Biaxial Mechanical Characterizations of Atrioventricular Heart Valves

An investigation of how specimen dimensions affect biaxial mechanical characterizations with CellScale BioTester and constitutive modeling of porcine tricuspid valve leaflets

Biaxial mechanical characterizations are the accepted approach to determine the mechanical response of many biological soft tissues. Although several computational and experimental studies have examined how experimental factors (e.g., clamped vs. suture mounting) affect the acquired tissue mechanical behavior, little is known about the role of specimen dimensions in data acquisition and the subsequent modeling. In this study, we combined our established mechanical characterization framework with an iterative size-reduction protocol to test the hypothesis that specimen dimensions affect the observed mechanical behavior of biaxial characterizations. Our findings indicated that there were non-significant differences in the peak equibiaxial stretches of tricuspid valve leaflets across four specimen dimensions ranging from 4.5×4.5mm to 9 × 9mm. Further analyses revealed that there were significant differences in the low-tensile modulus of the circumferential tissue direction. These differences resulted in significantly different constitutive model parameters for the Tong-Fung model between different specimen dimensions of the posterior and septal leaflets. Overall, our findings demonstrate that specimen dimensions play an important role in experimental characterizations, but not necessarily in constitutive modeling of soft tissue mechanical behavior during biaxial testing with the commercial CellScale BioTester.

Soft-Tissue Material Properties and Mechanogenetics during Cardiovascular Development

During embryonic development, changes in the cardiovascular microstructure and material properties are essential for an integrated biomechanical understanding. This knowledge also enables realistic predictive computational tools, specifically targeting the formation of congenital heart defects. Material characterization of cardiovascular embryonic tissue at consequent embryonic stages is critical to understand growth, remodeling, and hemodynamic functions. Two biomechanical loading modes, which are wall shear stress and blood pressure, are associated with distinct molecular pathways and govern vascular morphology through microstructural remodeling. Dynamic embryonic tissues have complex signaling networks integrated with mechanical factors such as stress, strain, and stiffness. While the multiscale interplay between the mechanical loading modes and microstructural changes has been studied in animal models, mechanical characterization of early embryonic cardiovascular tissue is challenging due to the miniature sample sizes and active/passive vascular components. Accordingly, this comparative review focuses on the embryonic material characterization of developing cardiovascular systems and attempts to classify it for different species and embryonic timepoints. Key cardiovascular components including the great vessels, ventricles, heart valves, and the umbilical cord arteries are covered. A state-of-the-art review of experimental techniques for embryonic material characterization is provided along with the two novel methods developed to measure the residual and von Mises stress distributions in avian embryonic vessels noninvasively, for the first time in the literature. As attempted in this review, the compilation of embryonic mechanical properties will also contribute to our understanding of the mature cardiovascular system and possibly lead to new microstructural and genetic interventions to correct abnormal development.

An Information-Theoretic Framework for Optimal Design: Analysis of Protocols for Estimating Soft Tissue Parameters in Biaxial Experiments

A new framework for optimal design based on the information-theoretic measures of mutual information, conditional mutual information and their combination is proposed. The framework is tested on the analysis of protocols—a combination of angles along which strain measurements can be acquired—in a biaxial experiment of soft tissues for the estimation of hyperelastic constitutive model parameters. The proposed framework considers the information gain about the parameters from the experiment as the key criterion to be maximised, which can be directly used for optimal design. Information gain is computed through k-nearest neighbour algorithms applied to the joint samples of the parameters and measurements produced by the forward and observation models. For biaxial experiments, the results show that low angles have a relatively low information content compared to high angles. The results also show that a smaller number of angles with suitably chosen combinations can result in higher information gains when compared to a larger number of angles which are poorly combined. Finally, it is shown that the proposed framework is consistent with classical approaches, particularly D-optimal design.

