Dynamic and fluid-structure interaction simulations of bioprosthetic heart valves using parametric design with T-splines and Fung-type material models

Computational construction and design optimization of a novel tri-tube heart valve

A finite-element-based algorithm for the in silico construction of a novel tri-tube heart valve was developed to facilitate optimization of the leaflet geometry. An anisotropic hyperelastic model fitted to high-strain rate planar equibiaxial tension and compression data was used to approximate the nonlinear and anisotropic material behavior of biologically-engineered tubes and simulate valve closure under steady back pressure and steady forward flow. Four metrics were considered to evaluate valve performance in simulated closure: coaptation area, regurgitation area, pinwheel index, and prolapse area. Response surfaces revealed competing objectives between metrics for a valve of target 24 mm diameter in terms of two design parameters, tube diameter and leaflet height. A multi-objective genetic algorithm determined an intermediate tube diameter and leaflet height (16 mm and 11 mm, respectively) of the design space as optimal. Additionally, steady flow simulations were performed using two-way fluid-structure interaction with selected designs to examine washout behind leaflets with particle tracking. One design close to the optimal point for valve closure indicated washout for particles initially distributed behind leaflets. Though comprehensive valve design optimization requires flow analysis over multiple valve cycles to capture all effects associated with flow, this methodology based on diastolic state geometry optimization followed by steady washout analysis reduces the space of design variables for further optimization.

Homogenized multiscale modelling of an electrically active double poroelastic material representing the myocardium

In this work, we present the derivation of a novel model for the myocardium that incorporates the underlying poroelastic nature of the material constituents as well as the electrical conductivity. The myocardium has a microstructure consisting of a poroelastic extracellular matrix with embedded poroelastic myocytes, i.e. a double poroelastic material. Due to the sharp length scale separation that exists between the microscale, where the individual myocytes are clearly resolved from the surrounding matrix, and the length of the entire heart muscle, we can apply the asymptotic homogenization technique. The novel PDE model accounts for the difference in the electric potentials, elastic properties as well as the differences in the hydraulic conductivities at different points in the microstructure. The differences in these properties are encoded in the coefficients and are to be computed by solving differential cell problems arising when applying the asymptotic homogenization technique. We present a numerical analysis of the obtained Biot's modulus, Young's moduli as well as shears and the effective electrical activity. By investigating the poroelastic and electrical nature of the myocardium in one model, we can understand how the differences in elastic displacements between the extracellular matrix and the myocytes affect mechanotransduction and the influence of disease.

Algorithmic Generation of Parameterized Geometric Models of the Aortic Valve and Left Ventricle

Simulating the cardiac valves is one of the most complex tasks in cardiovascular modeling. As fluid-structure interaction simulations are highly computationally demanding, machine-learning techniques can be considered a good alternative. Nevertheless, it is necessary to design many aortic valve geometries to generate a training set. A method for the design of a synthetic database of geometric models is presented in this study. We suggest using synthetic geometries that enable the development of several aortic valve and left ventricular models in a range of sizes and shapes. In particular, we developed 22 variations of left ventricular geometries, including one original model, seven models with varying wall thicknesses, seven models with varying heights, and seven models with varying shapes. To guarantee anatomical accuracy and physiologically acceptable fluid volumes, these models were verified using actual patient data. Numerical simulations of left ventricle contraction and aortic valve leaflet opening/closing were performed to evaluate the electro-physiological potential distribution in the left ventricle and wall shear stress distribution in aortic valve leaflets. The proposed synthetic database aims to increase the predictive power of machine-learning models in cardiovascular research and, eventually, improve patient outcomes after aortic valve surgery.

Computational methods for biofabrication in tissue engineering and regenerative medicine - a literature review

This literature review rigorously examines the growing scientific interest in computational methods for Tissue Engineering and Regenerative Medicine biofabrication, a leading-edge area in biomedical innovation, emphasizing the need for accurate, multi-stage, and multi-component biofabrication process models. The paper presents a comprehensive bibliometric and contextual analysis, followed by a literature review, to shed light on the vast potential of computational methods in this domain. It reveals that most existing methods focus on single biofabrication process stages and components, and there is a significant gap in approaches that utilize accurate models encompassing both biological and technological aspects. This analysis underscores the indispensable role of these methods in understanding and effectively manipulating complex biological systems and the necessity for developing computational methods that span multiple stages and components. The review concludes that such comprehensive computational methods are essential for developing innovative and efficient Tissue Engineering and Regenerative Medicine biofabrication solutions, driving forward advancements in this dynamic and evolving field.

Nature of aortic annulus: Influence of annulus dynamic on the aortic valve hemodynamics

Accurate imaging reports of the aortic valve indicate that the diameter of the aortic annulus changes regularly during a cardiac cycle. Most of these studies aim to demonstrate the proper method for estimating the aortic annulus diameter before performing TAVR surgery, revealing that the aortic annulus is dynamic and not constant throughout the cardiac cycle. This raises the question of how fixing the aortic annulus might affect valve function, which is a question that still needs to be addressed. Therefore, the present study seeks to address this question and elucidate the dynamic impact of the aortic annulus on aortic valve hemodynamics. Two computational models based on this hypothesis were created and solved, and then their results were compared. Both models are identical, except for the intrinsic dynamic nature of the aortic annulus. One model consists of the dynamic behavior, and the other simulates a fixed annulus, resembling the effect of a TAVR operation, SAVR, or any phenomenon that eliminates the dynamic nature of the annulus. Our research findings indicate that the dynamic nature of the annulus enhances blood flow (+2.7 %), increases mean velocity (+11.9) and kinetic energy density (+34 %), prolongs momentum retention during systole, stabilizes the flow jet at the end of systole, reduces the required pressure to keep the leaflets open (-40.9 % at 0.3s), and sustains ventricular pressure superiority (+9.4 %) over the aorta for a longer duration (+17.7 % of systole), a crucial factor in preventing backflow during aortic valve closure. Based on these results, more attention should be paid to the dynamic nature of the annulus.

Effect of bioprosthetic leaflet anisotropy on stent dynamics of Transcatheter Aortic Valve Replacement devices

The assessment of stent fatigue in Transcatheter Aortic Valve Replacement (TAVR) systems is critical for the design of next-generation devices, both in vitro and in vivo. The mechanical properties of the bioprosthetic heart valves (BHVs) have a significant impact on the fatigue life of the metallic stent and thus must be taken into consideration when evaluating new TAVR device designs. This study aims to investigate the relationship between BHV anisotropic behaviour and the asymmetric deflections of the stent frame observed during in vitro testing. An explicit dynamics finite element model of the nitinol stent with attached bioprosthetic valve leaflets was developed to evaluate the deflections of the TAVR device under haemodynamic loading. Our results demonstrate that pericardium behaviour plays a dominant role in determining stent frame deflection. The anisotropic behaviour of the leaflets, resulting from collagen fibre orientation, affects the extent of deflection encountered by each commissure of the frame. This leads to asymmetric variation in frame deflection that can influence the overall fatigue life of the nitinol stent. This study highlights the importance of considering both the flexible nature of the metallic stent as well as the leaflet anisotropic behaviour in the design and fatigue assessment of TAVR systems.

