An immersogeometric variational framework for fluid-structure interaction: application to bioprosthetic heart valves

Image-guided subject-specific modeling of glymphatic transport and amyloid deposition

The glymphatic system is a brain-wide system of perivascular networks that facilitate exchange of cerebrospinal fluid (CSF) and interstitial fluid (ISF) to remove waste products from the brain. A greater understanding of the mechanisms for glymphatic transport may provide insight into how amyloid beta (A β ) and tau agglomerates, key biomarkers for Alzheimer's disease and other neurodegenerative diseases, accumulate and drive disease progression. In this study, we develop an image-guided computational model to describe glymphatic transport and A β deposition throughout the brain. A β transport and deposition are modeled using an advection-diffusion equation coupled with an irreversible amyloid accumulation (damage) model. We use immersed isogeometric analysis, stabilized using the streamline upwind Petrov-Galerkin (SUPG) method, where the transport model is constructed using parameters inferred from brain imaging data resulting in a subject-specific model that accounts for anatomical geometry and heterogeneous material properties. Both short-term (30-min) and long-term (12-month) 3D simulations of soluble amyloid transport within a mouse brain model were constructed from diffusion weighted magnetic resonance imaging (DW-MRI) data. In addition to matching short-term patterns of tracer deposition, we found that transport parameters such as CSF flow velocity play a large role in amyloid plaque deposition. The computational tools developed in this work will facilitate investigation of various hypotheses related to glymphatic transport and fundamentally advance our understanding of its role in neurodegeneration, which is crucial for the development of preventive and therapeutic interventions.

Modeling isovolumetric phases in cardiac flows by an Augmented Resistive Immersed Implicit Surface method

A major challenge in the computational fluid dynamics modeling of the heart function is the simulation of isovolumetric phases when the hemodynamics problem is driven by a prescribed boundary displacement. During such phases, both atrioventricular and semilunar valves are closed: consequently, the ventricular pressure may not be uniquely defined, and spurious oscillations may arise in numerical simulations. These oscillations can strongly affect valve dynamics models driven by the blood flow, making unlikely to recovering physiological dynamics. Hence, prescribed opening and closing times are usually employed, or the isovolumetric phases are neglected altogether. In this article, we propose a suitable modification of the Resistive Immersed Implicit Surface (RIIS) method (Fedele et al., Biomech Model Mechanobiol 2017, 16, 1779-1803) by introducing a reaction term to correctly capture the pressure transients during isovolumetric phases. The method, that we call Augmented RIIS (ARIIS) method, extends the previously proposed ARIS method (This et al., Int J Numer Methods Biomed Eng 2020, 36, e3223) to the case of a mesh which is not body-fitted to the valves. We test the proposed method on two different benchmark problems, including a new simplified problem that retains all the characteristics of a heart cycle. We apply the ARIIS method to a fluid dynamics simulation of a realistic left heart geometry, and we show that ARIIS allows to correctly simulate isovolumetric phases, differently from standard RIIS method. Finally, we demonstrate that by the new method the cardiac valves can open and close without prescribing any opening/closing times.

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.

A time-consistent stabilized finite element method for fluids with applications to hemodynamics

Several finite element methods for simulating incompressible flows rely on the streamline upwind Petrov-Galerkin stabilization (SUPG) term, which is weighted by [Formula: see text]. The conventional formulation of [Formula: see text] includes a constant that depends on the time step size, producing an overall method that becomes exceedingly less accurate as the time step size approaches zero. In practice, such method inconsistency introduces significant error in the solution, especially in cardiovascular simulations, where small time step sizes may be required to resolve multiple scales of the blood flow. To overcome this issue, we propose a consistent method that is based on a new definition of [Formula: see text]. This method, which can be easily implemented on top of an existing streamline upwind Petrov-Galerkin and pressure stabilizing Petrov-Galerkin method, involves the replacement of the time step size in [Formula: see text] with a physical time scale. This time scale is calculated in a simple operation once every time step for the entire computational domain from the ratio of the L2-norm of the acceleration and the velocity. The proposed method is compared against the conventional method using four cases: a steady pipe flow, a blood flow through vascular anatomy, an external flow over a square obstacle, and a fluid-structure interaction case involving an oscillatory flexible beam. These numerical experiments, which are performed using linear interpolation functions, show that the proposed formulation eliminates the inconsistency issue associated with the conventional formulation in all cases. While the proposed method is slightly more costly than the conventional method, it significantly reduces the error, particularly at small time step sizes. For the pipe flow where an exact solution is available, we show the conventional method can over-predict the pressure drop by a factor of three. This large error is almost completely eliminated by the proposed formulation, dropping to approximately 1% for all time step sizes and Reynolds numbers considered.

