Bayesian uncertainty quantification in linear models for diffusion MRI.

Area of Science:

• Neuroimaging
• Biophysics
• Medical Physics

Background:

• Diffusion MRI (dMRI) is crucial for assessing tissue microstructure.
• Current dMRI models often use least-squares fitting, lacking uncertainty quantification.
• Uncertainty estimation is valuable for robust group analyses in dMRI.

Purpose of the Study:

• To recast popular dMRI signal models into a Bayesian framework.
• To enable accurate quantification of uncertainty for derived dMRI metrics.
• To validate the proposed probabilistic approach using simulated and in vivo data.

Main Methods:

• Probabilistic interpretation of linear least-squares methods for dMRI signal modeling.
• Bayesian model formulation for uncertainty quantification.
• Validation using simulated data from Diffusion Tensor Imaging (DTI), Mean Apparent Propagator MRI (MAP-MRI), and Constrained Spherical Deconvolution (CSD) models, alongside residual bootstrap comparison.
• Application to in vivo dMRI data for visualization and group analysis.

Main Results:

• Developed a Bayesian framework for dMRI, providing closed-form posterior distributions for affine quantities.
• Validated the accuracy of uncertainty quantification against empirical observations from simulated data.
• Demonstrated good agreement with residual bootstrap methods.
• Visualized quantitative features and their uncertainties on in vivo data.
• Showcased utility in group analysis by downweighting subjects with high uncertainty.

Conclusions:

• The proposed Bayesian approach successfully converts linear dMRI models into probabilistic ones.
• This method provides accurate uncertainty quantification for derived dMRI metrics.
• The approach is validated and applicable to various dMRI models and real-world data, improving analysis robustness.