Overset meshing in combination with novel blended weak-strong fluid-structure interactions for simulations of a translating valve in series with a second valve

Mechanical circulatory support (MCS) devices can bridge the gap to transplant whilst awaiting a viable donor heart. The Realheart Total Artificial Heart is a novel positive-displacement MCS that generates pulsatile flow via bileaflet mechanical valves. This study developed a combined computational fluid dynamics and fluid-structure interaction (FSI) methodology for simulating positive displacement bileaflet valves. Overset meshing discretised the fluid domain, and a blended weak-strong coupling FSI algorithm was combined with variable time-stepping. Four operating conditions of relevant stroke lengths and rates were assessed. The results demonstrated this modelling strategy is stable and efficient for modelling positive-displacement artificial hearts.

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.

Comparison of Immersed Boundary Simulations of Heart Valve Hemodynamics Against In Vitro 4D Flow MRI Data

The immersed boundary (IB) method is a mathematical framework for fluid-structure interaction problems (FSI) that was originally developed to simulate flows around heart valves. Direct comparison of FSI simulations around heart valves against experimental data is challenging, however, due to the difficulty of performing robust and effective simulations, the complications of modeling a specific physical experiment, and the need to acquire experimental data that is directly comparable to simulation data. Such comparators are a necessary precursor for further formal validation studies of FSI simulations involving heart valves. In this work, we performed physical experiments of flow through a pulmonary valve in an in vitro pulse duplicator, and measured the corresponding velocity field using 4D flow MRI (4-dimensional flow magnetic resonance imaging). We constructed a computer model of this pulmonary artery setup, including modeling valve geometry and material properties via a technique called design-based elasticity, and simulated flow through it with the IB method. The simulated flow fields showed excellent qualitative agreement with experiments, excellent agreement on integral metrics, and reasonable relative error in the entire flow domain and on slices of interest. These results illustrate how to construct a computational model of a physical experiment for use as a comparator.

The Impact of Left Ventricular Assist Device Outflow Graft Positioning on Aortic Hemodynamics: Improving Flow Dynamics to Mitigate Aortic Insufficiency

Heart failure is a global health concern with significant implications for healthcare systems. Left ventricular assist devices (LVADs) provide mechanical support for patients with severe heart failure. However, the placement of the LVAD outflow graft within the aorta has substantial implications for hemodynamics and can lead to aortic insufficiency during long-term support. This study employs computational fluid dynamics (CFD) simulations to investigate the impact of different LVAD outflow graft locations on aortic hemodynamics. The introduction of valve morphology within the aorta geometry allows for a more detailed analysis of hemodynamics at the aortic root. The results demonstrate that the formation of vortex rings and subsequent vortices during the high-velocity jet flow from the graft interacted with the aortic wall. Time-averaged wall shear stress (TAWSS) and oscillatory shear index (OSI) indicate that modification of the outflow graft location changes mechanical states within the aortic wall and aortic valve. Among the studied geometric factors, both the height and inclination angle of the LVAD outflow graft are important in controlling retrograde flow to the aortic root, while the azimuthal angle primarily determines the rotational direction of blood flow in the aortic arch. Thus, precise positioning of the LVAD outflow graft emerges as a critical factor in optimizing patient outcomes by improving the hemodynamic environment.

Perfect prosthetic heart valve: generative design with machine learning, modeling, and optimization

Majority of modern techniques for creating and optimizing the geometry of medical devices are based on a combination of computer-aided designs and the utility of the finite element method This approach, however, is limited by the number of geometries that can be investigated and by the time required for design optimization. To address this issue, we propose a generative design approach that combines machine learning (ML) methods and optimization algorithms. We evaluate eight different machine learning methods, including decision tree-based and boosting algorithms, neural networks, and ensembles. For optimal design, we investigate six state-of-the-art optimization algorithms, including Random Search, Tree-structured Parzen Estimator, CMA-ES-based algorithm, Nondominated Sorting Genetic Algorithm, Multiobjective Tree-structured Parzen Estimator, and Quasi-Monte Carlo Algorithm. In our study, we apply the proposed approach to study the generative design of a prosthetic heart valve (PHV). The design constraints of the prosthetic heart valve, including spatial requirements, materials, and manufacturing methods, are used as inputs, and the proposed approach produces a final design and a corresponding score to determine if the design is effective. Extensive testing leads to the conclusion that utilizing a combination of ensemble methods in conjunction with a Tree-structured Parzen Estimator or a Nondominated Sorting Genetic Algorithm is the most effective method in generating new designs with a relatively low error rate. Specifically, the Mean Absolute Percentage Error was found to be 11.8% and 10.2% for lumen and peak stress prediction respectively. Furthermore, it was observed that both optimization techniques result in design scores of approximately 95%. From both a scientific and applied perspective, this approach aims to select the most efficient geometry with given input parameters, which can then be prototyped and used for subsequent in vitro experiments. By proposing this approach, we believe it will replace or complement CAD-FEM-based modeling, thereby accelerating the design process and finding better designs within given constraints. The repository, which contains the essential components of the study, including curated source code, dataset, and trained models, is publicly available at https://github.com/ViacheslavDanilov/generative_design.

A contact model based on the coefficient of restitution for simulations of bio-prosthetic heart valves

A new general contact model is proposed for preventing inter-leaflet penetration of bio-prosthetic heart valves (BHV) at the end of the systole, which has the advantage of applying kinematic constraints directly and creating smooth free edges. At the end of each time step, the impenetrability constraints and momentum exchange between the impacting bodies are applied separately based on the coefficient of restitution. The contact method is implemented in a rotation-free, large deformation, and thin shell finite-element (FE) framework based on loop's subdivision surfaces. A nonlinear, anisotropic material model for a BHV is employed which uses Fung-elastic constitutive laws for in-plane and bending responses, respectively. The contact model is verified and validated against several benchmark problems. For a BHV-specific validation, the computed strains on different regions of a BHV under constant pressure are compared with experimentally measured data. Finally, dynamic simulations of BHV under physiological pressure waveform are performed for symmetrical and asymmetrical fiber orientations incorporating the new contact model and compared with the penalty contact method. The proposed contact model provides the coaptation area of a functioning BHV during the closing phase for both of the fiber orientations. Our results show that fiber orientation affects the dynamic of leaflets during the opening and closing phases. A swirling motion for the BHV with asymmetrical fiber orientation is observed, similar to experimental data. To include the fluid effects, fluid-structure interaction (FSI) simulation of the BHV is performed and compared to the dynamic results.

