Constrained maximum likelihood estimation of the diffusion kurtosis tensor using a Rician noise model.

Area of Science:

• Neuroimaging
• Biophysics
• Computational Biology

Background:

• Diffusion kurtosis imaging (DKI) quantifies non-Gaussian water diffusion in brain tissues.
• DKI estimates a diffusion tensor and a higher-order kurtosis tensor.
• Physical constraints are crucial to avoid confounding diffusion and kurtosis parameter interpretation.

Purpose of the Study:

• To develop a computational framework for accurate quantification of Gaussian and non-Gaussian diffusion components.
• To ensure physical relevance of diffusion and kurtosis tensor estimates in DKI.
• To address the overestimation of kurtosis values due to Rician noise in diffusion-weighted images.

Main Methods:

• Proposed a constrained estimation approach for diffusion and kurtosis tensors.
• Maximized the joint likelihood function of Rician distributed diffusion-weighted images.
• Imposed nonlinear constraints to ensure physically acceptable tensor estimates.

Main Results:

• The constrained estimator accurately quantifies Gaussian and non-Gaussian diffusion components.
• Accounting for Rician noise structure prevents significant kurtosis overestimation.
• Unconstrained methods led to constraint violations in approximately 70% of human brain voxels.

Conclusions:

• Constrained estimation is necessary for physically relevant DKI parameter quantification.
• The proposed framework improves the accuracy of diffusion and kurtosis tensor estimation.
• This method is essential for reliable analysis of brain tissue microstructure using DKI.