Simulating the time evolving geometry, mechanical properties, and fibrous structure of bioprosthetic heart valve leaflets under cyclic loading

Identifying heterogeneous micromechanical properties of biological tissues via physics-informed neural networks

The heterogeneous micromechanical properties of biological tissues have profound implications across diverse medical and engineering domains. However, identifying the full-field heterogeneous elastic properties of soft materials using traditional computational and engineering approaches is fundamentally challenging due to difficulties in estimating local stress fields. Recently, there has been a growing interest in using data-driven models to learn full-field mechanical responses such as displacement and strain from experimental or synthetic data. However, research studies on inferring the full-field elastic properties of materials, a more challenging problem, are scarce, particularly for large deformation, hyperelastic materials. Here, we propose a physics-informed machine learning approach to identify the elastic modulus distribution in nonlinear, large deformation hyperelastic materials. We evaluate the prediction accuracies and computational efficiency of physics-informed neural networks (PINNs) on inferring the heterogeneous material parameter maps across three nonlinear materials with structural complexity that closely resemble real tissue patterns, such as brain tissue and tricuspid valve tissue. Our improved PINN architecture accurately estimates the full-field elastic properties of three hyperelastic constitutive models, with relative errors of less than 5% across all examples. This research has significant potential for advancing our understanding of micromechanical behaviors in biological materials, impacting future innovations in engineering and medicine.

Influence of Polymer Stiffness and Geometric Design on Fluid Mechanics in Tissue-Engineered Pulmonary Valve Scaffolds

There is still much unknown about the fluid mechanical response to cardiac valve scaffolds, even as their implementation in the clinic is on the horizon. Specifically, while degradable polymer valve scaffolds are currently being tested in the pulmonary valve position, their material and mechanical properties have not been fully elucidated. Optimizing these properties are important determinants not only of acute function, but long-term remodeling prospects. This study aimed to characterize fluid profiles downstream of electrospun valve scaffolds under dynamic pulmonary conditions. Valve scaffold design was changed by either blending poly(carbonate urethane) urea (PCUU) with poly(ε-caprolactone) (PCL) to modulate material stiffness or by changing the geometric design of the valve scaffolds. Specifically, two designs were utilized: one modeled after a clinically used bioprosthetic valve design (termed Mk1 design), and another using a geometrically "optimized" design (termed Mk2) based on anatomical data. Particle image velocimetry results showed that material stiffness only had a mild impact on fluid mechanics, measured by velocity magnitude, vorticity, viscous shear stress, Reynolds shear stress, and turbulent kinetic energy. However, comparing the two geometric designs yielded a much greater impact, with the Mk2 valve groups containing the highest PCUU/PCL ratio demonstrating the overall best performance. This report highlights the easily manipulable design features of polymeric valve scaffolds and demonstrates their relative significance for valve function.

Current progress toward isogeometric modeling of the heart biophysics

In this paper, we review a powerful methodology to solve complex numerical simulations, known as isogeometric analysis, with a focus on applications to the biophysical modeling of the heart. We focus on the hemodynamics, modeling of the valves, cardiac tissue mechanics, and on the simulation of medical devices and treatments. For every topic, we provide an overview of the methods employed to solve the specific numerical issue entailed by the simulation. We try to cover the complete process, starting from the creation of the geometrical model up to the analysis and post-processing, highlighting the advantages and disadvantages of the methodology.

Cardiac valve scaffold design: Implications of material properties and geometric configuration on performance and mechanics

Development of tissue engineered scaffolds for cardiac valve replacement is nearing clinical translation. While much work has been done to characterize mechanical behavior of native and bioprosthetic valves, and incorporate those data into models improving valve design, similar work for degradable valve scaffolds is lacking. This is particularly important given the implications mechanics have on short-term survival and long-term remodeling. As such, this study aimed to characterize spatially-resolved strain profiles on the leaflets of degradable polymeric valve scaffolds, manipulating common design features such as material stiffness by blending poly(carbonate urethane)urea with stiffer polymers, and geometric configuration, modeled after either a clinically-used valve design (Mk1 design) or an anatomically "optimized" design (Mk2 design). It was shown that material stiffness plays a significant role in overall valve performance, with the stiffest valve groups showing asymmetric and incomplete opening during systole. However, the geometric configuration had a significantly greater effect on valve performance as well as strain magnitude and distribution. Major findings in the strain maps included systolic strains having overall higher strain magnitudes than diastole, and peak radial-direction strain concentrations in the base region of Mk1 valves during systole, with a significant mitigation of radial strain in Mk2 valves. The high tunability of tissue engineered scaffolds is a great advantage for valve design, and the results reported here indicate that design parameters have significant and unequal impact on valve performance and mechanics.

