Chang li^{1,2}, Xianfu luo^{2}, Weiqiang Dou^{3}, Yun Peng^{1}, Jingtao wu^{2}, and Jing Ye^{2}

We aimed to investigate if a stretched exponential diffusion weighted imaging model (SEM) can be applied to assess nonalcoholic liver disease (NAFLD) disease by providing distributed-diffusion-coefficient (DDC) and α separately evaluating mean intravoxel diffusion rate and diffusion heterogeneity. The SEM model was then applied to analyze NAFLD in a rabbit model and compared with a mono-exponential (ME) model. While DDC from the SEM model showed comparable values with apparent-diffusion-coefficient (ADC) estimated in the ME model, alpha indicated more robust performance in the diagnosis of nonalcoholic steatohepatitis (NASH). Therefore, SEM model showed a great potential in early diagnosis of NASH.

**Introduction**

**Rabbit model**

**MR experiments**

**Data analysis**

All data were processed at a GE workstation (AW4.6; GE Medical Systems).

The acquired DWI images were analyzed using the SEM model. The DDC and α were obtained by equation 1: S(b)/S(0)=exp[-(b·DDC)^{α}] [Eq.1], where α varies from 0 to 1, being related to intravoxel water molecular diffusion heterogeneity, and DDC represents the mean intravoxel diffusion rate.

For comparison, ME model was also applied for ADC calculation using the equation 2: S(b)/S(0)=exp(-b·ADC) [Eq.2], where S(0) represents the signal intensity in the absence of diffusion sensitization, and S(b) represents the corresponding signal intensity at different b values.

**Histological analysis**

**Statistical analysis**

**Results**

Both ADC and DDC showed significant inverse relationships (P<.05) with the severity of NAFLD (Figs.1-3). The separate correlation coefficients were -0.552 and -0.596. However, for α, a positive correlation (r=0.729; P< .05) was found with the progress of NAFLD, and a significant difference was observed between borderline and NASH groups.

In addition, the area-under-the-receiver-operating-characteristic-curve (AUC) was calculated for ADC, DDC and α, respectively (Fig.4). While comparable AUC values for DDC and ADC were showed (0.736 vs 0.784), the largest AUC value was observed in α (0.900; P<.05), indicating the most robust diagnosis for NASH. .

**Discussion ****and conclusion**

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2. Anderson S, Barry B, Soto J, Ozonoff A, O'Brien M, Jara H. Characterizing non-gaussian, high b-value diffusion in liver fibrosis: Stretched exponential and diffusional kurtosis modeling. Journal of magnetic resonance imaging : JMRI 2014;39(4):827-834.

3. Hu G, Liang W, Wu M, Chan Q, Li Y, Xu J, Luo L, Quan X. Staging of rat liver fibrosis using monoexponential, stretched exponential and diffusion kurtosis models with diffusion weighted imaging- magnetic resonance. Oncotarget 2018;9(2):2357-2366.

Fig. 1 A-D is axial diffusion weighted imaging (DWI) of normal liver. A is b value of 0 s/mm^{2} DWI and B-D is pesudo-color maps of ADC, DDC and α with mean values of 1.30×10^{-3}mm^{2}/s, 0.926×10^{-3}mm^{2}/s and 0.429, respectively. E-H is axial diffusion weighted imaging of nonalcoholic steatohepatitis. E is b value of 0 s/mm^{2} DWI and F-H is pesudo-color maps of ADC, DDC and α with mean values of 1.09×10^{-3}mm^{2}/s, 0.74×10^{-3}mm^{2}/s and 0.693, respectively.

Fig.2 Box plots show (a) ADC, (b) DDC and (c) Alpha for normal and NAFLD. Boundaries of boxes indicate 95% confidence interval and lines in boxes indicate mean.

Fig.3 The correlation curve of diffusion parameters and the severity stage of histology. SS indicates simple steatosis.

Fig.4 Receiver operating characteristic curve for ADC, DDC and Alpha in distinguishing NASH from borderline or less severity group. Alpha has the largest area under curve (0.900).