1$ we set $\bF^{\mathrm{e}^\mathrm{f}} = \bF(\bF^{\mathrm{g}^\mathrm{f}})^{-1}$ and $\bF^{\mathrm{v}} = {\bf 1}$ for no cavitation. Otherwise, since $\mathrm{det}[\bF(\bF^{\mathrm{g}^\mathrm{f}})^{-1}] > 1$, we specify $\bF^{\mathrm{e}^\mathrm{f}} =
\mathrm{det}[\bF(\bF^{\mathrm{g}^\mathrm{f}})^{-1}]^{-1/3}\bF(\bF^{\mathrm{g}^\mathrm{f}})^{-1}$ thus restricting $\bF^{\mathrm{e}^\mathrm{f}}$ to be unimodular and allow cavitation by writing $\bF^{\mathrm{v}} = \bF(\bF^{\mathrm{e}^\mathrm{f}}\bF^{\mathrm{g}^\mathrm{f}})^{-1}$. These conditional relations are summarized as

$$\bF^{\mathrm{e}^\mathrm{f}} = \left\{ \begin{array}{ll}
  \bF(\bF^{\mathrm{g}^\mathrm{f}})^{-1},\; \bF^{\mathrm{v}} = {\bf 1},&
 \mathrm{det}[\bF(\bF^{\mathrm{g}^\mathrm{f}})^{-1}] \le 1\\
  \mathrm{det}[\bF(\bF^{\mathrm{g}^\mathrm{f}})^{-1}]^{-1/3}\bF(\bF^{\mathrm{g}^\mathrm{f}})^{-1},
  & \\
  \qquad\qquad \bF^{\mathrm{v}} = \bF(\bF^{\mathrm{e}^\mathrm{f}}\bF^{\mathrm{g}^\mathrm{f}})^{-1}
  & \mathrm{otherwise.}
\end{array}\right.
\label{cavitation}$$

Constitutive relations for fluxes {#flux const}
---------------------------------

From @growthpaper, the constitutive relation for the flux of extra-cellular fluid relative to collagen in the reference configuration takes the following form,

$$\bM^\mathrm{f} = \bD^\mathrm{f}\left(\rho_0^\mathrm{f}\bF^T\bg +
      \bF^T\mathrm{\small{DIV}}\left[\bP^{\,\mathrm{f}}\right] -
      \rho_0^\mathrm{f}\mathrm{\small{GRAD}}\mu^\mathrm{f}\right),
\label{fluidflux}$$

where $\bD^\mathrm{f}$ is the positive semi-definite mobility of the fluid, and isothermal conditions are assumed in order to approximate the physiological ones. Experimentally determined transport coefficients (e.g. for mouse tail skin [@Swartzetal:99] and rabbit Achilles tendons [@Hanetal:2000]) are used for the fluid mobility values. The terms in the parenthesis on the right hand-side of sum to give the total driving force for transport. The first term is the contribution due to gravitational acceleration. In order to maintain physiological relevance, this term has been neglected in the following treatment. The second term arises from stress divergence; for 