NORRED EXHIBIT 2190 - Page 1
`Medtronic, Inc., Medtronic Vascular, Inc.,
`& Medtronic Corevalve, LLC
`v. Troy R. Norred, M.D.
`Case IPR2014-00111
`
`

`

`NORRED EXHIBIT - Page 2
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`This book represents information obtained from authentic and highly regarded sources. Reprinted material-
`is quoted with permission, and sources are indicated. A wide variety of references. are listed Every reasonable effort
`has been made to give reliable data and information. but the author and the publisher cannot assume responsibility for
`the validity of all materials or for the consequences of their use.
`
`©1990 by CRC Press, Inc.
`
`International Standard Book. Number 0—8493-4171-8
`
`Library of Congress Card Number 89-9992-
`Printed in. the United States
`
`NORRED EXHIBIT - Page 2
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`Library of Congress Cataloging-in-Publication Data
`
`'I'hubrikar, Mano.
`The aortic valve: author. Mano Thubrikar.
`p.
`cm.
`Includes bibliographies and- index.
`ISBN 0-8493—4771-8
`l. Aortic valve.
`
`1. Title
`
`[DNLM: l. Aortic Valve.
`QP1l4.A57T48
`1990
`612’.12—-dc20
`DNLMfDLC
`for Library of Congress
`
`WG.265-T53'2a1
`
`89—9992
`CIP
`
`All rights reserved. This book, or any parts thereof, may not be reproduced in any form without written
`consent from the publisher.
`'1
`
`Direct all" inquiries to CRC Press, Inc., 2000 Corporate Blvd.1 N.W., Boca R'aton, Florida, 3-343l.
`
`

`

`
`
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`
`PREFACE
`
`The aortic valve is a fascinating structure. It opens and closes about 103,000 times a day. Its
`dymamics are quite demanding because they are traumatic. The aortic valve sustains variable
`pressure, undergoes complete reversal of curvature, and is subjected to a large amount of flexion
`for billions of cycles and still survives. No man—made structure can boast this achievement. In
`understanding this structure lies enhancement of our knowledge. A vivid picture of the aortic
`valve can be created by simply imagining three flaps moving back and forth in a swing—and-
`pausemotion, constantly opening and closing the valve.
`The book probes step-by-step into various aspects of this structure. The geometry is
`considered and the principles of valve design are revealed. The tissue composition is described
`- as well as how the tissue'is best suited for the valve function. The dynamic motion, which
`describes the very function of the valve, is considered. The mechanism of valve opening and
`changes in the leaflet shape are considered. The blood flow, for the control of which the valve
`exists, is described. The mechanism of closure and how the flow governs the leaflet position is
`described. The mechanical properties of the tissue and the stresses that develop in the
`functioning valve are described. Throughout these descriptions a link is maintained between the
`geometry, tissue, motion, flow, and mechanics.
`
`The echocardiographic studies are described to relate the clinical findings with the experi-
`mental observ ations. The mechanism of second heart sound production is described. The diseaes
`of the valve are described and theories for valvular stenosis explained. Finally, mechanical and
`bioprosthetic valves are described. A broad perspective is developed in dealing with normal,
`pathologic, and bioprosthetic valves by exploring the commonality between them through
`comparisons of their design, dynamics, properties, function, and outcome. Interrelationships
`between several different aspects of the valve are constantly pointed out so as to develop a
`complete cohesive understanding of how the valve works.
`At the present time there is a compelling reason to bring together the knowledge of the aortic
`valve. Most bioprosthetic valves implanted in humans fail in 8 to 16 years and, therefore, the
`search fer a better valve continues. The information contained in this book will help in
`developing a better bioprosthesis. Theories of calcific stenosis in the natural aortic and
`bioprosthetic valves can be understood with the help of this book. The book enhances our ability
`to interpret angiographic and echocardiographic images of the aortic valve. Owing to technical
`developments during the last 15 years, new fundamental information was discovered about the
`aortic valve. This book brings newly discovered information together and presents it in such a
`way that the subject can be understood comprehensively. Each chapter in the book was reviewed
`by two or three outside and internal experts in the field, which has imparted an unusually high
`quality to the text. The book is also an example of how interdisciplinary work can achieve results
`that are otherwise impossible to obtain.
