Diffusion weighting imaging (DWI) has been shown to be useful in differentiating low- and high-grade tumors in the brain. The decreased apparent diffusion coefficient (ADC) in high-grade tumors has been associated with increased tumor cellularity ¹. However, changes of the ADC may be associated with other microstructural changes related to tumor malignancy ^2-4. An alternative way to assess water diffusion in the complex microstructure is through the diffusion heterogeneity measured by the stretched exponential model (α-DWI), S(b) = exp( ̶ b × DDC)^{α 5-7}. Recent studies using the α-DWI model showed the increased diffusion heterogeneity in high-grade tumors ^8-11. However, the relation between the α-DWI and the tissue microstructure remains unclear. The purpose of this study was to investigate how the α-DWI model responds to tumor malignancy related microstructural changes. We simulated DWI experiments in 3-dimensional (3-D) microenvironments with varying microstructural parameters associated with tumor malignancy. We studied how ADC and the fitted parameters of the α-DWI model responded to the microstructural changes.3-D microenvironments in low-grade tumors were simulated through randomly packed spheres with a gamma distributed diameter (mean ± std: 10 ± 7 µm ¹²). Each sphere have two free-exchange compartments: nucleus and cytoplasm with their volumetric ratio (NC ratio): 6.4 % ^4,13 and diffusivities: 1.17 and 0.3 × 10^-3 mm²/s respectively ¹⁴ (Fig. 1a-b). The simulated cell volume fraction (VF) was 65 % ^2,3. The extracellular diffusivity was determined based on the tortuosity measured in low-grade tumors ^2-3: D_ex = D_free/(tortuosity)² = 1.19 × 10^-3 mm²/s. The cell membrane permeability was 0.03 mm/s ^15,16. According to the histopathological studies in tumors, four independent microstructural changes related to tumor malignancy were simulated: decreased VF from 65 to 55 % ^2,3, increased extracellular tortuosity (T_ex) from 1.6 to 1.7 ^2,3, increased cell density by a factor of 3.6 ¹, and increased NC ratio from 6.4 to 21.6 % ¹³ (Fig. 1c). The cell density was computed as the number of cells per unit volume. A pulsed gradient spin-echo (PGSE) experiment in human DWI (δ/Δ= 40/46 ms, G_MAX = 40 mT/m) was simulated using a Monte Carlo simulation developed in C++ ^15,17. 40,000 spins were randomly distributed in the 3-D microenvironment and performed a random walk of 80,000 steps/sec. The spin phase accrual during applied diffusion gradients was computed to generate DWI signals with b-values up to 5500 s/mm² in increments of 500 s/mm². The signals were fitted with the α-DWI model using the Levenberg-Marquardt algorithm in Matlab (Mathworks, Inc.). The ADC was computed with signals of b = 0 and 1000 s/mm². The goodness of fit was assessed using the reduced chi-square statistic (χ_ν²). Each simulation was repeated five times to quantify the precision. All the data fits were within the 95 % confidence interval (0.3 < χ_ν² < 1.9) (Fig. 2). The increases of the ADC and DDC were related to the decreased VF and increased NC ratio. The percentage changes were 15.4, 16 % and 7.7, 9.8 %. Their decreases were related to the increased T_ex and cell density. The percentage changes were ̶ 10.1, ̶ 11.1 % and ̶ 6.6, ̶ 4.8 %. Interestingly, the increase of the diffusion heterogeneity (decreased α) was specifically related to the decreased VF. The percentage change was ̶ 2.8 %. The decrease (increased α) was specifically related to the decreased T_ex. The percentage change was 3.7 % compared to the percentage changes: 0.8 and 0.6 % in response to the increased cell density and NC ratio. It has been postulated that the elevated cellularity in high-grade tumors is related to a decreased diffusivity. However, our results consistent with a previous finding ¹⁸ suggest that the increased NC ratio, despite being correlated with cellularity ¹⁹, may result in an increased diffusivity (Fig. 3). Our results also showed that the diffusion heterogeneity measured by the α was more specifically related to the microstructural changes in VF and T_ex compared with the measured diffusivity (Fig. 3). This suggests that the diffusion heterogeneity may help better identify the changes in VF and T_ex that are associated with the proliferation and mitotic activity in tumors ³.We demonstrated that the diffusion heterogeneity measured by the α-DWI provided distinct information from the measured diffusivity, and specifically reflected tumor malignancy related microstructural changes in VF and T_ex.