A sharp interface Lagrangian-Eulerian method for flexible-body fluid-structure interaction

This paper introduces a sharp-interface approach to simulating fluid-structure interaction (FSI) involving flexible bodies described by general nonlinear material models and across a broad range of mass density ratios. This new flexible-body immersed Lagrangian-Eulerian (ILE) scheme extends our prior work on integrating partitioned and immersed approaches to rigid-body FSI. Our numerical approach incorporates the geometrical and domain solution flexibility of the immersed boundary (IB) method with an accuracy comparable to body-fitted approaches that sharply resolve flows and stresses up to the fluid-structure interface. Unlike many IB methods, our ILE formulation uses distinct momentum equations for the fluid and solid subregions with a Dirichlet-Neumann coupling strategy that connects fluid and solid subproblems through simple interface conditions. As in earlier work, we use approximate Lagrange multiplier forces to treat the kinematic interface conditions along the fluid-structure interface. This penalty approach simplifies the linear solvers needed by our formulation by introducing two representations of the fluid-structure interface, one that moves with the fluid and another that moves with the structure, that are connected by stiff springs. This approach also enables the use of multi-rate time stepping, which allows us to use different time step sizes for the fluid and structure subproblems. Our fluid solver relies on an immersed interface method (IIM) for discrete surfaces to impose stress jump conditions along complex interfaces while enabling the use of fast structured-grid solvers for the incompressible Navier-Stokes equations. The dynamics of the volumetric structural mesh are determined using a standard finite element approach to large-deformation nonlinear elasticity via a nearly incompressible solid mechanics formulation. This formulation also readily accommodates compressible structures with a constant total volume, and it can handle fully compressible solid structures for cases in which at least part of the solid boundary does not contact the incompressible fluid. Selected grid convergence studies demonstrate second-order convergence in volume conservation and in the pointwise discrepancies between corresponding positions of the two interface representations as well as between first and second-order convergence in the structural displacements. The time stepping scheme is also demonstrated to yield second-order convergence. To assess and validate the robustness and accuracy of the new algorithm, comparisons are made with computational and experimental FSI benchmarks. Test cases include both smooth and sharp geometries in various flow conditions. We also demonstrate the capabilities of this methodology by applying it to model the transport and capture of a geometrically realistic, deformable blood clot in an inferior vena cava filter.

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.

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.

Computational cardiac physiology for new modelers: Origins, foundations, and future

Mathematical models of the cardiovascular system have come a long way since they were first introduced in the early 19th century. Driven by a rapid development of experimental techniques, numerical methods, and computer hardware, detailed models that describe physical scales from the molecular level up to organs and organ systems have been derived and used for physiological research. Mathematical and computational models can be seen as condensed and quantitative formulations of extensive physiological knowledge and are used for formulating and testing hypotheses, interpreting and directing experimental research, and have contributed substantially to our understanding of cardiovascular physiology. However, in spite of the strengths of mathematics to precisely describe complex relationships and the obvious need for the mathematical and computational models to be informed by experimental data, there still exist considerable barriers between experimental and computational physiological research. In this review, we present a historical overview of the development of mathematical and computational models in cardiovascular physiology, including the current state of the art. We further argue why a tighter integration is needed between experimental and computational scientists in physiology, and point out important obstacles and challenges that must be overcome in order to fully realize the synergy of experimental and computational physiological research.

A Computational Framework for Atrioventricular Valve Modeling Using Open-Source Software

Atrioventricular valve regurgitation is a significant cause of morbidity and mortality in patients with acquired and congenital cardiac valve disease. Image-derived computational modeling of atrioventricular valves has advanced substantially over the last decade and holds particular promise to inform valve repair in small and heterogeneous populations, which are less likely to be optimized through empiric clinical application. While an abundance of computational biomechanics studies has investigated mitral and tricuspid valve disease in adults, few studies have investigated its application to vulnerable pediatric and congenital heart populations. Further, to date, investigators have primarily relied upon a series of commercial applications that are neither designed for image-derived modeling of cardiac valves nor freely available to facilitate transparent and reproducible valve science. To address this deficiency, we aimed to build an open-source computational framework for the image-derived biomechanical analysis of atrioventricular valves. In the present work, we integrated an open-source valve modeling platform, SlicerHeart, and an open-source biomechanics finite element modeling software, FEBio, to facilitate image-derived atrioventricular valve model creation and finite element analysis. We present a detailed verification and sensitivity analysis to demonstrate the fidelity of this modeling in application to three-dimensional echocardiography-derived pediatric mitral and tricuspid valve models. Our analyses achieved an excellent agreement with those reported in the literature. As such, this evolving computational framework offers a promising initial foundation for future development and investigation of valve mechanics, in particular collaborative efforts targeting the development of improved repairs for children with congenital heart disease.

