Unravelling how the human brain structure gives rise to function is a central question in neuroscience and remains partially answered. Recent studies show that the graph Laplacian of the human brain’s structural connectivity (SC) plays a dominant role in shaping the pattern of resting-state functional connectivity (FC). The modeling of FC using the graph Laplacian of the brain’s SC is limited, owing to the sparseness of the Laplacian matrix. It is unable to model the negative functional correlations. We extended the graph Laplacian to the hypergraph p-Laplacian in order to describe better the nonlinear and high-order relations between SC and FC. First we estimated those possible links showing negative correlations between the brain areas shared across subjects by statistical analysis. Then we presented a hypergraph p-Laplacian model by embedding the two matrices referring to the sign of the correlations between the brain areas relying on the brain structural connectome. We tested the model on two experimental connectome datasets and evaluated the predicted FC by estimating its Pearson correlation with the empirical FC matrices. The results showed that the proposed diffusion model based on hypergraph p-Laplacian can predict functional correlations more accurately than the models using graph Laplacian as well as hypergraph Laplacian.

中文翻译：

---

使用超图 p-拉普拉斯算子对人脑功能连接的高阶非线性进行数值模拟

解开人类大脑结构如何产生功能是神经科学中的一个核心问题，并且仍有部分答案。最近的研究表明，人脑结构连接 (SC) 的拉普拉斯图在塑造静息状态功能连接 (FC) 模式方面起着主导作用。由于拉普拉斯矩阵的稀疏性，使用大脑 SC 的拉普拉斯图对 FC 进行建模是有限的。它无法对负函数相关性进行建模。我们将图拉普拉斯算子扩展到超图p-Laplacian 为了更好地描述 SC 和 FC 之间的非线性和高阶关系。首先，我们通过统计分析估计了那些在受试者共享的大脑区域之间显示负相关的可能联系。然后我们通过嵌入两个矩阵来提出一个超图p-拉普拉斯模型，这些矩阵指的是依赖于大脑结构连接组的大脑区域之间相关性的符号。我们在两个实验连接组数据集上测试了模型，并通过估计其与经验 FC 矩阵的 Pearson 相关性来评估预测的 FC。结果表明，所提出的基于超图p 的扩散模型- 拉普拉斯算子可以比使用图拉普拉斯算子和超图拉普拉斯算子的模型更准确地预测函数相关性。