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Biophys. J. BioFAST: First Published August 12, 2005. doi:10.1529/biophysj.105.063016
© 2005 by the Biophysical Society.

A more recent version of this article appeared on November 1, 2005.
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BIOPHYSICAL THEORY AND MODELING

A model for diffusion in white matter in the brain

Pabitra N Sen 1* and Peter J. Basser 2

1 Schlumberger-Doll Research
2 National Institutes of Health

* To whom correspondence should be addressed. E-mail: sen1{at}slb.com.

Submitted on March 23, 2005
Revised on April 4, 2005
Accepted on 25 July 2005


  Abstract
Diffusion of molecules in brain and other tissues is important in a wide range of biological processes and measurements ranging from the delivery of drugs to diffusion-weighted magnetic resonance imaging. Diffusion tensor imaging (DTI) is a powerful non-invasive method to characterize neuronal tissue in the human brain in vivo. As a first step towards understanding the relationship between the measured macroscopic apparent diffusion tensor (ADT) and underlying microscopic compartmental geometry and physical properties, we treat a white matter fascicle as an array of identical thick-walled cylindrical tubes arranged periodically in a regular lattice and immersed in an outer medium. Both square and hexagonal arrays are considered. The diffusing molecules may have different diffusion coefficients and concentrations (or densities) in different domains, namely within the tubes' inner core, membrane, myelin sheath, and within the outer medium. Analytical results are used to explore the effects of a large range of microstructural and compositional parameters on the ADT and the degree of diffusion anisotropy, allowing the characterization of diffusion in normal physiological conditions as well as changes occurring in development, disease, and aging. Implications for DTI and for the possible in situ estimation of microstructural parameters from diffusion weighted MR data are discussed in the context of this modelling framework.

Key Words: Brain, Diffusion tensor imaging, Tortuosity, white matter




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Copyright © 2005 by the Biophysical Society.