mass transport (via the flux terms) and inter-conversion of species (via the source/sink terms) introduced above, the concentrations, $\rho_0^\iota$, change with time. In local form, the balance of mass for an arbitrary species in the reference configuration is

$$\frac{\partial\rho_0^\iota}{\partial t} = \Pi^\iota -
\mathrm{\small{DIV}}[\bM^\iota],\;\forall\,\iota,
\label{massbalance1}$$

recalling that, in particular, $\bM^{c} = \bzero$. Here, $\mathrm{\small{DIV}[\bullet]}$ is the divergence operator in the reference configuration. The functional forms of $\Pi^\iota$ are abstractions of the underlying biochemistry, physiologically relevant examples of which are discussed in Section \[sources\], and the fluxes, $\bM^\iota$, are determined from the thermodynamically-motivated constitutive relations described in Section \[flux const\].

The behaviour of the entire system can be determined by summing over all species $\iota$. Additionally, sources and sinks satisfy the relation

$$\sum\limits_\iota\Pi^\iota = 0, \label{sourcebalance}$$

which is consistent [@growthpaper] with the Law of Mass Action for reaction rates and with Mixture Theory [@TruesdellNoll:65].

### The role of mass balance in the current configuration {#curr-ref-mb}

In order to proceed, we must first introduce the central kinematic assumption underlying the formulation: We assume that the pore structure deforms with the collagenous phase. Therefore, the deformation gradient, $\bF$, is common to c and the fluid-filled pore spaces. Furthermore, in what follows, we will 