Functional mechanical behavior of the murine pulmonary heart valve

Genetically modified mouse models provide a versatile and efficient platform to extend our understanding of the underlying disease processes and evaluate potential treatments for congenital heart valve diseases. However, applications have been limited to the gene and molecular levels due to the small size of murine heart valves, which prohibits the use of standard mechanical evaluation and in vivo imaging methods. We have developed an integrated imaging/computational mechanics approach to evaluate, for the first time, the functional mechanical behavior of the murine pulmonary heart valve (mPV). We utilized extant mPV high resolution µCT images of 1-year-old healthy C57BL/6J mice, with mPVs loaded to 0, 10, 20 or 30 mmHg then chemically fixed to preserve their shape. Individual mPV leaflets and annular boundaries were segmented and key geometric quantities of interest defined and quantified. The resulting observed inter-valve variations were small and consistent at each TVP level. This allowed us to develop a high fidelity NURBS-based geometric model. From the resultant individual mPV geometries, we developed a mPV shape-evolving geometric model (SEGM) that accurately represented mPV shape changes as a continuous function of transvalvular pressure. The SEGM was then integrated into an isogeometric finite element based inverse model that estimated the individual leaflet and regional mPV mechanical behaviors. We demonstrated that the mPV leaflet mechanical behaviors were highly anisotropic and nonlinear, with substantial leaflet and regional variations. We also observed the presence of strong axial mechanical coupling, suggesting the important role of the underlying collagen fiber architecture in the mPV. When compared to larger mammalian species, the mPV exhibited substantially different mechanical behaviors. Thus, while qualitatively similar, the mPV exhibited important functional differences that will need to accounted for in murine heart valve studies. The results of this novel study will allow detailed murine tissue and organ level investigations of semi-lunar heart valve diseases.

Biomechanical analysis of novel leaflet geometries for bioprosthetic valves

Objectives

Although bioprosthetic valves have excellent hemodynamic properties and can eliminate the need for lifelong anticoagulation therapy, these devices are associated with high rates of reoperation and limited durability. Although there are many distinct bioprosthesis designs, all bioprosthetic valves have historically featured a trileaflet pattern. This in silico study examines the biomechanical effect of modulating the number of leaflets in a bioprosthetic valve.

Methods

Bioprosthetic valves with 2 to 6 leaflets were designed in Fusion 360 using quadratic spline geometry. Leaflets were modeled with standard mechanical parameters for fixed bovine pericardial tissue. A mesh of each design was structurally evaluated using finite element analysis software Abaqus CAE. Maximum von Mises stresses during valve closure were assessed for each leaflet geometry in both the aortic and mitral position.

Results

Computational analysis demonstrated that increasing the number of leaflets is associated with reduction in leaflet stresses. Compared with the standard trileaflet design, a quadrileaflet pattern reduces leaflet maximum von Mises stresses by 36% in the aortic position and 38% in the mitral position. Maximum stress was inversely proportional to the square of the leaflet quantity. Surface area increased linearly and central leakage increased quadratically with leaflet quantity.

Conclusions

A quadrileaflet pattern was found to reduce leaflet stresses while limiting increases in central leakage and surface area. These findings suggest that modulating the number of leaflets can allow for optimization of the current bioprosthetic valve design, which may translate to more durable valve replacement bioprostheses.

