The Sensitivities of the Phenomenological DWI Models in the Presence of Cellular Compartments

Chu-Yu Lee¹, Josef P. Debbins²

The distance of water movement during a DWI experiment is beyond the microstructural dimension (4-100μm), a fact that is demonstrated as a non-monoexponential decay when b-value is high. Considering the multiple physical compartments in tissues, there can be more than two diffusion components. More generally, the signal can be given by a summation of a statistical distribution of diffusion rates. The stretched exponential (α-DWI) [1] and diffusion kurtosis imaging (DKI) [2] models can be used to characterize the distribution of diffusion rates. Another approach is to model the signal decay with a statistical distribution: the truncated Gaussian distribution [3] and gamma distribution [4] models. Those phenomenological models fit the data well with only two parameters within a certain range of b-value. Their model parameters can quantify the diffusion heterogeneity, related to the width of the distribution of diffusion rates. However, their theoretical underpinnings are very different and how to infer the tissue structures from the measured diffusion heterogeneity is unclear. In this work, we created a simulation where cell sizes were statistically distributed, and the cellular volume fraction, mean cell sizes, and membrane permeability were varied to study how the measured diffusion heterogeneity correlated with the changes. We focused on three fitted parameters: α, Kapp, and σgamma (standard deviation of gamma distribution) of α-DWI, DKI, and gamma distribution models. The diffusion models were also applied to a clinical case of recurrent tumor to compare with the simulation results.