Analysis of the Effect of Thickness on the Performance of Polymeric Heart Valves

Polymeric heart valves (PHVs) are a promising and more affordable alternative to mechanical heart valves (MHVs) and bioprosthetic heart valves (BHVs). Materials with good durability and biocompatibility used for PHVs have always been the research focus in the field of prosthetic heart valves for many years, and leaflet thickness is a major design parameter for PHVs. The study aims to discuss the relationship between material properties and valve thickness, provided that the basic functions of PHVs are qualified. The fluid-structure interaction (FSI) approach was employed to obtain a more reliable solution of the effective orifice area (EOA), regurgitant fraction (RF), and stress and strain distribution of the valves with different thicknesses under three materials: Carbothane PC-3585A, xSIBS and SIBS-CNTs. This study demonstrates that the smaller elastic modulus of Carbothane PC-3585A allowed for a thicker valve (>0.3 mm) to be produced, while for materials with an elastic modulus higher than that of xSIBS (2.8 MPa), a thickness less than 0.2 mm would be a good attempt to meet the RF standard. What is more, when the elastic modulus is higher than 23.9 MPa, the thickness of the PHV is recommended to be 0.l-0.15 mm. Reducing the RF is one of the directions of PHV optimization in the future. Reducing the thickness and improving other design parameters are reliable means to reduce the RF for materials with high and low elastic modulus, respectively.

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.

Aortic Leaflet Stresses Are Substantially Lower Using Pulmonary Visceral Pleura Than Pericardial Tissue

Background: Porcine heart and bovine pericardium valves, which are collagen-based with relatively little elastin, have been broadly utilized to construct bioprosthetic heart valves (BHVs). With a larger proportion of elastin, the pulmonary visceral pleura (PVP) has greater elasticity and could potentially serve as an advantageous biomaterial for the construction/repair of BHVs. The question of how the aortic valve’s performance is affected by its bending rigidity has not been well studied.

Methods: Based on the stress–strain relationships of the pericardium and PVP determined by planar uni-axial tests, a three-dimensional (3D) computational fluid–structure interaction (FSI) framework is employed to numerically investigate the aortic valve’s performance by considering three different cases with Young’s modulus as follows: E=375, 750, and 1500 kPa, respectively.

Results: The stroke volumes are 112, 99.6, and 91.4 ml as Young’s modulus increases from 375 to 750 and 1500 kPa, respectively. Peak geometric opening area (GOA) values are 2.3, 2.2, and 2.0 cm² for E=375, 750, and 1500 kPa, respectively. The maximum value of the aortic leaflet stress is about 271 kPa for E=375 kPa, and it increases to about 383 and 540 kPa for E=750 and 1500 kPa in the belly region at the peak systole, while it reduces from 550 kPa to 450 and 400 kPa for E=375, 750, and 1500 kPa, respectively, at the instant of peak “water-hammer”.

Conclusion: A more compliant PVP aortic leaflet valve with a smaller Young’s modulus, E, has a higher cardiac output, larger GOA, and lower hemodynamic resistance. Most importantly, the aortic leaflet stresses are substantially lower in the belly region within the higher compliance PVP aortic valve tissue during the systole phase, even though some stress increase is also found during the fast-closing phase due to the “water-hammer” effect similar to that in the pericardial tissue. Future clinical studies will be conducted to test the hypothesis that the PVP-based valve leaflets with higher compliance will have lower fatigue or calcification rates due to the overall lower stress.

Improving transcatheter aortic valve interventional predictability via fluid-structure interaction modelling using patient-specific anatomy

Transcatheter aortic valve replacement (TAVR) is now a standard treatment for high-surgical-risk patients with severe aortic valve stenosis. TAVR is being explored for broader indications including degenerated bioprosthetic valves, bicuspid valves and for aortic valve (AV) insufficiency. It is, however, challenging to predict whether the chosen valve size, design or its orientation would produce the most-optimal haemodynamics in the patient. Here, we present a novel patient-specific evaluation framework to realistically predict the patient's AV performance with a high-fidelity fluid-structure interaction analysis that included the patient's left ventricle and ascending aorta (AAo). We retrospectively evaluated the pre- and post-TAVR dynamics of a patient who underwent a 23 mm TAVR and evaluated against the patient's virtually de-calcified AV serving as a hypothetical benchmark. Our model predictions were consistent with clinical data. Stenosed AV produced a turbulent flow during peak-systole, while aortic flow with TAVR and de-calcified AV were both in the laminar-to-turbulent transitional regime with an estimated fivefold reduction in viscous dissipation. For TAVR, dissipation was highest during early systole when valve deformation was the greatest, suggesting that an efficient valve opening may reduce energy loss. Our study demonstrates that such patient-specific modelling frameworks can be used to improve predictability and in the planning of AV interventions.

Effects of membrane and flexural stiffnesses on aortic valve dynamics: identifying the mechanics of leaflet flutter in thinner biological tissues

Valvular pathologies that induce deterioration in the aortic valve are a common cause of heart disease among aging populations. Although there are numerous available technologies to treat valvular conditions and replicate normal aortic function by replacing the diseased valve with a bioprosthetic implant, many of these devices face challenges in terms of long-term durability. One such phenomenon that may exacerbate valve deterioration and induce undesirable hemodynamic effects in the aorta is leaflet flutter, which is characterized by oscillatory motion in the biological tissues. While this behavior has been observed for thinner bioprosthetic valves, the specific underlying mechanics that lead to leaflet flutter have not previously been identified. This work proposes a computational approach to isolate the fundamental mechanics that induce leaflet flutter in thinner biological tissues during the cardiac cycle. The simulations in this work identify reduced flexural stiffness as the primary factor that contributes to increased leaflet flutter in thinner biological tissues, while decreased membrane stiffness and mass of the thinner tissues do not directly induce flutter in these valves. The results of this study provide an improved understanding of the mechanical tissue properties that contribute to flutter and offer significant insights into possible developments in the design of bioprosthetic tissues to account for and reduce the incidence of flutter.

