Improving Microstructural Estimation in Time-Dependent Diffusion MRI With a Bayesian Method

Abstract

Background: Accurately fitting diffusion-time-dependent diffusion MRI (t_d-dMRI) models poses challenges due to complex and nonlinear formulas, signal noise, and limited clinical data acquisition.

Purpose: Introduce a Bayesian methodology to refine microstructural fitting within the IMPULSED (Imaging Microstructural Parameters Using Limited Spectrally Edited Diffusion) model and optimize the prior distribution within the Bayesian framework.

Study type: Retrospective.

Population: Involving 69 pediatric patients (median age 6 years, interquartile range [IQR] 3-9 years, 61% male) with 41 low-grade and 28 high-grade gliomas, of which 76.8% were identified within the brainstem or cerebellum.

Field strength/sequence: 3 T, oscillating gradient spin-echo (OGSE) and pulsed gradient spin-echo (PGSE).

Assessment: The Bayesian method's performance in fitting cell diameter ( $d$ ), intracellular volume fraction ( $f_{\text{in}}$ ), and extracellular diffusion coefficient ( $D_{\mathrm{ex}}$ ) was compared against the NLLS method, considering simulated and experimental data. The tumor region-of-interest (ROI) were manually delineated on the b0 images. The diagnostic performance in distinguishing high- and low-grade gliomas was assessed, and fitting accuracy was validated against H&E-stained pathology.

Statistical tests: T-test, receiver operating curve (ROC), area under the curve (AUC) and DeLong's test were conducted. Significance considered at P < 0.05.

Results: Bayesian methodology manifested increased accuracy with robust estimates in simulation (RMSE decreased by 29.6%, 40.9%, 13.6%, and STD decreased by 29.2%, 43.5%, and 24.0%, respectively for $d$ , $f_{\text{in}}$ , and $D_{\mathrm{ex}}$ compared to NLLS), indicating fewer outliers and reduced error. Diagnostic performance for tumor grade was similar in both methods, however, Bayesian method generated smoother microstructural maps (outliers ratio decreased by 45.3% ± 19.4%) and a marginal enhancement in correlation with H&E staining result (r = 0.721 for $f_{\text{in}}$ compared to r = 0.698 using NLLS, P = 0.5764).

Data conclusion: The proposed Bayesian method substantially enhances the accuracy and robustness of IMPULSED model estimation, suggesting its potential clinical utility in characterizing cellular microstructure.

Evidence level: 3 TECHNICAL EFFICACY: Stage 1.

Keywords: Bayesian estimation; IMPULSED; glioma; microstructure; time‐dependent diffusion MRI.