Biomechanical Properties of Fiber Bundle and Membrane Mesostructures of the Porcine Aortic Valve.

BACKGROUND AND AIM OF THE STUDY: Aortic valve leaflets have a complex, anisotropic structure that likely plays an important role in their biomechanical function. The larger scale (bulk) biomechanical properties of the valve have been well documented. However, limited data are available regarding the biomechanical properties of individual fiber bundles and membranes that connect the bundles. The study aim was to characterize these intermediate-scale 'mesostructures' and explore biomechanical variability across the three leaflets of the aortic valve. Methods: A custom uniaxial micro-testing system was developed to test mesostructures of the aortic valve leaflet. This system uses elliptically polarized light to enhance collagen features, providing 'texture' for image correlation-based strain measurements. Porcine aortic valve membrane and fiber bundle specimens were subjected to controlled stretch-and-hold tests. Synchronized video and load data were used to measure strain, elastic modulus, relaxation time, and degree of relaxation (among other parameters). These metrics were then compared between specimen types and across the three leaflets. METHODS: A custom uniaxial micro-testing system was developed to test mesostructures of the aortic valve leaflet. This system uses elliptically polarized light to enhance collagen features, providing 'texture' for image correlation-based strain measurements. Porcine aortic valve membrane and fiber bundle specimens were subjected to controlled stretch-and-hold tests. Synchronized video and load data were used to measure strain, elastic modulus, relaxation time, and degree of relaxation (among other parameters). These metrics were then compared between specimen types and across the three leaflets. RESULTS: Fiber bundles were found to have a significantly higher elastic modulus (13.87 ± 2.81 MPa) than the membranes (2.27± 0.36 MPa). Both specimen types had similar relaxation time constants (6.75 ± 0.73 s) and degrees of relaxation (0.223 ± 0.016). The elastic modulus of the fiber bundles from the left coronary and non-coronary leaflets was significantly higher than that of the right coronary leaflet. The fiber bundle elastic modulus also negatively correlated with the fiber bundle width. CONCLUSION: The resulting differences in biomechanical properties of mesostructures are likely related to their biomechanical and hemodynamic requirements. The study findings highlight the importance of considering aortic valve leaflets as inhomogeneous. Further studies are required to characterize the morphologies, nonaffine deformations, and biomechanical properties of the valve's complex fiber-membrane mesostructures, potentially enabling the development of improved models and designs for durable replacement/repair strategies.

Fascicle-scale loading and failure behavior of the Achilles tendon.

Although the overall bulk properties of the Achilles tendon have been measured, there is little information detailing the properties of individual fascicles or their interactions. The knowledge of biomechanical properties at the fascicle-scale is critical in understanding the biomechanical behavior of tendons and for the construction of accurate and detailed computational models. Seven tissue samples (approximately 15x4x1 mm(3)) harvested from four freshly thawed human (all male) tendons, each sample having four to six fascicles, were tested in uniaxial tension. A sequential sectioning protocol was used to isolate interaction effects between adjacent fascicles and to obtain the loading response for a single fascicle. The specimen deformation was measured directly using a novel polarized light imaging system with digital image correlation (DIC) for marker-free deformation measurement. The modulus of the single fascicle was significantly higher compared with the intact fascicle group (single: 226 MPa (SD 179), group: 68 MPa (SD 33)). The interaction effect between the adjacent fascicles was less than 10% of the applied load and evidence of sub- and postfailure fascicle sliding was clearly visible. The DIC direct deformation measurements revealed that the modulus of single fascicles could be as much as three to four times the intact specimen. The consistently higher moduli values of the single (strongest) fascicle indicate that the overall response of the tendon may be dominated by a subset of "strongest" fascicles. Also, fascicle-to-fascicle interactions were small, which was <10% of the overall response. This knowledge is useful for developing computational models representing single fascicle and/or fascicle group mechanical behavior and provides valuable insights into fascicle-scale Achilles tendon material properties.

Mesostructures of the aortic valve.

