of the tissue. This phenomenon has been accounted for previously by us in fields unrelated to Biology, using the idea of thermal expansion. See, for example, @Rao2:00 and @Garikipatietal:01, which, too, are probably not the first instances of this idea. In the literature on biological growth this connection was made by @KlischHoger:2003.

In the present paper, we seek to restrict the range of physically-admissible models in order to gain greater physiological relevance for modelling growth in soft biological tissue. We also include one improvement in the mathematical/numerical treatment: The advection-diffusion equations for mass transport require numerical stabilisation in the advection-dominated regime (the hyperbolic limit). We draw upon the enforcement of the incompressibility limit for the fluid phase to facilitate this development. Below, we briefly introduce each aspect that we have considered, but postpone details until relevant sections in the paper.

-   For a tissue undergoing finite strain, the transport equations can be formulated, mathematically, in terms of concentrations with respect to either the reference or current (deformed) configuration. However, the physics of fluid-tissue interactions and the imposition of relevant boundary conditions is best understood and represented in the current configuration.

-   The state of saturation is crucial in determining whether 