The Huiskes specific reaction rate has the form $$k=\frac{B}{J-\varphi_{r}^{s}}\left(\frac{\Psi_{r}}{\rho_{r}^{s}}-\psi_{0}\right)\,,$$ where $\Psi_{r}$ is the strain energy density of the solid (strain energy in current configuration per mixture volume in the reference configuration) and $\rho_{r}^{s}=\sum\nolimits _{\sigma}\rho_{r}^{\sigma}$ is the referential apparent solid density (mass of solid in current configuration per mixture volume in reference configuration). The ratio $\Psi_{r}/\rho_{r}^{s}$ is the specific strain energy (strain energy per mass of solid in the current configuration). The Huiskes specific reaction rate may assume positive and negative values; it reduces to zero at homeostasis, when $\Psi_{r}/\rho_{r}^{s}=\psi_{0}$ .

Example:

To reproduce the interstitial solid remodeling theory proposed by Weinans et al. [56], consider the forward reaction $$\mbox{cells}+\mbox{solutes}\to\mbox{cells}+\mbox{solid}\,,$$ where cells convert solutes (e.g., nutrients) into synthesized solid when the specific strain energy exceeds the homeostatic value. If the cells and solutes are implicit in this reaction (e.g., if it is assumed that their concentrations change negligibly), the production rate of the solid may be given by $\hat{\zeta}=k$ using the law of mass action for a forward rection, where $k$ has the form given above.

<reaction name="solid remodeling" type="mass-action-forward">
  <vP sbm="1">1</vP>
  <forward_rate type="Huiskes reaction rate">
    <B>1.0</B>
    <psi0>0.01</psi0>
  </forward_rate>
  <Km>5.0</Km>
</reaction>