Using a mathematical model of cadherin-based adhesion to understand the function of the actin cytoskeleton

The actin cytoskeleton plays a role in cell-cell adhesion but its specific function is not clear. Actin might anchor cadherins or drive membrane protrusions in order to facilitate cell-cell adhesion. Using a mathematical model of the forces involved in cadherin-based adhesion we investigate its possible functions. The immersed boundary method is used to model the cell membrane and cortex with cadherin binding forces added as linear springs. The simulations indicate that cells in suspension can develop normal cell-cell contacts without actin-based cadherin anchoring or membrane protrusions. The cadherins can be fixed in the membrane or free to move and the end results are similar. For adherent cells, simulations suggest that the actin cytoskeleton must play an active role for the cells to establish cell-cell contact regions similar to those observed in vitro

A theoretical and numerical investigation of a family of immersed finite element methods

In this article we consider the widely used immersed finite element method (IFEM), in both explicit and implicit form, and its relationship to our more recent one-field fictitious domain method (FDM). We review and extend the formulation of these methods, based upon an operator splitting scheme, in order to demonstrate that both the explicit IFEM and the one-field FDM can be regarded as particular linearizations of the fully implicit IFEM. However, the one-field FDM can be shown to be more robust than the explicit IFEM and can simulate a wider range of solid parameters with a relatively large time step. In addition, it can produce results almost identical to the implicit IFEM but without iteration inside each time step. We study the effect on these methods of variations in viscosity and density of fluid and solid materials. The advantages of the one-field FDM within the IFEM framework are illustrated through a selection of parameter sets for two benchmark cases

Efficient and accurate simulations of deformable particles immersed in a fluid using a combined immersed boundary lattice Boltzmann finite element method

The deformation of an initially spherical capsule, freely suspended in simple shear flow, can be computed analytically in the limit of small deformations [D. Barthes-Biesel, J. M. Rallison, The Time-Dependent Deformation of a Capsule Freely Suspended in a Linear Shear Flow, J. Fluid Mech. 113 (1981) 251-267]. Those analytic approximations are used to study the influence of the mesh tessellation method, the spatial resolution, and the discrete delta function of the immersed boundary method on the numerical results obtained by a coupled immersed boundary lattice Boltzmann finite element method. For the description of the capsule membrane, a finite element method and the Skalak constitutive model [R. Skalak et al., Strain Energy Function of Red Blood Cell Membranes, Biophys. J. 13 (1973) 245-264] have been employed. Our primary goal is the investigation of the presented model for small resolutions to provide a sound basis for efficient but accurate simulations of multiple deformable particles immersed in a fluid. We come to the conclusion that details of the membrane mesh, as tessellation method and resolution, play only a minor role. The hydrodynamic resolution, i.e., the width of the discrete delta function, can significantly influence the accuracy of the simulations. The discretization of the delta function introduces an artificial length scale, which effectively changes the radius and the deformability of the capsule. We discuss possibilities of reducing the computing time of simulations of deformable objects immersed in a fluid while maintaining high accuracy.Comment: 23 pages, 14 figures, 3 table

Augmenting the Immersed Boundary Method with Radial Basis Functions (RBFs) for the Modeling of Platelets in Hemodynamic Flows

We present a new computational method by extending the Immersed Boundary (IB) method with a spectrally-accurate geometric model based on Radial Basis Function (RBF) interpolation of the Lagrangian structures. Our specific motivation is the modeling of platelets in hemodynamic flows, though we anticipate that our method will be useful in other applications as well. The efficacy of our new RBF-IB method is shown through a series of numerical experiments. Specifically, we compare our method with the traditional IB method in terms of convergence and accuracy, computational cost, maximum stable time-step size and volume loss. We conclude that the RBF-IB method has advantages over the traditional Immersed Boundary method, and is well-suited for modeling of platelets in hemodynamic flows.Comment: 25 pages, 4 figure

Investigation of in vitro flow-dependent blood-material interactions.

Investigation of in vitro flow-dependent blood-material interactions

Simulating Cardiovascular Fluid Dynamics by the Immersed Boundary Method

The immersed boundary method is both a general mathematical framework and a par-ticular numerical approach to problems of fluid-structure interaction. In this paper, we describe the application of the immersed boundary method to the simulation of cardiovas-cular fluid dynamics, focusing on the fluid dynamics of the aortic heart valve (the valve which prevents the backflow of blood from the aorta into the left ventricle of the heart) and aortic root (the initial portion of the aorta, which attaches to the heart). The aor-tic valve and root are modeled as a system of elastic fibers, and the blood is modeled as a viscous incompressible fluid. Three-dimensional simulation results obtained using a parallel and adaptive version of the immersed boundary method are presented. These results demonstrate that it is feasible to perform three-dimensional immersed boundary simulations of cardiovascular fluid dynamics in which realistic cardiac output is obtained at realistic pressures. Nomenclature U physical domain x = (x, y, z) ∈ U Cartesian (physical) coordinates u(x, t) fluid velocity p(x, t) fluid pressure f(x, t) Eulerian force density applied by the structure to the fluid δ(x) = δ(x) δ(y) δ(z) three-dimensional Dirac delta function δh(x) = δh(x) δh(y) δh(z) three-dimensional regularized Dirac delta function Ω Lagrangian coordinate domain (q, r, s) ∈ Ω Lagrangian (material) coordinates X(q, r, s, t) physical position of Lagrangian (material) point (q, r, s) at time t F(q, r, s, t) Lagrangian force density applied by the structure to the fluid I