(cid:40)(cid:91)(cid:75)(cid:76)(cid:69)(cid:76)(cid:87)(cid:3)200(cid:24)(cid:3)
`
`

`

`ADVANCES IN
`
`
`
`ANTICALCIFIC AND
`
`ANTI DEGENERATIVE
`
`
`
`TREATMENT OF HEART
`
`VALVE BIOPROSTHESES
`
`Proceedings of the Fourth Scientific Meeting
`
`
`
`of the International Association
`
`for Cardiac Biological Implants
`
`EDITED BY _______
`
`_
`
`Shlomo Gabbay, M.D.
`
`Department of Cardiothoracic Surgery
`
`
`
`
`UMDNJ-New Jersey Medical School
`
`Newark, NJ
`
`David J. Wheatley, M.D.
`
`
`
`Department of Cardiac Surgery
`
`University of Glasgow
`
`Glasgow, Scotland
`
`Water Techs. Corp. v. Biomedical Device Consultants & Labs
`IPR2018-00498
`Ex. 2005
`
`Page 1 of 18
`
`

`

`ADVANCES IN ANTICALCIFIC AND
`
`
`
`ANTIDEGENERATIVE TREATMENT OF HEART
`
`VALVE BIOPROSTHESES
`
`Meeting
`Proceedings of the Fourth Scientific
`
`
`of the International Association
`
`for Cardiac Biological Implants
`
`
`
`Held in Washington, D.C. on May 4, 1997
`
`© 1997.
`Copyright
`
`All rights reserved. No part of this publication may be reproduced, stored
`
`
`
`
`
`
`
`in a retrieval system, or transmitted, in any form or by any means, elec­
`
`
`
`
`
`
`tronic, mechanical, photocopying, recording, or otherwise, without the
`
`
`
`
`
`prior written permission of the International Association for Cardiac Bio­
`
`
`
`
`logical Implants or Silent Partners, Inc.
`
`
`
`Printed in the United States of America.
`
`
`
`ISBN 1-878353-42-X
`
`
`
`Published by
`
`Silent Partners, Inc.
`872 7 Shoal Creek Blvd.
`
`USA Austin, TX 78757-6815
`
`Telephone: 512-458-n91
`FAX: 512-458-1234
`E-mail:
`
`publish@silentpartners.com
`www.silentpartners.com
`Web site:
`J018199
`
`Page 2 of 18
`
`

`

`Advances in Anticalcific and Antidegenerative
`
`
`
`
`
`Treatment of Heart Valve Bioprostheses, First Edition,
`
`
`
`edited by Shlomo Gabbay, M.D., David J. Wheatley, M.D.
`
`
`
`Silent Partners, Inc., Austin© 1997
`
`CHAPTER 3
`
`BIAXIAL MECHANICAL BEHAVIOR OF
`
`
`
`B10PROSTHET1c HEART VALVE Cusps
`
`
`SUBJECTED TO ACCELERATED TESTING
`
`M.S. Sacks, K.L. Billiar
`
`
`Engineering Department of Biomedical
`
`
`University of Miami
`Coral Gables, Florida
`
`
`Abstract
`
`bioprosthetic behavior loading The effects of in vivo cyclic on the mechanical of porcine
`
`
`
`
`
`
`
`
`
`
`poor related to their continued heart valves are largely unknown, and ore undoubtedly
`
`
`
`
`
`long-term durability. To elucidate the mechanisms that eventually produce failure in por­
`
`
`
`
`
`biaxial mechanical cine bioprosthetic tension-controlled heart valves, tests were performed
`
`
`
`cycles of accel­on the cuspal tissue following 0, 1.4, 5.7, 10.1, 50, 100, and 200 million
`
`
`
`
`
`the changes to estimate constitutive model was employed erated testing. A microstructural
`
`
`
`
`
`fibers. in the effective mechanical behavior of the collagen Under o 60-N/m equibiaxial
`
`
`
`was found, with no tension state, a trend toward increasing circumferential extensibility
`
`
`
`
`model Simulations trend in the corresponding radial extension. using the microstructural
`
`demonstrated that slight
`
`
`
`test axes can misalignments with respect to the biaxial
`specimen
`
`
`
`in the measured extensibilities. potentially cause large variations When the model was
`
`
`
`valve, cycle fatigued used to fit representative data from a nonfatigued and a 200 million
`
`
`
`
`
`the effective fiber stiffness For the fatigued specimen was markedly lower than the nonfatigued
`
`
`
`
`studies revealed delominations but no evidence of damage to the
`
`specimen. Histologic
`
`
`
`
`
`structural level. fiber structure, suggesting that tissue damage occurs on a subfibril
`collagen
`
`
`
`
`
`
`weakening of produces cyclic loading Overall, imply that long-term our results a gradual
`
`
`
`
`
`
`the collagen fiber network, potentially facilitating calcification and ultimately valve failure.
`
`Introduction
`
`Although bioprosthetic heart valves remain a popular choice for heart valve re­
`
`
`
`
`
`
`
`
`
`
`placement, they continue to suffer from limited long-term durability. The mecha­
`
`nisms of valve material degeneration, especially when related to calcification, are
`
`
`
`
`
`
`
`
`1 In vivo structural deterioration of porcine aortic valve
`not well understood.
`
`
`
`foR CORRESPONDENCE OR REPRINTS:
`
`Michael Sacks, Ph.D.
`
`
`
`
`Department of Biomedical Engineering
`
`University of Miami
`P.O. Box 248294
`
`Coral Gables, Fl 33124-0621
`Tel: 1 305 284 5434
`
`Fax: 1 305 2 84 64 94
`E -mail: msacks@coeds.eng.miaml.edu
`
`Page 3 of 18
`
`

