Uncertainty estimates in pharmacokinetic modelling of DCE-MRI

Dynamic contrast-enhanced (DCE) MRI is a powerful technique for detecting and characterising various diseases by quantifying tissue perfusion. However, accurate perfusion quantification remains challenging due to noisy data and the complexity of pharmacokinetic modelling. Conventional non-linear least squares (NLLS) fitting often yields noisy parameter maps. Although deep-learning algorithms generate smoother, more visually appealing maps, these may lure clinicians into a false sense of security when the maps are incorrect. Hence, reliable uncertainty estimation is crucial for assessing model performance and ensuring clinical confidence. Therefore, we implemented an ensemble of mean-variance estimation (MVE) neural networks to quantify perfusion parameters alongside aleatoric (data-driven) and epistemic (model-driven) uncertainties in DCE-MRI. We compared MVE with NLLS and a physics-informed neural network (PINN), both of which used conventional covariance matrix-based uncertainty estimation. Simulations demonstrated that MVE achieved the highest accuracy in perfusion and uncertainty estimates. MVE's aleatoric uncertainty strongly correlated with true errors, whereas NLLS and PINN tended to overestimate uncertainty. Epistemic uncertainty was significantly higher for the data deviating from what was encountered in training (out-of-distribution) in both MVE and PINN ensembles. In vivo, MVE produced smoother and more reliable uncertainty maps than NLLS and PINN, which exhibited outliers and overestimation. Within a liver region of interest, MVE's uncertainty estimates matched the standard deviation of the data more closely than NLLS and PINN, making it the most accurate method. In conclusion, an MVE enhances quantitative DCE-MRI by providing robust uncertainty estimates alongside perfusion parameters. This approach improves the reliability of AI-driven MRI analysis, supporting clinical translation.