Algorithm 1.

Implementation of the tumour-induced brain deformation model.

1. Initialise: $t=\mathbf{0}$, $\mathit{u}(t=\mathbf{0})={\mathit{u}}_{\mathbf{0}}$, ${\mathit{\omega }}_s(t=\mathbf{0})={\mathit{\omega }}_{{\mathit{s}}_{\mathbf{0}}}$ for $s\in \{w,\hspace{0.17em}g,\hspace{0.17em}c\}$

2. Compute tissue percentage by equation (2.14)

3. while $(t\le T)$ do

4. Compute time step $\tau =min({\tau }_1,\hspace{0.17em}{\tau }_2)$, where ${\tau }_1$ and ${\tau }_2$ are time steps constrained by the numerical stability of equations (2.1) and (2.11)

5. Compute the pressure $\mathit{p}(t)$ by solving equations (2.15) and (2.16)

6. Compute the deformation field $\overrightarrow{\mathit{v}}(t)$ by solving equations (2.5) and (2.7)

7. Update the tumour state by solving equations (2.1) and (2.2)

8. Update the brain tissue by solving equations (2.11) and (2.12)

9. Recompute the tissue percentage by equation (2.14)

10. $t=t+\tau$

11. end while