Brain-imaging data have been increasingly utilized to understand intellectual disabilities. Despite significant progress in biomedical research, the mechanisms for most of the intellectual disabilities remain unknown. Finding the underlying neurological mechanisms has proved difficult, especially in children due to the rapid development of their brains. We investigate verbal reasoning, which is a reliable measure of an individual’s general intellectual abilities, and develop a class of high-order imaging regression models to identify brain subregions which might be associated with this specific intellectual ability. A key novelty of our method is to take advantage of spatial brain structures, and specifically the piecewise smooth nature of most imaging coefficients in the form of high-order tensors. Our approach provides an effective and urgently needed method for identifying brain subregions potentially underlying certain intellectual disabilities. The idea behind our approach is a carefully constructed concept called Internal Variation (IV). The IV employs tensor decomposition and provides a computationally feasible substitution for Total Variation (TV), which has been considered suitable to deal with similar problems but may not be scalable to high-order tensor regression. Before applying our method to analyze the real data, we conduct comprehensive simulation studies to demonstrate the validity of our method in imaging signal identification. Next, we present our results from the analysis of a dataset based on the Philadelphia Neurodevelopmental Cohort for which we preprocessed the data including re-orienting, bias-field correcting, extracting, normalizing and registering the magnetic resonance images from 978 individuals. Our analysis identified a subregion across the cingulate cortex and the corpus callosum as being associated with individuals’ verbal reasoning ability, which, to the best of our knowledge, is a novel region that has not been reported in the literature. This finding is useful in further investigation of functional mechanisms for verbal reasoning.

脑成像数据已越来越多地用于理解智力障碍。尽管生物医学研究取得了重大进展，但大多数智力障碍的机制仍然未知。发现潜在的神经机制已被证明是困难的，特别是在儿童中，由于其大脑的快速发育。我们调查口头推理，这是对个人一般智力的可靠度量，并开发了一类高阶成像回归模型来识别可能与该特定智力相关的脑子区域。我们方法的关键新颖之处在于利用空间大脑结构，特别是大多数成像系数以高阶张量形式的分段平滑特性。我们的方法提供了一种有效且迫切需要的方法，用于识别可能导致某些智力障碍的脑子区域。我们的方法背后的想法是一个精心构造的概念，称为内部变化（IV）。IV使用张量分解，并提供了在计算上可以替代总变化量（TV）的方法，该方法被认为适合解决类似问题，但可能无法扩展到高阶张量回归。在将我们的方法用于分析实际数据之前，我们进行了全面的仿真研究，以证明我们的方法在成像信号识别中的有效性。接下来，我们将基于费城神经发育队列的数据集进行分析，然后对结果进行预处理，包括重新定向，偏差场校正，从978个人中提取，归一化和配准磁共振图像。我们的分析确定了扣带回皮层和call体的一个子区域与个人的言语推理能力有关，据我们所知，这是一个尚未在文献中报道的新颖区域。这一发现对于进一步研究言语推理的功能机制很有用。