`The book will be useful to cardiovascular surgeons, cardiologists, and cardiac pathologists,
`since it describes normal and abnormal geometries of the aortic valve, valvular pathology,
`replacement valves, angiography, and ultrasonography. It will be useful to anatomists in relating
`structure of the valve to function. It will be useful to manufacturers of mechanical and
`
`to students in physiology and biomedical
`bioprosthetic valves. The“ book will be «useful
`engineering because it describes the principles of physiology and engineering and illustrates
`their applications to the aortic valve. It brings medicine and engineering disciplines together
`using the aortic valve as an example and therefore serves as a unique source of teaching and
`interdisciplinary approaches. From this book both the medical and engineering students can
`benefit by learning how to study the problems in medicine and how to discover scientific
`explanations for them. With the help of the book many researchers will be able to expand their
`research to include interdisciplinary approaches.
`
`
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`”wwwmwnwsmmmmwwummmmwmStilt-mm“mvsyj-iwwyi-au—nA-u‘h
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`
`THE AUTHOR
`
`Mano Thubrikar, Ph.D., is Associate Professor in the Department of Surgery and Director
`of Surgical Research at the University of Virginia Health Sciences Center at Charlottesville,
`Virginia.
`Dr. Thubrikar obtained his B.E. degree (first in the Order of Merit) in 1969 in Metallurgy and
`Materials Science from Nagpur University, India. From New York University he obtained his
`M.S. in 1971 in the same field and his Ph.D. in 1975 in Biomedical Engineering. He served as
`a Research Instructor and as a Research Assistant Professor from 1975 to 1982 in the Department
`of Surgery at the University of Virginia, where he also assumed his present position in 1982.
`Dr. Thubrikar is a member of the American Association of University Professors, Alliance
`of Engineering in Medicine and Biology Society, American Society of Artificial Internal
`Organs, Biomedical Engineering Society, International Association for Cardiac Biological
`Implants, and Council on Arteriosclerosis.
`He has been the recipient of the Research Career Development Award (1980—1985) from
`the National Institutes of Health and the Certificate of Merit awarded by the New York Academy
`of Medicine. He has been the recipient of research grants from the National Institutes of Health,
`the Diabetes Research Center of the University of Virginia, and private industries.
`He has published more than 68 papers and presented 29 lectures at national and international
`meetings. He has been an invited Speaker at several international symposiums. He has been a
`consultant to private industries and has developed collaborative programs between universities.
`His current research interests are in natural, pathologic, and bioprosthetic aortic valves and the
`mechanism of atherosclerosis.
`
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`ACKNOWLEDGMENTS
`
`I am deeply indebted to Dr. Stanton P. Nolan who has contributed immensely to the work
`presented here and whose support and encouragement were essential for the preparation of this
`book.
`
`Deck, Ph.D. and Richard E. Clark, M.D. (Chapter 1); Victor J. Ferrans, M.D. (Chapter 2);
`Stanton P. Nolan, MD. and James L. Heckman, Ph.D. (Chapter 3); Anton A. van Steenhoven,
`Ph.D. and Charles S. Peskin, Ph.D. (Chapter4); Richard T. Eppink, Ph.D. and Phillip L. Gould,
`Ph.D. (Chapter 5); Sanjiv Kaul, M.D. (Chapter 6); Louis G. Durand, M.D., Ph.D. (Chapter 7);
`R. Scott Jones, M.D., Stanton P. Nolan, M.D., and Kuldeep Teja, M.D. (Chapter 8); and
`Frederick J. Schoen, MD. and Neil D. Broom, Ph.D. (Chapter 9). Their comments have
`enhanced the quality of each chapter. I am thankful to Drs. Robert Harry, Paul Bosher, William
`Piepgrass, James Skinner, Jaafar Aouad, Lynn Levitt, Mr. Anthony Broccoli, and Ms. Marjorie
`Garmey‘for their contribution to the research headed by Dr. Nolan and myself, which makes up
`a substantial part of this book. Thanks are due to Gail K. Schroeder, Norma Miller, Linda
`Powley, and Carole Hoadley fortheir assistance in preparing the manuscript. Finally, thanks are
`also due to my wife, Sudha Thubrikar, for her patience during the writing of the book.
`
`
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`To my parents,
`Jumdeojl and Varanasi Thubrikar
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`
`TABLE OF CONTENTS
`
`.
