An approach to estimate time-varying casual coherence function

Objectives: This paper describes the development of a model-based approach to estimating both open-loop and causal time-varying coherence functions (TVCF). Theoretical derivations of the coherence bounds using the proposed approach are also provided. Methods: A time-varying vector autoregressive (VAR) model was used to estimate both open-loop and causal TVCF. The time-varying optimal parameter search method was employed to identify the time-varying model coefficients as well as the model order of the VAR model. Results: Simulation results revealed interesting observations, and they were corroborated using experimental renal blood pressure and flow data. Specifically, experimental data showed that in certain cases, the calculation of the open-loop TVCF might provide incorrect interpretation of the results when the system under investigation was a closed-loop system, which is consistent with theoretical derivations. Conclusions: The use of the closed-loop 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 system.