Interpretation of diffusion MR imaging data using a gamma distribution model

Purpose: Although many models have been proposed to interpret non-Gaussian diffusion MRI data in biological tissues, it is often difficult to see the correlation between the MRI data and the histological changes in the tissue. Among these models, so called statistical models, which assume the diffusion coefficient D is distributed continuously within a voxel, are more suitable for interpreting the data in a histological context than others. In this work, we examined a statistical model based on the gamma distribution.

Methods: First, the proposed gamma model, the bi-exponential model, and the truncated Gaussian model were compared for goodness of fit. To evaluate diagnostic capability, area fractions of certain D ranges were evaluated. The area fraction for D < 1.0mm²/s (frac < 1) was attributed to small cancer cells with restricted diffusion, and the area fraction for D > 3.0mm²/s (frac > 3) was considered to reflect perfusion component. A clinical data set of histologically proven prostate cancer cases from previous study was used.

Results: For the cancer tissue, the gamma model was better fit than the truncated Gaussian model, and there was no significant difference between the gamma model and the biexponential model. For the normal peripheral zone tissue, there was no significant differences among all models. In the 2D scatter plot of frac < 1 vs. frac > 3, Cancer and noncancer tissues were clearly separated.

Conclusion: Using the proposed model, the diffusion MR data was well fit, and histological interpretation of the data appears possible.