This article provides Abaqus input files and user subroutines for performing finite element simulations of the tricuspid heart valve with an idealized geometry. Additional post-processing steps to obtain a ParaView visualization file (*.vtk) of the deformed geometry are also provided to allow the readers to use the included ParaView state file (*.pvsm) for customizable visualization and evaluation of the simulation results. We expect this first-of-its-kind in-silico benchmark dataset will facilitate user-friendly simulations considering material nonlinearity, leaflet-to-leaflet contact, and large deformations. Additionally, the information included herein can be used to rapidly evaluate other novel in-silico approaches developed for simulating cardiac valve function. The benchmark can be expanded to consider more complex features of the tricuspid valve function, such as the dynamic annulus motion or the time-varying transvalvular pressure. Interested readers are referred to the companion article (Johnson et al., 2021) for an example application of this in-silico tool for isogeometric analysis of tricuspid valves.

Data-driven modeling directly utilizes experimental data with machine learning techniques to predict a materials 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.

Extensive biaxial mechanical testing of the atrioventricular heart valve leaflets can be utilized to derive optimal parameters used in constitutive models, which provide a mathematical representation of the mechanical function of those structures. This presented biaxial mechanical testing protocol involves (i) tissue acquisition, (ii) the preparation of tissue specimens, (iii) biaxial mechanical testing, and (iv) postprocessing of the acquired data. First, tissue acquisition requires obtaining porcine or ovine hearts from a local Food and Drug Administration-approved abattoir for later dissection to retrieve the valve leaflets. Second, tissue preparation requires using tissue specimen cutters on the leaflet tissue to extract a clear zone for testing. Third, biaxial mechanical testing of the leaflet specimen requires the use of a commercial biaxial mechanical tester, which consists of force-controlled, displacement-controlled, and stress-relaxation testing protocols to characterize the leaflet tissues mechanical properties. Finally, post-processing requires the use of data image correlation techniques and force and displacement readings to summarize the tissues mechanical behaviors in response to external loading. In general, results from biaxial testing demonstrate that the leaflet tissues yield a nonlinear, anisotropic mechanical response. The presented biaxial testing procedure is advantageous to other methods since the method presented here allows for a more comprehensive characterization of the valve leaflet tissue under one unified testing scheme, as opposed to separate testing protocols on different tissue specimens. The proposed testing method has its limitations in that shear stress is potentially present in the tissue sample. However, any potential shear is presumed negligible.

A variety of constitutive models have been developed for soft tissue mechanics. However, there is no established criterion to select a suitable model for a specific application. Although the model that best fits the experimental data can be deemed the most suitable model, this practice often can be insufficient given the inter-sample variability of experimental observations. Herein, we present a Bayesian approach to calculate the relative probabilities of constitutive models based on biaxial mechanical testing of tissue samples. Forty-six samples of porcine aortic valve tissue were tested using a biaxial stretching setup. For each sample, seven ratios of stresses along and perpendicular to the fiber direction were applied. The probabilities of eight invariant-based constitutive models were calculated based on the experimental data using the proposed model selection framework. The calculated probabilities showed that, out of the considered models and based on the information available through the utilized experimental dataset, the May-Newman model was the most probable model for the porcine aortic valve data. When the samples were further grouped into different cusp types, the May-Newman model remained the most probable for the left- and right-coronary cusps, whereas for non-coronary cusps two models were found to be equally probable: the Lee-Sacks model and the May-Newman model. This difference between cusp types was found to be associated with the first principal component analysis (PCA) mode, where this modes amplitudes of the non-coronary and right-coronary cusps were found to be significantly different. Our results show that a PCA-based statistical model can capture significant variations in the mechanical properties of soft tissues. The presented framework is applicable to other tissue types, and has the potential to provide a structured and rational way of making simulations population-based.

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.

