What Does FEXI Measure in Neurons?

Abstract: Exchange between tissue compartments is crucial for interpretation of diffusion MRI measurements in brain gray matter. Reported values of exchange time are broadly dispersed, about two orders of magnitude. We analyze the measurement technique called Filtered Exchange Imaging (FEXI) using numerical solution of Bloch--Torrey equation in digitalized neurons downloaded from NeuroMorpho.org. The FEXI outcome, the recovery of diffusion coefficient in cells with impermeable membrane is multiexponential, tightly related to the eigenvalues of the Laplace operator. Fitting the commonly used exponential recovery function results in a strong dependence of the apparent exchange time on the involved mixing time interval. For short mixing times, exchange time is of the order of 10 ms. It gets an order of magnitude larger for mixing times of a few hundreds of milliseconds. To obtain an estimate of membrane permeability, we reinterpret previously published data on preexchange lifetime in neuronal cell culture. It results in the permeability 0.005 micrometer/ms. The corresponding exchange time is about 140 ms. We conclude that essentially shorter exchange times are due to fast geometric exchange inside the ramified cells.