Blood-Artery Interaction in Calcified Aortas and Abdominal Aortic Aneurysms

A stabilized FSI method is presented for coupling shear-rate dependent model of blood with finitely deforming anisotropic hyperelastic model of arteries. The blood-artery coupling conditions are weakly enforced to accommodate non-matching blood-artery meshes which provides great flexibility in independent discretization of fluid and solid subdomains in the patient-specific geometric models. The variationally derived interface coupling terms play an important role in the concurrent solution of the nonlinear mixed-field problem across non-matching discretizations. Two test cases are presented that investigate the effect of growth of aortic aneurysm on local changes in blood flow and stress concentrations in calcified arteries under pulsating flows to highlight the clinical relevance of the proposed method for cardiovascular applications.

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.

Computational Methods for Fluid-Structure Interaction Simulation of Heart Valves in Patient-Specific Left Heart Anatomies

Given the complexity of human left heart anatomy and valvular structures, the fluid–structure interaction (FSI) simulation of native and prosthetic valves poses a significant challenge for numerical methods. In this review, recent numerical advancements for both fluid and structural solvers for heart valves in patient-specific left hearts are systematically considered, emphasizing the numerical treatments of blood flow and valve surfaces, which are the most critical aspects for accurate simulations. Numerical methods for hemodynamics are considered under both the continuum and discrete (particle) approaches. The numerical treatments for the structural dynamics of aortic/mitral valves and FSI coupling methods between the solid Ωs and fluid domain Ωf are also reviewed. Future work toward more advanced patient-specific simulations is also discussed, including the fusion of high-fidelity simulation within vivo measurements and physics-based digital twining based on data analytics and machine learning techniques.

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.

Image-Based Computational Hemodynamics Analysis of Systolic Obstruction in Hypertrophic Cardiomyopathy

Hypertrophic Cardiomyopathy (HCM) is a pathological condition characterized by an abnormal thickening of the myocardium. When affecting the medio-basal portion of the septum, it is named Hypertrophic Obstructive Cardiomyopathy (HOCM) because it induces a flow obstruction in the left ventricular outflow tract. In any type of HCM, the myocardial function can become compromised, possibly resulting in cardiac death. In this study, we investigated with computational analysis the hemodynamics of patients with different types of HCM. The aim was quantifying the effects of this pathology on the intraventricular blood flow and pressure gradients, and providing information potentially useful to guide the indication and the modality of the surgical treatment (septal myectomy). We employed an image-based computational approach, integrating fluid dynamics simulations with geometric and functional data, reconstructed from standard cardiac cine-MRI acquisitions. We showed that with our approach we can better understand the patho-physiological behavior of intraventricular blood flow dynamics due to the abnormal morphological and functional aspect of the left ventricle. The main results of our investigation are: (a) a detailed patient-specific analysis of the blood velocity, pressure and stress distribution associated to HCM; (b) a computation-based classification of patients affected by HCM that can complement the current clinical guidelines for the diagnosis and treatment of HOCM.

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.