BACKGROUND AND AIM OF THE STUDY: The aortic valve cusp is commonly described as a three-layered structure containing circumferentially aligned fiber bundles. Little is known, however, regarding fiber bundle sizes, branching patterns, or how they are connected. This is because previous morphological studies relied primarily on histological sectioning and staining techniques, which tend to affect all of the collagen, regardless of structure or orientation. METHODS: To address this problem, a novel system was developed for the visualization and analysis of the intermediate-scale 'mesostructures' of aortic valve cusps. Mesostructures are defined as the branching fiber bundle and membrane structures that make up the valve. This system uses elliptically polarized light to provide contrast between collagen mesostructures without the need for embedding, staining, or other contrast-enhancing techniques. Using this system, high-resolution images of 42 whole porcine aortic valve cusps were acquired in an unloaded (i.e. resting) condition and during application of controlled manipulation. Image-processing algorithms were developed to quantify fiber bundle morphological features and produce detailed maps of the fiber bundle patterns. RESULTS: Fiber bundle sizes and patterns were found to be significantly different for each of the three cusps. The non-coronary cusp had a significantly smaller bundle diameter (0.9 +/- 0.07 mm) than the left and right coronary cusps (1.1 +/- 0.08 mm). The left and non-coronary cusps appeared to be mirror images of each other, whereas the right coronary cusp was self-symmetric. When applying controlled loads to the cusp specimens, thin, overlapping, collagenous membranes were often found which connected the fiber bundles. Interesting pinnate fiber branching patterns were also found. CONCLUSION: These morphological results were strikingly different than the currently accepted three-layer description, and may provide valuable insight into aortic valve structure-function relationships.

Complex collagen fiber and membrane morphologies of the whole porcine aortic valve.

OBJECTIVES: Replacement aortic valves endeavor to mimic native valve function at the organ, tissue, and in the case of bioprosthetic valves, the cellular levels. There is a wealth of information about valve macro and micro structure; however, there presently is limited information on the morphology of the whole valve fiber architecture. The objective of this study was to provide qualitative and quantitative analyses of whole valve and leaflet fiber bundle branching patterns using a novel imaging system. METHODS: We developed a custom automated microscope system with motor and imaging control. Whole leaflets (n = 25) were imaged at high resolution (e.g., 30,000×20,000 pixels) using elliptically polarized light to enhance contrast between structures without the need for staining or other methods. Key morphologies such as fiber bundle size and branching were measured for analyses. RESULTS: The left coronary leaflet displayed large asymmetry in fiber bundle organization relative to the right coronary and non-coronary leaflets. We observed and analyzed three main patterns of fiber branching; tree-like, fan-like, and pinnate structures. High resolution images and quantitative metrics are presented such as fiber bundle sizes, positions, and branching morphological parameters. SIGNIFICANCE: To our knowledge there are currently no high resolution images of whole fresh leaflets available in the literature. The images of fiber/membrane structures and analyses presented here could be highly valuable for improving the design and development of more advanced bioprosthetic and/or bio-mimetic synthetic valve replacements.

Direct measurement of nonuniform large deformations in soft tissues during uniaxial extension.

Understanding the complex relationships between microstructural organization and macromechanical function is fundamental to our knowledge of the differences between normal, diseased/injured, and healing connective tissues. The long-term success of functional tissue-engineered constructs or scaffolds may largely depend on our understanding of the structural organization of the original tissue. Although innovative techniques have been used to characterize and measure the microstructural properties of collagen fibers, a large gap remains in our knowledge of the behavior of intermediate scale (i.e., "mesostructural") groups of fiber bundles in larger tissue samples. The objective of this study was to develop a system capable of directly measuring deformations of these smaller mesostructures during application of controlled loads. A novel mesostructural testing system (MSTS) has been developed to apply controlled multiaxial loads to medium (meso-) scale tissue specimens, while directly measuring local nonuniform deformations using synchronized digital video capture and "markerless" image correlation. A novel component of the MSTS is the use of elliptically polarized light to enhance collagen fiber contrast, providing the necessary texture for accurate markerless feature tracking of local fiber deformations. In this report we describe the components of the system, its calibration and validation, and the results from two different tissues: the porcine aortic valve cusp and the bovine pericardium. Validation tests on prepared samples showed maximum error of direct strain measurement to be 0.3%. Aortic valve specimens were found to have larger inhomogeneous strains during tensile testing than bovine pericardium. Clamping effects were more pronounced for the valve specimens. A new system for direct internal strain measurement in connective tissues during application of controlled loads has been developed and validated. The results from the two different tissues show that significant inhomogeneous deformations can occur even in simple tensile testing experiments.

