Mean Kärger Model Water Exchange Rate in Brain

Intercellular water exchange in brain is analyzed in terms of the multi-compartment Kärger model (KM), and the mean KM water exchange rate is used as a summary statistic for characterizing the exchange processes. Prior work is extended by deriving a stronger lower bound for mean exchange rate that can be determined from the time dependence of the diffusional kurtosis. In addition, an analytic formula giving the time dependence of the kurtosis for a model of thin cylindrical neurites is demonstrated, and this formula is applied to numerically test the accuracy of the lower bound for a range of model parameters. Finally, the lower bound is measured in vivo with diffusional kurtosis imaging for the dorsal hippocampus and cerebral cortex of eight-month-old mice. From the stronger lower bound, the mean KM exchange rate is found to be $46.1\pm 11.0s^{-1}$ or greater in dorsal hippocampus and $20.5\pm 8.5s^{-1}$ or greater in cortex.