Immersed finite element method and its applications to biological systems

Abstract

This paper summarizes the newly developed immersed finite element method (IFEM) and its applications to the modeling of biological systems. This work was inspired by the pioneering work of Professor T.J.R. Hughes in solving fluid-structure interaction problems. In IFEM, a Lagrangian solid mesh moves on top of a background Eulerian fluid mesh which spans the entire computational domain. Hence, mesh generation is greatly simplified. Moreover, both fluid and solid domains are modeled with the finite element method and the continuity between the fluid and solid subdomains is enforced via the interpolation of the velocities and the distribution of the forces with the reproducing Kernel particle method (RKPM) delta function. The proposed method is used to study the fluid-structure interaction problems encountered in human cardiovascular systems. Currently, the heart modeling is being constructed and the deployment process of an angioplasty stent has been simulated. Some preliminary results on monocyte and platelet deposition are presented. Blood rheology, in particular, the shear-rate dependent de-aggregation of red blood cell (RBC) clusters and the transport of deformable cells, are modeled. Furthermore, IFEM is combined with electrokinetics to study the mechanisms of nano/bio filament assembly for the understanding of cell motility.

A partitioned coupling approach for dynamic fluid–structure interaction with applications to biological membranes

“…The three values { A=1,2,3 } are the so-called principal stretches and I denotes the identity tensor. The strain invariants of Equation (25) can be expressed as functions of 2 A as…”

“…Within the biomedical field, for example, the interaction of a viscous incompressible fluid, such as blood with a deformable membrane, as found within heart valves, arteries or veins represents an extraordinary challenge. Research within the biomedical field could influence many aspects of diagnosis and treatment as well as the design and implementation of components such as artificial heart valves, stents and many others [1][2][3][4].…”

Cell and nanoparticle transport in tumour microvasculature: the role of size, shape and surface functionality of nanoparticles

“…The IMFEM [78][79][80][81][82][83] is a computational framework to concurrently deal with the relevant physical interactions in biological environments [80,84,85], including fluid-structure interaction (FSI) [82,86,87], cell-cell interaction [81,88,89], thermal fluctuation [78,79,90], electrokinetics [83,91,92], self-assembly behaviour [79,[93][94][95] and other mesoscale and molecular effects [96]. In this work, the IMFEM will be used to simulate the blood flow as well as the microcirculation of NPs.…”

Microscale Flow Dynamics of Red Blood Cells in Microchannels: An Experimental and Numerical Analysis

“…Some examples for this type of approach are the boundary element method [23,26,34], the immersed boundary method [2,7,24,31], the lattice Boltzmann method [6,29] and the moving particle semi-implicit (MPS) method [19,30]). Recent reviews on these numerical methods can be found in Liu et al [18], Yamaguchi et al [33] and Lima et al [14]. Although the multiphase flow approach is a very promising method it requires massive computational power.…”