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Mechanical properties of tracheal cartilage Rains, Jeffrey K. 1989

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M E C H A N I C A L P R O P E R T I E S O F T R A C H E A L C A R T I L A G E B y J E F F R E Y K . R A I N S B A S c . University of Toronto A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF APPLIED SCIENCE in THE FACULTY OF GRADUATE STUDIES CHEMICAL ENGINEERING We accept this thesis as conforming to the required standard THE UNIVERSITY OF BRITISH COLUMBIA July 1989 © J E F F R E Y K . R A I N S , 1989 In presenting this thesis in partial fulfilment of the requirements for an advanced degree at the University of British Columbia, I agree that the Library shall make it freely available for reference and study. I further agree that permission for extensive copying of this thesis for scholarly purposes may be granted by the head of my department or by his or her representatives. It is understood that copying or publication of this thesis for financial gain shall not be allowed without my written permission. Department The University of British Columbia Vancouver, Canada DE-6 (2/88) A B S T R A C T Large airways collapse has been implicated as one of the causes of maximal expiratory flow limitation. Since cartilage plays an important role in maintaining the form of these airways, an understanding of the mechanical properties of the cartilage is necessary for a better understanding of the mechanisms which l imit maximal expiratory flow. This work establishes a technique whereby the tensile stiffness of human tracheal cartilage can be determined using uniaxial equilibrium tensile tests. A technique was developed in which standard shaped specimens were cut from tracheal cartilage rings and tested in a specially designed tensile tester in order to determine the stress-strain relationship of the specimen. The stress-strain relationship of the cartilage test specimens was found to be linear up to approximately 10 % strain. However, irreversible disruption of the cartilage matrix occurred at strains greater than 10 %. The tensile stiffness of the tracheal cartilage fell i n the range 1-20 M P a and was found to decrease with increasing depth from the outer surface of the tissue. This layer-wise variation in tensile stiffness reflected the orientation of the collagen fibrils in the tissue. A n age-related increase i n the tensile stiffness of tracheal cartilage was found. This age-related change in tensile stiffness may reflect an increase in collagen cross-Unking in specimens from older individuals. A possible bias of the test method toward the measurement of the mechanical properties of the collagen fibrils, as opposed the combined effects of the collagen and proteoglycans, was suspected. However, to the extent that equilibrium tensile testing reflects the ability of tracheal cartilage to bend in response to alterations in transmural pressure, these results suggest that age-related changes in large airway cartilage stiffness are not the cause of the age-related decrease in maximal expiratory flow. i i A C K N O W L E D G E M E N T I would like to thank my supervisors, Dr . Joel Bert of the Department of Chemical Engi-neering and Dr . Peter Pare of the Respiratory Division of the Department of Medicine at the University of Brit ish Columbia, for their guidance throughout the course of this work. A great number of people made a signicant contribution to the expedient completion of this thesis; their names and main areas of contribution are listed below. Trevor Blogg - Assistance with M P T T Jenny Hards - Collection of tracheas Andre Mackenzie - Preparation of cartilage for S E M Stuart Greene - Photography Lyle Kil lough - Assistance with M P T T Peter Roberts - Construction of clamps Dr . Clive Roberts - Cartilage biochemistry and biomechanics Dr. R. Romilly - Mechanical engineering aspects of the project Socksie (my cat) - Typing and editing the final manuscript Joanne Sunahara - Assistance wi th the vibrating microtome David Taylor - General scope of the project Dr. David Walker - Scanning electron microscopy Barry Wiggs - Statistical analysis of data Finally, I would like to dedicate this work to the green cylindrical bin in my back alley. I'm sure it wi l l be in good company. i i i Table of Contents A B S T R A C T ii A C K N O W L E D G E M E N T iii List of Tables List of Figures * . 1 I N T R O D U C T I O N 1 2 P H Y S I O L O G I C A L P R I N C I P L E S 5 2.1 Collagen 6 2.2 Proteoglycans 8 2.3 Water 13 2.4 Structural Organisation of Cartilage 14 2.5 Interaction Between Matr ix Components in Cartilage 16 2.6 Correlation of the Mechanical Properties of Cartilage with its Chemical Composition 17 2.7 Effect of Ageing on Cartilage 22 3 T I S S U E P R E P A R A T I O N A N D T E N S I L E T E S T I N G 26 3.1 Tissue Preparation 26 3.1.1 Storage of Cartilage 26 3.1.2 Specimen Preparation for Testing 27 IV 3.1.3 Measurement of Specimen Dimensions 30 3.1.4 Tissue Bathing Solutions 34 3.1.5 Specimen Clamps 35 3.2 Principles of Tensile Testing 35 3.2.1 Effect of Strain Rate on Cartilage Tensile Tests 36 4 M A T E R I A L S A N D M E T H O D S 38 4.1 Collection and Storage of Tracheas 38 4.2 Sectioning of Tracheal Cartilage 39 4.3 Tensile Tests 40 4.3.1 Calibration of Tensile Tester 43 4.3.2 Testing of the Material Standards 43 4.3.3 Tensile Testing of Tracheal Cartilage 47 4.4 Biochemical Analysis of Tracheal Cartilage 53 4.4.1 Water Content 53 4.4.2 Proteoglycan Content 54 4.5 Scanning Electron Microscopy of Tracheal Cartilage 54 4.5.1 Dry Fracture Technique 54 4.5.2 Wet Cut Technique 55 4.6 Data Analysis 55 5 R E S U L T S 57 5.1 Calibration of the M P T T 58 5.2 Results of the Tensile Tests 58 5.2.1 Estimation of the M a x i m a l Measurement Error Associated with the Calculation of Stress and Strain 59 5.2.2 Comparison of the Results obtained using the M P T T and T A T T . 59 v 5.2.3 Results of Tensile Tests Performed on Tracheal Cartilage 60 5.2.4 Scanning Electron Micrographs of Tracheal Cartilage 77 5.2.5 Results of Biochemical Analyses of Tracheal Cartilage 93 6 D I S C U S S I O N 98 6.1 Analysis of the Results of the Tensile Tests 99 6.1.1 Analysis of the Max imum Measurement Errors Associated W i t h the Calculation of Stress and Strain 99 6.1.2 Comparison of the Results Obtained using the M P T T and T A T T to Test the Material Standards 100 6.1.3 Analysis of the Stress-Strain Curve of Tracheal Cartilage 101 6.2 Physiological Significance of the Tensile Tests Performed on Tracheal Car-tilage I l l 6.2.1 Tensile Stiffness as a Measure of the Abi l i ty of the Cartilage to Maintain Form In Vivo I l l 6.2.2 Physiological Significance of Layer-Wise Variations in the Tensile Stiffness of Tracheal Cartilage 116 6.2.3 Physiological Significance of the Age-Related Changes in the Ten-sile Stiffness of Tracheal Cartilage 117 7 C O N C L U S I O N S 119 8 R E C O M M E N D A T I O N S 121 Bibliography 123 A N O M E N C L A T U R E 132 VI B G L O S S A R Y 134 C C A L I B R A T I O N C U R V E O F M P T T 136 D D E S C R I P T I O N O F K R E B S B U F F E R 138 E L I N E A R R E G R E S S I O N O N E X P E R I M E N T A L R E S U L T S 139 E . l Least Squares Linear Regression 139 E.2 Least Squares Linear Regression Forcing the Regression Line Through the Origin 141 E . 3 Tables of Linear Regression Coefficients for Cartilage Tension Tests . . . 142 F W E I G H T E D L E A S T S Q U A R E S R E G R E S S I O N 147 F. l Statistical Mode l 147 F.2 Est imation of Individual Lines 149 F.3 Est imation of Variance Components 151 F.4 Est imation of Weight Matrices 152 F.5 Results of Weighted Least Squares Regression on the Tracheal Cartilage Tensile Tests 154 F.6 Restricted M a x i m u m Likelihood Technique 154 F.7 Results of R E M L Regression on the Tracheal Cartilage Tensile Tests . . . 155 G P E A R S O N C O R R E L A T I O N C O E F F I C I E N T 157 H E R R O R A N A L Y S I S 158 H . l Measurement Error 158 H . l . l Measurement Error in the Stress Calculation 158 H . l . 2 Measurement Error in the Strain Calculation 159 vii H.1.3 Sample Calculation of Stress, Strain and Measurement Errors . . 161 H.2 Tables of Experimental Results 163 vm List of Tables E . l Linear regression values for the cartilage tensile tests 143 E.2 Linear regression values for the cartilage tensile tests 144 E.3 Linear regression values for the cartilage tensile tests 145 E . 4 Linear regression values for the cartilage tensile tests 146 F. 5 Results of weighted least squares regression on the tracheal cartilage tensile tests 154 F.6 Results of REML regression on the tracheal cartilage tensile tests 155 IX List of Figures 1:1 The trachea and major bronchi. Reproduced from Weiss [104] 2 2.1 General organisation of the helical segment of type II collagen. (Reproduced from Serafini-Fracassini and Smith [93].) 6 2.2 (A) Diagram of cartilage proteoglycan molecule. Reproduced from Muir [77]. (B) Schematic representation of proteoglycan aggregates. R eproduced from Muir [77] and Myers [78]. HA, hyaluronic acid; CS, chondroitin sulphate; KS, keratan sulphate; PG, proteoglycan molecule; Subunit, proteoglycan molecule. 9 2.3 The repeating disaccharide unit of chondroitin 4-sulphate. Reproduced from Muir [77] 10 2.4 The repeating disaccharide unit of chondroitin 6-sulphate. Reproduced from Muir [77] . 11 2.5 The repeating disaccharide unit of keratan sulphate. Reproduced from Muir [77] 11 2.6 Diagram of the layer-wise variation in structure in articular cartilage. Adapted from Clarke [13] and Meachim and Stockwell [70] 15 2.7 The effect of proteoglycan degradation on the tensile stiffness of articular cartilage. Specimen oriented (a) parallel, (b) perpendic ular to the surface orientation of the collagen fibrils . Surface layer: (•) before treatment with trypsin; ((J) after 24 h in trypsin; ( O ) after 48 h in trypsin. Middle layer: ( A ) before treatment with trypsin; (i^) a fter 24 h in trypsin; ( A ) after 48 h in trypsin. Reproduced from Kempson [49] 18 x 2.8 The effect of collagenase on the mechanical properties of cartilage in tension. Surface layer, parallel to surface collagen fibril or ientation: (•) before collage-nase treatment; ( o) after 24 h in collagenase. Middle layer, parallel to surface collagen fibril orientation: ( A ) before collagenase treatment; ( A ) after 24 h in collagenase. Middle layer, perpendicular to surface collagen, fibril-orientation: ( y ) before collagenase treatment; ( y ) after 24 h in collagenase. Reproduced from Kempson et al. [50] 19 2.9 The effect of the enzyme leucocyte elastase on the mechanical properties of cartilage in tension. Superficial zone: (•) befo re elastase treatment; (o) after 72 h in elastase. Deep zone: ( A ) before elastase treatment; ( A ) after 72 h in elastase. Reproduced from Bader et al. [5] 21 2.10 Three sizes of proteoglycans showing a constant hyaluronic acid binding region and shorter chondroitin sulphate-binding region with decreasing length of the protein core. Reproduced from M uir [77] 24 2.11 The effect of aging on the size of proteoglycan aggregates. Reproduced from Roughiey and Mort [91] 25 3.1 A typical base sledge microtome. Reproduced from Culling et al [16] 28 3.2 A typical vibrating microtome 29 3.3 Illustration of Saint-Venant's principle using photoelasticity. The alternating light and dark bands give an indication of the stress pattern within the material. Reproduced from Durelli [2 0] 31 3.4 The effect of changing the bathing fluid on the tensile stiffness of cartilage. Reproduced from Akizuki et al [ 2] 34 3.5 The effect of strain rate on the tensile stiffness of cartilage. Reproduced from Li et al [61] 37 x i 4.1 Illustration of how the curved cartilage strips were flattened for microtome sectioning 39 4.2 Close-up view of the tracheal cartilage glued to the sectioning dish clamped to the vibrating microtome 41 4.3 Photograph of the Multi-Purpose Tensile Tester usedrto perform the tensile tests on the cartilage 42 4.4 Photograph of the control panel of the Multi-Purpose Tensile Tester 44 4.5 Photograph of the Thwing Albert Tensile Tester used to test the material standards 46 4.6 Titanium clamps used to grip the ends of the cartilage test specimens. . . . 48 4.7 The organ bath used to immerse the cartilage specimen in Krebs buffer during the tensile test. Note: 1) the jacket around the organ b ath which allows the bathing fluid to be maintained at physiological temperature, 2) the flat glass window which allows the cartilage test specimen to be viewed without distortion. 49 4.8 Close-up view of the test specimen immersed in the organ bath and attached to the M P T T 50 4.9 Photograph of the PTI optical micrometer positioned to measure the elonga-tion of the test specimen 51 5.1 Results of experiments comparing the stress-strain curves obtained using the M P T T and T A T T to test three materials used as testing st andards. A) Entire stress-strain range measured for tan gum rubber. B) Close-up of the stress-strain curve shown in (A). C) Entire stress-strain range measured for latex tubing. D) Entire stress-strain range measured for tygon tubing 61 X l l 5.2 Results of tensile tests performed on tracheal cartilage slices. A) and B) Stress-strain curves for humans #1 and #2 respectively. C) and D) Tensile stiffness vs. layer number for human #1 and #2 respectively 62 5.3 Results of tensile tests performed on tracheal cartilage slices. A) and B) Stress-strain corves for humans #3 and #4 respectively. C) and D) Tensile stiffness vs. layer number for human #3 and #4 respectively 63 5.4 Results of tensile tests performed on tracheal cartilage slices. A) and B) Stress-strain curves for humans #5 and #6 respectively. C) and D) Tensile stiffness vs. layer number for human #5 and #6 respectively 64 5.5 Results of tensile tests performed on tracheal cartilage slices. A) and B) Stress-strain curves for humans #7 and #8 respectively. C) and D) Tensile stiffness vs. layer number for human #7 and #8 respectively 65 5.6 Results of tensile tests performed on tracheal cartilage slices. A) and B) Stress-strain curves for humans #9 and #10 respectively. C) and D) Tensile stiffness vs. layer number for human #9 and #10 respectively 66 5.7 REML regression results for layers #1-6 of all of the human subjects combined. Although the regression was performed only on the data which fell between 0-10 % strain, for clarity, the regression lines are plotted up to 20 % strain. . 69 5.8 Stress-strain curves of tracheal cartilage representing four tensile tests per-formed on layer #4 obtained from four di fferent cartilage rings of human #3. 70 5.9 Results of hysteresis experiments performed on the stress-strain response of tracheal cartilage. Human #7 was 20 years old 71 5.10 Results of hysteresis experiments performed on the stress-strain response of tracheal cartilage. Note that in parts (B), (C) and (D) the decreasing portion of the stress-strain curve is su per-imposed on the increasing part. Human #8 was 60 years old 72 xi i i 5.11 Results of hysteresis experiments performed on the stress-strain response of tracheal cartilage. Note that in part (C) the decreasin g portion of the stress-strain curve is super-imposed o n the increasing part. Human #8 was 60 years old 73 5.12 Results of hysteresis experiments performed on the stress-strain response of tracheal cartilage. Humans #9 and #10 were 18 and 21 years old respectively. 74 5.13 Results of hysteresis experiments performed on the stress-strain response of tracheal cartilage. Human #10 was 21 years old 75 5.14 The effect of maximal strain on residual strain 76 5.15 Tensile stiffness of tracheal cartilage as a function of age. A) The tensile stiffness' of layers #1-3 are averaged. B) The tensil e stiffness' of layers #4-6 are averaged. C) The tens ile stiffness' of layers #1-6 are averaged. . 78 5.16 Scanning electron micrograph of tracheal cartilage showing the smeared region where the cartilage was cut with a razor blade and the fibrous region where the cartilage was dry fractured 79 5.17 Scanning electron micrograph of tracheal cartilage showing the border between the region which was cut with the razor blade and the region which was dry fractured. The craters are lacunae 81 5.18 Scanning electron micrograph of tracheal cartilage showing a close-up view of a lacuna and aligned collagen fibrils oriented perpend icular to the cartilage surface 82 5.19 Scanning electron micrograph of tracheal cartilage showing the diameter, alignment and charged ends of the collagen fibrils. 84 5.20 Scanning electron micrograph of tracheal cartilage showing the division of the tissue into three ultrastructural zones 85 xiv 5.21 Scanning electron micrograph of tracheal cartilage showing the change in the orientation of the collagen fibrils between the middle zone and the inner su-perficial zone 86 5.22 Scanning electron micrograph of tracheal cartilage showing the transition re-gion between the middle zone and the inner superficial z one. 88 5.23 Scanning electron micrograph of tracheal cartilage showing the layered ar-rangement of the inner superficial zone at low magnificatio n 89 5.24 Scanning electron micrograph of tracheal cartilage showing the layered ar-rangement of the inner superficial zone at high magnificati on 90 5.25 Scanning electron micrograph of tracheal cartilage showing the outer superfi-cial zone at low magnification 91 5.26 Scanning electron micrograph of tracheal cartilage showing the outer superfi-cial zone at high magnification 92 5.27 Correlation of the biochemical composition of tracheal cartilage with age. Glycosaminoglycan content expressed on A) a dry weight ba sis and B) a wet weight basis. C) Cartilage water conte nt 94 5.28 Correlation of the tensile stiffness of tracheal cartilage with the total gly-cosaminoglycan content expressed as a percentage of the cartilage wet mass. A) The tensile stiffness' of layers #1-3 are averaged. B) The tensile stiff-ness' of layers #4-6 are averaged. C) The tensile stiffness' of layers #1-6 are averaged 95 5.29 Correlation of the tensile stiffness of tracheal cartilage with the total gly-cosaminoglycan content expressed as a percentage of the cartilage dry mass. A) The tensile stiffness' of layers #1-3 are averaged. B) The tensile stiff-ness' of layers #4-6 are averaged. C) The tensile stiffness' of layers #1-6 are averaged 96 xv 5.30 Correlation of the tensile stiffness of tracheal cartilage with the water content. A) The tensile stiffness' of layers #1-3 are av eraged. B) The tensile stiffness' of layers #4-6 are averaged. C) The tensile stiffness' of layers #1-6 are averaged 97 6.1 A) The effect of non-equilibrium stress-strain data on the development, of hysteresis in the stress-strain curve. B) Hysteresis observ ed when the cartilage specimens were strained more than 10 % 103 6.2 Schematic depiction of the ultrastructural alignment of the collagen fibrils in tracheal cartilage. IZ, inner superficial zone; MZ, m iddle zone; OZ, outer superficial zone 105 6.3 A) The results of Kempson on the age-related changes in the tensile stiffness of articular (knee) cartilage. Reproduced from Kempson [47]. B) Age-related changes in the tensile stiffness of tracheal cartilage (Tensile stiffness* of layers #1-6 are averaged) 108 6.4 The reaction of tracheal cartilage to in vivo stresses. The inner superficial zone is subjected to compressive stresses (C) while the outer superficial zone - is under a tensile stre ss (T). Somewhere in the middle zone, there is a neutral plane (N) of zero stress I l l C .5 Calibration curve for the force measurement on the M P T T 137 F.6 Estimated difference between the REML regression lines of layer #1 and layer #4 at the 95 % confidence level 156 xvi Chapter 1 I N T R O D U C T I O N The trachea serves as a conduit for the passage of gases to and from the lungs. In humans, it is an elastic tube 10-12 cm long extending from the larynx to the carina where it bifurcates to form the two main bronchi. In vivo, the upper half of the trachea is in the cervical region of the body while the lower half is in the thoracic cavity where it is exposed to intrathoracic pressure changes. The walls of the trachea are held apart by crescent-shaped cartilaginous rings whose role is to maintain tracheal architecture and resist deformation of the airway while providing a certain degree of flexibility (see figure 1.1). When gases are expired maximally from the lungs, the pressure within the thoracic cavity tends to collapse the large airways such as the trachea and main bronchi. This creates a choke point within the airways where flow limitation occurs. Thus, beyond a critical level of effort, the flow of air from the lungs is independent of the thoracic pressure. This pressure independent flow regime indicates that there is a mechanism within the airway which limits expiratory flow [17]. It has been predicted that flow l imitation in elastic tubes occurs at the speed at which the fluid in the tube propagates pressure waves. The basic speed of propagation of these pressure waves is (Y/p) 1/ 2, where Y is the elastic modulus of the tube cross-section and p is the density of the fluid within the tube [17]. This equation is the basis of wave speed theory of maximal expiratory flow limitation which has been used to emphasize that maximal flow depends on lung elasticity, the airway area and the degree to which 1 Figure 1.1: The trachea and major bronchi. Reproduced from Weiss Chapter 1. INTRODUCTION 3 the airway wall resists bending (i.e. airway wall stiffness) [17]. It has been shown that enzymatic degradation of airway cartilage causes a reduction in maximal expiratory flow ( M E F ) [71]. Papain, a proteolytic enzyme which degrades cartilage [25] (specifically proteoglycans), was administered intravenously to rabbits and the in vivo and ex vivo mechanical characteristics of-the trachea were studied. Papain treatment was found to produce a decrease in the unstressed diameter of the trachea and a significant decrease in the ability of the trachea to withstand negative transmural (collapsing) pressures. It was argued by Moreno [71] that these results were caused by the enzymatically induced changes in the mechanical properties of the cartilage. In vivo, the above effects of papain treatment were determined to be the probable cause of a decrease in M E F and an increase in airway resistance [67, 71]. The results of these studies emphasized the fact that airway cartilage degradation can result in reduced M E F . Maximal expiratory flow ( M E F ) is known to decrease with ageing [54]. In addition, a reduction in M E F is one of the characteristic signs of chronic bronchitis and emphysema. These two diseases — generally referred to as chronic obstructive pulmonary disease ( C O P D ) — are a major cause of disability in older people. Knowledge of the possible role of the mechanical properties of tracheal cartilage in the reduction of maximal expiratory flow could provide a better understanding of the age-related decrease in M E F as well as the effects of these debilitating diseases. The aim of the present study was to develop an ex vivo method of determining the stiffness of tracheal cartilage. In doing so, it was intended that the material testing procedure be relatively simple and the results be reproducible. To this end, it was not necessary that the mechanical test simulate the in vivo functioning of the trachea; rather, it was required that the test be capable of identifying changes in the mechanical properties of tracheal cartilage which could arise as a result of ageing or disease. Tensile testing has been shown to be a simple, reproducible and. sensitive measure of the material properties Chapter 1. INTRODUCTION 4 of articular cartilage [2, 5, 49, 107, 108, 109] For these reasons, it was decided that the tensile properties of tracheal cartilage would be studied. Previous researchers have found that the mechanical properties of articular cartilage exhibit both regional [48] and age-related [88, 47] differences. A knowledge of both the regional and age-related variations in the mechanical properties of tracheal cartilage is, therefore, required for a more complete understanding of the mechanical properties of the airways and the mechanism limiting maximal expiratory flow. As such, a further goal of this study was to determine the regional and age-related variations in the tensile properties of tracheal cartilage. This thesis is organised in the following manner: • Chapter 2 provides background information on the composition of cartilage and how the individual cartilage components contribute to give the tissue its overall mechanical properties. • Chapter 3 reviews the current state of knowledge regarding the methods of cartilage tensile testing. • Chapter 4 describes the experimental protocol of this thesis. • Chapter 5 presents the pertinent results obtained from the experiments. • Chapter 6 discusses the results presented in chapter 5 and comments on the phys-iological significance of these results. • Chapter 7 forms the conclusions of this thesis. • Chapter 8 makes recommendations for future research in this field. Chapter 2 P H Y S I O L O G I C A L P R I N C I P L E S The mechanical properties of cartilage are determined by the biochemical composition of the cartilage and the structural organisation of the dominant components of the tissue: collagen and proteoglycans [2]. In addition, hydration and the degree of both cartilage cal-cification and enzymatic degradation of the structural components are important. These factors must be considered when investigating the mechanical behaviour of cartilage. Cartilage is composed of 60-80% water and 20-40% solids. The solid components of cartilage are collagen, proteoglycans, glycoproteins, lipids and the structural components of chondrocytes. The major solid components are collagen and proteoglycans, which constitute approximately 65% and 25% of the dry weight of cartilage respectively. The components of cartilage which function in load bearing are collagen, proteo-glycans, and water. Collagen fibrils are organized into a mesh that forms a system of compartments in which the hydrophilic proteoglycans are enclosed. Together, these components form a fib re-reinforced composite material displaying the characteristics of a porous-permeable solid filled with water [2]. Each of the structural components of cartilage confers on the tissue certain characteristics which make cartilage an excellent load bearing material. The structural components of cartilage and their contribution to its mechanical properties are discussed in detail in the following sections. 5 Chapter 2. PHYSIOLOGICAL PRINCIPLES Figure 2.1: General organisation of the helical segment of type II collagen. (Reproduced from Serafini-Fracassini and Smith [93].) 2.1 Collagen The collagens are a family of structural proteins found in many tissues within the body. There are several structurally different types of collagen found in human tissue. In hyaline cartilage, such as the cartilage of the trachea, type II collagen predominates [9.3]. The functional form of type II collagen is the the collagen fibril which is composed of left-handed helical polypeptide chains organized into right-handed triple helices wi th non-helical N-terminal and C-terminal ends (see figure 2.1). The characteristics of type II collagen which are important in determining the overall mechanical properties of cartilage are as follows: • collagen fibrils form fibrillar networks through covalent intermolecular cross-links • the collagen fibril network immobilizes proteoglycans • collagen fibrils are stiff in tension, but lack resistance to compression. Chapter 2. PHYSIOLOGICAL PRINCIPLES 7 These properties wi l l be discussed in the remaining paragraphs of this section. Collagen fibrils interact through cross-links to form a meshwork of definite architecture [2]. The major covalent cross-links between collagen molecules connect the non-helical terminal portions of the molecules. The presence of these cross-links has been shown to have a tremendous effect on the tensile properties of cartilage [5]. The interfibrillar networks formed by the cross-links may result in the collagen fibrils being oriented in a particular direction or appearing as a seemingly random mesh. The actual form of the collagen network depends on the type of cartilage, the location of the network within the cartilage and, presumably, on the loads and deformations that the tissue experiences [78]. The individual fibrils which make up the collagen network range from 30 nm to 80 nm in diameter [103] while the gaps between them are on the order of 100 nm or more [66]. At first glance, these values may create the impression that the collagen network forms a relatively coarse mesh; however, when compared to the free solution size of proteoglycan aggregates, which are entrapped within the mesh, it becomes clear that the collagen network forms a very fine mesh. As wi l l be discussed in section 2.2, the unhindered length of a proteoglycan aggregate in solution is on the order of 2 fim (i.e. 2000 nm). Clearly, this is much larger than the gaps between the collagen fibrils. As a result, the proteoglycans become intertwined and immobilised within the collagen network. The tensile stiffness of collagenous tissues has been measured previously. Human tendon, with a typical collagen content of 85 % (dry weight basis) has been found to have a tensile stiffness of approximately 600 M P a [46] while that of human and primate ligaments has been reported as approximately 100 M P a [80]. The differences between these values have been explained to be a result of the less dense and less aligned collagen fibre structure in ligaments [46]. In cartilage, the mechanical stiffness of the collagen fibrils is illustrated when the collagen fibrils are aligned at high values of strain. Kempson Chapter 2. PHYSIOLOGICAL PRINCIPLES 8 [47] has found that at high values of strain, the tensile stiffness of articular cartilage was in the range of 40-125 M P a . Thus, aligned collagen fibrils can confer on cartilage a high tensile stiffness. Whi le the collagen fibrils are stiff in tension, they exhibit virtually no resistance to compression or bending. However, the collagen fibril matrix does play a role i n con-junction with the proteoglycans in resisting compression. As wil l be discussed in section 2.2, proteoglycans form the compression resisting element of cartilage. The movement of these proteoglycans within cartilage is restricted by the collagen fibril matrix. Thus, when loaded in compression, proteoglycans are not free to move to an unloaded area. This results in a higher compressive stiffness. Clearly, the collagen network is an important determinant i n the mechanical proper-ties of cartilage. It forms the reinforcement in the fibre composite structure of cartilage. As such, the collagen network contributes significantly to the strength and stiffness of cartilage. 