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

Michal Bartoš*, Pavel Rajmic, Michal Šorel, Marie Mangová, Olivier Keunen, Radovan Jiřík

*Corresponding author for this work

Research output: Contribution to journalArticleResearchpeer-review

3 Citations (Scopus)


Purpose: The Tofts and the extended Tofts models are the pharmacokinetic models commonly used in dynamic contrast-enhanced MRI (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 voxelwise. 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 solve the problem numerically. Results: The proposed algorithm helps to reduce noise in the estimated perfusion-parameter maps together with improving 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 of the quality of fit. 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.

Original languageEnglish
Pages (from-to)2257-2272
Number of pages16
JournalMagnetic Resonance in Medicine
Issue number6
Publication statusPublished - 1 Dec 2019


  • perfusion parameter estimation
  • proximal methods
  • spatial regularization
  • tissue homogeneity model
  • total variation


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