`

`
`
`Biaxial Mechanical Behavior
`
`
`
`Biaxial Mechanical Behavior
`
`The purpose of the present study was to examine the effects of cyclic loading of
`
`
`
`
`
`
`
`
`
`
`
`intact porcine aortic valve bioprostheses. Any valve that undergoes prolonged
`
`
`
`
`
`
`accelerated testing will eventually fail. We hypothesize that gradual cycle-depen­
`
`
`
`
`dent changes in the properties of a tissue valve will occur due solely to the me­
`
`
`
`
`
`
`
`
`chanical loading. Long-term fatigue of intact porcine aortic bioprostheses up to
`
`
`
`
`
`200 X 106 cycles (equivalent to approximately 5.4 years at 70 beats/min) was
`
`
`
`
`
`
`studied to develop a better understanding of the initial mechanisms that eventu­
`
`ally lead to fatigue failure of porcine aortic valves.
`
`
`
`Materials and Methods
`
`
`
`SPECIMEN PREPARATION
`
`Porcine bioprosthetic heart valves were prepared by chemical fixation in 0.625%
`
`
`
`
`
`
`
`
`
`
`
`glutaraldehyde under 0.5 kPa (4 mmHg) differential pressure (forcing leaflets to
`
`
`
`
`
`
`coapt) and provided by St. Jude Medical (St. Paul, MN). The intact valves were
`
`
`
`
`
`
`subjected to standard accelerating testing protocols for O (noncycled), 1.4, 5.7,
`
`
`
`
`10.1, 50, and 200 million cycles. The fixed valves were mounted in silastic con­
`
`
`
`
`
`duits to simulate the aortic root, and subjected to standard accelerated testing
`
`
`
`
`used for Food and Drug Administration approval in sterile saline at a rate of
`
`
`
`
`
`approximately 1000 cycles/min (16 Hz). After cycling, the valves were stored in
`
`at 4°C and sent to our laboratory in their mounts. All
`0.625% glutaraldehyde
`
`
`
`
`
`
`
`valves were fully functional and without visual evidence of tearing or perforation.
`
`
`
`
`
`Before testing, the cusps were carefully excised from the valves using microscissors.
`
`
`
`
`At least eight cusps from each accelerated testing level were mechanically tested.
`
`
`
`
`
`
`All biaxial experiments were performed in isotonic (0.9% wt/wt) saline at room
`(20°C-25°C).
`temperature
`
`
`
`BIAXIAL TESTING
`
`One square specimen was cut from the center of each leaflet with the edges aligned
`
`
`
`
`
`
`
`to the circumferential and radial directions (Fig. 1). The specimen sizes ranged
`
`
`
`from 10 to 16 mm on each side depending upon valve annular diameter, which
`
`ranged from 20 to 28 mm. Four small graphite markers (75-150 µm) were af­
`
`
`
`
`fixed to the ventricular surface with low-viscosity cyanoacrylate adhesive
`
`
`
`
`
`(Permabond International, Englewood, NJ). A 2.5-mm intermarker spacing was
`
`
`
`used in most cases. Thus the central measurement area was less than 10% of the
`
`total leaflet area in all specimens.
`
`While the specimen was floating unconstrained in the saline bath, the reference
`
`
`
`
`
`
`
`
`
`marker positions (gauge lengths) were recorded with a CCD camera. The strain
`
`
`
`
`resolution was approximately 0.5% with the typical marker spacing of 200 pix­
`
`
`
`els. Two loops of nylon suture of equal length were attached to each side of the
`
`
`
`
`
`specimen with four stainless steel surgical staples (one staple at each end of each
`
`
`
`
`loop). This procedure was completed in saline on a lab bench away from the
`
`
`
`
`
`biaxial testing device to minimize tissue deformation.
`
`bioprostheses (PBHVs) is strongly time-dependent, with complication rates in­
`
`
`
`
`
`
`
`1'2 Mechanical deformation, es­
`
`
`creasing rapidly after 10 years postimplantation,
`
` Although the bio­
`
`
`
`
`pecially in bending, is believed to potentiate mineralization,
`
`
`
`
`chemical aspects of mineralization and valve deterioration have been studied ex­
