Numerical Simulation of Anisotropic Tissue Growth Using a Total Lagrangian Formulation

Abstract

This paper describes a new method for simulating tissue growth which can handle anisotropic changes in volume. The method takes advantage of the total Lagrangian formulation which allows the computation of nodal forces for each element in a finite element mesh based on a theoretical stress-free configuration, obtained by considering the unconstrained anisotropic growth of the considered element. The method allows the modelling of shrinking (atrophy), swelling, or tissue growth and the computation of the resulting mechanical stresses in the surrounding tissue. The steady-state solution is obtained using an explicit integration method and dynamic relaxation. The proposed method allows the coupling of continuum mechanical simulations with underlying growth mechanisms, offering a tool for the multiscale study of tissue growth.