2.2 Proteoglycans Aggregating proteoglycans are the most studied proteoglycans in cartilage. While non-aggregating proteoglycans exist in cartilage, aggregating proteoglycans comprise the ma-jority of the proteoglycan content in cartilage. These proteoglycan aggregates have a molecular weight of 200 million daltons and a length of about 2 fim [86]. They consist of a hyaluronate ( H A ) core to which 50-100 proteoglycan molecules ( P G ) are attached (see figure 2.2). The bond between each proteoglycan molecule and the hyaluronate core is stabilized by a link protein which effectively locks each proteoglycan onto the hyaluronate [9, 39]. Chapter 2. PHYSIOLOGICAL PRINCIPLES 9 ( 6 ) Hyaluronic Acid Protein Core A Typical Ouster of Fixed Negative Charge Groups Solution Domain of the Proteoglycan Aggregate Figure 2.2: (A) Diagram of cartilage proteoglycan molecule. Reproduced from Muir [77]. (B) Schematic representation of proteoglycan aggregates. Reproduced from Muir [77] and Myers [78], HA, hyaluronic acid; CS, chondroitin sulphate; KS, keratan sulphate; PG, proteoglycan molecule; Subunit, proteoglycan molecule. Chapter 2. PHYSIOLOGICAL PRINCIPLES 10 Figure 2.3: The repeating disaccharide unit of chondroitin 4-suIphate. Reproduced from Muir [77]. The proteoglycan molecule has a molecular weight of approximately 2.5 mill ion dal-tons and it consists of a protein core with 100-150 laterally attached chains of repeating disaccharide units; these chains are called glycosaminoglycans. The specific glycosamino-glycans present in cartilage are chondroitin sulphate (CS) and keratan sulphate (KS) . Chondroitin sulphate and keratan sulphate contain sulphate and carboxyl groups which are negatively charged in solution and confer on the proteoglycan molecule a high con-centration of fixed negative charges at physiological p H (see figure 2.2). A typical chondroitin sulphate chain contains approximately 25-30 repeating disac-charide units comprised of a hexuronic acid and a hexosamine residue [77]. In chondroitin sulphate, there is, on average, one sulphate group per disaccharide; however, the distri-bution of sulphate residues along the chain is not uniform. There are fewer sulphate groups on the chondroitin sulphate chains in the vicinity of the core protein [102]. Chondroitin sulphate has two places on the hexosamine residue where the sulphate group can attach. In chondroitin 4-sulphate, the sulphate groups are attached to the C-4 of the hexosamine residue, while i n chondroitin 6-sulphate, the sulphate groups are attached to the C-6 of the hexosamine residue (see figures 2.3 and 2.4). The fact that the sulphate groups of chondroitin 6-sulphate project further from the disaccharide chain may be of physiological significance. Chapter 2. PHYSIOLOGICAL PRINCIPLES 11 Figure 2.4: The repeating disaccharide unit of chondroitin 6-sulphate. Reproduced from Muir [77]. Figure 2.5: The repeating disaccharide unit of keratan sulphate. Reproduced from Muir [77]. Keratan sulphate is smaller than chondroitin sulphate and contains, on average, thir-teen repeating disaccharide units. However, the length of the keratan sulphate chain is more variable than that of chondroitin sulphate. In keratan sulphate, the repeating dis-accharide unit is comprised of a hexose and a hexosamine residue (see figure 2.5). There also appears to be roughly two populations of keratan sulphate; one has approximately one sulphate group per disaccharide unit , while the other has considerably more. The sulphate groups are located on the C-6 of either the hexose or the hexosamine residues. In cartilage proteoglycans, chondroitin sulphate is the principal glycosaminoglycan with lesser but variable amounts of keratan sulphate. The current model for cartilage proteoglycans has a central core protein to which approximately 100 chondroitin sulphate and 50 keratan sulphate chains are attached. Heingard and Axelson (1977) [43] proposed that 60 % of the keratan sulphate is attached to a region near the hyaluronate-binding Chapter 2. PHYSIOLOGICAL PRINCIPLES 12 region of the protein core where there are few chondroitin sulphate chains. About 20 % of the keratan sulphate is attached along the protein core close to clusters of chondroitin sulphate chains, while the remaining keratan sulphate chains are probably attached to the hyaluronate-binding region [43]. * The typical proteoglycan content of cartilage is about 5-10% of the wet weight while the actual value appears to vary according to the load bearing requirements, age, and health of the cartilage. Although present in relatively small quantities, proteoglycans are responsible for some of the most important characteristics of cartilage. These character-istics are listed below: • a high swelling pressure, • a low hydraulic conductivity, and • resistance to compression. The concentration of non-mobile electrical charges within cartilage is expressed as a fixed charge density. Cartilage has a typical fixed charge density of about 0.15 m E q / g [64, 101]. The proteoglycans are almost entirely responsible for this high concentration of fixed negatively charged groups. The result of this high fixed charge density is that a large Donnan osmotic swelling pressure is created, thus conferring on cartilage the propensity to imbibe water. In fact, when left unconstrained by the collagen network, proteoglycan monomers have been found to entrain approximately 50 m l of solvent per gram of solute [40]. In cartilage, however, the swelling is balanced by the tension developed in the collagen network. As a result cartilage proteoglycans are confined to approximately 20 % of their free solution volume [41]. The resistance to fluid flow in cartilage can account for the majority of the dynamic response of cartilage to a load [2]. This resistance is a result of the fine macro molecular Chapter 2. PHYSIOLOGICAL PRINCIPLES 13 mesh created by the proteoglycans; the pores within the proteoglycan-water gel are in the range of 2-10 n m [65]. As a result, cartilage exhibits a low hydraulic conductivity. The resistance of cartilage to compression in static loading arises from the high fixed charge density of the proteoglycans and the bulk compressive stiffness of the proteogly-cans in the absence of any charge [78]. As stated earlier, the high fixed charge density of the proteoglycans confers on cartilage the propensity to imbibe water. This serves to l imit the amount of l iquid lost when the cartilage is loaded in compression [64]. It also ensures the quick recovery of the cartilage during the 'off-load' intervals [64]. In addition, the negative charges on the glycosaminoglycan chains of the proteoglycans are approxi-mately 0.5-1.5 n m apart. Their mutual repulsion works to maintain the proteoglycans in an extended state, thus aiding the resistance to compression. Clearly, the above-mentioned properties of proteoglycans serve an important role in the proper mechanical functioning of cartilage. 2.3 Water Water in cartilage accounts for 60-80 % of the wet weight. The actual water content of a given specimen is determined by the balance between the swelling pressure of the proteoglycans and the tension developed in the collagen network. Very little of the water i n cartilage is intracellular. As such, most of it is freely exchangeable with the surrounding fluid. Water is important in cartilage as it is the resistance to the flow of water which forms the dynamic compression resisting element in cartilage. In cartilage, where there is a mixture of freely moving fluid and a permeable solid, the stresses are dissipated by forcing the fluid through the solid [78]. As a result, both the water content of cartilage and the conductivity of the collagen-proteoglycan matrix are important factors in deformation Chapter 2. PHYSIOLOGICAL PRINCIPLES 14 and load carriage. 2.4 Structural Organisation of Cartilage Although little is known about the ultrastructural arrangement of collagen in tracheal car-tilage, articular cartilage has been well studied [107, 74]. Art icular cartilage is generally regarded as a layered medium comprised of four separate histological and ultrastructural zones (see figure 2.6). In this tissue, the most superficial layer is comprised of sheets of tightly woven collagen fibrils arranged tangentially to the surface [74]. This region has been determined to contain the highest concentration of collagen in articular cartilage [62]. In contrast to the superficial zone, the collagen fibrils in the intermediate zone are randomly oriented and homogeneously distributed. In addition, the superficial zone has been found to contain more water, fewer proteoglycans and a higher chondroitin^ sulphate to keratan sulphate ratio than the intermediate zone [55]. In the deep zone, the collagen fibrils form a tighter meshwork and are predominantly oriented perpendicular to the cartilage surface [70]. The fourth zone of articular cartilage, the calcified zone, is adjacent to the subchondral bone and is heavily impregnated with crystals of calcium salts [70]. Thus, an analog to the calcined zone is not present in normal tracheal cartilage. The tensile properties of articular cartilage have been studied using strips of cartilage 200-300 / i m thick cut parallel to the articular surface [2, 5, 49, 107, 108, 109]. The layer-wise variation of these tensile properties has, to a certain extent, been attributed to the ultrastructural variation of the collagen fibre architecture [48]. The surface layers, having a more aligned collagen ultrastructure, tend to exhibit a higher tensile stiffness than the deeper layers in which the collagen fibrils are more randomly oriented [48]. Layer-wise differences in the proteoglycan content of articular cartilage have also been found [64]. Chapter 2. PHYSIOLOGICAL PRINCIPLES 15 SUPERFICIAL ZONE MIDDLE 20NE DEEP ZONE CALCIFIED TLONE. BONE Figure 2.6: Diagram of the layer-wise variation in structure in articular cartilage. Adapted from Clarke [13] and Meachim and Stockwell [70]. The concentration of proteoglycans gradually increases approximately four-fold from the articular surface to the deep zone [64]. The presence of a low proteoglycan concentration at the articular surface avoids the problem of a high osmotic pressure gradient that would be created by a high surface proteoglycan concentration. Whereas a high osmotic pressure gradient would impose exceptionally high tensile stresses on the surface collagen fibrils, the relatively low osmotic pressure gradient caused by the low surface proteoglycan concentration generates considerably lower tensile stresses on the surface collagen fibrils. This grading of stresses may function to prevent long term fatigue in the cartilage [64]. Although the above discussion of the collagen ultrastructure and the proteoglycan concentration profile was made in specific reference to articular cartilage, the same general principles may apply to tracheal cartilage as well. As a result, layer-wise variations of structure and composition may optimise the ability of tracheal cartilage to withstand the in vivo mechanical stresses. * CHONDROCYTES Chapter 2. PHYSIOLOGICAL PRINCIPLES 2.5 Interaction Between Matrix Components in Cartilage 16 The interactions between the collagen, proteoglycans and water are responsible for the macroscopic material properties of cartilage. The collagen fibrils form a mesh of def-inite architecture with the interfibrillar spaces filled with proteoglycans and water. It is believed that the structural features of the proteoglycan aggregates are essential for the organisation of the cartilage matrix by promoting physical, chemical, and mechani-cal interactions with the surrounding collagen network [41]. Whi le very little is known about the nature of these interactions, evidence suggests that electrostatic interactions and physical entanglements exist between • collagen fibrils, • proteoglycan aggregates, and t collagen fibrils and proteoglycan aggregates. The collagen fibrils interact through cross-links to form fibrillar networks while the proteoglycans interact with each other to form a fine macromolecular mesh which ensures a low hydraulic conductivity in the tissue. The glycosaminoglycan chains of proteoglycans are known to interact with collagen fibrils, presumably via the glycosidic linkages in the glycosaminoglycans [79]; however, little is known about this interaction. Proteoglycans are believed to organise and immobilise the collagen framework in an extended state to ensure that the stiff collagen fibrils are tensed during deformation [38]. Recent experiments have indicated that the aggregation of proteoglycans promotes their intermolecular network formation [38]. This network formation helps to retain a high concentration of proteoglycans within the cartilage by restricting the movement of the proteoglycans. Due to their size, proteoglycan aggregates are immobilised very effectively Chapter 2. PHYSIOLOGICAL PRINCIPLES 17 within the collagen network. In addition, aggregates may be less compressible than pro-teoglycan molecules and may, therefore, make a greater contribution to the compressive stiffness of cartilage [77]. Hence, the network formed by aggregated proteoglycans helps to provide the material properties needed for the cartilage to maintain form and resist deformation. 2.6 Correlation of the Mechanical Properties of Cartilage with its Chemical Composition Load carriage within cartilage is shared between the resistance to interstitial fluid flow and the extra-cellular matrix. Previous investigators have attempted to correlate the mechanical properties of articilar cartilage with its chemical constituents. Tests were performed on normal, osteoarthritic and enzymatically degraded cartilage. Their results are described in the following paragraphs. Kempson [51] performed indentation tests and biochemical analyses on articular carti-lage. In correlating the results, he found that there was a significant positive correlation between cartilage stiffness and total glycosaminoglycan content. His results indicated that stiffness depended on the content of both chondroitin sulphate and keratan sul-phate with a stronger correlation based on keratan sulphate content. Collagen and water were found to have virtually no significant correlation with stiffness in indentation. In another study, Kempson [49] correlated a dynamically measured tensile stiffness with collagen content at varying depths in articular cartilage. This time, a good cor-relation between tensile stiffness and collagen content was obtained. The correlation was found to be less significant in the deeper zones of the cartilage presumably because the collagen fibrils were more randomly oriented in that region. Collagen content was also found to correlate better with dynamic tensile stiffness when the tensile tests were Chapter 2. PHYSIOLOGICAL PRINCIPLES 18 150 kgl/cm2 [ a II 30 kgl/cm-A' f 0 10 20 30 40 50 Strain (•/.) '0 20 40 60 80 ' ICC' 120 Strain (°/o) Figure 2.7: The effect of proteoglycan degradation on the tensile stiffness of articular car-tilage. Specimen oriented (a) parallel, (b) perpendicular to the surface orientation of the collagen fibrils. Surface layer: (•) before treatment with trypsin; ((J) after 24 h in trypsin; ( O ) a f t e r 48 h in trypsin. Middle layer: ( A ) before treatment with trypsin; ( A ) after 24 h in trypsin; ( A ) after 48 h in trypsin. Reproduced from Kempson [49]. performed with the stress applied parallel—and not perpendicular—to the predominant collagen fibril orientation. In an attempt to better understand the role of proteoglycans in the mechanical prop-erties of cartilage, Kempson [49] used the enzymes chondroitinase and trypsin to degrade the proteoglycans. Decreasing the proteoglycan content was found to cause a significant decrease in the dynamic tensile stiffness at low stresses; however, there was no observed effect on the tensile stiffness measured at high stresses (see figure 2.7). Unfortunately, Kempson used the results measured at high stresses to correlate cartilage mechanical properties with the amount of proteoglycans present. As a result, no correlation was reported between dynamic tensile stiffness and proteoglycan content. Chapter 2. PHYSIOLOGICAL PRINCIPLES 19 Tensile stroln (per cent) Figure 2.8: The effect of collagenase on the mechanical properties of cartilage in tension. Surface layer, parallel to surface collagen fibril orientation: (•) before collagenase treatment; (o) after 24 h in collagenase. Middle layer, parallel to surface collagen fibril orientation: (A) before collagenase treatment; ( A ) after 24 h in collagenase. Middle layer, perpendicular to surface collagen fibril orientation: ( y ) before collagenase treatment; (v) after 24 h in collagenase. Reproduced from Kempson et al. [50]. In a further study, Kempson(1976) [50] considered the effects of the enzymes cathep-sin D and collagenase on the tensile strength and dynamic stiffness of articular cartilage. Cathepsin D caused the degradation and release of the proteoglycans from the cartilage while collagenase caused the cleavage of the central helical region of the collagen molecule. Proteoglycan degradation was found to cause a significant reduction in the compressive stiffness and the dynamic tensile stiffness at low stresses. A t higher stresses, the dynamic tensile stiffness of the cartilage was, again, unchanged by proteoglycan degradation. Co l -lagen degradation, however, caused a significant reduction in the tensile strength and stiffness of the cartilage at all levels of stress (see figure 2.8). The above results were explained by arguing that at low values of applied stress the tensile stiffness of cartilage depends on the extent to which the collagen fibrils are Chapter 2. PHYSIOLOGICAL PRINCIPLES 20 initially aligned in the direction of the applied stress and on the resistance which fibrils experience when they realign in the direction of the stress. Under normal circumstances, the hydrated proteoglycan gel tends to restrict the alignment of the collagen fibre mesh under stress. W h e n the proteoglycans are degraded and released form the matrix the resistance to alignment of the collagen fibrils is reduced and this causes a reduction in the tensile stiffness at low stress. Since collagen fibrils are the main tension-resistant elements in cartilage, degradation of the collagen fibrils causes a significant reduction in the tensile stiffness at all levels of stress. In a more recent study, A k i z u k i et al. [2] performed equilibrium tensile tests on artic-ular cartilage in attempt to determine the 'intrinsic' flow-independent properties of the extra-cellular matrix. Their results indicated that, in normal cartilage, the most signifi-cant correlation with the tensile stiffness was the collagen/proteoglycan ratio; however, no significant correlations were found when osteoarthritic cartilage was tested. Clearly, the cartilage composition and the interaction between the chemical components of cartilage plays an important role in determining its macroscopic mechanical properties. In an attempt to determine the effect of collagen cross-linking on the mechanical properties of cartilage, Bader et al. [5] measured the tensile stiffness of cartilage which had been treated with the enzyme leucocyte elastase. This enzyme degrades and releases a large amount of proteoglycans. In addition, leucocyte elastase degrades the the non-helical terminal peptides of collagen. This type of degradation leaves the helical region of the molecule intact but eliminates most of the covalent cross-links between molecules [6], thus eliminating the interaction between collagen fibrils. The results of this study showed that leucocyte elastase caused a decrease in tensile strength and a reduction of tensile stiffness at all levels of stress (see figure 2.9). Since the main action of elastase on collagen is to disrupt the major intermolecular cross-link, the results indicate that this cross-link is important in determining the tensile properties of cartilage. Chapter 2. PHYSIOLOGICAL PRINCIPLES 21 MN/m 2 15 -Tensile Strain Figure 2.9: The effect of the enzyme leucocyte elastase on the mechanical properties of cartilage in tension. Superficial zone: (•) before elastase treatment; (o) after 72 h in elastase. Deep zone: (A) before elastase treatment; ( A ) after 72 h in elastase. Reproduced from Bader et al. [5]. Chapter 2. PHYSIOLOGICAL PRINCIPLES 22 2.7 Effect of Ageing on Cartilage In a study on the mechanical properties of human tendon and their age dependence, Hubbard and Soutas-Little [46] found no significant correlation between age and the tensile stiffness of collagen; however, they noted that any possible age effect may have been masked by a lack of control over subject nutrition, activity and disease. In contrast to this result, Roth et al. [88] and Kempson [47] found that the tensile properties of articular cartilage d id , indeed, change with age. Roth et al. [88] found that there was a considerable difference between the tensile properties of immature and mature bovine articular cartilage while Kempson [47] found that the tensile properties of human articular cartilage deteriorated with increasing age from the middle of the third decade of life. Kempson attributed this deterioration of cartilage to changes in the organisation and integrity of the collagen mesh since collagen fibrils have been observed to become more widely spaced and larger in diameter with increasing age [52]. Age-related changes in the macroscopic material properties of cartilage are probably a result of the age-related changes in the matrix components. Some of the changes which may, ultimately, affect the mechanical properties of cartilage are as follows: • collagen cross-linking • the ratio of chondroitin 6-sulphate to chondroitin 4-sulphate • the ratio of chondroitin sulphate to keratan sulphate • the size of proteoglycan aggregates and molecules. The solubility of collagen in a tissue can be used to quantify the amount of cross-Unking in the collagen [12, 33]. Collagen cross-linking is known to increase with age as is demonstrated by the age-related decrease in the amount of soluble collagen in Chapter 2. PHYSIOLOGICAL PRINCIPLES 23 collagenous tissues [12, 33] and the age-related decrease in the proportion of extractable proteoglycans from cartilage [55, 100]. In immature cartilage, the collagen cross-links have not been established, thus resulting in a more flexible collagen network in which proteoglycans are less confined [24, 55]. W i t h maturation, cross-Unking results in a more effective entrapment of proteoglycans [100]. As a result, during the maturing process, cartilage should become stiffer mechanically. As stated in section 2.2, articular cartilage contains both chondroitin 4-sulphate and chondroitin 6-sulphate. In chondroitin 4-sulphate, the sulphate groups are attached to the C-4 of the hexosamine residue, while in chondroitin 6-sulphate, the sulphate groups are attached to the C-6 of the hexosamine residue. The ratio of chondroitin 6-sulphate to chondroitin 4-sulphate increases by a factor of 10-25 during maturation and then remains relatively constant after the third decade [55, 89]. W h i l e the biological signifi-cance of the position of the sulphate group is not known, it is known that the sulphate groups project further from the chain in chondroitin 6-sulphate than in chondroitin 4-sulphate [4]. Therefore, chondroitin 6-sulphate may interact more strongly than chon-droitin 4-sulphate with the charged groups of collagen [77]. In fact, it has been found that proteoglycans containing a high proportion of chondroitin 6-sulphate are more resis-tant to extraction from articular cartilage [77]. Thus, an increase in the relative amount of chondroitin 6-sulphate may aid in the restriction of proteoglycan movement within cartilage. A n age-related decrease in the relative amount of chondroitin sulphate compared with keratan sulphate has been observed [55, 89, 101]. Between birth and maturity the chondroitin sulphate to keratan sulphate ratio decreases by a factor of 7-10 [55, 89]. This phenomenon can be explained by the reported age-related decrease i n the length of the chondroitin sulphate chains [96], decrease in the length of the protein core [96] and increase in the absolute amount [96] and length [55] of keratan sulphate (see figure 2.10). Chapter 2. PHYSIOLOGICAL PRINCIPLES 24 constant variable Figure 2.10: Three sizes of proteoglycans showing a constant hyaluronic acid binding region and shorter chondroitin sulphate-binding region with decreasing length of the protein core. Reproduced from Muir [77]. The biomechanical significance of these changes has not been elucidated, however, it is expected that they result from a combination of biosynthetic changes and enzymatic degradations [91]. The size of proteoglycan aggregates [100] and molecules [89, 100] has been found to decrease wi th age. This is believed to result primarily from proteolysis and an accumu-lation of free core protein fragments with the ability to bind to hyaluronate. These frag-ments sterically hinder the attachment of newly synthesized aggregating proteoglycans to the hyaluronate [90] (see figure 2.11). As a result, these non-aggregated aggregating Chapter 2. PHYSIOLOGICAL PRINCIPLES 25 NEONATE — H y a l u r o n i c add • U * p r o U k i Figure 2.11: The effect of aging on the size of proteoglycan aggregates. Reproduced from Roughley and Mort [91]. proteoglycans may leave the cartilage prematurely. The biomechanical result of a de-creased proteoglycan size could be a reduced ability of the collagen network to entrap the proteoglycans and, therefore, a decreased stiffness. Chapter 3 T I S S U E P R E P A R A T I O N A N D T E N S I L E T E S T I N G 3.1 Tissue Preparation W h e n performing tensile tests on a biological material such as cartilage, autolytic degra-dation, strain rate, and the ionic conditions of the bathing fluid are important parameters which must be controlled. Furthermore, the size and compliance of the cartilage test spec-imen require the use of special techniques and customized equipment. The effects of these parameters and techniques are discussed in the following sub-sections. 3.1.1 Storage of Cartilage During life, enzymes capable of degrading cartilage proteoglycans and collagen are pro-duced by the cartilage cells [77] and are involved with the constant turnover of the collagen and proteoglycans. Following death, the release of these enzymes from the chondrocytes would be expected to cause autolysis of the cartilage and alteration of the mechanical properties i f the tissue were not stored properly. Since the immediate mechanical testing of fresh tissue is not usually possible, cartilage is normally stored frozen before being tested. However, freezing biological tissues results in rupture of the cell membranes. In the case of cartilage, this would subsequently result in a small amount of enzyme being released. H o n [45] has studied the effect of autolytic degradation on the mechanical behaviour of cartilage and found that the effects of autolysis only become noticeable af-ter about 20 hours at room temperature. Furthermore, previous researchers have found 26 Chapter 3. TISSUE PREPARATION AND TENSILE TESTING 27 that cartilage may be stored at — 20°C for up to a year with no significant change in its mechanical properties (2, 49]. Finally, repetitive freezing of cartilage has been observed to have no effect on cartilage mechanical properties measured by indentation tests [45]. These results suggest that cartilage has either a low enzyme content and/or low activity of degradative enzymes or a low susceptability of the mechanically important elements to degradation. 3.1.2 Specimen Preparation for Testing To prepare cartilage for tensile testing, normal practise involves cutting the sample to a standard shape. Previous researchers have cut a rectangular or circular block of cartilage from the tissue [2, 5, 49, 107, 108, 109]. To cut out blocks of cartilage, such tools as trephines, circular saws, scalpels and plug cutters have been used [87]. However, some of these tools create a considerable amount of friction which tends to heat the cartilage. Roth et al. [87] have pointed out that, in order to avoid degradation of the cartilage, it is important to prevent the temperature of the tissue from rising above physiological values. Therefore, if the above cutting tools are used, sufficient coolant should be available to maintain a low temperature during the cutting procedure. Typically, once cut, the cartilage block is placed on a microtome for serial horizontal slicing into layers 100-400 microns thick [2, 49, 107, 109]. A microtome is a mechanical device used to cut thin uniform slices of tissue. There are approximately six basic types of microtome each named according to the sectioning mechanism employed. The base sledge microtome has been used successfully i n cartilage sectioning [2, 49, 107, 109]. In this type of microtome, the holder for the block of tissue is mounted on a steel carriage which slides backwards and forwards against a fixed horizontal knife [16] (see figure 3.1). Another instrument, the vibrating microtome, makes use of a vibrating razor blade to section the tissue (see figure 3.2). This instrument can be used to cut thick sections (40 Figure 3.1: A typical base sledge microtome. Reproduced from Culling et al [16]. fim and greater). It is also useful for cutting fresh tissue and it is suitable for immersion of the tissue block in solution during the cutting procedure. These qualities make the vibrating microtome suitable for cartilage sectioning. In previous experiments on articular cartilage, dumbell-shaped specimens have been cut from the cartilage either before [107, 108, 109] or after [5, 49, 88] sectioning on the mi-crotome. However, successful tensile experiments have been performed using rectangular specimens [2]. The important feature of the dumbell-shaped specimen, common to engi-neering tests, is that the central parallel sided section should experience uniform tensile stress and that the magnitude of this stress should be greater than the maximum stress at the enlarged ends so that failure will occur in the central section. The advantage of this is that the entire stress-strain curve including fracture stress can be measured. However, Saint-Venant's principle can be used to justify the use of rectangular specimens. Briefly, Chapter 3. TISSUE PREPARATION AND TENSILE TESTING 29 Figure 3.2: A typical vibrating microtome. Chapter 3. TISSUE PREPARATION AND TENSILE TESTING 30 Saint-Venant's principle states: If a system of forces acting on one portion of the bound-ary is replaced by _a statically equivalent system of forces acting on the same portion of the boundary, then the stresses, strains and nonrigid-body displacements i n the parts of the body sufficiently far removed from this portion of boundary remain approximately the same [20]. Therefore, given a long enough specimen, the non-uniform stress field that would be present at the clamped ends of the specimen would have a negligible effect on the measurement of applied stress and strain. Furthermore, if a rectangular specimen is used, it can be assumed that a uniform stress field wil l have developed at a distance of 2-4 specimen widths from either clamp [20, 85] (see figure 3.3). In this manner, a uniform stress field can develop in a central gauge section of a rectangular test specimen. Thus, tensile stiffness can be accurately measured with a rectangular specimen; however, fracture wi l l tend to occur near the clamped ends due to the non-uniformities i n the stress field in that region (see figure 3.3). Therefore, fracture stress cannot be measured accurately when rectangular strips are used. This does not present a problem as the present study is devoted soley to an examination of the tensile stiffness of the tracheal cartilage. 3.1.3 Measurement of Specimen Dimensions W h e n performing stress-strain experiments, it is necessary to be able to accurately mea-sure the dimensions of the test specimen. Measurement of the cross-sectional area is required for the calculation of stress while measurement of the length of the specimen is required for the calculation of strain. Typical specimen dimensions used by other researchers [2, 5, 49, 107, 109] are as follows: • Total length — 10-32 mm • Gauge section length — 2-10 mm Chapter 3. TISSUE PREPARATION AND TENSILE TESTING Figure 3.3: Illustration of Saint-Venant's principle using photoelasticity. The alternating light and dark bands give an indication of the stress pattern within the material. Reproduced from Durelli [20]. Chapter 3. TISSUE PREPARATION AND TENSILE TESTING 32 • W i d t h — 1-2 m m • Thickness — 100-400 fxm. Typical engineering tensile test specimens are relatively hard and can be cut to stan-dard dimensions. In comparison, cartilage test specimens have a high water content and are relatively small and compliant [87]. For this reason special techniques have been developed for the measurement of cartilage test specimen dimensions. Some of these techniques are outlined in the following paragraphs. The thickness of cartilage test specimens has been measured by a variety of methods. Generally, these methods are sensitive to the compressibility of the cartilage. Roth and Mow [88] measured the cartilage thickness with a differential focusing method using an incident light microscope with a differential interference contrast prism. This method had a reported resolution of 2 fim. However, A k i z u k i et al [2] have noted that the technique is somewhat time consuming [2]. It is also not clear whether or not the hydration of the tissue was maintained during the thickness measurement. These factors may affect the accuracy of the results. Akizuki et al. [2] used an electro-optical micrometer in a device designed to measure tissue thickness by sensing the electrical conductivity of the tissue, while Woo et al. [107] used a similar current sensing micrometer apparatus to measure the cartilage thickness. The measurements obtained using these methods have been verified to be within 3 fim of those obtained using the optical non-contacting technique [2] described above. The advantage of these current sensing techniques is that they can be performed in less than one minute; however, the cost of the equipment needed for this technique may prove prohibitive in a preliminary study. The width of typical cartilage test specimens is such that it can be measured accu-rately using simple optical techniques. A k i z u k i et al. [2] and Roth and Mow [88] used a Chapter 3. TISSUE PREPARATION AND TENSILE TESTING 33 stereo-zoom microscope adapted with a precision X - Y translation stage to measure the width of test specimens. This method appears to be relatively simple and effective. In measuring the width of test specimens, Woo et al. [107] used a video camera attached to a dimensional analyser. Whi le this technique is quite suitable for dynamic experiments, the expected cost and complexity of the system appears to be unwarranted for experiments in which equilibrium measurements are made. There are several direct contact methods of measuring strain [1, 21, 28, 99]. However, because these methods require direct contact with the tissue, there is some uncertainty in the measured strains due to the possibility of device-tissue slippage or local damage caused by the gauge [110]. To overcome the problems associated with direct contact, noncontact optical strain measurement techniques have been developed. To make use of these optical methods, a gauge section is usually marked on the specimen [88, 49, 107]; although clamp-to-clamp measurements have been made [2]. Akizuki et al. [2], Roth and Mow [88] and Woo et al. [107] all used the same equipment to measure strain as they used to determine the width of the test specimen. In performing dynamic tests on cartilage, Kempson [49] used a telescope and a grid positioned immediately behind the test specimen. As each gauge mark on the test spec-imen passed a division on the grid, a mark was made in the appropriate place on a load-extension curve. When these points were joined, two curves were obtained repre-senting the position of each gauge mark as a function of time. From these two curves, the dynamic stress-strain curve could be calculated. The accuracy of this method was not reported but, it is reasonable to assume that the measurement error would increase with increasing strain rate. Chapter 3. TISSUE PREPARATION AND TENSILE TESTING 34 Figure 3.4: The effect of changing the bathing fluid on the tensile stiffness of cartilage. Reproduced from Akizuki et al [2]. 