Experimental and computational models for tissue-engineered heart valves: a narrative review

Valvular heart disease is currently a common problem which causes high morbidity and mortality worldwide. Prosthetic valve replacements are widely needed to correct narrowing or backflow through the valvular orifice. Compared to mechanical valves and biological valves, tissue-engineered heart valves can be an ideal substitute because they have a low risk of thromboembolism and calcification, and the potential for remodelling, regeneration, and growth. In order to test the performance of these heart valves, various animal models and other models are needed to optimise the structure and function of tissue-engineered heart valves, which may provide a potential mechanism responsible for substantial enhancement in tissue-engineered heart valves. Choosing the appropriate model for evaluating the performance of the tissue-engineered valve is important, as different models have their own advantages and disadvantages. In this review, we summarise the current state-of-the-art animal models, bioreactors, and computational simulation models with the aim of creating more strategies for better development of tissue-engineered heart valves. This review provides an overview of major factors that influence the selection and design of a model for tissue-engineered heart valve. Continued efforts in improving and testing models for valve regeneration remain crucial in basic science and translational researches. Future research should focus on finding the right animal model and developing better in vitro testing systems for tissue-engineered heart valve.

A design-based model of the aortic valve for fluid-structure interaction

This paper presents a new method for modeling the mechanics of the aortic valve and simulates its interaction with blood. As much as possible, the model construction is based on first principles, but such that the model is consistent with experimental observations. We require that tension in the leaflets must support a pressure, then derive a system of partial differential equations governing its mechanical equilibrium. The solution to these differential equations is referred to as the predicted loaded configuration; it includes the loaded leaflet geometry, fiber orientations and tensions needed to support the prescribed load. From this configuration, we derive a reference configuration and constitutive law. In fluid-structure interaction simulations with the immersed boundary method, the model seals reliably under physiological pressures and opens freely over multiple cardiac cycles. Further, model closure is robust to extreme hypo- and hypertensive pressures. Then, exploiting the unique features of this model construction, we conduct experiments on reference configurations, constitutive laws and gross morphology. These experiments suggest the following conclusions: (1) The loaded geometry, tensions and tangent moduli primarily determine model function. (2) Alterations to the reference configuration have little effect if the predicted loaded configuration is identical. (3) The leaflets must have sufficiently nonlinear material response to function over a variety of pressures. (4) Valve performance is highly sensitive to free edge length and leaflet height. These conclusions suggest appropriate gross morphology and material properties for the design of prosthetic aortic valves. In future studies, our aortic valve modeling framework can be used with patient-specific models of vascular or cardiac flow.

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

Currently, the most common replacement heart valve design is the 'bioprosthetic' heart valve (BHV), which has important advantages in that it does not require permanent anti-coagulation therapy, operates noiselessly, and has blood flow characteristics similar to the native valve. BHVs are typically fabricated from glutaraldehyde-crosslinked pericardial xenograft tissue biomaterials (XTBs) attached to a rigid, semi-flexible, or fully collapsible stent in the case of the increasingly popular transcutaneous aortic valve replacement (TAVR). While current TAVR assessments are positive, clinical results to date are generally limited to <2 years. Since TAVR leaflets are constructed using thinner XTBs, their mechanical demands are substantially greater than surgical BHV due to the increased stresses during in vivo operation, potentially resulting in decreased durability. Given the functional complexity of heart valve operation, in-silico predictive simulations clearly have potential to greatly improve the TAVR development process. As such simulations must start with accurate material models, we have developed a novel time-evolving constitutive model for pericardial xenograft tissue biomaterials (XTB) utilized in BHV (doi: 10.1016/j.jmbbm.2017.07.013). This model was able to simulate the observed tissue plasticity effects that occur in approximately in the first two years of in vivo function (50 million cycles). In the present work, we implemented this model into a complete simulation pipeline to predict the BHV time evolving geometry to 50 million cycles. The pipeline was implemented within an isogeometric finite element formulation that directly integrated our established BHV NURBS-based geometry (doi: 10.1007/s00466-015-1166-x). Simulations of successive loading cycles indicated continual changes in leaflet shape, as indicated by spatially varying increases in leaflet curvature. While the simulation model assumed an initial uniform fiber orientation distribution, anisotropic regional changes in leaflet tissue plastic strain induced a complex changes in regional fiber orientation. We have previously noted in our time-evolving constitutive model that the increases in collagen fiber recruitment with cyclic loading placed an upper bound on plastic strain levels. This effect was manifested by restricting further changes in leaflet geometry past 50 million cycles. Such phenomena was accurately captured in the valve-level simulations due to the use of a tissue-level structural-based modeling approach. Changes in basic leaflet dimensions agreed well with extant experimental studies. As a whole, the results of the present study indicate the complexity of BHV responses to cyclic loading, including changes in leaflet shape and internal fibrous structure. It should be noted that the later effect also influences changes in local mechanical behavior (i.e. changes in leaflet anisotropic tissue stress-strain relationship) due to internal fibrous structure resulting from plastic strains. Such mechanism-based simulations can help pave the way towards the application of sophisticated simulation technologies in the development of replacement heart valve technology.

Parameterization, geometric modeling, and isogeometric analysis of tricuspid valves

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 valve's structural deformation, perform future investigations of native valve configurations under healthy and disease conditions, and optimize prosthetic valve designs.

Radial Basis Functions Vector Fields Interpolation for Complex Fluid Structure Interaction Problems

Fluid structure interaction (FSI) is a complex phenomenon that in several applications cannot be neglected. Given its complexity and multi-disciplinarity the solution of FSI problems is difficult and time consuming, requiring not only the solution of the structural and fluid domains, but also the use of expensive numerical methods to couple the two physics and to properly update the numerical grid. Advanced mesh morphing can be used to embed into the fluid grid the vector fields resulting from structural calculations. The main advantage is that such embedding and the related computational costs occur only at initialization of the computation. A proper combination of embedded vector fields can be used to tackle steady and transient FSI problems by structural modes superposition, for the case of linear structures, or to impose a full non-linear displacement time history. Radial basis functions interpolation, a powerful and precise meshless tool, is used in this work to combine the vector fields and propagate their effect to the full fluid domain of interest. A review of industrial high fidelity FSI problems tackled by means of the proposed method and RBF is given for steady, transient, and non-linear transient FSI problems.

Isogeometric finite element-based simulation of the aortic heart valve: Integration of neural network structural material model and structural tensor fiber architecture representations

The functional complexity of native and replacement aortic heart valves (AVs) is well known, incorporating such physical phenomenons as time-varying non-linear anisotropic soft tissue mechanical behavior, geometric non-linearity, complex multi-surface time varying contact, and fluid-structure interactions to name a few. It is thus clear that computational simulations are critical in understanding AV function and for the rational basis for design of their replacements. However, such approaches continued to be limited by ad-hoc approaches for incorporating tissue fibrous structure, high-fidelity material models, and valve geometry. To this end, we developed an integrated tri-leaflet valve pipeline built upon an isogeometric analysis framework. A high-order structural tensor (HOST)-based method was developed for efficient storage and mapping the two-dimensional fiber structural data onto the valvular 3D geometry. We then developed a neural network (NN) material model that learned the responses of a detailed meso-structural model for exogenously cross-linked planar soft tissues. 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. Results of parametric simulations were then performed, as well as population-based bicuspid AV fiber structure, that demonstrated the efficiency and robustness of the present approach. In summary, the present approach that integrates HOST and NN material model provides an efficient computational analysis framework with increased physical and functional realism for the simulation of native and replacement tri-leaflet heart valves.

