows. PMMA monomer – C4H8O3 twenty 300-monomer molecules forty 250-monomer molecules thirty 350-monomer molecules ten 400-monomer molecules Find its number-average molecular weight, its weight-average molecular weight, and its polydispersity index. 2) Repeat the previous problem with the following conditions: PTFE monomer – C2F4 thirty 200-monomer molecules fifty 300-monomer molecules eighty 350-monomer molecules twenty 400-monomer molecules 3) Repeat the previous problem with the following conditions: PE monomer – C2H4 forty 300-monomer molecules fifty 400-monomer molecules seventy 550-monomer molecules thirty 700-monomer molecules 4) Find the degradation rates of three polymers. Give the conditions in which the degradation rates apply, and any other information that you feel is important to make this information useful for designing a biomedical device. Cite your source(s). 6.8

References for Further Study

1) Batchelor, A. W., Chandrasekaran, M., 2004. Service Characteristics of Biomedical Materials and Implants (Series on Biomaterials and Bioengineering, Vol. 3), Imperial College Press. 2) Kambic, H. E., Yokobori, A. T. Jr. (eds.), 1994. Biomaterials’ Mechanical Properties, ASTM. 3) Kutz, M., 2002. Standard Handbook of Biomedical Engineering & Design, McGrawHill. 4) Ratner, B. D., Hoffman, A. S., Schoen, F. J., and Lemons, J. E., 2004. Biomaterials Science: An Introduction to Materials in Medicine, 2nd ed., Elsevier.

51

Chapter 7: Choosing Biomaterials using Performance Indices As is by now very apparent, the selection of materials for biomedical devices is one of the key steps influencing how well devices perform. Fortunately, a large amount of information exists to help the designer to choose materials which suit a given application. However, this can sometimes present a problem due to the difficulty of sorting through the volume of data available. This chapter contains some guidelines for using biomaterials information effectively. 7.1

General Guidelines for Choice of Biomaterials

Sometimes it is useful to distill information down to the level of generalizations. So let us begin by presenting a number of generalizations regarding the various classes of biomaterials discussed to this point. Table 7.1 gives a list of pros and cons which are typically true of the material classes, along with specific examples of materials and applications. Table 7.1. General tradeoffs in material selection for biomedical devices. Material Pros Cons Examples Metals

High strength Good wear resistance Ductile energy absorption

Polymers

Resilience Easy fabrication Low density Degradable

Ceramics

Good biocompatibility Corrosion resistance Compressive strength

Composites Good biocompatibility Inert, corrosion resistance High strength

Uses

Low biocompatibility Corrosion Mismatched mechanical properties for most tissues High density Low strength Time-dependent degradation

Stainless 316 Vitallium Titanium alloys Nitinol

Orthopedic screws, pins, plates, wires Rods, staples, nails Dental implants Stent springs

Silastic Teflon Dacron Nylon

Low tensile strength Hard to fabricate Low resilience High density

Aluminum oxides Calcium aluminates Titanium oxides Carbon Ceramiccoated metal Carbon-coated materials

Sutures Stents/vessels Plastic surgery Cements Artificial tendon Hip prosthesis Teeth

Inconsistency in fabrication

Artificial heart valve (carbon on graphite Knee implants (carbon fiberreinforced HDPE)