3.1.4 Tissue Bathing Solutions In 1963, Elmore [23] pointed out the importance of immersing the cartilage specimen in a bathing fluid. Without such immersion, the cartilage was found to exhibit residual deformities following application of static loads [23]. The tonicity of the immersion medium has also been reported to affect the stress-strain response of cartilage [2, 23]. Akizuki et al. [2] have found that the tensile stiffness of cartilage is higher in deionised water than in isotonic saline (see figure 3.4). Roth and Mow [88] and Kempson [49] immersed the cartilage test specimen in buffered Ringer's solution at a p H of 7.2. Woo et al. [107] immersed the test specimen in saline maintained at 37 °C . Ogawa [81] performed the test in air with the back of the specimen exposed to a piece of saline-soaked filter paper. A k i z u k i et al. [2] did not immerse the tissue; however, a continuous supply of bathing fluid was maintained. Although their bathing solutions and techniques may have differed, their results indicate the importance Chapter 3. TISSUE PREPARATION AND TENSILE TESTING 35 of maintaining the cartilage in a hydrated state during the experiment. 3.1.5 Specimen Clamps Clamping the ends of the cartilage test specimen has presented a problem to previous researchers. Not only does the small size of the test specimen necessitate the design of miniature clamps, but reported slippage of the test specimen within these clamps [110] has compromised the fidelity of strain estimates from clamp-to-clamp measurements [2]. Device-tissue slippage can also lead to inaccurate estimates of stress. To date, most experiments appear to have made use of tissue clamps which rely on friction to grip the cartilage [2, 5, 49, 107, 108, 109] and, therefore, have been susceptible to tissue slippage. 3.2 Principles of Tensile Testing A material body deforms when subjected to external mechanical stimuli and the resulting deformation depends on its composition, intrinsic materials properties and its extrinsic geometric form. To compare and to contrast materials according to their mechanical properties, the extrinsic dependence of mechanical response on geometry must be sep-arated from the intrinsic dependence on the material's composition and structure. To remove the geometric influence on the force-deformation behaviour of a material, stress and strain are used in determining material properties. Stress (cr) is defined as the force (F) per unit original cross-sectional area (A0), ' = i < 31) and strain (e) is defined as the change in length (Al) per unit original length (Zc), Chapter 3. TISSUE PREPARATION AND TENSILE TESTING 36 The stress-strain relationship of a material is independent of its geometric form and size and thus is a measure of the intrinsic mechanical properties of the material. While the action of forces on a material may be quite complex in a given loading situation, the loading mode is usually greatly simplified, during material testing, for easy theoretical analysis and determination of material properties. W h e n the applied force acts to stretch a material, it is referred to as a tensile force. The tensile stiffness is one measure of a material's mechanical properties. As such, it can be used to compare and to contrast the mechanical properties of tracheal cartilage. The tensile stiffness (T) of a material is given by the slope of the tensile stress-strain curve at any point on the curve, T = f f • <3-3> 3.2.1 Effect of Strain Rate on Cartilage Tensile Tests Load carriage in cartilage is shared between the interstitial fluid and the intrinsic material properties of the extra cellular matrix [2]. During rapid compressions, up to 90% of the stiffness of cartilage „can be attributed to the frictional drag associated with interstitial fluid flow; the properties of the extra cellular matrix contribute to the remainder of the stiffness [57]. This flow-generated stiffening effect is the result of a nonlinear biphasic behaviour of the tissue [75]. Thus, constant strain-rate tensile experiments [49, 88, 107] yield tensile stiffnesses that are not flow-independent [61]. As a result, mechanical testing protocols which include slightly different strain rates can yield drastically different results due to flow-generated stiffening [2] (see figure 3.5). A k i z u k i et al. [2] have recommended that, in order to avoid ambiguous results, tensile experiments should be performed using equilibrium measurements of stress and strain. Chapter 3. TISSUE PREPARATION AND TENSILE TESTING 37 Figure 3.5: The effect of strain rate on the tensile stiffness of cartilage. Reproduced from Li et al [61]. Chapter 4 M A T E R I A L S A N D M E T H O D S The experimental method used in this study can be subdivided into the following sections: • Collection and Storage of Tracheas • Sectioning of Tracheal Cartilage • Tensile Testing of Tracheal Cartilage • Calibration of Tensile Tester • Testing of the Material Standards • Biochemical Analysis of Tracheal Cartilage • Scanning Electron Microscopy of Tracheal Cartilage The protocol used for each of these aspects of this research is described in the following sections. 4.1 Collection and Storage of Tracheas Over a nine month period, ten tracheas were obtained from deceased humans ranging from 17 to 81 years in age. In nine of the ten cases, the cause of death was determined either to be accidental or suicide; one death was attributed to Parkinson's Disease. The tracheas were obtained from the Vancouver General Hospital morgue less than 24 hours post mortem. After dissection from the body, each trachea was immersed in fresh, aerated 38 Chapter 4. MATERIALS AND METHODS 39 Figure 4.1: Illustration of how the curved cartilage strips were flattened for microtome sec-tioning. Krebs buffer solution. The tracheas were then stored at -70° C in the isotonic Krebs buffer (see description of composition in appendix D) until sectioned. It was assumed that immersion of the cartilage in a Krebs buffer would allow the in vivo cartilage hydration to be simulated. 4.2 Sectioning of Tracheal Cartilage The frozen trachea described in section 4.1 was thawed and a cartilage ring was dissected out. A 1.5-2.0 cm strip of cartilage was cut out of the anteromedial section of the cartilage ring and the soft connective tissue on the outer surface and on the sides of the cartilage was removed using a scalpel, forceps and a straight edge. The inner luminal surface of the tracheal cartilage strip was then firmly affixed to a sectioning dish using a cyanoacrylate glue. In performing this step, the naturally curved cartilage strips were pressed flat against the sectioning dish (see figure 4.1). The sectioning dish was then clamped firmly in place in a vibrating microtome (Oxford Vibratome-Model G) (see Chapter 4. MATERIALS AND METHODS 40 figures 3.2 and 4.2). It was assumed that immersion in a Krebs buffer would allow the cartilage to assume its naturally hydrated state. To this end, isotonic Krebs buffer was added to the sectioning dish followed by a 15 minute equilibration period. Using the vibrating microtome, the first 50-100 ^ m of cartilage was sectioned to provide a clean surface from which test specimens could begin to be taken. Sectioning was performed with the following Oxford Vibratome settings: • Blade angle—20° • Speed—3 • Amplitude—7 Cartilage specimens 100 /xm thick were serially sectioned from the cartilage block. The first, or outer, 100 /zm layer of cartilage removed was labelled layer #1 and the subsequent deeper layers removed were numbered in succession. After sectioning, the thickness of the cartilage slices was measured using a Mitutoyo micrometer (model no. 193-101, instrument accuracy - 10 /im). The cartilage slices were then individually packaged, labelled and stored in isotonic Krebs buffer at —70°C. For each human subject, more than one tracheal cartilage ring was sectioned on the vibrating microtome. As a result, in most cases, more than one tensile test was performed on each cartilage layer from a given human subject. This enabled the reproducibility of the tensile tests to be examined. 4.3 Tensile Tests The tensile tests were performed on a Mult i-Purpose Tensile Tester ( M P T T ) designed and constructed by members of the pulmonary research group at St. Paul's Hospital, Vancouver, Brit ish Columbia (figure 4.3). This unit is capable of performing a variety of Chapter 4. MATERIALS AND METHODS 41 Figure 4.2: Close-up view of the tracheal cartilage glued to the sectioning dish clamped to the vibrating microtome. Chapter 4. MATERIALS AND METHODS 42 Figure 4.3: Photograph of the Multi-Purpose Tensile Tester used to perform the tensile tests on the cartilage. Chapter 4. MATERIALS AND METHODS 43 different tensile experiments. In the experiments described in this thesis, the M P T T was used to perform isotonic tensile tests. To do this, the M P T T was set in isometric mode with the length dial turned fully clockwise. W i t h the M P T T set up in this manner, the 'max load' control (figure 4.4) could be used to control the force imposed on the test specimen with the length of the specimen free to equilibrate with the imposed force. Thus, a series of equilibrium force-length measurements could be made from which a stress-strain curve could be calculated for each test specimen. As indicated by equation 3.3, the tensile stiffness of the test coecimen could be determined by calculating the slope of the stress-strain curve. The following subsections explain the methods used to calibrate the tensile tester, and to perform the tensile tests on both the material standards and the cartilage specimens. 4.3.1 Calibration of Tensile Tester In order to calibrate the M P T T used to stretch the cartilage specimens, the arm of the M P T T was balanced with zero applied load. Then, weights with accurately known masses were hung from the arm of the M P T T and the force required to balance the arm was noted. These data were recorded and used to produce a calibration curve for the tensile tester. 4.3.2 Testing of the Material Standards In order to validate the stress-strain measurements obtained using the M P T T , a number of material standards were prepared and tested on both the M P T T and a Thwing Albert Tensile Tester ( T A T T ) model QCII equipped with a 20 N load cell (figure 4.5). In contrast to the equilibrium measurements provided by the M P T T , the T A T T operated in a manner such that the test specimens were tested at a constant strain rate. This apter 4. MATERIALS AND METHODS Figure 4.4: Photograph of the control panel of the Multi-Purpose Tensile Teste Chapter 4. MATERIALS AND METHODS 45 introduced the possibility that the M P T T and T A T T might produce different results if the material standards used exhibited significant stress-relaxation. Three material standards, each having a tensile stiffness similar to that of cartilage, were used to validate the results obtained using the M P T T . These materials were, • Tan G u m Rubber—Supplied by the Accurate Rubber Co. , Richmond, British Columbia • Tygon Tubing—Supplied by the Fisher Scientific Company. • Latex Tubing—Supplied by Canlab. The material standards were prepared for testing on the M P T T in a manner similar to that used for the preparation of the cartilage specimens (see subsection 4.3.3). A 15 m m long by 2 mm wide block of material was sectioned on the vibrating microtome into slices 100 fxm thick. The thickness of each slice was measured using a Mitutoyo micrometer (model no. 193-101). Three thickness measurements were made: one in the centre of the test specimen and one at either end. The average of these measurements was recorded as the thickness of the specimen. However, if the three thickness measurements varied by more than 10 fim, then the test specimen was rejected. Each slice was then prepared and tested in the M P T T in a manner identical to that described in subsection 4.3.3. In order to test the standard materials on the T A T T , material test strips were cut with the following dimensions: • Gauge Length—5-15 cm • Width—0.3-0.6 cm • Thickness—0.2-0.3 cm Figure 4.5: Photograph of the Thwing Albert Tensile Tester used to test the material stan-dards. Chapter 4. MATERIALS AND METHODS 47 These test strips were attached to the T A T T and stretched at various contant strain rates (1 %/min-20 %/min) . This wide variation in strain rates enabled the stress-relaxation behaviour of the material standards to be studied. Since the lengths of these test specimens were considerably greater than either the width or the thickness, St. Venant's principle could be applied and a clamp-to-clamp strain was measured. The corresponding force and strain values were recorded directly from the T A T T . The stress-strain curves resulting from the above independent tests were compared and any differences were noted. 4.3.3 Tensile Testing of Tracheal Cartilage The cartilage slice described in section 4.2 was thawed and a 14 m m long by 1 mm wide test specimen was cut from the slice using a scalpel and a straight edge. Each end of the test specimen was attached to a t itanium clamp (figure 4.6) with cyanoacrylate glue. Then, in order to avoid measuring strain in the non-uniform stress region of the specimen (refer to section 3.1.2), a felt pen was used to draw gauge marks on the test specimen at a distance of approximately 2 mm from each clamped end. This created a central gauge section 6 - 8 mm long in which accurate strain measurements could be taken. Another mark was drawn in the centre of the gauge section to facilitate the width measurement needed for the calculation of stress. Then a stainless steel hook was attached to each specimen clamp and the test specimen was placed in a specially designed organ bath (figures 4.7 and 4.8) and attached to the M P T T . The tensile force was set to zero and a balance adjustment was made on the force transducer to ensure that there was no net force on the test specimen. At this point, a small load of less than 0.001 N was imposed on the specimen and the init ial length and width of the central gauge section was measured using a P T I optical micrometer (model no. 2158, instrument accuracy - 10 /zm) (see figure 4.9). Figure 4.6: Titanium clamps used to grip the ends of the cartilage test specimens. Chapter 4. MATERIALS AND METHODS Figure 4.7: The organ bath used to immerse the cartilage specimen in Krebs buffer during the tensile test. Note: 1) the jacket around the organ bath which allows the bathing fluid to be maintained at physiological temperature, 2) the flat glass window which allows the cartilage test specimen to be viewed without distortion. Chapter 4. MATERIALS AND METHODS Figure 4.8: Close-up view of the test specimen immersed in the organ bath and attached the M P T T . Figure 4.9: Photograph of the PTI optical micrometer positioned to measure the elongation of the test specimen. Chapter 4. MATERIALS AND METHODS 52 A force was then imposed on the test specimen causing it to stretch. After the test specimen appeared to have stopped stretching—normally 5-15 minutes—an equilib-r ium length measurement was made and the corresponding force and length values were recorded. This step was repeated several times with increasing forces unti l either the test specimen broke or the maximum force of 0.2 N registered on the force transducer. The M P T T was capable of monitoring both the position of the lever arm and the force imposed on it. Two stainless steel wires (1 m m dia.) hooked around the specimen clamps were used to attach the test specimen to the M P T T . During an experiment, one hook was fixed in position within the organ bath while the other hook was attached to the lever arm of the M P T T . This set-up provided a rigid attachment between the M P T T and the test specimen. Therefore, one could assume that, during a tensile experiment, a change in position of the lever arm of the M P T T would reflect the elongation of the entire test specimen—not just the gauge section. Since both the position of the M P T T lever arm and the force imposed on it were monitored throughout the course of an experiment, the entire force'and elongation history of the test specimen could be recorded. To do this, a Graphtec WR7500 chart recorder was used to record both the force vs. time and elongation vs. time curves for the test specimens. The information provided by these curves was used to help determine when the elongation of the test specimen had equilibrated with the imposed force. In approximately 20% of the cartilage specimens tested, a hysteresis curve was ob-tained. To do this, several equilibrium force-length measurements were made in increasing order to a pre-set maximum force. Then, the force was decreased and a series of equi-l ibr ium force-length measurements were recorded until the force reached zero. In doing this, the hysteresis in the stress-strain curve could be studied. Chapter 4. MATERIALS AND METHODS 53 4.4 Biochemical Analysis of Tracheal Cartilage The tracheal cartilage of the human subjects was analysed for its composition of water and proteoglycans. Water content was determined by comparing the wet and dry weight of a block of cartilage. The proteoglycan content of the cartilage was measured using the technique of Farndale et al. [26] in which the result is expressed in terms of a chondroitin sulphate equivalent. These methods are discussed in greater detail in the following subsections. 4.4.1 Water Content The water content of cartilage was determined using the following procedure. Cartilage blocks were cut from the tracheal rings and all of the soft connective tissue was removed so that only the cartilage remained. These clean blocks of cartilage were equilibrated in isotonic Krebs buffer for approximately 30 minutes. Then, each cartilage block was removed from the Krebs buffer and padded lightly with a cellulose tissue to remove any surface water. Care was taken to perform this step quickly and to ensure that as little water as possible was removed from within the cartilage. The cartilage block was then weighed on a Sartorius analytical balance (model # 2007MP, instrument accuracy—0.1 mg). This weight was recorded as the wet weight of the cartilage. At this point, each cartilage block was placed in a glass vial of known mass. (Tests were performed to ensure that the mass of these vials didn't change on drying.) These vials were then placed in a dessicator, over B D H silica gel (self indicating) dessicant, where they remained for two weeks. During this period the mass of the cartilage blocks was measured twice weekly. The specimens were assumed to be dry when the change in mass from one measurement to the next was less than 0.3 mg. A t this point, the cartilage blocks were weighed again to determine their dry weight. Using the values for the wet and dry weight of the cartilage, Chapter 4. MATERIALS AND METHODS 54 the water content was determined and expressed as a percentage of the wet weight. 4.4.2 Proteoglycan Content The proteoglycan content of the cartilage was determined by Dr . Clive Roberts who is currently studying the biochemistry of tracheal cartilage at St. Paul 's-Hospital in Van-couver, British Columbia. The method used has been previously described by Farndale et al. [26]. The dried cartilage described in subsection 4.4.1 were digested using a buffered papain solution. Suitable dilutions of these solubilised tissue samples were assayed using the dimethylmethylene blue dye-binding assay, standardized with chondroitin sulphate. 4.5 Scanning Electron Microscopy of Tracheal Cartilage To determine the ultrastructural arrangement of the collagen fibrils, a scanning electron microscope (SEM) study was performed on a few select pieces of tracheal cartilage. These specimens were prepared for S E M using standard techniques [16] as described below. 4.5.1 Dry Fracture Technique The previously frozen cartilage pieces were thawed and the connective tissue sheath and epithelium were removed. The cartilage was fixed overnight in 2.5% glutaraldehyde in 0.1 M sodium cacodylate buffer and then washed and stored in cacodylate buffer. The cartilage was dehydrated through a graded series of ethanol-water solutions followed by isoamylacetate. At this point, the cartilage was critical point dried in a Balzers Union critical point dryer CPD020. Subsequently, a razor blade was used to cut lines part way into the cartilage and the cartilage was dry fractured along these lines. The cartilage was mounted on aluminum stubs using silver dag adhesive and then placed in the chamber of a Balzers sputter coating unit SCA010 and sputter coated with gold-palladium. Finally, Chapter 4. MATERIALS AND METHODS 55 the coated cartilage was observed on a Cambridge scanning electron microscope. 4.5.2 Wet Cut Technique The previously frozen cartilage pieces were thawed fixed overnight in 2.5% glutaraldehyde in 0.1 M sodium cacodylate buffer. Upon removal from the cacodylate buffer, the-cartilage pieces were sectioned using a sharp Wilkinson Sword razor blade. These cartilage sections were then dehydrated through a graded, series of ethanol-water solutions followed by isoamylacetate. A t this point, the cartilage sections were critical point dried in a Balzers Union critical point dryer CPD020 . The cartilage sections were mounted on aluminum stubs using silver dag adhesive and then placed in the chamber of a Balzers sputter coating unit SCA010 and sputter coated with gold-palladium. Finally, the coated cartilage was observed on a Cambridge scanning electron microscope. 4.6 Data Analysis The stress-strain data were analysed in order to provide estimates of the maximum error associated with the measurement of these quantities. The method used to perform this error analysis is outlined in appendix H . Examination of equation 3.3 indicates that the tensile stiffness of a material can be determined by calculating the slope of the stress-strain curve. To do this, a least squares linear regression was performed on the stress-strain data obtained from the experiments. As described in appendix E , the regression was performed in two ways. The first method, M E T H O D A , determined the 'best' fit by minimising the sum of the squares of the residuals while the second method, M E T H O D B, imposed the additional stipulation that the regression line must pass through the origin. The 90 % confidence intervals for both the slope and intercept of the regression lines, determined using M E T H O D A , Chapter 4. MATERIALS AND METHODS 56 were also calculated. These calculations are also outlined in appendix E . The layer-wise variations in the tensile stiffness of the tracheal cartilage were analysed statistically, by Barry Wiggs of St. Paul's hospital in Vancouver, Brit ish Columbia, using the restricted maximum likelihood technique which is described in detail by Feldman [27]. To perform this analysis of the layer-wise variation in the stress-strain curves for all of the human subjects combined, the stress-strain data were grouped according to their layer number. Then, a weighted least squares analysis (see appendix F) was performed on the grouped data in order to provide reasonable estimates of the slope and intercept of the regression line for each group. These values were used as the init ia l 'guesses' for the iterative restricted maximum likelihood technique which provided refined values for the slope and intercept of the average regression line for each layer of cartilage. The linear relationships between a) the cartilage biochemistry and age, and b) the tensile stiffness and cartilage biochemistry, were determined by calculating the Pearson correlation coefficients for these sets of data. This procedure is outlined in appendix G . Chapter 5 R E S U L T S The results of the experiments are presented as follows: • Calibration of the M P T T . • Results of Tensile Tests. 1. Estimation of the maximal measurement errors associated with the calculation of stress and strain. 2. Comparison of the results obtained using the M P T T and the T A T T to test the material standards. 3. Results of tensile tests performed on tracheal cartilage. (a) Layer-wise variations in tensile stiffness. (b) Hysteresis in the stress-strain curves. (c) Age-related changes in the tensile stiffness. • Scanning electron micrographs of tracheal cartilage. • Results of biochemical analyses of tracheal cartilage. 1. Correlations of cartilage biochemistry with age. 2. Correlations of tensile stiffness with cartilage biochemistry. These results are presented in the following sections. 57 Chapter 5. RESULTS 58 5.1 Calibration of the M P T T The data obtained from the procedure described in section 4.3.1 were used to prepare a calibration curve for the M P T T force measurements. This calibration curve, which is a plot of measured vs. applied force, can be found in appendix C . The difference between the force measured by the M P T T and the actual applied force is shown to be, on average, approximately 1 % of the measured force. This estimate of the average force measurement error was used in the determination of the estimated maximum error in the calculation of stress for the cartilage test specimens (see appendix H) . 5.2 Results of the Tensile Tests Tensile tests were performed on the three materials used as standards for this research using both the M P T T and the T A T T . A total of 24 tests were performed on these materials with a minimum of two tests performed on a given material using a given tensile tester. The results of these tests are described in subsection 5.2.2. Tensile tests were also performed on tracheal cartilage specimens obtained from the ten human cadavers. Using the M P T T , A total of 91 tests were performed on these specimens. Tables E . l , E.2, E.3 and E.4 i n appendix E provide details regarding the number of specimens tested, the number of different cartilage rings tested and the number of duplicate tests performed at a given depth within the cartilage for each human subject. In addition these tables contain the results of the linear regression analyses performed on each cartilage test specimen. These results wi l l be discussed in the following subsections. A l l of the tensile tests were performed in such a manner as to provide a set of force-elongation data for each specimen tested. These force-elongation data were translated into stress-strain data using equations 3.1 and 3.2 respectively. Subsection 5.2.1 describes these data and the estimated maximal error in the stress-strain measurements. Chapter 5. RESULTS 59 5.2.1 Estimation of the Maximal Measurement Error Associated with the Calculation of Stress and Strain The calculation of the estimated maximal error in the stress and strain measurements was performed in order to quantify the effect of combining the errors associated with the individual measurements used in the calculation of stress and strain. The details of these calculations are presented in appendix H . The tables of raw results included in appendix H indicate that the stress calculations were subject to an approximately 15 % relative error while the strain calculations ex-hibited an absolute error of approximately 1 %. The calculations in appendix H clearly demonstrate that approximately 2/3 of the error associated with the calculation of stress is a result of the error in the measurement of the cartilage thickness. About 1/3 of the error in the stress calculation can be attributed to the error i n the measurement of the width of the cartilage specimen while the error in the force measurment was responsible for only about 1/20 of the total. In addition, the calculations presented in appendix H emphasize that the error in the strain calculation has approximately equal dependence on the accuracy with which the initial and current positions of the gauge marks were measured. 5.2.2 Comparison of the Results obtained using the M P T T and T A T T The data obtained from the procedure described in section 4.3 was used to prepare the graphs shown in figure 5.1. Figure 5.1 displays the results of the tensile tests performed on the three materials used as standards. The results of the tests performed using the M P T T are compared with those obtained using the T A T T . The graph of the stress-strain curve for the tangum rubber clearly shows that, at strains below 60 %, there was no difference between the results obtained using the M P T T Chapter 5. RESULTS 60 and the T A T T . A t 100 % strain, the average relative difference between the M P T T and T A T T results was 10 % — w i t h i n the maximum estimated measurement errors tabulated in appendix H . Figure 5.1 (C) also shows that there was no difference between the M P T T and T A T T stress-strain curves for latex tubing over the entire range of strains tested. In addition, between 0 % and 15 % strain, figure 5.1 (D) shows a negligible difference between the M P T T and T A T T results for the tests performed on tygon tubing. However, at strains greater than 15 %, the results obtained using the equilibrium measurements of the M P T T were consistently lower than those of the constant strain-rate tests performed using the T A T T . The implications of these results wi l l be discussed in section 6.1.2. 