A material modeling approach for the effective response of planar soft tissues for efficient computational simulations

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.

A viscoelastic constitutive model for human femoropopliteal arteries

High failure rates present challenges for surgical and interventional therapies for peripheral artery disease of the femoropopliteal artery (FPA). The FPA's demanding biomechanical environment necessitates complex interactions with repair devices and materials. While a comprehensive understanding of the FPA's mechanical characteristics could improve medical treatments, the viscoelastic properties of these muscular arteries remain poorly understood, and the constitutive model describing their time-dependent behavior is absent. We introduce a new viscoelastic constitutive model for the human FPA grounded in its microstructural composition. The model is capable of detailing the contributions of each intramural component to the overall viscoelastic response. Our model was developed utilizing fractional viscoelasticity and tested using biaxial experimental data with hysteresis and relaxation collected from 10 healthy human subjects aged 57 to 65 and further optimized for high throughput and automation. The model accurately described the experimental data, capturing significant nonlinearity and hysteresis that were particularly pronounced circumferentially, and tracked the contribution of passive smooth muscle cells to viscoelasticity that was twice that of the collagen fibers. The high-throughput parameter estimation procedure we developed included a specialized objective function and modifications to enhance convergence for the common exponential-type fiber laws, facilitating computational implementation. Our new model delineates the time-dependent behavior of human FPAs, which will improve the fidelity of computational simulations investigating device-artery interactions and contribute to their greater physical accuracy. Moreover, it serves as a useful tool to investigate the contribution of arterial constituents to overall tissue viscoelasticity, thereby expanding our knowledge of arterial mechanophysiology. STATEMENT OF SIGNIFICANCE: The demanding biomechanical environment of the femoropopliteal artery (FPA) necessitates complex interactions with repair devices and materials, but the viscoelastic properties of these muscular arteries remain poorly understood with the constitutive model describing their time-dependent behavior being absent. We hereby introduce the first viscoelastic constitutive model for the human FPA grounded in its microstructures. This model was tested using biaxial mechanical data collected from 10 healthy human subjects between the ages of 57 to 65. It can detail the contributions of each intramural component to the overall viscoelastic response, showing that the contribution of passive smooth muscle cells to viscoelasticity is twice that of collagen fibers. The usefulness of this model as tool to better understand arterial mechanophysiology was demonstrated.

Modeling planar response of vascular tissues using quadratic functions of effective strain

Simulation-based studies of the cardiovascular structure such as aorta have become increasingly popular for many biomedical problems such as predictions of aneurysm rupture. A critical step in these simulations is the development of constitutive models that accurately describe the tissue's mechanical behavior. In this work, we present a new constitutive model, which explicitly accounts for the gradual recruitment of collagen fibers. The recruitment is considered using an effective stretch, which is a continuum-scale kinematic variable measuring the uncrimped stretch of the tissue in an average sense. The strain energy of a fiber bundle is described by a quadratic function of the effective strain. Constitutive models formulated in this manner are applied to describe the responses of ascending thoracic aortic aneurysm and porcine thoracic aorta tissues. The heterogeneous properties of the ATAA tissue are extracted from bulge inflation test data, and then used in finite element analysis to simulate the inflation test. The descriptive and predictive capabilities are further assessed using planar testing data of porcine thoracic aortic tissues. It is found that the constitutive model can accurately describe the stress-strain relations. In particular, the finite element simulation replicates the displacement, strain, and stress distributions with excellent fidelity.

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.