7.2

Performance Indices for Material Selection

When the requirements imposed on a device are known or can be assumed, the device can be optimized to most fully satisfy those requirements. This optimization can include parameters which describe the material (e.g., its density, stiffness, etc.) as well as parameters which describe the form of the device (its size, shape, etc.). In many cases, these different categories of optimization parameters can be separated or decoupled from each other, creating multiple distinct and individually simpler optimization problems. The optimization process begins by defining an objective or goal function. For example, one might seek a structural beam design which is both light and strong. Then the goal function to minimize might be an expression for the beam’s weight, expressed in terms of some strength characteristic. For a rectangular beam with constant cross section, m  bhL where m is mass, b, h, and L are width, height, and length of the beam, and  is density. In order to express the goal function in a way which can lead to intelligent choice of materials, we must also know or assume what conditions or constraints are imposed on the problem. For example, which parameters are considered fixed, and which are the variables over which to optimize? How is the beam loaded, and what are the physical laws or mathematical models governing the behavior of interest? Let us assume that the beam’s stiffness is fixed and its strength is a variable to optimize (through selection of a particular material). Let us also assume that the beam is loaded with some bending moment M, and its width b is fixed. The beam’s height h is a variable by which the beam can be optimized. Then we have the governing equation and substitutions as follows. My Mh   I 2I 2 I M h bh3 I 12 bh2 M 6 Solving for the free dimensional variable h, 6M h b Substituting this into the goal function gives:    m  L 6Mb  1/ 2    Now that the goal function is expressed as a function of the strength characteristic, we can see how a material’s performance would change with respect to material properties. Specifically, L(6b)1/2 represents the problem geometry, M1/2 represents the conditions in which the beam is required to function, and 1/2 is the material property index specific to the optimization problem for a light, stiff beam under the constraints previously stated. This index is to be minimized, or its inverse is to be maximized. Note that the goal

function is expressed as the product of these three quantities. If the physical, functional, and material parts of the function are not separable, then there is not a clearly defined index for the material selection subproblem. In general, the derivation of indices for material selection can be broken down into several steps:  Define a goal function  Identify the variables, fixed parameters, and constraints  Use governing laws to express the goal function in terms of the parameters of interest  Separate the resulting goal function expression into a product of its physical, functional, and material-specific parts The performance indices can then be used as tools to guide the process of material selection. Often, the material properties appear in the performance indices with fractional powers. When converted to a log scale, however, contours of constant performance appear as straight lines on material property charts, and the fractional powers simply affect the slope of these contours. These log-scale property diagrams are commonly referred to as Ashby diagrams after the individual who pioneered this approach to material selection. They can be very helpful for quickly directing one’s search for appropriate materials by eliminating the bulk of the options characterized by low relative performance. Unfortunately, biocompatibility is not an easily quantified aspect of performance, and inclusion of biocompatibility as a performance criterion remains a difficult aspect of design. It thus falls to the designer to gauge biocompatibility from a heuristic or qualitative standpoint, in addition to the more rigorous quantitative approach of properties-based performance criteria just illustrated. Table 7.2 lists a number of common performance indices encountered in mechanical design. Many other indices can be found in textbooks and specialized software which target this topic.

Table 7.2. Some common performance indices. Conditions Fixed Variables Free Variables Maximize Index Tension load, stiffness, section area strength f/ length Torsion (tube) load, stiffness, section area strength f2/3/ length Beam (tube) load, stiffness, section area strength f2/3/ bending length Plate bending load, stiffness, thickness strength f1/2/ length, width Pressure vessel distortion, wall thickness strength f/ pressure, radius Tension load, stiffness, section area stiffness E/ length Torsion load, stiffness, section area stiffness G1/2/ length Beam bending load, stiffness, section area stiffness E1/2/ length Plate bending load, stiffness, thickness stiffness E1/3/ length, width Pressure vessel distortion, wall thickness stiffness E/ pressure, radius Insulation thickness temp constancy Cp f = failure stress (yield or other); in all cases optimize for minimum weight 7.3

Topics for Thought and Discussion

1) What are some of the general pros and cons of different classes of biomaterials? 2) Can you think of good performance index definitions for some classic biomedical devices? 3) How does the intended function of a biomedical device influence what the performance index (or indices) should be? 7.4

Problems

1) You are designing a cylindrical artificial heart chamber (pressure vessel), and you wish to reduce the weight primarily by varying the wall thickness. You also want the chamber to thermally insulate the blood. Use Ashby diagrams to find 3 materials which are suitable for this application, and choose one of them based on biocompatibility as well as properties from the Ashby diagrams. [You may wish to draw or write directly on prints of the Ashby diagrams.] 2) To a certain extent, a bone repair plate acts like a beam in bending. Derive the material performance index for minimizing weight of the plate when strength is the constraining characteristic and the plate thickness (beam width) is the variable.

