Monte Carlo Assessment of Accuracy for Mean Kärger Model Water Exchange Rate Estimates From Diffusional Kurtosis Time Dependence

Abstract

Intercompartmental water exchange in brain and other biological tissue can be probed in vivo with diffusion MRI (dMRI). We assess the accuracy of a recently proposed method for estimating a mean exchange rate by performing Monte Carlo simulations of random walkers through a packing of permeable, randomly placed, parallel cylinders to model water exchange within axonal fiber bundles. The diffusivity and kurtosis of the full system are calculated for a broad range of diffusion times and model parameters. The mean exchange rate is estimated from the logarithmic derivative of the kurtosis with respect to the diffusion time and compared with the exchange rate predicted by the Kärger model (KM), which is exact in certain limits. The mean exchange rate is also compared with the reciprocal exchange time obtained by conventional fitting of the kurtosis time dependence to a two-compartment KM, with a high correlation being found between the two quantities. The estimates from the logarithmic derivative are in good agreement with the KM predictions when the exchange time is long in comparison to the compartment traversal times, which corresponds to barrier-limited exchange. Compared to the standard procedure of fitting the kurtosis to the KM over a broad range of diffusion times, using the logarithmic derivative reduces the data acquisition burden by only requiring a narrow range of times and increases generality in that number of compartments need not be specified. This method may be useful for estimating the mean exchange rate from the kurtosis time dependence measured with dMRI.

Keywords: Kärger model; MRI; Monte Carlo; brain; diffusion; kurtosis; numerical simulations; water exchange.