Multivariate System Identification for Cerebral Autoregulation

The effect of spontaneous beat-to-beat mean arterial blood pressure (ABP) fluctuations and breath-to-breath end-tidal carbon dioxide $(P_{ETCO_2})$ and end-tidal oxygen $(P_{ETO_2})$ fluctuations on beat-to-beat cerebral blood flow velocity (CBFV) variations is studied using a multiple coherence function. Multiple coherence is a measure of the extent to which the output, CBFV, can be represented as a linear time invariant system of multiple input signals. Analysis of experimental measurements from 13 different healthy subjects reveal that, with additional inputs, $P_{ETCO_2}$ and $P_{ETO_2},$ the multiple coherence for frequencies < 0.05 Hz is significantly higher than the corresponding values obtained for univariate coherence with a single input of ABP. The result illustrates that the low value of univariate coherence at small frequencies may be due to the effects of $P_{ETCO_2}$ and $P_{ETO_2}$ fluctuations on CBFV variability. Moreover, it is also found that the transfer function between ABP and CBFV time series identified from previous univariate techniques at low frequencies can be modified by CO ₂ and O ₂ reactivity and no longer represents pressure autoregulation only. Multivariate system identification provides a technique of incorporating additional variability and recovering from this artifact. Finally, a physiologically based model and its linear transfer function are used as a simulation tool to investigate possible causes of low univariate coherence.