Biaxial Mechanical Properties of the Natural and Glutaraldehyde Treated Aortic Valve Cusp Part I: Experimental Results

Transcription

1 Biaxial Mechanical Properties of the Natural and Glutaraldehyde Treated Aortic Valve Cusp Part I: Experimental Results K. L. Billiar M. S. Sacks 1 Department of Biomedical Engineering, University of Miami, Coral Gables, FL To date, there are no constitutive models for either the natural or bioprosthetic aortic valve (AV), in part due to experimental complications related to the AV s small size and heterogeneous fibrous structure. In this study, we developed specialized biaxial testing techniques for the AV cusp, including a method to determine the local structure strain relationship to assess the effects of boundary tethering forces. Natural and glutaraldehyde (GL) treated cusps were subjected to an extensive biaxial testing protocol in which the ratios of the axial tensions were held at constant values. Results indicated that the local fiber architecture clearly dominated cuspal deformation, and that the tethering effects at the specimen boundaries were negligible. Due to unique aspects of cuspal fiber architecture, the most uniform region of deformation was found at the lower portion as opposed to the center of the cuspal specimen. In general, the circumferential strains were much smaller than the radial strains, indicating a profound degree of mechanical anisotropy, and that natural cusps were significantly more extensible than the GL treated cusps. Strong mechanical coupling between biaxial stretch axes produced negative circumferential strains under equibiaxial tension. Further, the large radial strains observed could not be explained by uncrimping of the collagen fibers, but may be due to large rotations of the highly aligned, circumferential-oriented collagen fibers in the fibrosa. In conclusion, this study provides new insights into the AV cusp s structure function relationship in addition to requisite data for constitutive modeling. S Introduction 1 Corresponding author. Present address: Dept. of Bioengineering, Room 749 Benedum Hall, Univ. of Pittsburgh, Pittsburgh, PA Contributed by the Bioengineering Division for publication in the JOURNAL OF BIOMECHANICAL ENGINEERING. Manuscript received by the Bioengineering Division November 24, 1998; revised manuscript received July 28, Associated Technical Editor: L. A. Taber. The aortic valve AV is essentially a check-valve that serves to prevent retrograde blood flow from the aorta back into the left ventricle. This seemingly simple function belies the structural complexity and the elegant solid fluid mechanical interaction necessary for normal AV function. The AV is capable of withstanding million cycles per year, resulting in a total of 3 billion cycles in single lifetime 1. This staggering level of performance can be cut short by aortic valve disease, the most common being stenosis resulting from calcification. Currently, the treatment of such diseases is complete valve replacement using either a mechanical or bioprosthetic heart valve. Porcine bioprosthetic heart valves PBHV have excellent hemodynamics and generally do not require the anti-coagulation therapy necessary for mechanical prostheses. Despite their excellent short-term performance, PBHV continue to suffer from poor long-term durability due to calcification and mechanical damage. A rigorous study of the mechanics of the natural and bioprosthetic aortic valve could aid in understanding how the natural AV functions, as well as provide insight into the degradative process of the PBHV. Most previous work on the mechanical properties of the natural and chemically treated AV has relied on uniaxial mechanical testing 2 4. While yielding important qualitative information, uniaxial loading is nonphysiologic and the fiber kinematics are not preserved. Mayne et al. 5 and Christie and Barratt- Boyes 6 have performed equibiaxial testing i.e., equal level of tension applied to each test axis, which overcomes the limitations of uniaxial loading. However, derivation of a constitutive relationship from solely equibiaxial test data is limited due to multiple collinearities that confound the ability to obtain reliable, unique model parameter values 7. Clearly, multi-protocol biaxial mechanical data are necessary for the complete, rigorous mechanical characterization of the AV cusp. However, the application of standard biaxial mechanical testing techniques e.g., 8 11 to the aortic valve cusp is not straightforward due to the AV cusp s small size and heterogeneous, curved structure. For example, in biaxial mechanical studies, markers are placed in the center region of the specimen where it is assumed that the stress and strain fields are the most homogeneous e.g., 12. Due to the curvilinear path of the collagen fibers within the cusp and the presence of thick tissue structures such as the nodulus of Arantii, it is unclear if this assumption is valid for the AV cusp. Furthermore, the curved shape of the cusp complicates basic questions such as the choice of reference state. The purpose of this study was to