Els Fieremans1, Dmitry S. Novikov1,
Jens H. Jensen1, Joseph A. Helpern1,2
1Radiology, New York University School
of Medicine, New York, United States; 2Center for Advanced Brain
Imaging, Nathan S. Kline Institute, Orangeburg, NY, United States
Chemical
exchange models have been frequently applied to quantify diffusion
measurement in living tissues. Here we investigate numerically a
two-compartment exchange (Krger) model as applied to diffusion in a system
of parallel cylinders with permeable walls, which serves as a model for axons
in white matter. We show that the Krger model accurately predicts the
diffusivity and the diffusional kurtosis when the membranes are sufficiently
impermeable. The exchange time can then be derived from the time-dependence
of the diffusional kurtosis. For larger permeabilities, the Krger model
overestimates the actual exchange time.