Multivariate autoregressive modelling provides a method to analyse the dynamic interactions between heart rate (HR), blood pressure (BP) and respiration (RESP) by means of noise source contributions (NSCs). The conventional approach presumes the modelled noise sources are mutually independent. This presumption is, in general, not satisfied and causes an error in the results. In the present study, the effect of this error is analysed. A method is presented to remove the error by making the noise sources independent. The method is based on the inclusion of immediate transfer paths in the model. To quantify the strength of the interactions, a measure called NSC ratio (NSCR); is calculated; this states the amount of variability of the signal arising from other signals. The method is demonstrated by studying the inter-relationships between HR, BP and RESP in a healthy male subject in supine and standing positions. It is found that the error is marked and that the presented method provides corrected estimates for spectral decomposition and NSC analysis. The results show it is necessary to include the immediate transfer mechanisms in the model, while analysing the cardiopulmonary dynamics by means of HR and BP variability.
Korhonen, I., Takalo, R., & Turjanmaa, V. (1996). Multivariate autoregressive model with immediate transfer paths for assessment of interactions between cardiopulmonary variability signals. Medical and Biological Engineering and Computing, 34(3), 199-206. https://doi.org/10.1007/BF02520074