Cortical thickness computation in magnetic resonance imaging (MRI) is an important method to study the brain morphological changes induced by neurodegenerative diseases. This paper presents an algorithm of thickness measurement based on a volumetric Laplacian operator (VLO), which is able to capture accurately the geometric information of brain images. The proposed algorithm is a novel three-step method: 1) The rule of parity and the shrinkage strategy are combined to detect and fix the intersection error regions between the cortical surface meshes separated by FreeSurfer software and the tetrahedral mesh is constructed which reflects the original morphological features of the cerebral cortex, 2) VLO and finite element method are combined to compute the temperature distribution in the cerebral cortex under the Dirichlet boundary conditions, and 3) the thermal gradient line is determined based on the constructed local isothermal surfaces and linear geometric interpolation results. Combined with half-face data storage structure, the cortical thickness can be computed accurately and effectively from the length of each gradient line. With the obtained thickness, we set experiments to study the group differences among groups of Alzheimer's disease (AD, N = 110), mild cognitive impairment (MCI, N = 101) and healthy control people (CTL, N = 128) by statistical analysis. The results show that the q-value associated with the group differences is 0.0458 between AD and CTL, 0.0371 between MCI and CTL, and 0.0044 between AD and MCI. Practical tests demonstrate that the algorithm of thickness measurement has high efficiency and is generic to be applied to various biological structures that have internal and external surfaces.

中文翻译：

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通过求解基于四面体的谐波场来计算皮质厚度。

磁共振成像（MRI）中的皮质厚度计算是研究神经退行性疾病引起的大脑形态变化的重要方法。本文提出了一种基于体积拉普拉斯算子（VLO）的厚度测量算法，该算法能够准确捕获大脑图像的几何信息。所提出的算法是一种新颖的三步法：1）结合奇偶性规则和收缩策略来检测并修复由FreeSurfer软件分离的皮质表面网格之间的相交误差区域，并构建反映原始图像的四面体网格大脑皮层的形态特征； 2）结合VLO和有限元方法，计算Dirichlet边界条件下大脑皮层的温度分布，3）根据构造的局部等温面和线性几何插值结果确定热梯度线。结合半脸数据存储结构，可以从每条梯度线的长度准确而有效地计算出皮层厚度。利用获得的厚度，我们进行实验以通过统计分析研究阿尔茨海默氏病（AD，N = 110），轻度认知障碍（MCI，N = 101）和健康对照组（CTL，N = 128）之间的组差异。 。结果表明，与组差异相关的q值在AD和CTL之间为0.0458，在MCI和CTL之间为0.0371，在AD和MCI之间为0.0044。