`
`
`
`
`5·7 little work has been completed on the effects of purely mechanical
`tensively,
`
`
`
`
`cyclic loading of chemically treated valve tissue.
`
`3•5
`
`8
`
`At present, "adequate" fatigue life of an intact valve is validated by accelerated
`
`
`
`
`
`
`
`
`testing. In this procedure, the PBHV is cycled at 15 to 20 times the normal heart
`
`
`
`
`
`rate in a pulsatile flow loop using sterile saline as the working fluid. The load
`
`
`
`
`
`
`magnitude and loading pattern are believed to adequately simulate the in vivo
`
`
`
`
`
`environment, with failure patterns generally similar to those found in pathologi­
`
`
`
`
`
`cal studies of explanted tissue. In general, the study of failure of bioprosthetic
`
`
`
`
`
`
`
`valves requires an understanding of the gradual mechanical changes leading up to
`
`
`
`
`
`complete valve failure. A study of the subfailure mechanical properties and their
`
`
`
`
`
`progression with time (number of opening and closing cycles) is needed to estab­
`
`
`
`
`
`lish a quantitative representation of the fatigue process in tissue valves and to
`
`
`
`
`
`elucidate the predominant mechanisms and mechanical factors involved.
`Broom8·10 completed a series of studies on the effects of combined uniaxial ten­
`
`
`
`
`
`
`
`
`
`
`sion and flexure on circumferential strips of glutaraldehyde-treated bovine and
`
`
`
`
`
`
`
`
`porcine mitral and porcine aortic valves. The circumferential tissue strips stiff­
`
`and the stiffening ened markedly with as few as 2.3 X 106 cycles,
`
`
`progressed with
`
`
`
`8 Collagen disruption was observed in areas of pro­
`
`
`increased numbers of cycles.
`
`
`
`
`
`
`
`nounced flexure by 300 X 106 cycles. In porcine mitral leaflet tissue, collagen
`
`
`
`
`disruption increased with the number of cycles and became extensive by 500 X
`106 cycles.
`
`
`
`
`9 Low pressure fixed porcine aortic valves (PAVs) (<l mmHg) sus­
`
`
`
`
`
`
`tained little damage, whereas high pressure fixed valves (100 mmHg) demon­
`
`
`
`
`
`
`strate damage similar to the mitral valve tissue. A cycle-dependent reduction in
`
`
`
`
`the native collagen fiber crimp was found in all but the high pressure fixed valves,
`
`
`
`in which the crimp pattern was already lost during fixation.
`
`These uniaxial studies provide the only information on the effects of repeated
`
`
`
`
`
`
`
`
`
`mechanical loading of heart valve tissue found in the literature. Tests on thin
`
`
`
`
`
`tissue strips, however, cannot mimic the heterogeneous deformation fields and
`
`
`
`
`
`combined loading sequences found in the physiologic environment. In addition,
`
`
`
`
`
`the collagen fiber architecture is disrupted in uniaxial specimens and the com­
`
`
`
`
`plex interactions between the axes are lost. Accelerated testing of intact valves
`
`
`
`
`preserves the 2-dimensional fiber network. Although the local loading is depen­
`
`
`
`
`dent upon the individual valve geometry and testing apparatus and cannot be
`
`
`
`
`
`
`
`directly measured, the cuspal stresses more closely resemble the complex patterns
`
`
`
`
`experienced in vivo. Materials tests performed on the cusps following predeter­
`
`
`
`
`
`
`mined accelerated testing intervals could provide a measure of the changes of the
`
`
`
`
`
`
`
`valve tissue subjected to realistic purely mechanical loading patterns as a function
`
`
`
`
`
`
`of time. However, the gains of intact fatigue cycling, such as the preservation of
`
`
`
`
`
`
`the mechanics of the intact valve tissue, are not preserved unless multiaxial test­
`
`
`
`
`ing is performed to assess the mechanical property changes.
`
`36
`
`Sacks
`
`Sacks
`
`37
`
`Page 4 of 18
`
`