Manifold learning based data-driven modeling for soft biological tissues

Data-driven modeling directly utilizes experimental data with machine learning techniques to predict a material's response without the necessity of using phenomenological constitutive models. Although data-driven modeling presents a promising new approach, it has yet to be extended to the modeling of large-deformation biological tissues. Herein, we extend our recent local convexity data-driven (LCDD) framework (He and Chen, 2020) to model the mechanical response of a porcine heart mitral valve posterior leaflet. The predictability of the LCDD framework by using various combinations of biaxial and pure shear training protocols are investigated, and its effectiveness is compared with a full structural, phenomenological model modified from Zhang et al. (2016) and a continuum phenomenological Fung-type model (Tong and Fung, 1976). We show that the predictivity of the proposed LCDD nonlinear solver is generally less sensitive to the type of loading protocols (biaxial and pure shear) used in the data set, while more sensitive to the insufficient coverage of the experimental data when compared to the predictivity of the two selected phenomenological models. While no pre-defined functional form in the material model is necessary in LCDD, this study reinstates the importance of having sufficiently rich data coverage in the date-driven and machine learning type of approaches. It is also shown that the proposed LCDD method is an enhancement over the earlier distance-minimization data-driven (DMDD) against noisy data. This study demonstrates that when sufficient data is available, data-driven computing can be an alternative method for modeling complex biological materials.

A Pilot Study on Linking Tissue Mechanics with Load-Dependent Collagen Microstructures in Porcine Tricuspid Valve Leaflets

The tricuspid valve (TV) is composed of three leaflets that coapt during systole to prevent deoxygenated blood from re-entering the right atrium. The connection between the TV leaflets’ microstructure and the tissue-level mechanical responses has yet to be fully understood in the TV biomechanics society. This pilot study sought to examine the load-dependent collagen fiber architecture of the three TV leaflets, by employing a multiscale, combined experimental approach that utilizes tissue-level biaxial mechanical characterizations, micro-level collagen fiber quantification, and histological analysis. Our results showed that the three TV leaflets displayed greater extensibility in the tissues’ radial direction than in the circumferential direction, consistently under different applied biaxial tensions. Additionally, collagen fibers reoriented towards the direction of the larger applied load, with the largest changes in the alignment of the collagen fibers under radially-dominant loading. Moreover, collagen fibers in the belly region of the TV leaflets were found to experience greater reorientations compared to the tissue region closer to the TV annulus. Furthermore, histological examinations of the TV leaflets displayed significant regional variation in constituent mass fraction, highlighting the heterogeneous collagen microstructure. The combined experimental approach presented in this work enables the connection of tissue mechanics, collagen fiber microstructure, and morphology for the TV leaflets. This experimental methodology also provides a new research platform for future developments, such as multiscale models for the TVs, and the design of bioprosthetic heart valves that could better mimic the mechanical, microstructural, and morphological characteristics of the native tricuspid valve leaflets.

Integration of polarized spatial frequency domain imaging (pSFDI) with a biaxial mechanical testing system for quantification of load-dependent collagen architecture in soft collagenous tissues