Computational investigation of left ventricular hemodynamics following bioprosthetic aortic and mitral valve replacement

The left ventricle of the heart is a fundamental structure in the human cardiac system that pumps oxygenated blood into the systemic circulation. Several valvular conditions can cause the aortic and mitral valves associated with the left ventricle to become severely diseased and require replacement. However, the clinical outcomes of such operations, specifically the postoperative ventricular hemodynamics of replacing both valves, are not well understood. This work uses computational fluid-structure interaction (FSI) to develop an improved understanding of this effect by modeling a left ventricle with the aortic and mitral valves replaced with bioprostheses. We use a hybrid Arbitrary Lagrangian-Eulerian/immersogeometric framework to accommodate the analysis of cardiac hemodynamics and heart valve structural mechanics in a moving fluid domain. The motion of the endocardium is obtained from a cardiac biomechanics simulation and provided as an input to the proposed numerical framework. The results from the simulations in this work indicate that the replacement of the native mitral valve with a tri-radially symmetric bioprosthesis dramatically changes the ventricular hemodynamics. Most significantly, the vortical motion in the left ventricle is found to reverse direction after mitral valve replacement. This study demonstrates that the proposed computational FSI framework is capable of simulating complex multiphysics problems and can provide an in-depth understanding of the cardiac mechanics.

A deep learning application to approximate the geometric orifice and coaptation areas of the polymeric heart valves under time - varying transvalvular pressure

Machine learning and deep learning frameworks have been presented as a substitute for lengthy computational analysis, such as finite element analysis, computational fluid dynamics, and fluid-structure interaction. In this study, our objective was to apply a deep learning framework to predict the geometric orifice (GOA) and the coaptation areas (CA) of the polymeric heart valves under the time-varying transvalvular pressure. 377 different valve geometries were generated by changing the control coordinates of the attachment and the belly curve. The GOA and the CA values were obtained at the maximum and the minimum transvalvular pressure, respectively. The results showed that the applied framework can accurately predict the GOA and the CA despite being trained with a relatively smaller data set. The presented framework can reduce the required time of the lengthy FE frameworks.

Cavitation Suppression of Bileaflet Mechanical Heart Valves

PURPOSE

Mechanical heart valves (MHVs) are widely used to replace diseased heart valves, but it may suffer from cavitation due to the rapid closing velocity of the leaflets, resulting in the damage of red blood cells and platelets. The aim of this study is to apply computational fluid dynamics (CFD) method to investigate the cavitation in bileaflets mechanical heart valves (BMHVs) and discuss the effects of the conduit and leaflet geometries on cavitation intensity.

METHODS

Firstly, CFD method together with moving-grid technology were applied and validated by comparing with experimental results obtained from other literature. Then the leaflets movement and the flow rate of BMHVs with different conduit geometries and leaflet geometries are compared. At last, the duration time of the saturated vapor pressure and the closing velocity of leaflets at the instant of valve closure were used to represent the cavitation intensity.

RESULTS

Larger closing velocity of leaflets at the instant of valve closure means higher cavitation intensity. For BMHVs with different conduit geometries, the conduit with Valsalva sinuses has the maximum cavitation intensity and the straight conduit has the minimum cavitation intensity, but the leaflets cannot reach the fully opened state in a straight conduit. For BMHVs with different leaflet geometries, in order to minimize the cavitation intensity, the leaflets are better to have a large thickness and a small rotational radius.

CONCLUSION

CFD method is a promising method to deal with cavitation in BMHVs, and the closing velocity of leaflets has the same trend with the cavitation intensity. By using CFD method, the effects of the conduit geometry and the leaflet geometry on cavitaion in BMHVs are found out.

Thinner biological tissues induce leaflet flutter in aortic heart valve replacements

Valvular heart disease has recently become an increasing public health concern due to the high prevalence of valve degeneration in aging populations. For patients with severely impacted aortic valves that require replacement, catheter-based bioprosthetic valve deployment offers a minimally invasive treatment option that eliminates many of the risks associated with surgical valve replacement. Although recent percutaneous device advancements have incorporated thinner, more flexible biological tissues to streamline safer deployment through catheters, the impact of such tissues in the complex, mechanically demanding, and highly dynamic valvular system remains poorly understood. The present work utilized a validated computational fluid-structure interaction approach to isolate the behavior of thinner, more compliant aortic valve tissues in a physiologically realistic system. This computational study identified and quantified significant leaflet flutter induced by the use of thinner tissues that initiated blood flow disturbances and oscillatory leaflet strains. The aortic flow and valvular dynamics associated with these thinner valvular tissues have not been previously identified and provide essential information that can significantly advance fundamental knowledge about the cardiac system and support future medical device innovation. Considering the risks associated with such observed flutter phenomena, including blood damage and accelerated leaflet deterioration, this study demonstrates the potentially serious impact of introducing thinner, more flexible tissues into the cardiac system.

Fluid-Structure Interaction Models of Bioprosthetic Heart Valve Dynamics in an Experimental Pulse Duplicator

Computer modeling and simulation is a powerful tool for assessing the performance of medical devices such as bioprosthetic heart valves (BHVs) that promises to accelerate device design and regulation. This study describes work to develop dynamic computer models of BHVs in the aortic test section of an experimental pulse-duplicator platform that is used in academia, industry, and regulatory agencies to assess BHV performance. These computational models are based on a hyperelastic finite element extension of the immersed boundary method for fluid-structure interaction (FSI). We focus on porcine tissue and bovine pericardial BHVs, which are commonly used in surgical valve replacement. We compare our numerical simulations to experimental data from two similar pulse duplicators, including a commercial ViVitro system and a custom platform related to the ViVitro pulse duplicator. Excellent agreement is demonstrated between the computational and experimental results for bulk flow rates, pressures, valve open areas, and the timing of valve opening and closure in conditions commonly used to assess BHV performance. In addition, reasonable agreement is demonstrated for quantitative measures of leaflet kinematics under these same conditions. This work represents a step towards the experimental validation of this FSI modeling platform for evaluating BHVs.

