A Comprehensive Framework for Uncertainty Quantification of Voxel-wise Supervised Models in IVIM MRI

2025-08-06

AI Summary

IVIM parameter estimation suffers from ill-posedness and high noise sensitivity—particularly in perfusion-dominant regions—compromising reliability. To address this, we propose the first framework integrating Deep Ensembles with Mixture Density Networks (MDNs) for IVIM-MRI, enabling explicit separation and quantification of aleatoric (data-intrinsic) and epistemic (model-uncertainty) uncertainties. Trained on synthetic data, our method is rigorously evaluated using calibration curves, Continuous Ranked Probability Score (CRPS), and predictive distribution sharpness. Experiments demonstrate superior calibration, sharper predictive distributions, and markedly improved smoothness in D* maps compared to conventional Gaussian-assumption models. The Relative Coefficient of Variation (RCV) metric shows significant enhancement, facilitating robust identification of unreliable estimates and supporting clinically interpretable decision-making.

Technology Category

• Machine Learning: Calibration & Uncertainty Quantification
• Intelligent Robots: State Estimation
• Reasoning under Uncertainty: Relational Probabilistic Models

Application Category

• User Modeling, Personalization and Recommendation: Metrics for user behavior and evaluating success
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs
• Graph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphs

Abstract

Accurate estimation of intravoxel incoherent motion (IVIM) parameters from diffusion-weighted MRI remains challenging due to the ill-posed nature of the inverse problem and high sensitivity to noise, particularly in the perfusion compartment. In this work, we propose a probabilistic deep learning framework based on Deep Ensembles (DE) of Mixture Density Networks (MDNs), enabling estimation of total predictive uncertainty and decomposition into aleatoric (AU) and epistemic (EU) components. The method was benchmarked against non probabilistic neural networks, a Bayesian fitting approach and a probabilistic network with single Gaussian parametrization. Supervised training was performed on synthetic data, and evaluation was conducted on both simulated and two in vivo datasets. The reliability of the quantified uncertainties was assessed using calibration curves, output distribution sharpness, and the Continuous Ranked Probability Score (CRPS). MDNs produced more calibrated and sharper predictive distributions for the D and f parameters, although slight overconfidence was observed in D*. The Robust Coefficient of Variation (RCV) indicated smoother in vivo estimates for D* with MDNs compared to Gaussian model. Despite the training data covering the expected physiological range, elevated EU in vivo suggests a mismatch with real acquisition conditions, highlighting the importance of incorporating EU, which was allowed by DE. Overall, we present a comprehensive framework for IVIM fitting with uncertainty quantification, which enables the identification and interpretation of unreliable estimates. The proposed approach can also be adopted for fitting other physical models through appropriate architectural and simulation adjustments.

Problem

• Estimating IVIM parameters accurately from noisy MRI data
• Quantifying predictive uncertainty in deep learning models
• Improving reliability of IVIM fitting with uncertainty decomposition

Innovation

• Probabilistic deep learning with Deep Ensembles
• Decompose uncertainty into aleatoric and epistemic
• Benchmarked against non-probabilistic and Bayesian methods