Collagen fiber networks provide the structural strength of tissues, such as tendons, skin and arteries. Quantifying the fiber architecture in response to mechanical loads is essential towards a better understanding of the tissue-level mechanical behaviors, especially in assessing disease-driven functional changes. To enable novel investigations into these load-dependent fiber structures, a polarized spatial frequency domain imaging (pSFDI) device was developed and, for the first time, integrated with a biaxial mechanical testing system. The integrated instrument is capable of a wide-field quantification of the fiber orientation and the degree of optical anisotropy (DOA), representing the local degree of fiber alignment. The opto-mechanical instrument''s performance was assessed through uniaxial loading on tendon tissues with known collagen fiber microstructures. Our results revealed that the bulk fiber orientation angle of the tendon tissue changed minimally with loading (median ± 0.5*IQR of 52.7° ± 3.3° and 51.9° ± 3.3° under 0 and 3% longitudinal strains, respectively), whereas on a micro-scale, the fibers became better aligned with the direction of loading: the DOA (mean ± SD) increased from 0.149 ± 0.032 to 0.198 ± 0.056 under 0 and 3% longitudinal strains, respectively, p < 0.001. The integrated instrument was further applied to study two representative mitral valve anterior leaflet (MVAL) tissues subjected to various biaxial loads. The fiber orientations within these representative MVAL tissue specimens demonstrated noticeable heterogeneity, with the local fiber orientations dependent upon the sample, the spatial and transmural locations, and the applied loading. Our results also showed that fibers were generally better aligned under equibiaxial (DOA = 0.089 ± 0.036) and circumferentially-dominant loading (DOA = 0.086 ± 0.037) than under the radially-dominant loading (DOA = 0.077 ± 0.034), indicating circumferential predisposition. These novel findings exemplify a deeper understanding of the load-dependent collagen fiber microstructures obtained through the use of the integrated opto-mechanical instrument. STATEMENT OF SIGNIFICANCE: In this study, a novel quantitative opto-mechanical system was developed by combining a polarized Spatial Frequency Domain Imaging (pSFDI) device with a biaxial mechanical tester. The integrated system was used to quantify the load-dependent collagen fiber microstructures in representative tendon and mitral valve anterior leaflet (MVAL) tissues. Our results revealed that MVAL's fiber architectures exhibited load-dependent spatial and transmural heterogeneities, suggesting further microstructural complexity than previously reported in heart valve tissues. These novel findings were possible through the system's ability to, for the first time, capture the load-dependent collagen architecture in the mitral valve anterior leaflet tissue over a wide field of view (e.g., 10 × 10 mm for the MVAL tissue specimens). Such capabilities afford unique future opportunities to improve patient outcomes through concurrent mechanical and microstructural assessments of healthy and diseased tissues in conditions such as heart valve regurgitation and calcification.

Load-dependent collagen fiber architecture data of representative bovine tendon and mitral valve anterior leaflet tissues as quantified by an integrated opto-mechanical system

The data presented in this article provide load-dependent collagen fiber architecture (CFA) of one representative bovine tendon tissue sample and two representative porcine mitral valve anterior leaflet tissues, and they are stored in a MATLAB MAT-file format. Each dataset contains: (i) the number of pixel points, (ii) the array of pixel's x- and y-coordinates, (iii) the three acquired pixel intensity arrays, and (iv) the Delaunay triangulation for visualization purpose. This dataset is associated with a companion journal article, which can be consulted for further information about the methodology, results, and discussion of the opto-mechanical characterization of the tissue's CFA's (Jett etal. [1]).

Effect of Residual and Transformation Choice on Computational Aspects of Biomechanical Parameter Estimation of Soft Tissues

Several nonlinear and anisotropic constitutive models have been proposed to describe the biomechanical properties of soft tissues, and reliably estimating the unknown parameters in these models using experimental data is an important step towards developing predictive capabilities. However, the effect of parameter estimation technique on the resulting biomechanical parameters remains under-analyzed. Standard off-the-shelf techniques can produce unreliable results where the parameters are not uniquely identified and can vary with the initial guess. In this study, a thorough analysis of parameter estimation techniques on the resulting properties for four multi-parameter invariant-based constitutive models is presented. It was found that linear transformations have no effect on parameter estimation for the presented cases, and nonlinear transforms are necessary for any improvement. A distinct focus is put on the issue of non-convergence, and we propose simple modifications that not only improve the speed of convergence but also avoid convergence to a wrong solution. The proposed modifications are straightforward to implement and can avoid severe problems in the biomechanical analysis. The results also show that including the fiber angle as an unknown in the parameter estimation makes it extremely challenging, where almost all of the formulations and models fail to converge to the true solution. Therefore, until this issue is resolved, a non-mechanical—such as optical—technique for determining the fiber angle is required in conjunction with the planar biaxial test for a robust biomechanical analysis.