`

`
`
`Biaxial Mechanical Behavior
`
`
`
`The purpose of the present study was to examine the effects of cyclic loading of
`
`
`
`
`
`
`
`
`
`
`
`intact porcine aortic valve bioprostheses. Any valve that undergoes prolonged
`
`
`
`
`
`accelerated testing will eventually fail. We hypothesize that gradual cycle-depen­
`
`
`
`
`dent changes in the properties of a tissue valve will occur due solely to the me­
`
`
`
`
`
`
`
`
`chanical loading. Long-term fatigue of intact porcine aortic bioprostheses up to
`
`
`
`was 5.4 years at 70 beats/min) 200 X 106 cycles (equivalent to approximately
`
`
`
`
`
`studied to develop a better understanding of the initial mechanisms that eventu­
`
`
`
`
`ally lead to fatigue failure of porcine aortic valves.
`
`
`
`Materials and Methods
`
`
`
`SPECIMEN PREPARATION
`
`Porcine bioprosthetic heart valves were prepared by chemical fixation in 0.625%
`
`
`
`
`
`
`
`
`
`
`glutaraldehyde under 0.5 k:Pa (4 mmHg) differential pressure (forcing leaflets to
`coapt)
`
`
`
`
`
`and provided by St. Jude Medical (St. Paul, MN). The intact valves were
`
`
`
`
`
`subjected to standard accelerating testing protocols for O (noncyded), 1.4, 5.7,
`
`
`
`
`
`10.1, 50, and 200 million cycles. The fixed valves were mounted in silastic con­
`
`
`
`
`
`duits to simulate the aortic root, and subjected to standard accelerated testing
`
`
`
`
`used for Food and Drug Administration approval in sterile saline at a rate of
`
`
`
`
`
`approximately 1000 cycles/min (16 Hz). After cycling, the valves were stored in
`
`at 4°C and sent to our laboratory in their mounts. All
`0.625% glutaraldehyde
`
`
`
`
`
`valves were fully functional and without visual evidence of tearing or perforation.
`
`
`
`
`
`Before testing, the cusps were carefully excised from the valves using microscissors.
`
`
`
`
`
`At least eight cusps from each accelerated testing level were mechanically tested.
`
`
`
`
`
`All biaxial experiments were performed in isotonic (0.9% wt/wt) saline at room
`(20°C-25°C).
`temperature
`
`
`
`BIAXIAL TESTING
`
`One square specimen was cut from the center of each leaflet with the edges align ed
`
`
`
`
`
`
`
`
`
`
`to the circumferential and radial directions (Fig. 1). The specimen sizes ranged
`
`
`
`from 10 to 16 mm on each side depending upon valve annular diameter, which
`
`
`ranged from 20 to 28 mm. Four small graphite markers 150 µm) were af­
`
`
`
`
`fixed to the ventricular surface with low-viscosity Lyanoacrylate adhesive
`
`
`
`
`(Permabond International, Englewood, NJ). A 2.5-mm intermarker spacing was
`
`
`
`used in most cases. Thus the central measurement area was less than 10% of the
`
`total leaflet area in all specimens.
`While the specimen was floating unconstrained in the saline bath, the reference
`
`
`
`
`
`
`
`
`
`marker positions (gauge lengths) were recorded with a CCD camera. The strain
`
`
`
`
`
`resolution was approximately 0.5% with the typical marker spacing of 200 pix­
`
`
`
`els. Two loops of nylon suture of equal length were attached to each side of the
`
`
`
`
`
`
`specimen with four stainless steel surgical staples (one staple at each end of each
`
`
`
`This procedure was completed in saline on a lab bench away from the
`loop).
`
`
`
`
`
`biaxial testing device to minimize tissue deformation.
`
`Sacks
`
`37
`
`Page 5 of 18
`
`