specialize biaxial testing techniques for both the natural and glutaraldehyde-treated porcine AV, and to apply these methods to generate sufficient planar mechanical property data for constitutive modeling. For the first time, multiple loading protocols were utilized to include the entire range of physiologic loading and to provide sufficient data for constitutive modeling. Further, a technique was developed to examine the inter-relationship between the local fiber architecture and the principal strain field quantitatively. This technique allowed us to test the hypothesis that the highly aligned AV fiber architecture 13, rather than the local stress concentrations induced by tethering, dominated the local strain field. Indices of extensibility and anisotropy were defined for specimen comparison, and special characteristics of the mechanical behavior of the aortic valve cusps were discussed. Methods Tissue Preparation. Eleven fresh valves were obtained from a local abattoir and stored in phosphate buffered saline at 4 C for Journal of Biomechanical Engineering Copyright 2000 by ASME FEBRUARY 2000, Vol. 122 Õ 23

2 Fig. 1 A partially polarized image of an aortic cusp highlighting the heterogeneous fibrous structure, and main anatomical and biaxial specimen regions. Also shown are the locations of the optical markers as white circles, with the large circles denoting the nine markers used for structure strain measurements and the smaller four markers used for strain measurements for all subsequent tests. no more than 72 hours. Eleven chemically treated porcine bioprosthetic heart valves PBHV were provided by St. Jude Medical St. Paul, MN. These intact, non-stented valves were treated in percent aqueous glutaraldehyde GL saline solution under 0.5 kpa 4 mmhg transvalvular pressure. For each valve, the cusps were carefully excised from intact heart valves using microscissors, and one square specimen was cut from each cusp with its edges aligned with the circumferential and radial axes in the center of the cusp Fig. 1. Specimen dimensions were measured using a dial caliper micrometer to an accuracy of 0.25 mm. Three thickness measurements were made in the center of the belly region using a non-rotating gage resolution 12.5 m and averaged for the thickness of each specimen. The specimen widths ranged from 10 mm to 16 mm depending upon valve annular diameter, which ranged from 20 mm to 28 mm. All experiments were performed in isotonic 0.9 percent wt/wt saline at room temperature. Fresh cusps were neutrally buoyant whereas the fixed cusps were slightly negatively buoyant. Biaxial Test Device. A detailed description of the biaxial testing device, including modifications to allow the test specimen to undergo in-plane shear, has been previously presented 12,14. For the current study the load cells were replaced by more sensitive transducers with a resolution 0.6 mn. The video resolution was approximately 76 pixels/mm with a corresponding strain resolution of 0.5 percent. Although the markers were separated by only 2.5 mm when the tissue was unloaded, the field of view was substantially larger (8.5 mm 6.3 mm) to accommodate radial strains in excess of 100 percent Fig. 1. The axial forces and marker positions were continuously recorded at 15 Hz with custom marker tracking software 12. Experimental Protocol. Two loops of 000 nylon suture of equal length were attached to each side of the specimens with four stainless steel surgical staples. Small floats were attached to each staple to make the mounted sample neutrally buoyant. This procedure was completed in isotonic saline on a lab bench away from the biaxial testing device to minimize tissue deformation. The specimens were then mounted onto the biaxial device with the radial and circumferential directions aligned with the lab axes. In this study, we used membrane stress (T ij,n/m instead of a measure of the three-dimensional stress since not all layers of the cusp bear equal amounts of load see Discussion. T ij is defined as the axial force per unit length of tissue over which it is applied. During testing, the value of T ij along each axis was ramped slowly from a small pre-stress ( 0.5 N/m) to a peak value that depended upon the protocol using a triangular waveform. The complete biaxial testing regimen consisted of following membrane stress controlled protocols: T CC :T RR 10:60, 30:60, 45:60, 60:60, 60:45, 60:30, and 60:2.5 N/m, where the subscripts C and R correspond to the circumferential and radial directions, respectively. Specimens were preconditioned for twelve contiguous cycles for each protocol, with the loading period typically seconds, yielding loading rates of N/m s 1. In the radial and circumferential directions, the strain rates were 4 15 percent/s and 1 4 percent/s, respectively. Loading rates in this quasi-static range do not appear to affect the stress-strain behavior of the aortic cusp appreciably 15. The choices of the specific protocols, and peak stress values are explained in the Discussion. Quantitative Structural Measurement. Following the biaxial testing, the fiber architecture