Poskanzer Craig, Anzellotti Stefano
Department of Psychology, Columbia University, New York City, NY, USA.
Department of Psychology and Neuroscience, Boston College, Boston, MA, USA.
Netw Neurosci. 2022 Oct 1;6(4):1296-1315. doi: 10.1162/netn_a_00264. eCollection 2022.
Here, we propose a novel technique to investigate nonlinear interactions between brain regions that captures both the strength and type of the functional relationship. Inspired by the field of functional analysis, we propose that the relationship between activity in separate brain areas can be viewed as a point in function space, identified by coordinates along an infinite set of basis functions. Using Hermite polynomials as bases, we estimate a subset of these values that serve as "functional coordinates," characterizing the interaction between BOLD activity across brain areas. We provide a proof of the convergence of the estimates in the limit, and we validate the method with simulations in which the ground truth is known, additionally showing that functional coordinates detect statistical dependence even when correlations ("functional connectivity") approach zero. We then use functional coordinates to examine neural interactions with a chosen seed region: the fusiform face area (FFA). Using -means clustering across each voxel's functional coordinates, we illustrate that adding nonlinear basis functions allows for the discrimination of interregional interactions that are otherwise grouped together when using only linear dependence. Finally, we show that regions in V5 and medial occipital and temporal lobes exhibit significant nonlinear interactions with the FFA.
在此，我们提出一种新颖的技术来研究脑区之间的非线性相互作用，该技术能够捕捉功能关系的强度和类型。受功能分析领域的启发，我们提出不同脑区活动之间的关系可被视为函数空间中的一个点，由沿着一组无穷基函数的坐标来确定。以埃尔米特多项式作为基函数，我们估计这些值的一个子集，作为“功能坐标”，以表征全脑区域血氧水平依赖（BOLD）活动之间的相互作用。我们证明了估计值在极限情况下的收敛性，并用已知真实情况的模拟验证了该方法，此外还表明即使相关性（“功能连接性”）趋近于零时，功能坐标也能检测到统计依赖性。然后，我们使用功能坐标来检查与选定种子区域——梭状面孔区（FFA）的神经相互作用。通过对每个体素的功能坐标进行K均值聚类，我们表明添加非线性基函数能够区分区域间的相互作用，而这些相互作用在仅使用线性依赖性时会被归为一类。最后，我们表明V5区以及枕叶内侧和颞叶区域与FFA表现出显著的非线性相互作用。
