Limitation of Finite Element Analysis of Poroelastic Behavior of Biological Tissues Undergoing Rapid Loading

摘要

The finite element method is used in biomechanics to provide numerical solutions to simulations of structures having complex geometry and spatially differing material properties. Time-varying load deformation behaviors can result from solid viscoelasticity as well as viscous fluid flow through porous materials. Finite element poroelastic analysis of rapidly loaded slow-draining materials may be ill-conditioned, but this problem is not widely known in the biomechanics field. It appears as instabilities in the calculation of interstitial fluid pressures, especially near boundaries and between different materials. Accurate solutions can require impractical compromises between mesh size and time steps. This article investigates the constraints imposed by this problem on tissues representative of the intervertebral disc, subjected to moderate physiological rates of deformation. Two test cylindrical structures were found to require over 10⁴ linear displacement-constant pressure elements to avoid serious oscillations in calculated fluid pressure. Fewer Taylor–Hood (quadratic displacement–linear pressure elements) were required, but with complementary increases in computational costs. The Vermeer–Verruijt criterion for 1D mesh size provided guidelines for 3D mesh sizes for given time steps. Pressure instabilities may impose limitations on the use of the finite element method for simulating fluid transport behaviors of biological soft tissues at moderately rapid physiological loading rates.