of each aortic valve cusp was quantified using small angle light scattering SALS as previously described 13. Briefly, each fixed specimen was cleared in hyperosmotic solutions of increasing osmolarity following a 24 hour equilibration period in saline. Graded solutions were used to minimize dimensional changes during dehydration. The preferred fiber direction and degree of fiber orientation using an orientation index, OI were then measured at 254 m increments over the entire cusp using methods described in Sacks et al. 13. Any rigid body rotation occurring between the biaxial and SALS devices was determined by polar decomposition 16 and subtracted from the preferred fiber direction to assure that it was defined with respect to the circumferential stretch axis Fig. 1. Structure Strain Mapping. In this study we tested the hypothesis that the highly aligned AV fiber architecture rather than the boundary stress concentrations induced by suture lines dominated the local strain field. This hypothesis is especially important when testing small heterogeneous tissue specimens such as the AV, where boundary tethering effects may propagate toward the interior of the specimen, affecting the homogeneity of the stress field within the region delimited by the markers. In addition, there are also practical experimental concerns including: 1 determining the degree of heterogeneity of the strain field, hence the maximum size, of the area delimited by the optical markers, and 2 determining optimal location for strain measurements i.e., the placement of the optical markers. To address these questions, we performed the following preliminary experiments on six additional PBHV specimens. Our ap- 24 Õ Vol. 122, FEBRUARY 2000 Transactions of the ASME

3 proach was to perform two experiments where the specimen fiber orientation was varied and examine its effects on the local strain field. Three specimens had their edges aligned on-axis with the fiber direction in the center of the cusps, whereas three other specimens had their edges cut at 45 deg to the fiber direction off-axis. To track the tissue displacements, nine small graphite markers m diameter were affixed to the ventricular surface with low-viscosity cyanoacrylate adhesive Permabond International, Englewood, NJ in a roughly square array. Nine markers were used to achieve quadratic interpolation of the strain field, using a nine node biquadratic Lagrangian finite element 17. The extent of adhesive spreading on the tissue was assessed with polarized microscopy to be no greater than 50 m past the edges of each marker. The nine markers encompassed a 5 mm 5 mm area of the cusp, corresponding to approximately 1/3 of the total cuspal surface area Fig. 1. The in-plane deformation gradient tensor F ij, with physical components F CC C, F CR C, F RC R, F RR R, was computed for each data point from the biquadratic Lagrangian finite element shape functions 17. The in-plane Green s strain components E CC and E RR are then computed from the stretch ratios in the circumferential and radial directions C and R using: E CC 1 2 C C 2 R 2 1 E RR 1 2 R R 2 C 2 1 (1) E CR E RC 1 2 C C R R 2. The index of anisotropy was defined as the ratio of peak strains, i.e., E peak C /E peak R, where 1 indicated an isotropic material response. Statistics. Statistical comparisons of the mechanical property indices between the fresh and fixed groups were performed using unpaired t-tests. The significance was set at p Values listed in the tables and plotted in the figures are mean SEM standard error of the mean, unless otherwise indicated. Results Relationship Between Local Fiber Structure and Local Strain Field. The strong effect of the underlying fiber architecture on the two-dimensional strain distribution was clear in all six samples for which detailed deformation-structure analyses were performed. This relationship is clearly demonstrated when the local fiber preferred directions and the corresponding principal strains are superimposed Fig. 2. The principal strains at peak equibiaxial load were calculated within the relatively large marker area for these representative GL samples. In both the on-axis Fig. 2 a and off-axis cases Fig. 2 b, the maximum principal strains were approximately perpendicular to the preferred fiber directions, with the second lesser principal strains aligned with the fiber directions. These results demonstrate quantitatively that the local tissue is much more compliant perpendicular to the preferred fiber direction than along the fiber direction, and appears to be relatively unaffected by the stress concentrations due to suture tethering forces. The shear angle,, defined as the change in the angle of two line elements that were orthogonal in the undeformed state, was used in lieu of the shear strain for simpler geometric interpretation and is given by the following 1 equation: 2E CR sin 1 2E CC 1 2E RR (2) Since the strains within the specimens were not uniform, the computed values were valid only for the area delimited by the markers. The marker positions gage lengths from the unconstrained reference condition