Spatially regularized estimation of the tissue homogeneity model parameters in DCE-MRI using proximal minimization

Purpose: The Tofts and the extended Tofts models are the pharmacokinetic models commonly used in DCE-MRI perfusion analysis, although they do not provide two important biological markers, namely the plasma flow and the permeability-surface area product. Estimates of such markers are possible using advanced pharmacokinetic models describing the vascular distribution phase, such as the tissue homogeneity model. However, the disadvantage of the advanced models lies in biased and uncertain estimates, especially when the estimates are computed voxel-wise. The goal of this work is to improve the reliability of the estimates by including information from neighboring voxels.
Theory and Methods: Information from the neighboring voxels is incorporated in the estimation process through spatial regularization in the form of total variation. The spatial regularization is applied on five maps of perfusion parameters estimated using the tissue homogeneity model. Since the total variation is not differentiable, two proximal techniques of convex optimization are used to numerically solve the problem.
Results: The proposed algorithm helps to reduce noise in the estimated perfusion-parameter maps together with improved accuracy of the estimates. These conclusions are proved using a numerical phantom. In addition, experiments on real data show improved spatial consistency and readability of perfusion maps without considerable lowering the quality of fits.
Conclusion: The reliability of the DCE-MRI perfusion analysis using the tissue homogeneity model can be improved by employing spatial regularization. The proposed utilization of modern optimization techniques implies only slightly higher computational costs compared to the standard approach without spatial regularization.