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11.2018 - SpinDoctor: a Matlab toolbox for diffusion MRI simulation

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).     A  mathematical  model  for  the  time-dependent effective  diffusion coefficient,  called  the  H-ADC  model,  was  obtained  recently    using  homogenization  techniques.   The effective  diffusion coefficient  of the medium  can be  computed  after solving a diffusion  equation (DE) subject  to  a time-dependent  Neumann boundary condition, under the assumption of negligible water exchange between compartments.

This project concerns a Matlab toolbox called SpinDoctor that can be used 1) to solve the BTPDE to obtain the  dMRI  signal;  2)  to  solve  the  DE  to  obtain  the time-dependent  effective  diffusion  coefficient; 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   The class project used some code from this toolbox to solve the diffusion equation, so the intern should have some experience already with this toolbox.
Specifically: the intern will
  1. 1.    run many 3-dimensional examples using this toolbox.
  2. 2.    save the computational times and compute the errors of the solutions.
  3. 3.    make plots and figures for the User Manual.
  4. 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.
Follow-up PhD position: If the student is interested in starting a PhD position in France or elsewhere, and if the internship project is successfully completed, the superviser will help the student in putting together an application to a PhD position, by providing advice regarding writing a research statement and preparing for a PhD scholarship interview.  This is not a guarantee of a PhD position after the internship, rather an offer of help with preparing the application for a PhD position.
References
http://www.cmap.polytechnique.fr/~jingrebeccali/papers/main_intracellular.pdf
http://www.cmap.polytechnique.fr/~jingrebeccali/papers/fem_rkc_btpde.pdf