were used for all strain calculations used for statistical comparisons. To compare the local strain field to the local fiber architecture quantified by SALS, we computed the direction and magnitude of the principal Green s strains at the locations of the SALS structural measurements. Due to the non-invertible form of the shape functions used in the finite element procedure, the finite element coordinates for each set of SALS measurement coordinates were numerically evaluated using Powell s least-squares method for two-dimensional optimization 18. The principal Green s strains were superimposed on the map of local preferred fiber directions to compare the strain field and structural data graphically. Mechanical Property Indices. Mechanical data from the equibiaxial loading protocol were used to define indices of extensibility, shear, and anisotropy to facilitate comparison between specimens groups and related studies e.g., 5. Due to the nonlinearity of the stress strain response, the following three measures were chosen to quantify the extensibility. The peak strains were defined as the Green s strains at peak equibiaxial membrane stress 60 N/m, i.e., E peak C and E peak R, which most closely represent the deformation under peak diastolic load. The midstrains were defined as the Green s strains at equibiaxial membrane stress of 8 N/m, i.e., E mid C and E mid R, which were chosen for comparison with previous measurements. The pre-strains were defined as the Green s strain at 1 N/m, i.e., E pre C and E pre R, which represent the deformation due to mounting the specimen under a slight preload. The shear was quantified by the shear angle at peak stress Eq. Fig. 2 Peak principal Green s strains under equibiaxial tension 60 NÕm for the AV cusp superimposed over the preferred collagen fiber directions as determined by SALS for an a on-axis and b 45 deg specimen. Lines represent local collagen fiber preferred directions and arrows the principal strains, with lengths proportional to strain magnitude see scale. The principal strains were closely oriented to the local preferred fiber directions throughout most of the region for both orientations. This result suggests that the local fiber architecture dominates the local strain field and that the boundary tethering effects were minimal in the interior of the specimen. Journal of Biomechanical Engineering FEBRUARY 2000, Vol. 122 Õ 25

4 Fig. 3 a Plot of collagen fiber orientation lines superposed over the local degree of orientation OI, gray scale in units of degrees for an AV biaxial test specimen. Here, the white holes in the plot correspond to the displacement markers. b Corresponding tension strain plots for different portions of the AV cusp shown in a, with NÄnodulus, MÄmidregion, B Äbelly. Although the stress tensor may be slightly different at each point due to the proximity of the tethering points black lines, these results clearly highlight the nonhomogeneity of the mechanical response of the test specimen. Optimal Strain Measurement Location. Also demonstrated by the structure-strain studies is that the strain field was most uniform in the center of the belly and most variable near the nodulus. The nodulus is a thicker region of the cusp with relatively large proportions of elastin and proteoglycans. The influence of the local tissue structure on the measured mechanical properties is further demonstrated in Fig. 3. Here, the preferred fiber field is shown in relation to where the strain data was computed using the nine node data Fig. 1. Note the profound difference in the stress strain data between the nodulus and central belly region Fig. 3 b. Since the central belly region is structurally most similar to the bulk of the tissue specimen and the fibers are approximately aligned with the test axes in this region, the lower belly region B in Fig. 3 b appeared to be the optimal strain measurement site. Further, analysis of the strain field indicated that the values for E ij did not vary by more than 5 percent of the mean value typically 2 3 percent within a 3 mm 3 mm area in the lower belly region. Based on these results, we choose to reduce the number of markers to four to minimize specimen preparation time and streamline subsequent data analysis. Further, there was no need for additional strain data over a larger area of the cusp or high order strain interpolation of the marker area. Four small graphite markers were affixed to the ventricular surface as before, only now using a roughly square array Fig. 1. The markers were placed in the central belly region between the nodulus and basal attachment, with a 2.5 mm intermarker spacing, creating a strain measurement area of 3 to 5 percent of the total specimen area. Strain computations were carried out as before, only now using a four node element as done previously 12. General Response. The loading curves for all protocols were stable and repeatable after the first few preconditioning cycles. The initial dimensions were recovered following unconstrained equilibration in isotonic saline overnight, indicating that the tissues were not damaged