csc 博士 申请

法国inria csc 2023 博士岗位招生，有意请直接邮件联系。
CSC - Institut Polytechnique de Paris PhD Scholarship

Deadline for CSC PhD scholarship application January 5 2023

Deadline for IPP PhD scholarship application April 15 2023

Proposed PhD Topic

Analysis of neuron morphological characteristics

using a PDE model for diffusion MRI

PhD supervisor

Jing-Rebecca Li, INRIA Saclay Equipe IDEFIX, UMA ENSTA Paris, France, jingrebecca.li@inria.fr

Profile of candidate

Undergraduate degree or Master's degree in Mathematics (Computational or Applied); Class or

project experience in PDEs; Class or project experience in machine learning algorithms; Programming experience (Matlab or Python or Julia);

Work conditions

Standard work conditions and benefits for PhD student members of INRIA Saclay and UMA ENSTA

Paris;

Further information and contact

Contact (as soon as possible and before Dec 30 2022 for CSC PhD scholarship application)

jingrebecca.li@inria.fr

https://perso.ensta-paris.fr/~jing-rebecca.li/

To submit an application

https://www.adum.fr/as/ed/voirpr...atricule_prop=44672#version

Summary

The diffusion MRI signal arising from neurons can be numerically simulated by solving the Bloch-

Torrey partial differential equation. In a previous work [Fang et al., NeuroImage, 2020], we constructed high quality finite element meshes for a set of human neurons whose morphological descriptions were found in the publicly available neuron repository NeuroMorpho.Org. To produce a

database of simulated diffusion MRI signals under a large number of experimental acquisition conditions, we numerically computed the eigenfunctions and the eigenvalues of the Laplace operators

on the full set of neuron geometries using a P1 finite elements discretization and stored the relevant

simulation data. A preliminary statistical study on a small subset of neurons was performed to test

some candidate biomakers that can potentially indicate the soma size.

In this PhD project, we propose a systematic analysis of the connection between the diffusion MRI

signal and neuron morphology by conducting statistical studies on a large number of neurons, using

the Bloch-Torrey PDE model that connects the neuron geometry to the diffusion MRI signal. We

also plan to produce robust machine learning algorithms that can output selected morphological

properties from the diffusion MRI signals. Finally, as usual, we will make resulting software and

data available for public use.

Below is a preliminary roadmap for the project.

1. Familiarize with and add to our database of over 1000 human neurons (high quality finite

elements meshes) and their morphological properties;

2. Run and store the simulated diffusion MRI signals under many different experimental conditions for the full set of neurons, by running the Matrix Formalism solver [Li et al. NMR in

Biomedicine, 2020] (numerical computation of Laplace eigenfunctions) from the SpinDoctor toolbox [Li et al. Neuroimage. 2019].

3. From the simulated diffusion MRI signals, explain the relationships found between candidate

biomakers and soma size.

4. Incorporate additional morphological properties such as total dendrite length and dendrite to

soma ratio to the statistical study.

5. Test, implement, and optimize machine learning algorithms that robustly output selected

morphological properties from the diffusion MRI signals.

6. Analyse the connections between the input-output relationships from the chosen machine

learning algorithms and the underlying properties of the Bloch-Torrey PDE.