Nonlinear Incompressible Finite Element for Simulating Loading of Cardiac Tissue—Part II: Three Dimensional Formulation for Thick Ventricular Wall Segments (original) (raw)
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Journal of Biomechanical Engineering, 1988
A two-dimensional incompressible plane-stress finite element is formulated for the simulation of the passive-state mechanics of thin myocardial strips. The formulation employs a total Lagrangian and materially nonlinear approach, being based on a recently proposed structural material law, which is derived from the histological composition of the tissue. The ensuing finite element allows to demonstrate the mechanical properties of a single myocardial layer containing uniformly directed fibers by simulating various loading cases such as tension, compression and shear. The results of these cases show that the fiber direction is considerably stiffer than the cross-fiber direction, that there is significant coupling between these two directions, and that the shear stiffness of the tissue is lower than its tensile and compressive stiffness.
Orthotropic active strain models for the numerical simulation of cardiac biomechanics
International Journal For Numerical Methods in Biomedical Engineering, 2012
A model for the active deformation of cardiac tissue considering orthotropic constitutive laws is introduced and studied. In particular, the passive mechanical properties of the myocardium are described by the Holzapfel-Ogden relation, whereas the activation model is based on the concept of active strain. There, an incompatible intermediate configuration is considered, which entails a multiplicative decomposition between active and passive deformation gradients. The underlying Euler-Lagrange equations for minimizing the total energy are written in terms of these deformation factors, where the active part is assumed to depend, at the cell level, on the electrodynamics and on the specific orientation of the cardiomyocytes. The active strain formulation is compared with the classical active stress model from both numerical and modeling perspectives. The well-posedness of the linear system derived from a generic Newton iteration of the original problem is analyzed, and different mechanical activation functions are considered. Taylor-Hood and MINI finite elements are used in the discretization of the overall mechanical problem. The results of several numerical experiments show that the proposed formulation is mathematically consistent and is able to represent the main features of the phenomenon, while allowing savings in computational costs. Copyright 762 S. ROSSI ET AL.
Computational modeling of passive myocardium
International Journal For Numerical Methods in Biomedical Engineering, 2011
This work deals with the computational modeling of passive myocardial tissue within the framework of mixed, non-linear finite element methods. We consider a recently proposed, convex, anisotropic hyperelastic model that accounts for the locally orthotropic micro-structure of cardiac muscle. A coordinate-free representation of anisotropy is incorporated through physically relevant invariants of the Cauchy-Green deformation tensors and structural tensors of the corresponding material symmetry group. This model, which has originally been designed for exactly incompressible deformations, is extended towards entirely three-dimensional inhomogeneous deformations by additively decoupling the strain energy function into volumetric and isochoric parts along with the multiplicative split of the deformation gradient. This decoupled constitutive structure is then embedded in a mixed finite element formulation through a threefield Hu-Washizu functional whose simultaneous variation with respect to the independent pressure, dilatation, and placement fields results in the associated Euler-Lagrange equations, thereby minimizing the potential energy. This weak form is then consistently linearized for uniform-pressure elements within the framework of an implicit finite element method. To demonstrate the performance of the proposed approach, we present a three-dimensional finite element analysis of a generic biventricular heart model, subjected to physiological ventricular pressure. The parameters employed in the numerical analysis are identified by solving an optimization problem based on six simple shear experiments on explanted cardiac tissue.
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 enddiastole to end-systole. The results of our simulations are shown to be in good agreement with subjectspecific CMR-derived strain measurements and also with earlier clinical studies on human LV strain distributions.
