Interpretation of Diffusion MR Imaging Data using a Gamma Distribution Model

Abstract

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 < 1.0 mm 2 /s (frac < 1) was attributed to small cancer cells with restricted diffusion, and the area fraction for D > 3.0 mm 2 /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.

Diffusion-weighted imaging of prostate cancer using a statistical model based on the gamma distribution

“…A statistical comparison of the curve fits between the gamma model and the truncated Gaussian model was performed on PCa, BPH, and healthy PZ by F tests using R 2 values of each fit. In addition, the parameters of the gamma model [mean ( α / β ), standard deviation ( ), the area fraction of D < 1.0 mm 2 /s (Frac<1.0), the area fraction of D > 3.0 mm 2 /s (Frac>3.0)], which were proposed in the previous study , and the truncated Gaussian model ( D m , σ, Frac<1.0, and Frac>3.0) were compared between PCa, BPH, and healthy PZ using a one‐way analysis of variance (ANOVA). Post‐hoc Tukey–Kramer tests for pairwise comparisons were used to determine whether there was any significant difference between PCa, BPH, and healthy PZ (MedCalc, v. 11.6.2.0, MedCalc Software, Mariakerke, Belgium).…”

“…They proposed a truncated Gaussian-type function, restricted to positive ADC values, as the distribution of ADCs. Recently, we reported that the gamma function provided a better fit than the truncated Gaussian function as a distribution function for ADCs using a clinical dataset from histologically proven prostate cancer (16,17). The b-values used for the latter study were within the 0 to 1000 s/mm 2 range; however, the non-monoexponential diffusionrelated signal decay generally becomes more apparent over more extended b-value ranges (8,9,18).…”

Precise Inference and Characterization of Structural Organization (PICASO) of tissue from molecular diffusion

“…Several groups of methods have been proposed for modeling the dMRI signal acquired using a standard single diffusion encoding (SDE) experiment (Basser et al, 1994; Assaf et al, 2002; Jensen et al, 2005; Schultz et al, 2014; Özarslan et al, 2009; Morozov et al, 2014; Huang et al, 2015). A large family of methods focus on estimating the ensemble average propagator (EAP) of the diffusing spins under the narrow pulse approximation (Cheng et al, 2010; Merlet and Deriche, 2013; Özarslan et al, 2013; Scherrer et al, 2013; Rathi et al, 2014; Ning et al, 2015; Ghosh and Deriche, 2016).…”

Gamma Distribution Model in the Evaluation of Breast Cancer Through Diffusion‐Weighted MRI: A Preliminary Study

“…Another approach is the application of the gamma function to the statistical distribution of ADC values: the gamma distribution (GD) model . This model is expected to reflect the probability of the distribution of water molecule mobility in different regions of the tissue .…”

“…This model is expected to reflect the probability of the distribution of water molecule mobility in different regions of the tissue . Based on this statistical approach, one can also obtain the fraction of intracellular, extracellular, and perfusion components of tissue . All this information, obtained through only one model, may surpass the advantages offered by other models.…”