5.2.3 Results of Tensile Tests Performed on Tracheal Cartilage Using the M P T T , tensile tests were performed on slices of tracheal cartilage. The results of these experiments are shown in figures 5.2 through 5.6. For each tensile test, the stress and strain values were calculated using equations 3.1 and 3.2 respectively. These values were used to produce the stress-strain curves contained in the aforementioned figures. These figures serve to illustrate that the stress-strain curves for the tracheal cartilage test specimens were essentially linear. Some curvature was found in the graphs, but this usually occurred at strains greater than 10 %. At strains less than 10 %, almost all of the stress-strain curves demonstrated linearity. Equation 3.3 indicates that the tensile stiffness of a material can be determined by calculating the slope of the.material's stress-strain curve. Thus, in order to calculate the tensile stiffness of the cartilage test specimens, a least squares linear regression was performed on the stress-strain data. In an attempt to analyse the data without bias, only the stress-strain data obtained at strains less than 10 % were used in the linear regression. The linear regression was performed in two different ways as outlined in appendix E. The first method, M E T H O D A , involved a standard linear regression in which the 'best' Chapter 5. RESULTS 61 (A) tangum rubber o.o o.o (C) latex tubing 0.0 40.0 80.0 120.0 160.0 200.0 0.0 20.0 40.0 60.0 80.0 100.0 strain (%) strain (%) TENSILE TESTER (B) ! f ™ T . (D) * = MPTT tangum rubber 0.8 tygon tubing 1.6 fx 0.6 0.4 0.2 ,9" 0.0 1^-0.0 10.0 20.0 30.0 strain (%) 40.0 CL, 1.2 0.8 20.0 strain (%) 30.0 40.0 Figure 5.1: Results of experiments comparing the stress-strain curves obtained using the M P T T and T A T T to test three materials used as testing standards. A) Entire stress-strain range measured for tangum rubber. B) Close-up of the stress-strain curve shown in (A). C) Entire stress-strain range measured for latex tubing. D) Entire stress-strain range measured for tygon tubing. Chapter 5. RESULTS 62 (A) human #1, age 81 LAYER ° = 1 * = 2 • =3 0.0 3.0 6.0 9.0 strain (%) GO 1.0 0.6 0.6 0.4 0.2 (B) human #2, age 17 0.0 LAYER x = 4 • = 5 * =6 LAYER - = 7 « =8 • =9 ia.0 15.0 o o O v X i L _ 0.0 20.0 40.0 60.0 strain (%) 80.0 100.0 (C) human #1, age 81 20.0 4 ° 00 01 OJ C on V 00 fl <D 10.0 2.0 4.0 6.0 layer number (D) human #2, age 17 o.o 2.0 4.0 6.0 layer number 8.0 8.0 10.0 10.0 Figure 5.2: Results of tensile tests performed on tracheal cartilage slices. A) and B) Stress-strain curves for humans #1 and #2 respectively. C) and D) Tensile stiffness vs. layer number for human #1 and #2 respectively. Chapter 5. RESULTS 63 (A) LAYER o = i * =2 • =3 LAYER x = 4 « = 5 * = 6 LAYER « = 7 « = 8 • = 9 (0 human #3, age 50 human #3, age 50 £§. GO CO V 0.0 4.0 8.0 12.0 strain (%) 16.0 05" OH 00 m v 0] G 20.0 20.0 15.0 10.0 0.0 ao 4.0 6.0 layer number 10.0 12 0.6 0.4 (B) human #4, age 58 * A + X X » 0.0 La; 0.0 4.0 6.0 strain (%) 8.0 10.0 20.0 0.0 0>) human #4, age 58 0.0 2.0 4.0 6.0 layer number 8.0 Figure 5.3: Results of tensile tests performed on tracheal cartilage slices. A) and B) Stress-strain curves for humans #3 and #4 respectively. C) and D) Tensile stiffness vs. layer number for human #3 and #4 respectively. Chapter 5. RESULTS 64 (A) human #5, age 21 LAYER o = i • =2 < = 3 CL. 00 2 10.0 20.0 30.0 strain (%) (B) human #6, age 28 • PL, 0) LAYER « = 4 • = 5 ' = 6 40.0 0.0 4.0 8.0 12.0 strain (%) 16.0 20.0 LAYER • = 7 - = 8 - = 9 20.0 2S.0 0.0 0.0 human #5, age 21 4.0 6.0 layer number (D) human #6, age 28 2.0 4.0 6.0 10.0 8.0 10.0 layer number Figure 5.4: Results of tensile tests performed on tracheal cartilage slices. A) and B) Stress-strain curves for humans #5 and #6 respectively. C) and D) Tensile stiffness vs. layer number for human #5 and #6 respectively. Chapter 5. RESULTS 65 (A) human #7, age 20 2.5 0.0 0.0 5.0 10.0 15.0 strain (5<) (B) human #8, age 60 01 0} 21 2.0 1.5 1.0 0.5 0.0 LAYER o = i ' =2 - =3 LAYER « = 4 « = 5 ' = 6 20.0 25.0 0.0 6.0 10.0 strain ( 15.0 20.0 CL, 0} TO CO 0) TO G 0) LAYER « = 7 « = 8 • = 9 (9 human #7, age 20 25.0 20.0 15.0 h 10.0 r 5.0 o.o 0.0 2-0 4.0 6.0 layer number human #8, age 60 25.0 2.0 4.0 6.0 layer number 8.0 10 Figure 5.5: Results of tensile tests performed on tracheal cartilage slices. A) and B) Stress-strain curves for humans #7 and #8 respectively. C) and D) Tensile stiffness vs. layer number for human #7 and #8 respectively. Chapter 5. RESULTS 66 (A) human #9, age 18 LAYER o = 1 . = 2 • =3 1.0 0.8 <£ 0-6 V] CO 0.2 0.0 0.0 10.0 20.0 30.0 strain (%) (B) human #10, age 21 LAYER x = 4 • = 5 ' = 6 LAYER • = 7 - = 8 • = 9 o o O A O A o • A X • O x 4 O « X » ° * X » - o * . o * • 01 0) a) 1« 0.0 10.0 20.0 30.0 strain (%) 40.0 40.0 (C) human #9, age 18 0.0 2.0 4.0 6.0 layer number human #10, age 21 •JP OH m ft) C 20.0 15.0 h JS 10.0 CO 0.0 2.0 4.0 6.0 layer number 10.0 10.0 Figure 5.6: Results of tensile tests performed on tracheal cartilage slices. A) and B) Stress-strain curves for humans #9 and #10 respectively. C) and D) Tensile stiffness vs. layer number for human #9 and #10 respectively. Chapter 5. RESULTS 67 straight line fit of the data was determined by minimising the sum of the squares of the residuals while the second method, M E T H O D B, imposed the additional stipulation that the regression line must pass through the origin. The results of this curve fitting procedure are tabulated in appendix E and plotted in -parts (C) and (D) of figures 5.2-5.6. These results indicate that the equilibrium tensile stiffness of tracheal cartilage falls in the range of approximately 1-20 M P a . In addition, the tables in appendix E contain the 90 % confidence intervals for both the slope and Y-intercept of the regression lines calculated using M E T H O D A . These results clearly illustrate that the slopes of the regression lines calculated using M E T H O D B fell within the 90 % confidence intervals of the slopes calculated using M E T H O D A . In addition, in all of the cartilage stress-strain curves, the 90 % confidence interval for the Y-intercept calculated using M E T H O D A bracketted the origin. Layer-Wise Variations in the Tensile Stiffness Figures 5.2-5.6 illustrate the layer-wise variations in the tensile stiffness of tracheal car-tilage. The stress-strain curves in these figures show the response of the different layers of cartilage to an imposed tensile stress. Equation 3.3 indicates that the slopes of these stress-strain curves give the tensile stiffness of the respective cartilage layers. Thus, in-cluded in figures 5.2-5.6 are plots of tensile stiffness vs. layer number for the tracheal cartilage of a given human subject. In an attempt to avoid placing any bias on the results of the tensile tests, the tensile stiffness values recorded in these figures were calculated by performing a least squares linear regression on only the stress-strain data which was in the range of 0-10 % strain. This step was taken in order to avoid the change in slope of the stress-strain curves which appeared to occur at a strain of approximately 10 % in some specimens. In addition, since it is obvious that under normal conditions the stress-strain curve should pass through the Chapter 5. RESULTS 68 origin, the regression values used to produce the tensile stiffness vs. layer number graphs were those in which the regression line was forced through the origin (ie. M E T H O D B). As described in section 4.2, layer #1 represents the outer-most superficial 100 fim layer of the cartilage; subsequent 100 fim layers are numbered in succession. Figures 5.2-5.6 clearly show a layer-wise variation in the tensile stiffness of the tracheal carti-lage specimens studied. The tensile stiffness is greatest in layer #1 and decreases with increasing depth from the cartilage surface. As mentioned in section 4.6, the layer-wise variations in the tensile stiffness were analysed statistically using the restricted maximum likelihood technique. The results of this analysis, illustrated in figure 5.7, indicate that the tensile stiffness of layer #1 was greatest and that the tensile stiffness progressively decreased with increasing depth in the tissue. In addition, figure 5.7 illustrates that the layers of cartilage studied in these experiments could be divided into two zones: 1. an outer superficial zone comprised of layers # 1,2 and 3. 2. a middle zone comprised of layers # 4,5 and 6. Results of Tensile Tests Performed on Duplicate Layers of Cartilage As outlined i n section 4.2, in some cases, duplicate tensile tests were performed on identi-cal cartilage layers which were sectioned from different cartilage rings of a given trachea. As a result, the reproducibility of the tensile tests could be examined. A n illustration of the reproducibility of the tensile tests is given in figure 5.8 where the stress-strain curves of layer #4 obtained from four different cartilage rings of human #3 are plotted. This figure indicates that, at 10 % strain, the maximum difference in stress is approximately 35 % of the average stress at that strain. Chapter 5. RESULTS 69 Figure 5.7: REML regression results for layers #1-6 of all of the human subjects combined. Although the regression was performed only on the data which fell between 0-10 % strain, for clarity, the regression lines are plotted up to 20 % strain. Chapter 5. RESULTS 70 h u m a n #3 layer #4 1.6 CO a. CO CO <u u 1.2 0.8 -0.4 0.0 X X x 5 X x 0.0 4.0 8.0 12.0 s tra in (%) 16.0 20.0 Figure 5.8: Stress-strain curves of tracheal cartilage representing four tensile tests performed on layer #4 obtained from four different cartilage rings of human #3. The results of al l of the duplicate tests are shown in parts (C) and (D) of figures 5.2-5.6 where the tensile stiffness of each specimen tested is plotted as a function of its layer number. In general, the degree of scatter in these duplicate tests is small when compared with the overall layer-wise changes in tensile stiffness for a given human subject. Hysteresis in the Stress-Strain curves A study of hysteresis in the stress-strain curve was performed on approximately 20 % of the cartilage specimens tested. The results of these experiments are shown i n figures 5.9-5.13. These results show that hysteresis in the stress-strain curve is negligible up to a maximal strain of about 10 %. Above this value, hysteresis and residual strain are clearly evident. A clearer illustration of the relationship between maximal strain and residual strain Chapter 5. RESULTS 71 (A) human #7, ring #2, layer #2 2.0 I 1.5 -strain (%) Figure 5.9: Results of hysteresis experiments tracheal cartilage. Human #7 was 20 years old (C) human #7, ring #2, layer #7 1.6 i 12 -25.0 strain (%) performed on the stress-strain response of Chapter 5. RESULTS 72 (A) human #8, ring #3, layer #1 ZJ5 I strain (%) (B) human #8, ring #3, layer #2 i.e • 1.2 -10.0 strain (%) (C) human #8, ring #3, layer #3 1.6 i 0.0 5.0 10.0 1S.0 20.0 strain (%) (D) human #8, ring #3, layer #4 1.6 1 1 15.0 20.0 strain (%) Figure 5.10: Results of hysteresis experiments performed on the stress-strain response of tra-cheal cartilage. Note that in parts (B), (C) and (D) the decreasing portion of the stress-strain curve is super-imposed on the increasing part. Human #8 was 60 years old. Chapter 5. RESULTS 73 (A) human #8, ring #2, layer #4 1.6 (C) human #8, ring #2, layer #6 1.6 Figure 5.11: Results of hysteresis experiments performed on the stress-strain response of tracheal cartilage. Mote that in part (C) the decreasing portion of the stress-strain curve is super-imposed on the increasing part. Human #8 was 60 years old. Chapter 5. RESULTS 74 Figure 5.12: Results of hysteresis experiments performed on the stress-strain response of tracheal cartilage. Humans #9 and #10 were 18 and 21 years old respectively. Chapter 5. RESULTS 75 (A) human #10, ring #1, layer #5 1.0 (C) human #10, ring #3, layer #7 1.0 Figure 5.13: Results of hysteresis experiments performed on the stress-strain response of tracheal cartilage. Human #10 was 21 years old. Chapter 5. RESULTS 76 40.0 Maximal Strain (%) Figure 5.14: The effect of maximal strain on residual strain. was produced by extracting this data from the aforementioned hysteresis curves. M a x i -mal strain was defined as the strain corresponding to the maximal applied stress i n the hysteresis loop and the residual strain was defined as the strain corresponding to zero stress on the downward portion of the hysteresis loop. The effect of maximal strain on residual strain is plotted in figure 5.14. This figure emphasizes the fact that hysteresis is negligible up to about 10 % strain. A least squares linear regression was performed on the data which comprise figure 5.14. Since a change in the slope of this curve occurred at a maximal strain of about 9-10 %, only the data having a maximal strain greater than 9 % were used in the regression. The results of this analysis indicated that the regression line had a slope of 0.725 and crossed the abscissa at a maximal strain of 9.5 %. The Pearson correlation coefficient for the 14 data points used in this regression was r = 0.943—a clearly significant linear correlation. Chapter 5. RESULTS 77 Age-Related Changes in the Tensile Stiffness of Tracheal Cartilage Using the designations of the cartilage zones described above, plots of cartilage tensile stiffness as a function of age were constructed. These plots are shown in figure 5.15. To produce these plots, the tensile stiffness of the outer superficial zone was defined as the average stiffness of layers # 1 , 2 and 3 while the tensile stiffness of the middle zone was denned as the average stiffness of layers # 4,5 and 6. The average stiffness of layers 1 through 6 was also calculated for each human subject and plotted as a function of age. The graphs in figure 5.15 clearly show an age-related increase i n the tensile stiffness of tracheal cartilage from the middle of the second decade to the end of the third decade of life. Between the fourth and eighth decades, the tensile stiffness appears to remain relatively constant; however, the number of data points in this region is small and the degree of scatter is significant. 5.2.4 Scanning Electron Micrographs of Tracheal Cartilage In an attempt to better understand the layer-wise variation i n the tensile properties of the tracheal cartilage, a scanning electron microscope (SEM) study was performed on a few cartilage samples. Pertinent scanning electron micrographs are shown in figures 5.16 through 5.26. Results of D r y Fracture Technique The specimen in figure 5.16 was prepared by dry fracturing the cartilage along the two planes perpendicular to the inner surface of the tracheal cartilage ring. The part of the exposed surface which appears to be smooth is a result of the smearing of the tissue which was caused by the razor blade used to cut into the tissue. The rest of the micrograph represents the part of the tissue that was dry fractured. In the fractured region, which Chapter5. RESULTS 78 (A) OUTER SUPERFICIAL ZONE (C) AVERAGE VALUES 20.0 15.0 15.0 0> 10.0 in 01 a> 10.0 to "53 C 5.0 CO 0 5.0 0.0 0.0 20.0 40.0 60.0 Age (years) 80.0 100.0 o.o 0.0 20.0 40.0 Age (years) 60.0 80.0 100.0 (B) MIDDLE ZONE 20.0 15.0 4) C 10.0 to 93 c 5.0 0.0 I ' ' ' ' • 1 ' " ' 1 0.0 20.0 40.0 60.0 80.0 100.0 Age (years) Figure 5.15: Tensile stiffness of tracheal cartilage as a function of age. A) The tensile stiffness' of layers #1-3 are averaged. B) The tensile stiffness' of layers #4-6 are averaged. C) The tensile stiffness' of layers #1-6 are averaged. Chapter 5. R E S U L T S 79 1 mm Figure 5.16: Scanning electron micrograph of tracheal cartilage showing the smeared region where the cartilage was cut with a razor blade and the fibrous region where the cartilage was dry fractured. Chapter 5. RESULTS 80 represents the middle zone, there is an apparent fibre alignment perpendicular to the cartilage surface; however, due to the low magnification of this micrograph, the figure lacks detail. For the cartilage specimen illustrated i n figure 5.16, the razor blade was used to cut into the inner surface of the cartilage. Thus, the fibre alignment in the inner superficial region of the cartilage ring is not shown. As noted above, the fibre alignment in the middle zone of the cartilage appears to be perpendicular to the cartilage surface. In this figure, the outer superficial zone of the cartilage appears between the two perpendicularly aligned regions of the split cartilage. Although it is difficult to determine the alignment of the fibres in the outer superficial zone because it was not possible to fracture through this region, this fact.alone suggests that, in moving from the middle zone to the outer superficial zone, the fibres appear to turn and run tangentially to the plane of the cartilage surface. Figure 5.17 provides a closer view of the border between the part of the cartilage which was cut with the razor blade and the region which was dry fractured. The cut portion appears in the upper left corner of the figure while the fractured portion, representing the middle zone, is located in the lower right corner. The lacunae, or 'pits', visible in this figure indicate where chondrocytes previously existed. Again the fibre alignment in the fractured portion of the cartilage appears to be oriented perpendicular to the cartilage surface. Figure 5.18 provides a closer view of the cartilage in the region of the lacuna appearing in the upper right quadrant of figure 5.17. Again, the upper left portion of the micrograph displays the region of the cartilage which was cut with the razor blade while the remaining majority of the micrograph shows the dry fractured region. The elliptical image in the figure is a lacuna with its major axis aligned perpendicular to the cartilage surface. In this micrograph, the collagen appears as thin lines. The thickness of these lines indicates Chapter 5. R E S U L T S 81 40 (im Figure 5.17: Scanning electron micrograph of tracheal cartilage showing the border between t.ta region which was cut with the razor blade and the region which was dry fractured. The craters are lacunae. Chapter 5. RESULTS 82 10 [Ml Figure 5.18: Scanning electron micrograph of tracheal cartilage showing a close-up view of a lacuna and aligned collagen fibrils oriented perpendicular to the cartilage surface. Chapter 5. RESULTS 83 that the collagen in tracheal cartilage is organised into fibrils. The alignment of these fibrils, in the middle zone, exhibits a clear orientation perpendicular to the cartilage surface. Figure 5.19 provides a close-up view of the collagen fibrils in the middle zone of the cartilage. The bright spots on the micrograph represent the charged ends of the collagen fibrils. It is the electrical charge on these ends which causes them to appear brighter. From this figure, the diameter of the collagen fibrils can be estimated to be on the order of 100 nm. A primary diagonal alignment of the collagen fibrils is evident in this figure. Aga in , this orientation is perpendicular to the cartilage surface. Figures 5.16 through 5.19 indicate that the collagen is arranged into fibrils within tracheal cartilage and that the diameter of these fibrils is on the order of 100 nm. In addition, the orientation of these fibrils in the middle zone of the tissue is seen to be perpendicular to the cartilage surface. Results of Wet Cutting Technique Figure 5.20 shows a longitudinal section of tracheal cartilage prepared using the wet cutting technique. The outer surface of the cartilage is at the top of the figure while the inner surface is at the bottom. This figure suggests that tracheal cartilage is composed of three ultrastructural zones: an outer superficial zone, a middle zone and an inner super-ficial zone. Since the middle zone has already been described, the following paragraphs wi l l be devoted to a description of the inner and outer superficial zones. The inner superficial zone of tracheal cartilage is shown at low magnification in figure 5.21. This figure shows the orientation of the collagen fibrils changing from perpendicular to the cartilage surface in the middle zone to parallel to the cartilage surface in the inner superficial zone. Figure 5.22 is a close-up view of the cartilage shown in figure 5.21 showing the transition region between the middle zone and the inner superficial zone. Chapter 5. RESULTS 84 1 fim Figure 5,19: Scanning electron micrograph of tracheal cartilage showing the diameter, align-ment and charged ends of the collagen fibrils. Chapter 5. RESULTS 85 400 fim Figure 5.20: Scanning electron micrograph of tracheal cartilage showing the division of the tissue into three ultrastructural zones. Chapter 5. RESULTS 86 100 [Ml Figure 5.21: Scanning electron micrograph of tracheal cartilage showing the change in the orientation of the collagen fibrils between the middle zone and the inner superficial zone. Chapter 5. RESULTS 87 In this figure, the cartilage surface is in the horizontal plane and the collagen fibrils are oriented at an angle of about 20° from the horizontal axis at the bottom of the figure ranging to about 40° from the horizontal axis at the top of the figure. figure 5.23 shows an apparent layered arrangement of the collagen fibrils in the inner superficial zone. A close-up view of the central part of this figure is shown in figure 5.24. Figure 5.24 shows alternating light and dark bands of collagen fibrils. As stated earlier, when collagen fibrils are cut, the exposed ends appear brighter under the scanning electron microscope. Therefore, the alternating light and dark bands present in the inner superficial zone probably represent collagen fibrils oriented along two perpendicular axes in a plane parallel to the cartilage surface. Figure 5.25 is a micrograph of the outer superficial zone of tracheal cartilage. The cartilage is oriented in the vertical direction with the connective tissue and outer surface of the cartilage on the right side of the figure and the cartilage middle zone on the left side. This figure shows the orientation of the collagen fibrils changing from perpendicular to the cartilage surface in the middle zone to parallel to the cartilage surface in the outer superficial zone. Figure 5.26 shows the outer superficial zone at high magnification. In this figure, the collagen fibrils are aligned parallel to the cartilage surface and oriented longitudinally. Notice that the alternating light and dark bands, present in the scanning electron micro-graphs of the inner superficial zone, are absent i n the figures showing the outer superficial zone. This indicates that, in the outer superficial zone, the collagen fibrils are primarily oriented longitudinally. Figures 5.20-5.26 indicate that tracheal cartilage can be divided into three ultrastruc-tural zones with the collagen fibrils in both the inner and outer superficial zones aligned parallel to the cartilage surface. Chapter 5. RESULTS 88 40 fim Figure 5.22: Scanning electron micrograph of tracheal cartilage showing the transition region between the middle zone and the inner superficial zone. Chapter 5. RESULTS 40 fim Figure 5.23: Scanning electron micrograph of tracheal cartilage showing the layered arrange ment of the inner superficial zone at low magnification. Chapter 5. R E S U L T S 90 10 fim Figure 5.24: Scanning electron micrograph of tracheal cartilage showing the layered arrange-ment of the inner superficial zone at high magnification. Chapter 5. RESULTS 91 100 fim Figure 5.25: Scanning electron micrograph of tracheal cartilage showing the outer superficial zone at low magnification. Chapters. RESULTS 10 fim Figure 5.26: Scanning electron micrograph of tracheal cartilage showing the outer superficial zone at high magnification. Chapter 5. RESULTS 93 5.2.5 Results of Biochemical Analyses of Tracheal Cartilage The determination of the biochemical composition of the tracheal cartilage enabled a study of the variation of biochemical composition with age. The results of this study are shown in figure 5.27. Included in this figure are the Pearson correlation coeffiecients (r-values) for the plots. The degree of freedom in these correlations was 7. Thus, at the 95 % confidence level, the critical correlation coefficient was 0.666. Examination of the correlation coefficients in figure 5.27 indicates that no significant correlations existed between biochemical composition and age; however, a visual examination of the graphs reveals that water content may be related wi th age, but the degree of scatter is high. The tensile stiffness of the tracheal cartilage was correlated with its biochemical com-position. Figures 5.28 through ?? present the plots of tensile stiffness vs. biochemical composition. Again, the number of degrees of freedom in these graphs is 7 and the critical correlation coefficient at the 95 % confidence level is 0.666. Figure 5.28 shows the relationship between the tensile stiffness and the cartilage glycosaminoglycan content expressed as a percentage of the wet mass. Examination of the data and the correlation coefficients for each plot indicates that there was no significant correlation between tensile stiffness and the glycosaminoglycan content expressed as a percentage of the wet mass. Similarly, examination of figure 5.29 indicates that there was also no significant correlation between tensile stiffness and the glycosaminoglycan content expressed as a percentage of the dry mass of the cartilage. Figure 5.30 clearly illustrates that there was a significant negative correlation between the tensile stiffness and the water content of the cartilage. This correlation was significant for both the outer superficial zone and the middle zone as well as for the average of all the tensile stiffness values for each subject. Chapter 5. RESULTS 94 (A) (C) DRY WEIGHT BASIS (r=-0.132) CARTILAGE WATER CONTENT (r=-0.514) OJ2S 80.0 0.20 75.0 03 & Q 3 o n CO a 0.15 0.10 0.05 IS I cS u 70.0 65.0 0.00 0.0 20.0 40.0 Age (years) 60.0 80.0 100.0 60.0 0.0 20.0 40.0 Age (years) 60.0 80.0 100.0 WET WEIGHT BASIS (r=0.400) 0J0 1 0.05 -0.00 1 • 1 ' 1 • ' ' 1 1 1 0.0 20.0 40.0 60.0 80.0 100.0 Age (years) Figure 5.27: Correlation of the biochemical composition of tracheal cartilage with age. Gly-cosaminoglycan content expressed on A) a dry weight basis and B) a wet weight basis. C) Cartilage water content. Chapter 5. RESULTS 95 (A) OUTER SUPERFICIAL ZONE (r=0.402) 20.0 0.00 0.05 Mass GAG / Wet Mass 0.10 (C) AVERAGE VALUES (r=0.498) 20.0 0.00 0.05 Mass GAG / Wet Mass o.io (B) MIDDLE ZONE (r=0.605) 20.0 0.0 0.00 0.05 Mass GAG / Wet Mass o.io Figure 5.28: Correlation of the tensile stiffness of tracheal cartilage with the total gly-cosaminoglycan content expressed as a percentage of the cartilage wet mass. A) The tensile stiffness' of layers #1-3 are averaged. B) The tensile stiffness' of layers #4-6 are averaged. C) The tensile stiffness' of layers #1-6 are averaged. Chapter 5. RESULTS 96 (A) OUTER SUPERFICIAL ZONE (r=-0.325) 20.0 0.0 0.100 0.125 0.150 0.175 Mass GAG / Dry Mass 0200 (C) AVERAGE VALUES (r=-0.246) as n 01 V C I—I 00 d 20.0 15.0 10.0 0.100 0.125 0.150 0.175 Mass GAG / Dry Mass 0.200 (B) MIDDLE ZONE (r=-0.120) 20.0 0.100 0.125 0.150 0.175 Mass GAG / Dry Mass 0200 Figure 5.29: Correlation of the tensile stiffness of tracheal cartilage with the total gly-cosaminoglycan content expressed as a percentage of the cartilage dry mass. A) The tensile stiffness' of layers #1-3 are averaged. B) The tensile stiffness' of layers #4-6 are averaged. C) The tensile stiffness' of layers #1-6 are averaged. Chapter 5. RESULTS 97 (A) (C) OUTER SUPERFICIAL ZONE (r=-0.716) AVERAGE VALUES (r=-0.727) 20.0 60.0 70.0 Water Content (%) 60.0 20.0 60.0 70.0 Water Content (%) 60.0 (B) MIDDLE ZONE (r=-0.700) o, 00 00 V 33 CO 00 20.0 15.0 10.0 0.0 60.0 70.0 Water Content (%) 80.0 Figure 5.30: Correlation of the tensile stiffness of tracheal cartilage with the water content. A) The tensile stiffness' of layers #1-3 are averaged. B) The tensile stiffness' of layers #4-6 are averaged. C) The tensile stiffness' of layers #1-6 are averaged. Chapter 6 D I S C U S S I O N This chapter is organised as follows: • Discussion of the results of the tensile tests. 1. Analysis of the maximal measurement errors associated with the calculation of stress and strain. 2. Comparison of the results obtained using the M P T T and the T A T T to test the material standards. 3. Analysis of the stress-strain curves of tracheal cartilage. (a) Comparison of the results of the tensile tests for tracheal cartilage with literature values reported for articular cartilage. (b) Analysis of the results of tensile tests performed on duplicate layers of cartilage. (c) Hysteresis in the stress-strain curves. (d) Layer-wise variations in tensile stiffness. (e) Age-related changes in the tensile stiffness. (f) Examination of cartilage creep. • Physiological significance of the tensile tests. 1. Tensile stiffness as a measure of the ability of the cartilage to maintain form in vivo. 98 Chapter 6. DISCUSSION 99 2. Significance of the layer-wise variations in the tensile stiffness of tracheal car-tilage. 3. Significance of the age-related changes in the tensile stiffness of tracheal car-tilage. These points are discussed in the following sections. 6.1 Analysis of the Results of the Tensile Tests 6.1.1 Analysis of the Max imum Measurement Errors Associated W i t h the Calculation of Stress and Strain Errors in the stress calculation As described in section 5.2.1, the stress calculations, for the tensile tests performed on the M P T T , were subject to a relative error of approximately 15 %. A full 95 % of this error was a result of the errors associated with the specimen width and thickness measurements while only 5 % of the total stress error was attributable to the error inherent in the M P T T force measurement. Thus, in order to decrease the error associated with the calculation of stress, it is apparent that the errors in the measurement of specimen width and thickness must be reduced. Approximately 2/3 of the error in the stress calculation was attributable to the mea-surement of the thickness of the cartilage test specimen. To reduce this error, it is necessary to replace the micrometer used in these experiments with one which is sen-sitive to the compressibility of the cartilage. Previous researchers have found that the electrical conductivity of cartilage can be used in the determination of its thickness. In this regard, both Akizuk i et al. [2] and Woo et al. [107] have developed current sensing micrometers with a reported accuracy of 3 fim. Chapter 6. DISCUSSION 100 Errors in the strain calculation As described in section 5.2.1, the strain measurements were subject to an absolute error of approximately 1 %. This error was primarily due to the precision with which the optical micrometer could determine the positions of the gauge marks on the specimen (instrument accuracy-10 fim). Thus, in order to reduce this measurement error, either longer specimens or a more precise micrometer is required. 6.1.2 Comparison of the Results Obtained using the M P T T and T A T T to Test the Material Standards The method used to validate the tensile tests performed on the M P T T is described in section 4.3. Briefly, three standard materials were tested on both the M P T T and the T A T T . The T A T T was a standard commercially available materials testing apparatus while the M P T T was specially designed to test biological materials. The results of the tensile tests performed on the M P T T and T A T T were within experimental error as calculated in appendix H . However, two of the material standards—tan gum rubber and tygon tubing—exhibited a slightly higher tensile stiffness when tested on the T A T T . This result was probably due to the fact that the experiments performed using the T A T T were dynamic while those of the M P T T were static equilibrium tests. Since it is normal for rubber materials to exhibit some degree of stress relaxation, the small differences observed in the stress-strain curves obtained using the two different methods are quite reasonable. Therefore, the method used to perform the tensile tests on the M P T T were valid. Chapter 6. DISCUSSION 101 6.1.3 Analysis of the Stress-Strain Curve of Tracheal Cartilage Comparison of the Results of Tensile Tests for Tracheal Cartilage with Liter-ature Values reported for Articular Cartilage The results of the equilibrium, tensile tests performed on the tracheal cartilage specimens indicated that the stress-strain curves were linear up to approximately 10 % strain. In addition, the tensile stiffness' of the tracheal cartilage specimens were found to fall in the range between 1 M P a and 20 M P a . In performing equilibrium tensile tests on articular cartilage, A k i z u k i et al. found that the stress-strain curves were linear up to approximately 15 % strain and that the tensile stiffness' of most of the articular cartilage specimens fell in the range between 1 M P a and 15 M P a . Thus, the results of the tensile tests performed on the tracheal cartilage using the M P T T are very similar to those obtained by previous researchers studying articular cartilage. Analysis of the Results of Tensile Tests Performed on Duplicate Layers of Cartilage The results of the tensile tests performed on duplicate layers of cartilage illustrated that the scatter in these data was substantial. Figure 5.8 shows the results of tensile tests performed on layer #4 obtained from four tracheal cartilage rings of human #3. These results demonstrate that, at 10 % strain, the maximum difference in the stress is 35 % of the average stress at that strain. This variability appears to be quite significant. However, examination of figure 5.3 indicates that this variability in results may be due to a significant layer-wise variation in the tensile stiffness of the tracheal cartilage of human #3. In this figure, layer #3 appears to have an average tensile stiffness of 11.0 M P a while the single value recorded for layer #5 is approximately 5.4 M P a . In addition, layer #4 appears to have an average tensile stiffness of about 6.0 M P a with a range Chapter 6. DISCUSSION 102 of 2.5 M P a . These values indicate that between layer #3 and layer #5—a distance of 200 fim—the difference in tensile stiffness is about 5.6 M P a or 2.8 MPa/100 fim. If the variability in these results were attributed to the layer-wise variation in tensile stiffness, then the 2.5 M P a range in tensile stiffness exhibited by layer #4 would represent a ±50fim variability in the depth within the cartilage from which layer #4 was taken. Such a value is quite reasonable since the actual variability i n assigning layer numbers was probably on the order of 100 /jm. Therefore, the variability i n the results of experiments performed on duplicate layers of cartilage can safely be assumed to be, primarily, a result of the error associated with assigning the layer numbers to the cartilage test specimens. Analysis of the Hysteresis in the Stress-Strain Curves of Tracheal Cartilage As illustrated in figures 5.2-5.6, the stress-strain response of the tracheal cartilage is linear in the range 0-10 % strain. In addition, figure 5.14 shows an absence of hysteresis in the stress-strain curve up to approximately 10 % strain. These results indicate that the equilibrium tensile properties of tracheal cartilage are elastic for strains up to ap-proximately 10 %. Therefore, at strains less than about 10 %, the tensile stiffness of the cartilage is equivalent to its modulus of elasticity. A t strains greater than 10 %, both a marked hysteresis in the stress-strain curve and a residual strain occur. These results indicate that irreversible disruption of the cartilage matrix becomes apparent when the material is stretched more than 10 % of its original length. As illustrated in figure 6.1, the hysteresis present in the stress-strain curves could result from insufficient time being allowed for the cartilage test specimen to reach equi-librium under the imposed stress. If this were the case, then the increasing and decreasing parts of the stress-strain