`

`Behavior
`Mechanical
`Biaxial
`
`cycle was calculated
`by
`the loading
`Tension (T, in units of Nim) throughout
`width
`specimen
`undeformed
`axial force (F) by the original
`the measured
`dividing
`(L) over which it acts (R = radial,
`C = circumferential).
`The equations
`for the
`graphically
`in
`are defined
`and lengths
`and the corresponding
`forces
`axial tensions
`1 (c).
`Figure
`valve cusp are complicated
`in the aortic
`of the strain
`and analysis
`Measurement
`and large radial
`properties,
`material
`anisotropic
`structure,
`by its heterogeneous
`is also profoundly
`af­
`of the tissue
`of the extensibility
`Calculation
`compliance.
`For these studies,
`all
`length).
`(reference
`of the gauge length
`by the choice
`fected
`state where the specimen
`was
`were calculated relative
`to the unloaded
`strains
`and any deformation
`was im­
`it was mounted
`in the saline bath
`before
`floating
`(E.)
`tensor
`strain
`the Green's
`large deformation,
`Since the cusps undergo
`posed.
`from the marker data using an isoparametric
`finite
`was used and was calculated
`axes, the
`to the stretch
`4 When the sample axes are aligned
`method.13
`element
`= ER, = radial
`strain,
`E22 = EC' = circum­
`tensor
`are E11
`of the strain
`components
`at any point within
`The strains
`= ERc' = shear strain.
`= E21
`ferential strain,
`and E12
`the homogeneity
`of the
`the marker area can be linearly interpolated
`to assess
`comparisons
`with
`and to facilitate
`For ease of understanding
`field.
`deformation
`in terms of percent strain,
`are presented
`in the heart valve literature,
`results
`values
`with the equation:
`which is computed
`= (V2E + 1 -1)*100% (1)
`in% = (A -1)*100%
`Strain
`ratio and E is Green's strain
`of the marker area
`in the center
`where A is the stretch
`direction.
`or circumferential
`the radial
`in either
`tissue
`of the cuspal
`behavior
`anisotropic
`the complete
`In order to fully capture
`was sub­
`each specimen
`modeling,
`data from material
`sufficient
`and to obtain
`The ratio of peak
`protocols.
`experimental
`of seven different
`to a series
`jected
`in a triangular
`loading
`pat­
`the two lab axes was held constant
`between
`tensions
`R:Tc
`The followingT
`using a 10�20 second loading
`period.
`tern in each protocol
`and 1:0.2 (Fig. 2). The
`1:0.5,
`1:1, 1:0.75,
`0.75:1,
`0.5:1,
`were used: 0.05:1,
`ratios
`in the 0.5: 1 protocol
`were
`was 60 Nim; thus the maximum tensions
`peak tension
`were performed
`experiments
`= 30 Nim and Tc= 60 N/m. Single-axis
`TR
`Tension on the
`(1 :0.2 protocol).
`and radially
`1 protocol)
`circumferentially
`(0.05:
`In each protocol the
`to avoid folding of the specimen.
`axis was necessary
`lateral
`representative.
`Al­
`considered
`the last cycle
`12 times with
`was cycled
`specimen
`due to hyster­
`different
`were slightly
`phases
`and unloading
`though the loading
`study.
`in the current
`phase was analyzed
`only the loading
`esis,
`
`•1
`
`MODELING
`MICROSTRUCTURAL
`
`characteriza­
`in material
`models avoid ambiguities
`constitutive
`Microstructural
`into the function, structure,
`of tissue
`com­
`and mechanics
`tion and offer insights
`when mounting
`of the tissue
`misalignment
`such as
`effects
`In particular,
`ponents.
`axes can also be examined. Moreover, struc­
`the material
`between
`and coupling
`and the fiber properties
`can be
`for in the analysis
`are accounted
`tural differences
`This tech-
`themselves.
`fibers
`in the collagen
`changes
`thus assessing
`predicted,
`
`Behavior
`Mechanical
`Biaxial
`
`nodulus free edge
`
`belly
`basal attachment
`
`(a)
`
`(b)
`
`(c)
`
`Figu re 1.
`areas
`(a) the belly and nodulus
`demonstrating
`valve leaflet
`aortic
`porcine
`An excised
`marker positioning,
`and (c) a
`and approximate
`specimen
`of a biaxial
`and (b) selection
`for radial
`and the equations
`of the axial forces and lengths
`representation
`schematic
`to avoid mechanical
`are off-center
`The marker positions
`tensions.
`and circumferential
`are shown.
`directions
`and circumferential
`The radial
`of the nodulus.
`effects
`
`with the radial
`and
`carriages
`onto the biaxial
`was then mounted
`The specimen
`device,
`testing
`with the lab axes. The biaxial
`aligned
`directions
`circumferential
`to accommo­
`carriages
`rotating
`with special
`11 was modified
`elsewhere,
`described
`around small
`were looped
`The sutures
`specimens.
`nonhomogenous
`date the small,
`equal
`rod. This method assured
`to a pivoting
`which were connected
`pulleys,
`multiple
`force
`the use of hydraulics,
`on a given side without
`staple
`force on each
`were at­
`Small floats
`line tensions.
`suture
`or tuning of individual
`transducers,
`The axial
`buoyant.
`sample neutrally
`mounted
`to make the
`to each staple
`tached
`at 12 to 15 Hz during
`recorded
`were continuously
`forces and marker positions
`was 1 mN (0.1 g).
`of the force transducers
`The resolution
`and unloading.
`loading
`solution
`and
`in saline
`each cusp was bathed
`During the biaxial mechanical
`tests,
`positioned stepper
`motors.
`by two sets of orthogonally
`stretched
`The char­
`back pressure.
`by the aortic
`the PAV cusps are loaded
`During diastole,
`choice
`for
`axes the natural
`on the tissue
`makes the forces
`acter of this loading
`were run under load
`the experiments
`Accordingly,
`testing.
`of the biaxial
`control
`of the force per unit of undeformed
`and peak values
`profile
`The triangular
`control.
`(force/
`Tension (force/length)
`or stress
`by custom software.
`were controlled
`length
`the force for the size of the leaflet.
`In the
`area) could be chosen to normalize
`in the fibrosa
`fibers
`and elastin
`by the collagen
`most of the load is carried
`leaflet,
`load and is believed
`to
`tensile
`very little
`carries
`the spongiosa
`and ventricularis;
`Thus the total thick­
`the other layers.
`the shear forces between
`to reduce
`function
`the load-bearing
`cross­
`represent
`does not accurately
`all three layers
`ness including
`and a peak level
`variable
`as the control
`was chosen
`area.12 Thus tension
`sectional
`loads in the belly of the cusp.
`physiologic
`to produce
`of 60 Nim was selected
`
`Sacks
`
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`
`39
`
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`
`