An investigation of the effect of freezing storage on the biaxial mechanical properties of excised porcine tricuspid valve anterior leaflets

The atrioventricular heart valve (AHV) leaflets are critical to the facilitation of proper unidirectional blood flow through the heart. Previously, studies have been conducted to understand the tissue mechanics of healthy AHV leaflets to inform the development of valve-specific computational models and replacement materials for use in diagnosing and treating valvular heart disease. Generally, these studies involved biaxial mechanical testing of the AHV leaflet tissue specimens to extract relevant mechanical properties. Most of those studies considered freezing-based storage systems based on previous findings for other connective tissues such as aortic tissue or skin. However, there remains no study that specifically examines the effects of freezing storage on the characterized mechanical properties of the AHV leaflets. In this study, we aimed to address this gap in knowledge by performing biaxial mechanical characterizations of the tricuspid valve anterior leaflet (TVAL) tissue both before and after a 48-h freezing period. Primary findings of this study include: (i) a statistically insignificant change in the tissue extensibilities, with the frozen tissues being slightly stiffer and more anisotropic than the fresh tissues; and (ii) minimal variations in the stress relaxation behaviors between the fresh and frozen tissues, with the frozen tissues demonstrating slightly lessened relaxation. The findings from this study suggested that freezing-based storage does not significantly impact the observed mechanical properties of one of the five AHV leaflets-the TVAL. The results from this study are useful for reaffirming the experimental methodologies in the previous studies, as well as informing the tissue preservation methods of future investigations of AHV leaflet mechanics.

An investigation of the glycosaminoglycan contribution to biaxial mechanical behaviours of porcine atrioventricular heart valve leaflets

The atrioventricular heart valve (AHV) leaflets have a complex microstructure composed of four distinct layers: atrialis, ventricularis, fibrosa and spongiosa. Specifically, the spongiosa layer is primarily proteoglycans and glycosaminoglycans (GAGs). Quantification of the GAGs' mechanical contribution to the overall leaflet function has been of recent focus for aortic valve leaflets, but this characterization has not been reported for the AHV leaflets. This study seeks to expand current GAG literature through novel mechanical characterizations of GAGs in AHV leaflets. For this characterization, mitral and tricuspid valve anterior leaflets (MVAL and TVAL, respectively) were: (i) tested by biaxial mechanical loading at varying loading ratios and by stress-relaxation procedures, (ii) enzymatically treated for removal of the GAGs and (iii) biaxially mechanically tested again under the same protocols as in step (i). Removal of the GAG contents from the leaflet was conducted using a 100 min enzyme treatment to achieve approximate 74.87% and 61.24% reductions of all GAGs from the MVAL and TVAL, respectively. Our main findings demonstrated that biaxial mechanical testing yielded a statistically significant difference in tissue extensibility after GAG removal and that stress-relaxation testing revealed a statistically significant smaller stress decay of the enzyme-treated tissue than untreated tissues. These novel findings illustrate the importance of GAGs in AHV leaflet behaviour, which can be employed to better inform heart valve therapeutics and computational models.

Mechanics of the Tricuspid Valve-From Clinical Diagnosis/Treatment, In-Vivo and In-Vitro Investigations, to Patient-Specific Biomechanical Modeling

Proper tricuspid valve (TV) function is essential to unidirectional blood flow through the right side of the heart. Alterations to the tricuspid valvular components, such as the TV annulus, may lead to functional tricuspid regurgitation (FTR), where the valve is unable to prevent undesired backflow of blood from the right ventricle into the right atrium during systole. Various treatment options are currently available for FTR; however, research for the tricuspid heart valve, functional tricuspid regurgitation, and the relevant treatment methodologies are limited due to the pervasive expectation among cardiac surgeons and cardiologists that FTR will naturally regress after repair of left-sided heart valve lesions. Recent studies have focused on (i) understanding the function of the TV and the initiation or progression of FTR using both in-vivo and in-vitro methods, (ii) quantifying the biomechanical properties of the tricuspid valve apparatus as well as its surrounding heart tissue, and (iii) performing computational modeling of the TV to provide new insight into its biomechanical and physiological function. This review paper focuses on these advances and summarizes recent research relevant to the TV within the scope of FTR. Moreover, this review also provides future perspectives and extensions critical to enhancing the current understanding of the functioning and remodeling tricuspid valve in both the healthy and pathophysiological states.