curve would bracket the actual equilibrium stress-strain response of the cartilage. The increasing part of the curve would effectively underestimate the equi-librium strain at a given stress while the decreasing part of the curve would overestimate Chapter 6. DISCUSSION 103 (B) (A) human #7, ring #2. layer #2 2.0 Figure 6.1: A) The effect of non-equilibrium stress-strain data on the development of hys-teresis in the stress-strain curve. B) Hysteresis observed when the cartilage specimens were strained more than 10 % . ' the strain at that same stress; the equilibrium strain would rest somewhere between the two strain values. The non-equilibrium stress-strain curve discussed in the previous paragraph is similar to the results obtained when the maximal strain was greater than approximately 10 %. However, there is one significant difference between the two curves; in the experimental results, a residual strain remains at the bottom of the decreasing portion of the stress-strain curve. This residual strain was found to prevail regardless of the amount of time allotted for equilibration. As noted previously, such a result indicates an irreversible disruption of the cartilage matrix. Thus, the hysteresis in the stress-strain curves can be explained, at least in part, by the irreversible disruption of the cartilage matrix. The above argument does not preclude the possibility of non-equilibrium stress-strain data having been recorded. However, the absence of hysteresis i n the curves where Chapter 6. DISCUSSION 104 the maximal strain was less than 10 % verifies that the stress-strain data, for those experiments, were obtained at equilibrium. Since all of the experiments were performed in an identical manner, the hysteresis observed in some of the stress-strain curves cannot be attributed to the recording of non-equilibrium strain values. Layer-Wise Variation in the Stress-Strain Curve of Tracheal Cartilage The results of the tensile tests on the tracheal cartilage clearly indicate a layer-wise vari-ation in the equilibrium tensile stiffness. The outer superficial zone (layers #1-3) of the cartilage (see figures 5.2-5.6) was shown to have a significantly greater tensile stiffness than the middle zone (layers #4-6). Unfortunately, the experimental protocol did not include a study of the stress-strain response of the inner superficial zone. In retrospect, such information would have been interesting as the scanning electron micrographs indi-cate that tracheal cartilage has three ultrastructural zones. The layer-wise variation in the equilibrium tensile stiffness of the tracheal cartilage can be explained by the heterogeneous organisation of the collagen fibril matrix. The scanning electron micrographs clearly show that the collagen fibrils are aligned radially in the middle zone and essentially perpendicular to the radial direction in both the inner and outer superficial zones (see figure 6.2). This structural arrangement is similar to that found in articular cartilage where the collagen fibrils rise up from the subchondral bone and, in the superficial zone, turn to run tangentially to the cartilage surface. Since it is the longitudinally oriented collagen fibrils which provide the cartilage with a high tensile stiffness, the observed layer-wise variation i n the tensile stiffness is expected. In the outer superficial zone, the tangential alignment of the collagen fibrils allows the cartilage to withstand greater tensile stresses in that region. However, in the middle zone, the alignment of the collagen fibrils perpendicular to the direction of the applied stress results in a lower tensile stiffness. The significance of the layer-wise variation in Chapter 6. DISCUSSION 105 Figure 6.2: Schematic depiction of the ultrastructural alignment of the collagen fibrils in tracheal cartilage. IZ, inner superficial zone; MZ, middle zone; OZ, outer superficial zone. the collagen ultrastructure and tensile stiffness w i l l be discussed in section 6.2. Age-Related Changes in the Tensile Stiffness of Tracheal Cartilage Tensile tests were performed on tracheal cartilage specimens from humans ranging in age from 17 to 81 years. This wide range of ages permitted the age-related changes in the tensile stiffness of tracheal cartilage to be studied. It is important to note, at the outset, that al l of the data from the tensile tests were used in the age study. Therefore, no distinction was made between smokers, non-smokers or diseased individuals. It could be argued that such a lack of control over the test specimens could lead to a high degree of scatter in the results. However, examination of figure 5.15 clearly shows that this was not the case. Calcined cartilage was found in the older subjects in the study. Calcification was Chapter 6. DISCUSSION 106 believed to have had a significant effect on the fracture stress of the tracheal cartilage from the 81 year old subject (human #1). This subjects' cartilage was a yellowish colour and was highly calcified; the cartilage from younger subjects was white and non-calcified. Calcification made the cartilage difficult to section on the vibrating microtome. In addi-tion, in the case of the 81 year old subject, calcification made the cartilage significantly more fragile than that of other subjects. Evidence of this increased fragility is given by the stress-strain data of the test specimens. Most test specimens either did not fracture or fractured close to the maximum imposed stress of about 1.6 M P a . However, many of the test specimens from the 81 year old subject fractured at an imposed stress of about 0.4 M P a . Apparently, calcification may have caused a decrease in the tensile strength of the cartilage without affecting the tensile stiffness, but the mechanisms which caused this effect are not known. The age-related change in the tensile stiffness of tracheal cartilage is shown in figure 5.15. These plots exhibit a significant increase in tensile stiffness from the middle of the second to the end of the third decade of life. The tensile stiffness of the cartilage remained relatively constant from the fourth through the eighth decade; however, between the fourth and eighth decades, the number of data points was few and the degree of scatter was large. Venn [101] has reported an age-related linear decrease in the water content of articular cartilage. Similarly, a biochemical analysis of the tracheal cartilage revealed a trend toward an age-related decrease in the water content. In addition, the tensile stiffness of the cartilage specimens was found to have a significant negative correlation with the water content. While it has already been stated that collagen cross-Unking increases with age [12, 33], it is also beheved that an increased cross-Unking of the collagen fibrils wi l l Umit the size of the proteoglycans to a greater extent. This would result in a decreased ability of the proteoglycans to imbibe water which would be manifested by a decreased Chapter 6. DISCUSSION 107 cartilage water content. Furthermore, Bader et al. [5] have shown that a change in the amount of collagen cross-linking has a significant effect on the tensile stiffness of cartilage. In consideration of these findings, the fact that water content tended to decrease with age, and tensile stiffness increased with both age and decreased water content, leads one to bekeve that an age-related increase in the amount of collagen cross-linking was a reasonable cause of the decreased water content and increased tensile stiffness. It has been previously determined that the size of proteoglycan molecules [89, 100] and aggregates [100] decreases with age. Therefore, it is possible that an age-related decrease in the size of the proteoglycan molecules and aggregates may also be a factor in the age-related reduction in the water content of the cartilage. However, the effect that these changes in the size of the proteoglycans would have on the tensile stiffness of cartilage is unclear. In some ways, the observed age-related changes in the tensile stiffness of tracheal cartilage are similar to those obtained by Kempson [47] in a study of articular (knee) cartilage. Kempson [47] found that the tensile stiffness of articular (knee) cartilage increased to a maximum in the middle of the third decade of life and thereafter decreased with increasing age (see figure 6.3). Thus, the init ial portions of the tensile stiffness vs. age curves are similar for the two types of cartilage. However, after the end of the third decade of life, the two curves appear to differ; the tensile stiffness of the tracheal cartilage remains relatively constant while that of articular cartilage decreases with age. This is, to some extent, understandable when one considers that throughout the course of one's life, the cartilage of the knee is likely to be subjected to considerably more physical abuse than the cartilage of the trachea. Therefore, the differences in the shapes of the tensile stiffness vs. age curves of tracheal cartilage and articular cartilage could result from the differences in the imposed stresses on the two cartilages throughout the course of life. A t this point, it should be clearly reiterated that the results of tensile stiffness vs. age Chapter 6. DISCUSSION (*) Mn/KI 2 300 r 2 0 3 0 * 0 5 0 6 0 7 0 8 0 9 0 1 0 0 * G E < r o w l 20.0 00 <D « c 10.0 -5.0 0.0 0.0 108 (B) 20.0 40.0 Age (years) 60.0 80.0 100.0 Figure 6.3: A) The results of Kempson on the age-related changes in the tensile stiffness of articular (knee) cartilage. Reproduced from Kempson [47]. B) Age-related changes in the tensile stiffness of tracheal cartilage (Tensile stiffness' of layers #1-6 are averaged). exhibited a significant degree of scatter between the fourth and eighth decades. Therefore, it is really not clear as to whether or not the results of these experiments were different from those of Kempson [47]. In fact, it is quite possible that the tensile stiffness of tracheal cartilage may also decrease after the end of the third decade of life; however, the results of these experiments contain too much scatter and, as a result, too few points to make any conclusive statements regarding the age-related changes in the tensile stiffness of tracheal cartilage after the end of the third decade of life. Examination of Cartilage Creep The chart recordings of force vs. time and length vs. time produced during the exper-iments indicated that the transient response of tracheal cartilage could have layer-wise or age-related variations. Ak izuk i et al. [2] have noted that, during rapid compressions, up to 90 % of the compressive stiffness of articular cartilage may be attributed to the Chapter 6. DISCUSSION 109 resistance to interstitial fluid flow. Since the duration of a maximal expiration of air from the lungs is short (< 3 seconds), the transient response of the tracheal cartilage to the stresses applied during such a manoeuvre may be of paramount importance in the understanding of tracheal mechanics. To this end, a further analysis of the results of the tensile tests was performed. As described in section 4.3, the experiments were set up in such a manner that a force was imposed on the cartilage test specimen and the length of the specimen was left free to change in response to the imposed force. In this manner, the creep occurring within the cartilage specimens could be monitored, thus pro-viding a measure of the transient response of the tracheal cartilage to an imposed tensile stress. However, the continuous monitoring capabilities of the M P T T were restricted to measurements representing a change in length of the entire specimen. Thus, these mea-surements were different from those provided by the optical micrometer used to monitor the gauge section of the test specimen. As a result, the chart recorder, which obtained its input from the M P T T , included the non-uniform stress regions, near the ends of the test specimen, in its recordings. This may have produced erroneous results. Of greater consequence, however, was the fact that the scale used by the chart recorder to measure the length of the cartilage as a function of time was not large enough to enable a reliable analysis. This dilemma wi l l be discussed in the following paragraphs. In most cases, the scale used to graph the elongation of the cartilage was the same for each subject (approximately 0.08 c m / % strain). The maximal strain for each experiment was on average 5-20 % with approximately 10 equilibrium force-length measurements made during each experiment. Thus, for each step change in force, the corresponding elongation was on average 0.5-2.0 % which translated to a 0.04-0.16 cm change in position of the arm of the chart recorder monitoring the length. Coupled with these small changes in position was the fact that the line produced by the chart recorder was approximately 0.05 cm thick. Furthermore, in many cases, after each step change in force, the majority Chapter 6. DISCUSSION 110 of the lengthening was complete in a matter of seconds. Unfortunately, the chart speed was such that, in many experiments, the elongation of the cartilage was recorded as virtually a step change. Due to the scale and relative magnitude of these values, it would be difficult to make meaningful quantitative calculations regarding the time response of the cartilage in stretching. However, even a qualitative analysis of the dynamic portion of the elongation-time curve is obfuscated by the scale of the curve. For example, it has already been determined that the tensile stiffness of tracheal cartilage increases with age (see figure 5.15). In terms of the elongation-time curve plotted by the chart recorder, this means that, for a given step change i n force, younger specimens would stretch more than older ones. For the younger specimens, this would result in a larger displacement being recorded on the elongation-time curve. Conversely, a smaller displacement would result for older specimens. Due to the actual scale of the elongation-time curves, it is quite reasonable to assume that considerably more detail would be shown by the slightly magnified curve of the younger specimens. In the older specimens, less detail of the dynamic response of the cartilage would be evident. In order to provide ample and equal detail of the elongation-time curves, the scale of these curves would have to be markedly increased. In their present state, however, the elongation-time curves appear to reflect a greater time dependence on the part of the younger specimens. This apparent result may be physiologically significant or an artifact caused by the scale of the plots and, therefore, could conceivably change if the elongation-time curves were plotted on a larger scale. Chapter 6. DISCUSSION 111 (A) (B) T Figure 6.4: The reaction of tracheal cartilage to in vivo stresses. The inner superficial zone is subjected to compressive stresses (C) while the outer superficial zone is under a tensile stress (T). Somewhere in the middle zone, there is a neutral plane of zero stress. 6.2 Physiological Significance of the Tensile Tests Performed on Tracheal 6.2.1 Tensile Stiffness as a Measure of the Abil i ty of the Cartilage to M a i n -tain Form In Vivo In vivo, the trachea is subjected to intrathoracic pressures which cause the tracheal cartilage to bend. This results in the application of a tensile stress and a compressive stress on the outer and inner superficial zones of cartilage respectively while in the middle zone a neutral plane exists (see figure 6.4). Close to this neutral plane, the compressive and tensile stresses are small. In studying the mechanical properties of tracheal cartilage, an attempt was made to measure what could be considered to be an intrinsic material property. To this end, the tensile stiffness of the cartilage was measured. In the elastic region of the material's Cartilage Chapter 6. DISCUSSION 112 stress-strain curve, this tensile stiffness could be thought of as the modulus of elasticity measured in tension. For an isotropic, homogeneous material, the modulus of elasticity can be determined using a number of different tests. For example, compressive, tensile, shear or flexural tests could be used to determine the elastic modulus of an isotropic homogeneous material. Although these tests differ greatly in the manner i n which they are performed, the value of the elastic modulus calculated from each test would be the same. The scanning electron micrographs clearly demonstrate that tracheal cartilage, as a whole, is anisotropic and inhomogeneous. Therefore, it cannot be assumed that the elastic modulus is the same in compression, tension, and flexion. In fact, since the collagen fibrils are the tension-resistant elements and the proteoglycans are the compression-resistant elements of cartilage, one might expect the tensile and compressive moduli of cartilage to be dependent, to a considerable degree, on these respective components. As a result, the compressive and tensile modulus of cartilage can be expected to be different. In addition, since flexion consists of both tension and compression, one might expect the flexural modulus of cartilage to depend in some complex manner on the compressive and tensile moduli . While the tensile and compressive moduli are likely to reflect the properties of the collagen fibrils and the proteoglycans respectively, the primary functions of these indi-vidual components of cartilage remain the same regardless of whether cartilage is loaded in compression or i n tension. Proteoglycans are the compression resisting elements of cartilage. W h e n cartilage is loaded in compression, the proteoglycans resist the compres-sive forces of the load by osmotically retaining water in the matrix and by impeding the loss of water from the loaded matrix both osmotically and by reducing the conductivity of the tissue. W h e n loaded in tension, the realignment of the collagen fibrils imposes a Chapter 6. DISCUSSION 113 compressive stress on the entrapped proteoglycans. In resisting compression, the proteo-glycans restrict the elongation of the collagen which limits the extension of the cartilage. In contrast to the role of the proteoglycans, the collagen fibrils form the tension-resistant element of cartilage and restrict the movement of the proteoglycans. W h e n loaded in tension, the stress is clearly transmitted through the collagen fibrils. W h e n loaded in compression, the cartilage exudes water and the swelling pressure of the proteoglycans in-creases. In order to attain equilibrium, this increased swelling pressure must be balanced by an increased tension in the collagen fibrils. From the above discussion, it is apparent that the mechanical properties of the indi-vidual components of cartilage combine to form the overall response of the tissue whether the imposed stress is one of tension or compression. As such, any change in the individual components of the cartilage, which could affect the mechanical properties of the tissue as a whole, should be reflected by a change in both the tensile modulus and the compressive modulus. Although the mechanical properties of the proteoglycans and collagen fibrils should be reflected by both compressive and tensile tests, in this work, a certain degree of bias may have been placed on the experimental results simply by choosing to perform equilibrium tensile tests on the cartilage. It is possible that equilibrium tensile tests are unable to quantify the mechanical contribution of the proteoglycans to cartilage, thereby, biasing the results toward the measurement of the mechanical properties of the collagen fibrils. W i t h this in mind, it seems quite reasonable that the layer-wise variation in the tensile stiffness of the cartilage reflected differences in the orientation of the collagen fibrils and that the age-related changes in the tensile stiffness were a likely result of increased collagen cross-linking. Both of these observations reflect a possible bias of the experimental results toward the measurement of the mechanical properties of the tension-resistant collagen fibrils. Therefore, it may be that equilibrium tensile tests are Chapter 6. DISCUSSION 114 only capable of providing limited information regarding the mechanical properties of the cartilage. Whi le equilibrium tensile tests may neglect the contribution of the proteoglycans toward the mechanical properties of tracheal cartilage, it is possible that the resistance provided by the proteoglycans to interstitial fluid flow-involved in dynamic tensile tests may enable the proteoglycans to make a greater contribution to the dynamic tensile stiffness. In fact, Kempson [49, 50] has found that degradation of the proteoglycans does, indeed, affect the dynamic tensile properties of cartilage at low strains (see figure 2.7). To date, no data has been reported with regard to the effect of proteoglycan degradation on the equilibrium tensile stiffness of cartilage. The ability to use the equilibrium tensile stiffness of tracheal cartilage to make in-ferences regarding its in vivo mechanical properties is, presently, unclear. If the stiffness of the cartilage i n bending depends, significantly, on the tensile stiffness of the cartilage, then the equilibrium tensile stiffness should be a good measure of its in vivo mechani-cal properties. If, on the other hand, cartilage bending relies considerably more heavily on compressive stiffness, then the equilibrium tensile stiffness would be a poor measure of the in vivo mechanical properties of cartilage. However, in all likelihood, cartilage bending is governed by some combination of its compressive and tensile stiffness, but the relative weights of these two quantities are presently unknown. As stated above, performing equilibrium tensile tests on tracheal cartilage may bias the results toward the measurement of the mechanical properties of the collagen fibrils. Moreno et al. [72] and McCormack et al. [67] have already demonstrated that degrada-tion of tracheal cartilage proteoglycans causes a decrease in the unstressed diameter of the trachea and a significant decrease in the ability of the trachea to withstand negative transmural (collapsing) pressures. These results emphasize the fact that proteoglycan degradation could result in a reduction of M E F . Chapter 6. DISCUSSION 115 The quality of the cartilage proteoglycans is known to change with age. A n age-related decrease in the amount of chondroitin sulphate relative to keratan sulphate has been observed [55, 89, 101]. In addition, the size of proteoglycan aggregates [100] and molecules [89, 100] decreases with age with a relative increase in the amount of non-aggregated aggregating proteoglycans. These changes in the quality of the proteoglycans may influence the in vivo mechanical functioning of tracheal cartilage. If the equilibrium tensile tests did , in fact, bias the results in favour of the measure-ment of the mechanical properties of the collagen fibrils, then any possible mechanical effect of an age-related change in the proteoglycans may have been masked. Some of Kempson's [49] results indicate that dynamic tensile tests are able to detect changes in tensile stiffness at low strains (< 15 %) when considerable degradation of articular cartilage proteoglycans is induced. However, the bias of the dynamic tensile tests at higher strains (> 15 %) is clear in that proteoglycan degradation has no effect on the observed tensile stiffness [49] (see figure 2.7). It is evident that the mechanical effect of a gross degradation of proteoglycans would be detected by tensile tests while more subtle changes in the quality of the proteoglycans may be overshadowed by the tensile stiffness of the collagen fibril network. If this is the case, then the mechanical effect of the age-related deterioration of the proteoglycans may go unnoticed in both equilibrium and dynamic tensile tests. Recently, Lambert et al. [59] have applied thin curved beam theory to study the elastic modulus of intact tracheal cartilage i n bending. In this method, three tracheal rings of cartilage are tested in a specially designed bending apparatus (see Lambert et al. [59]). The model used in these experiments assumes that the tracheal cartilage is homogeneous and uniform in both cross-sectional area and flexural rigidity. These assumptions are obviously erroneous as the scanning electron micrographs in figures 5.16-5.26 clearly demonstrate that tracheal cartilage is heterogeneous and Lambert et al. [59] have noted Chapter 6. DISCUSSION 116 that both the cross-sectional area and flexural rigidity can vary with position in the cartilage ring; however, it is also clear that these assumptions were made i n order to analyse a loading situation which was more representative of the in vivo functioning of the cartilage. As a result of these model assumptions, the elastic modulus calculated from such a test is necessarily an approximate average value for the intact cartilage rings. In applying thin curved beam theory to the mechanics of tracheal cartilage bending, Lambert et al. [59] have reported elastic moduli in the range of 2.5-7.7 M P a . These results compare favourably to the 1-20 M P a range of elastic moduli encountered in this work. Since the elastic moduli reported by Lambert et al. [59] were average values and those reported in this work are values pertaining to individual regions within the heterogeneous tracheal cartilage, it is reasonable that the range of values for the elastic moduli reported in this work is larger. The bending experiments described by Lambert et al. [59] are likely to mimic the in vivo functioning of the tracheal cartilage better than the equilibrium tensile tests performed in this work. In this regard, a parallel study using the two different test methods could provide useful information in determining the physiological significance of the equilibrium tensile tests. Since the equipment required to perform both experiments is available i n the pulmonary research laboratory at St. Pauls Hospital in Vancouver, Canada, a parallel study would be relatively easy to undertake. 6.2.2 Physiological Significance of Layer-Wise Variations in the Tensile Stiff-ness of Tracheal Cartilage The tangential alignment of the collagen fibrils in the outer superficial zone enables that region of the cartilage to withstand the tensile stresses imposed on it during bending. Similarly, the combination of the proteoglycans and the alternating perpendicular ori-entation of the tangentially aligned collagen fibrils in the inner superficial zone should Chapter 6. DISCUSSION 117 provide this region of the cartilage with a good compressive stiffness. The middle zone of tracheal cartilage contains radially oriented collagen fibrils. This region is essentially unstressed during bending and, therefore, does not require a high tensile stiffness. This ultrastructural arrangement of the tracheal cartilage appears to make it particularly adept at performing its in vivo mechanical role of providing resistance to bending. 6.2.3 Physiological Significance of the Age-Related Changes in the Tensile Stiffness of Tracheal Cartilage In humans, maximal expiratory flow ( M E F ) is a function of lung elasticity, airway area and airway wall stiffness. M E F increases with age and growth unti l the beginning of the third decade of life [54]. Thereafter, there is a linear decrease in M E F with age [54]. It is possible that these changes i n M E F are due to changes in the stiffness of the airway wall which, in turn, depend on changes in the cartilage stiffness. The results of the tensile tests indicate that the tensile stiffness of tracheal cartilage increases with age until the end of the third decade; thereafter, tensile stiffness appears to remain relatively constant. However, the degree of scatter in the tensile stiffness vs. age data is quite large after the end of the third decade. Since increasing the tensile stiffness of the cartilage should increase the stiffness of the airway wall which, in turn, should allow higher flowrates in the airway, the age-related increase i n the tensile stiffness of younger specimens could be involved in the increase in M E F up to the beginning of the third decade. However, the high degree of scatter in the tensile stiffness vs. age curve after the end of the third decade of life limits the validity of any conclusions made regarding the possible role of tracheal cartilage stiffness i n the age-related changes of maximal expiratory flow limitation after the age of thirty. In dynamic tensile tests performed on articular cartilage Kempson [47] found that tensile stiffness increases with age unt i l the middle of the third decade and thereafter Chapter 6. DISCUSSION 118 decreases with increasing age. As stated earlier, it is possible that tracheal cartilage exhibits similar age-related changes in stiffness as does articular cartilage. If this were the case, then the age-related trend in tracheal cartilage stiffness would coincide with the changes i n maximal expiratory flow. Unfortunately, the scatter in the tensile stiff-ness results obtained for subjects over the age of thirty was too large for any definite conclusions to be drawn from these results. Previous researchers have established that lung elasticity, a major determinant in maximal expiratory flow, decreases with age after the end of the second decade of life [14]. This decrease in lung elasticity coincides with the age-related decrease in maximal expiratory flow. If, after the end of the third decade of life, the tensile stiffness of cartilage does, in fact, remain relatively constant, then the age-related decrease in lung elasticity— and not the stiffness of the tracheal cartilage—may be the precipitating factor in the reduction of maximal expiratory flow. However, in order to conclusively elucidate the factors involved in the age-related decrease in maximal expiratory flow, a more complete understanding of the variations in tracheal cartilage stiffness with age is required. To do this, the physiological significance of performing equilibrium tensile tests must be determined and more tests must be performed i n the age range of 30-80 years. Chapter 7 C O N C L U S I O N S 1. A technique for determining the tensile properties of human tracheal cartilage has been developed and validated. 2. The equilibrium tensile stress-strain curves are linear up to approximately 10 % strain. 3. At strains above 10 %, hysteresis and residual strain i n the stress-strain curve indicates that the cartilage matrix has been irreversibly disrupted. 4. Preliminary results suggest that tracheal cartilage can be divided into three struc-tural and functional zones. These zones reflect the alignment of the collagen fibrils. Outer Superficial Zone - collagen fibrils are oriented tangent to the cartilage surface. Middle Zone - collagen fibrils are oriented perpendicular to the cartilage surface. Inner Superficial Zone - collagen fibrils are oriented tangent to the cartilage surface. 5. The tensile stiffness of tracheal cartilage decreases with depth into the tissue be-tween the outer superficial zone and the middle zone. This layer-wise variation in tensile stiffness reflects the ultrastructural arrangement of the collagen fibrils. 6. The tensile stiffness of tracheal cartilage increases with age between the middle of the second and the end of the third decades of fife. Thereafter, the tensile stiffness 119 Chapter 7. CONCLUSIONS 120 appears to remain relatively constant; however, the degree of scatter is large after the end of the third decade. 7. The age-related increase in the tensile stiffness of tracheal cartilage may be a result of an increased cross-Unking of the coUagen fibrils. 8. A significant negative correlation was found between the tensile stiffness and water content of tracheal cartilage. This result may have been due to a decrease in water content which would Ukely occur with an increase in collagen cross-Unking. 9. Performing equiUbrium tensile tests on cartilage may bias the results toward the measurement of the mechanical properties of the coUagen fibrils. 10. Age-related increases in maximal expiratory flow during youth may be related to changes in tensile stiffness of the tracheal cartilage; however, wi th the degree of scatter in the present data, the age-related decrease in maximal expiratory flow which occurs in the adult years cannot be related to the tensile stiffness of tracheal cartilage. Chapter 8 R E C O M M E N D A T I O N S 1. Improving the Accuracy of the Stress-Strain Measurements - In the stress calculations, the error associtaed with the thickness measurement accounts for about two-thirds of the total measurement error. In order to reduce the error, the micrometer used in the experiments should be replaced by an instrument that is more sensitive to the compressibility of cartilage. Both Akizuk i et al. [2] and Woo et al. [107] have described such an instrument. 