Time-varying causal coherence function and its application to renal blood pressure and blood flow data

This paper describes the development of a model-based approach to estimating both feedforward and feedback paths of causal time-varying coherence functions (TVCF). Theoretical derivations of the coherence bounds of the causal TVCF using the proposed approach are also provided. Both theoretical derivations and simulation results revealed interesting observations, and they were corroborated using experimental renal blood pressure and flow data. Specifically, both theoretical derivations and experimental data showed that in certain cases, the calculation of the traditional TVCF was inappropriate when the system under investigation was a causal system. Moreover, the use of the causal TVCF not only provides quantitative assessment of the coupling between the two signals, but it also provides valuable insights into the composition of the physical structure of the renal autoregulatory system.