121 research outputs found
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
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
A coupled mitral valve - left ventricle model with fluid-structure interaction
Understanding the interaction between the valves and walls of the heart is important in assessing and subsequently treating heart dysfunction. This study presents an integrated model of the mitral valve (MV) coupled to the left ventricle (LV), with the geometry derived from in vivo clinical magnetic resonance images. Numerical simulations using this coupled MV–LV model are developed using an immersed boundary/finite element method. The model incorporates detailed valvular features, left ventricular contraction, nonlinear soft tissue mechanics, and fluid-mediated interactions between the MV and LV wall. We use the model to simulate cardiac function from diastole to systole. Numerically predicted LV pump function agrees well with in vivo data of the imaged healthy volunteer, including the peak aortic flow rate, the systolic ejection duration, and the LV ejection fraction. In vivo MV dynamics are qualitatively captured. We further demonstrate that the diastolic filling pressure increases significantly with impaired myocardial active relaxation to maintain a normal cardiac output. This is consistent with clinical observations. The coupled model has the potential to advance our fundamental knowledge of mechanisms underlying MV–LV interaction, and help in risk stratification and optimisation of therapies for heart diseases
A fully resolved active musculo-mechanical model for esophageal transport
Esophageal transport is a physiological process that mechanically transports
an ingested food bolus from the pharynx to the stomach via the esophagus, a
multi-layered muscular tube. This process involves interactions between the
bolus, the esophagus, and the neurally coordinated activation of the esophageal
muscles. In this work, we use an immersed boundary (IB) approach to simulate
peristaltic transport in the esophagus. The bolus is treated as a viscous fluid
that is actively transported by the muscular esophagus, which is modeled as an
actively contracting, fiber-reinforced tube. A simplified version of our model
is verified by comparison to an analytic solution to the tube dilation problem.
Three different complex models of the multi-layered esophagus, which differ in
their activation patterns and the layouts of the mucosal layers, are then
extensively tested. To our knowledge, these simulations are the first of their
kind to incorporate the bolus, the multi-layered esophagus tube, and muscle
activation into an integrated model. Consistent with experimental observations,
our simulations capture the pressure peak generated by the muscle activation
pulse that travels along the bolus tail. These fully resolved simulations
provide new insights into roles of the mucosal layers during bolus transport.
In addition, the information on pressure and the kinematics of the esophageal
wall due to the coordination of muscle activation is provided, which may help
relate clinical data from manometry and ultrasound images to the underlying
esophageal motor function
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