during testing. In general, the most prominent characteristic of the mechanical behavior of the AV cusps was the large disparity in the extensibilities between the circumferential and radial directions Fig. 4, Table 1. In the circumferential direction, the strains were extremely small under equibiaxial loading and even negative in many of the GL treated specimens. The stress-strain curves for the fresh samples appeared almost bilinear with a rapid transition between the low and high- Fig. 4 Representative circumferential and radial stress strain curves from a fresh and fixed AV cusp, demonstrating the pronounced mechanical anisotropy of both tissues. While the radial curves were similar, the circumferential stiffness is negative for the fresh specimen due to the strong in-plane coupling for this state. 26 Õ Vol. 122, FEBRUARY 2000 Transactions of the ASME

5 Table 1 Mechanical parameters for fresh and GL treated aortic valve under equi-biaxial tension width R width C thickness E Cpre E Rpre E Cmid E Rmid E Cpeak E Rpeak deg Fresh mean sem Fixed mean sem p n.s n.s Fig. 5 Average AV cuspal stress strain data for both fresh and GL treated specimens, with data presented as mean ÁSEM, nä11 for both groups. GL fixation appears to affect the tissue differently if the strains were calculated with respect to a the unconstrained configuration or the b preloaded and preconditioned configuration. Note the difference in the stretch ratio scales between a and b. modulus regions, whereas the curves for the fixed samples had a less distinct transition region Fig. 4. No significant differences between the cuspal types left, right, and non-coronary cusps were found. This finding should be interpreted cautiously since there were generally less than five cusps of each type in each group. Similar behavior has been reported previously for equibiaxially loaded fresh and low-pressure GL treated aortic cusps 5. We chose the free-floating unconstrained reference state over a preloaded reference state since it is more physically meaningful, and so that no data from the toe region along the radial direction would be lost. The fresh cusps were on average significantly more extensible than the fixed cusps Fig. 5 a, Table 1, however, the radial extensibility of the fresh cusps was smaller than the fixed cusps when calculated with respect to a preloaded state of 5 mn equi-biaxial load Fig. 5 b, Table 1. This counter-intuitive behavior of the preloaded tissues clearly hides the large compliance of the fresh specimens and demonstrates the need for use of the unloaded reference state. Equibiaxial Behavior. As indicated in Fig. 5 and Table 1, significant differences in the mean extensibility were found between the fresh and fixed groups in both the circumferential and radial directions at the low, mid, and peak membrane stress levels Fig. 6 AV cuspal stress strain data for the a circumferential and b radial directions for a GL treated cusp demonstrating the effects of transverse loading in-plane coupling. Number adjacent to curves indicate biaxial test protocol number Fig. 2. Note the non-monotonic relationship between tension and stretch ratio in the circumferential direction in all but the protocol 1 for this specimen. In contrast, in many fixed and most fresh samples, the circumferential strain increased monotonically with increasing stress. Journal of Biomechanical Engineering FEBRUARY 2000, Vol. 122 Õ 27

6 in all but the peak radial case. The strains at 8 N/m were not statistically different than previously reported for cusps under similar loading conditions with similar numbers of specimens 5. On the other hand, the standard deviation of our extensibility measurements at this stress level was less than half of that reported in the previous study. The GL samples were significantly more anisotropic than the fresh samples, and all samples were highly anisotropic, as confirmed by the small values ( 0.5) Table 1. Non-Equibiaxial Behavior. The response to multiple loading protocols revealed the complex planar behavior of the natural and GL treated AV cusp. Specifically, we observed a non-monotonic relationship between circumferential stress and strain Fig. 6 a. Examination of the progression of the stress strain curves with decreasing radial stress in non-equibiaxial loading protocols demonstrated that the negative circumferential strain values were due to a very strong mechanical coupling between the axes. The degree of coupling was not as severe in the radial direction Fig. 6 b. Another factor in the analysis of the biaxial data was the existence of nontrivial shear strains Table 1. Significantly larger shear strains in the fixed groups were found but attributed to slight differences in the degree of off axis mounting rather than differences in the intrinsic tissue properties. Discussion In this study, specialized biaxial testing methods for the AV cusp were developed. Utilizing these methods, biaxial data from fresh and low-pressure glutaraldehyde treated aortic valve cusps spanning a sufficient stress-strain range for constitutive modeling were obtained for the first