`Chapter I
`Geometry of the Aortic Valve ............................................................................................... 1
`I.
`Introduction .................................................................................................................... 1
`II.
`Heart'and Heart Valves1 '
`III. Valve Anatomy2
`A.
`Functional Importance of Valve Anatomy ........................................................... 6
`IV. Dimensions of the Valve ................................................................................................ 8
`
`V.
`Principles of Valve Design ................'. ....................................................................... 11
`A.
`Constructionrof the Valve Model
`..................................................... 11
`B.
`Valves ofVarious Designs
`12
`C.
`Performance Criteria ...........................'. ............................................................... 12
`D.
`Geometric Relationships ...................................................................................... 14
`E.
`Process of Optimization ...................................................................................... 15
`F.
`The Design of the Natural Aortic Valve ............................................................. 16
`The Effect of Dimensional Changes .................................................................... 17
`G.
`The Role of the Coapting Surface of the Leaflet ................................................ 17
`H.
`References .............................................................................................................................. 1 9
`
`Chapter 2
`Histology and Cytology of the Aortic Valve ....................................................................... 2.1
`I.
`Introduction .................................................................................................................... 21
`II.
`General Features and Histology of the Valve22
`III.
`Electron Microscopy of the Valve27
`IV. Tissue Renewal33
`References36
`
`
`
`Chapter 3
`-
`Dynamics of the Aortic Valve .............................................................................................. 39
`I.
`Introduction39
`H.
`Opening and Closing of the Valve39
`'A.
`The Valve Orifice ................................................................................................ 39
`The LeafletMotion40
`III.
`IV. Motion of Various Parts of the Valve45
`A. Motion of the Commlssures46
`B.
`The Mechanism of Opening of the. Aortic Valve ............................................... 48
`C. Motion of the-Base
`...54
`D, Motion of the Aortic Annulus and Aortic Sinuses, and Change in
`........... 59
`Leaflet Length
`Design of the Valve In Vivo61
`V.
`VI. High-Speed” Studies_of the LeafletMotion
`66
`References .................................................................................................................................72
`
`
`
`
`'
`-
`Chapter 4
`Fluid Dynamics ofthe Aortic Valve75
`
`I.
`Introduction 75
`
`II. Model I75
`
`A.
`Leaflet Position at Peak systole in Steady- Flow78
`B.
`Deceleration Phase
`81
`
`III. ModelII
`.-. ........................... 83
`'
`'IV. Model-III«.90
`
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`3
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`E
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`
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`V.
`Velocity Distribution“
`.... 90
`VI. Blood Flowin the Ascending Aorta ofHumans .......................................................... 92
`References .............................................................................................................................. 94
`
`Chapter 5
`Mechanical Stresses in the Aortic Valve ............................................................................ 97
`I. Introduction............................. 97
`II.
`Stress«Strain Properties of the Leaflet In Vitro ............................................................ 97
`A.
`Uniaxial Stress—Strain Properties...
`.97
`B.
`Stress-Strain Properties of the Leafletin an"IntactClosedValve ....... . ............ 101
`Stress—Strain Properties of the Leaflet In Vivo (Changes1n the Length of
`
`
`
`. .............. 101
`the Leaflet) ..............'. ..........
`Leaflet Length in the Circumferential Direction .............................................. 101
`A.
`B.
`Leaflet Length in the Radial Direction ............................................................. 105
`IV. Determination of Stresses in the Leaflet In Vitro ....................................................... 108
`A.
`Human Aortic Valve in the Closed Position ..................................................... 108
`Determination of Stresses in the Leaflet In Vivo ........................................................ 112
`A.
`Canine Aortic Valve in a Functional State ....................................................... 113
`
`
`III.
`
`V.
`
`VI.
`
`119
`Stress Sharing between the Sinuses and the Leaflets ..
`A. Malformed Valves and Bioprostheses .............................................................. 123
`References 126
`
`Chapter 6
`Echocardiography of the Aortic Valve ............................................................................ 129
`I.
`Introduction ................................................................................................................ 129
`
`...
`II. M-Mode Echocardiography of the Aortic Valve“
`130
`Two-Dimensional Echocardiography of the AorticValve......................................... 132
`111.
`IV. Echocardiography of Diseased Aortic Valves ........................................................... 136
`References ..................................................... 139
`
`_
`Chapter 7
`Production of Aortic Valve Sound .................................................................................... 141
`i.
