The Relation Between Distribution of Effective Diffusivity and Multi-Exponential Models in a Varying Microstructure: A Monte Carlo Study

Chu-Yu Lee¹, ², Kevin M. Bennett³, Josef P. Debbins, ¹²

The non-monoexponential DWI decay at high b-values has been attributed to the multiplicity of water diffusion rates, which may provide the information about the water compartmentation. The common way to compute the diffusion rates is through the multi-exponential analysis. The bi-exponential model assumes two diffusion rates. Considering the multiple length scales in tissues, the distributed exponential model makes no assumption about the number of diffusion rates, and can be empirically described by the stretched exponential model (α-DWI). Those fitting models: bi-exponential and α-DWI have a few parameters, and have been shown to correlate with the pathology. However, it remains difficult to pin down the underlying biophysical mechanisms. In addition, the multi-exponential relation is phenomenological, because each diffusion rate is no longer associated with a mono-exponential decay when diffusion time is long (>30 ms in a clinical DWI). In this study, the distribution of ‘effective’ diffusivity of water molecules diffusing in a simulated cell structure was created using Monte Carlo simulation. DW experiments were also simulated, and the DWI signals were fitted by the bi-exponential and α-DWI models. We studied how the fitted parameters: Dfast, Dslow, Vfast (fraction of Dfast) of bi-exponential fit, DDC, α of α-DWI, tracked the distribution of effective diffusivity when the microstructures were changed. This may give insights into the relationship between the phenomenological fitting models and the tissue structure.