time. We established that the lower belly region was the optimal site for strain measurements due to: 1 its locally homogenous fiber structure, 2 the parallel alignment of the collagen fibers to the circumferential axis, and 3 the most homogeneous strain field compared to other regions of the cusp. This region is not the center of the specimen, but rather slightly below the center, away from the nodulus of Arantii. Further, the additional distance of our markers in this region from the relatively nonhomogeneous nodulus may also explain the lower variability of our data compared to previous studies 5. Biaxial Specimen Size Limitations. Biaxial tests require discrete point loading to allow unconstrained transverse motion. In small samples, the effects of stress concentrations generated at the suture attachment sites may propagate into the measurement region, negating reliable estimates of the stress. For example, the aortic heart valve cusp is smaller and more structurally heterogeneous than most tissues examined with biaxial mechanical testing techniques. Typical widths for biological tissues previously tested with biaxial techniques are two to three times the size of a cusp and many times larger than a single structural region in a cusp i.e., belly region 19 21,12. Using finite element analysis and biaxial tests on synthetic membranes, Nielsen and colleagues 15 attempted to determine the validity of biaxial testing methods for small specimens 10 mm square. The authors found that, for homogeneous isotropic materials loaded at four discrete locations per side, the strain and stress were relatively uniform in the central 25 percent of the sample. However, the authors correctly note that the stress and strain distributions would be less uniform for anisotropic and/or heterogeneous materials. For complex anisotropic tissues, direct experimental evidence is clearly needed to demonstrate that a sufficiently homogeneous area for strain measurement exists and that the stress distribution in the central region is sufficiently homogeneous despite the point loading at the boundary. For the AV cusp, the orthogonal relationship between the principal strain and the underlying preferred collagen fiber direction was not altered substantially even near the suture attachment points Fig. 2. The strain-fiber direction relationship would have been skewed if the stress concentration near the tethers propagated into the measurement region. Thus, the stress concentrations caused by tethering at the boundary did not adversely affect the stress and strain estimations in the central region for the AV cusp. Although dependence of tissue deformation on fiber orientation is commonly assumed 22, this study was the first quantitative point-by-point comparison of local deformation with corresponding underlying structure in a soft tissue. The result for the AV cusp stands in contrast to bovine pericardium, which experienced large fiber reorientation in the vicinity of the sutures, which dissipated before affecting the central measurement region 23. Thus, the methodology presented here may be used to estimate the influence of edge effects and the lower limit of biaxial specimen size. Cuspal Micro- and Mesomechanics. For the fresh tissue specimens, the stress along both the circumferential and radial axes increased approximately exponentially with increasing strain. This nonlinear material behavior is characteristic of soft biological tissues and is attributed to the uncrimping of the collagen fibers in the relatively compliant ground substance 24. In the fully relaxed state, the AV collagen fibers are highly crimped with a period of approximately 20 m 25,26. Modern commercial PBHV are fixed at 4 mmhg to preserve the shape of the cusp. We have found that most of the crimp is removed by pressure fixation greater than 1 mmhg, with only small changes above 4 mmhg and is virtually eliminated at 90 mmhg 27. Reduction of crimp magnitude is believed to explain the significantly smaller circumferential extensibility in pressure-fixed tissues compared with fresh tissues in this and other studies 28,29,2,3,5,30,31. However, uncrimping of the collagen fibers alone cannot explain the extreme extensibility in the radial direction Fig. 4. The eventual stiffening in the radial direction has been explained by realignment of the collagen fibers in the ventricularis toward the direction of stretch 32. However, we have shown that even under extreme loading the fiber alignment in the cusp does not change sufficiently to explain the large radial strains 23. This complex behavior, as well as the overall anisotropic behavior of the cusp, can be explained by the tight angular distribution of collagen fibers Fig. 7. As one axis is loaded, the radial forces cause the fibers to rotate, which in turn cause a contraction along the circumferential axis. This effect will become more dramatic as the radial loads become larger with respect to the circumferential loads Fig. 7 b, c, d. This effect illustrates that negative strains can be generated even though the stress magnitude is the same along both axes and no buckling of the tissue is observed. Thus, radial loads are ultimately resisted by the highly circumferentially aligned fibrosa collagen fibers, whose rotation as opposed to stretch allows for large radial strains. Further, the relatively large Fig. 7 a A schematic of the biaxial test specimen, with the fibrous structure of the cusp depicting the large collagen cords, which undergo large rotations with loading b d. Asthe radial loads become larger with respect to the circumferential loads, the collagen fibers undergo large rotations. This causes contraction along the circumferential axis without buckling and allows for very large radial strains. 28 Õ Vol. 122, FEBRUARY 2000 Transactions of the ASME