A partition of unity approach to fluid mechanics and fluid-structure interaction

For problems involving large deformations of thin structures, simulating fluid-structure interaction (FSI) remains a computationally expensive endeavour which continues to drive interest in the development of novel approaches. Overlapping domain techniques have been introduced as a way to combine the fluid-solid mesh conformity, seen in moving-mesh methods, without the need for mesh smoothing or re-meshing, which is a core characteristic of fixed mesh approaches. In this work, we introduce a novel overlapping domain method based on a partition of unity approach. Unified function spaces are defined as a weighted sum of fields given on two overlapping meshes. The method is shown to achieve optimal convergence rates and to be stable for steady-state Stokes, Navier-Stokes, and ALE Navier-Stokes problems. Finally, we present results for FSI in the case of 2D flow past an elastic beam simulation. These initial results point to the potential applicability of the method to a wide range of FSI applications, enabling boundary layer refinement and large deformations without the need for re-meshing or user-defined stabilization.

A Deep Learning Framework for Design and Analysis of Surgical Bioprosthetic Heart Valves

Bioprosthetic heart valves (BHVs) are commonly used as heart valve replacements but they are prone to fatigue failure; estimating their remaining life directly from medical images is difficult. Analyzing the valve performance can provide better guidance for personalized valve design. However, such analyses are often computationally intensive. In this work, we introduce the concept of deep learning (DL) based finite element analysis (DLFEA) to learn the deformation biomechanics of bioprosthetic aortic valves directly from simulations. The proposed DL framework can eliminate the time-consuming biomechanics simulations, while predicting valve deformations with the same fidelity. We present statistical results that demonstrate the high performance of the DLFEA framework and the applicability of the framework to predict bioprosthetic aortic valve deformations. With further development, such a tool can provide fast decision support for designing surgical bioprosthetic aortic valves. Ultimately, this framework could be extended to other BHVs and improve patient care.

Immersogeometric fluid-structure interaction modeling and simulation of transcatheter aortic valve replacement

The transcatheter aortic valve replacement (TAVR) has emerged as a minimally invasive alternative to surgical treatments of valvular heart disease. TAVR offers many advantages, however, the safe anchoring of the transcatheter heart valve (THV) in the patients anatomy is key to a successful procedure. In this paper, we develop and apply a novel immersogeometric fluid-structure interaction (FSI) framework for the modeling and simulation of the TAVR procedure to study the anchoring ability of the THV. To account for physiological realism, methods are proposed to model and couple the main components of the system, including the arterial wall, blood flow, valve leaflets, skirt, and frame. The THV is first crimped and deployed into an idealized ascending aorta. During the FSI simulation, the radial outward force and friction force between the aortic wall and the THV frame are examined over the entire cardiac cycle. The ratio between these two forces is computed and compared with the experimentally estimated coefficient of friction to study the likelihood of valve migration.

Mechanical considerations for polymeric heart valve development: Biomechanics, materials, design and manufacturing

The native human heart valve leaflet contains a layered microstructure comprising a hierarchical arrangement of collagen, elastin, proteoglycans and various cell types. Here, we review the various experimental methods that have been employed to probe this intricate microstructure and which attempt to elucidate the mechanisms that govern the leaflet's mechanical properties. These methods include uniaxial, biaxial, and flexural tests, coupled with microstructural characterization techniques such as small angle X-ray scattering (SAXS), small angle light scattering (SALS), and polarized light microscopy. These experiments have revealed complex elastic and viscoelastic mechanisms that are highly directional and dependent upon loading conditions and biochemistry. Of all engineering materials, polymers and polymer-based composites are best able to mimic the tissue-level mechanical behavior of the native leaflet. This similarity to native tissue permits the fabrication of polymeric valves with physiological flow patterns, reducing the risk of thrombosis compared to mechanical valves and in some cases surpassing the in vivo durability of bioprosthetic valves. Earlier work on polymeric valves simply assumed the mechanical properties of the polymer material to be linear elastic, while more recent studies have considered the full hyperelastic stress-strain response. These material models have been incorporated into computational models for the optimization of valve geometry, with the goal of minimizing internal stresses and improving durability. The latter portion of this review recounts these developments in polymeric heart valves, with a focus on mechanical testing of polymers, valve geometry, and manufacturing methods.

Mechanical and finite element evaluation of a bioprinted scaffold following recellularization in a rat subcutaneous model

Tissue engineered heart valves (TEHV) provide several advantages over currently available aortic heart valve replacements. Bioprinting provides a patient-specific means of developing a TEHV scaffold from imaging data, and the capability to embed the patient's own cells within the scaffold. In this work we investigated the remodeling capacity of a collagen-based bio-ink by implanting bioprinted disks in a rat subcutaneous model for 2, 4 and 12 weeks and evaluating the mechanical response using biaxial testing and subsequent finite element (FE) modeling. Samples explanted after 2 and 4 weeks showed inferior mechanical properties compared to native tissues while 12 week explants showed a mechanical response of similar magnitude but did not demonstrate the anisotropy present in native tissues. In the FE analysis, the model utilizing mechanical properties from samples explanted after 12 weeks showed the closest mechanical behavior to the native tissues. However, in diastole native tissues showed higher stress in the leaflet belly and lower strain at the commissures compared to 12 week explants, likely due to the anisotropy present in the native tissues. Thus, either further remodeling is required in situ in the aortic valve position or by in vitro preconditioning in an environment such as a bioreactor. Regardless, these results demonstrate the utility of FE analysis to optimize bioprinting process parameters for the most favorable in vivo mechanical performance.

Flow-Structure Interaction Simulations of the Aortic Heart Valve at Physiologic Conditions: The Role of Tissue Constitutive Model

The blood flow patterns in the region around the aortic valve depend on the geometry of the aorta and on the complex flow-structure interaction between the pulsatile flow and the valve leaflets. Consequently, the flow depends strongly on the constitutive properties of the tissue, which can be expected to vary between healthy and diseased heart valves or native and prosthetic valves. The main goal of this work is to qualitatively demonstrate that the choice of the constitutive model of the aortic valve is critical in analysis of heart hemodynamics. To accomplish that two different constitutive models were used in curvilinear immersed boundary-finite element-fluid-structure interaction (CURVIB-FE-FSI) method developed by Gilmanov et al. (2015, "A Numerical Approach for Simulating Fluid Structure Interaction of Flexible Thin Shells Undergoing Arbitrarily Large Deformations in Complex Domains," J. Comput. Phys., 300, pp. 814-843.) to simulate an aortic valve in an anatomic aorta at physiologic conditions. The two constitutive models are: (1) the Saint-Venant (StV) model and (2) the modified May-Newman&Yin (MNY) model. The MNY model is more general and includes nonlinear, anisotropic effects. It is appropriate to model the behavior of both prosthetic and biological tissue including native valves. Both models are employed to carry out FSI simulations of the same valve in the same aorta anatomy. The computed results reveal dramatic differences in both the vorticity dynamics in the aortic sinus and the wall shear-stress patterns on the aortic valve leaflets and underscore the importance of tissue constitutive models for clinically relevant simulations of aortic valves.