3) Derive the material performance index for minimizing weight of the plate when stiffness is the constraining characteristic and the plate thickness (beam width) is the variable. 4) Repeat the previous problem when plate width (beam height) is the variable. 5) A laparoscopic tool consists basically of a long, thin shaft with a gripper at the end. Its shaft is a hollow tube through which a wire is used to actuate the gripper. Derive a performance index for a light, stiff, thin-walled tube of this type under bending loads. Consider the diameter to be fixed and the tube thickness to be the free variable. [Hint: use the fact that this is a thin-walled tube to obtain a simplified moment of inertia expression for use in deriving the performance index.]

7.5

References for Further Study

1) Ashby, M. F., 2005. Materials Selection in Mechanical Design, 3rd ed., Elsevier. 2) Dieter, G. E., 2000. Engineering Design: A Materials and Processing Approach, 3rd ed., McGraw-Hill. 3) Granta Design, 2013. Granta CES EduPack and Teaching Resources, online at http://www.grantadesign.com/education.

Chapter 8: Defining and Meeting Product Requirements When conceptualizing and designing new products, perhaps the most important step is correct identification of the requirements. The design team must ask themselves and/or others the right questions and get accurate answers. For example:  What is the fundamental need being addressed?  What are current products capable of with respect to that need?  Where is the gap between what stakeholders want and what they are getting? In order to design a successful product, one must first identify a niche where a contribution can be made. This is dependent on a number of factors, including the available resources, the market conditions, the state of the art of competing products, etc. 8.1

Screening Matrix

One tool which can help in identifying and/or evaluating niche areas for product development is called a screening matrix. The screening matrix provides a repeatable, mathematical approach to decision making in the early stages of product design. It can incorporate information regarding competition, market conditions, customers, technical feasibility, legal issues, and various other practical considerations. The matrix is based on a 1-5 Likert scale for each consideration, and a 3-point weighting scale on the considerations themselves. It is essentially a scoring rubric such as teachers might use for grading assignments. To use the matrix for a product development scenario, one rates the scenario with respect to each consideration, multiplies the ratings by their respective weights, and sums the results. Although the value obtained has no physical meaning, comparison against other scenario results gives a qualitative way of deciding which product development scenario(s) to pursue. An example of a screening matrix for selecting new products to pursue is shown in Table 8.1. This approach to early decision making is very similar to the concept of quality, as will be shown later; the difference is that quality is measured from the customer’s perspective, and the screening matrix is used to make decisions based on the producer’s or company’s perspective.

57

Table 8.1. Screening matrix for selecting new products to produce. Consideration/Feature

Weight

Excellent (5)

Above avg. (4)

Avg. (3)

Below avg. (2)

Poor (1)

Est. profit/yr.

2

>50%

30-50%

20-30%

10-20%

10k

8-10k

5-8k

2-5k

50%

35-50%

20-35%

5-20%

1

0.8

Cheap

Catheters, tubing, bags Dialysis membranes Lenses, housings, etc.

Hydrocephalous shunt Adhesives etc. Hemodialysis membranes Pacemaker lead Artificial heart components Tubing Knitted vascular grafts, sutures, tendon reconstruction

y

See PGA

16

80

y

Degrades 5 times slower than Drug delivery PLA/PGA Elongation 1 order of magnitude higher than PLA/PGA Degrade enzymatically

20

220

0.3

50

Degradation by surface Drug delivery erosion enhanced by adding acidic or basic excipients

y

Degrade by surface erosion Drug delivery Inert, resistant to degradation, Drug delivery, catheter and can be heat sterilized other device coatings, soft contact lenses, dressings See PHEMA

-acrylamide -glyceryl methacrylate -methacrylic acid -ethylene glycol

PAAm

-vinyl alcohol -ethylene oxide

PVA PEO

See PHEMA See PHEMA See PHEMA See PHEMA Water soluble but crosslinks to form hydrogel Non-toxic Protein resistant See PHEMA See PEG