Mechanical behaviors of high-strength fabric composite membrane designed for cardiac valve prosthesis replacement

Bovine pericardium has been commonly used as leaflets in cardiac valve prosthesis replacement for decades because of its good short-term hemocompatibility and hemodynamic performance. However, fatigue, abrasion, permanent deformation, calcification, and many other failure modes have been reported as well. The degradation of the performance will have a serious impact on the function of valve prostheses, posing a risk to the patient's health. This study aimed to introduce a flexible fabric composite with better mechanical performance such that it can be employed as a substitute material for bioprosthetic valve leaflets. This composite has a multilayered thin film structure made of ultrahigh molecular weight polyethylene (UHMWPE) fabric and thermoplastic polyurethane (TPU) membranes. The mechanical properties of three specifications with different design parameters were tested. The tensile strength, shear behavior, tear resistance, and bending stiffness of the composites were characterized and compared to those of bovine pericardium. A constitutive model was also established to describe the composites' mechanical behaviors and predict their strength. According to the results of the tests, the composite could maintain a flexible bending stiffness with high in-plane tensile strength and tear strength. Therefore, bioprosthetic valve made of this substitute material can withstand harsher loads in the blood flow environment than those made of bovine pericardium. Moreover, all these test results and constitutive models can be used in future research to evaluate hemodynamic performance and clinical applications of fabric composite valve prostheses.

Simulation of Mitral Valve Plasticity in Response to Myocardial Infarction

Left ventricular myocardial infarction (MI) has broad and debilitating effects on cardiac function. In many cases, MI leads to ischemic mitral regurgitation (IMR), a condition characterized by incompetency of the mitral valve (MV). IMR has many deleterious effects as well as a high mortality rate. While various clinical treatments for IMR exist, success of these procedures remains limited, in large part because IMR dramatically alters the geometry and function of the MV in ways that are currently not well understood. Previous investigations of post-MI MV remodeling have elucidated that MV tissues have a significant ability to undergo a form of permanent inelastic deformations in the first phase of the post-MI period. These changes appear to be attributable to the altered loading and boundary conditions on the MV itself, as opposed to an independent pathophysiological process. Mechanistically, these results suggest that the MV mostly responds passively to MI during the first 8 weeks post-MI by undergoing a permanent deformation. In the present study, we developed the first computational model of this post-MI MV remodeling process, which we term "mitral valve plasticity." Integrating methodologies and insights from previous studies of in vivo ovine MV function, image-based patient-specific model development, and post-MI MV adaptation, we constructed a representative geometric model of a pre-MI MV. We then performed finite element simulations of the entire MV apparatus under time-dependent boundary conditions and accounting for changes to material properties equivalent to those observed 0-8 weeks post-MI. Our results suggest that during this initial period of adaptation, the MV response to MI can be accurately modeled using a soft tissue plasticity approach, similar to permanent set frameworks that have been applied previously in the context of exogenously crosslinked tissues.

Neural Network Approaches for Soft Biological Tissue and Organ Simulations

Given the functional complexities of soft tissues and organs, it is clear that computational simulations are critical in their understanding and for the rational basis for the development of therapies and replacements. A key aspect of such simulations is accounting for their complex, nonlinear, anisotropic mechanical behaviors. While soft tissue material models have developed to the point of high fidelity, in-silico implementation is typically done using the finite element (FE) method, which remains impractically slow for translational clinical time frames. As a potential path toward addressing the development of high fidelity simulations capable of performing in clinically relevant time frames, we review the use of neural networks (NN) for soft tissue and organ simulation using two approaches. In the first approach, we show how a NN can learn the responses for a detailed meso-structural soft tissue material model. The NN material model not only reproduced the full anisotropic mechanical responses but also demonstrated a considerable efficiency improvement, as it was trained over a range of realizable fibrous structures. In the second approach, we go a step further with the use of a physics-based surrogate model to directly learn the displacement field solution without the need for raw training data or FE simulation datasets. In this approach we utilize a finite element mesh to define the domain and perform the necessary integrations, but not the finite element method (FEM) itself. We demonstrate with this approach, termed neural network finite element (NNFE), results in a trained NNFE model with excellent agreement with the corresponding "ground truth" FE solutions over the entire physiological deformation range on a cuboidal myocardium specimen. More importantly, the NNFE approach provided a significantly decreased computational time for a range of finite element mesh sizes. Specifically, as the FE mesh size increased from 2744 to 175,615 elements, the NNFE computational time increased from 0.1108 s to 0.1393 s, while the "ground truth" FE model increased from 4.541 s to 719.9 s, with the same effective accuracy. These results suggest that NNFE run times are significantly reduced compared with the traditional large-deformation-based finite element solution methods. We then show how a nonuniform rational B-splines (NURBS)-based approach can be directly integrated into the NNFE approach as a means to handle real organ geometries. While these and related approaches are in their early stages, they offer a method to perform complex organ-level simulations in clinically relevant time frames without compromising accuracy.