Algorithm 1: Major steps followed to calculate the IVIM parameters

1 Step 1: Acquire DWI Data: A series of DWI images with different diffusion weighting factors (b-values) are acquired. The signal intensities $\left(S\right(b\left)\right)$ are obtained for each b-value. 2 Step 2: Preprocessing: Before fitting the IVIM model, some preprocessing steps can be utilized. The current study utilized motion correction, denoising, and image registration to ensure the quality and alignment of the DWI data. 3 Step 3: Initial Parameter Estimation: Initial estimates of the IVIM parameters $(S\left(0\right),f,D,D^{*})$ are required to initialize the fitting procedure. These initial estimates can be obtained through various methods, such as region-of-interest (ROI) analysis, manual selection, or prior knowledge from literature. 4 Step 4: Fitting Procedure: The fitting procedure involves minimizing the difference between the measured DWI data $\left(S\right(b\left)\right)$ and the model-predicted signal intensities based on the IVIM equation. Nonlinear least squares fitting is commonly employed, which aims to minimize the sum of squared residuals. The fitting algorithm iteratively adjusts the parameter values to minimize the difference between the model and the measured data. 5 Step 5: Parameter Optimization: The fitting procedure continues until convergence, where the optimal parameter values are obtained. Convergence is typically determined based on a predefined criterion, such as reaching a specific tolerance level or a maximum number of iterations. 6 Step 6: Parameter Interpretation: Once the optimal parameter values are determined, they can be interpreted to gain different insights into tissue diffusion and perfusion characteristics. For example, the perfusion fraction $\left(f\right)$ provides information about the contribution of perfusion to the overall signal, while the diffusion coefficients (D and $D^{*}$) quantify the diffusion properties of tissue and microcirculation-related effects.