7 proportion of highly extensible elastin in the ventricularis allows the large radial compliance without yielding 33. In addition to explaining the large radial compliance, the extreme alignment of the fibrosa collagen fibers can also explain the strong axial mechanical coupling found for the AV. Specifically, in the case of a network of highly aligned fibers, the scissor-like action of the fibers can cause contraction along the aligned axis when its load is comparable or less than the other axis Fig. 7. This asymmetric mechanical coupling helps to explain the circumferential contraction under equi-biaxial loading and the nonmonotonic stress strain response observed in many of our samples Fig. 6. In-plane coupling has been reported previously in other tissues 34,35,21,36,12. It is important to note that the mechanical coupling between the material axes and physiological fiber kinematics are lost in uniaxial tests. Additionally, unlike tendons and ligaments, a significant portion of the load bearing fibers are cut when the uniaxial specimens are prepared from planar tissues, leading to exaggerated extensibility and compliance 22. Even the quasistatic study of intact valves under gradually increasing transvalvular pressure 37 does not allow for well-controlled and variable biaxial stress states necessary for comprehensive elucidation of biaxial mechanical properties. Mechanical Indices. The tissue extensibility was defined at three equibiaxial tension levels to 1 demonstrate the large anisotropic pre-strain in the tissue under small load 1 N/m, 2 compare the mechanical response between the fresh and fixed groups at a high physiological load 60 N/m Table 1, and 3 compare our results with previous studies 8 N/m. In the working valve, radial extensibility is important for coadaptation of the cusps, which is necessary for producing an effective seal against retrograde flow. Low-pressure fixation significantly reduced the radial extensibility at the low and mid stress levels, but did not affect the extensibility at peak load. This finding suggests that, although less than ideal at lower loads, a near-physiologic coadaptation region could be achieved in these valves at peak diastolic load. In contrast, the extensibility in the circumferential direction was significantly reduced at all load levels. The profound decrease in circumferential extensibility is presumably due to the reduction in crimp magnitude with pressure fixation mentioned previously. The in-vivo effects of the significantly reduced circumferential extensibility with fixation are not readily apparent. However, the lack of extensibility may produce increased flexural rigidity affecting the valve opening/closing behavior during systole, potentially leading toward more rapid collagen degradation. Due to the curved trajectory of the fibers Fig. 1, the preferred direction of each sample was skewed with respect to the stretch axes at some point within the measurement region. In the AV cusp and other anisotropic tissues 7, such misalignment errors can cause difficulties in interpreting mechanical data. For example, misalignment produces larger apparent deformation in the circumferential direction, smaller deformation in the radial direction, and nontrivial shear deformation due to the relative angle between the fiber and stretch directions in the AV cusp. We found that the shear increased significantly with fixation but believe that the increase was due to greater misalignment errors with the fixed specimens rather than intrinsic changes in the tissue with chemical treatment. Being slightly smaller, the fixed samples were more difficult to mount in the apparatus. In a separate study, the misalignment of cuspal specimens correlated highly with the amount of shear 38. The relatively large shear values found in this study 5 deg indicate that a constitutive model that includes both the fiber angles and shear strains should be used to remove the error due to sample misalignment. Membrane Stress-Based Testing Protocol. Biaxial experiments on planar tissues have generally been run under strain control 8,9,19,20,36,12. For the AV cusp, stress control was more suitable due to the physiological loading and extreme mechanical anisotropy. During diastole, stresses in the cusp arise to resist the aortic back pressure as opposed to an imposed displacement. Further, the deformation in the