`Introduction ...................................
`141
`
`
`
`141
`[1.
`Timing of the Second Heart Sound ..
`III. Origin of the Second Heart Sound ............................................................................. 143
`A.
`Frequency Content of the Second Heart Sound ................................... , ............ 148
`B.
`Pathologic Conditions Affecting the Second Heart Sound ............................... 149
`IV. Theory of the Aortic Valve Vibration ........................................................................ 150
`References ............................................................................................................................ 156
`
`Chapter 8
`157
`Diseases of the Aortic Valve
`I.
`Introduction .......... L”. .................................................................................................... 157
`II.
`Aortic Stenosis ........................................................................................................... 157
`
`Ill. Aortic Insufficiency .................................................................................................... 157
`IV. Congenital Bicuspid Aortic Valve ............................................................................. 158
`V.
`Unicuspid and Quadricuspid Valves .............................................................
`... 160
`VI. Variation in Size of the Three Leaflets .
`.. 161
`VII. Theories of Isolated Aortic Stenosis .......................................................................... 162
`
`
`
`............................................................. 164
`VIII. Age-Related Changes in the Leaflets
`IX.
`Patterns of Caicific Deposits ...................................................................................... 167
`References..................................................................... 173
`
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`I
`
`I Chapter9
`
`Replacement Cardiac Valves175
`I.
`Introduction
`175
`11. Mechanical Valves
`175
`III. Bioprostheses .............................................................................................................. 178
`A.
`Design and Construction
`179
`B.
`Performance InViv0181
`C.
`Hemodynamic Evaluation and Durability
`188
`D. Mechanical Factors Related to Valve Life
`191
`IV. Homografts ................................................................................................................. 203
`References ...........
`‘
`206
`
`.................................... 209
`Appendix I
`Appendix II .......................................................................................................................... 21 I
`Index213
`
`‘
`
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`
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`...94 -
`
`............ 97
`...........97
`............ 97
`............97
`
`........... 108
`........... 112
`
`........... 129
`........... 129
`........... 130
`........... 132
`........... 136
`........... 139
`
`
`
`5
`
`‘
`
`;
`
`...... 157
`........... 157
`........... 157
`........... 157
`'; .......... 158
`........... 160
`
`' ........... 161
`........... 162
`-........... 164
`........... 167
`
`........_
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`173
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`.carer.»-
`
`191
`
` B
`
`FIGURE 18. Circumferential sections of pericardial bioprosthetic valve leaflets implanted in calves
`for 23 (A) and 31 (B) days. (A) Calcification (arrows) within and on the surface of the leaflet is seen.
`Calcific deposits within the leaflet are present along planes parallel to the surface of the leaflet. (B) Early
`calcification occurred along the planes between layers of collagen. (C) Magnified View of the tissue in
`(B), showing calcific deposits in places occupied previously by collagen fibers. (Hematoxylin—eosin
`Stain; original magnification for A. B, and C are x25, x50, and x125, respectively, reduced by 31%.)
`(From Tbubrikar, M. et al.. J. Thoma Cardiovasc. Surg, 86, 115, 1983. With permission.)
`
`x 106 cycles, respectively. Accelerated tests on Hancock porcine valves (Model 242), carried out
`at a cyclic rate of 1200 beats/min revealed that the valves break down in a smaller number of
`cycles.“ The signs of valve failure in the accelerated tester include fraying of the free edges,
`small tears near the commissures, and holes between collagen bundles at the base of the leaflet.
`It may be noted that different accelerated testers can produce different results.
`
`
`
`D. MECHANICAL FACTORS RELATED TO VALVE LIFE
`Patients will benefit even more if bioprostheses were made to last longer. Since most
`bioprostheses fail by calcific degeneration, one way to enhance their longevity is to slow down
`calcification. A variety of anticalcification treatments are being tried experimentally in an
`attempt to retard calcification in the valveffi‘m‘” The success of these treatments needs to be
`
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`
`
`73 (A) and 31 (B)
`
`it is important
`an accelerated
`
`: and flow per
`.iis test. Figure
`ously. To gain
`the following.
`aster if a valve
`ism that moves
`ant to evaluate
`
`for 20 years of
`g is lower than
`ate, one begins
`3e in viva.
