A Robust Causal Brain Network Measure and Its Application on Ictal Electrocorticogram Analysis of Drug-resistant Epilepsy

Measuring causal brain network is a significant topic for exploring complex brain functions. While various data-driven algorithms have been proposed, they still have some drawbacks such as ignoring time non-separability, cumbersome parameter settings, and poor robustness. To solve these deficiencies, we developed a novel framework: &#x201C;time-shift permutation cross-mapping, TPCM,&#x201D; integrating steps of (1) delayed improved phase-space reconstruction (DIPSR), (2) rank transformation of embedding vectors&#x2019; distances, (3) cross-mapping with a fitting estimation, and (4) causality quantification using multi-delays. Based on synthetic models and comparison with baseline methods, numerical validation results demonstrate that TPCM significantly improves the robustness for data length with or without noise interference, and achieves the best quantification accuracy in detecting time delay and coupling strength, with the highest determination coefficient ( <italic>R</italic>² = 0. 96 ) of fitting verse coupling parameters. The developed TPCM was finally applied to ictal electrocorticogram (ECoG) analysis of patients with drug-resistant epilepsy (DRE). A total of 17 patients with DRE were included into the retrospective study. For 8 patients undergoing successful surgeries, the causal coupling strength (0.58 &#x00B1; 0.20) within epileptogenic zone network is significantly higher than those suffering failed surgeries (0.38 &#x00B1; 0.16) with <italic>P</italic> &#x003C; 0. 001 through Mann-Whitney-U-test. Therefore, the epileptic brain network measured by TPCM is a credible biomarker for predicting surgical outcomes. These findings additionally confirm TPCM&#x2019;s superior performance and promising potential to advance precision medicine for neurological disorders.