Normalizing Flow-Based Distribution Estimation of Pharmacokinetic Parameters in Dynamic Contrast-Enhanced Magnetic Resonance Imaging

Objective: The pharmacokinetic (PK) parameters estimated from dynamic contrast-enhanced magnetic resonance imaging (DCE-MRI) provide valuable information for clinical research and diagnosis. However, these estimated PK parameters suffer from many sources of variability. Thus, the estimation of the posterior distributions of these PK parameters could provide a way to simultaneously quantify the values and uncertainties of the PK parameters. Our objective is to develop an efficient and flexible method to more closely approximate and estimate the underlying posterior distributions of the PK parameters. Methods: The normalizing flow model-based parameters distribution estimation neural network (FPDEN) is proposed to adaptively learn and estimate the posterior distributions of the PK parameters. The maximum likelihood estimation (MLE) loss is directly constructed based on the parameter distributions learned by the normalizing flow model, rather than pre-defined distributions. Results: Experimental analysis shows that the proposed method can improve parameter estimation accuracy. Moreover, the uncertainty derived from the parameter distribution constitutes an effective indicator to exclude unreliable parametric results. A successful demonstration is the improved classification performance of the glioma World Health Organization (WHO) grading task, specifically in terms of distinguishing between low and high grades, as well as between Grade III and Grade IV. Conclusion: The FPDEN method offers improved accuracy for estimation of PK parameters and boosts the performance of the glioma grading task. Significance: By enhancing the precision and reliability of DCE-MRI, the proposed method promotes its further applications in clinical practice.