Immersed boundary-conformal isogeometric method for linear elliptic problems

We present a novel isogeometric method, namely the Immersed Boundary-Conformal Method (IBCM), that features a layer of discretization conformal to the boundary while employing a simple background mesh for the remaining domain. In this manner, we leverage the geometric flexibility of the immersed boundary method with the advantages of a conformal discretization, such as intuitive control of mesh resolution around the boundary, higher accuracy per degree of freedom, automatic satisfaction of interface kinematic conditions, and the ability to strongly impose Dirichlet boundary conditions. In the proposed method, starting with a boundary representation of a geometric model, we extrude it to obtain a corresponding conformal layer. Next, a given background B-spline mesh is cut with the conformal layer, leading to two disconnected regions: an exterior region and an interior region. Depending on the problem of interest, one of the two regions is selected to be coupled with the conformal layer through Nitsche's method. Such a construction involves Boolean operations such as difference and union, which therefore require proper stabilization to deal with arbitrarily cut elements. In this regard, we follow our precedent work called the minimal stabilization method (Antolin et al in SIAM J Sci Comput 43(1):A330-A354, 2021). In the end, we solve several 2D benchmark problems to demonstrate improved accuracy and expected convergence with IBCM. Two applications that involve complex geometries are also studied to show the potential of IBCM, including a spanner model and a fiber-reinforced composite model. Moreover, we demonstrate the effectiveness of IBCM in an application that exhibits boundary-layer phenomena.

Fully coupled dynamic simulations of bioprosthetic aortic valves based on an embedded strategy for fluid-structure interaction with contact

AIMS

This work aims at presenting a fully coupled approach for the numerical solution of contact problems between multiple elastic structures immersed in a fluid flow. The key features of the computational model are (i) a fully coupled fluid-structure interaction with contact, (ii) the use of a fibre-reinforced material for the leaflets, (iii) a stent, and (iv) a compliant aortic root.

METHODS AND RESULTS

The computational model takes inspiration from the immersed boundary techniques and allows the numerical simulation of the blood-tissue interaction of bioprosthetic heart valves (BHVs) as well as the contact among the leaflets. First, we present pure mechanical simulations, where blood is neglected, to assess the performance of different material properties and valve designs. Secondly, fully coupled fluid-structure interaction simulations are employed to analyse the combination of haemodynamic and mechanical characteristics. The isotropic leaflet tissue experiences high-stress values compared to the fibre-reinforced material model. Moreover, elongated leaflets show a stress concentration close to the base of the stent. We observe a fully developed flow at the systolic stage of the heartbeat. On the other hand, flow recirculation appears along the aortic wall during diastole.

CONCLUSION

The presented FSI approach can be used for analysing the mechanical and haemodynamic performance of a BHV. Our study suggests that stresses concentrate in the regions where leaflets are attached to the stent and in the portion of the aortic root where the BHV is placed. The results from this study may inspire new BHV designs that can provide a better stress distribution.

A Variational Multiscale method with immersed boundary conditions for incompressible flows

This paper presents a new stabilized form of incompressible Navier-Stokes equations for weak enforcement of Dirichlet boundary conditions at immersed boundaries. The boundary terms are derived via the Variational Multiscale (VMS) method which involves solving the fine-scale variational problem locally within a narrow band along the boundary. The fine-scale model is then variationally embedded into the coarse-scale form that yields a stabilized method which is free of user defined parameters. The derived boundary terms weakly enforce the Dirichlet boundary conditions along the immersed boundaries that may not align with the inter-element edges in the mesh. A unique feature of this rigorous derivation is that the structure of the stabilization tensor which emerges is naturally endowed with the mathematical attributes of area-averaging and stress-averaging. The method is implemented using 4-node quadrilateral and 8-node hexahedral elements. A set of 2D and 3D benchmark problems is presented that investigate the mathematical attributes of the method. These test cases show that the proposed method is mathematically robust as well as computationally stable and accurate for modeling boundary layers around immersed objects in the fluid domain.

Weakly imposed boundary conditions for shear-rate dependent non-Newtonian fluids: application to cardiovascular flows

This paper presents a stabilized formulation for the generalized Navier-Stokes equations for weak enforcement of essential boundary conditions. The non-Newtonian behavior of blood is modeled via shear-rate dependent constitutive equations. The boundary terms for weak enforcement of Dirichlet boundary conditions are derived via locally resolving the fine-scale variational equation facilitated by the Variational Multiscale (VMS) framework. The proposed method reproduces the consistency and stabilization terms that are present in the Nitsche type approaches. In addition, for the shear-rate fluids, two more boundary terms appear. One of these terms is the viscosity-derivative term and is a function of the shear-rate, while the other term is a zeroth-order term. These terms play an important role in attaining optimal convergence rates for the velocity and pressure fields in the norms considered. A most significant contribution is the form of the stabilization tensors that are also variationally derived. Employing edge functions the edge stabilization tensor is numerically evaluated, and it adaptively adjusts itself to the magnitude of the boundary residual. The resulting formulation is variationally consistent and the weakly imposed no-slip boundary condition leads to higher accuracy of the spatial gradients for coarse boundary-layer meshes when compared with the traditional strongly imposed boundary conditions. This feature of the present approach will be of significance in imposing interfacial continuity conditions across non-matching discretizations in blood-artery interaction problems. A set of test cases is presented to investigate the mathematical attributes of the method and a patient-specific case is presented to show its clinical relevance.

