Dmitry S.
Novikov1, Valerij G. Kiselev2
1Radiology, NYU School of Medicine, New
York, NY, United States; 2Medical Physics, Diagnostic Radiology,
Uniklinikum Freiburg, Freiburg, Germany
We
consider the DWI signal from any medium (tissue) in which the diffusion
coefficient varies in space. Using recently developed effective-medium
approach, we relate the signal to the diffusivity correlation function.
Explicit formulas for time-dependent diffusion coefficient and diffusional
kurtosis are provided in the case when the local diffusivity varies on a
well-defined length scale. Our results are numerically confirmed by the
Monte-Carlo simulation of diffusion in a two-dimensional model tissue. While
the DWI signal has an approximately biexponential form, it is shown to be
qualitatively different from that of the two-compartment exchange (Krger)
model.