PEG

24 - 110

0 - 300

Sutures Bone screws Scaffolds Drug delivery

y

PNVP

230

Sutures Heart valve components Vascular graft Membrane patches Coatings

2-6

-N-vinyl pyrrolidone

85

Tubing (medium MW)

No toxic products Tough

-anhydrides Hydrogels -hydroxyethylmethacrylate PHEMA

Hard contact lenses Dentures Hemodialysis membranes Hip joints (UHMW)

Clear, tough, bio-stable

y 55

Hard and amorphous Good toughness Monomer not too toxic Amorphous, branched – LDPE Crystalline, linear – HDPE, UHMWPE Crystalline – isotactic Amorphous – atactic Repels most other molecules Low friction Excellent biocompatibility Highly crystalline Amorphous Elastomeric due to flexible SiO bonds Highly crystalline Large family Can H-bond – crystalline Can be elastomeric Tough, strong, stable Tough Relatively inert

y

-hydroxyalkanoates -ortho esters

Uses

More transparent than glass Bone cement

Plexiglas Lucite -ethylene

Comments

Appendix B: Sample QFD chart for a surgical tool design problem

+

+ + +

-

+

+

D

D

U

D

U

motor speed

actuation force

1

1 1 1 1 9 1 1

3

1

1 1 3

1

1

9 3

3

3 3 9

3

1

3 1

9

3 1

9 1

9

1

3

1 1 1 3 1

1 1 1 1

3 3 3 3

9 3

3 1

1

4 4 4 4 5 3 5 4 2 2 2

1 1 1 1 1 1 1 1 1 0.9 2.5

4 4 4 4 5 3 5 4 2 1.8 5

0.05 0.05 0.05 0.05 0.06 0.04 0.06 0.05 0.02 0.02 0.06

3 4 5 4 3

0.8 1.2 1 2.5 1

2.4 4.8 5 10 3

0.03 0.06 0.06 0.12 0.04

1 3 2 2 1 2 3

1 1 1 2 1 1 0.9

1 3 2 4 1 2 2.7

0.01 0.04 0.02 0.05 0.01 0.02 0.03

82.7

1

1 9 1 3 9

9 3 9 1

1

3

3

1 1 9

1 1 3 3

Competitive Evaluation

9 1

3 9

1

9

D

Weight

D

material type

D

9

1

+

+

Importance

+

motor size

+

power requirement

+

CG location

3

handle size

length

D

weight

3 1

9

1

1

3 1

1

1

1

3 3 3

4

5

4

4

3

5

4

5

5

3

5N

50 ksi 50 ksi

stainless/ stainless/ plastic plastic

8s

Current tools

Target Value

30 s

5

0

3

1 in

Technical Difficulty (1-5)

0

1.3 10

5W

1.8 14

0

0.8 6

0

1.7 13

10 mm

1.3 10

10 mm

1.3 10

4 in

0.7 6

4 in

0.7 5

12 in

0.4 3

12 in

1.4 11

8 oz

0.4 3

16 oz

1.1 8

5N

S

Technical Evaluation Absolute importance Relative importance (%)

1000 rpm 0

Customer Needs Features Cuts well Grasps well Retracts well Dissects well Can be operated with 1 hand Is durable - won't break Is robust - always works right Is self-contained Is reusable Is quiet Is adaptable/scalable Ergonomics Is light Has comfortable grip Is easy/intuitive to use Promotes easy/fast tool change Uses hand motion efficiently General Consumes low power Is mobile/portable Is easy to sterilize Uses OR space efficiently Is easily integr. with existing equip. Looks good/attractive Is low in cost

-

-

shaft diameter

+

Goal (Up/Down)

+

Improvement ratio

-

+

material strength

+

+

Priority (1-5)

+ +

time between tools

+

13 100

Appendix C: Sample DFA evaluation table

Part

Retrieve

Handle

Insert AL = alignment difficult NTD = not top down HIP = hold in place

Small Tangled Flexible