Dynamic finite-strain modelling of the human left ventricle in health and disease using an immersed boundary-finite element method

Detailed models of the biomechanics of the heart are important both for developing improved interventions for patients with heart disease and also for patient risk stratification and treatment planning. For instance, stress distributions in the heart affect cardiac remodelling, but such distributions are not presently accessible in patients. Biomechanical models of the heart offer detailed three-dimensional deformation, stress and strain fields that can supplement conventional clinical data. In this work, we introduce dynamic computational models of the human left ventricle (LV) that are derived from clinical imaging data obtained from a healthy subject and from a patient with a myocardial infarction (MI). Both models incorporate a detailed invariant-based orthotropic description of the passive elasticity of the ventricular myocardium along with a detailed biophysical model of active tension generation in the ventricular muscle. These constitutive models are employed within a dynamic simulation framework that accounts for the inertia of the ventricular muscle and the blood that is based on an immersed boundary (IB) method with a finite element description of the structural mechanics. The geometry of the models is based on data obtained non-invasively by cardiac magnetic resonance (CMR). CMR imaging data are also used to estimate the parameters of the passive and active constitutive models, which are determined so that the simulated end-diastolic and end-systolic volumes agree with the corresponding volumes determined from the CMR imaging studies. Using these models, we simulate LV dynamics from end-diastole to end-systole. The results of our simulations are shown to be in good agreement with subject-specific CMR-derived strain measurements and also with earlier clinical studies on human LV strain distributions

From medical images to individualized cardiac mechanics: A Physiome approach

Cardiac mechanics is a branch of science that deals with forces, kinematics, and material properties of the heart, which is valuable for clinical applications and physiological studies. Although anatomical and biomechanical experiments are necessary to provide the fundamental knowledge of cardiac mechanics, the invasive nature of the procedures limits their further applicability. In consequence, noninvasive alternatives are required, and cardiac images provide an excellent source of subject-specific and in vivo information. Noninvasive and individualized cardiac mechanical studies can be achieved through coupling general physiological models derived from invasive experiments with subject-specific information extracted from medical images. Nevertheless, as data extracted from images are gross, sparse, or noisy, and do not directly provide the information of interest in general, the couplings between models and measurements are complicated inverse problems with numerous issues need to be carefully considered. The goal of this research is to develop a noninvasive framework for studying individualized cardiac mechanics through systematic coupling between cardiac physiological models and medical images according to their respective merits. More specifically, nonlinear state-space filtering frameworks for recovering individualized cardiac deformation and local material parameters of realistic nonlinear constitutive laws have been proposed. To ensure the physiological meaningfulness, clinical relevance, and computational feasibility of the frameworks, five key issues have to be properly addressed, including the cardiac physiological model, the heart representation in the computational environment, the information extraction from cardiac images, the coupling between models and image information, and also the computational complexity. For the cardiac physiological model, a cardiac physiome model tailored for cardiac image analysis has been proposed to provide a macroscopic physiological foundation for the study. For the heart representation, a meshfree method has been adopted to facilitate implementations and spatial accuracy refinements. For the information extraction from cardiac images, a registration method based on free-form deformation has been adopted for robust motion tracking. For the coupling between models and images, state-space filtering has been applied to systematically couple the models with the measurements. For the computational complexity, a mode superposition approach has been adopted to project the system into an equivalent mathematical space with much fewer dimensions for computationally feasible filtering. Experiments were performed on both synthetic and clinical data to verify the proposed frameworks

Quasi-static imaged-based immersed boundary-finite element model of human left ventricle in diastole

SUMMARY: Finite stress and strain analyses of the heart provide insight into the biomechanics of myocardial function and dysfunction. Herein, we describe progress toward dynamic patient-specific models of the left ventricle using an immersed boundary (IB) method with a finite element (FE) structural mechanics model. We use a structure-based hyperelastic strain-energy function to describe the passive mechanics of the ventricular myocardium, a realistic anatomical geometry reconstructed from clinical magnetic resonance images of a healthy human heart, and a rule-based fiber architecture. Numerical predictions of this IB/FE model are compared with results obtained by a commercial FE solver. We demonstrate that the IB/FE model yields results that are in good agreement with those of the conventional FE model under diastolic loading conditions, and the predictions of the LV model using either numerical method are shown to be consistent with previous computational and experimental data. These results are among the first to analyze the stress and strain predictions of IB models of ventricular mechanics, and they serve both to verify the IB/FE simulation framework and to validate the IB/FE model. Moreover, this work represents an important step toward using such models for fully dynamic fluid–structure interaction simulations of the heart