Valvular heart diseases are complex disorders, varying in pathophysiological mechanism and affected valve components. Understanding the effects of these diseases on valve functionality requires a thorough characterization of the mechanics and structure of the healthy heart valves. In this study, we performed biaxial mechanical experiments with extensive testing protocols to examine the mechanical behaviors of the mitral valve and tricuspid valve leaflets. We also investigated the effect of loading rate, testing temperatures, species (porcine versus ovine hearts), and age (juvenile vs adult ovine hearts) on the mechanical responses of the leaflet tissues. In addition, we evaluated the structure of chordae tendineae within each valve and performed histological analysis on each atrioventricular leaflet. We found all tissues displayed a characteristic nonlinear anisotropic mechanical response, with radial stretches on average 30.7% higher than circumferential stretches under equibiaxial physiological loading. Tissue mechanical responses showed consistent mechanical stiffening in response to increased loading rate and minor temperature dependence in all five atrioventricular heart valve leaflets. Moreover, our anatomical study revealed similar chordae quantities in the porcine mitral (30.5 ± 1.43 chords) and tricuspid valves (35.3 ± 2.45 chords) but significantly more chordae in the porcine than the ovine valves (p < 0.010). Our histological analyses quantified the relative thicknesses of the four distinct morphological layers in each leaflet. This study provides a comprehensive database of the mechanics and structure of the atrioventricular valves, which will be beneficial to development of subject-specific atrioventricular valve constitutive models and toward multi-scale biomechanical investigations of heart valve function to improve valvular disease treatments.

Approximately 1.6 million patients in the United States are affected by tricuspid valve regurgitation, which occurs when the tricuspid valve does not close properly to prevent backward blood flow into the right atrium. Despite its critical role in proper cardiac function, the tricuspid valve has received limited research attention compared to the mitral and aortic valves on the left side of the heart. As a result, proper valvular function and the pathologies that may cause dysfunction remain poorly understood. To promote further investigations of the biomechanical behavior and response of the tricuspid valve, this work establishes a parameter-based approach that provides a template for tricuspid valve modeling and simulation. The proposed tricuspid valve parameterization presents a comprehensive description of the leaflets and the complex chordae tendineae for capturing the typical three-cusp structural deformation observed from medical data. This simulation framework develops a practical procedure for modeling tricuspid valves and offers a robust, flexible approach to analyze the performance and effectiveness of various valve configurations using isogeometric analysis. The proposed methods also establish a baseline to examine the tricuspid valves structural deformation, perform future investigations of native valve configurations under healthy and disease conditions, and optimize prosthetic valve designs.

Current clinical assessment of functional tricuspid valve regurgitation relies on metrics quantified from medical imaging modalities. Although these clinical methodologies are generally successful, the lack of detailed information about the mechanical environment of the valve presents inherent challenges for assessing tricuspid valve regurgitation. In the present study, we have developed a finite element-based in silico model of one porcine tricuspid valve (TV) geometry to investigate how various pathological conditions affect the overall biomechanical function of the TV. There were three primary observations from our results. Firstly, the results of the papillary muscle (PM) displacement study scenario indicated more pronounced changes in the TV biomechanical function. Secondly, compared to uniform annulus dilation, nonuniform dilation scenario induced more evident changes in the von Mises stresses (83.8-125.3 kPa vs 65.1-84.0 kPa) and the Green-Lagrange strains (0.52-0.58 vs 0.47-0.53) for the three TV leaflets. Finally, results from the pulmonary hypertension study scenario showed opposite trends compared to the PM displacement and annulus dilation scenarios. Furthermore, various chordae rupture scenarios were simulated, and the results showed that the chordae tendineae attached to the TV anterior and septal leaflets may be more critical to proper TV function. This in silico modeling-based study has provided a deeper insight into the tricuspid valve pathologies that may be useful, with moderate extensions, for guiding clinical decisions. NOVELTY STATEMENT: The novelties of the research are summarized below: A comprehensive in silico pilot study of how isolated functional tricuspid regurgitation pathologies and ruptured chordae tendineae would alter the tricuspid valve function; An extensive analysis of the tricuspid valve function, including mechanical quantities (eg, the von Mises stress and the Green-Lagrange strain) and clinically-relevant geometry metrics (eg, the tenting area and the coaptation height); and A developed computational modeling pipeline that can be extended to evaluate patient-specific tricuspid valve geometries and enhance the current clinical diagnosis and treatment of tricuspid regurgitation.

