Characterizing directed information flow in brain networks is difficult because neural circuits are full of recurrent feedback loops. Many existing tools for directed dependence assume a directed acyclic graph (DAG) structure to resolve directional ambiguity, and therefore cannot represent these loops. We present a nonparametric, information-theoretic framework that addresses this by coupling the discrete Hodge decomposition with lead-lag mutual information, splitting the resulting edge flow into three orthogonal components: a gradient term capturing hierarchical, feed-forward relationships; a curl term isolating triangle-level feedback loops; and a harmonic term capturing cyclic flow around topological holes. This separation makes it possible to disentangle feed-forward drive from recurrent circulation, which conventional measures conflate. We further develop a permutation-based hypothesis-testing layer that identifies nodes and triangular motifs whose information-flow signatures change significantly between conditions. We validate the framework on simulations with known ground-truth structure and apply it to local field potential recordings from a rodent model of focal ischemic stroke. In three of four animals, we find a post-stroke shift toward hierarchical, source-driven propagation at the expense of recurrent feedback, while the fourth shows no significant change.

翻译：刻画脑网络中的有向信息流动十分困难，因为神经回路充满了递归反馈环路。许多现有的有向依赖性分析工具为了解决方向歧义问题，假设了有向无环图结构，因此无法表征这些环路。我们提出一个非参数化的信息论框架，通过将离散霍奇分解与超前滞后互信息相结合来解决此问题，并将得到的边流分解为三个正交分量：捕捉层级前馈关系的梯度项、分离三角级反馈环路的旋度项，以及捕捉拓扑孔周围循环流的调和项。这种分解使得能够将前馈驱动与循环流通分离开来，而传统测量方法则会混淆二者。我们还进一步开发了一个基于排列的假设检验层，用于识别其信息流动特征在不同条件下发生显著变化的节点和三角模式。我们通过已知真实结构的模拟验证了该框架，并将其应用于局灶性缺血性脑卒中啮齿动物模型局部场电位记录的实验数据。在四只动物中的三只中，我们观察到卒中后向层级化、源驱动的传播模式转变，以牺牲递归反馈为代价，而第四只动物则未显示显著变化。