Elastic model for crimped collagen fibrils.

A physiologic constitutive expression is presented in algorithmic format for the nonlinear elastic response of wavy collagen fibrils found in soft connective tissues. The model is based on the observation that crimped fibrils in a fascicle have a three-dimensional structure at the micron scale that we approximate as a helical spring. The symmetry of this wave form allows the force/displacement relationship derived from Castigliano's theorem to be solved in closed form: all integrals become analytic. Model predictions are in good agreement with experimental observations for mitral-valve chordae tendinece.

Fractional order viscoelasticity of the aortic valve cusp: an alternative to quasilinear viscoelasticity.

BACKGROUND: Quasilinear viscoelasticity (QLV) theory has been widely and successfully used to describe the time-dependent response of connective tissues. Difficulties remain, however, particularly in material parameter estimation and sensitivities. In this study, we introduce a new alternative: the fractional order viscoelasticity (FOV) theory, which uses a fractional order integral to describe the relaxation response. FOV implies a fractal-like tissue structure, reflecting the hierarchical arrangement of collagenous tissues. METHOD OF APPROACH: A one-dimensional (I-D) FOV reduced relaxation function was developed, replacing the QLV "box-spectrum" function with a fractional relaxation function. A direct-fit, global optimization method was used to estimate material parameters from stress relaxation tests on aortic valve tissue. RESULTS: We found that for the aortic heart valve, FOV had similar accuracy and better parameter sensitivity than QLV, particularly for the long time constant (tau2). The mean (n = 5) fractional order was 0.29, indicating that the viscoelastic response of the tissue was strongly fractal-like. RESULTS SUMMARY: mean QLV parameters were C = 0.079, tau1 = 0.004, tau2 = 76, and mean FOV parameters were beta = 0.29, tau = 0.076, and rho = 1.84. CONCLUSIONS: FOV can provide valuable new insights into tissue viscoelastic behavior Determining the fractional order can provide a new and sensitive quantitative measure for tissue comparison.

The effect of strain rate on the viscoelastic response of aortic valve tissue: a direct-fit approach.

Knowledge of strain-rate sensitivity of soft tissue viscoelastic and nonlinear elastic properties is important for accurate predictions of biomechanical behavior and for quantitative assessment of the effects of disease or surgical/pharmaceutical intervention. Soft tissues are known to exhibit mild rate sensitivity, but experimental artifacts related to testing system control can confound estimation of these effects. "Perfect" ramp-and-hold stress-relaxation tests become difficult at high strain rates because of problems related to undershoot/overshoot error and vibrations. These errors can introduce unwanted bias into parameter estimation methods that rely on idealizations of the applied ramp-and-hold displacement. To address these problems, we describe a new method for estimating quasilinear viscoelastic (QLV) parameters that directly fits the QLV constitutive model to the actual point-wise stress-time history of the test, using an adaptive grid refinement (AGR) global optimization algorithm. This new method significantly improves the accuracy and predictivity of QLV parameter estimates for heart valve tissues, compared to traditional methods that use idealized displacement data. We estimated QLV parameters for aortic valve tissue over a range of physiologic displacement rates, finding that the viscoelastic content parameter (C) increased slightly with increasing strain rate, but the fast (tau1) and slow (tau2) time constants were strain rate insensitive.