`

`
`
`Biaxial Mechanical Behavior
`
`Tension (T, in units of Nim) throughout the loading cycle was calculated by
`
`
`
`
`
`
`
`
`
`dividing the measured axial force (F) by the original undeformed specimen width
`
`
`
`
`(L)over which it acts (R = radial, C = circumferential). The equations for the
`
`
`
`
`
`
`axial tensions and the corresponding forces and lengths are defined graphically in
`
`Figure I (c).
`Measurement and analysis of the strain in the aortic valve cusp are complicated
`
`
`
`
`
`
`
`by its heterogeneous structure, anisotropic material properties, and large radial
`compliance.
`
`
`
`
`Calculation of the extensibility of the tissue is also profoundly af­
`
`
`
`
`
`
`fected by the choice of the gauge length (reference length). For these studies, all
`
`
`
`
`
`strains were calculated relative to the unloaded state where the specimen was
`
`
`
`
`
`floating in the saline bath before it was mounted and any deformation was im­
`(E.)
`
`
`
`
`
`posed. Since the cusps undergo large deformation, the Green's strain tensor
`
`
`
`was used and was calculated from the marker data using an isoparametric finite
`
`4 When the sample axes are aligned to the stretch axes, the
`
`
`element method.13
`
`
`
`
`strain, components of the strain tensor are E11 = ER, = radial E22 = EC' = circum­
`
`
`
`ferential strain, and E12 = E21 = ERc' = shear strain.
`
`The strains at any point within
`
`
`
`the marker area can be linearly interpolated to assess the homogeneity of the
`
`
`
`deformation field. For ease of understanding and to facilitate comparisons with
`
`
`
`
`
`values in the heart valve literature, results are presented in terms of percent strain,
`
`which is computed with the equation:
`
`
`Strain in%= (A -1)*100% = (-Y2E + I -1)*100% (I)
`
`where A is the stretch ratio and E is Green's strain
`
`in the center of the marker area
`
`
`
`in either the radial or circumferential direction.
`In order to fully capture the complete anisotropic behavior of the cuspal tissue
`
`
`
`
`
`
`
`
`
`
`and to obtain sufficient data from material modeling, each specimen was sub­
`
`
`
`
`jected to a series of seven different experimental protocols. The ratio of peak
`
`
`
`
`
`tensions between the two lab axes was held constant in a triangular loading pat­
`
`
`
`
`
`TR:Tc The followingloading period. tern in each protocol using a 10�20 second
`
`
`
`ratios were used: 0.05: I, 0.5: I, 0.75: I, I: I, I :0.75, I :0.5, and I :0.2 (Fig. 2). The
`
`
`
`peak tension was 60 Nim; thus the maximum tensions in the 0.5:1 protocol were
`
`
`TR= 30 Nim and Tc= 60 Nim. Single-axis experiments were performed
`
`
`
`
`
`circumferentially (0.05: I protocol) and radially (I :0.2 protocol). Tension on the
`
`
`
`lateral axis was necessary to avoid folding of the specimen. In each protocol the
`
`
`
`
`specimen was cycled 12 times with the last cycle considered representative. Al­
`
`
`
`
`
`though the loading and unloading phases were slightly different due to hyster­
`
`
`
`
`esis, only the loading phase was analyzed in the current study.
`
`'1
`
`
`MICROSTRUCTURAL MODELING
`Microstructural constitutive models avoid ambiguities in material characteriza­
`
`
`
`
`
`
`
`
`tion and offer insights into the function, structure, and mechanics of tissue com­
`
`
`
`
`
`ponents. In particular, effects such as misalignment of the tissue when mounting
`
`
`
`
`and coupling between the material axes can also be examined. Moreover, struc­
`
`
`
`
`tural differences are accounted for in the analysis and the fiber properties can be
`
`
`
`
`
`
`predicted, thus assessing changes in the collagen fibers themselves. This tech-
`
`Sacks
`
`39
`
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`
`

`

`
`
`
`
`Biaxial Mechanical Behavior
`
`70
`
`60
`
`� 50
`
`C 40
`
`'iii
`C
`30
`
`- �
`
` 20
`
`10
`
`0
`0 10 20 30 40 50 60 70
`
`
`Circumferential tension (N/m)
`
`Figur e 2.
`
`
`
`
`
`
`The seven tension protocols used for tension-controlled biaxial materials testing. The
`
`
`
`
`
`
`
`ratios indicate the ratio of radial to circumferential tensions in each protocol. The outer
`
`
`
`
`
`
`
`
`
`
`
`in cross-coupling due to the differences are different protocols (0.2: 1 and 1 :0.05)
`between the axes.
`
`nique may reduce the variation in material parameters such as peak extension
`
`
`
`
`
`
`due to structural inhomogeneities and mounting artifact.
`15 it is assumed that the PBHV cusps consist of a
`
`
`
`Following Lanir and colleagues,
`
`
`
`
`
`
`
`network of primarily collagen fibers embedded in a fluid-like matrix. It is further
`
`
`
`
`
`
`
`assumed that the strain energy is stored as extensional strain energy of the fibers
`
`
`
`
`and that the fiber deformations are affine. The angular distribution of fibers,
`
`
`
`Rcf(8), and the fiber material constants can be estimated from the mechanical
`
`
`
`
`data. The resulting expressions for the two tensions for the collagen fiber net­
`
`
`work, T;; and T;�, are given for a biaxial testing state by:
`
`8°1tl2
`
`T;; = JRcf(8)Tcf (E)cos2(8)d8
`
`8°-1t/2
`
`8°1t/2
`
`T�;= JRcf(8)Tc{(E)sin
`2(8)d8
`
`8°-1t/2
`
`(2)
`
`where 8 is the angle is the angle with respect to the x1 stretch
`
`axis and Er is the
`
`fiber strain given by:
`
`where E,j are the Green's
`
`
`
`(3)
`
`strains. T/ is the effective collagen fiber tension. In this
`
`
`
`40
`
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`
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`
`