2. Improving the Accuracy of Creep Measurements - If it is desirable to study the transient portion of the stress-strain curve, then the scale of the elongation-time curve produced by the chart recorder should be significantly increased. Chart speed should be increased from 0.5 c m / m i n to approximately 5.0 cm/min and the step changes i n force should be increased to provide a change in strain of approximately 5 %. Alternatively, a video camera with close-up lenses could be used to monitor the elongation of the gauge section of the test specimen. This latter technique—similar to that which has been previously described by Woo et al. [107, 108, 109]—would probably provide better results. 3. Testing the Physiologic Validity of Tensile Tests - Two studies could be performed in order to determine whether or not tensile tests are representive of the in vivo functioning of tracheal cartilage: 121 Chapter 8. RECOMMENDATIONS 122 (a) Enzymes could be used to degrade the collagen and proteoglycans in the car-tilage. Tests on a graded series of degraded cartilage could provide some idea of the sensitivity of the tensile tests toward degradation of the cartilage con-stituents. If these experiments were to indicate that tensile tests are sensitive to various forms of collagen and proteoglycan degradation, then one could ex-pect that tensile tests are qualitatively representative of the in vivo mechanical properties of tracheal cartilage. (b) A comparative study between the results of tensile tests and bending tests could be performed. Bending tests analysed in the manner proposed by Lam-bert et al. [59] could provide good insight into the physiologic validity of tensile tests. 4. E x p a n d i n g the Scope o f the S t u d i e s - Future studies should include cartilage specimens from deceased individuals with known pulmonary dysfunction. 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Appendix A N O M E N C L A T U R E A - cross-sectional area (m.2) a - Y-intercept of regression line b - slope of regression line df - estimated error in the force measurement (m) dL r estimated error in the measurement of the position of the gauge mark (m) dt - estimated error in the thickness measurement (m) dw - estimated error in the width measurement (m) F - applied force (N) / - applied force (g) L - position of the gauge mark (m) I - length of the gauge section (m) n - number of data points 5 - sum of the squares of the residuals se - standard error of estimate T - tensile stiffness (MPa) t - thickness of the test specimen (m) ta/2 - value of random variables having the t distribution with n — 2 degrees of freedom w - width of the test specimen (m) x - x-coordinate of the data points used in the regression x - average of the n x-values 132 Appendix A. NOMENCLATURE Y - elastic modulus (MPa) y - y-coordinate of the data points used in the regression G R E E K S Y M B O L S : a - actual y-intercept 3 - actual slope e - strain (m/m) a - stress (MPa) A - small change p - density (kg/m3) S U B S C R I P T S : B - bottom 0 - initial T - top 1 - i th value Appendix B G L O S S A R Y chondrocyte - a cartilage cell. chondroitin sulphate - a glycosaminoglycan found in proteoglycans (see figures 2.2, 2.3, and 2.4). conductivity - a measure of the ease with which fluid moves through a matrix. critical correlation coefficient - the value above which a given correlation is signifi-cant at a given level of confidence for a given number of data points. elastic modulus - the slope of any stress-strain curve in the material's region of elastic deformation. fixed charge density - a measure of the concentration of fixed ionic groups within cartilage. Donnan equilibrium - the particular equilibrium set up when two coexisting phases are subject to the restriction that one or more of the ionic components cannot pass from one phase into the other. glycosaminoglycan - a molecule made up of repeating disaccharide units consisting of a hexose unit and a hexosamine unit. hyaluronate - (aka hyaluronic acid) a glycosaminoglycan which is the back-bone of a proteoglycan aggregate (see figure 2.2). 134 Appendix B. GLOSSARY 135 hyaluronate-binding region - the region of the protein core on a proteoglycan molecule which binds to hyaluronate. keratan sulphate - a glycosaminoglycan found in proteoglycans (see figures 2.2, 2.5). lacuna - a small pit or hollow cavity. link protein - a protein which strengthens the bond between hyaluronate and the bind-ing region of a proteoglycan molecule. protein core - the protein back-bone of a proteoglycan molecule (see figure 2.2). proteoglycan aggregate - an aggregation of proteoglycan molecules held together by a hyaluronate back-bone (see figure 2.2). proteoglycan molecule - a molecule consisting of a protein core and laterally attached glycosaminoglycan side chains (see figure 2.2). strain - the elongation of a specimen divided by its original length. (Usually expressed as a percentage) stress - the force imposed on a material divided by the material's cross-sectional area. tensile modulus - the slope of a tensile stress-strain curve in the material's region of elastic deformation. tensile stiffness - the slope of a tensile stress-strain curve at any point on the curve. tensile strength - the tensile fracture stress of a material, (i.e. the stress at which the material fractures) Young's modulus - see elastic modulus. Appendix C C A L I B R A T I O N C U R V E O F M P T T The M P T T was calibrated to ensure proper force measurements. The calibration curve for the M P T T is shown in the following figure. 136 Appendix C. CALIBRATION CURVE OF MPTT applied force (g) Figure C.5: Calibration curve for the force measurement on the M P T T . Appendix D D E S C R I P T I O N O F K R E B S B U F F E R One litre of Krebs buffer solution was made according to the following formula: 1. To 800 m l of distilled deionised water were added (a) NaCl - 6.9 g (b) KCl - 0.35 g (c) CaCl2 - 0.28 g (d) MgS04 • 7H20 - 0.29 g (e) KH2POA - 0.16 g (f) NaHCOz - 2.1 g (g) Glucose - 2.0 g. 2. Sufficient water was added to make 1000 ml of solution. 3. The solution was oxygenated for 15 minutes at a flowrate of 2 1/min. 138 Appendix E L I N E A R R E G R E S S I O N O N E X P E R I M E N T A L R E S U L T S E . l Least Squares Linear Regression A least squares fit of the data was performed by minimising the sum of the squares of the error. This was accomplished by solving the following two equations: + b ± x t = ± y i (E.4) an t=i t=i n (E.5) 1=1 1=1 t=i where, a - Y-intercept of regression line b - slope of regression line n - number of data points x, — i th x-value Vi — i ih y-value Equations E.4 and E.5 can be solved for (a) and (b) as shown below. The Y -intercept (a) of the regression line is given by n E r = i 2 / t a = n. (E.6) 139 endix E. LINEAR REGRESSION ON EXPERIMENTAL RESULTS 140 The slope (b) of the regression line is given by 6 = 5Di=i  xt S t=i  xiVi The 90 % confidence interval for the slope is given by the following equation: (E.7) n 3 = b±ta/2 • seJ — (E.8) The 90 % confidence interval for the Y-intercept is given by the following equation: Sxx + (nx)2 . N a = a±ta/2-sJ ; (E.9) V nbxx where, a - actual y-intercept 8 - actual slope • value of random variables having the t distribution with n — 2 degrees of freedom x - average of the n x-values s, - standard error of estimate defined as follows: s2 = 1 n - 2 ^ - ( a + bx^ 1 = 1 Sxx - defined as follows: Sxx = ~ ( X z . ) 2 i=i i=i Definitions for the variables used in these equations are given in appendix A . Appendix E. LINEAR REGRESSION ON EXPERIMENTAL RESULTS 141 E . 2 Least Squares Linear Regression Forcing the Regression Line Through the Origin A least squares fit of the equation y — bx was performed on the data. This fitting procedure forced the regression line through the origin. The equation used to perform this regression is shown below: where, S - sum of the squares of the residuals b - slope of regression line n - number of data points xt —X th x-value Vi —  l t h y-value To minimise the sum of the squares of the residuals, the derivative of equation E.10 was set to zero. n (E.10) 1=1 = 2±[(yi - bXl) x (-Xl)} = 0 ( E . l l ) 1=1 Solving this equation for the slope, 6, yields the following equation: b = Sr=i Styi -^lt = l I (E.12) endix E. LINEAR REGRESSION ON EXPERIMENTAL RESULTS 142 E.3 Tables of Linear Regression Coefficients for Cartilage Tension Tests The following tables provide the coefficients for the least squares linear regression analysis of the results of the tensile tests performed on the cartilage specimens. For a description of how the data was analysed, see section 4.6. Appendix E. LINEAR REGRESSION ON EXPERIMENTAL RESULTS 143 Table E . l : Linear regression values for the cartilage tensile tests. H u m a n A g e R i n g L a y e r S l o p e t S l o p e } Y - i n t e r c e p t % 90 % C o n f . i n t . for S l o p e } 90 % C o n f . in t . for Y - i n t e r c e p t { 1 81 1 1 9.5 10 .6 - 0 . 0 6 9.1 12 .0 -0.21 0 .10 1 81 1 2 11 .9 12.8 - 0 . 0 5 12.0 1 3 . 7 - 0 . 1 6 0 .05 1 81 1 3 13 .0 12 .7 0.01 12.2 13 .3 - 0 . 0 8 0.11 1 81 1 4 6.8 6.2 0.00 6.0 6 .5 -0 .02 0.02 1 81 1 5 6 .3 6.4 -0 .02 5.8 7.0 - 0 . 0 8 0 .04 1 81 2 1 15 .3 19.2 - 0 . 2 0 14.6 23.8 - 0 .74 0 .34 2 1 7 1 1 2.6 2.3 0 .00 2.1 2 .6 - 0 . 0 3 0 .03 2 1 7 1 2 0 .9 0.6 0 .00 0.3 0 .9 -0 .05 0 .05 I 17 1 f 1:1 1:8 8:82 8:1 1:7 :8:8I 8:8? 2 1 7 2 2 1.9 1.6 0 .03 0.9 2.2 -0.10 0.15 2 1 7 2 3 1.2 0.6 0.01 -0.7 1.9 - 0 . 13 0.14 2 1 7 2 4 0 .7 0.6 0.01 -0.1 1.3 -0 .15 0 .17 2 1 7 3 6 1.2 1.1 0.00 1.0 1.2 -0 .01 0.01 2 17 4 1 9 .6 8.2 0.08 7.3 9.2 - 0 .04 0 .20 2 17 4 4 0.8 0 .7 0 .00 0.5 0.9 -0 .02 0.02 2 1 7 4 5 0.6 0 .3 0 .00 0.1 0.4 -0 .02 0.02 3 50 4 4 6.1 6.0 0.01 5.8 6.2 -0 .02 0 .04 3 50 5 1 16 .9 21.5 - 0 . 1 8 19 .7 23 .3 -0 .42 0 .06 3 50 5 3 11 .6 13.1 - 0 . 0 9 12.2 14.1 -0 .25 0 .08 3 50 5 4 6.8 6 .7 0.00 6.3 7.0 -0 .06 0 .07 3 50 5 5 5.4 5.3 0 .00 5.1 5.4 -0 .02 0.02 3 50 5 6 5.0 5.0 -0.01 4.8 5.3 -0 .05 0 .03 3 50 5 7 4 .6 4.5 -0 .00 4.4 4 .7 -0 .02 0.02 3 50 6 4 4 .6 4.4 0.02 4.3 4 .5 -0.01 0.06 3 50 7 3 9.8 9.6 0.01 9.4 9.8 -0 .02 0.04 3 50 7 4 5.9 6.1 -0 .02 5.8 6.5 - 0 . 0 9 0 .05 3 50 8 1 12.5 14.1 -0 .10 13.0 15.2 - 0 . 2 8 0 .07 3 50 8 2 12 .3 12.6 -0 .02 12.1 13 .0 - 0 . 0 7 0 .03 f- l inear regress ion f o r c e d t h r o u g h t h e or ig in M E T H O D B t- least s q u a r e s l inear regress ion M E T H O D A I Appendix E. LINEAR REGRESSION ON EXPERIMENTAL RESULTS 144 Table E.2: Linear regression values for the cartilage tensile tests. Human Age Ring Layer Slope j Slope X Y-intercept t 90 % Conf. int. for Slope J 90 % Conf. int. for Y-intercept J 4 58 1 2 13.2 13.6 -0.02 13.2 14.1 -0.09 0.05 4 58 1 3 14.4 9.0 0.00 8.8 9.3 -0.00 0.00 4 58 1 4 8.6 7.7 0.05 7.3 8.1 -0.01 0.11 4 58 1 S 5.7 5.5 0.01 5.3 5.7 -0.02 0.03 4 58 3 1 14.4 16.5 -0.07 13.5 19.4 -0.27 0.14 4 58 3 2 18.5 21.5 -0.12 19.0 24.1 -0.38 0.14 4 58 3 3 19.3 20.0 -0.03 19.2 20.8 -0.11 0.05 4 58 3 4 16.9 16.4 0.01 15.7 17.1 -0.04 0.07 4 58 3 5 14.5 12.3 0.00 11.7 13.0 -0.02 0.02 4 58 4 3 9.7 8.2 0.05 7.2 9.3 -0.03 0.13 4 58 4 4 11.7 10.6 0.02 10.0 11.2 -0.02 0.06 5 21 1 3 8.4 8.0 0.01 7.6 8.4 -0.03 0.05 5 21 1 4 2.7 2.6 0.00 2.3 3.0 -0.04 0.04 5 21 1 5 2.9 2.6 0.00 2.4 2.8 -0.02 0.03 5 21 2 3 10.9 11.3 -0.03 10.9 11.7 -0.10 0.04 5 21 2 4 9.2 9.2 -0.00 8.9 9.5 -0.05 0.05 5 21 2 5 4.7 4.2 0.02 3.6 4.8 -0.04 0.09 5 21 2 6 3.1 2.9 0.00 2.4 3.4 -0.06 0.07 5 21 2 7 2.9 2.5 0.00 2.4 2.7 -0.02 0.02 6 28 1 2 21.2 19.3 0.09 18.3 20.2 -0.02 0.20 6 28 1 3 15.0 15.0 -0.00 14.5 15.4 -0.06 0.06 6 28 1 4 6.8 6.5 0.01 6.1 7.0 -0.04 0.07 6 28 2 3 11.1 10.7 0.02 9.7 11.8 -0.13 0.17 6 28 2 5 6.9 6.5 0.01 5.7 7.2 -0.07 0.10 6 28 3 3 11.2 10.2 0.05 9.2 11.2 -0.06 0.16 6 28 3 4 10.5 9.7 0.04 9.0 10.3 -0.05 0.14 6 28 3 5 11.5 10.9 0.02 10.4 11.4 -0.04 0.08 6 28 3 6 7.2 6.5 0.03 5.9 7.0 -0.03 0.09 6 28 3 9 3.8 3.7 -0.01 3.3 4.1 -0.05 0.04 f- linear regression forced through the origin M E T H O D B J- least squares linear regression M E T H O D A Appendix E. LINEAR REGRESSION ON EXPERIMENTAL RESULTS Table E.3: Linear regression values for the cartilage tensile tests. Human Age Ring Layer Slope f Slope t Y-intercept } 90 % Conf. int. for Slope t 90 % Conf. int. for Y-intercept J 7 20 2 1 17.2 17.0 0.01 16.1 17.8 -0.15 0.18 7 20 2 2 8.9 8.4 0.02 7.8 9.1 -0.06 0.09 7 20 2 3 7.0 6.4 0.03 5.9 7.0 -0.05 0.11 7 20 2 4 6.2 5.7 0.01 4.4 7.1 -0.07 0.10 7 20 2 6 3.9 3.6 0.02 3.2 4.0 -0.04 0.07 7 20 2 7 4.9 4.4 0.01 4.1 4.7 -0.01 0.03 8 60 2 2 19.4 19.0 0.00 18.2 19.8 -0.05 0.05 8 60 2 3 18.9 16.5 0.08 15.0 18.1 -0.05 0.21 § § 8 I i M 8:84 m :8:8g 8:?1 8 60 2 6 9.6 8.9 0.02 8.1 9.8 -0.08 0.12 8 60 3 1 22.5 23.1 -0.04 22.4 23.7 -0.15 0.07 8 60 3 2 16.6 16.3 0.01 15.5 17.1 -0.08 0.10 8 60 3 3 14.2 13.4 0.04 12.9 13.9 -0.03 0.11 8 60 3 4 12.2 11.4 0.04 10.8 12.0 -0.04 0.12 8 60 3 5 7.9 8.4 -0.04 8.0 8.9 -0.11 0.04 8 60 3 6 10.1 9.7 0.00 9.1 10.3 -0.07 0.07 i- linear regression forced through the origin M E T H O D B {- least squares linear regression M E T H O D A Appendix E. LINEAR REGRESSION ON EXPERIMENTAL RESULTS Table E.4: Linear regression values for the cartilage tensile tests. Human Age Ring Layer Slope f Slope t Y-intercept } 90 % Conf. int. for Slope { 90 % Conf. int. for Y-intercept J 9 18 1 1 8.1 8.0 -0.00 7.7 8.3 -0.05 0.05 9 18 1 2 6.7 6.1 0.02 5.9 6.4 -0.02 0.05 9 18 2 1 9.9 9.8 -0.00 9.4 10.2 -0.05 0.04 9 18 2 2 5.7 5.5 0.00 5.0 6.1 -0.08 0.08 9 18 2 3 5.6 4.3 0.03 2.9 5.8 -0.09 0.14 9 18 2 4 3.5 3.0 0.01 2.5 3.4 -0.04 0.07 9 18 2 5 2.6 2.4 0.01 1.9 2.9 -0.05 0.07 9 18 2 6 3.0 2.8 0.00 2.8 2.9 -0.00 0.01 18 §1 1 £¥ 8:83 n li :8:8I 8:1? 10 21 1 5 6.0 5.6 0.01 5.1 6.0 -0.04 0.07 10 21 2 1 10.0 10.0 0.00 9.7 10.3 -0.05 0.05 10 21 2 3 5.9 5.3 0.02 4.6 5.9 -0.05 0.08 10 21 2 4 4.5 4.0 0.02 3.2 4.8 -0.06 0.09 10 21 3 2 5.6 5.2 0.02 4.8 5.6 -0.04 0.08 10 21 3 4 4.3 4.0 0.02 3.5 4.5 -0.05 0.08 t- linear regression forced through the origin M E T H O D B J- least squares linear regression M E T H O D A Appendix F W E I G H T E D L E A S T S Q U A R E S R E G R E S S I O N The bulk of the material contained in this appendix has been extracted from the paper by Feldman [27] with the excellent tutilage of Barry Wiggs of St. Paul's Hos-pital , Vancouver, Canada. This apppendix is organised into the following sections: (a) Statistical model (b) Estimation of individual lines (c) Estimation of variance components (d) Estimation of weight matrices (e) Restricted maximum likelihood technique F . l Statistical Model The data for the all of the subjects were assembled into 6 groups corresponding to layers #1-6 of the tracheal cartilage specimens. The mean parameter vector aj for group i and the individual parameter vector ay for subject j are, respectively a; and a ; j = OLij (F.13) (F.14) 147 endix F. WEIGHTED LEAST SQUARES REGRESSION 148 where, cti - is the actual intercept of the group line aij - is the actual intercept of the subject line Bi - is the actual slope of the group line 6ij - is the actual slope of the subject line The experiment on subject j in group i yields mj data points given by the following matrices. and w here, 1 x iji 1 x Yij = Viji y (F.15) (F.16) (xijk,yijk) - represents the k data point for subject j in group i. The data are assumed to follow the equation, (F.17) where, Sijk - represents the residual error of the k ih measurement for subject j in group i. Equation F.17 can be written in matrix form as comprising three terms: one for group effects, one for subject variationwithin a group, and one for each subjects endix F. WEIGHTED LEAST SQUARES REGRESSION 149 residual variation about a regression line. Thus, equation F.17 can be expressed as, Vij - X i j + Zi j Oiij - Oli _ A . _ P a . (F.18) The following sections describe how the group mean parameter vector can be esti-mated using a weighted least squares regression analysis which accounts for both random subject variation within a group and residual variation. F .2 E s t i m a t i o n of I n d i v i d u a l L i n e s Least squares linear regression provides the intercepts and slopes for each subjects line. The regression equation can be expressed in the following manner: y « = X a a u (F.19) where, (F.20) Thus, ay is the vector containing the estimate of the intercept (aij) and the slope (6,j) of the regression line for subject j in group i. Equation F.19 can be solved by the following matrix manipulations. ( X j X y ^ X j y y = ( X g X ^ X g X y a y (F.21) where, 1 • • • 1 *iji is the transpose of X y , and n (F.22) Sfc = l  Xijk Efc = l  xi Efcil  Xijk 2 jk (F.23) Appendix F. WEIGHTED LEAST S Q U A R E S R E G R E S S I O N 150 and (XJjXy)-1 Tnij T2 Z^ fc=i xijk fc=l xijk Sfc = l xijk nij Sfc = l xijk (Efc=l Xijk)2 (F.24) w here, rat-j - represents the number of data points collected for subject j in group i. B y definition, ( X 5 X y ) - 1 X 5 x « = I (F.25) where, I is the identity matrix. Therefore, equation F.21 reduces to ay = ( X j X ^ ^ X j y y (F.26) Equation F.26 is identical to equations E.6 and E.7 given in appendix E . The equally weighted mean parameter vector, for group i is given by the following equation: 1 n i (F.27) w here, ni - represents the number of subjects in group i. F.3 Estimation of Variance Components Assuming that the mean square residual errors of all subjects are comparable, the residual variance (s2) is pooled across all subjects and all groups. Hi = l E j = l Efc = l(yijfc — aij ~ bijXijk)2 s2 = E?=i - 2) (F.28) Appendix F. WEIGHTED LEAST SQUARES REGRESSION 151 where, rig - represents the number of groups. Thus, equation F.28 provides an estimate of the average overall residual variance of the regressions. A covariance matrix (D) for random effects can be estimated as follows: Ei=i Ej=i(ay — aij)(aij — ai j) T where, D = (ay - ay) = E S t e - 1 ) aij ~ L,jzzl  aij and and (ay-ay) = o-a - ^ E j L i Otj - £ E^=i bij (F.29) (F.30) (F.31) (ay — ay)(ay — ay)T — (ay - ± E ^ ai5f (a{j - i E "= i a y ) ( 6 « - i E £ i 6y) (ay - £ E £ i ay)(fty - J E ? = 1 6y) (6y - J E ? = 1 ^ i ) 2 The covariance matrix, D , as calculated above gives D 5ab (F.32) where. s\ - estimate of the variance of the intercept of the regression l ine" si - estimate of the variance of the slope of the regression line s2b - estimate of the covariance of the slope and intercept of the regression line Appendix F. WEIGHTED LEAST S Q U A R E S R E G R E S S I O N 152 F . 4 E s t i m a t i o n of W e i g h t M a t r i c e s Each subject's data is weighted according to how well it fits the group average and how well it is fit by a regression line. The subject variance matrix, V y , is estimated by summing the residual variation, s2e, and the random subject variation D as follows: V y = s\l + Z y D Z g (F.33) where, D - is as calculated in equation F.29 I - is the identity matrix si - is the overall residual variance for all of the measurements of all of the subjects in all of the groups Z y - is as defined in equation F.15 V y - is the variance matrix for a given subject Thus, solving equation F.33 results in the following matrix. s2a + 2s2abxin + slxfa +s2c ••• s2a + a^ajyi + s2abxijni. + slxi:jlxijnii V y = i •. ; (F.34) The variance matrix, V y , gives an indication of how well each subject's data fits the group average and how well it is fit by a regression line. A large variance indicates a poor fit while a small variance indicates a good fit. Thus, in order to weight the data according to its goodness of fit, the weight matrix for each subject is given by the inverse of the subject's variance matrix. W y = V J J 1 (F.35) Appendix F. WEIGHTED LEAST S Q U A R E S R E G R E S S I O N 153 where, W y - is a weight matrix for each subject This weight matrix can be used to calculate a new unequally weighted group pa-rameter vector a;. ai = a{ hi = ExJWijXiji-MExJWijXij] i=i i=i where. (F.36) ai - represents the estimate of the intercept of the group line bi - represents the estimate of the slope of the group line The covariance matrix for this estimate is given by Q = ExJWjjXij]-1 where, (F.37) CQ. - represents the revised estimate of the variance of the intercept of the group regression line c 2. - represents the revised estimate of the variance of the slope of the group regression line c2a.b. - represents the revised estimate of the covariance of the slope and intercept of the group regression line A revised estimate of the overall average residual variation can be estimated by the equation £ r = G i [ ( £ - = 1 n t i ) - 2 ] t Appendix F. WEIGHTED LEAST SQUARES REGRESSION 154 Table F.5: Results of weighted least squares regression on the tracheal cartilage tensile tests Layer Y-intercept Slope 1 11 -0.055 13.88 2 13 0.018 10.67 3 19 0.029 9.56 4 21 0.036 6.36 5 13 0.027 5.87 6 8 0.033 4.56 F.5 Results of Weighted Least Squares Regression on the Tracheal Cartilage Tensile Tests The results of the weighted least squares regression, performed on the stress-strain data obtained from the tracheal cartilage tensile tests, are given in table F.5. F.6 Restricted Max imum Likelihood Technique The restricted maximum likelihood technique is an iterative procedure in which refined estimates of the regression line for each group are obtained by using the new estimates of both the overall residual variance (equation F.38) and the covariance matrices (equation F.37) for the group lines to calculate a new weight matrix (equation F.35) and, therefore, new estimates of the group lines from which new estimates of both the overall residual variance and the group line covariance can be calculated. In this work, the procedure was allowed to continue until the change in the residual variance and each of the values in the group covariance matrices was less than 1 % from one iteration to the next. Appendix F. WEIGHTED LEAST SQUARES REGRESSION 155 Table F.6: Results of REML regression on the tracheal cartilage tensile tests Layer 71; Y-intercept Slope 1 11 -0.054 13.84 2 13 0.019 10.63 3 19 0.029 9.53 4 21 0.037 6.35 5 13 0.028 5.84 6 8 0.033 4.57 F.7 Results of R E M L Regression on the Tracheal Cartilage Tensile Tests The results of the R E M L regression, performed on the stress-strain data obtained from the tracheal cartilage tensile tests, are given in table F.6. Appendix F. WEIGHTED LEAST SQUARES REGRESSION 156 Appendix G P E A R S O N C O R R E L A T I O N C O E F F I C I E N T The correlation coefficient (r) used to determine the degree of linear association between two variables, (x) and (y), is calculated using the following formula: r = S x y (G.39) \J SXX • Syy where, sxx = » X X - ( X X ) 2 t=i t=i n n Syy = n^Vi ~ (XS/O2 t=l i=l n n n 1=1 1=1 1=1 Definitions for the variables used in these equations are given in appendix A . The significance of the correlation can be determined by comparing the value of (r) with the table of values of the critical correlation coefficients. 157 Appendix H E R R O R A N A L Y S I S H . l Measurement Error H . l . l Measurement Error in the Stress Calculation Stress (<r) is calculated using the following equation: < r = A where, cr - Stress (Pa) F - Force (N) A - Cross-sectional area (m 2). The measured variables in the tensile tests are (H.40) / - equivalent force (g) w0 - init ial specimen width (m) ta - initial specimen thickness (m). Using these values, stress can be calculated in the following manner: ^ = f(g) x 9.8 x l ( T 3 ( A 7 g ) w0(m) x t0(m) (H.41) 158 endixH. ERROR ANALYSIS 159 The error in the stress calculation can be determined from the following differential equation: der der , der , d° = efdf +<h,dw+mdL ( H 4 2 ) where, df - estimated error in the force measurement (m) dt - estimated error in the measurement of the position of the gauge mark (m) dw - estimated error in the width measurement (m) Applying equation H.42 to equation H.41 leads to the following equation: "9.8 x 10- 3 " der = f f df dw dt (H.43) W0 X ta W i t h suitable estimates of (df), (dw) and (dt), equation H.43 can be used to calculate the maximum expected measurement error in the stress calculation. H . l . 2 Measurement Error in the Strain Calculation The strain (e) of a test specimen is given by the following equation: e = ^ (H.44) where, AZ - elongation (m) lQ - initial length of gauge section (m). Experimentally, strain (e) is calculated using the measurements of the positions of the top and bottom gauge marks. e = ( L T - L B ) - ( L T - L B O ) ( H 4 5 ) (LTO - LBO) where, endix H. ERROR ANALYSIS 160 LB0 - init ial position of the bottom gauge mark (m) LB - current position of the bottom gauge mark (m) LT0 - init ial position of the top gauge mark (m) Li - current position of the top gauge mark (m) Thus, the error in the strain measurement is given by the following differential equation: de de de de .__ A n . de = —dLT + 7 ^ d L B + ——dLTo + ——dLBo. H.46 oLT oLB oLTo oLBo w here, dLBo - estimated error in the init ial position of the bottom gauge mark (m) dLB - estimated error in the current position of the bottom gauge mark (m) dLjo - estimated error in the init ia l position of the top gauge mark (m) dLr - estimated error in the current position of the top gauge mark (m) Taking the partial derivatives of equation H.45 and substituting them in equation H.46 gives the following equation: de = dLx — dLB — — dLx ~\~ dLB . LT0—LBO LT0 — LBO (LTO — LBO)2 " (LTO — LBO)2 (H.47) This equation emphasizes that the error in the strain calculation has approximately equal dependence on the accuracy with which the initial and current positions of the gauge marks are measured. W i t h suitable estimates of (dLBa), (dLB), (dLjo) and (dLx), equation H.47 can be used to calculate the maximum expected measurement error in the strain calculation. Appendix H. ERROR ANALYSIS 161 H . l . 3 Sample Calculation of Stress, Strain and Measurement Errors The following example demonstrates how stress, strain and their associated measurement errors were calculated using the experimental data. Subject: - Human # 1 0 Ring # 3 Layer # 4. / = 1.58(flr) w0 = 0.00094(m) tD = 0.000090(m) LTo = 0.01036(m) LBo = 0.00168(m) LT = 0.01075(m) LB = 0.00175(m) LTo ~ LBo = 0.00868(m) df = 0.01 x / = 0.0158(y) dw = 0.00005(m) dt = O.OOOOl(m) dLTo = dLBo = dLT = dLB = 0.00002(m). These values can be used to calculate stress (a) and strain (e). Stress is given by the equation 1.58{g) x 9.8 x lQ- 3(N/g) a = 0.00094(m) x 0.000090(m) endix H. ERROR ANALYSIS 162 = 1.83 x 10 5(N/m 2) = O.lSZ(MPa). Strain is given by the equation (0.01075 - 0.00175) - (0.01036 - 0.00168) e = (0.01036 - 0.00168) = 0.0369(m/m) = 3.69% The maximum estimated measurement error in the stress calculation can be calculated by summing the absolute values of the individual error terms in equation H.43. 9.8 x 10- 3(JV/g) r n A i c o . . d < T = 0.00094(m) x 0.000090(m) X [ 0 " ° 1 5 8 ( 5 ) + nL 5l[ 9) x x 0.00005(m) + n}'**$ x x O.OOOOl(m) 0.00094(m) v 1 0.000090(m) v ; N = 1.158 x 105(——) [0.0158(flf) + 0.0840(5) + 0.1756(5)] m g = 1.158 x 1 0 5 ( - 4 - ) x 0.2754( 5) = 31902(AT/m 2) = 0 .032 (MPa) . This calculation clearly shows that approximately 2/3 of the measurement error in the stress calculation is a result of the error in the measurement of the thickness of the specimen. Another 1/3 of the stress calculation error can be attributed to the error in the width measurement while the error in the force measurement is responsible for only about 1/20 of the error in the calculation of stress. Appendix H. ERROR ANALYSIS 163 The maximum estimated measurement error in the strain calculation can be calculated by summing the absolute values of the individual error terms i n equation H.47. 1 l n nnnnns „ 0.01075 - 0.00175) , n n n n n n . d e =  2 x TTT^n: x 0.00002 + 2 x ^ ; x (0.00002) 0.00868 ^ ; (0.00868) 2 v ' = 9.39 x 1 0 - 3 ( m / m ) = 0.94%. H . 2 Tables o f E x p e r i m e n t a l R e s u l t s The following pages contain tables of the experimental results. These tables contain the init ial specimen dimensions and the stress-strain results along with the estimates of maximum measurement error for stress and strain. Appendix H. ERROR ANALYSIS 164 SPECIMEN DIMENSIONS MEASUREMENT MEASUREMENT (m) ERROR (m) INITIAL WIDTH .001250 .000050 INITIAL THICKNESS .000100 .000010 INITIAL LENGTH .011070 .000040 FORCE(N) STRAIN(%) ERROR(%) STRESS(MPa) ERROR(MPa) 0.0000 0.00 0.72 0.000 0.000 0.0085 1.27 0.73 0.068 0.010 0.0151 1.99 0.73 0.121 0.018 0.0298 3.34 0.73 0.238 0.036 0.0489 4.43 0.74 0.391 0.059 0.0688 5.33 0.74 0.550 0.083 0.0979 7.77 0.75 0.783 0.117 Table A 1.1.1 : Results of uniaxial tensile test of human # 1 ring #1 layer #1 Appendix H. ERROR ANALYSIS 165 SPECIMEN DIMENSIONS MEASUREMENT MEASUREMENT (m) ERROR (m) INITIAL WIDTH .001340 .000050 INITIAL THICKNESS .000100 .000010 INITIAL LENGTH .010830 .000040 FORCE(N) STRAIN(%) ERROR(%) STRESS(MPa) ERROR(MPa) 0.0000 0.00 0.74 0.000 0.000 0.0059 0.83 0.74 0.044 0.006 0.0147 1.66 0.74 0.110 0.016 0.0299 2.31 0.75 0.223 0.033 0.0498 3.32 0.75 0.372 0.055 0.0784 4.89 0.76 0.585 0.086 0.1078 6.83 0.76 0.804 0.119 0.1376 8.22 0.77 1.027 0.151 Table A 1.1.2 : Results of uniaxial tensile test of human # 1 ring #1 layer #2 Appendix H. ERROR ANALYSIS 166 SPECIMEN DIMENSIONS MEASUREMENT MEASUREMENT (m) ERROR (m) INITIAL WIDTH .001370 .000050 INITIAL THICKNESS .000100 .000010 INITIAL LENGTH .009140 000040 FORCE(N) STRAIN(%) ERROR(%) STRESS(MPa) ERROR(MPa) 0.0000 0.00 0.88 0.000 0.000 0.0062 0.55 0.88 0.045 ' 0.007 0.0123 0.77 0.88 0.090 0.013 0.0216 1.20 0.88 0.158 0.023 0.0404 2.08 0.88 0.295 0.043 0.0547 2.74 0.89 0.399 0.058 0.0726 3.72 0.89 0.530 0.078 0.0893 4.92 0.90 0.652 0.096 0.1051 6.01 0.90 0.767 0.112 0.1251 6.78 0.90 0.913 0.134 0.1425 7.99 0.91 1.040 0.152 0.1548 9.19 0.92 1.130 0.166 Table A 1.1.3 : Results of uniaxial tensile test of human # 1 ring #1 layer #3 Appendix H. ERROR ANALYSIS 167 SPECIMEN DIMENSIONS MEASUREMENT MEASUREMENT (m) ERROR (m) INITIAL WIDTH .001430 .000050 INITIAL THICKNESS .000100 .000010 INITIAL LENGTH .011260 000040 FORCE(N) STRAIN(%) ERROR(%) STRESS(MPa) ERROR(MPa) 0.0000 0.00 0.71 0.000 0.000 0.0061 0.71 0.71 0.043 0.006 0.0192 1.95 0.72 0.134 0.019 0.0393 4.17 0.73 0.275 0.040 0.0599 6.12 0.73 0.419 0.061 Table A 1.1.4 : Results of uniaxial tensile test of human # 1 ring #1 layer #4 Appendix H. ERROR ANALYSIS 168 SPECIMEN DIMENSIONS MEASUREMENT MEASUREMENT (m) ERROR (m) INITIAL WIDTH .001380 000050 INITIAL THICKNESS .000100 000010 INITIAL LENGTH .012910 .000040 FORCE(N) STRAIN(%) ERR0R(%) STRESS(MPa) ERROR(MPa) 0.0000 0.00 0.62 0.000 0.000 0.0040 0.85 0.62 0.029 0.004 0.0102 1.70 0.62 0.074 0.011 0.0200 2.48 0.63 0.145 0.021 0.0312 3.64 0.63 0.226 0.033 0.0433 5.11 0.64 0.314 0.046 0.0556 5.96 0.64 0.403 0.059 Table A 1.1.5 : Results of uniaxial tensile test of human # 1 ring #1 layer #5 Appendix H. ERROR ANALYSIS 169 SPECIMEN DIMENSIONS MEASUREMENT MEASUREMENT (m) ERROR (m) INITIAL WIDTH .001450 .000050 INITIAL THICKNESS .000100 .000010 INITIAL LENGTH .008900 000040 FORCE(N) STRAIN(%) ERROR(%) STRESS(MPa) ERROR(MPa) 0.0000 0.00 0.90 0.000 0.000 0.0048 1.01 0.90 0.033 0.005 0.0098 1.80 0.91 0.068 0.010 0.0343 3.15 0.91 0.237 0.034 0.0588 4.05 0.92 0.405 0.059 0.0980 4.83 0.92 0.676 0.098 0.1470 6.07 0.93 1.014 0.147 0.1955 7.08 0.93 1.348 0.195 Table A 1.2.1 : Results of uniaxial tensile test of human # 1 ring #2 layer #1 Appendix H. ERROR ANALYSIS 170 SPECIMEN DIMENSIONS MEASUREMENT MEASUREMENT (m) ERROR (m) INITIAL WIDTH .001380 000050 INITIAL THICKNESS .000150 000010 INITIAL LENGTH .004700 000040 FORCE(N) STRAIN(%) ERR0R(%) STRESS(MPa) ERROR(MPa) 0.0000 0.00 1.70 0.000 0.000 0.0101 2.34 1.72 0.049 0.006 0.0207 3.62 1.73 0.100 0.011 0.0329 5.74 1.75 0.159 0.018 0.0553 10.21 1.79 0.267 0.030 0.0698 19.15 1.87 0.337 0.038 0.0884 32.77 1.98 0.427 0.048 0.1184 43.62 2.07 0.572 0.065 0.1476 52.98 2.15 0.713 0.080 0.1956 71.60 2.31 0.945 0.107 Table A 2.1.1 : Results of uniaxial tensile test of human # 2 ring #1 layer #1 Appendix H. ERROR ANALYSIS 171 SPECIMEN DIMENSIONS MEASUREMENT MEASUREMENT (m) ERROR (m) INITIAL WIDTH .001770 .000050 INITIAL THICKNESS .000150 .000010 INITIAL LENGTH .004370 « 000040 FORCE(N) STRAIN(%) ERROR(%) STRESS(MPa) ERROR(MPa) 0.0000 0.00 1.83 0.000 0.000 0.0175 6.86 1.89 0.066 0.007 0.0337 14.60 1.96 0.127 0.013 0.0518 30.90 2.11 0.195 0.020 0.0720 54.70 2.33 0.271 0.028 0.1049 93.20 2.68 0.395 0.041 Table A 2.1.2 : Results of uniaxial tensile test of human # 2 ring #1 layer #2 Appendix H. ERROR ANALYSIS SPECIMEN DIMENSIONS MEASUREMENT MEASUREMENT (m) ERROR (m) INITIAL WIDTH .001680 .000050 INITIAL THICKNESS .000150 .000010 INITIAL LENGTH .006440 000040 FORCE(N) STRAIN(%) ERROR(%) STRESS(MPa) ERROR(MPa) 0.0000 0.00 1.24 0.000 0.000 0.0118 1.55 1.25 0.047 0.005 0.0290 7.76 1.29 0.115 0.012 0.0491 15.20 1.34 0.195 0.021 0.0688 27.80 1.41 0.273 0.029 0.0930 42.50 1.51 0.369 0.039 0.1177 56.10 1.59 0.467 0.050 Table A 2.1.3 : Results of uniaxial tensile test of human # 2 ring #1 layer #3 Appendix H. E R R O R ANALYSIS 173 SPECIMEN DIMENSIONS MEASUREMENT MEASUREMENT (m) ERROR (m) INITIAL WIDTH .001600 .000050 INITIAL THICKNESS .000150 .000010 INITIAL LENGTH .008250 000040 FORCE(N) STRAIN(%) ERROR(%) STRESS(MPa) ERROR(MPa) 0.0000 0.00 0.97 0.000 0.000 0.0094 1.21 0.98 0.039 0.004 0.0194 4.12 0.99 0.081 0.009 0.0295 6.06 1.00 0.123 0.013 0.0497 14.06 1.04 0.207 0.022 0.0720 22.79 1.08 0.300 0.032 0.0931 33.09 1.13 0.388 0.042 0.1217 42.18 1.17 0.507 0.055 0.1481 58.91 1.26 0.617 0.067 Table A 2.1.4 : Results of uniaxial tensile test of human # 2 ring #1 layer #4 Appendix H. ERROR ANALYSIS 174 SPECIMEN DIMENSIONS MEASUREMENT MEASUREMENT (m) ERROR (m) INITIAL WIDTH .001520 .000050 INITIAL THICKNESS .000100 .000010 INITIAL LENGTH .005450 000040 FORCE(N) STRAIN(%) ERROR(%) STRESS(MPa) ERROR(MPa) 