Time Delay and Causality in Biological Systems

In the study of biological systems, it is often desirable to investigate causality between two simultaneously recorded signals. This paper suggests applying whitening filters to the signals and estimating their cross-correlation. The Cross-correlation sequence can be used to detect time lag between the signals. A positive lag can be interpreted as the reference signal causing the delayed signal. This method is analyzed both by computer simulated signals and arterial blood pressure (ABP) together with central venous pressure (CVP) signals. An estimate of the power spectral density (PSD) of each of the whitened signals is used to assess the quality of the whitening filters. The simulation results show that the method proposed in this paper provides an accurate representation of the causal relationship between the simulated signals. High degree of correlation among the samples of ABP and CVP had a negative effect on the performance of the whitening filters, however the causal relationship between the two signals was still detectable.