Intracranial aneurysms (ICAs) are focal dilatations that imply a weakening of the brain artery. Incidental rupture of an ICA is increasingly responsible for significant mortality and morbidity in the Americans aging population. Previous studies have quantified the pressure-volume characteristics, uniaxial mechanical properties, and morphological features of human aneurysms. In this pilot study, for the first time, we comprehensively quantified the mechanical, collagen fiber microstructural, and morphological properties of one resected human posterior inferior cerebellar artery aneurysm. The tissue from the dome of a right posterior inferior cerebral aneurysm was first mechanically characterized using biaxial tension and stress relaxation tests. Then, the load-dependent collagen fiber architecture of the aneurysm tissue was quantified using an in-house polarized spatial frequency domain imaging system. Finally, optical coherence tomography and histological procedures were used to quantify the tissues microstructural morphology. Mechanically, the tissue was shown to exhibit hysteresis, a nonlinear stress-strain response, and material anisotropy. Moreover, the unloaded collagen fiber architecture of the tissue was predominantly aligned with the testing Y-direction and rotated towards the X-direction under increasing equibiaxial loading. Furthermore, our histological analysis showed a considerable damage to the morphological integrity of the tissue, including lack of elastin, intimal thickening, and calcium deposition. This new unified characterization framework can be extended to better understand the mechanics-microstructure interrelationship of aneurysm tissues at different time points of the formation or growth. Such specimen-specific information is anticipated to provide valuable insight that may improve our current understanding of aneurysm growth and rupture potential.

Coronary atherosclerosis is the main cause of death worldwide. Advancing the understanding of coronary microstructure-based mechanics is fundamental for the development of therapeutic tools and surgical procedures. Although the passive biaxial properties of the coronary arteries have been extensively explored, their regional differences and the relationship between tissue microstructure and mechanics have not been fully characterized. In this study, we characterized the passive biaxial mechanical properties and microstructural properties of the proximal, medial, and distal regions of the porcine left anterior descending artery (LADA). We also attempted to relate the biaxial stress-stretch response of the LADA and its respective birefringent responses to the polarized light for obtaining information about the load-dependent microstructural variations. We found that the LADA extensibility is reduced in the proximal-to-distal direction and that the medial region exhibits more heterogeneous mechanical behavior than the other two regions. We have also observed highly dynamic microstructural behavior where fiber families realign themselves depending on loading. In addition, we found that the microstructure of the distal region exhibited highly aligned fibers along the longitudinal axis of the artery. To verify this microstructural feature, we imaged the LADA specimens with multi-photon microscopy and observed that the adventitia microstructure transitioned from a random fiber network in the proximal region to highly aligned fibers in the distal region. Our findings could offer new perspectives for understanding coronary mechanics and aid in the development of tissue-engineered vascular grafts, which are currently limited due to their mismatch with native tissue in terms of mechanical properties and microstructural features. STATEMENT OF SIGNIFICANCE: The tissue biomechanics of coronary arteries is fundamental for the development of revascularization techniques such as coronary artery bypass. These therapeutics require a deep understanding of arterial mechanics, microstructure, and mechanobiology to prevent graft failure and reoperation. The present study characterizes the unique regional mechanical and microstructural properties of the porcine left anterior descending artery using biaxial testing, polarized-light imaging, and confocal microscopy. This comprehensive characterization provides an improved understanding of the collagen/elastin architecture in response to mechanical loads using a region-specific approach. The unique tissue properties obtained from this study will provide guidance for the selection of anastomotic sites in coronary artery bypass grafting and for the design of tissue-engineered vascular grafts.