Modeling diffusion in white matter in the brain: a composite porous medium.

We model diffusion in white matter fascicles as a problem of diffusion in an array of identical thick-walled cylindrical tubes immersed in an outer medium and arranged periodically in a regular lattice. The diffusing molecules have different diffusion coefficients and concentrations (or densities) within the tubes' inner core, membrane, myelin sheath, and within the outer medium. For an impermeable myelin sheath, diffusing molecules within the inner core are completely restricted, while molecules in the outer medium are hindered due to the tortuosity of the array of impenetrable tubes.

[1]  Ross C. McPhedran,et al.  Optical resonances of three-phase composites and anomalies in transmission , 1995 .

[2]  P. Basser,et al.  New modeling and experimental framework to characterize hindered and restricted water diffusion in brain white matter , 2004, Magnetic resonance in medicine.

[3]  Graeme W. Milton,et al.  Transport properties of a three-phase composite material: the square array of coated cylinders , 1993, Proceedings of the Royal Society of London. Series A: Mathematical and Physical Sciences.

[4]  David R. McKenzie,et al.  Transport properties of regular arrays of cylinders , 1979, Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences.

[5]  A. Snyder,et al.  Normal brain in human newborns: apparent diffusion coefficient and diffusion anisotropy measured by using diffusion tensor MR imaging. , 1998, Radiology.

[6]  S. Patz,et al.  Tortuosity measurement and the effects of finite pulse widths on xenon gas diffusion NMR studies of porous media. , 2000, Magnetic resonance imaging.

[7]  Scott N. Hwang,et al.  An image‐based finite difference model for simulating restricted diffusion , 2003, Magnetic resonance in medicine.

[8]  P. Basser,et al.  Diffusion tensor MR imaging of the human brain. , 1996, Radiology.

[9]  P. Sen,et al.  Multiple scattering of acoustic waves with application to the index of refraction of fourth sound , 1981 .

[10]  P. Basser,et al.  In vivo fiber tractography using DT‐MRI data , 2000, Magnetic resonance in medicine.

[11]  P. Hüppi,et al.  Diffusion tensor imaging of normal and injured developing human brain ‐ a technical review , 2002, NMR in biomedicine.