numerous species, of which the following groupings are of importance for the models: A solid species, consisting of solid *collagen fibrils* and *cells*,[^5] denoted by $\mathrm{c}$, an extra-cellular *fluid* species denoted by $\mathrm{f}$ and consisting primarily of water, and *solute* species, consisting of precursors to reactions, byproducts, nutrients, and other regulatory chemicals. A generic solute will be denoted by $\mathrm{s}$. In what follows, an arbitrary species will be denoted by $\iota$, where $\iota = \mathrm{c,f,s}$.

The fundamental quantities of interest are mass concentrations, $\rho_0^\iota(\bX,t)$. These are the masses of each species per unit system volume in $\Omega_0$. Formally, these quantities can also be thought of in terms of the maps $\rho_0^\iota: \overline{\Omega}_0
\times [0,T] \rightarrow \mathbb{R}$, upon which the formulation imposes some smoothness requirements. By definition, the total [*material density*]{} of the tissue at a point is a sum of these concentrations over all species $\sum\limits_{\iota}\rho_0^\iota =
\rho_0$. Other than the solid species, $\mathrm{c}$, all phases have mass fluxes, $\bM^\iota$.[^6] These are mass flow rates per unit cross-sectional area in the reference configuration *defined relative to the solid phase*. The species have mass sources (or sinks), $\Pi^\iota$.

Balance of mass for an open system {#bomass}
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As a result of 