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Mapping spatiotemporal diffusion inside the human brain using a numerical solution of the diffusion equation
- Source :
- Magnetic Resonance Imaging. 26:694-702
- Publication Year :
- 2008
- Publisher :
- Elsevier BV, 2008.
-
Abstract
- Diffusion is an important mechanism for molecular transport in living biological tissues. Diffusion magnetic resonance imaging (dMRI) provides a unique probe to examine microscopic structures of the tissues in vivo, but current dMRI techniques usually ignore the spatio-temporal evolution process of the diffusive medium. In the present study, we demonstrate the feasibility to reveal the spatio-temporal diffusion process inside the human brain based on a numerical solution of the diffusion equation. Normal human subjects were scanned with a diffusion tensor imaging (DTI) technique on a 3-Tesla MRI scanner, and the diffusion tensor in each voxel was calculated from the DTI data. The diffusion equation, a partial-derivative description of Fick’s Law for the diffusion process, was discretized into equivalent algebraic equations. A finite-difference method was employed to obtain the numerical solution of the diffusion equation with a Crank-Nicholson iteration scheme to enhance the numerical stability. By specifying boundary and initial conditions, the spatio-temporal evolution of the diffusion process inside the brain can be virtually reconstructed. Our results exhibit similar medium profiles and diffusion coefficients as those of light fluorescence dextrans measured in integrative optical imaging experiments. The proposed method highlights the feasibility to non-invasively estimate the macroscopic diffusive transport time for a molecule in a given region of the brain.
- Subjects :
- Adult
Male
Diffusion equation
Discretization
Biomedical Engineering
Biophysics
computer.software_genre
Article
Imaging, Three-Dimensional
Optics
Voxel
Image Processing, Computer-Assisted
Humans
Radiology, Nuclear Medicine and imaging
Diffusion (business)
Brain Mapping
Models, Statistical
Echo-Planar Imaging
Chemistry
business.industry
Algebraic equation
Diffusion Magnetic Resonance Imaging
Diffusion process
Feasibility Studies
Female
business
Biological system
computer
Diffusion MRI
Numerical stability
Subjects
Details
- ISSN :
- 0730725X
- Volume :
- 26
- Database :
- OpenAIRE
- Journal :
- Magnetic Resonance Imaging
- Accession number :
- edsair.doi.dedup.....89882cc879c3134ba6ad25ea72acb3d4