Computational modeling guides tissue-engineered heart valve design for long-term in vivo performance in a translational sheep model

Valvular heart disease is a major cause of morbidity and mortality worldwide. Current heart valve prostheses have considerable clinical limitations due to their artificial, nonliving nature without regenerative capacity. To overcome these limitations, heart valve tissue engineering (TE) aiming to develop living, native-like heart valves with self-repair, remodeling, and regeneration capacity has been suggested as next-generation technology. A major roadblock to clinically relevant, safe, and robust TE solutions has been the high complexity and variability inherent to bioengineering approaches that rely on cell-driven tissue remodeling. For heart valve TE, this has limited long-term performance in vivo because of uncontrolled tissue remodeling phenomena, such as valve leaflet shortening, which often translates into valve failure regardless of the bioengineering methodology used to develop the implant. We tested the hypothesis that integration of a computationally inspired heart valve design into our TE methodologies could guide tissue remodeling toward long-term functionality in tissue-engineered heart valves (TEHVs). In a clinically and regulatory relevant sheep model, TEHVs implanted as pulmonary valve replacements using minimally invasive techniques were monitored for 1 year via multimodal in vivo imaging and comprehensive tissue remodeling assessments. TEHVs exhibited good preserved long-term in vivo performance and remodeling comparable to native heart valves, as predicted by and consistent with computational modeling. TEHV failure could be predicted for nonphysiological pressure loading. Beyond previous studies, this work suggests the relevance of an integrated in silico, in vitro, and in vivo bioengineering approach as a basis for the safe and efficient clinical translation of TEHVs.

Immersed Methods for Fluid-Structure Interaction

Fluid-structure interaction is ubiquitous in nature and occurs at all biological scales. Immersed methods provide mathematical and computational frameworks for modeling fluid-structure systems. These methods, which typically use an Eulerian description of the fluid and a Lagrangian description of the structure, can treat thin immersed boundaries and volumetric bodies, and they can model structures that are flexible or rigid or that move with prescribed deformational kinematics. Immersed formulations do not require body-fitted discretizations and thereby avoid the frequent grid regeneration that can otherwise be required for models involving large deformations and displacements. This article reviews immersed methods for both elastic structures and structures with prescribed kinematics. It considers formulations using integral operators to connect the Eulerian and Lagrangian frames and methods that directly apply jump conditions along fluid-structure interfaces. Benchmark problems demonstrate the effectiveness of these methods, and selected applications at Reynolds numbers up to approximately 20,000 highlight their impact in biological and biomedical modeling and simulation.

Mechanical characterisation of human and porcine scalp tissue at dynamic strain rates

Several biomedical applications require knowledge of the behaviour of the scalp, including skin grafting, skin expansion and head impact biomechanics. Scalp tissue exhibits a non-linear stress-strain relationship, anisotropy and its mechanical properties depend on strain rate. When modelling the behaviour of the scalp, all these factors should be considered in order to perform realistic simulations. Here, tensile tests at strain rates between 0.005 and 100 s^-1 have been conducted on porcine and human scalp in order to investigate the non-linearity, anisotropy, and strain rate dependence of the scalp mechanical properties. The effect of the orientation of the sample with respect to the Skin Tension Lines (STLs) was considered during the test. The results showed that anisotropy is evident in the hyperelastic response at low strain rates (0.005 s^-1) but not at higher strain rates (15-100 s^-1). The mechanical properties of porcine scalp differ from human scalp. In particular, the elastic modulus and the Ultimate Tensile Strength (UTS) of the porcine scalp were found to be almost twice the values of the human scalp, whereas the stretch at failure was not found to be significantly different. An anisotropic hyperelastic model (Gasser-Ogden-Holzapfel) was used to model the quasi-static behaviour of the tissue, whereas three different isotropic hyperelastic models (Fung, Gent and Ogden) were used to model the behaviour of scalp tissue at higher strain rates. The experimental results outlined here have important implications for those wishing to model the mechanical behaviour of scalp tissue both under quasi-static and dynamic loading conditions.

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.

Parametric Modeling of Biomimetic Cortical Bone Microstructure for Additive Manufacturing

In this work we present a novel algorithm for generating in-silico biomimetic models of a cortical bone microstructure towards manufacturing biomimetic bone via additive manufacturing. The software provides a tool for physicians or biomedical engineers to develop models of cortical bone that include the inherent complexity of the microstructure. The correspondence of the produced virtual prototypes with natural bone tissue was assessed experimentally employing Digital Light Processing (DLP) of a thermoset polymer resin to recreate healthy and osteoporotic bone tissue microstructure. The proposed tool was successfully implemented to develop cortical bone structure based on osteon density, cement line thickness, and the Haversian and Volkmann channels to produce a user-designated bone porosity that matches within values reported from literature for these types of tissues. Characterization of the specimens using a Scanning Electron Microscopy with Focused Ion Beam (SEM/FIB) and Computer Tomography (CT) revealed that the manufacturability of intricated virtual prototype is possible for scaled-up versions of the tissue. Modeling based on the density, inclination and size range of the osteon and Haversian and Volkmann´s canals granted the development of a dynamic in-silico porosity (13.37⁻21.49%) that matches with models of healthy and osteoporotic bone. Correspondence of the designed porosity with the manufactured assessment (5.79⁻16.16%) shows that the introduced methodology is a step towards the development of more refined and lifelike porous structures such as cortical bone. Further research is required for validation of the proposed methodology model of the real bone tissue and as a patient-specific customization tool of synthetic bone.

In Silico Performance of a Recellularized Tissue Engineered Transcatheter Aortic Valve

Commercially available heart valves have many limitations, such as a lack of re-modeling, risk of calcification and thromboembolic problems. Many state-of-the-art tissue engineered heart valves rely on recellularization. Current in vitro testing is insufficient in characterizing a soon to be living valve. It is imperative to understand the performance of an in situ valve, but due to the complex in vivo environment this is difficult to accomplish. Finite element analysis has become a standard tool for modeling mechanical behavior of heart valves; yet, research to date has mostly focused on commercial valves. The purpose of this study has been to develop finite element models of a decellularized and recellularized tissue engineered heart valve. Mechanical properties from porcine aortic valves were utilized to develop finite element models, which were run through a full physiological cardiac cycle. Maximum principal stresses and strains from the leaflets and commissures were analyzed. The results of this study demonstrate that the explanted tissues had reduced mechanical strength compared to the implants but were similar to the native tissues. For the finite element models the explanted recellularized leaflets showed lower stress but increased compliance in the leaflet belly compared to native tissues and higher compliance than implant tissues. Histology demonstrated recellularization and remodeling although remodeled collagen had no clear directionality. In conclusion, we observed successful recellularization and remodeling of the tissue, however, the mechanical response indicates the further remodeling is required following implantation in the aortic/pulmonary position.

