Tensor-based morphometry (TBM) aims at showing local differences in brain volumes with respect to a common template. TBM images are smooth but they exhibit (especially in diseased groups) higher values in some brain regions called lateral ventricles. More specifically, our voxelwise analysis shows both a mean-variance relationship in these areas and evidence of spatially dependent skewness. We propose a model for 3-dimensional functional data where mean, variance, and skewness functions vary smoothly across brain locations. We model the voxelwise distributions as skew-normal. The smooth effects of age and sex are estimated on a reference population of cognitively normal subjects from the Alzheimer's Disease Neuroimaging Initiative (ADNI) dataset and mapped across the whole brain. The three parameter functions allow to transform each TBM image (in the reference population as well as in a test set) into a Gaussian process. These subject-specific normative maps are used to derive indices of deviation from a healthy condition to assess the individual risk of pathological degeneration.

翻译：张量形态测量学旨在显示相对于通用模板的脑体积局部差异。TBM图像具有平滑特性，但在某些称为侧脑室的脑区（尤其在疾病组中）会呈现较高数值。具体而言，我们的体素分析显示这些区域同时存在均值-方差关系以及空间依赖性偏度的证据。我们提出了一种针对三维功能数据的模型，其中均值、方差和偏度函数在大脑空间位置上平滑变化。我们将体素分布建模为偏态正态分布。基于阿尔茨海默病神经影像倡议数据集中的认知正常参照人群，我们估计了年龄和性别在整个大脑范围内的平滑效应。通过三个参数函数，可将每个TBM图像（包括参照群体和测试集）转换为高斯过程。这些个体特异性标准化图谱可用于推导偏离健康状态的指标，从而评估个体病理性退变的风险。