1676 Some advances in modeling multiphysics-biomedical applications Nagi Elabbasi a , Klaus-Jürgen Bathe b,* a ADINA R &D, Inc., 71 Elton Avenue, Watertown, MA 02472, USA b Department of Mechanical Engineering, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, MA 02139, USA Abstract The ﬁnite element analysis of biomedical applications requires powerful solid, ﬂuid and multiphysics capabilities. In this paper, a brief summary of some recent multiphysics developments is provided, followed by three demonstrative examples. The ﬁrst is an illustrative multiphysics problem showing ﬂuid–structure interaction (FSI), ﬂow through porous media, thermal coupling and mass transfer. The second example is a coupled FSI problem involving blood ﬂow through a stenotic artery. The third example involves a helmet impact simulation. Keywords: Multiphysics; Biomedical applications; Fluid–structure interaction; FSI; ADINA 1. Introduction During recent years there has been an increasing in- terest in the numerical solution of biomedical problems [1,2]. Typical problems analyzed are found in the ar- eas related to hemodynamics, artiﬁcial organs, orthotics, prosthetics, medical devices, cell mechanics, bioreactors, cartilage/bone mechanics, eye surgery, crash testing, abla- tion procedures, and drug delivery systems. For the analysis of many such problems multiphysics ﬁnite element solution capabilities are needed. The objective of this paper is to highlight some new ﬁnite element multiphysics capabilities that we have been developing, and to provide examples to demonstrate these capabilities [3–5]. 2. Features needed for biomedical multiphysics applications Frequently, in biomedical applications ﬂuid–structure interaction (FSI) capabilities are needed. The FSI capa- bilities relevant to the biomedical ﬁeld include coupling along solid-ﬂuid boundaries, which is essential for mod- eling blood circulation problems such as those involving arteriosclerosis, aneurysms, grafts, endovascular stents, or heart valves [6–8]. The coupling between ﬂuids and solid porous media where both the solid and ﬂuid models share * Corresponding author. Tel.: +1 (617) 253-6645; Fax: +1 (617) 253-2275; E-mail: kjb@mit.edu the same space is also relevant. This feature is useful in modeling bones and brain tissue. Thermo-mechanical cou- pling is another multiphysics capability that is needed in biomedical applications such as in eye surgery simulation and ablation procedures [9]. While each physical component in the analysis of a multiphysics problem may be represented by its own dif- ferent ﬁnite element type, mesh topology, and numerical integration procedure, they should all contribute to a single coupled system of equations. And then it is beneﬁcial to have both direct and iterative solution algorithms for the coupled system of equations. The iterative solution algo- rithm can use existing ﬂuid and structural solvers. However, for problems involving strong coupling a direct solver is required. Regarding the modeling of the kinematics and material behavior, the accurate simulation of biomedical problems requires powerful 2D/3D solid elements, beam and shell elements, with linear and nonlinear responses and an ex- tensive material library. The material library should include several hyperelastic models suitable for blood vessels, vis- coelastic models suitable for cells, and porous models suitable for biological tissues. A robust frictional contact algorithm is required for numerous biomedical problems such as encountered in nerve contact, orthotic components and spine mechanics [10–12]. The ﬂuids module of a com- putational code should be able to handle the Navier-Stokes incompressible, slightly compressible and low-speed com- pressible ﬂows. It should handle mass transfer equations, which are useful in simulating drug delivery problems or bioreactors [13]. It should also include Poisson-type equa-  2003 Elsevier Science Ltd. All rights reserved. Computational Fluid and Solid Mechanics 2003 K.J. Bathe (Editor)