Time Delay and Causality in Biological Systems Using Whitened Cross-Correlation Analysis

In the study of biological systems, it is often desirable to study the relationship between two simultaneously recorded signals and investigate whether one signal is causing the other. Correlation between signals can be revealed by spectral analysis techniques such as coherence. While coherence reveals the interaction strength between two signals, it does not provide directional information about the direction of causality of the signals, if any. Cross-correlation can be reliably used to test whether a linear association exists between two processes. It can also be used to test whether a time lag exists between the signals by identifying the mean value of their cross-correlation sequence. In this paper, we propose applying a whitening filter to signals prior to estimating the cross-correlation. This whitening removes correlation of the signals with themselves, which generally blurs the cross-correlation over a broad range of lags and limits cross-correlation as a tool for causality analysis. In this application, a Kalman filter is used adaptively to whiten the signals. An example of the increased sensitivity of whitened cross-correlation analysis is given by studying the relationship between the mean intracranial pressure (ICP) and the heart rate (HR) of pediatric patients with traumatic brain injury. Results show that in five recordings from five patients, the heart rate process lags the mean intracranial pressure