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

Abstract

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.

Unfolded Low-rank + Sparse Reconstruction for MRI

“…( 1) contains all the data as vectors. The regularization term 𝜆𝑅(x) adds a priori spatial and/or temporal information, typically using total variation [3,4,5] or its generalized form [6,7]. Some methods use purely deep-learning-based using large image-to-image networks.…”

Bayesian non-linear regression with spatial priors for noise reduction and error estimation in quantitative MRI with an application in T1 estimation

“…Structured spatial regularisation terms and priors have been used in qMRI by several authors. They have, for instance, been used when estimating relaxation times and proton density (Wang and Cao 2012, Baselice et al 2016, Kumar et al 2012, Raj et al 2014, in diffusion and intra-voxel incoherent motion (IVIM) estimation (While 2017, Orton et al 2014, for B 0 -estimation (Baselice et al 2010), and for dynamic contrast-enhanced MRI (DCE-MRI) (Schmid et al 2006, Kelm et al 2009, Sommer and Schmid 2014, Bartos et al 2019.…”

“…Selecting the hyperparameter is difficult, and how it is done varies between studies. Examples of different approaches include visual inspection (Kumar et al 2012), finding good parameters for a representative dataset (Bartos et al 2019, Wang and Cao 2012, Freiman et al 2013, L-curve analysis (Kumar et al 2012), constraints on the size of the residuals (Raj et al 2014), and non-informative priors have been used in the Bayesian framework (Orton et al 2014).…”