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.

Numerical Simulation of Dynamic Fluid-Structure Interaction with Elastic Structure–Rigid Obstacle Contact

An implicit scheme by partitioned procedures is proposed to solve a dynamic fluid–structure interaction problem in the case when the structure displacements are limited by a rigid obstacle. For the fluid equations (Sokes or Navier–Stokes), the fictitious domain method with penalization was used. The equality of the fluid and structure velocities at the interface was obtained using the penalization technique. The surface forces at the fluid–structure interface were computed using the fluid solution in the structure domain. A quadratic optimization problem with linear inequalities constraints was solved to obtain the structure displacements. Numerical results are presented.

Fluid-structure coupled biotransport processes in aortic valve disease

Biological transport processes near the aortic valve play a crucial role in calcific aortic valve disease initiation and bioprosthetic aortic valve thrombosis. Hemodynamics coupled with the dynamics of the leaflets regulate these transport patterns. Herein, two-way coupled fluid-structure interaction (FSI) simulations of a 2D bicuspid aortic valve and a 3D mechanical heart valve were performed and coupled with various convective mass transport models that represent some of the transport processes in calcification and thrombosis. Namely, five different continuum transport models were developed to study biochemicals that originate from the blood and the leaflets, as well as residence-time and flow stagnation. Low-density lipoprotein (LDL) and platelet activation were studied for their role in calcification and thrombosis, respectively. Coherent structures were identified using vorticity and Lagrangian coherent structures (LCS) for the 2D and 3D models, respectively. A very close connection between vortex structures and biochemical concentration patterns was shown where different vortices controlled the concentration patterns depending on the transport mechanism. Additionally, the relationship between leaflet concentration and wall shear stress was revealed. Our work shows that blood flow physics and coherent structures regulate the flow-mediated biological processes that are involved in aortic valve calcification and thrombosis, and therefore could be used in the design process to optimize heart valve replacement durability.

Turbulent Systolic Flow Downstream of a Bioprosthetic Aortic Valve: Velocity Spectra, Wall Shear Stresses, and Turbulent Dissipation Rates

Every year, a quarter million patients receive prosthetic heart valves in aortic valve replacement therapy. Prosthetic heart valves are known to lead to turbulent blood flow. This turbulent flow field may have adverse effects on blood itself, on the aortic wall and on the valve performance. A detailed characterization of the turbulent flow downstream of a valve could yield better understanding of its effect on shear-induced thrombocyte activation, unphysiological wall shear stresses and hemodynamic valve performance. Therefore, computational simulations of the flow past a bioprosthetic heart valve were performed. The computational results were validated against experimental measurements of the turbulent flow field with tomographic particle image velocimetry. The turbulent flow was analyzed for disturbance amplitudes, dissipation rates and shear stress distributions. It was found that approximately 26% of the hydrodynamic resistance of the valve was due to turbulent dissipation and that this dissipation mainly took place in a region about one valve diameter downstream of the valve orifice. Farther downstream, the turbulent fluctuations became weaker which was also reflected in the turbulent velocity spectra of the flow field. Viscous shear stresses were found to be in the range of the critical level for blood platelet activation. The turbulent flow led to elevated shear stress levels along the wall of the ascending aorta with strongly fluctuating and chaotic wall shear stress patterns. Further, we identified leaflet fluttering at 40 Hz which was connected to repeated shedding of vortex rings that appeared to feed the turbulent flow downstream of the valve.

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.

An image-based computational hemodynamics study of the Systolic Anterior Motion of the mitral valve

Systolic Anterior Motion (SAM) of the mitral valve - often associated with Hypertrophic Obstructive Cardiomyopathy (HOCM) - is a cardiac pathology in which a functional subaortic stenosis is induced during systole by the mitral leaflets partially obstructing the outflow tract of the left ventricle. Its assessment by diagnostic tests is often difficult, possibly underestimating its severity and thus increasing the risk of heart failure. In this paper, we propose a new computational pipeline, based on cardiac cine Magnetic Resonance Imaging (cine-MRI) data, for the assessment of SAM. The pipeline encompasses image processing of the left ventricle and the mitral valve, and numerical investigation of cardiac hemodynamics by means of Computational Fluid Dynamics (CFD) in a moving domain with image-based prescribed displacement. Patient-specific geometry and motion of the left ventricle are considered in view of an Arbitrary Lagrangian-Eulerian approach for CFD, while the reconstructed mitral valve is immersed in the computational domain by means of a resistive method. We assess clinically relevant flow and pressure indicators in a parametric study for different degrees of SAM severity, in order to provide a better quantitative evaluation of the pathological condition. Moreover, we provide specific indications for its possible surgical treatment, i.e. septal myectomy.

