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Mathematical Problems in Engineering
Volume 2015 (2015), Article ID 674639, 5 pages
http://dx.doi.org/10.1155/2015/674639
Research Article

Numerical Simulation of Anisotropic Tissue Growth Using a Total Lagrangian Formulation

Intelligent Systems for Medicine Laboratory, School of Mechanical and Chemical Engineering, The University of Western Australia, 35 Stirling Highway, Crawley, Perth, WA 6009, Australia

Received 18 December 2014; Revised 30 January 2015; Accepted 30 January 2015

Academic Editor: Davide Spinello

Copyright © 2015 Grand Roman Joldes and Benjamin Zwick. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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.