User Manual

Growth of Lesion

The optimization problem is solved thanks to the minimization of the Lagrangian

\[\begin{split}\mathcal{L}(a,D) = \frac{1}{2} \int_{t_3}^{t_7} \int_\Omega (u({\bf x},t, \theta) - u_{reg}({\bf x},t))^2 d{\bf x} dt \\ + \int_{t_3}^{t_7} \int_\Omega \left( \frac{\partial u({\bf x},t, \theta)}{\partial t} - D \Delta u({\bf x},t, \theta) \right. \\ \hskip1cm \left. - \; a u({\bf x},t, \theta)\left( 1-\frac{u({\bf x},t, \theta)}{K} \right) \right) \lambda({\bf x},t, \theta) d{\bf x} dt.\end{split}\]

See our paper for more details.

Tutorial

Open Parameters.py and modify them as you wish:

• f is a scaling parameters such that the size of the original image is multiplied by f.

• T, dt, N is the time in day, the time step and the number of iterations respectively.

• tol, (rho1, rho2), Maxiter is the tolerance of the cost function, the parmaters of the gradient method, and the maximum number of iteration to compute the gradient respectively.

In a terminal, you can run the code as sequential using

python LoopOnFolders.py

In a terminal, you can run the code as parallel using

mpirun -n 4 python LoopOnFolders.py

The results will be in the res folder. VTI files require paraview to be visualised.