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.

An Immersed Interface Method for Discrete Surfaces

Fluid-structure systems occur in a range of scientific and engineering applications. The immersed boundary (IB) method is a widely recognized and effective modeling paradigm for simulating fluid-structure interaction (FSI) in such systems, but a difficulty of the IB formulation of these problems is that the pressure and viscous stress are generally discontinuous at fluid-solid interfaces. The conventional IB method regularizes these discontinuities, which typically yields low-order accuracy at these interfaces. The immersed interface method (IIM) is an IB-like approach to FSI that sharply imposes stress jump conditions, enabling higher-order accuracy, but prior applications of the IIM have been largely restricted to numerical methods that rely on smooth representations of the interface geometry. This paper introduces an immersed interface formulation that uses only a C 0 representation of the immersed interface, such as those provided by standard nodal Lagrangian finite element methods. Verification examples for models with prescribed interface motion demonstrate that the method sharply resolves stress discontinuities along immersed boundaries while avoiding the need for analytic information about the interface geometry. Our results also demonstrate that only the lowest-order jump conditions for the pressure and velocity gradient are required to realize global second-order accuracy. Specifically, we demonstrate second-order global convergence rates along with nearly second-order local convergence in the Eulerian velocity field, and between first- and second-order global convergence rates along with approximately first-order local convergence for the Eulerian pressure field. We also demonstrate approximately second-order local convergence in the interfacial displacement and velocity along with first-order local convergence in the fluid traction along the interface. As a demonstration of the method's ability to tackle more complex geometries, the present approach is also used to simulate flow in a patient-averaged anatomical model of the inferior vena cava, which is the large vein that carries deoxygenated blood from the lower extremities back to the heart. Comparisons of the general hemodynamics and wall shear stress obtained by the present IIM and a body-fitted discretization approach show that the present method yields results that are in good agreement with those obtained by the body-fitted approach.

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.

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.

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.

Image-Guided Fluid-Structure Interaction Simulation of Transvalvular Hemodynamics: Quantifying the Effects of Varying Aortic Valve Leaflet Thickness

When flow-induced forces are altered at the blood vessel, maladaptive remodeling can occur. One reason such remodeling may occur has to do with the abnormal functioning of the aortic heart valve due to disease, calcification, injury, or an improperly-designed prosthetic valve, which restricts the opening of the valve leaflets and drastically alters the hemodynamics in the ascending aorta. While the specifics underlying the fundamental mechanisms leading to changes in heart valve function may differ from one cause to another, one common and important change is in leaflet stiffness and/or mass. Here, we examine the link between valve stiffness and mass and the hemodynamic environment in aorta by coupling magnetic resonance imaging (MRI) with high-resolution fluid–structure interaction (FSI) computational fluid dynamics to simulate blood flow in a patient-specific model. The thoracic aorta and a native aortic valve were re-constructed in the FSI model from the MRI data and used for the simulations. The effect of valve stiffness and mass is parametrically investigated by varying the thickness (h) of the leaflets (h = 0.6, 2, 4 mm). The FSI simulations were designed to investigate systematically progressively higher levels of valve stiffness by increasing valve thickness and quantifying hemodynamic parameters known to be linked to aortopathy and valve disease. The computed results reveal dramatic differences in all hemodynamic parameters: (1) the geometric orifice area (GOA), (2) the maximum velocity V max of the jet passing through the aortic orifice area, (3) the rate of energy dissipation E ˙ diss ( t ) , (4) the total loss of energy E diss , (5) the kinetic energy of the blood flow E kin ( t ) , and (6) the average magnitude of vorticity Ω a ( t ) , illustrating the change in hemodynamics that occur due to the presence of aortic valve stenosis.