circumferential direction was much smaller than in the radial direction, which led to practical difficulties in simultaneously controlling the disparate strains with a single tracking camera with a fixed field of view. Another factor to consider was what protocols to utilize in biaxial testing. Two major considerations are 1 generation of stress strain data to encompass the complete in-plane response, and 2 coverage of the estimated physiological loading range. Of these two, we decided to choose the former since it encompasses the physiological range. An additional consideration was for the study of fatigue damage in BHV may require simulation of non-physiological stress states. Utilization of membrane stresses avoided the use of ambiguous thickness measurements in the stress calculations. The thickness of the cusp has been shown to vary by almost an order of magnitude between the functional areas in human cusps fixed in the stressed state 80 mmhg 39. In addition, thickness measurements including the spongiosa, the gelatinous inner layer between the fibrosa and ventricularis, do not accurately represent the loadbearing cross-sectional area and may add to the uncertainty of stress calculations 5,40. A peak tension value of 60 N/m was chosen to produce physiological fiber stresses of 240 kpa 41 43,32 in the belly region, assuming a thickness of 500 m and a volume fraction of 0.5. Limitations. The results from this study are limited to the in vitro setting and cannot be directly applied to the whole valve in vivo. Although in vitro testing is necessary to quantify the mechanical properties of the aortic cusp and multiple biaxial loading protocols were utilized in this study, harvesting the sample disrupts the tissue structure and mechanics. Since the AV cusp is not a flat tissue in its native state, the curved geometry also introduces error in applying the appropriate stresses and strains in vitro. The results should not be generalized to all areas of the cusp, considering the vastly different structures such as the tendon-like commissures and the thick nodulus Fig. 1. Even for the belly region, the stress and strain fields in the intact cusp may be affected by the properties of these other regions. The type of regional stress strain analysis as shown in Fig. 3 must be interpreted with caution. Although we demonstrated a tight correlation between fiber direction and principal strain direction Fig. 2, the assumption that the stress field is sufficiently homogeneous over the region delimited by the optical markers could not be directly tested. Futures studies will be required in which an anisotropic, large deformation constitutive model incorporated into an inverse-fem code will be needed to verify these results fully. Biaxial tension experiments simulate diastole only, and the data obtained in this study represent only the belly region. The complex flexural patterns and reversals of curvature in systole impart a far different stress distribution in the cusps than can be applied in planar biaxial tests. The layered structure, although extremely important in the bending behavior of the valve during systole 4,44, is ignored in our analysis. Thubrikar et al. 45 calculated that the bending stresses are larger than the membrane stresses at the free edge and the attachment points. The bending stiffness and shear modulus are non-linear and change markedly with fixation 46. Characterization of the bending behavior of the AV cusp and its relationship to fatigue damage is underscored by recent results in our lab which indicate a profound loss of flexural rigidity with accelerated testing 47. Summary and Conclusions. The biaxial mechanical behavior of untreated and low-pressure glutaraldehyde-treated aortic heart valve cusps were measured. Comparison of the local structure and strain patterns demonstrated that the deformation of the tissue was dominated by the underlying fibrous architecture. The most suitable area for strain quantification was the most homoge- Journal of Biomechanical Engineering FEBRUARY 2000, Vol. 122 Õ 29

8 neous area located in the central belly region. In addition, due to the strong effects of the fibrous structure, the localized tethering forces at the boundaries did not appear to alter the strain distribution over a large portion of the sample. Multiple loading protocols were employed, yielding the first set of mechanical data suitable for constitutive modeling of the aortic valve cusp. All cusps exhibited highly nonlinear and anisotropic behavior with strong inplane coupling. The chemically treated cusps were significantly less extensible and more anisotropic than the fresh cusps. These mechanical changes due to fixation were probably due to a locking of the collagen in a less wavy state during low-pressure fixation. Rather than a profound reorientation of ventricularis collagen fibers, it is more likely that the radial load is ultimately resisted by the highly circumferentially aligned fibrosa collagen fibers, whose rotation as opposed to stretch allows for large radial strains. 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