`.ict factors that
`
`tions. Also by
`
`vitro generally
`mens, and high
`ts are useful in
`
`ine pericardial
`[onescu-Shiley
`-2 x 10" and 49
`
`
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`

`

`192
`
`The Aortic Valve
`
`
`
`C
`
`FIGURE 18C
`
`NORRED EXHIBIT - Page 11
`
`established by clinical implants over the next several years. We saw that bioprostheses fail in
`the accelerated tester mainly from mechanical stress. Calcification is not possible in the
`accelerated tester. The component of a bioprosthesis that fails in vitro is often the component
`that fails in viva. There are also observations to support the theory that calcification is initiated
`and/or accelerated by tissue degeneration caused by mechanical stress. Therefore, another way
`of enhancing the longevity of bioprostheses is to minimize tissue degeneration by minimizing
`the mechanical stress. In this section we will consider the mechanical stresses in bioprostheses
`and how the stresses can be reduced.
`
`Mechanical stress in a functioning bioprosthetic valve is dependent upon valve geometry,
`material properties, and deformation changes during a cardiac cycle. If one examines these
`parameters in the natural aortic valve, they are different from those in most bioprostheses. In the
`natural aortic valve, when the design deviates from trileaflet configuration, which occurs in
`congenitally malformed bileaflet or unileaflet valves, some of the malformed valves become
`calcified and diseased (Chapter 8). This observation suggests that proper design is necessary to
`achieve longer life for the valve. Therefore, to improve longevity of bioprostheses, the first step
`is to improve their geometry. In Chapter 1 we discussed that the design of any trileaflet valve
`can be made optimal. Based upon the principles of the natural aortic valve design, the design of
`trileaflet bioprostheses should be made optimal to achieve efficiency and longevity in these
`valves.
`
`The material properties of bioprostheses should be considered from the perspectives of
`thrombogenicity and mechanical stress. Since thrombogenicity does not seem to be a significant
`problem with these valves, we will consider the material properties from the point of view of
`mechanical stress. The uniaxial stress—strain test and the effect of orientation of the leaflet upon
`the stress—strain properties are described in Chapter 5. Figure 21 shows stress-strain curves in
`the circumferential directions of a porcine bioprosthetic valve leaflet and a natural aortic valve
`
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`193
`
`
`
`FIGURE 19. Schematic representation of bending and shearing deformations. When a rela-
`tively homogeneous tissue (A) undergoes bending defonnation, large compressive and tensile
`slIesses are produced in the tissue, which can result in void formation (B). In porcine
`bioprosthetic leaflets, the probable site of void formation is the same as the site of calcification
`shown in Figure 16B. When a tissue made of multiple layers (shaded in C) undergoes shear
`deformation, individual layers can slide over each other (D), damaging the structure between
`the layers (E). In pericardial bioprosthetic leaflets, the sites of structural damage along the
`planes of shear (shown in E) are also the sites of calcification shown in Figure 18A. (From
`Thubrikar, M. et al., J. Thorac. Cardiovasc. Surg., 86, US, 1983. With permission.)
`
`
`
`FIGURE 20. Edwards durability tester and high-speed cinematography.
`(Figure courtesy of American Edwards Laboratories, Santa Ana, CA)
`
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`:ri E
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`
`rnponent
`initiated
`
`ther way
`iimizing
`ostheses
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`rccurs in
`become
`
`essary to
`first step
`let valve
`
`[esign of
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`:tives of
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`let upon
`:urves in
`tic valve
`
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`

`
` 194
`
`The Aortic Valve
`
`
`
`Canine Norma!
`
`Porcine Fixed
`
`
`0-! 0'1
`
`
` OJ 0
`
`
`
`STRESS(gm/mm2)
`
`
`
`
`
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`5
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`
`—NN01om
`
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` 20 l4
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`8
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`STRAIN (%)
`
`FIGURE 21. Stress~strain curves of the natural canine aortic and the porcine fixed (bio-
`
`prosthetic) leaflets.
