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User Manual
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Growth of Lesion
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The optimization problem is solved thanks to the minimization of the Lagrangian


.. math::

 \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. 



See our `paper`_ for more details.

.. _paper: https://www.biorxiv.org/content/10.1101/2022.01.13.476165v1



Tutorial
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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.

.. image:: /solora.jpg
    :width: 600