Quest for cardiovascular interventions: precise modeling and 3D printing of heart valves

Digitalization of health care practices is substantially manifesting itself as an effective tool to diagnose and rectify complex cardiovascular abnormalities. For cardiovascular abnormalities, precise non-invasive imaging interventions are being used to develop patient specific diagnosis and surgical planning. Concurrently, pre surgical 3D simulation and computational modeling are aiding in the effective surgery and understanding of valve biomechanics, respectively. Consequently, 3D printing of patient specific valves that can mimic the original one will become an effective outbreak for valvular problems. Printing of these patient-specific tissues or organ components is becoming a viable option owing to the advances in biomaterials and additive manufacturing techniques. These additive manufacturing techniques are receiving a full-fledged support from burgeoning field of computational fluid dynamics, digital image processing, artificial intelligence, and continuum mechanics during their optimization and implementation. Further, studies at cellular and molecular biomechanics have enriched our understanding of biomechanical factors resulting in valvular heart diseases. Hence, the knowledge generated can guide us during the design and synthesis of biomaterials to develop superior extra cellular matrix, mimicking materials that can be used as a bioink for 3D printing of organs and tissues. With this notion, we have reviewed current opportunities and challenges in the diagnosis and treatment of heart valve abnormalities through patient-specific valve design via tissue engineering and 3D bioprinting. These valves can replace diseased valves by preserving homogeneity and individuality of the patients.

A Non-Invasive Material Characterization Framework for Bioprosthetic Heart Valves

Computational modeling and simulation has become more common in design and development of bioprosthetic heart valves. To have a reliable computational model, considering accurate mechanical properties of biological soft tissue is one of the most important steps. The goal of this study was to present a non-invasive material characterization framework to determine mechanical propertied of soft tissue employed in bioprosthetic heart valves. Using integrated experimental methods (i.e., digital image correlation measurements and hemodynamic testing in a pulse duplicator system) and numerical methods (i.e., finite element modeling and optimization), three-dimensional anisotropic mechanical properties of leaflets used in two commercially available transcatheter aortic valves (i.e., Edwards SAPIEN 3 and Medtronic CoreValve) were characterized and compared to that of a commonly used and well-examined surgical bioprosthesis (i.e., Carpentier-Edwards PERIMOUNT Magna aortic heart valve). The results of the simulations showed that the highest stress value during one cardiac cycle was at the peak of systole in the three bioprostheses. In addition, in the diastole, the peak of maximum in-plane principal stress was 0.98, 0.96, and 2.95 MPa for the PERIMOUNT Magna, CoreValve, and SAPIEN 3, respectively. Considering leaflet stress distributions, there might be a difference in the long-term durability of different TAV models.

High resolution three-dimensional strain mapping of bioprosthetic heart valves using digital image correlation

Transcatheter aortic valve replacement (TAVR) is a safe and effective treatment option for patients deemed at high and intermediate risk for surgical aortic valve replacement. Similar to surgical aortic valves (SAVs), transcatheter aortic valves (TAVs) undergo calcification and mechanical wear over time. However, to date, there have been limited publications on the long-term durability of TAV devices. To assess longevity and mechanical strength of TAVs in comparison to surgical bioprosthetic valves, three-dimensional deformation analysis and strain measurement of the leaflets become an inevitable part of the evaluation. The goal of this study was to measure and compare leaflet displacement and strain of two commonly used TAVs in a side-by-side comparison with a commonly used SAV using a high-resolution digital image correlation (DIC) system. 26-mm Edwards SAPIEN 3, 26-mm Medtronic CoreValve, and 25-mm Carpentier-Edwards PERIMOUNT Magna surgical bioprosthesis were examined in a custom-made valve testing apparatus. A time-varying, spatially uniform pressure was applied to the leaflets at different loading rates. GOM ARAMIS® software was used to map leaflet displacement and strain fields during loading and unloading. High displacement regions were found to be at the leaflet belly region of the three bioprosthetic valves. In addition, the frame of the surgical bioprosthesis was found to be remarkably flexible, in contrary to CoreValve and SAPIEN 3 in which the stent was nearly rigid under a similar loading condition. The experimental DIC measurements can be used to characterize the anisotropic materiel behavior of the bioprosthetic heart valve leaflets and validate heart valve computational simulations.

Fluid-structure interaction simulation of artificial textile reinforced aortic heart valve: Validation with an in-vitro test

Prosthetic heart valves deployed in the left heart (aortic and mitral) are subjected to harsh hemodynamical conditions. Most of the tissue engineered heart valves have been developed for the low pressure pulmonary position because of the difficulties in fabricating a mechanically strong valve, able to withstand the systemic circulation. This necessitates the use of reinforcing scaffolds, resulting in a tissue-engineered textile reinforced tubular aortic heart valve. Therefore, to better design these implants, material behaviour of the composite, valve kinematics and its hemodynamical response need to be evaluated. Experimental assessment can be immensely time consuming and expensive, paving way for numerical studies. In this work, the material properties obtained using the previously proposed multi-scale numerical method for textile composites was evaluated for its accuracy. An in silico immersed boundary (IB) fluid structure interaction (FSI) simulation emulating the in vitro experiment was set-up to evaluate and compare the geometric orifice area and flow rate for one beat cycle. Results from the in silico FSI simulation were found to be in good coherence with the in vitro test during the systolic phase, while mean deviation of approximately 9% was observed during the diastolic phase of a beat cycle. Merits and demerits of the in silico IB-FSI method for the presented case study has been discussed with the advantages outweighing the drawbacks, indicating the potential towards an effective use of this framework in the development and analysis of heart valves.

An anisotropic constitutive model for immersogeometric fluid-structure interaction analysis of bioprosthetic heart valves

This paper considers an anisotropic hyperelastic soft tissue model, originally proposed for native valve tissue and referred to herein as the Lee-Sacks model, in an isogeometric thin shell analysis framework that can be readily combined with immersogeometric fluid-structure interaction (FSI) analysis for high-fidelity simulations of bioprosthetic heart valves (BHVs) interacting with blood flow. We find that the Lee-Sacks model is well-suited to reproduce the anisotropic stress-strain behavior of the cross-linked bovine pericardial tissues that are commonly used in BHVs. An automated procedure for parameter selection leads to an instance of the Lee-Sacks model that matches biaxial stress-strain data from the literature more closely, over a wider range of strains, than other soft tissue models. The relative simplicity of the Lee-Sacks model is attractive for computationally-demanding applications such as FSI analysis and we use the model to demonstrate how the presence and direction of material anisotropy affect the FSI dynamics of BHV leaflets.