`
`
`
`leaflet. The bioprosthetic leaflet has a shorter region of low modulus of elasticity than does the
`
`natural leaflet, indicating that the bioprosthetic leaflets have become stiffer from the chemical
`
`treatment during valve processing. Broom et al. have observed that when porcine valves are
`
`
`processed with the closing pressure of fixation kept at l mmHg or less, the low modulus region
`
`
`is preserved.”43 Standard bioprostheses are prepared with 80 to 100 mmHg closing pressure
`
`
`during fixation which results in the loss of the low modulus region. The observation of leaflet
`
`
`components by light microscopy indicates that low pressure fixation retains the full collagen
`
`
`crimp geometry originally present in the relaxed fresh tissue, whereas high pressure fixation
`
`
`eliminates the collagen crimp geometry and makes tissue less flexible. Figure 22 shows
`
`
`micrographs of tissue fixed at a pressure of 100 mmHg (Figure 22A) and 0 mmHg (Figure 228)
`
`
`where the absence and presence, respectively, of waviness in collagen can be seen. The low
`
`
`pressure fixed valves have better opening characteristics and a lesser degree of strain localiza-
`
`
`tion, whereas the high pressure fixed valves show sites of local strain and kinks in the leaflet
`
`
`during opening. The low pressure fixed valves are observed to show longer life in the accelerated
`
`
`tester. Hence, material properties. have a significant effect on valve behavior. For bovine
`
`
`pericardium, mechanical properties can be changed by glutaraldehyde treatment.“4
`
`
`The effect of mechanical stress on bioprosthetic valves can be understood by examining what
`
`
`happens to the glutaraldehyde fixed porcine mitral leaflet tissue when subjected to the
`
`
`accelerated fatigue test. Broom et a1. carried out these experiments with strips of tissue which
`
`
`were cycled so that the regions of flexure and contraflexure were produced as shown in Figure
`
`
`23.45 In these experiments, tensile loading did not contribute significantly to the disruption of
`
`
`tissue. Compressive flexure occurring during the unloading half of the fatigue cycle did induce
`damage in the tissue. Tissue compression is produced in the regions of flexure and counterflex-
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`chemical
`Ialves are
`
`ius region
`; pressure
`of leaflet
`
`l collagen
`e fixation
`22 shows
`
` 1 does the
`
`gure 22B)
`. The low
`1 localiza-
`:he leaflet
`:celerated
`)r bovine
`
`ning what
`
`ad to the
`me which
`
`in Figure
`‘uption of
`lid induce
`interflex-
`
`195
`
`
`
`FIGURE 22. Nomarski micrographs of wet tissue showing appearance of collagen geometry in the interior belly
`of the leaflet from porcine aortic valves fixed at 100 mmHg (A) and 0 mmI-[g (B) (magnification (A) x500, (B)
`X700). (From Broom, N. D. and Thomson, F. J., Thorax. 34, 166, I979. With permission.)
`
`ure (Figure 23). The compression results in tissue buckling and in lateral opening of cavities
`separating fiber bundles. Figure 24 shows an example of compressive flexure resulting in fiber
`separation and opening of cavities. The bundles of fibers appear to have become “teased” out
`into smaller fibers. Their observations suggest that porcine mitral leaflets treated with fixative
`have a very low tolerance for compressive stress and that porcine aortic bioprostheses are also
`likely to show the same behavior. Hence, bioprostheses may perform better if they develop
`minimum or no compressive stress.
`The deleterious effect of compressive stress was also demonstrated by a correlation between
`the areas of high compressive stress and calcification in the porcine bioprosthetic valves.
`Thubrikar et al. carried out the stress analysis of porcine bioprosthetic valves using a procedure
`similar to that used for the stress analysis of the natural aortic valve.46 Their approach is discussed
`below. With the marker-fliioroscopy technique, the movement of the leaflets was examined in
`vivo in bioprostheses implanted in the aortic position in calves. Figure 25 shows the configura-
`tions of the leaflet during a cardiac cycle. From the leaflet geometry, pressure gradient across
`the leaflet, and changes in the leaflet configuration, the stresses were determined as follows.
`.
`In diastole the leaflet has a cylindrical shape and the stresses in the leaflet are calculated as
`membrane stresses in a cylinder. Membrane stress in the circumferential direction, cm], is given
`by (Pa — P“) X Rd/T, where the difference between the aortic pressure Pa and the ventricular
`pressure Pv represents the diastolic pressure gradient across the leaflet. Rd represents the radius
`
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`196
`
`The Aortic Valve
`
`
`
`FIGURE 23. VenLricular and auricular faces of the fatigued test piece of glutaraldehyde-preserved porcine
`mitral
`leaflet. The three regions of compressive flexure and contraflexure are marked with arrows
`(magnification X 4.4 reduced 1/2). (From Broom, N. D., J. Thorac. Cardiovasc. Res, 76(2), 202, £978. With
`permission.)