`

`
`
`
`
`Biaxial Mechanical Behavior
`
`60
`
`-+I I
`0
`0
`81
`01
`50 81
`'6 I
`01
`
`
`
`Peak radial strain •
`•
`•
`•
`•
`•
`•
`•
`•
`•
`
`
`
`Peak circumferential strain
`
`:
`I
`
`40
`--E
`�
`C 30
`
`'iii
`C
`
`20
`
`10
`
`-10 0 10
`50 60 70 80
`20 30
`40
`
`Strain(%)
`
`Figu re 3.
`Representative tension-strain plot for an equibiaxial tension protocol ( 1: 1 in Fig. 2) of a
`
`
`
`
`
`
`
`
`
`fixed porcine aortic valve cusp. The definitions of peak radial (closed circles) and
`
`
`
`
`circumferential (open circles) strains are shown graphically. Note the nonlinear shape of
`
`
`
`
`between the axes. strains due to coupling the curves and the negative circumferential
`
`formulation, the effective fiber tension-strain law incorporates the effects of fiber
`
`
`
`
`
`
`
`
`crimp, and is assumed to be of the form:
`
`Tt = A[exp(B E)-1]
`(4)
`
`
`
`where A and B are constants. A and B are computed by nonlinear regression
`
`
`using the Powell method for multidimensional minimization.
`16 With this model,
`
`
`
`
`simulation of the stresses for a given strain state is straightforward. However, to
`
`
`
`
`
`simulate the strains resulting from the experimental tension protocols, equation
`
`(2)was numerically inverted.
`
`Results
`
`The tension-strain curves for equibiaxial tensile loading of a noncycled valve are
`
`
`
`
`
`
`
`
`
`
`shown in Figure 3. The nonlinear monotonically increasing curve for the radial
`
`
`
`direction is characteristic of most soft biological tissues.
`
`17 In contrast, the nega­
`
`
`
`tive strains and slope of the curve for the circumferential direction is found only
`
`
`
`
`
`mechanical coupling between the tissues with pronounced in highly anisotropic
`
`
`
`
`
`material axes. This mechanical coupling causes the strain to decrease along an
`
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`
`4I
`
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`
`

`

`
`
`
`
`Biaxial Mechanical Behavior
`
`0.5:1
`
`0.75:1
`
`"' i+ 0.2:1
`
`Increasing
`
`radial load
`
`Increasing
`circumferential
`load
`
`70
`
`60
`
`50
`
`40
`
`'iii 30
`
`20
`
`10
`
`0
`
`-20 0
`
`20 40 60 80
`
`Strain(%)
`
`Figu re 4.
`Representative tension-strain curves from a noncycled porcine aortic valve cusp for all
`
`
`
`
`
`
`
`
`seven tension protocols. Note the changes in the curves due to increasing lateral
`
`
`loading. The ratio of radial to circumferential tensions is given next to each curve.
`
`7
`6 • Data mean ± SEM
`1.54*1og(N)-0.5,r2=0.60
`....... 5
`c"o'!-
`0 _.
`·-C 4
`Ill ·-
`C ca
`-= 3
`Q)
`:!:: Ill
`:::,-
`CT.� 2
`Q) -C
`E a,
`:::J ...
`E .!·-E 0
`>< :::J ca u
`:!: .!::: -1
`(J
`-2
`
`-3
`
`10
`
`100
`
`1000
`
`6
`N X 10
`
`Figu re 5.
`Circumferential strains at 60 N/m equibiaxial tension. A trend towards increasing
`
`
`
`
`
`
`
`
`extensibility with number of cycles was found in the circumferential direction.
`
`42
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`Sacks
`
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`
`

