The Czech Academy of Sciences, Institute of Information Theory and Automation, Prague, Czech Republic.
SPLab, Department of Telecommunications, FEEC, Brno University of Technology, Brno, Czech Republic.
Magn Reson Med. 2019 Dec;82(6):2257-2272. doi: 10.1002/mrm.27874. Epub 2019 Jul 17.
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.
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.
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.
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.
托夫茨（Tofts）模型和扩展托夫茨模型是动态对比增强磁共振成像（DCE-MRI）灌注分析中常用的药代动力学模型，尽管它们不能提供两个重要的生物学标志物，即血浆流量和渗透性表面积产物。使用描述血管分布阶段的先进药代动力学模型（如组织均一性模型）可以估计这些标志物。然而，先进模型的缺点在于估计值存在偏差和不确定性，尤其是在进行体素估计时。本研究的目的是通过包含相邻体素的信息来提高估计的可靠性。
通过总变差的形式在估计过程中加入来自相邻体素的信息。将空间正则化应用于使用组织均一性模型估计的五个灌注参数图上。由于总变差不可微，因此使用两种凸优化的近端技术来数值求解问题。
该算法有助于降低估计的灌注参数图中的噪声，并提高估计的准确性。这些结论通过数值体模得到了验证。此外，对真实数据的实验表明，在不显著降低拟合质量的情况下，灌注图的空间一致性和可读性得到了改善。
通过采用空间正则化，可以提高使用组织均一性模型的 DCE-MRI 灌注分析的可靠性。与没有空间正则化的标准方法相比，所提出的利用现代优化技术仅略微增加了计算成本。