Hybrid finite difference/finite element immersed boundary method

The immersed boundary method is an approach to fluid-structure interaction that uses a Lagrangian description of the structural deformations, stresses, and forces along with an Eulerian description of the momentum, viscosity, and incompressibility of the fluid-structure system. The original immersed boundary methods described immersed elastic structures using systems of flexible fibers, and even now, most immersed boundary methods still require Lagrangian meshes that are finer than the Eulerian grid. This work introduces a coupling scheme for the immersed boundary method to link the Lagrangian and Eulerian variables that facilitates independent spatial discretizations for the structure and background grid. This approach employs a finite element discretization of the structure while retaining a finite difference scheme for the Eulerian variables. We apply this method to benchmark problems involving elastic, rigid, and actively contracting structures, including an idealized model of the left ventricle of the heart. Our tests include cases in which, for a fixed Eulerian grid spacing, coarser Lagrangian structural meshes yield discretization errors that are as much as several orders of magnitude smaller than errors obtained using finer structural meshes. The Lagrangian-Eulerian coupling approach developed in this work enables the effective use of these coarse structural meshes with the immersed boundary method. This work also contrasts two different weak forms of the equations, one of which is demonstrated to be more effective for the coarse structural discretizations facilitated by our coupling approach

A COMPUTATIONAL STUDY OF PATCH IMPLANTATION AND MITRAL VALVE MECHANICS

Myocardial infarction (i.e., a heart attack) is the most common heart disease in the United States. Mitral valve regurgitation, or the backflow of blood into the atrium from the left ventricle, is one of the complications associated with myocardial infarction. In this dissertation, a validated model of a sheep heart that has suffered myocardial infarction has been employed to study mitral valve regurgitation. The model was rebuilt with the knowledge of geometrical changes captured with MRI technique and is assigned with anisotropic, inhomogeneous, nearly incompressible and highly non-linear material properties. Patch augmentation was performed on its anterior leaflet, using a simplified approach, and its posterior leaflet, using a more realistic approach. In this finite element simulation, we virtually installed an elliptical patch within the central portion of the posterior leaflet. To the best of the author’s knowledge, this type of simulation has not been performed previously. In another simulation, the effect of patch within the anterior leaflet was simulated. The results from the two different surgical simulations show that patch implantation helps the free edges of the leaflets come close to one another, which leads to improved coaptation. Additionally, the changes in chordal force distributions are also reported. Finally, this study answers a few questions regarding mitral valve patch augmentation surgeries and emphasizes the importance of further investigations on the influence of patch positioning and material properties on key outcomes. The ultimate goal is to use the proposed techniques to assess human models that are patient-specific

Doctor of Philosophy

dissertationImage-based biomechanics, particularly numerical modeling using subject-specific data obtained via imaging, has proven useful for elucidating several biomechanical processes, such as prediction of deformation due to external loads, applicable to both normal function and pathophysiology of various organs. As the field evolves towards applications that stretch the limits of imaging hardware and acquisition time, the information traditionally expected as input for numerical routines often becomes incomplete or ambiguous, and requires specific acquisition and processing strategies to ensure physical accuracy and compatibility with predictive mathematical modeling. These strategies, often derivatives or specializations of traditional mechanics, effectively extend the nominal capability of medical imaging hardware providing subject-specific information coupled with the option of using the results for predictive numerical simulations. This research deals with the development of tools for extracting mechanical measurements from a finite set of imaging data and finite element analysis in the context of constructing structural atlases of the heart, understanding the biomechanics of the venous vasculature, and right ventricular failure. The tools include: (1) application of Hyperelastic Warping image registration to displacement-encoded MRI for reconstructing absolute displacement fields, (2) combination of imaging and a material parameter identification approach to measure morphology, deformation, and mechanical properties of vascular tissue, and (3) extrapolation of diffusion tensor MRI acquired at a single time point for the prediction the structural changes across the cardiac cycle with mechanical simulations. Selected tools were then applied to evaluate structural changes in a reversible animal model for right ventricular failure due to pressure overload