Patient-Specific Quantification of Normal and Bicuspid Aortic Valve Leaflet Deformations from Clinically Derived Images

The clinical benefit of patient-specific modeling of heart valve disease remains an unrealized goal, often a result of our limited understanding of the in vivo milieu. This is particularly true in assessing bicuspid aortic valve (BAV) disease, the most common cardiac congenital defect in humans, which leads to premature and severe aortic stenosis or insufficiency (AS/AI). However, assessment of BAV risk for AS/AI on a patient-specific basis is hampered by the substantial degree of anatomic and functional variations that remain largely unknown. The present study was undertaken to utilize a noninvasive computational pipeline ( https://doi.org/10.1002/cnm.3142 ) that directly yields local heart valve leaflet deformation information using patient-specific real-time three-dimensional echocardiographic imaging (rt-3DE) data. Imaging data was collected for patients with normal tricuspid aortic valve (TAV, [Formula: see text]) and those with BAV ([Formula: see text] with fused left and right coronary leaflets and [Formula: see text] with fused right and non-coronary leaflets), from which the medial surface of each leaflet was extracted. The resulting deformation analysis resulted in, for the first time, quantified differences between the in vivo functional deformations of the TAV and BAV leaflets. Our approach was able to capture the complex, heterogeneous surface deformation fields in both TAV and BAV leaflets. We were able to identify and quantify differences in stretch patterns between leaflet types, and found in particular that stretches experienced by BAV leaflets during closure differ from those of TAV leaflets in terms of both heterogeneity as well as overall magnitude. Deformation is a key parameter in the clinical assessment of valvular function, and serves as a direct means to determine regional variations in structure and function. This study is an essential step toward patient-specific assessment of BAV based on correlating leaflet deformation and AS/AI progression, as it provides a means for assessing patient-specific stretch patterns.

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.

Numerical analysis of stenoses severity and aortic wall mechanics in patients with supravalvular aortic stenosis

Supravalvular aortic stenosis (SVAS) is an aortic malformation characterized by a narrowing of the ascending aorta, resulting in abnormal hemodynamics and pressure drop across the stenosed region. It has been observed that the pressure drops measured from Doppler ultrasound exams often tend to be higher than those obtained from invasive cardiac catheterization. These misleadingly elevated pressure measurements may drive the decision to refer patients for surgical treatment prematurely. Considering this strong clinical association, the purpose of this work is to develop a computational modeling approach using a two-way coupled fluid-structure interaction methodology to determine an accurate prediction of trans-stenotic pressure drop and to further highlight the discrepancy between the SVAS assessment methods. Blood is modeled using Navier-Stokes equations while the aortic wall is simulated by a composite poroelastic structure to represent the three main layers of the arterial wall. The relationship between aortic wall elasticity and the blood flow conditions is examined in varying levels of stenosis, ranging from mild to severe degrees of vessel diameter narrowing. A substantial overestimation of the traditional Doppler pressure drop measurement is observed, especially for severe stenosis levels. The simulation results indicate that elasticity of the aortic wall has a relatively little effect on trans-stenotic pressure drop for the range of mild to moderate SVAS cases, but predicted to have a profound effect for severe SVAS cases. Moreover, significant sensitivity to the pressure drop across the SVAS region from stenosis severity is observed.

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.

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

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

Contribution of nascent cohesive fiber-fiber interactions to the non-linear elasticity of fibrin networks under tensile load

Fibrin is a viscoelastic proteinaceous polymer that determines the deformability and integrity of blood clots and fibrin-based biomaterials in response to biomechanical forces. Here, a previously unnoticed structural mechanism of fibrin clots' mechanical response to external tensile loads is tested using high-resolution confocal microscopy and recently developed three-dimensional computational model. This mechanism, underlying local strain-stiffening of individual fibers as well as global stiffening of the entire network, is based on previously neglected nascent cohesive pairwise interactions between individual fibers (crisscrossing) in fibrin networks formed under tensile load. Existence of fiber-fiber crisscrossings of reoriented fibers was confirmed using 3D imaging of experimentally obtained stretched fibrin clots. The computational model enabled us to study structural details and quantify mechanical effects of the fiber-fiber cohesive crisscrossing during stretching of fibrin gels at various spatial scales. The contribution of the fiber-fiber cohesive contacts to the elasticity of stretched fibrin networks was characterized by changes in individual fiber stiffness, the length, width, and alignment of fibers, as well as connectivity and density of the entire network. The results show that the nascent cohesive crisscrossing of fibers in stretched fibrin networks comprise an underappreciated important structural mechanism underlying the mechanical response of fibrin to (patho)physiological stresses that determine the course and outcomes of thrombotic and hemostatic disorders, such as heart attack and ischemic stroke. STATEMENT OF SIGNIFICANCE: Fibrin is a viscoelastic proteinaceous polymer that determines the deformability and integrity of blood clots and fibrin-based biomaterials in response to biomechanical forces. In this paper, a novel structural mechanism of fibrin clots' mechanical response to external tensile loads is tested using high-resolution confocal microscopy and newly developed computational model. This mechanism, underlying local strain-stiffening of individual fibers as well as global stiffening of the entire network, is based on previously neglected nascent cohesive pairwise interactions between individual fibers (crisscrossing) in fibrin networks formed under tensile load. Cohesive crisscrossing is an important structural mechanism that influences the mechanical response of blood clots and which can determine the outcomes of blood coagulation disorders, such as heart attacks and strokes.

