follows: Balance equations and kinematics are discussed in Section \[sec:2\], constitutive relations for reactions, transport and mechanics in Section \[sec:3\], and numerical examples are presented in Section \[numericalimplementation\]. Conclusions are drawn in Section \[sec:5\].

Balance equations and kinematics of growth {#sec:2}
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In this section, the coupled, continuum balance equations governing the behaviour of growing tissue are summarised and specialised as outlined in Section \[sec:1\]. For detailed continuum mechanical arguments underlying the equations, the interested reader is directed to @growthpaper.

The tissue of interest is an open subset of $\mathbb{R}^3$ with a piecewise smooth boundary. At a reference placement of the tissue, $\Omega_0$, points in the tissue are identified by their reference positions, $\bX \in \Omega_0$. The motion of the tissue is a sufficiently smooth bijective map $\Bvarphi: \overline{\Omega}_0
\times [0,T] \rightarrow \mathbb{R}^3$, where $\overline{\Omega}_0 :=
\Omega_0 \cup \partial\Omega_0$; $\partial\Omega_0$ being the boundary of $\Omega_0$. At a typical time $t \in [0,T]$, $\Bvarphi(\bX,t)$ maps a point $\bX$ to its current position, $\bx$. In its current configuration, the tissue occupies a region $\Omega_t = \Bvarphi_t
(\Omega_0)$. These details are depicted in Figure \[cp\]. The deformation gradient $\bF := \partial \Bvarphi/ \partial\bX$ is the tangent map of $\Bvarphi$.

The tissue consists of 