Non-parametric full cross mapping (NFCM): a highly-stable measure for causal brain network and a pilot application

<i>Objective.</i>Measuring causal brain network from neurophysiological signals has recently attracted much attention in the field of neuroinformatics. Traditional data-driven algorithms are computationally time-consuming and unstable due to parameter settings.<i>Approach.</i>To resolve these limits, we proposed a novel parameter-free technique, called 'non-parametric full cross mapping (NFCM)'. The NFCM adapts current convergent cross-mapping concept, and makes two improvements: (1) an improved phase-space reconstruction with constant embedding parameters and (2) cross-mapping estimate of all embedding vectors on manifolds following simplex projection.<i>Main results.</i>Numerical experiments verify that our NFCM has the highest quantization stability even when perturbed by system noise, and its coefficient of variation is almost lower than that of the six baseline methods. The developed NFCM is finally used in stereoelectroencephalogram analysis of drug-resistant epilepsy in children (DREC). A total of 36 seizures, comprising 18 surgical successes and 18 failures, were included to explore the brain network dynamics. The average causal coupling in epileptogenic zones of successful surgery (0.81 ± 0.04) is significantly higher than that in non-epileptogenic zones (0.40 ± 0.03) withP<0.001via Mann-Whitney-U-test. While there is no significant difference among the 18 failed surgeries.<i>Significance.</i>The causal brain network measured by our NFCM is confirmed as a credible biomarker for localizing epileptogenic zones in DREC. These findings promise to advance precision medicine for DREC.