0.0000 0.00 1.47 0.000 0.000 0.0152 3.30 1.49 0.100 0.014 0.0286 8.44 1.53 0.188 0.027 0.0444 16.70 1.59 0.292 0.042 0.0625 31.70 1.70 0.411 0.059 0.0780 45.90 1.80 0.513 0.073 0.0964 63.50 1.93 0.634 0.091 Table A 2.2.2 : Results of uniaxial tensile test of human # 2 ring #2 layer #2 Appendix H. ERROR ANALYSIS 175 SPECIMEN DIMENSIONS MEASUREMENT MEASUREMENT (m) ERROR (m) INITIAL WIDTH .001530 .000050 INITIAL THICKNESS .000100 .000010 INITIAL LENGTH .005730 .000040 FORCE(N) STRAIN (%) ERROR(%) STRESS(MPa) ERROR(MPa) 0.0000 0.00 1.40 0.000 0.000 0.0076 2.62 1.41 0.050 0.007 0.0184 10.30 1.47 0.120 0.017 0.0283 22.30 1.55 0.185 0.026 0.0465 52.50 1.76 0.304 0.043 0.0614 78.20 1.94 0.401 0.057 Table A 2.2.3 : Results of uniaxial tensile test of human # 2 ring #2 layer #3 Appendix H. ERROR ANALYSIS SPECIMEN DIMENSIONS MEASUREMENT MEASUREMENT (m) ERROR (m) INITIAL WIDTH .001560 000050 INITIAL THICKNESS .000100 000010 INITIAL LENGTH .007400 .000040 FORCE(N) STRAIN(%) ERROR(%) STRESS(MPa) ERROR(MPa) 0.0000 0.00 1.08 0.000 0.000 0.0097 5.68 1.11 0.062 0.009 0.0245 23.10 1.21 0.157 0.022 0.0342 42.00 1.31 0.219 0.031 0.0423 61.90 1.42 0.271 0.038 0.0534 88.90 1.56 0.342 0.049 Table A 2.2.4 : Results of uniaxial tensile test of human # 2 ring #2 layer #4 Appendix H. ERROR ANALYSIS 177 SPECIMEN DIMENSIONS MEASUREMENT MEASUREMENT (m) ERROR (m) INITIAL WIDTH .001450 .000050 INITIAL THICKNESS .000100 .000010 INITIAL LENGTH .004820 .000040 FORCE(N) STRAIN(%) ERROR(%) STRESS(MPa) ERROR (MPa) 0.0000 0.00 1.66 0.000 0.000 0.0041 0.00 1.66 0.028 0.005 0.0109 0.00 1.66 0.075 0.012 0.0180 0.20 1.66 0.124 0.020 0.0277 0.64 1.67 0.191 0.031 0.0377 1.91 1.68 0.260 0.043 0.0478 2.54 1.68 0.330 0.054 0.0684 4.45 1.70 0.472 0.078 0.0918 6.36 1.71 0.633 0.104 0.1108 8.90 1.73 0.764 0.126 0.1311 11.02 1.75 0.904 0.149 0.1467 13.14 1.77 1.012 0.166 0.1637 15.89 1.79 1.129 0.186 0.1937 21.40 1.84 1.336 0.220 Table A 2.4.1 : Results of uniaxial tensile test of human # 2 ring #4 layer #1 Appendix H. ERROR ANALYSIS SPECIMEN DIMENSIONS MEASUREMENT MEASUREMENT (m) ERROR (m) INITIAL WIDTH .001400 000050 INITIAL THICKNESS .000100 000010 INITIAL LENGTH .007580 .000040 FORCE(N) STRAIN(%) ERR0R(%) STRESS(MPa) ERROR(MPa) 0.0000 0.00 1.06 0.000 0.000 0.0070 6.33 1.09 0.050 0.008 0.0104 9.89 1.11 0.074 0.012 0.0158 18.60 1.15 0.113 0.019 0.0202 35.75 1.24 0.144 0.024 0.0246 51.72 1.33 0.176 0.029 0.0293 80.08 1.48 0.209 0.035 Table A 2.4.4 : Results of uniaxial tensile test of human # 2 ring #4 layer #4 Appendix H. ERROR ANALYSIS 179 SPECIMEN DIMENSIONS MEASUREMENT MEASUREMENT (m) ERROR (m) INITIAL WIDTH .001520 000050 INITIAL THICKNESS .000100 .000010 INITIAL LENGTH .005450 .000040 FORCE(N) STRAIN(%) ERROR(%) STRESS(MPa) ERROR(MPa) 0.0000 0.00 1.47 0.000 0.000 0.0033 2.42 1.49 0.021 0.003 0.0072 7.55 1.52 0.047 0.007 0.0105 12.08 1.56 0.069 0.010 0.0152 21.30 1.62 0.100 0.014 0.0199 33.84 1.72 0.131 0.019 0.0246 51.06 1.84 0.162 0.023 0.0301 66.47 1.96 0.198 0.028 Table A 2.4.5 : Results of uniaxial tensile test of human # 2 ring #4 layer #5 Appendix H. ERROR ANALYSIS 180 SPECIMEN DIMENSIONS MEASUREMENT MEASUREMENT (m) ERROR (m) INITIAL WIDTH .001490 .000050 INITIAL THICKNESS .000100 .000010 INITIAL LENGTH .004310 .000040 FORCE(N) STRAIN(%) ERR0R(%) STRESS(MPa) ERROR(MPa) 0.0000 0.00 1.86 0.000 0.000 0.0045 2.32 1.88 0.030 0.004 0.0122 6.50 1.92 0.082 0.012 0.0186 10.67 1.96 0.125 0.018 0.0231 14.39 1.99 0.155 0.022 0.0328 23.90 2.08 0.220 0.032 0.0393 29.00 2.13 0.264 0.038 Table A 2.3.6 : Results of uniaxial tensile test of human # 2 ring #3 layer #6 Appendix H. ERROR ANALYSIS SPECIMEN DIMENSIONS MEASUREMENT MEASUREMENT (m) ERROR (m) INITIAL WIDTH .001410 .000050 INITIAL THICKNESS .000100 .000010 INITIAL LENGTH .008810 .000040 FORCE(N) STRAIN(%) ERROR(%) STRESS(MPa) ERROR(MPa) 0.0003 0.00 0.91 0.002 0.000 0.0059 0.45 0.91 0.042 0.006 0.0115 1.36 0.91 0.081 0.012 0.0204 2.27 0.92 0.145 0.021 0.0299 3.29 0.92 0.212 0.031 0.0397 4.31 0.93 0.281 0.041 0.0509 5.56 0.93 0.361 0.052 0.0602 7.15 0.94 0.427 0.062 0.0737 8.40 0.95 0.523 0.076 0.0931 11.01 0.96 0.660 0.096 0.1116 13.51 0.97 0.792 0.115 0.1298 16.35 0.98 0.921 0.134 0.1503 18.84 0.99 1.066 0.155 Table A 3.4.4 : Results of uniaxial tensile test of human # 3 ring #4 layer #4 Appendix H. ERROR ANALYSIS 182 SPECIMEN DIMENSIONS MEASUREMENT MEASUREMENT On) ERROR (m) INITIAL WIDTH .001650 .000050 INITIAL THICKNESS .000100 000010 INITIAL LENGTH .004530 000040 FORCE(N) STRAIN(%) ERROR(%) STRESS (MPa) ERROR(MPa) 0.0000 0.00 1.77 0.000 0.000 0.0031 1.10 1.78 0.019 0.003 0.0081 0.88 1.77 0.049 0.007 0.0127 1.10 1.78 0.077 0.011 0.0181 1.77 1.78 0.110 0.015 0.0279 1.77 1.78 0.169 0.024 0.0356 1.99 1.78 0.216 0.030 0.0478 2.65 1.79 0.290 0.041 0.0597 2.87 1.79 0.362 0.051 0.0733 2.87 1.79 0.444 0.062 0.0866 3.53 1.80 0.525 0.074 0.1038 3.75 1.80 0.629 0.088 0.1208 4.19 1.80 0.732 0.103 0.1379 4.53 1.81 0.836 0.117 0.1538 4.86 1.81 0.932 0.131 0.1666 5.30 1.81 1.010 0.142 0.1952 6.18 1.82 1.183 0.166 Table A 3.5.1 : Results of uniaxial tensile test of human # 3 ring #5 layer #1 Appendix H. ERROR ANALYSIS 183 SPECIMEN DIMENSIONS MEASUREMENT MEASUREMENT On) ERROR (m) INITIAL WIDTH .001810 000050 INITIAL THICKNESS .000100 000010 INITIAL LENGTH .006420 .000040 FORCE(N) STRAIN(%) ERROR(%) STRESS(MPa) ERROR(MPa) 0.0000 0.00 1.25 0.000 0.000 0.0040 0.78 1.25 0.022 0.003 0.0114 1.25 1.25 0.063 0.009 0.0190 1.71 1.26 0.105 0.014 0.0288 2.18 1.26 0.159 0.022 0.0396 2.80 1.26 0.219 0.030 0.0532 3.27 1.27 0.294 0.040 0.0691 3.89 1.27 0.382 0.053 0.0903 4.36 1.27 0.499 0.069 0.1102 4.83 1.28 0.609 0.084 0.1309 5.61 1.28 0.723 0.100 0.1517 6.54 1.29 0.838 0.115 0.1705 8.10 1.30 0.942 0.130 0.1955 9.03 1.30 1.080 0.149 Table A 3.5.3 : Results of uniaxial tensile test of human # 3 ring #5 layer #3 Appendix H. ERROR ANALYSIS 184 SPECIMEN DIMENSIONS MEASUREMENT MEASUREMENT (m) ERROR (m) INITIAL WIDTH .001810 000050 INITIAL THICKNESS .000100 .000010 INITIAL LENGTH .007260 000040 FORCE(N) STRAIN(%) ERROR(%) STRESS(MPa) ERROR(MPa) 0.0000 0.00 1.10 0.000 0.000 0.0033 0.14 1.10 0.018 0.002 0.0092 1.10 1.11 0.051 0.007 0.0206 1.65 1.11 0.114 0.016 0.0311 2.75 1.12 0.172 0.024 0.0422 3.17 1.12 0.233 0.032 0.0525 3.99 1.12 0.290 0.040 0.0635 4.41 1.13 0.351 0.048 0.0744 6.20 1.14 0.411 0.057 0.0878 7.30 1.14 0.485 0.067 0.1034 8.54 1.15 0.571 0.079 0.1225 10.06 1.16 0.677 0.093 0.1390 11.85 1.17 0.768 0.106 0.1658 13.64 1.18 0.916 0.126 0.1937 15.29 1.19 1.070 0.147 Table A 3.5.4 : Results of uniaxial tensile test of human # 3 ring #5 layer #4 Appendix H. ERROR ANALYSIS SPECIMEN DIMENSIONS MEASUREMENT MEASUREMENT (m) ERROR (m) INITIAL WIDTH .001880 .000050 INITIAL THICKNESS .000100 .000010 INITIAL LENGTH .005710 .000040 FORCE(N) STRAIN(%) ERROR(%) STRESS(MPa) ERROR(MPa) 0.0000 0.00 1.40 0.000 0.000 0.0062 0.70 1.41 0.033 0.005 0.0147 1.40 1.41 0.078 0.011 0.0244 2.28 1.42 0.130 0.018 0.0348 3.68 1.43 0.185 0.025 0.0479 4.73 1.43 0.255 0.035 0.0652 6.30 1.45 0.347 0.047 0.0771 7.71 1.46 0.410 0.056 0.0931 9.28 1.47 0.495 0.068 0.1120 12.78 1.49 0.596 0.081 Table A 3.5.5 : Results of uniaxial tensile test of human # 3 ring #5 layer #5 Appendix H. ERROR ANALYSIS SPECIMEN DIMENSIONS MEASUREMENT MEASUREMENT (m) ERROR (m) INITIAL WIDTH .001880 .000050 INITIAL THICKNESS .000100 000010 INITIAL LENGTH .007310 .000040 FORCE(N) STRAIN(%) ERR0R(%) STRESS(MPa) ERROR(MPa) 0.0000 0.00 1.09 0.000 0.000 0.0130 1.64 1.10 0.069 0.009 0.0203 2.60 1.11 0.108 0.015 0.0301 3.42 1.11 0.160 0.022 0.0425 4.51 1.12 0.226 0.031 0.0566 5.75 1.13 0.301 0.041 0.0697 7.39 1.13 0.371 0.051 0.0893 9.44 1.15 0.475 0.065 0.1209 12.86 1.16 0.643 0.088 0.1359 15.18 1.18 0.723 0.099 Table A 3.5.6 : Results of uniaxial tensile test of human # 3 ring #5 layer #6 Appendix H. ERROR ANALYSIS 187 SPECIMEN DIMENSIONS MEASUREMENT MEASUREMENT (m) ERROR (m) INITIAL WIDTH .001960 .000050 INITIAL THICKNESS .000100 .000010 INITIAL LENGTH .006880 .000040 FORCE(N) STRAIN (%) ERROR(%) STRESS(MPa) ERROR(MPa) 0.0000 0.00 1.16 0.000 0.000 0.0114 1.16 1.17 0.058 0.008 0.0204 2.33 1.18 0.104 0.014 0.0292 3.49 1.18 0.149 0.020 0.0449 5.09 1.19 0.229 0.031 0.0555 6.25 1.20 0.283 0.038 0.0680 7.41 1.21 0.347 0.047 0.0798 8.72 1.21 0.407 0.055 0.1027 10.90 1.23 0.524 0.071 0.1188 12.65 1.24 0.606 0.082 0.1384 14.83 1.25 0.706 0.096 0.1599 18.17 1.27 0.816 0.111 Table A 3.5.7 : Results of uniaxial tensile test of human # 3 ring #5 layer #7 Appendix H. ERROR ANALYSIS 188 SPECIMEN DIMENSIONS MEASUREMENT MEASUREMENT (m) ERROR (m) INITIAL WIDTH .000940 .000050 INITIAL THICKNESS .000075 .000010 INITIAL LENGTH .006680 000040 FORCE(N) STRAIN(%) ERROR(%) STRESS(MPa) ERROR(MPa) 0.0007 -0.00 1.20 0.010 0.002 0.0050 0.60 1.20 0.071 0.014 0.0109 2.84 1.21 0.154 0.030 0.0156 4.64 1.23 0.221 0.043 0.0206 5.99 1.23 0.292 0.057 0.0267 8.38 1.25 0.378 0.074 0.0379 11.53 1.27 0.538 0.106 0.0476 14.82 1.29 0.676 0.133 0.0584 18.26 1.31 0.828 0.163 Table A 3.6.4 : Results of uniaxial tensile test of human # 3 ring #6 layer #4 Appendix i f . ERROR ANALYSIS 189 SPECIMEN DIMENSIONS MEASUREMENT MEASUREMENT (m) ERROR (m) INITIAL WIDTH .001470 .000050 INITIAL THICKNESS .000100 .000010 INITIAL LENGTH .009590 000040 FORCE(N) STRAIN(%) ERROR(%) STRESS(MPa) ERROR(MPa) 0.0000 0.00 0.83 0.000 0.000 0.0068 0.31 0.84 0.046 0.007 0.0140 0.94 0.84 0.095 0.014 0.0203 1.36 0.84 0.138 0.020 0.0309 2.19 0.84 0.210 0.030 0.0407 2.71 0.85 0.277 0.040 0.0500 3.34 0.85 0.340 0.049 0.0637 4.28 0.85 0.433 0.062 0.0766 5.42 0.86 0.521 0.075 0.0960 6.57 0.86 0.653 0.094 0.1095 7.72 0.87 0.745 0.107 0.1274 8.97 0.87 0.867 0.125 0.1470 10.32 0.88 1.000 0.144 0.1690 12.51 0.89 1.150 0.166 0.1926 14.29 0.89 1.310 0.189 Table A 3.7.3 : Results of uniaxial tensile test of human # 3 ring #7 layer #3 Appendix H. ERROR ANALYSIS 190 SPECIMEN DIMENSIONS MEASUREMENT MEASUREMENT (m) ERROR (m) INITIAL WIDTH .001240 000050 INITIAL THICKNESS .000100 .000010 INITIAL LENGTH .006860 000040 FORCE(N) STRAIN(%) ERROR(%) STRESS(MPa) ERROR(MPa) 0.0005 -0.00 1.17 0.004 0.001 0.0051 0.73 1.17 0.041 0.006 0.0111 1.75 1.18 0.089 0.013 0.0175 2.62 1.18 0.141 0.021 0.0235 3.94 1.19 0.190 0.029 0.0316 4.66 1.19 0.254 0.038 0.0420 6.12 1.20 0.339 0.051 0.0506 7.14 1.21 0.408 0.061 0.0604 8.16 1.21 0.487 0.073 0.0739 10.35 1.23 0.596 0.090 0.0930 11.81 1.24 0.750 0.113 0.1090 14.43 1.25 0.879 0.132 0.1277 17.78 1.27 1.030 0.155 Table A 3.7.4 : Results of uniaxial tensile test of human # 3 ring #7 layer #4 Appendix H. ERROR ANALYSIS 191 SPECIMEN DIMENSIONS MEASUREMENT MEASUREMENT (m) ERROR (m) INITIAL WIDTH .000790 000050 INITIAL THICKNESS .000100 000010 INITIAL LENGTH .006130 000040 FORCE(N) STRAIN(%) ERROR(%) STRESS(MPa) ERROR(MPa) 0.0000 0.00 1.31 0.000 0.000 0.0058 1.63 1.32 0.074 0.013 0.0107 2.12 1.32 0.135 0.023 0.0195 2.77 1.32 0.247 0.043 0.0289 3.43 1.33 0.366 0.063 0.0386 4.08 1.33 0.489 0.085 0.0514 5.06 1.34 0.651 0.113 0.0659 6.85 1.35 0.834 0.145 0.0853 8.16 1.36 1.080 0.187 0.1035 9.95 1.37 1.310 0.227 0.1217 11.09 1.38 1.540 0.267 Table A 3.8.1 : Results of uniaxial tensile test of human # 3 ring #8 layer #1 Appendix H. ERROR ANALYSIS 192 SPECIMEN DIMENSIONS MEASUREMENT MEASUREMENT (m) ERROR (m) INITIAL WIDTH .001000 000050 INITIAL THICKNESS .000100 .000010 INITIAL LENGTH .007540 .000040 FORCE(N) STRAIN(%) ERROR(%) STRESS(MPa) ERROR(MPa) 0.0000 0.00 1.06 0.000 0.000 0.0037 0.57 1.06 0.037 0.006 0.0068 0.66 1.06 0.068 0.011 0.0140 1.33 1.07 0.140 0.022 0.0222 1.99 1.07 0.222 0.036 0.0357 3.05 1.08 0.357 0.057 0.0495 3.85 1.08 0.495 0.079 0.0663 5.31 1.09 0.663 0.106 0.0851 6.90 1.10 0.851 0.136 Table A 3.8.2 : Results of uniaxial tensile test of human # 3 ring #8 layer #2 Appendix H. ERROR ANALYSIS 193 SPECIMEN DIMENSIONS MEASUREMENT MEASUREMENT (m) ERROR (m) INITIAL WIDTH .001690 .000050 INITIAL THICKNESS .000100 .000010 INITIAL LENGTH .007220 .000040 FORCE(N) STRAIN (%) ERROR(%) STRESS(MPa) ERROR(MPa) 0.0000 0.00 1.11 0.000 0.000 0.0057 0.36 1.11 0.034 0.005 0.0110 0.73 1.11 0.065 0.009 0.0169 0.83 1.11 0.100 0.014 0.0250 1.09 1.11 0.148 0.021 0.0341 1.70 1.12 0.202 0.028 0.0455 1.82 1.12 0.269 0.038 0.0455 2.43 1.12 0.269 0.038 0.0586 2.67 1.12 0.347 0.048 0.0693 3.40 1.13 0.410 0.057 0.0853 4.01 1.13 0.505 0.070 0.1000 4.37 1.13 0.592 0.083 0.1153 5.22 1.14 0.682 0.095 0.1315 5.83 1.14 0.778 0.109 0.1494 6.44 1.14 0.884 0.123 0.1668 7.29 1.15 0.987 0.138 Table A 4.1.2 : Results of uniaxial tensile test of human # 4 ring #1 layer #2 Appendix H. ERROR ANALYSIS 194 SPECIMEN DIMENSIONS MEASUREMENT MEASUREMENT (m) ERROR (m) INITIAL WIDTH .001700 .000050 INITIAL THICKNESS .000100 000010 INITIAL LENGTH .008580 000040 FORCE(N) STRAIN(%) ERROR(%) STRESS(MPa) ERROR(MPa) 0.0000 0.00 0.93 0.000 0.000 0.0059 0.23 0.93 0.035 0.005 0.0114 0.47 0.93 0.067 0.009 0.0168 0.70 0.94 0.099 0.014 0.0289 1.17 0.94 0.170 0.024 0.0396 1.63 0.94 0.233 0.032 Table A 4.1.3 : Results of uniaxial tensile test of human # 4 ring #1 layer #3 Appendix H. ERROR ANALYSIS SPECIMEN DIMENSIONS MEASUREMENT MEASUREMENT (m) ERROR (m) INITIAL WIDTH .001680 .000050 INITIAL THICKNESS .000100 .000010 INITIAL LENGTH .007220 .000040 FORCE(N) STRAIN(%) ERR0R(%) STRESS(MPa) ERROR(MPa) 0.0000 0.00 1.11 0.000 0.000 0.0049 -0.28 1.11 0.029 0.004 0.0106 0.14 1.11 0.063 0.009 0.0153 0.55 1.11 0.091 0.013 0.0218 1.11 1.11 0.130 0.018 0.0297 1.66 1.12 0.177 0.025 0.0396 2.08 1.12 0.236 0.033 0.0524 3.32 1.13 0.312 0.044 0.0672 4.16 1.13 0.400 0.056 0.0828 5.40 1.14 0.493 0.069 0.1072 7.62 1.15 0.638 0.089 0.1267 9.42 1.16 0.754 0.105 Table A 4.1.4 : Results of uniaxial tensile test of human # 4 ring #1 layer #4 Appendix H. ERROR ANALYSIS 196 SPECIMEN DIMENSIONS MEASUREMENT MEASUREMENT (m) ERROR (m) INITIAL WIDTH .001810 ' .000050 INITIAL THICKNESS .000100 000010 INITIAL LENGTH .008040 .000040 FORCE(N) STRAIN(%) ERROR(%) STRESS(MPa) ERROR(MPa) 0.0000 0.00 1.00 0.000 0.000 0.0067 0.62 1.00 0.037 0.005 0.0136 1.12 1.00 0.075 0.010 0.0233 1.99 1.00 0.129 0.018 0.0357 3.48 1.01 0.197 0.027 0.0487 4.48 1.02 0.269 0.037 0.0655 6.47 1.03 0.362 0.050 0.0849 8.33 1.04 0.469 0.065 Table A 4.1.5 : Results of uniaxial tensile test of human # 4 ring #1 layer #5 Appendix H. ERROR ANALYSIS SPECIMEN DIMENSIONS MEASUREMENT MEASUREMENT <m) ERROR (m) INITIAL WIDTH .001600 .000050 INITIAL THICKNESS .000100 .000010 INITIAL LENGTH .006480 .000040 FORCE(N) STRAIN(%) ERR0R(%) STRESS(MPa) ERROR (MPa) 0.0000 0.00 1.23 0.000 0.000 0.0054 0.63 1.24 0.034 0.005 0.0128 0.79 1.24 0.080 0.011 0.0192 1.42 1.24 0.120 0.017 0.0278 1.57 1.24 0.174 0.025 0.0373 2.04 1.25 0.233 0.033 0.0490 2.36 1.25 0.306 0.043 0.0581 2.83 1.25 0.363 0.051 0.0699 2.99 1.25 0.437 0.062 0.0806 3.14 1.25 0.504 0.071 0.0931 3.14 1.25 0.582 0.082 Table A 4.3.1 : Results of uniaxial tensile test of human # 4 ring #3 layer #1 Appendix H. ERROR ANALYSIS 198 SPECIMEN DIMENSIONS MEASUREMENT MEASUREMENT (m) ERROR (m) INITIAL WIDTH .000990 .000050 INITIAL THICKNESS .000100 .000010 INITIAL LENGTH .009060 000040 FORCE(N) STRAIN(%) ERR0R(%) STRESS(MPa) ERROR(MPa) 0.0000 0.00 0.88 0.000 0.000 0.0043 0.55 0.89 0.043 0.007 0.0113 1.43 0.89 0.114 0.018 0.0211 1.66 0.89 0.213 0.034 0.0335 2.32 0.89 0.338 0.054 0.0424 2.76 0.90 0.428 0.069 0.0521 3.20 0.90 0.526 0.084 0.0642 3.64 0.90 0.648 0.104 0.0773 4.30 0.90 0.781 0.125 0.0952 4.53 0.90 0.962 0.154 0.1057 5.08 0.91 1.068 0.171 Table A 4.3.2 : Results of uniaxial tensile test of human # 4 ring #3 layer #2 Appendix H. ERROR ANALYSIS 199 SPECIMEN DIMENSIONS MEASUREMENT MEASUREMENT (m) ERROR (m) INITIAL WIDTH .001190 .000050 INITIAL THICKNESS .000100 .000010 INITIAL LENGTH .008560 .000040 FORCE(N) STRAIN(%) ERR0R(%) STRESS(MPa) ERROR(MPa) 0.0000 0.00 0.93 0.000 0.000 0.0059 0.35 0.94 0.050 0.008 0.0131 0.82 0.94 0.110 0.017 0.0225 1.17 0.94 0.189 0.029 0.0326 1.52 0.94 0.274 0.042 0.0431 1.99 0.94 0.362 0.055 0.0531 2.57 0.95 0.446 0.068 0.0621 2.80 0.95 0.522 0.079 0.0741 3.15 0.95 0.623 0.095 0.0887 3.74 0.95 0.745 0.113 0.1064 4.44 0.96 0.894 0.136 0.1235 5.37 0.96 1.038 0.158 Table A 4.3.3 : Results of uniaxial tensile test of human # 4 ring #3 layer #3 Appendix H. ERROR ANALYSIS 200 SPECIMEN DIMENSIONS MEASUREMENT MEASUREMENT (m) ERROR (m) INITIAL WIDTH .001550 .000050 INITIAL THICKNESS .000100 .000010 INITIAL LENGTH .007230 .000040 FORCE(N) STRAIN(%) ERROR(%) STRESS(MPa) ERROR(MPa) 0.0000 0.00 1.11 0.000 0.000 0.0057 0.14 1.11 0.037 0.005 0.0115 0.55 1.11 0.074 0.011 0.0214 0.69 1.11 0.138 0.020 0.0329 1.11 1.11 0.212 0.030 0.0504 1.80 1.12 0.325 0.046 0.0671 2.49 1.12 0.433 0.062 0.0883 3.46 1.13 0.570 0.081 0.1048 3.87 1.13 0.676 0.096 0.1262 4.98 1.13 0.814 0.116 Table A 4.3.4 : Results of uniaxial tensile test of human # 4 ring #3 layer #4 Appendix H. ERROR ANALYSIS 201 SPECIMEN DIMENSIONS MEASUREMENT MEASUREMENT (m) ERROR (m) INITIAL WIDTH .001340 .000050 INITIAL THICKNESS .000100 000010 INITIAL LENGTH .008120 .000040 FORCE(N) STRAIN(%) ERROR(%) STRESS(MPa) ERROR(MPa) 0.0000 0.00 0.99 0.000 0.000 0.0044 0.12 0.99 0.033 0.005 0.0102 0.49 0.99 0.076 0.011 0.0159 0.74 0.99 0.119 0.018 0.0225 1.11 0.99 0.168 0.025 0.0297 1.48 0.99 0.222 0.033 0.0367 1.97 0.99 0.274 0.040 0.0446 2.34 1.00 0.333 0.049 Table A 4.3.5 : Results of uniaxial tensile test of human # 4 ring #3 layer #5 Appendix H. ERROR ANALYSIS 202 SPECIMEN DIMENSIONS MEASUREMENT MEASUREMENT (m) ERROR (m) INITIAL WIDTH .001440 .000050 INITIAL THICKNESS .000100 .000010 INITIAL LENGTH .007350 000040 FORCE(N) STRAIN(%) ERR0R(%) STRESS(MPa) ERROR(MPa) 0.0000 0.00 1.09 0.000 0.000 0.0058 -0.27 1.09 0.040 0.006 0.0137 0.54 1.09 0.095 0.014 0.0220 1.22 1.10 0.153 0.022 0.0300 1.90 1.10 0.208 0.030 0.0396 2.45 1.10 0.275 0.040 0.0575 3.67 1.11 0.399 0.058 0.0770 6.12 1.12 0.535 0.077 Table A 4.4.3 : Results of uniaxial tensile test of human # 4 ring #4 layer #3 Appendix H. ERROR ANALYSIS 203 SPECIMEN DIMENSIONS MEASUREMENT MEASUREMENT (m) ERROR (m) INITIAL WIDTH .001080 .000050 INITIAL THICKNESS .000100 .000010 INITIAL LENGTH .007000 000040 FORCE(N) STRAIN(%) ERROR(%) STRESS(MPa) ERROR(MPa) 0.0000 0.00 1.14 0.000 0.000 0.0059 0.29 1.14 0.055 0.009 0.0106 0.57 1.15 0.098 0.015 0.0170 1.29 1.15 0.157 0.025 0.0248 1.71 1.15 0.230 0.036 0.0387 3.00 1.16 0.358 0.056 0.0490 4.00 1.17 0.454 0.071 0.0617 5.00 1.17 0.571 0.089 Table A 4.4.4 : Results of uniaxial tensile test of human # 4 ring #4 layer #4 Appendix H. ERROR ANALYSIS 204 SPECIMEN DIMENSIONS MEASUREMENT MEASUREMENT On) ERROR (m) INITIAL WIDTH .000800 .000050 INITIAL THICKNESS .000100 .000010 INITIAL LENGTH .007060 .000040 FORCE(N) STRAIN(%) ERROR(%) STRESS(MPa) ERROR(MPa) 0.0006 0.00 1.13 0.007 0.001 0.0059 0.71 1.14 0.073 0.013 0.0128 1.70 1.14 0.160 0.028 0.0214 3.26 1.15 0.267 0.046 0.0328 4.67 1.16 0.410 0.071 0.0468 7.08 1.17 0.586 0.101 Table A 5.1.3 : Results of uniaxial tensile test of human # 5 ring #1 layer #3 Appendix H. ERROR ANALYSIS 205 SPECIMEN DIMENSIONS MEASUREMENT MEASUREMENT (m) ERROR (m) INITIAL WIDTH .001110 000050 INITIAL THICKNESS .000100 000010 INITIAL LENGTH .007010 000040 FORCE(N) STRAIN(%) ERROR(%) STRESS(MPa) ERROR(MPa) 0.0008 -0.00 1.14 0.007 0.001 0.0087 3.28 1.16 0.079 0.012 0.0174 5.85 1.17 0.157 0.024 0.0283 9.42 1.19 0.255 0.040 0.0402 15.41 1.23 0.362 0.056 0.0544 23.54 1.28 0.490 0.076 0.0711 33.81 1.33 0.641 0.099 Table A 5.1.4 : Results of uniaxial tensile test of human # 5 ring #1 layer #4 Appendix H. ERROR ANALYSIS 206 SPECIMEN DIMENSIONS MEASUREMENT MEASUREMENT (m) ERROR (m) INITIAL WIDTH .001200 .000050 INITIAL THICKNESS .000100 .000010 INITIAL LENGTH .007860 000040 FORCE(N) STRAIN(%) ERROR(%) STRESS(MPa) ERROR (MPa) 0.0008 -0.00 1.02 0.007 0.001 0.0054 1.65 1.03 0.045 0.007 0.0113 2.93 1.03 0.094 0.014 0.0201 5.85 1.05 0.167 0.025 0.0296 8.52 1.06 0.247 0.037 0.0423 13.36 1.09 0.353 0.054 0.0533 17.30 1.11 0.444 0.067 0.0689 25.32 1.15 0.574 0.087 0.0838 30.41 1.17 0.698 0.106 0.1002 39.82 1.22 0.835 0.127 Table A 5.1.5 : Results of uniaxial tensile test of human # 5 ring #1 layer #5 Appendix H. ERROR ANALYSIS 207 SPECIMEN DIMENSIONS MEASUREMENT MEASUREMENT (m) ERROR (m) INITIAL WIDTH .001370 .000050 INITIAL THICKNESS .000100 000010 INITIAL LENGTH .007690 .000040 FORCE(N) STRAIN(%) ERROR(%) STRESS(MPa) ERROR(MPa) 0.0007 -0.00 1.04 0.005 0.001 0.0062 0.65 1.04 0.045 0.007 0.0152 1.30 1.05 0.111 0.016 0.0229 1.82 1.05 0.167 0.025 0.0319 2.34 1.05 0.233 0.034 0.0464 3.25 1.06 0.338 0.050 0.0581 4.29 1.06 0.424 0.062 0.0739 5.20 1.07 0.539 0.079 0.0930 6.50 1.07 0.679 0.099 0.1097 7.28 1.08 0.800 0.117 0.1319 8.45 1.08 0.963 0.141 0.1525 10.01 1.09 1.113 0.163 0.1703 11.18 1.10 1.243 0.182 0.1924 12.48 1.11 1.404 0.206 Table A 5.2.3 : Results of uniaxial tensile test of human # 5 ring #2 layer #3 Appendix H. ERROR ANALYSIS 208 SPECIMEN DIMENSIONS MEASUREMENT MEASUREMENT On) ERROR (m) INITIAL WIDTH .001500 .000050 INITIAL THICKNESS .000100 000010 INITIAL LENGTH .008840 000040 FORCE(N) STRAIN(%) ERROR(%) STRESS(MPa) ERROR(MPa) 0.0005 0.00 0.90 0.003 0.000 0.0054 0.34 0.91 0.036 0.005 0.0128 1.02 0.91 0.086 0.012 0.0207 1.81 0.91 0.138 0.020 0.0290 2.15 0.91 0.193 0.028 0.0402 3.05 0.92 0.268 0.038 0.0535 3.51 0.92 0.357 0.051 0.0661 4.86 0.93 0.440 0.063 0.0792 5.66 0.93 0.528 0.076 0.0927 6.90 0.94 0.618 0.089 0.1103 8.03 0.94 0.736 0.105 0.1327 9.62 0.95 0.885 0.127 0.1596 11.88 0.96 1.064 0.153 0.1936 14.37 0.97 1.291 0.185 Table A 5.2.4 : Results of uniaxial tensile test of human # 5 ring #2 layer #4 Appendix H. ERROR ANALYSIS 209 SPECIMEN DIMENSIONS MEASUREMENT MEASUREMENT (m) ERROR (m) INITIAL WIDTH .001480 000050 INITIAL THICKNESS .000100 .000010 INITIAL LENGTH .007900 000040 FORCE(N) STRAIN(%) ERR0R(%) STRESS(MPa) ERROR(MPa) 0.0006 -0.00 1.01 0.004 0.001 0.0062 0.76 1.02 0.042 0.006 0.0128 1.27 1.02 0.087 0.012 0.0202 2.41 1.02 0.136 0.020 0.0318 3.67 1.03 0.215 0.031 0.0405 5.70 1.04 0.273 0.039 0.0517 8.10 1.05 0.350 0.050 0.0642 11.77 1.07 0.434 0.062 0.0786 17.97 1.10 0.531 0.076 Table A 5.2.5 : Results of uniaxial tensile test of human # 5 ring #2 layer #5 Appendix H. ERROR ANALYSIS SPECIMEN DIMENSIONS MEASUREMENT MEASUREMENT (m) ERROR (m) INITIAL WIDTH .001410 000050 INITIAL THICKNESS .000100 .000010 INITIAL LENGTH .006520 .000040 FORCE(N) STRAIN(%) ERROR(%) STRESS(MPa) ERROR(MPa) 0.0004 0.00 1.23 0.003 0.000 0.0057 1.99 1.24 0.040 0.006 0.0106 2.30 1.24 0.075 0.011 0.0192 3.68 1.25 0.136 0.020 0.0272 5.67 1.26 0.193 0.028 0.0408 9.66 1.29 0.289 0.042 0.0507 13.65 1.31 0.359 0.052 0.0624 18.25 1.34 0.443 0.064 0.0755 25.61 1.38 0.535 0.078 0.0931 34.05 1.44 0.660 0.096 Table A 5.2.6 : Results of uniaxial tensile test of human # 5 ring #2 layer #6 Appendix H. ERROR ANALYSIS 211 SPECIMEN DIMENSIONS MEASUREMENT MEASUREMENT (m) ERROR (m) INITIAL WIDTH .001320 .000050 INITIAL THICKNESS .000100 .000010 INITIAL LENGTH .006200 .000040 FORCE(N) STRAIN(%) ERR0R(%) STRESS(MPa) ERROR(MPa) 0.0004 -0.00 1.29 0.003 0.000 0.0049 1.29 1.30 0.037 0.005 0.0109 2.74 1.31 0.082 0.012 0.0197 5.00 1.32 0.149 0.022 0.0293 7.90 1.34 0.222 0.033 0.0386 12.74 1.37 0.293 0.043 0.0516 17.26 1.40 0.391 0.058 0.0615 24.68 1.45 0.466 0.069 Table A 5.2.7 : Results of uniaxial tensile test of human # 5 ring #2 layer #7 Appendix H. ERROR ANALYSIS 212 SPECIMEN DIMENSIONS MEASUREMENT MEASUREMENT (m) ERROR (m) INITIAL WIDTH .000770 000050 INITIAL THICKNESS .000100 .000010 INITIAL LENGTH .008630 .000040 FORCE(N) STRAIN(%) ERROR(%) STRESS(MPa) ERROR(MPa) 0.0008 0.00 0.93 0.010 0.002 0.0066 -0.12 0.93 0.085 0.015 0.0147 0.23 0.93 0.191 0.033 0.0222 1.04 0.93 0.289 0.051 0.0356 1.97 0.94 0.462 0.081 0.0523 3.01 0.94 0.680 0.119 0.0668 4.06 0.95 0.868 0.152 0.0783 4.63 0.95 1.017 0.178 0.0930 5.68 0.95 1.208 0.211 0.1119 7.18 0.96 1.453 0.254 Table A 6.1.2 : Results of uniaxial tensile test of human # 6 ring #1 layer #2 Appendix H. ERROR ANALYSIS 213 SPECIMEN DIMENSIONS MEASUREMENT MEASUREMENT (m) ERROR (m) INITIAL WIDTH .000820 000050 INITIAL THICKNESS .000100 000010 INITIAL LENGTH .007890 .000040 FORCE(N) STRAIN(%) ERROR(%) STRESS(MPa) ERROR(MPa) 0.0006 -0.00 1.01 0.007 0.001 0.0071 0.63 1.02 0.086 0.015 0.0136 1.27 1.02 0.166 0.028 0.0201 1.65 1.02 0.245 0.042 0.0288 2.28 1.03 0.351 0.060 0.0380 3.30 1.03 0.464 0.079 0.0515 4.06 1.03 0.629 0.107 0.0688 5.45 1.04 0.839 0.143 0.0868 6.97 1.05 1.059 0.181 0.1011 8.36 1.06 1.233 0.211 0.1186 10.52 1.07 1.446 0.247 0.1368 12.55 1.08 1.668 0.285 Table A 6.1.3 : Results of uniaxial tensile test of human # 6 ring #1 layer #3 Appendix H. ERROR ANALYSIS 214 SPECIMEN DIMENSIONS MEASUREMENT MEASUREMENT On) ERROR (m) INITIAL WIDTH .001200 .000050 INITIAL THICKNESS .000100 .000010 INITIAL LENGTH .008690 000040 FORCE(N) STRAIN(%) ERR0R(%) STRESS(MPa) ERROR(MPa) 0.0008 0.00 0.92 0.007 0.001 0.0065 0.92 0.92 0.054 0.008 0.0149 1.61 0.93 0.124 0.019 0.0225 2.53 0.93 0.188 0.028 0.0370 4.14 0.94 0.309 0.047 0.0510 6.10 0.95 0.425 0.064 0.0674 8.63 0.96 0.562 0.085 0.0846 13.23 0.98 0.705 0.107 Table A 6.1.4 : Results of uniaxial tensile test of human # 6 ring #1 layer #4 Appendix H. ERROR ANALYSIS 215 SPECIMEN DIMENSIONS MEASUREMENT MEASUREMENT (m) ERROR (m) INITIAL WIDTH .000620 .000050 INITIAL THICKNESS .000100 .000010 INITIAL LENGTH .007010 000040 FORCE(N) STRAIN(%) ERROR(%) STRESS(MPa) ERROR(MPa) 0.0003 -0.00 1.14 0.005 0.001 0.0035 0.86 1.15 0.057 0.011 0.0102 1.57 1.15 0.164 0.031 0.0156 2.14 1.15 0.251 0.048 0.0246 3.00 1.16 0.397 0.076 0.0320 4.42 1.17 0.517 0.099 0.0413 5.42 1.17 0.665 0.127 0.0497 7.13 1.18 0.801 0.153 0.0585 9.27 1.19 0.944 0.180 Table A 6.2.3 : Results of uniaxial tensile test of human # 6 ring #2 layer #3 Appendix H. ERROR ANALYSIS 216 SPECIMEN DIMENSIONS MEASUREMENT MEASUREMENT (m) ERROR (m) INITIAL WIDTH .001260 000080 INITIAL THICKNESS .000100 .000010 INITIAL LENGTH .007750 000040 FORCE(N) STRAIN(%) ERROR(%) STRESS(MPa) ERROR(MPa) 0.0008 -0.00 1.03 0.006 0.001 0.0082 1.29 1.04 0.065 0.011 0.0155 1.68 1.04 0.123 0.021 0.0255 2.45 1.04 0.202 0.035 0.0374 3.87 1.05 0.297 0.052 0.0519 5.81 1.06 0.412 0.072 0.0684 8.39 1.08 0.543 0.094 0.0856 12.13 1.09 0.679 0.118 0.1011 14.58 1.11 0.803 0.139 Table A 6.2.5 : Results of uniaxial tensile test of human # 6 ring #2 layer #5 -Appendix H. ERROR ANALYSIS 217 SPECIMEN DIMENSIONS MEASUREMENT MEASUREMENT (m) ERROR (m) INITIAL WIDTH .000900 000050 INITIAL THICKNESS .000100 .000010 INITIAL LENGTH .006580 000040 FORCE(N) STRAIN(%) ERR0R(%) STRESS(MPa) ERROR(MPa) 0.0008 0.00 1.22 0.009 0.001 0.0079 0.76 1.22 0.088 0.015 0.0155 1.06 1.22 0.172 0.028 0.0225 1.82 1.23 0.250 0.041 0.0331 2.74 1.23 0.368 0.061 0.0450 3.95 1.24 0.500 0.083 0.0590 5.93 1.25 0.656 0.109 0.0729 7.75 1.26 0.810 0.134 Table A 6.3.3 : Results of uniaxial tensile test of human # 6 ring #3 layer #3 Appendix H. ERROR ANALYSIS SPECIMEN DIMENSIONS MEASUREMENT MEASUREMENT (m) ERROR (m) INITIAL WIDTH .001220 .000050 INITIAL THICKNESS .000100 .000010 INITIAL LENGTH .007140 000040 FORCE(N) STRAIN(%) ERROR(%) STRESS(MPa) ERROR(MPa) 0.0008 0.00 1.12 0.006 0.001 0.0059 0.42 1.12 0.048 0.007 0.0116 0.70 1.12 0.095 0.014 0.0204 1.26 1.13 0.167 0.025 0.0301 1.40 1.13 0.247 0.037 0.0417 2.66 1.14 0.342 0.052 0.0418 3.08 1.14 0.343 0.052 0.0517 3.92 1.14 0.424 0.064 0.0677 5.04 1.15 0.555 0.084 0.0794 6.16 1.15 0.651 0.098 0.0929 7.28 1.16 0.762 0.115 0.1120 9.38 1.17 0.918 0.139 0.1300 11.06 1.18 1.066 0.161 Table A 6.3.4 : Results of uniaxial tensile test of human # 6 ring #3 layer #4 Appendix H. ERROR ANALYSIS 219 SPECIMEN DIMENSIONS MEASUREMENT MEASUREMENT (m) ERROR (m) INITIAL WIDTH .001290 .000050 INITIAL THICKNESS .000100 .000010 INITIAL LENGTH .006370 000040 FORCE(N) STRAIN(%) ERROR(%) STRESS(MPa) ERROR(MPa) 0.0008 -0.00 1.26 0.006 0.001 0.0073 0.31 1.26 0.057 0.008 0.0147 0.94 1.26 0.114 0.017 0.0252 1.26 1.26 0.195 0.029 0.0366 2.20 1.27 0.283 0.042 0.0495 3.30 1.28 0.384 0.057 0.0616 4.40 1.28 0.478 0.071 0.0751 5.02 1.29 0.582 0.087 0.0927 6.12 1.29 0.719 0.107 0.1088 7.54 1.30 0.843 0.125 Table A 6.3.5 : Results of uniaxial tensile test of human # 6 ring #3 layer #5 Appendix H. ERROR ANALYSIS 220 SPECIMEN DIMENSIONS MEASUREMENT MEASUREMENT (m) ERROR (m) INITIAL WIDTH .001370 .000050 INITIAL THICKNESS .000100 .000010 INITIAL LENGTH .008810 .000040 FORCE(N) STRAIN(%) ERR0R(%) STRESS(MPa) ERROR(MPa) 0.0008 0.00 0.91 0.006 0.001 0.0069 0.23 0.91 0.050 0.007 0.0146 1.14 0.91 0.107 0.016 0.0220 1.93 0.92 0.161 0.024 0.0346 2.95 0.92 0.253 0.037 0.0503 4.88 0.93 0.367 0.054 0.0696 7.49 0.94 0.508 0.074 0.0906 11.69 0.96 0.662 0.097 Table A 6.3.6 : Results of uniaxial tensile test of human # 6 ring #3 layer #6 Appendix H. ERROR ANALYSIS 221 SPECIMEN DIMENSIONS MEASUREMENT MEASUREMENT On) ERROR (m) INITIAL WIDTH .001410 .000050 INITIAL THICKNESS .000100 .000010 INITIAL LENGTH .006310 000040 FORCE(N) STRAIN(%) ERROR(%) STRESS(MPa) ERROR(MPa) 0.0007 0.00 1.27 0.005 0.001 0.0060 1.74 1.28 0.042 0.006 0.0122 2.22 1.28 0.087 0.013 0.0207 3.80 1.29 0.147 0.021 0.0293 5.71 1.30 0.208 0.030 0.0514 9.19 1.33 0.365 0.053 Table A 6.3.9 : Results of uniaxial tensile test of human # 6 ring #3 layer #9 Appendix H, ERROR ANALYSIS 222 SPECIMEN DIMENSIONS MEASUREMENT MEASUREMENT (m) ERROR (m) INITIAL WIDTH .001000 .000050 INITIAL THICKNESS .000100 .000010 INITIAL LENGTH .005780 .000040 FORCE(N) STRAIN(%) ERROR(%) STRESS(MPa) ERROR(MPa) 0.0008 0.00 1.38 0.008 0.001 0.0069 -0.17 1.38 0.069 0.011 0.0155 0.87 1.39 0.155 0.025 0.0236 1.38 1.39 0.236 0.038 0.0334 1.90 1.40 0.334 0.053 0.0466 2.60 1.40 0.466 0.075 0.0616 3.63 1.41 0.616 0.099 0.0788 4.84 1.42 0.788 0.126 0.0932 5.71 1.42 0.932 0.149 0.1122 7.09 1.43 1.122 0.180 0.1304 7.61 1.44 1.304 0.209 0.1511 8.65 1.44 1.511 0.242 0.1742 9.52 1.45 1.742 0.279 0.1935 10.90 1.46 1.935 0.310 Table A 7.2.1 : Results of uniaxial tensile test of human # 7 ring #2 layer #1 Appendix H. ERROR ANALYSIS 223 SPECIMEN DIMENSIONS MEASUREMENT MEASUREMENT (m) ERROR (m) INITIAL WIDTH .000720 000080 INITIAL THICKNESS .000100 000010 INITIAL LENGTH .008770 .000040 FORCE(N) STRAIN(%) ERROR(%) STRESS(MPa) ERROR(MPa) 0.0005 0.00 0.91 0.007 0.002 0.0057 1.03 0.92 0.079 0.017 0.0133 1.82 0.92 0.185 0.041 0.0216 2.96 0.93 0.299 0.066 0.0301 4.33 0.93 0.418 0.092 0.0392 6.16 0.94 0.544 0.120 0.0514 8.32 0.95 0.713 0.158 0.0597 10.60 0.96 0.829 0.183 0.0701 14.14 0.98 0.973 0.215 0.0836 19.38 1.00 1.161 0.257 Table A 7.2.2 : Results of uniaxial tensile test of human # 7 ring #2 layer #2 Appendix H. ERROR ANALYSIS 224 SPECIMEN DIMENSIONS MEASUREMENT MEASUREMENT (m) ERROR (m) INITIAL WIDTH .001200 .000050 INITIAL THICKNESS .000090 .000010 INITIAL LENGTH .008210 .000040 FORCE(N) STRAIN(%) ERR0R(%) STRESS(MPa) ERROR(MPa) 0.0007 0.00 0.97 0.006 0.001 0.0072 0.73 0.98 0.066 0.011 0.0166 1.71 0.98 0.153 0.025 0.0253 3.05 0.99 0.234 0.038 0.0377 4.38 1.00 0.349 0.057 0.0482 6.21 1.00 0.446 0.073 0.0591 7.67 1.01 0.547 0.089 0.0685 9.87 1.02 0.634 0.103 0.0812 13.28 1.04 0.752 0.122 Table A 7.2.3 : Results of uniaxial tensile test of human # 7 ring #2 layer #3 Appendix H. ERROR ANALYSIS 225 SPECIMEN DIMENSIONS MEASUREMENT (m) MEASUREMENT ERROR (m) INITIAL WIDTH INITIAL THICKNESS INITIAL LENGTH .001430 .000070 .008820 .000050 .000010 .000040 FORCE(N) STRAIN(%) ERR0R(%) STRESS(MPa) ERROR(MPa) 0.0003 0.0119 0.0210 0.0331 0.0477 0.00 1.36 3.29 5.56 12.70 0.91 0.91 0.92 0.93 0.96 0.003 0.118 0.210 0.331 0.477 0.001 0.022 0.039 0.062 0.090 Table A 7.2.4 : Results of uniaxial tensile test of human # 7 ring #2 layer #4 Appendix H. ERROR ANALYSIS SPECIMEN DIMENSIONS MEASUREMENT MEASUREMENT (m) ERROR (m) INITIAL WIDTH .001430 .000050 INITIAL THICKNESS .000100 .000010 INITIAL LENGTH .008400 .000040 FORCE(N) STRAIN(%) ERROR(%) STRESS(MPa) ERROR(MPa) 0.0005 -0.00 0.95 0.003 0.000 0.0059 0.83 0.96 0.041 0.006 0.0134 2.14 0.96 0.094 0.014 0.0210 2.98 0.97 0.147 0.021 0.0305 4.88 0.98 0.213 0.031 0.0420 7.26 0.99 0.294 0.043 0.0509 9.76 1.00 0.356 0.052 0.0640 15.60 1.03 0.448 0.065 0.0768 23.45 1.06 0.537 0.078 a Table A 7.2.6 : Results of uniaxial tensile test of human # 7 ring #2 layer #6 Appendix H. ERROR ANALYSIS 227 SPECIMEN DIMENSIONS MEASUREMENT MEASUREMENT (in) ERROR (m) INITIAL WIDTH .001250 .000050 INITIAL THICKNESS ,000155 .000010 INITIAL LENGTH .009050 .000040 FORCE(N) STRAIN(%) ERROR(%) STRESS(MPa) ERROR(MPa) 0.0007 0.00 0.88 0.004 0.000 0.0073 0.55 0.89 0.037 0.004 0.0185 1.77 0.89 0.096 0.011 0.0373 3.76 0.90 0.193 0.022 0.0592 6.41 0.91 0.306 0.035 0.0929 11.60 0.94 0.480 0.055 0.1158 16.35 0.96 0.598 0.068 0.1393 21.33 0.98 0.719 0.082 Table A 7.2.7 : Results of uniaxial tensile test of human # 7 ring #2 layer #7 Appendix H. ERROR ANALYSIS 228 SPECIMEN DIMENSIONS MEASUREMENT MEASUREMENT (m) ERROR (m) INITIAL WIDTH .001430 .000080 INITIAL THICKNESS .000100 .000010 INITIAL LENGTH .008360 000040 FORCE(N) STRAIN(%) ERR0R(%) STRESS(MPa) ERROR(MPa) 0.0005 0.00 0.96 0.003 0.001 0.0110 0.48 0.96 0.077 0.013 0.0213 0.72 0.96 0.149 0.025 0.0337 1.20 0.96 0.236 0.039 0.0464 1.67 0.96 0.324 0.054 0.0603 2.27 0.97 0.421 0.070 0.0795 2.87 0.97 0.556 0.092 0.1008 3.47 0.97 0.705 0.117 0.1105 4.07 0.98 0.773 0.128 Table A 8.2.2 : Results of uniaxial tensile test of human # 8 ring #2 layer #2 Appendix H. ERROR ANALYSIS 229 SPECIMEN DIMENSIONS MEASUREMENT MEASUREMENT (m) ERROR (m) INITIAL WIDTH .001110 000050 INITIAL THICKNESS .000085 .000010 INITIAL LENGTH .008130 000040 FORCE(N) STRAIN(%) ERROR(%) STRESS(MPa) ERROR(MPa) 0.0003 0.00 . 