Estimating Transcytolemmal Water Exchange From the Kärger Model Using a Bayesian Method in the Human Gray Matter

We aim to evaluate the performance of the Bayesian method compared with the nonlinear least squares (NLLS) method in estimating exchange time (τ_ex) with the Kärger model (KM) in the human brain and identify a simplified protocol for reliable τ_ex estimation of the human brain in clinical settings. Simulation was performed using the finite difference method to generate diffusion MRI signals in spherical cells with various membrane permeabilities and extracellular fractions. Seven healthy participants underwent stimulated echo acquisition mode (STEAM) encoded diffusion MRI on a 3T scanner using diffusion times (t_d) ranging from 50 to 500 ms. KM fitting was performed using both Bayesian and NLLS methods with comparisons of their performance based on fitting accuracy and robustness in the gray matter (GM). The KM parameter estimations for both deep GM and cortical GM of the human brain were mapped and analyzed. The simulation demonstrated that Bayesian-estimated τ_ex values exhibited lower root mean square error (RMSE) and estimation error than NLLS, particularly under low signal-to-noise ratio conditions. Among the Bayesian approaches, the method incorporating logarithmic priors demonstrated optimal performance. In the analysis of human data, Bayesian estimates of τ_ex showed superior consistency and reduced variability relative to NLLS-derived estimates. The Bayesian method yielded τ_ex values in the human brain GM ranging from 40 to 70 ms, with deep GM showing significantly higher τ_ex values compared with cortical GM. The results demonstrated the superior performance of the Bayesian method over NLLS for τ_ex mapping in the human brain.