Principles of TAVR valve design, modelling, and testing

INTRODUCTION

Transcatheter aortic valve replacement (TAVR) has emerged as an effective minimally-invasive alternative to surgical valve replacement in medium- to high-risk, elderly patients with calcific aortic valve disease and severe aortic stenosis. The rapid growth of the TAVR devices market has led to a high variety of designs, each aiming to address persistent complications associated with TAVR valves that may hamper the anticipated expansion of TAVR utility.

AREAS COVERED

Here we outline the challenges and the technical demands that TAVR devices need to address for achieving the desired expansion, and review design aspects of selected, latest generation, TAVR valves of both clinically-used and investigational devices. We further review in detail some of the up-to-date modeling and testing approaches for TAVR, both computationally and experimentally, and additionally discuss those as complementary approaches to the ISO 5840-3 standard. A comprehensive survey of the prior and up-to-date literature was conducted to cover the most pertaining issues and challenges that TAVR technology faces.

EXPERT COMMENTARY

The expansion of TAVR over SAVR and to new indications seems more promising than ever. With new challenges to come, new TAV design approaches, and materials used, are expected to emerge, and novel testing/modeling methods to be developed.

A unified continuum and variational multiscale formulation for fluids, solids, and fluid-structure interaction

We develop a unified continuum modeling framework using the Gibbs free energy as the thermodynamic potential. This framework naturally leads to a pressure primitive variable formulation for the continuum body, which is well-behaved in both compressible and incompressible regimes. Our derivation also provides a rational justification of the isochoric-volumetric additive split of free energies in nonlinear elasticity. The variational multiscale analysis is performed for the continuum model to construct a foundation for numerical discretization. We first consider the continuum body instantiated as a hyperelastic material and develop a variational multiscale formulation for the hyper-elastodynamic problem. The generalized-α method is applied for temporal discretization. A segregated algorithm for the nonlinear solver, based on the original idea introduced in [107], is carefully analyzed. Second, we apply the new formulation to construct a novel unified formulation for fluid-solid coupled problems. The variational multiscale formulation is utilized for spatial discretization in both fluid and solid subdomains. The generalized-α method is applied for the whole continuum body, and optimal high-frequency dissipation is achieved in both fluid and solid subproblems. A new predictor multi-corrector algorithm is developed based on the segregated algorithm. The efficacy of the new formulations is examined in several benchmark problems. The results indicate that the proposed modeling and numerical methodologies constitute a promising technology for biomedical and engineering applications, particularly those necessitating incompressible models.

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.

Robust variational segmentation of 3D bone CT data with thin cartilage interfaces

We present a two-stage variational approach for segmenting 3D bone CT data that performs robustly with respect to thin cartilage interfaces. In the first stage, we minimize a flux-augmented Chan-Vese model that accurately segments well-separated regions. In the second stage, we apply a new phase-field fracture inspired model that reliably eliminates spurious bridges across thin cartilage interfaces, resulting in an accurate segmentation topology, from which each bone object can be identified. Its mathematical formulation is based on the phase-field approach to variational fracture, which naturally blends with the variational approach to segmentation. We successfully test and validate our methodology for the segmentation of 3D femur and vertebra bones, which feature thin cartilage regions in the hip joint, the intervertebral disks, and synovial joints of the spinous processes. The major strength of the new methodology is its potential for full automation and seamless integration with downstream predictive bone simulation in a common finite element framework.

Synergy between Diastolic Mitral Valve Function and Left Ventricular Flow Aids in Valve Closure and Blood Transport during Systole

Highly resolved three-dimensional (3D) fluid structure interaction (FSI) simulation using patient-specific echocardiographic data can be a powerful tool for accurately and thoroughly elucidating the biomechanics of mitral valve (MV) function and left ventricular (LV) fluid dynamics. We developed and validated a strongly coupled FSI algorithm to fully characterize the LV flow field during diastolic MV opening under physiologic conditions. Our model revealed that distinct MV deformation and LV flow patterns developed during different diastolic stages. A vortex ring that strongly depended on MV deformation formed during early diastole. At peak E wave, the MV fully opened, with a local Reynolds number of ~5500, indicating that the flow was in the laminar-turbulent transitional regime. Our results  showed that during diastasis, the vortex structures caused the MV leaflets to converge, thus increasing mitral jet’s velocity. The vortex ring became asymmetrical, with the vortex structures on the anterior side being larger than on the posterior side. During the late diastolic stages, the flow structures advected toward the LV outflow tract, enhancing fluid transport to the aorta. This 3D-FSI study demonstrated the importance of leaflet dynamics, their effect on the vortex ring, and their influence on MV function and fluid transport within the LV during diastole.