0.98 0.003 0.001 0.0103 0.12 0.98 0.109 0.019 0.0225 0.86 0.99 0.239 0.041 0.0329 1.35 0.99 0.349 0.060 0.0450 2.09 0.99 0.477 0.082 0.0591 3.20 1.00 0.626 0.108 0.0779 4.31 1.01 0.826 0.143 0.0992 6.03 1.01 1.051 0.182 Table A 8.2.3 : Results of uniaxial tensile test of human # 8 ring #2 layer #3 Appendix H. ERROR ANALYSIS 230 SPECIMEN DIMENSIONS MEASUREMENT MEASUREMENT (m) ERROR (m) INITIAL WIDTH .001280 .000050 INITIAL THICKNESS .000110 .000010 INITIAL LENGTH .009330 .000040 FORCE(N) STRAIN(%) ERROR(%) STRESS(MPa) ERROR(MPa) 0.0006 0.00 0.86 0.004 0.001 0.0138 0.75 0.86 0.098 0.014 0.0239 1.18 0.86 0.170 0.024 0.0400 2.04 0.87 0.284 0.040 0.0606 2.79 0.87 0.430 0.060 0.0834 3.75 0.87 0.592 0.083 0.1032 4.93 0.88 0.733 0.103 0.1231 5.79 0.88 0.874 0.122 0.1421 6.75 0.89 1.009 0.141 0.1637 8.15 0.89 1.162 0.163 0.1866 9.11 0.90 1.325 0.185 Table A 8.2.4 : Results of uniaxial tensile test of human # 8 ring #2 layer #4 Appendix H. ERROR ANALYSIS SPECIMEN DIMENSIONS MEASUREMENT MEASUREMENT (m) ERROR (m) INITIAL WIDTH .001300 .000050 INITIAL THICKNESS .000087 000010 INITIAL LENGTH .007960 .000040 FORCE(N) STRAIN(%) ERR0R(%) STRESS(MPa) ERROR(MPa) 0.0008 0.00 1.01 0.007 0.001 0.0203 1.13 1.01 0.179 0.029 0.0400 2.89 1.02 0.354 0.058 0.0610 4.77 1.03 0.539 0.088 0.0818 7.16 1.04 0.724 0.118 0.1048 8.92 1.05 0.926 0.151 0.1267 11.18 1.06 1.120 0.183 0.1467 12.94 1.07 1.297 0.212 0.1707 15.45 1.08 1.509 0.247 Table A 8.2.5 : Results of uniaxial tensile test of human # 8 ring #2 layer #5 Appendix H. ERROR ANALYSIS 232 SPECIMEN DIMENSIONS MEASUREMENT MEASUREMENT (m) ERROR (m) INITIAL WIDTH .000910 .000050 INITIAL THICKNESS .000115 .000010 INITIAL LENGTH .008470 000040 FORCE(N) STRAIN(%) ERROR(%) STRESS(MPa) ERROR(MPa) 0.0005 0.00 0.94 0.005 0.001 0.0112 0.83 0.95 0.107 0.016 0.0226 2.48 0.96 0.216 0.033 0.0330 2.95 0.96 0.316 0.048 0.0465 4.13 0.96 0.445 0.068 0.0592 5.79 0.97 0.566 0.086 0.0785 8.15 0.98 0.750 0.114 0.0979 10.27 0.99 0.936 0.142 Table A 8.2.6 : Results of uniaxial tensile test of human # 8 ring #2 layer #6 Appendix H. E R R O R ANALYSIS 233 SPECIMEN DIMENSIONS MEASUREMENT MEASUREMENT (m) ERROR (m) INITIAL WIDTH .001080 000050 INITIAL THICKNESS .000080 .000010 INITIAL LENGTH .009370 .000040 FORCE(N) STRAIN(%) ERROR(%) STRESS(MPa) ERROR(MPa) 0.0006 -0.00 0.85 0.007 0.001 0.0122 0.85 0.86 0.141 0.025 0.0239 1.71 0.86 0.277 0.050 0.0412 2.24 0.86 0.476 0.086 0.0591 3.20 0.87 0.684 0.124 0.0826 4.16 0.87 0.956 0.173 0.1042 5.34 0.88 1.206 0.219 0.1218 6.19 0.88 1.410 0.256 0.1416 7.26 0.88 1.639 0.297 0.1624 8.32 0.89 1.879 0.341 0.1866 9.61 0.89 2.160 0.392 Table A 8.3.1 : Results of uniaxial,tensile test of human # 8 ring #3 layer #1 dix H. ERROR ANALYSIS SPECIMEN DIMENSIONS MEASUREMENT MEASUREMENT (m) ERROR (m) INITIAL WIDTH .001190 000050 INITIAL THICKNESS .000090 .000010 INITIAL LENGTH .007010 .000040 FORCE(N) STRAIN(%) ERROR(%) STRESS(MPa) ERROR(MPa) 0.0003 0.00 1.14 0.003 0.000 0.0094 0.43 1.14 0.088 0.014 0.0198 0.86 1.15 0.185 0.030 0.0305 1.85 1.15 0.285 0.046 0.0423 2.28 1.15 0.395 0.064 0.0506 2.71 1.16 0.472 0.077 0.0643 3.85 1.16 0.600 0.098 0.0807 4.71 1.17 0.753 0.123 0.1030 5.56 1.17 0.962 0.157 0.1191 6.70 1.18 1.112 0.181 Table A 8.3.2 : Results of uniaxial tensile test of human # 8 ring #3 layer #2 Appendix H. ERROR ANALYSIS 235 SPECIMEN DIMENSIONS MEASUREMENT MEASUREMENT (m) ERROR (m) INITIAL WIDTH .001010 000050 INITIAL THICKNESS .000080 .000010 INITIAL LENGTH .007780 000040 FORCE(N) STRAIN(%) ERROR(%) STRESS(MPa) ERROR(MPa) 0.0008 -0.00 1.03 0.010 0.002 0.0114 0.51 1.03 0.141 0.026 0.0209 1.80 1.04 0.258 0.048 0.0306 2.44 1.04 0.378 0.070 0.0465 3.86 1.05 0.576 0.106 0.0640 5.53 1.06 0.792 0.146 0.0828 7.20 1.07 1.025 0.189 0.1037 9.25 1.08 1.283 0.237 0.1223 11.44 1.09 1.514 0.279 Table A 8.3.3 : Results of uniaxial tensile test of human # 8 ring #3 layer #3 Appendix H. ERROR ANALYSIS 236 SPECIMEN DIMENSIONS MEASUREMENT MEASUREMENT (m) ERROR (m) INITIAL WIDTH .001250 .000050 INITIAL THICKNESS .000080 .000010 INITIAL LENGTH .006730 .000040 FORCE(N) STRAIN(%) ERROR(%) STRESS(MPa) ERROR(MPa) 0.0006 -0.00 1.19 0.006 0.001 0.0115 0.59 1.19 0.115 0.020 0.0207 1.63 1.20 0.207 0.036 0.0317 2.23 1.20 0.317 0.055 0.0453 3.27 1.21 0.453 0.079 0.0609 4.90 1.22 0.609 0.107 0.0828 6.83 1.23 0.828 0.145 0.1026 8.77 1.24 1.026 0.180 0.1225 10.25 1.25 1.225 0.214 0.1421 12.78 1.26 1.421 0.249 Table A 8.3.4 : Results of uniaxial tensile test of human # 8 ring #3 layer #4 Appendix H. ERROR ANALYSIS 237 SPECIMEN DIMENSIONS MEASUREMENT MEASUREMENT (m) ERROR (m) INITIAL WIDTH .001350 .000050 INITIAL THICKNESS .000105 .000010 INITIAL LENGTH .007720 .000040 FORCE(N) STRAIN(%) ERROR(%) STRESS(MPa) ERROR(MPa) 0.0006 0.00 1.04 0.004 0.001 0.0102 1.42 1.04 0.072 0.010 0.0165 2.07 1.05 0.116 0.017 0.0262 2.85 1.05 0.185 0.026 0.0357 3.50 1.05 0.252 0.036 0.0467 4.15 1.06 0.330 0.047 0.0580 5.18 1.06 0.409 0.058 0.0705 6.22 1.07 0.497 0.071 0.0862 7.38 1.07 0.608 0.087 0.1067 9.33 1.08 0.753 0.107 Table A 8.3.5 : Results of uniaxial tensile test of human # 8 ring #3 layer #5 Appendix H. ERROR ANALYSIS SPECIMEN DIMENSIONS MEASUREMENT MEASUREMENT (m) ERROR (m) INITIAL WIDTH .001120 .000080 INITIAL THICKNESS .000080 .000010 INITIAL LENGTH .007300 .000040 FORCE(N) STRAIN(%) ERR0R(%) STRESS(MPa) ERROR(MPa) 0.0003 0.00 1.10 0.003 0.001 0.0113 1.37 1.10 0.126 0.026 0.0239 2.74 1.11 0.267 0.055 0.0390 3.97 1.12 0.435 0.090 0.0584 6.44 1.13 0.652 0.135 0.0780 8.77 1.14 0.871 0.180 0.0984 11.64 1.16 1.098 0.227 0.1199 14.38 1.17 1.338 0.276 Table A 8.3.6 : Results of uniaxial tensile test of human # 8 ring #3 layer #6 Appendix H. ERROR ANALYSIS 239 SPECIMEN DIMENSIONS MEASUREMENT MEASUREMENT <m) ERROR (m) INITIAL WIDTH .000750 .000050 INITIAL THICKNESS .000100 .000010 INITIAL LENGTH .009400 .000040 FORCE(N) STRAIN(%) ERROR(%) STRESS(MPa) ERROR(MPa) 0.0004 -0.00 0.85 0.005 0.001 0.0074 1.28 0.86 0.099 0.018 0.0182 2.98 0.86 0.243 0.043 0.0264 4.57 0.87 0.351 0.062 0.0395 6.28 0.88 0.527 0.093 0.0511 8.62 0.89 0.681 0.120 0.0705 11.49 0.90 0.939 0.166 Table A 9.1.1 : Results of uniaxial tensile test of human # 9 ring #1 layer #1 Appendix H. ERROR ANALYSIS SPECIMEN DIMENSIONS MEASUREMENT MEASUREMENT (m) ERROR (m) INITIAL WIDTH .000690 .000050 INITIAL THICKNESS .000090 .000010 INITIAL LENGTH .007200 000040 FORCE(N) STRAIN(%) ERROR(%) STRESS(MPa) ERROR(MPa) 0.0010 0.00 1.11 0.016 0.003 0.0114 2.64 1.13 0.183 0.035 0.0212 4.86 1.14 0.341 0.066 0.0316 7.78 1.15 0.508 0.098 0.0408 9.86 1.17 0.656 0.127 Table A 9.1.2 : Results of uniaxial tensile test of human # 9 ring #1 layer'#2 Appendix if. ERROR ANALYSIS SPECIMEN DIMENSIONS MEASUREMENT MEASUREMENT (m) ERROR (m) INITIAL WIDTH .001090 .000050 INITIAL THICKNESS .000115 .000010 INITIAL LENGTH .008410 .000040 FORCE(N) STRAIN(%) ERR0R(%) STRESS(MPa) ERROR(MPa) 0.0008 0.00 0.95 0.006 0.001 0.0087 0.59 0.95 0.070 0.010 0.0172 1.55 0.96 0.138 0.020 0.0253 2.14 0.96 0.202 0.029 0.0386 3.33 0.97 0.308 0.044 0.0494 4.04 0.97 0.394 0.056 0.0641 5.35 0.98 0.511 0.073 0.0785 6.18 0.98 0.626 0.089 0.0931 7.37 0.99 0.743 0.106 0.1077 8.09 0.99 0.859 0.123 Table A 9.2.1 : Results of uniaxial tensile test of human # 9 ring #2 layer #1 Appendix H. ERROR ANALYSIS 242 SPECIMEN DIMENSIONS MEASUREMENT M EASUREMENT (m) ERROR (m) INITIAL WIDTH .000970 .000050 INITIAL THICKNESS .000103 .000010 INITIAL LENGTH .009650 .000040 FORCE(N) STRAIN(%) ERROR(%) STRESS(MPa ) ERROR(MPa) 0.0008 0.00 0.83 0.008 0.001 0.0110 2.38 0.84 0.110 0.017 0.0207 3.63 0.84 0.207 0.033 0.0311 5.08 0.85 0.311 0.049 0.0428 7.15 0.86 0.429 0.068 0.0589 10.57 0.87 0.590 0.094 0.0746 15.75 0.89 0.746 0.118 Table A 9.2.2 : Results of uniaxial tensile test of human # 9 ring #2 layer #2 Appendix H. ERROR ANALYSIS 243 SPECIMEN DIMENSIONS MEASUREMENT MEASUREMENT (m) ERROR (m) INITIAL WIDTH .001080 .000050 INITIAL THICKNESS .000075 000010 INITIAL LENGTH .008300 .000040 FORCE(N) STRAIN(%) ERROR(%) STRESS(MPa) ERROR(MPa) 0.0008 0.00 0.96 0.010 0.002 0.0112 1.57 0.97 0.138 0.026 0.0211 4.46 0.99 0.260 0.049 0.0301 6.99 1.00 0.371 0.070 0.0398 11.69 1.02 0.491 0.093 0.0501 16.27 1.04 0.618 0.117 Table A 9.2.3 : Results of uniaxial tensile test of human # 9 ring #2 layer #3 Appendix H. ERROR ANALYSIS 244 SPECIMEN DIMENSIONS MEASUREMENT MEASUREMENT (m) ERROR (m) INITIAL WIDTH .001240 .000050 INITIAL THICKNESS .000090 .000010 INITIAL LENGTH .009280 000040 FORCE(N) STRAIN(%) ERROR(%) STRESS(MPa) ERROR(MPa) 0.0008 -0.00 0.86 0.007 0.001 0.0073 1.62 0.87 0.066 0.011 0.0165 3.56 0.88 0.148 0.024 0.0253 6.14 0.89 0.227 0.037 0.0340 9.27 0.90 0.305 0.049 0.0439 13.47 0.92 0.393 0.064 0.0520 17.46 0.94 0.466 0.075 Table A 9.2.4 : Results of uniaxial tensile test of human # 9 ring #2 layer #4 Appendix H. ERROR ANALYSIS 245 SPECIMEN DIMENSIONS MEASUREMENT MEASUREMENT <m) ERROR (m) INITIAL WIDTH .001270 .000050 INITIAL THICKNESS .000085 .000010 INITIAL LENGTH .010810 000040 FORCE(N) STRAIN(%) ERROR(%) STRESS(MPa) ERROR(MPa) 0.0008 -0.00 0.74 0.007 0.001 0.0110 3.70 0.75 0.102 0.017 0.0172 5.37 0.76 0.160 0.027 0.0296 11.01 0.78 0.274 0.046 0.0398 16.74 0.80 0.369 0.062 0.0504 24.70 0.83 0.467 0.078 0.0611 35.80 0.87 0.566 0.094 Table A 9.2.5 : Results of uniaxial tensile test of human # 9 ring #2 layer #5 Appendix H. ERROR ANALYSIS 246 SPECIMEN DIMENSIONS MEASUREMENT MEASUREMENT On) ERROR (m) INITIAL WIDTH .001500 .000050 INITIAL THICKNESS .000087 .000010 INITIAL LENGTH .009480 .000040 FORCE(N) STRAIN(%) ERROR(%) STRESS(MPa) ERROR(MPa) 0.0008 0.00 0.84 0.006 0.001 0.0080 1.90 0.85 0.062 0.010 0.0156 4.01 0.86 0.119 0.019 0.0232 5.80 0.87 0.178 0.028 0.0312 8.02 0.88 0.239 0.038 0.0407 10.55 0.89 0.312 0.049 0.0483 13.08 0.90 0.370 0.059 0.0571 17.51 0.92 0.438 0.069 Table A 9.2.6 : Results of uniaxial tensile test of human # 9 ring #2 layer #6 Appendix H. ERROR ANALYSIS 247 SPECIMEN DIMENSIONS MEASUREMENT MEASUREMENT (m) ERROR (m) INITIAL WIDTH .001230 000050 INITIAL THICKNESS .000095 .000010 INITIAL LENGTH .011100 .000040 FORCE(N) STRAIN(%) ERROR(%) STRESS(MPa) ERROR(MPa) 0.0008 0.00 0.72 0.007 0.001 0.0092 0.72 0.72 0.079 0.012 0.0200 1.62 0.73 0.171 0.027 0.0315 2.70 0.73 0.269 0.042 0.0428 4.14 0.74 0.367 0.057 0.0575 6.13 0.74 0.492 0.077 0.0735 8.56 0.75 0.629 0.098 0.0929 13.51 0.77 0.795 0.124 0.1109 20.27 0.79 0.949 0.148 Table A10.1.3 : Results of uniaxial tensile test of human #10 ring #1 layer #3 Appendix H. ERROR ANALYSIS SPECIMEN DIMENSIONS MEASUREMENT MEASUREMENT (m) ERROR (m) INITIAL WIDTH .001060 .000050 INITIAL THICKNESS .000055 .000010 INITIAL LENGTH .007910 .000040 FORCE(N) STRAIN(%) ERROR(%) STRESS(MPa) ERROR(MPa) 0.0009 0.00 1.01 0.015 0.004 0.0071 1.52 1.02 0.121 0.029 0.0134 2.78 1.03 0.230 0.055 0.0219 5.44 1.04 0.375 0.090 0.0304 8.22 1.05 0.521 0.125 0.0413 14.16 1.08 0.708 0.169 Table A10.1.4 : Results of uniaxial tensile test of human #10 ring #1 layer #4 Appendix H. ERROR ANALYSIS 249 SPECIMEN DIMENSIONS MEASUREMENT MEASUREMENT (m) ERROR (m) INITIAL WIDTH .001120 000050 INITIAL THICKNESS .000093 000010 INITIAL LENGTH .009230 000040 FORCE(N) STRAIN(%) ERROR(%) STRESS(MPa) ERROR(MPa) 0.0003 0.00 0.87 0.003 0.000 0.0106 1.30 0.87 0.102 0.016 0.0199 3.14 0.88 0.191 0.031 0.0301 4.88 0.89 0.289 0.047 0.0413 6.28 0.89 0.396 0.064 0.0552 9.21 0.91 0.530 0.086 0.0741 15.82 0.94 0.711 0.115 Table A10.1.5 : Results of uniaxial tensile test of human #10 ring #1 layer #5 Appendix H. ERROR ANALYSIS SPECIMEN DIMENSIONS MEASUREMENT MEASUREMENT 9 On) ERROR (m) INITIAL WIDTH .001120 .000050 INITIAL THICKNESS .000153 000010 INITIAL LENGTH .009840 000040 FORCE(N) STRAIN(%) ERR0R(%) STRESS(MPa) ERROR(MPa) 0.0009 0.00 0.81 0.005 0.001 0.0136 0.91 0.82 0.079 0.010 0.0263 1.73 0.82 0.153 0.018 0.0416 2.34 0.82 0.243 0.029 0.0611 3.35 0.83 0.356 0.043 0.0816 4.78 0.83 0.476 0.057 0.0991 5.69 0.84 0.578 0.069 0.1205 7.01 0.84 0.703 0.084 0.1424 8.13 0.85 0.831 0.100 0.1642 9.76 0.85 0.958 0.115 0.1930 10.87 0.86 1.126 0.135 Table A10.2.1 : Results of uniaxial tensile test of human #10 ring #2 layer #1 Appendix H. ERROR ANALYSIS 251 SPECIMEN DIMENSIONS MEASUREMENT MEASUREMENT (m) ERROR (m) INITIAL WIDTH .001430 .000050 INITIAL THICKNESS .000088 .000010 INITIAL LENGTH .005970 000040 FORCE(N) STRAIN(%) ERROR(%) STRESS(MPa) ERROR(MPa) 0.0007 -0.00 1.34 0.005 0.001 0.0114 1.51 1.35 0.090 0.014 0.0216 2.51 1.36 0.171 0.027 0.0307 3.85 1.37 0.244 0.039 0.0447 5.70 1.38 0.355 0.056 0.0567 8.21 1.40 0.451 0.072 0.0746 12.40 1.42 0.593 0.094 Table A10.2.3 : Results of uniaxial tensile test of human #10 ring #2 layer #3 Appendix H. ERROR ANALYSIS 252 SPECIMEN DIMENSIONS MEASUREMENT MEASUREMENT On) . ERROR (m) INITIAL WIDTH .001140 .000050 INITIAL THICKNESS .000060 .000010 INITIAL LENGTH .010920 000040 FORCE(N) STRAIN(%) ERROR(%) STRESS(MPa) ERROR(MPa) 0.0005 0.00 0.73 0.007 0.002 0.0072 2.01 0.74 0.105 0.023 0.0153 4.58 0.75 0.224 0.049 0.0216 7.42 0.76 0.315 0.070 0.0289 12.64 0.78 0.423 0.093 0.0336 18.13 0.80 0.491 0.108 0.0379 24.36 0.82 0.554 0.122 0.0430 30.49 0.84 0.629 0.139 Table A10.2.4 : Results of uniaxial tensile test of human #10 ring #2 layer #4 Appendix H. ERROR ANALYSIS SPECIMEN DIMENSIONS MEASUREMENT MEASUREMENT (m) ERROR (m) INITIAL WIDTH .001100 .000050 INITIAL THICKNESS .000160 .000010 INITIAL LENGTH .008600 .000040 FORCE(N) STRAIN(%) ERROR(%) STRESS(MPa) ERROR(MPa) 0.0007 0.00 0.93 0.004 0.000 0.0151 1.05 0.94 0.086 0.010 0.0270 2.44 0.94 0.154 0.018 0.0394 3.84 0.95 0.224 0.026 0.0580 5.47 0.96 0.330 0.039 0.0772 8.37 0.97 0.439 0.052 0.0931 9.42 0.97 0.529 0.062 0.1113 12.44 0.99 0.633 0.075 0.1337 15.12 1.00 0.759 0.090 0.1531 18.60 1.02 0.870 0.103 0.1726 22.44 1.03 0.981 0.116 Table A10.3.2 : Results of uniaxial tensile test of human #10 ring #3 layer #2 Appendix H. ERROR ANALYSIS 254 SPECIMEN DIMENSIONS MEASUREMENT MEASUREMENT (m) ERROR (m) INITIAL WIDTH .000940 .000050 INITIAL THICKNESS .000090 000010 INITIAL LENGTH .008680 .000040 FORCE(N) STRAIN(%) ERR0R(%) STRESS(MPa) ERROR(MPa) 0.0008 -0.00 0.92 0.009 0.002 0.0155 3.69 0.94 0.183 0.032 0.0251 6.91 0.95 0.297 0.052 0.0376 10.71 0.97 0.445 0.078 0.0565 18.09 1.01 0.668 0.117 0.0771 27.30 1.05 0.912 0.159 0.0930 37.56 1.09 1.099 0.192 Table A10.3.4 : Results of uniaxial tensile test of human #10 ring #3 layer #4 Appendix H. ERROR ANALYSIS 255 SPECIMEN DIMENSIONS MEASUREMENT MEASUREMENT (m) ERROR (m) INITIAL WIDTH .005250 000100 INITIAL THICKNESS .001680 000100 INITIAL LENGTH .100000 001000 FORCE(N) STRAIN(%) ERROR(%) STRESS(MPa) ERROR(MPa) 0.0000 0.00 2.00 0.000 0.000 0.0882 0.50 2.00 0.010 0.001 0.2822 1.50 2.01 0.032 0.003 0.5468 3.00 2.03 0.062 0.005 0.7321 4.00 2.04 0.083 0.007 1.0937 6.00 2.06 0.124 0.011 1.4288 8.00 2.08 0.162 0.014 1.7287 10.00 2.10 0.196 0.017 2.1168 12.50 2.12 0.240 0.021 2.6019 16.00 2.16 0.295 0.026 3.1135 20.00 2.20 0.353 0.031 3.7926 26.00 2.26 0.430 0.038 4.2071 30.00 2.30 0.477 0.042 4.7099 35.00 2.35 0.534 0.047 5.1773 40.00 2.40 0.587 0.052 5.6183 45.00 2.45 0.637 0.056 6.0417 50.00 2.50 0.685 0.061 6.4386 55.00 2.55 0.730 0.065 6.8179 60.00 2.60 0.773 0.068 7.1883 65.00 2.65 0.815 0.072 7.5587 70.00 2.70 0.857 0.076 7.9115 75.00 2.75 0.897 0.079 8.2467 80.00 2.80 0.935 0.083 8.9258 90.00 2.90 1.012 0.090 9.6050 100.00 3.00 1.089 0.096 10.2929 111.00 3.11 1.167 0.103 10.8486 120.00 3.20 1.230 0.109 11.4660 130.00 3.30 1.300 0.115 11.7923 135.00 3.35 1.337 0.118 12.1010 140.00 3.40 1.372 0.122 12.4009 145.00 3.45 1.406 0.125 12.7096 150.00 3.50 1.441 0.128 13.0801 156.00 3.56 1.483 0.131 13.3270 160.00 3.60 1.511 0.134 13.6269 165.00 3.65 1.545 0.137 13.9532 170.00 3.70 1.582 0.140 Table T . l .1 : Results of uniaxial tensile test on tan gum rubber performed using the TATT Appendix H. ERROR ANALYSIS SPECIMEN DIMENSIONS MEASUREMENT MEASUREMENT (m) ERROR (m) INITIAL WIDTH .005100 .000100 INITIAL THICKNESS .001630 .000100 INITIAL LENGTH .100000 ooiooo ; FORCE(N) STRAIN(%) ERROR(%) STRESS(MPa) ERROR (MPa) 0.0000 0.00 2.00 0.000 0.000 0.1081 0.50 2.00 0.013 0.001 0.2078 1.00 2.01 0.025 0.002 0.3907 2.00 2.02 0.047 0.004 0.5819 3.00 2.03 0.070 0.006 0.7565 4.00 2.04 0.091 0.008 0.9394 5.00 2.05 0.113 0.010 1.0973 6.00 2.06 0.132 0.012 1.4381 8.00 2.08 0.173 0.016 1.7374 10.00 2.10 0.209 0.019 2.4523 15.00 2.15 0.295 0.027 3.0924 20.00 2.20 0.372 0.034 3.6494 25.00 2.25 0.439 0.040 4.1565 30.00 2.30 0.500 0.045 5.4201 44.00 2.44 0.652 0.059 5.9770 51.00 2.51 0.719 0.065 6.6504 60.00 2.60 0.800 0.073 7.3570 70.00 2.70 0.885 0.080 8.0304 80.00 2.80 0.966 0.088 8.7037 90.00 2.90 1.047 0.095 9.3189 100.00 3.00 1.121 0.102 9.9590 110.00 3.10 1.198 0.109 10.5492 120.00 3.20 1.269 0.115 11.2641 132.00 3.32 1.355 0.123 11.7380 140.00 3.40 1.412 0.128 12.3282 150.00 3.50 1.483 0.135 12.9018 160.00 3.60 1.552 0.141 13.1927 165.00 3.65 1.587 0.144 Table T.1.2 : Results of uniaxial tensile test on tan gum rubber performed using the TATT Appendix if. ERROR ANALYSIS 257 SPECIMEN DIMENSIONS MEASUREMENT MEASUREMENT • (m) ERROR (m) INITIAL WIDTH .005000 .000100 INITIAL THICKNESS .001660 000100 INITIAL LENGTH .050000 .001000 FORCE(N) STRAIN(%) ERR0R(%) STRESS(MPa) ERROR(MPa) 0.0000 0.00 4.00 0.000 0.000 0.1992 1.00 4.02 0.024 0.002 0.4067 2.00 4.04 0.049 0.004 0.7719 4.00 4.08 0.093 0.008 1.1039 6.00 4.12 0.133 0.012 1.4359 8.00 4.16 0.173 0.016 1.7596 10.00 4.20 0.212 0.019 2.4568 15.00 4.30 0.296 0.027 3.0627 20.00 4.40 0.369 0.033 4.2330 . 31.00 4.62 0.510 0.046 5.0962 41.00 4.82 0.614 0.055 5.8100 50.00 5.00 0.700 0.063 6.5404 60.00 5.20 0.788 0.071 7.2293 70.00 5.40 0.871 0.079 7.8767 80.00 5.60 0.949 0.086 8.5407 90.00 5.80 1.029 0.093 9.1632 100.00 6.00 1.104 0.100 9.7608 110.00 6.20 1.176 0.106 10.3501 120.00 6.40 1.247 0.113 10.8979 130.00 6.60 1.313 0.118 11.4540 140.00 6.80 1.380 0.125 11.9769 150.00 7.00 1.443 0.130 12.5081 160.00 7.20 1.507 0.136 13.0393 170.00 7.40 1.571 0.142 Table T.1.3 : Results of uniaxial tensile test on tan gum rubber performed using the TATT Appendix H. ERROR ANALYSIS 258 SPECIMEN DIMENSIONS MEASUREMENT MEASUREMENT (m) ERROR (m) INITIAL WIDTH .002400 .000100 INITIAL THICKNESS .001650 .000100 INITIAL LENGTH .050000 001000 FORCE(N) STRAIN(%) ERR0R(%) STRESS(MPa) ERROR(MPa) 0.0000 0.00 4.00 0.000 0.000 0.0990 1.00 4.02 0.025 0.003 0.1901 2.00 4.04 0.048 0.005 0.3485 4.00 4.08 0.088 0.010 0.5108 6.00 4.12 0.129 0.014 0.6613 8.00 4.16 0.167 0.019 0.7999 10.00 4.20 0.202 0.023 1.1286 15.00 4.30 0.285 0.032 1.4810 21.00 4.42 0.374 0.042 1.9404 30.00 4.60 0.490 0.055 2.3681 40.00 4.80 0.598 0.067 2.7601 50.00 5.00 0.697 0.078 3.1284 60.00 5.20 0.790 0.089 3.6313 75.00 5.50 0.917 0.103 3.7897 80.00 5.60 0.957 0.107 4.1184 90.00 5.80 1.040 0.117 4.4194 100.00 6.00 1.116 0.125 4.7203 110.00 6.20 1.192 0.134 5.0213 120.00 6.40 1.268 0.142 5.3104 130.00 6.60 1.341 0.151 5.5915 140.00 6.80 1.412 0.159 5.8806 150.00 7.00 1.485 0.167 6.1618 160.00 7.20 1.556 0.175 Table T.1.4 : Results of uniaxial tensile test on tan gum rubber performed using the TATT Appendix H. ERROR ANALYSIS 259 SPECIMEN DIMENSIONS MEASUREMENT MEASUREMENT On) ERROR (m) INITIAL WIDTH .005300 .000100 INITIAL THICKNESS .001660 000100 INITIAL LENGTH .100000 001000 FORCE(N) STRAIN(%) ERROR(%) STRESS(MPa) ERROR(MPa) 0.0000 0.00 2.00 0.000 0.000 0.1320 0.60 2.01 0.015 0.001 0.2199 1.00 2.01 0.025 0.002 0.3079 1.50 2.01 0.035 0.003 0.4135 2.00 2.02 0.047 0.004 0.5983 3.00 2.03 0.068 0.006 0.7918 4.00 2.04 0.090 0.008 0.9678 5.00 2.05 0.110 0.010 1.1437 6.00 2.06 0.130 0.012 1.5133 8.20 2.08 0.172 0.015 1.7860 10.00 2.10 0.203 0.018 2.2435 13.00 2.13 0.255 0.023 2.6570 16.00 2.16 0.302 0.027 3.2113 20.30 2.20 0.365 0.033 3.8183 25.70 2.26 0.434 0.039 4.2670 30.00 2.30 0.485 0.043 5.2172 40.00 2.40 0.593 0.053 6.1674 51.60 2.52 0.701 0.062 6.8272 60.40 2.60 0.776 0.069 7.5135 70.00 2.70 0.854 0.076 8.1997 80.00 2.80 0.932 0.083 8.8596 90.10 2.90 1.007 0.090 Table T.1.5 : Results of uniaxial tensile test on tan gum rubber performed using the TATT Appendix H. ERROR ANALYSIS 260 SPECIMEN DIMENSIONS MEASUREMENT MEASUREMENT (m) ERROR (m) INITIAL WIDTH .001080 .000050 INITIAL THICKNESS .001200 .000100 INITIAL LENGTH .005410 000030 FORCE(N) STRAIN(%) ERROR(%) STRESS(MPa) ERROR(MPa) 0.0065 0.00 1.11 0.005 0.001 0.0402 1.29 1.12 0.031 0.004 0.1179 3.70 1.13 0.091 0.013 0.2242 8.87 1.16 0.173 0.024 0.3914 15.53 1.20 0.302 0.042 0.5962 29.39 1.27 0.460 0.064 0.7944 46.58 1.37 0.613 0.086 1.0225 75.23 1.53 0.789 0.110 1.1923 94.82 1.63 0.920 0.128 1.3517 127.91 1.82 1.043 0.146 1.5733 146.03 1.92 1.214 0.170 1.7690 161.55 2.00 1.365 0.191 1.9583 162.11 2.01 1.511 0.211 Table T.1.6 : Results of uniaxial tensile test on tan gum rubber performed using the MPTT Appendix H. ERROR ANALYSIS 261 SPECIMEN DIMENSIONS MEASUREMENT MEASUREMENT (m) ERROR (m) INITIAL WIDTH .001060 .000050 INITIAL THICKNESS .001400 000100 INITIAL LENGTH .006580 000030 FORCE(N) STRAIN(%) ERROR(%) STRESS(MPa) ERROR(MPa) 0.0045 0.00 0.91 0.003 0.000 0.0475 0.91 0.92 0.032 0.004 0.1187 2.89 0.93 0.080 0.010 0.2107 5.32 0.94 0.142 0.018 0.3532 11.40 0.96 0.238 0.031 0.5060 16.87 0.99 0.341 0.044 0.6915 30.09 1.05 0.466 0.060 0.9275 45.90 1.12 0.625 0.080 1.1709 73.10 1.25 0.789 0.101 1.4217 95.59 1.35 0.958 0.123 1.6369 129.33 1.50 1.103 0.142 1.8461 129.18 1.50 1.244 0.160 1.9574 130.40 1.51 1.319 0.170 Table T.1.7 : Results of uniaxial tensile test on tan gum rubber performed using the MPTT Appendix H. ERROR ANALYSIS SPECIMEN DIMENSIONS MEASUREMENT MEASUREMENT On) ERROR (in) INITIAL WIDTH .000990 000050 INITIAL THICKNESS .002200 .000100 INITIAL LENGTH .006660 .000030 FORCE(N) STRAIN(%) ERROR(%) STRESS(MPa) ERROR(MPa) 0.0065 0.00 0.90 0.003 0.000 0.0980 2.25 0.91 0.045 0.005 0.2200 5.41 0.93 0.101 0.011 0.3964 10.36 0.95 0.182 0.019 0.6098 15.92 0.97 0.280 0.030 0.7993 22.52 1.00 0.367 0.039 0.9845 29.13 1.03 0.452 0.048 1.1979 40.09 1.08 0.550 0.058 1.3983 49.40 1.12 0.642 0.068 1.5856 61.11 1.18 0.728 0.077 1.7707 72.22 1.23 0.813 0.086 1.9580 84.38 1.28 0.899 0.095 Table T.1.8 : Results of uniaxial tensile test on tan gum rubber performed using the MPTT Appendix H. ERROR ANALYSIS SPECIMEN DIMENSIONS MEASUREMENT MEASUREMENT (m) ERROR (m) INITIAL WIDTH .001230 000050 INITIAL THICKNESS .001150 .000100 INITIAL LENGTH .007370 .000030 FORCE(N) STRAIN(%) ERROR(%) STRESS(MPa) ERROR(MPa) 0.0085 0.00 0.81 0.006 0.001 0.0495 1.09 0.82 0.035 0.005 0.1047 3.12 0.83 0.074 0.010 0.1584 5.02 0.83 0.112 0.015 0.2192 6.92 0.84 0.155 0.021 0.3027 9.77 0.85 0.214 0.029 0.4102 14.25 0.87 0.290 0.040 0.4965 17.91 0.89 0.351 0.048 0.5884 23.47 0.91 0.416 0.057 0.6592 27.00 0.92 0.466 0.064 0.7624 33.65 0.95 0.539 0.074 0.8614 40.57 0.98 0.609 0.084 0.9293 46.27 1.00 0.657 0.090 Table T.1.9 : Results of uniaxial tensile test on tan gum rubber performed using the MPTT Appendix H. ERROR ANALYSIS 264 SPECIMEN DIMENSIONS MEASUREMENT MEASUREMENT (m) ERROR (m) INITIAL WIDTH .001300 .000050 INITIAL THICKNESS .000800 .000100 INITIAL LENGTH .008450 000030 FORCE(N) STRAIN(%) ERR0R(%) STRESS(MPa) ERROR(MPa) 0.0052 0.00 0.71 0.005 0.001 0.0510 2.25 0.72 0.049 0.008 0.0915 4.02 0.72 0.088 0.015 0.1331 5.80 0.73 0.128 0.022 0.1986 9.23 0.74 0.191 0.033 0.2465 12.07 0.75 0.237 0.041 0.3120 16.21 0.77 0.300 0.052 0.3994 20.83 0.78 0.384 0.067 0.4878 29.23 0.81 0.469 0.081 0.5668 35.38 0.84 0.545 0.095 0.6313 43.55 0.86 0.607 0.105 0.7062 51.72 0.89 0.679 0.118 0.7914 64.50 0.94 0.761 0.132 Table T.1.10 : Results of uniaxial tensile test on tan gum rubber performed using the MPTT Appendix H. ERROR ANALYSIS 265 SPECIMEN DIMENSIONS MEASUREMENT MEASUREMENT (m) ERROR (m) INITIAL WIDTH .001330 .000050 INITIAL THICKNESS .000650 .000100 INITIAL LENGTH .008830 .000030 FORCE(N) STRAIN(%) ERR0R(%) STRESS(MPa) ERROR(MPa) 0.0061 0.00 0.68 0.007 0.001 0.0597 2.60 0.69 0.069 0.014 0.1124 5.55 0.70 0.130 0.026 0.1876 9.85 0.71 0.217 0.044 0.2472 14.72 0.73 0.286 0.058 0.3069 19.93 0.75 0.355 0.072 0.3942 27.52 0.77 0.456 0.092 0.4642 33.98 0.79 0.537 0.108 0.5637 47.00 0.84 0.652 0.131 0.6536 58.89 0.88 0.756 0.152 0.7270 69.65 0.92 0.841 0.169 Table T . l . l l : Results of uniaxial tensile test on tan gum rubber performed using the MPTT Appendix H. ERROR ANALYSIS 266 SPECIMEN DIMENSIONS MEASUREMENT MEASUREMENT (m) ERROR (m) INITIAL WIDTH .005800 .000100 INITIAL THICKNESS .001600 .000100 INITIAL LENGTH .100000 .001000 FORCE(N) STRAIN(%) ERROR(%) STRESS(MPa) ERROR(MPa) 0.0000 0.00 2.00 0.000 0.000 0.1999 0.50 2.00 0.022 0.002 0.3998 1.00 2.01 0.043 0.004 0.5704 1.50 2.01 0.061 0.006 0.7497 2.00 2.02 0.081 0.007 1.1103 3.00 2.03 0.120 0.011 1.7003 4.50 2.04 0.183 0.016 2.1099 5.50 2.05 0.227 0.020 2.5098 6.50 2.06 0.270 0.024 3.1203 8.00 2.08 0.336 0.030 3.7397 9.50 2.09 0.403 0.036 4.3600 11.00 2.11 0.470 0.042 5.2224 13.00 2.13 0.563 0.051 6.0897 15.00 2.15 0.656 0.059 6.5395 16.00 2.16 0.705 0.063 7.4402 18.00 2.18 0.802 0.072 8.3300 20.00 2.20 0.898 0.081 9.2502 22.00 2.22 0.997 0.089 10.1401 24.00 2.24 1.093 0.098 11.0103 26.00 2.26 1.186 0.106 11.8903 28.00 2.28 1.281 0.115 Table T.2.1 : Results of uniaxial tensile test on tygon tubing performed using the TATT Appendix E. ERROR ANALYSIS SPECIMEN DIMENSIONS MEASUREMENT MEASUREMENT (m) ERROR (m) INITIAL WIDTH .005550 .000100 INITIAL THICKNESS .001530 000100 INITIAL LENGTH .150000 .001000 FORCE(N) STRAIN(%) ERR0R(%) STRESS(MPa) ERROR(MPa) 0.0000 0.00 1.33 0.000 0.000 0.i901 0.53 1.34 0.022 0.002 0.3900 1.00 1.34 0.046 0.004 0.7497 2.00 1.35 0.088 0.008 1.1103 3.00 1.35 0.131 0.012 1.4700 4.00 1.36 0.173 0.016 2.2001 6.00 1.37 0.259 0.024 2.9302 8.00 1.39 0.345 0.032 3.6799 10.00 1.40 0.433 0.040 4.4404 12.00 1.41 0.523 0.049 5.2097 14.00 1.43 0.614 0.057 5.9898 16.00 1.44 0.705 0.066 6.7796 18.00 1.45 0.798 0.075 7.5597 20.00 1.47 0.890 0.083 8.3496 22.00 1.48 0.983 0.092 9.1101 24.00 1.49 1.073 0.100 9.8696 26.00 1.51 1.162 0.109 10.5801 28.00 1.52 1.246 0.116 Table T.2.2 : Results of uniaxial tensile test on tygon tubing performed using the TATT Appendix H. ERROR ANALYSIS 268 SPECIMEN DIMENSIONS MEASUREMENT MEASUREMENT On) ERROR (m) INITIAL WIDTH .005800 .000100 INITIAL THICKNESS .001600 000100 INITIAL LENGTH .100000 001000 FORCE(N) STRAIN(%) ERROR(%) STRESS(MPa) ERROR(MPa) 0.0000 0.00 2.00 0.000 0.000 0.2097 0.50 2.00 0.023 0.002 0.3998 1.00 2.01 0.043 0.004 0.7801 2.00 2.02 0.084 0.008 1.1495 3.00 2.03 0.124 0.011 1.5200 4.00 2.04 0.164 0.015 2.2697 6.00 2.06 0.245 0.022 3.0400 8.00 2.08 0.328 0.029 3.8200 10.00 2.10 0.412 0.037 4.6197 12.00 2.12 0.498 0.045 5.4498 14.00 2.14 0.587 0.053 6.2798 16.00 2.16 0.677 0.061 7.3804 18.50 2.18 0.795 0.071 8.0095 20.00 2.20 0.863 0.077 8.8504 22.00 2.22 0.954 0.086 9.7196 24.00 2.24 1.047 0.094 10.5095 26.00 2.26 1.132 0.102 Table T.2.3 : Results of uniaxial tensile test on tygon tubing performed using the TATT Appendix H. ERROR ANALYSIS 269 SPECIMEN DIMENSIONS MEASUREMENT MEASUREMENT On) ERROR (m) INITIAL WIDTH .005600 .000100 INITIAL THICKNESS .001600 .000100 INITIAL LENGTH .100000 .001000 FORCE(N) STRAIN(%) ERROR(%) STRESS(MPa) ERROR(MPa) 0.0000 0.00 2.00 0.000 0.000 0.2097 0.50 2.00 0.023 0.002 0.3900 1.00 2.01 0.044 0.004 0.7497 2.00 2.02 0.084 0.008 1.1799 3.10 2.03 0.132 0.012 1.4798 4.00 2.04 0.165 0.015 2.2099 6.00 2.06 0.247 0.022 2.9498 8.00 2.08 0.329 0.030 3.7005 10.00 2.10 0.413 0.037 4.4600 12.00 2.12 0.498 0.045 5.2499 14.00 2.14 0.586 0.053 6.0299 16.00 2.16 0.673 0.061 6.8296 18.00 2.18 0.762 0.069 7.6401 20.00 2.20 0.853 0.077 8.4398 22.00 2.22 0.942 0.085 9.2404 24.00 2.24 1.031 0.093 10.0195 26.00 2.26 1.118 0.101 Table T.2.4 : Results of uniaxial tensile test on tygon tubing performed using the TATT Appendix H. ERROR ANALYSIS 270 SPECIMEN DIMENSIONS MEASUREMENT MEASUREMENT (m) ERROR (m) INITIAL WIDTH .001160 000050 INITIAL THICKNESS .000095 000010 INITIAL LENGTH .008510 .000040 FORCE(N) STRAIN(%) ERROR(%) STRESS(MPa) ERROR(MPa) 0.0003 -0.00 0.94 0.003 0.000 0.0109 2.47 0.95 0.099 0.016 0.0194 4.23 0.96 0.176 0.028 0.0318 6.70 0.97 0.288 0.046 0.0442 9.75 0.99 0.401 0.064 0.0589 12.93 1.00 0.534 0.085 0.0763 18.45 1.03 0.693 0.110 0.0931 22.68 1.05 0.845 0.134 0.1193 29.38 1.08 1.082 0.171 0.1472 37.96 1.12 1.336 0.212 Table T.2.5 : Results of uniaxial tensile test on tygon tubing performed using the MPTT Appendix H. ERROR ANALYSIS 271 SPECIMEN DIMENSIONS MEASUREMENT MEASUREMENT (m) ERROR (m) INITIAL WIDTH .001380 .000050 INITIAL THICKNESS .000090 .000010 INITIAL LENGTH .009420 .000040 FORCE(N) STRAIN(%) ERROR(%) STRESS(MPa) ERROR(MPa) 0.0008 -0.00 0.85 0.006 0.001 0.0091 1.70 0.86 0.073 0.012 0.0200 4.14 0.87 0.161 0.025 0.0336 7.01 0.88 0.271 0.043 0.0500 10.51 0.89 0.402 0.063 0.0701 15.07 0.91 0.564 0.089 0.0930 19.85 0.93 0.749 0.118 0.1200 25.16 0.96 0.967 0.152 0.1423 30.36 0.98 1.146 0.180 Table T.2.6 : Results of uniaxial tensile test on tygon tubing performed using the MPTT Appendix H. ERROR ANALYSIS 272 SPECIMEN DIMENSIONS MEASUREMENT MEASUREMENT (m) ERROR (m) INITIAL WIDTH .005300 000100 INITIAL THICKNESS .002000 .000100 INITIAL LENGTH .100000 001000 FORCE(N) STRAIN(%) ERROR(%) STRESS (MPa) ERROR(MPa) 0.0000 0.00 2.00 0.000 0.000 0.1303 0.50 2.00 0.012 0.001 0.2597 1.00 2.01 0.024 0.002 0.4998 2.00 2.02 0.047 0.004 0.9604 4.00 2.04 0.091 0.007 1.4102 6.00 2.06 0.133 0.010 1.8101 8.00 2.08 0.171 0.013 2.1697 10.00 2.10 0.205 0.016 2.5304 12.00 2.12 0.239 0.019 2.8498 14.00 2.14 0.269 0.021 3.1595 16.00 2.16 0.298 0.024 3.4604 18.00 2.18 0.326 0.026 3.7397 20.00 2.20 0.353 0.028 4.0102 22.00 2.22 0.378 0.030 4.2797 24.00 2.24 0.404 0.032 4.5296 26.00 2.26 0.427 0.034 Table T.3.1 : Results of uniaxial tensile test on latex tubing performed using the TATT Appendix H. ERROR ANALYSIS SPECIMEN DIMENSIONS MEASUREMENT (m) MEASUREMENT ERROR (m) INITIAL WIDTH INITIAL THICKNESS INITIAL LENGTH .003800 .002000 .100000 .000100 .000100 .001000 FORCE(N) STRAIN(%) ERROR(%) STRESS(MPa) ERROR(MPa) 0.0000 0.1000 0.1999 0.3802 0.5596 0.7105 1.0398 1.3299 1.7405 2.1099 2.3500 2.6205 2.7695 2.9704 3.1595 3.3496 0.00 0.50 1.00 2.00 3.00 4.00 6.00 8.00 11.00 14.00 16.00 18.50 20.00 22.00 24.00 26.00 2.00 2.00 2.01 2.02 2.03 2.04 2.06 2.08 2.11 2.14 2.16 2.18 2.20 2.22 2.24 2.26 0.000 0.013 0.026 0.050 0.074 0.093 0.137 0.175 0.229 0.278 0.309 0.345 0.364 0.391 0.416 0.441 0.000 0.001 0.002 0.004 0.006 0.008 0.012 0.015 0.020 0.024 0.027 0.030 0.031 0.034 0.036 0.038 Table T.3.2 : Results of uniaxial tensile test on latex tubing performed using the TATT Appendix H. ERROR ANALYSIS 274 SPECIMEN DIMENSIONS MEASUREMENT MEASUREMENT (m) ERROR (m) INITIAL WIDTH .004300 .000100 INITIAL THICKNESS .002000 .000100 INITIAL LENGTH .100000 .001000 FORCE(N) STRAIN(%) ERROR(%) STRESS(MPa) ERROR(MPa) 0.0000 0.00 2.00 0.000 0.000 0.2195 1.00 2.01 0.026 0.002 0.3998 2.00 2.02 0.046 0.004 0.7605 4.00 2.04 0.088 0.007 1.0898 6.00 2.06 0.127 0.011 1.6895 11.00 2.11 0.196 0.016 2.3197 15.00 2.15 0.270 0.022 2.6597 18.00 2.18 0.309 0.026 3.1801 23.00 2.23 0.370 0.031 3.7397 29.00 2.29 0.435 0.036 4.2601 35.00 2.35 0.495 0.041 4.7099 40.00 2.40 0.548 0.046 5.6301 50.00 2.50 0.655 0.055 6.7395 60.00 2.60 0.784 0.065 8.0703 70.00 2.70 0.938 0.078 9.4198 80.00 2.80 1.095 0.091 10.6497 90.00 2.90 1.238 0.103 11.9001 100.00 3.00 1.384 0.115 Table T.3.3 : Results of uniaxial tensile test on latex tubing performed using the TATT Appendix H. ERROR ANALYSIS 275 SPECIMEN DIMENSIONS MEASUREMENT MEASUREMENT (m) ERROR (m) INITIAL WIDTH .001470 .000050 INITIAL THICKNESS .000132 .000010 INITIAL LENGTH .008520 000040 FORCE(N) STRAIN(%) ERROR(%) STRESS(MPa) ERROR(MPa) 0.0007 0.00 0.94 0.004 0.000 0.0057 0.70 0.94 0.029 0.004 0.0143 2.70 0.95 0.074 0.009 0.0244 4.93 0.96 0.126 0.015 0.0337 7.51 0.97 0.174 0.021 0.0452 10.80 0.99 0.233 0.028 0.0579 14.67 1.01 0.298 0.036 0.0710 19.48 1.03 0.366 0.044 0.0835 24.53 1.05 0.430 0.052 0.0985 30.52 1.08 0.508 0.06i 0.1136 36.50 1.11 0.585 0.070 0.1319 44.25 1.15 0.680 0.081 0.1501 52.00 1.18 0.774 0.093 0.1867 66.08 1.25 0.962 0.115 Table T.3.4 : Results of uniaxial tensile test on latex tubing performed using the MPTT Appendix H. ERROR ANALYSIS 276 SPECIMEN DIMENSIONS MEASUREMENT MEASUREMENT (m) ERROR (m) INITIAL WIDTH .001170 000050 INITIAL THICKNESS .000075 000010 INITIAL LENGTH .007690 .000040 FORCE(N) STRAIN(%) ERR0R(%) STRESS(MPa) ERROR(MPa) 0.0004 -0.00 1.04 0.004 0.001 0.0093 4.81 1.07 0.106 0.020 0.0181 10.14 1.09 0.207 0.038 0.0281 18.08 1.13 0.321 0.060 0.0396 28.35 1.19 0.451 0.084 0.0497 45.51 1.28 0.566 0.105 0.0603 49.28 1.30 0.687 0.128 0.0698 58.65 1.35 0.795 0.148 0.0849 71.65 1.41 0.967 0.180 Table T.3.5 : Results of uniaxial tensile test on latex tubing performed using the MPTT Appendix H. ERROR ANALYSIS 277 SPECIMEN DIMENSIONS MEASUREMENT MEASUREMENT (m) ERROR (m) INITIAL WIDTH .001040 .000050 INITIAL THICKNESS .000100 .000010 INITIAL LENGTH .010340 .000040 FORCE (N) STRAIN(%) ERROR(%) STRESS (MPa) ERROR(MPa) 0.0007 -0.00 0.77 0.007 0.001 0.0087 3.09 0.79 0.084 0.013 0.0183 8.12 0.81 0.176 0.028 0.0284 13.44 0.83 0.273 0.043 0.0392 20.99 0.85 0.377 0.060 0.0502 30.17 0.89 0.482 0.076 0.0621 39.75 0.93 0.597 0.094 0.0738 49.52 0.97 0.710 0.112 Table T.3.6 : Results of uniaxial tensile test on latex tubing performed using the MPTT Appendix H. ERROR ANALYSIS SPECIMEN DIMENSIONS MEASUREMENT MEASUREMENT (m) ERROR (m) INITIAL WIDTH .001530 000050 INITIAL THICKNESS .000090 000010 INITIAL LENGTH .007480 000040 FORCE(N) STRAIN(%) ERROR(%) STRESS(MPa) ERROR(MPa) 0.0005 0.00 1.07 0.004 0.001 0.0078 2.27 1.08 0.057 0.009 0.0183 6.55 1.10 0.133 0.020 0.0289 11.63 1.13 0.210 0.032 0.0400 16.98 1.16 0.290 0.045 0.0505 23.40 1.19 0.367 0.056 0.0601 29.68 1.23 0.436 0.067 0.0706 38.10 1.27 0.512 0.079 0.0819 46.39 1.32 0.595 0.092 0.0931 53.61 1.36 0.676 0.104 0.1094 63.64 1.41 0.794 0.122 0.1282 74.33 1.47 0.931 0.143 Table T.3.7 : Results of uniaxial tensile test on latex tubing performed using the MPTT 

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