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.