6.2019 - Implementing the HEART Module in 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 equation. The total magnetization in a voxel is the diffusion MRI signal. We have developed a Matlab toolbox called SpinDoctor that solves the Bloch-Torrey equation; the space discretization uses P1 finite elements and the time discretiztion uses build-in Matlab routines for solving ordinary differential equations.
SpinDoctor was developed for modeling diffusion MRI for the brain. The modeling of diffusion MRI for moving and deforming organs such as the heart is more challenging due to significant motion and deformation of the imaged medium during the signal acquisition. Recently, a mathematical formulation of the Bloch-Torrey equation that accounts for motion and deformation was published and we have implemented the numerical solution of this new equation using finite elements.
The intern will
1. Improve an existing code that solves the Bloch-Torrey equation in moving and deforming domains;
2. Publish the above code as the HEART Module inside SpinDoctor on GibHub;
3. Help prepare the User Manual for the HEART Module;
4. Help prepare a scientific article about the HEART Module;
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 supervisor 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
1. SpinDoctor is located on GitHub: https://github.com/jingrebeccali/SpinDoctor
2. J.-R. Li, V.-D. Nguyen, T. N. Tran, J. Valdman, C.-B. Trang, K. V. Nguyen, D. T. S. Vu, H. A. Tran, H. T. A. Tran, T. M. P. Nguyen, SpinDoctor: a Matlab toolbox for diffusion MRI simulation. Neuroimage. 2019.