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A Comprehensive Framework for Uncertainty Quantification of Voxel-Wise Supervised Deep Learning Models in IVIM MRI
Nicola Casali1,2, Alessandro Brusaferri1, Giuseppe Baselli1,2
1Istituto di Sistemi e Tecnologie Industriali Intelligenti per il Manifatturiero Avanzato, Consiglio Nazionale delle Ricerche, Milan, Italy.
NMR in Biomedicine
|January 20, 2026
Summary
This study introduces a deep learning framework using deep ensembles of mixture density networks for more accurate intravoxel incoherent motion (IVIM) parameter estimation in MRI. The method quantifies uncertainty, improving reliability in diffusion MRI analysis.
Area of Science:
- Medical Imaging and Physics
- Machine Learning in Medical Diagnostics
- Quantitative MRI Techniques
Background:
- Accurate estimation of intravoxel incoherent motion (IVIM) parameters from diffusion-weighted MRI is challenging due to ill-posed inverse problems and noise sensitivity.
- Existing methods struggle with noise, especially in the perfusion compartment, limiting the reliability of IVIM parameter quantification.
- Uncertainty quantification is crucial for interpreting the reliability of estimated parameters in diffusion MRI.
Purpose of the Study:
- To develop and evaluate a probabilistic deep learning framework for robust IVIM parameter estimation.
- To enable the quantification and decomposition of predictive uncertainty into aleatoric (AU) and epistemic (EU) components.
- To benchmark the proposed framework against existing non-probabilistic and probabilistic methods.
Main Methods:
- A probabilistic deep learning framework utilizing deep ensembles (DEs) of mixture density networks (MDNs) was developed.
- Supervised training was performed on synthetic data, with evaluation on simulated and in vivo mouse brain MRI datasets.
- Uncertainty quantification reliability was assessed using calibration curves, predictive distribution sharpness, and CRPS.
Main Results:
- MDNs demonstrated more calibrated and sharper predictive distributions for diffusion coefficient (D) and perfusion fraction (f) compared to other methods.
- Slight overconfidence was noted for the pseudodiffusion coefficient (D*), but MDNs yielded smoother in vivo D* estimates.
- Elevated epistemic uncertainty (EU) in vivo indicated a potential mismatch with real acquisition conditions, highlighting the value of DEs.
Conclusions:
- The proposed deep ensemble MDN framework provides comprehensive uncertainty quantification for IVIM fitting, identifying unreliable estimates.
- This approach enhances the reliability and interpretability of diffusion MRI parameter estimation.
- The framework is adaptable for fitting other physical models with appropriate adjustments.
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