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.

A framework for designing patient-specific bioprosthetic heart valves using immersogeometric fluid-structure interaction analysis

Numerous studies have suggested that medical image derived computational mechanics models could be developed to reduce mortality and morbidity due to cardiovascular diseases by allowing for patient-specific surgical planning and customized medical device design. In this work, we present a novel framework for designing prosthetic heart valves using a parametric design platform and immersogeometric fluid-structure interaction (FSI) analysis. We parameterize the leaflet geometry using several key design parameters. This allows for generating various perturbations of the leaflet design for the patient-specific aortic root reconstructed from the medical image data. Each design is analyzed using our hybrid arbitrary Lagrangian-Eulerian/immersogeometric FSI methodology, which allows us to efficiently simulate the coupling of the deforming aortic root, the parametrically designed prosthetic valves, and the surrounding blood flow under physiological conditions. A parametric study is performed to investigate the influence of the geometry on heart valve performance, indicated by the effective orifice area and the coaptation area. Finally, the FSI simulation result of a design that balances effective orifice area and coaptation area reasonably well is compared with patient-specific phase contrast magnetic resonance imaging data to demonstrate the qualitative similarity of the flow patterns in the ascending aorta.

Fluid-structure interaction of a pulsatile flow with an aortic valve model: A combined experimental and numerical study

The complex fluid-structure interaction problem associated with the flow of blood through a heart valve with flexible leaflets is investigated both experimentally and numerically. In the experimental test rig, a pulse duplicator generates a pulsatile flow through a biomimetic rigid aortic root where a model of aortic valve with polymer flexible leaflets is implanted. High-speed recordings of the leaflets motion and particle image velocimetry measurements were performed together to investigate the valve kinematics and the dynamics of the flow. Large eddy simulations of the same configuration, based on a variant of the immersed boundary method, are also presented. A massively parallel unstructured finite-volume flow solver is coupled with a finite-element solid mechanics solver to predict the fluid-structure interaction between the unsteady flow and the valve. Detailed analysis of the dynamics of opening and closure of the valve are conducted, showing a good quantitative agreement between the experiment and the simulation regarding the global behavior, in spite of some differences regarding the individual dynamics of the valve leaflets. A multicycle analysis (over more than 20 cycles) enables to characterize the generation of turbulence downstream of the valve, showing similar flow features between the experiment and the simulation. The flow transitions to turbulence after peak systole, when the flow starts to decelerate. Fluctuations are observed in the wake of the valve, with maximum amplitude observed at the commissure side of the aorta. Overall, a very promising experiment-vs-simulation comparison is shown, demonstrating the potential of the numerical method.

A contact formulation based on a volumetric potential: Application to isogeometric simulations of atrioventricular valves

This work formulates frictionless contact between solid bodies in terms of a repulsive potential energy term and illustrates how numerical integration of the resulting forces is computationally similar to the "pinball algorithm" proposed and studied by Belytschko and collaborators in the 1990s. We thereby arrive at a numerical approach that has both the theoretical advantages of a potential-based formulation and the algorithmic simplicity, computational efficiency, and geometrical versatility of pinball contact. The singular nature of the contact potential requires a specialized nonlinear solver and an adaptive time stepping scheme to ensure reliable convergence of implicit dynamic calculations. We illustrate the effectiveness of this numerical method by simulating several benchmark problems and the structural mechanics of the right atrioventricular (tricuspid) heart valve. Atrioventricular valve closure involves contact between every combination of shell surfaces, edges of shells, and cables, but our formulation handles all contact scenarios in a unified manner. We take advantage of this versatility to demonstrate the effects of chordal rupture on tricuspid valve coaptation behavior.

Projection-based stabilization of interface Lagrange multipliers in immersogeometric fluid-thin structure interaction analysis, with application to heart valve modeling

This paper discusses a method of stabilizing Lagrange multiplier fields used to couple thin immersed shell structures and surrounding fluids. The method retains essential conservation properties by stabilizing only the portion of the constraint orthogonal to a coarse multiplier space. This stabilization can easily be applied within iterative methods or semi-implicit time integrators that avoid directly solving a saddle point problem for the Lagrange multiplier field. Heart valve simulations demonstrate applicability of the proposed method to 3D unsteady simulations. An appendix sketches the relation between the proposed method and a high-order-accurate approach for simpler model problems.