Metric Validation for Detection of Delayed and Directed Coupling
Abstract
Background
The brain functions as a complex network of billions of interconnected neurons, coordinating processes from basic reflexes to high-level cognition. Dysfunction in these networks contribute to neurological and psychiatric disorders, including epilepsy, depression, and Parkinson’s disease. Understanding these network alterations is essential for developing effective therapies. However, reconstructing network topology from human electrophysiology data is challenging due to sparse sampling, measurement noise, and variable time delays in interregional communication. Effective connectivity (EC) metrics have been developed to infer directed neural interactions, but their accuracy and robustness under real-world data constraints remain unclear. This study empirically evaluates common EC metrics to determine which most accurately reconstruct network topology in the presence of data limitations.
Methods
We generated Erdős–Rényi networks and simulated time series using a time-delayed vector autoregressive (VAR) model. We systematically varied network size, data length, measurement noise, and network coverage. Variations of four commonly used EC metrics, cross-correlation, Granger causality, mutual information, and transfer entropy, were evaluated for reconstruction accuracy using cosine distance to compare estimated and true connectivity matrices.
Results
Multivariate transfer entropy demonstrated the highest accuracy across various conditions but required significantly longer computation times. For small networks (<30 nodes), mutual information and Granger causality rapidly and accurately reconstructed networks. For larger networks, partial cross-correlation performed well with good computational efficiency. Notably, zero-lag metrics perform no better than chance in nearly all conditions.
Conclusion
The choice of an EC metric should consider specific data constraints.While multivariate transfer entropy is the most reliable across conditions, its long runtime limits its practical application. For large networks, partial cross-correlation offers a faster and reasonably accurate alternative. Granger causality and mutual information are effective for small networks. Critically, time-lagged metrics are essential for accurate network reconstructions, as failing to account for time delays leads to reconstructions no more accurate than random network models.
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