Sensitivity analysis of (renormalized) partial directed coherence for the study of corticomuscular causality

Stroke is a serious global health care problem for which rehabilitation is the main mode of therapy. Studying human corticomuscular communication with a measure that can reveal causality in a system with sensory and motor pathways has the potential to lead to an optimal, patient-tailored rehabilitation strategy. The goal of this study was to identify and solve potential problems in the use of (renormalized) partial directed coherence (PDC and rPDC) in corticomuscular coupling research. Simulations showed that A) an overestimation of the multivariate autoregressive (MVAR) model order p increases the effectiveness of PDC and rPDC, if a sufficiently high ratio ? between the number of samples and MVAR parameters is maintained. B) A difference in signal-to-measurement-noise ratio (SNR) between the channels i and j of a bivariate time series will only allow the comparison of PDCi ?j(f) to PDCj?i(f) at frequency f if both SNRs ?10dB. The same holds for rPDC. C) When using short segments of data, PDC and rPDC can be determined more accurately by averaging the covariance matrix R ?(?) of the time series at lag ? over segments than by averaging the MVAR parameters. We furthermore provide a way to obtain the analytical confidence limits of PDC and rPDC from segmented data. Finally, we show that PDC and rPDC can be correctly determined in real, segmented electroencephalography-electromyography (EEG-EMG) data using an order p several times higher than indicated by Akaike's Information Criterion or Schwarz's Bayesian Criterion.