| The numerical method based on PDEs has been implemented by a finite volume discretization instead of by Green's functions representation as originally planned. A finite volume discretization coupled with a Runge-Kutta Chebyshev(RKC) time stepping method was chosen instead. The code, called 'FVforDMRI', can produce simulated DMRI signals with an relative accuracy of 0.1-1 percent and has low computational time and memory requirements. It is written in Fortran90 and contains about 10000 lines. Completed. |
| Ph.D. student Dang Van Nguygen (funded by ANR) is implementing a C++ version of 'FVforDMRI' that incorporates linear finite elements discretization. This code has been written for two and three dimensional simulations and is being optimized. Ongoing. |
| We had planned to use the PDE simulation results to obtain parameters to feed into a well-known reduced model of DMRI signal attenuation, called the Karger model. Instead, we generalized the Karger model so that one of the limitations of its use, that the diffusion gradient has to be 'narrow pulse', is relaxed. Our new reduced ODE model can treat the case where the diffusion gradient is not 'narrow pulse', which is the case of diffusion MRI sequences under clinical conditions. Completed. |
| We combined a Monte Carlo Brownian dynamics simulator capable of simulating diffusion of spins in arbitrarily complex geometries with a diffusion weighted signal integrator emulating various MR pulse sequences. The flexibility and ability of Monte-Carlo modeling enabled us to investigate detail dynamics and mechanisms of molecular diffusion in complex systems which cannot be handled through analytical models. We have developed software to reproduce various tissue configurations using dynamic meshes. Complicated geometries mimicking neural tissue components, such as neurons, astrocytes, axons, etc. can be emulated, as well as tissue features (e.g. cell size, density, membrane permeability) and basic diffusion mechanisms in different compartments (presence of attractors, local viscosity, membrane interactions, etc.). The simulation code is called 'Microscopist', and is implemented in C++ on a high computing PC cluster for large-scale simulations. It contains 17000 lines of C++ code and 4000 lines of python code. Completed. |
| In Jan 2012 we began to image rat brains on the 17T Brucker small animal system at Neurospin. Preliminary experimental data have been obtained. Histology on the tissue samples is planned so as to provide the necessary geometrical parameters to input into the two codes. We plan to verify the simulation results of both the PDE method ('FVforDMRI') and the Monte-Carlo method ('Microscopist') against the experimental data obtained in rat brain on the 17T imaging system. Ongoing. |
| The Green's function formalism gives an interface condition that must be satisfied on the cellular membranes by any Monte-Carlo simulation so that the simulation results can be compared in a meaningful way with the PDE simulation results. This interface condition will be implemented in the Monte-Carlo code. We plan also to begin accelerate the Monte-Carlo code by incorporating known Green's function solutions in parts of the computational domain that are homogeneous. Planned. |
| We have begun to evaluate different ways of acquiring sample brain geometries using electron microscopy in order to extract more realistic membrane geometries to be used as input to 'Microscopist'. Ongoing. |