  In this paper we address some modelling issues related to biological growth.
Our treatment is based on a recently-proposed, general formulation for growth
within the context of Mixture Theory (Journal of the Mechanics and Physics of
Solids, 52, 2004, 1595--1625). We aim to enhance this treatment by making it
more appropriate for the biophysics of growth in porous soft tissue,
specifically tendon. This involves several modifications to the mathematical
formulation to represent the reactions, transport and mechanics, and their
interactions. We also reformulate the governing differential equations for
reaction-transport to represent the incompressibility constraint on the fluid
phase of the tissue. This revision enables a straightforward implementation of
numerical stabilisation for the hyperbolic, or advection-dominated, limit. A
finite element implementation employing an operator splitting scheme is used to
solve the coupled, non-linear partial differential equations that arise from
the theory. Motivated by our experimental model, an in vitro scaffold-free
engineered tendon formed by self-assembly of tendon fibroblasts (Tissue
Engineering, 10, 2004, 755--761), we solve several numerical examples
demonstrating biophysical aspects of tissue growth, and the improved numerical
performance of the models.
