3.2020 - SpinDoctor: a Matlab toolbox for diffusion MRI simulation

The complex transverse water proton magnetization subject to diffusion-encoding magnetic field gradient pulses in a heterogeneous medium can be modeled by the multiple compartment Bloch-Torrey partial differential equation (BTPDE). This project concerns a Matlab toolbox called SpinDoctor that can be used to solve the BTPDE to obtain the dMRI signal; SpinDoctor provides build-in examples of 1) ellipsoid cells with the option of inserting a nucleus; 2) cylindrical cells with the option of including a myelin layer; 3) enclosing the cells in a computational box is also allowed. The space discretization is by P1 finite elements
and the time discretiztion uses build-in Matlab routines for solving ordinary differential equations.
The intern will improve the code of this toolbox and help prepare the User Manual. The toolbox can be
found at GitHub: https://github.com/jingrebeccali/SpinDoctor.
Specifically: the intern will
        1. run many 3-dimensional examples using this toolbox.
        2. save the computational times and compute the errors of the solutions.
        3. make plots and figures for the User Manual.
        4. make changes to the code in order to make it more user-friendly.
Requirements: This project requires the knowledge of basic partial differential equations (diffusion equation properties), numerical analysis (ODE solvers, numerical stiffness), and finite elements (constructing finite element matrices). Very importantly, it is necessary that the student can write good code in “Matlab” (correct and fast to run, i.e., using matrix/vector operations rather than loops, etc...).
Supervisors: Jing-Rebecca Li (email: jingrebecca.li@inria.fr, web:
http://www.cmap.polytechnique.fr/~jingrebeccali)
Place: Centre de Mathématiques Appliquées (CMAP), École Polytechnique – 91128 Palaiseau, France.
This year, the student will stay in Vietnam to do the internship. There is no possibility of coming to
France in 2021.
References

http://www.cmap.polytechnique.fr/~jingrebeccali/papers/Paper_SpinDoctor.pdf