On the AIC-based model reduction for the general Holzapfel-Ogden myocardial constitutive law

Constitutive laws that describe the mechanical responses of cardiac tissue under loading hold the key to accurately model the biomechanical behaviour of the heart. There have been ample choices of phenomenological constitutive laws derived from experiments, some of which are quite sophisticated and include effects of microscopic fibre structures of the myocardium. A typical example is the strain-invariant-based Holzapfel-Ogden 2009 model that is excellently fitted to simple shear tests. It has been widely used and regarded as the state-of-the-art constitutive law for myocardium. However, there has been no analysis to show if it has both adequate descriptive and predictive capabilities for other tissue tests of myocardium. Indeed, such an analysis is important for any constitutive laws for clinically useful computational simulations. In this work, we perform such an analysis using combinations of tissue tests, uniaxial tension, biaxial tension and simple shear from three different sets of myocardial tissue studies. Starting from the general 14-parameter myocardial constitutive law developed by Holzapfel and Ogden, denoted as the general HO model, we show that this model has good descriptive and predictive capabilities for all the experimental tests. However, to reliably determine all 14 parameters of the model from experiments remains a great challenge. Our aim is to reduce the constitutive law using Akaike information criterion, to maintain its mechanical integrity whilst achieving minimal computational cost. A competent constitutive law should have descriptive and predictive capabilities for different tissue tests. By competent, we mean the model has least terms but is still able to describe and predict experimental data. We also investigate the optimal combinations of tissue tests for a given constitutive model. For example, our results show that using one of the reduced HO models, one may need just one shear response (along normal-fibre direction) and one biaxial stretch (ratio of 1 mean fibre : 1 cross-fibre) to satisfactorily describe Sommer et al. human myocardial mechanical properties. Our study suggests that single-state tests (i.e. simple shear or stretching only) are insufficient to determine the myocardium responses. We also found it is important to consider transmural fibre rotations within each myocardial sample of tests during the fitting process. This is done by excluding un-stretched fibres using an "effective fibre ratio", which depends on the sample size, shape, local myofibre architecture and loading conditions. We conclude that a competent myocardium material model can be obtained from the general HO model using AIC analysis and a suitable combination of tissue tests.

A Contemporary Look at Biomechanical Models of Myocardium

Understanding and predicting the mechanical behavior of myocardium under healthy and pathophysiological conditions are vital to developing novel cardiac therapies and promoting personalized interventions. Within the past 30 years, various constitutive models have been proposed for the passive mechanical behavior of myocardium. These models cover a broad range of mathematical forms, microstructural observations, and specific test conditions to which they are fitted. We present a critical review of these models, covering both phenomenological and structural approaches, and their relations to the underlying structure and function of myocardium. We further explore the experimental and numerical techniques used to identify the model parameters. Next, we provide a brief overview of continuum-level electromechanical models of myocardium, with a focus on the methods used to integrate the active and passive components of myocardial behavior. We conclude by pointing to future directions in the areas of optimal form as well as new approaches for constitutive modeling of myocardium.