A computational model of the left ventricle biomechanics using a composite material approach
International Journal of Engineering Science, 2017
Several computational models are available for studying cardiac mechanics. These models incorporate tissue passive/active response in conjunction with hyperelasticity and anisotropy. For capturing the active response they involve complicated non-conventional strain energy functions which account for tissue active contraction. They are either implemented as custom-developed non-linear finite element (FE) codes or require user-defined subroutines compiled within commercial FE software packages. Difficulty of computational implementation of such models remains an issue for the research community. Furthermore, myocardial tissue has sophisticated microstructure while pathologies may alter its constituents and their organization. Hence, cardiac mechanics models adaptable to various pathological conditions are advantageous. This paper aims at developing a cardiac mechanics model using a novel approach which does not require strain energy functions developed specifically for simulating myocardial tissue active response, lending itself for effective im plementation in off-the-shelf FE solvers. This model considers myocardial hyperelasticity, anisotropy, and active contraction. It was developed using a tissue composite material model which includes two major parts: background part and myofibers. The model was applied to an in silico geometry of a canine left ventricle (LV). Resulting diastolic pressure-volume curve shows very good agreement with corresponding experimental observations. Also, calculated mid-ventricular end-diastolic strain components are within one standard deviation of measurements performed through the LV equatorial area. Furthermore, computed end-systolic strain components and ejection fraction are close to or within one standard deviation of in-vivo measurements of a beating canine LV. These results demonstrate that the proposed model can be employed as an effective alternative for studying cardiac mechanics.
Computer methods in biomechanics and biomedical engineering, 2016
This study deals with the viscoelastic constitutive modeling and the respective computational analysis of the human passive myocardium. We start by recapitulating the locally orthotropic inner structure of the human myocardial tissue and model the mechanical response through invariants and structure tensors associated with three orthonormal basis vectors. In accordance with recent experimental findings the ventricular myocardial tissue is assumed to be incompressible, thick-walled, orthotropic and viscoelastic. In particular, one spring element coupled with Maxwell elements in parallel endows the model with viscoelastic features such that four dashpots describe the viscous response due to matrix, fiber, sheet and fiber-sheet fragments. In order to alleviate the numerical obstacles, the strictly incompressible model is altered by decomposing the free-energy function into volumetric-isochoric elastic and isochoric-viscoelastic parts along with the multiplicative split of the deformati...
Computer Methods in Applied Mechanics and Engineering, 2014
This paper presents the nodally integrated plate element (NIPE) formulation for the analysis of laminated composite plates based on the first-order shear deformation theory. The nodally integrated approach aims at providing smoothed derivative quantities by constructing nodal strain-displacement operators. Within this framework a new family of elements for plates with general monoclinic layers is developed: the strain-displacement operators are derived via nodal integration for linear triangles and quadrilateral elements. The degrees of freedom are only the primitive variables: displacements and rotations at the nodes. The NIPEs are locking-free elements, exhibit little sensitivity to geometric distortions and can be readily implemented into existing finite element codes. The efficiency of the proposed variational formulation is proved whereas effectiveness and convergence of the proposed finite elements are confirmed through several numerical applications. Finally, numerical results are compared with the corresponding analytical solutions as well as to other finite-element solutions.
A 2D FE model of the heart demonstrates the role of the pericardium in ventricular deformation
AJP: Heart and Circulatory Physiology, 2006
During pulmonary artery constriction (PAC), an experimental model of acute right ventricular (RV) pressure overload, the interventricular septum flattens and inverts. Finite element (FE) analysis has shown that the septum is subject to axial compression and bending when so deformed. This study examines the effects of acute PAC on the left ventricular (LV) free wall and the role the pericardium may play in these effects. In eight open-chest anesthetized dogs, LV, RV, aortic, and pericardial pressures were recorded under control conditions and with PAC. Model dimensions were derived from two-dimensional echocardiography minor-axis images of the heart. At control (pericardium closed), FE analysis showed that the septum was concave to the LV; stresses in the LV, RV, and septum were low; and the pericardium was subject to circumferential tension. With PAC, RV end-diastolic pressure exceeded LV pressure and the septum inverted. Compressive stresses developed circumferentially in the septu...
Journal of biomechanics, 2015
A key element of the cardiac cycle of the human heart is the opening and closing of the four valves. However, the material properties of the leaflet tissues, which fundamentally contribute to determine the mechanical response of the valves, are still an open field of research. The main contribution of the present study is to provide a complete experimental data set for porcine heart valve samples spanning all valve and leaflet types under tensile loading. The tests show a fair degree of reproducibility and are clearly indicative of a number of fundamental tissue properties, including a progressively stiffening response with increasing elongation. We then propose a simple anisotropic constitutive model, which is fitted to the experimental data set, showing a reasonable interspecimen variability. Furthermore, we present a dynamic finite element analysis of the aortic valve to show the direct usability of the obtained material parameters in computational simulations.