A segregated finite element method for cardiac elastodynamics in a fully coupled human heart model

One key characterstic of the cardiac function is its complexity, i.e., the multitude of different phenomena acting on various temporal and spatial scales interacting with each other. Over the past decades, many models varying in complexity describing these interactions were presented and are used in current research. Despite the incredible progress made in describing and simulating cardiac function, most of the more detailed models are not properly embedded within mathematical theory. This work aims to give a precise and comprehensive mathematical formulation of coupled cardiac elastodynamics, including electrophysiology, elasticity and physiological boundary conditions developed in recent years. Focussing on the analysis of dynamic elasticity, the concept of anisotropy is applied to common cardiac tissue models, such as the models of Guccione et al. and Holzapfel and Ogden. Frequently used modeling approaches, such as incompressibility and the active strain decomposition, are integrated in one overarching framework, allowing for propositions on polyconvexity of the materials and solvability of the elastic system. The equations of elastodynamics are then complemented by the monodomain equations, describing the propagation of the excitation potential in cardiac tissue, and a surrogate model to simulate cardiovascular blood pressure. The full mathematical description of this coupled model allows a detailed formulation of a discretization scheme in space and time for the electro-elastodynamical system. The classification of the coupled model within the context of weak solutions is presented and a time-segregated numerical approximation method for the full system is derived. The formulated numerical method is then examined by application on coupled test cases, providing first convergence results in space for the displacement in coupled cardiac problems

Competing mechanisms of stress-assisted diffusivity and stretch-activated currents in cardiac electromechanics

We numerically investigate the role of mechanical stress in modifying the conductivity properties of the cardiac tissue and its impact in computational models for cardiac electromechanics. We follow a theoretical framework recently proposed in [Cherubini, Filippi, Gizzi, Ruiz-Baier, JTB 2017], in the context of general reaction-diffusion-mechanics systems using multiphysics continuum mechanics and finite elasticity. In the present study, the adapted models are compared against preliminary experimental data of pig right ventricle fluorescence optical mapping. These data contribute to the characterization of the observed inhomogeneity and anisotropy properties that result from mechanical deformation. Our novel approach simultaneously incorporates two mechanisms for mechano-electric feedback (MEF): stretch-activated currents (SAC) and stress-assisted diffusion (SAD); and we also identify their influence into the nonlinear spatiotemporal dynamics. It is found that i) only specific combinations of the two MEF effects allow proper conduction velocity measurement; ii) expected heterogeneities and anisotropies are obtained via the novel stress-assisted diffusion mechanisms; iii) spiral wave meandering and drifting is highly mediated by the applied mechanical loading. We provide an analysis of the intrinsic structure of the nonlinear coupling using computational tests, conducted using a finite element method. In particular, we compare static and dynamic deformation regimes in the onset of cardiac arrhythmias and address other potential biomedical applications

Patient-Specific Quantification of the Relationship Between the Left Atrium Pressure and the Ostial Diameter of the Left Atrial Appendage

The left atrial appendage has been a historically understudied region of the heart until fairly recently with the new understanding of its role in the stroke pathway of patients with atrial fibrillation. The goal of this study is to take a look at the biomechanical behavior of the left atrium and left atrial appendage under normal physiological loading conditions using material properties taken from biaxial stretch tests. Several different options for material properties models were tested and biaxial stretch test data of cadaveric human tissue samples for the left atrium and appendage were fit to a Fung-type strain-energy function for input into simulation. Simulations were performed on geometry of the left atrium and appendage extracted from computed tomographical images of a single patient spanning from the pulmonary veins to the mitral valve annulus. Physiological pressure loading conditions were simulated at 5 mmHg, 7.5 mmHg, 10 mmHg, 15 mmHg, and 20 mmHg over two cardiac cycles. Results showed that peak stresses and strains were concentrated at branches in the atrium as well as the ostial entrance to the appendage. Ostial diameter of the appendage was measured across to axes and showed increases from a baseline of 1.347 cm x 2.927 cm in the unloaded configuration up to a size of 1.749 cm x 3.219 cm in the loaded configuration. Finite element simulations may be a useful tool for improving patient treatment options, especially when it comes to mechanical left atrial appendage occlusion devices