Relationship Between Mean Kärger Model Water Exchange Rate and Intercellular Water Transition Rate

ABSTRACT Purpose To derive a quantitative relationship between the mean Kärger model (KM) water exchange rate and the mean intercellular water transition rate applicable to brain and other complex biological tissues. Theory and Methods The mean KM water exchange rate applies to any KM, accommodates an arbitrary number of compartments, and can be estimated from the time dependence of the diffusional kurtosis. The mean intercellular water transition rate for a tissue is the average rate at which water leaves all cellular compartments and enters the extracellular space. It is shown that these two quantities are proportional to each other provided the exchange dynamics are uniform throughout an imaging voxel and the compartmental diffusivities and residence times are not correlated, with a proportionality coefficient depending on the diffusivities and compartmental water fractions. This relationship is illustrated for several white matter regions having highly aligned axons using diffusional kurtosis imaging (DKI) data from four healthy volunteers. Results For parallel axons, the proportionality coefficient simply reduces to the extracellular water fraction, which allows estimates for the KM exchange rates obtained with DKI to be translated into estimates for the axonal water transition rate. The axonal transition rate is found to vary from 0.83 s −1 in the posterior limb of the internal capsule to 2.00 s −1 in the body of the corpus callosum. Conclusion Under mild assumptions, the mean KM water exchange rate is proportional to the mean intercellular water transition rate. This provides a practical method for estimating intercellular water transition rates from DKI.