`
`NORRED EXHIBIT - Page 15
`
`of the leaflet, and T represents the thickness of the leaflet (Figure 26). Membrane stress in the
`radial direction, 01112, is given by (P3— P“) x Rd/ZT' The pressure gradient across the leaflet in
`mid—diastole is measured in viva. Rd is measured from the silicone mold of the valve prepared
`at the diastolic pressure. The thickness, T, of the leaflet is measured directly.
`In systole, membrane stresses occur because of the pressure gradient across the leaflet, and
`bending stresses occur because of the change in the configuration of the leaflet in its
`circumferential direction. Assuming that segments of the leaflet have different radii because
`they are sections of different cylinders membrane stress in the circumferential direction, oml,
`is given by (P— P)X RjT where P Prepresents the pressure gradient across the leaflet, R:
`represents the radius of the leaflet segment under consideration, and T represents the thickness
`of the leaflet (Figure 27). Membrane stress in the radial direction, cm, is given by (P— P) x
`R5/2T Since P is greater than P, membrane stress is tensile1n the region M and compressive
`in the regions L and N of Figure 27. The membrane stress is constant throughout the thickness
`of the leaflet.
`
`For bending stress, consider a strip of the leaflet in the circumferential direction (Figure 28).
`In systole, the strip has a radius RL in the region L and Rm in the region M. The configuration
`at Lts achieved by bending the leaflet from its original radius Rd to a new radius R. The
`maximum bending strain, E ii in the region L is given by EL =(T/2R) — (T/ZRd). The
`configuration at M15 achieved by first making the leaflet straightLand then by bending it in the
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`

`
`
`
`
`uorcine
`arrows
`i. With
`
`ss in the
`eaflet in
`
`Jrepared
`
`
`
`flet, and
`:t
`in its
`because
`
`m, cm,
`aflet, RS
`liCkl'leSS
`
`V H P8.) x
`pressure
`tickness
`
`um 28).
`guration
`
`Rr The
`1d). The
`it in the
`
`197
`
`
`
`FIGURE 24. Series of low-power mierographs show how increasing compressive flexure of fatigued
`tissue opens up large cavities in region of contraflexure. Flexure increases from micrograph (a) through
`to micrograph (c). (Magnifications X35; reduced 3/10.) (From Broom, N. D., J. Thorac. Cardiovasc.
`Res, 76(2). 202, 1978. With permission.)
`
`reverse direction. The maximum bending strain, e m, in the region M is given by e m: (T/ZRm)
`+ (TIZRd). The bending strain is tensile in one half of the thickness of the leaflet and compressive
`in the other half. Bending stress for a plate = [E/(l — 1.9)] x bending strain, where E (the modulus
`of elasticity) is constant and it is Poisson’s ratio. The total stress is the vectorial summation of
`the membrane stress and the bending stress (Figure 29):
`
`E
`+ (Pv — Pa)R5 +
`Total stress : _
`T
`__ 7—? >< bending strain
`
`The positive sign indicates tensiie stress and the negative Sign indicates compressive stress. For
`
`
`
`i:in.
`{ii
`r"’1’:i’!«
`was
`
`Er
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`198
`
`The Aortic Valve
`
`
`
`
`
`TOP VIEW
`
`TOP VIEW
`
`I
`
`'
`
`._ II
`
`-
`
`.
`
`SIDE VIEW
`
`III
`
`FIGURE 25. A schematic representation ofa bioprosthetic valve in an aortic root. The radiopaque markers were used
`to determine the leafleteonfigurations. (I) and (II): radii ofcurvature (mm) and the angle ofrotation as = 95 °) are shown.
`(11]): the angle of rotation (9 = 83°) and the distance (Y = 1.2 mm) are shown. (From Thubrikar, M., Skinner, J. R.,
`Eppink, R. T., and Nolan, S. P. Y. Biomed. Mat. Res., 16, 811, 1982. With permission.)
`
` Urn.
`
` (5mg
`
`
`
` FIGURE 26. Membra