A Coupled Soft Tissue Continuum-Transient Blood flow Model to Investigate the Circulation in Deep Veins of the Calf under Compression

Abstract

A coupled computational model of a 3D soft tissue continuum and a one-dimensional transient blood flow network is presented in this paper. The primary aim of the model is to investigate the reduction in vessel cross section area and resulting vessel wall shear stresses (WSS) in response to the compression applied on the calf. Application of external compression on the lower leg is a commonly used prophylaxis against thrombus formation in deep veins. The soft tissue continuum model is a tri-cubic Hermite finite element mesh representing all the muscles, skin and subcutaneous fat in the calf and treated as incompressible with homogeneous isotropic properties. The deformed state of the soft tissue due to the applied compression is obtained by solving large or nonlinear deformation mechanics equations using the Galerkin finite element method. The geometry of the main deep vein network is represented by a 1D Hermite cubic finite element mesh. The flow computational model consists of 1D Navier-Stokes equations and a non-linear constitutive equation to describe vessel radius-transmural pressure relationship. Once compression is applied, the transmural pressure is computed as the difference between the fluid and soft tissue hydrostatic pressure. The latter arises due to the incompressibility of the soft tissue material. Transient flow governing equations are solved using the McCormack finite difference method. The geometry of both the soft tissue continuum and vein network is anatomicallybased and was developed using data derived from magnetic resonance images (MRI). Simulation results from the computational model show a reasonably good agreement with the results reported in the literature on the degree of deformation in vein cross-section area estimated using MRI.