`

`
`
`Biaxial Mechanical Behavior
`
`
`
`axis even when the axial load is increasing. This cross-coupling effect can be seen
`
`
`
`
`
`
`
`even more readily in Figure 4 where the tension-strain curves are plotted for all
`
`
`seven tension loading protocols (Fig. 2).
`
`PEAK EXTENSIBILITY
`
`The peak extensions in both the circumferential and radial directions were highly
`
`
`
`
`variable
`
`
`
`
`within specimen groups at all fatigue levels. The mean strains at peak
`
`
`
`
`
`
`testing levels in for all accelerated equibiaxial tension of 60 Nim are plotted
`
`
`
`
`
`Figure 5 for the circumferential direction and in Figure 6 for the radial direction.
`
`
`
`
`
`A trend towards increased extensibility with the number of applied cycles was
`
`
`
`
`found in the circumferential direction. The radial extensibility did not change
`
`substantially. Analysis of the peak extensions in both directions for the other
`
`
`
`
`
`
`
`biaxial protocols yielded similar results.
`
`
`
`MICROSTRUCTURAL MODEL
`
`of the axes by curves caused by misalignment The alteration in the tension-strain
`
`
`
`
`
`
`
`
`in the micro­fiber distribution a 10° shift to the
`10° was simulated by adding
`
`
`
`
`
`structural model, as plotted in Figure 7. In this example, the peak extensibility in
`
`
`
`
`
`the radial direction decreased by 25%. This result suggests that much of the error
`
`
`
`
`in peak extensibility may be due to unavoidable specimen misalignments with
`
`80
`
`• Data mean ± SEM
`2=0.067
`-1.61 *log(N)+64,r
`
`I
`1
`I
`
`I!
`1
`
`·-C:
`:::J·-
`
`Q)
`
`C:
`0
`·en.-.
`c:�
`! _. 70
`CT ca
`-=Ill
`Em 60
`E-c ·- ca
`>< ...ca
`50
`
`:::,
`__
`
`0
`
`10
`
`100
`
`1000
`
`6
`N x 10
`
`
`
`Radial strains at 60 N/m equibiaxial tension. No trend in extensibility was found in the
`
`Figu re 6.
`
`
`
`
`radial direction.
`
`Sacks
`
`43
`
`Page 11 of 18
`
`

`

`
`
`Biaxial Mechanical Behavior
`
`
`
`60 circumferential
`
`c,ircumferential
`
`I
`
`Valve cusp axes aligned
`± 1 0° off of the biaxial I
`test axes
`�! I
`
`I
`
`50
`
`--I4
`
`C:
`
`0
`
`30
`"iii
`C:
`
`�
`20
`
`10 I
`
`I
`
`0
`
`-20 0
`
`I
`
`I
`
`,
`
`, ,
`,
`
`----- - -
`
`40 60
`20
`Strain(%)
`(a)
`
`-5.0 -2.50.0
`80
`Strain(%)
`(b)
`
`Figu re 7.
`Model simulation demonstrating a large shift in the effective radial extension due to a
`
`
`
`
`
`
`
`
`
`10° rotation of the specimen relative to the biaxial lest axes. Simulation of the valve
`
`
`
`aligned with the test axes is represented with the solid line. Simulation with a 10°
`
`
`
`rotation is represented with the dotted line. Both circumferential and radial curves are
`
`
`
`shown on the same strain scale in (a) for comparison. The circumferential curve only is
`
`shown with the expanded strain scale in (b) for clarity.
`
`the stress axis or specimen structural variations. Figure 8 shows the fit of the
`
`
`
`
`
`
`
`
`
`model to a nonfatigued cusp. Only the equibiaxial tension protocol and the two
`
`
`extreme protocols (0.05: 1 and 0.2: 1) are shown for clarity. The model captures
`
`
`
`
`the complex features of the raw data such as the strong dependence of the strains
`
`
`
`on the cross-axis loads (cross-coupling) and the shape of the curves. The fit is
`
`
`
`
`
`good considering that the extreme protocols were not used to determine the
`
`material parameters.
`
`The model was next used to estimate the fiber material parameters for cusps from
`
`
`
`
`tested valve (Fig. 9a). The a noncycled valve and a 200 X 106 cycle accelerated
`
`
`
`
`
`
`
`radial strains measured in the biaxial tests in the two cusps are similar; however,
`
`
`
`
`
`
`the circumferential strains are greater in the fatigued leaflet, as shown in detail in
`
`
`
`
`Figure 9b. The material constants, A and B, were computed with the micro­
`
`
`
`structural model using the method as described above. Fiber tension-strain curves
`
`
`
`
`generated using these constants (Fig. 10) show that the effective fiber stiffness of
`
`the 200 X 106 cycle cusp is much lower than the noncycled valve. The effective
`
`
`
`fiber tension represents the force per unit width of a load-bearing fiber. These
`
`
`
`
`
`
`results demonstrate that profound differences in the effective fiber properties can
`
`
`
`
`
`be extracted from seemingly similar whole tissue mechanical responses.
`
`44
`
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`
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`
`

`

`
`
`
`
`Biaxial Mechanical Behavior
`
`circumferential
`0.2:1
`1:1 '
`
`radial
`1:0.05
`
`70
`
`60
`
`50
`
`-i
`
` 40
`
`-C:
`
`"iii
`30
`C:
`
`20
`
`10
`
`0
`
`-20
`
`0
`
`20 40
`
`60
`
`80
`
`Strain(%)
`
`Figu re 8.
`Model simulations (lines) superimposed on real tension-strain data (circles) for the
`
`
`
`
`
`
`
`
`
`
`equibiaxial tension protocol and the extreme protocols (0.2: 1 and 1 :0.05). The extreme
`
`
`
`protocols were not used to fit the data. Note that the model simulates the form of th