A change of heart rate (HR), or beat-to-beat interval, in response to a change in arterial blood pressure (BP), provides a noninvasive measure of the sensitivity of the baroreceptor-cardiac reflex (baroreflex), which is essential in characterizing cardiovascular autonomic control and explaining the complex interactions between heartbeat dynamics and hemodynamics.27
Baroreflex sensitivity (BRS) assessment provides a valuable measure of cardiovascular regulation in normal or diseased states.26, 11, 44
The evaluation of baroreflex control of heart rate during or after general anesthesia has important implications for clinical practice and patient safety. 9, 12, 58, 60, 41, 52, 53
General anesthetic drugs are known to have direct effects on vascular tone and myocardial contractility, but little is known about how they influence cardiovascular regulation. The cardiovascular side-effects of general anesthetic agents can be serious and potentially life-threatening, particularly in very critically ill patients. Despite the importance of understanding the underlying physiological mechanism and its clinical value, few studies in the literature quantify the effect of anesthetic drugs to on the alteration of cardiovascular control under general anesthesia. Propofol (2,6-diisopropylphenol) is a lipid soluble intravenous anesthetic agent. It is widely used for the induction and maintenance of general anesthesia, as well as sedation.
One of the earliest studies quantifying the baroreceptor reflex under propofol anesthesia demonstrated a “resetting” of the baroreflex. In this study, patient volunteers were anesthetized with intravenous infusions of propofol combined with nitrous oxide. It was found that in the steady state the subjects maintained both low blood pressure and low heart rate. The authors concluded that this was the result of a “resetting” of the baroreflex, but that there was no impairment of baroreflex sensitivity.22
In contrast, in a study that investigated surgical subjects stimulated with mircrolaryngoscopy, it was found that under propofol anesthesia, in addition to the inhibition of sympathetic nervous activity in the periphery, the sensitivity of the baroreflex was decreased.58
Another study found that the sensitivity of the baroreceptors was depressed by propofol infusion during general anesthesia, lasting for up to 60 minutes after the discontinuation of the propofol infusion in 13 healthy human volunteer subjects.53
It should be emphasized that in these studies, BRS was estimated using a simple sequence method based on linear regression analysis; however, the baroreceptor gain function is known to be frequency-dependent, and the influence of vasculature and heart contractility on BP has to be simultaneously considered for a correct identification of the closed-loop cardiovascular control.3
Quantifying BRS under general anesthesia is an even more challenging statistical signal processing problem, because BRS can change rapidly in time as a result of anesthetic drug effects, compensatory maneuvers or pharmacological interventions, with not easily predictable physiological responses.
The idea of estimating time-varying transfer function or coherence function of physiological systems is not new (see reviews63, 49, 39
). In the literature, several methods have been proposed to estimate time-varying transfer or coherence function, such as the Kalman filter, recursive leasts-quares (RLS), or time-varying optimal parameter search (TVOPS) algorithms.3, 67, 65, 64
In a large body of reported work of our own,5, 13, 17, 18
we have previously applied probabilistic point process models for estimating instantaneous
indices of HR, HR variability (HRV), as well as respiratory sinus arrhythmia (RSA). By “instantaneous”, we mean that the statistics can be estimated in principle at any time point with arbitrarily fine time resolution, without resorting to approximation by interpolation. The point process framework enabled us to estimate these physiological indices in a dynamic fashion at a millisecond timescale. Since the cardiovascular system presents several closed-loop interactions between many variables, including R-R interval and BP, research efforts have been devoted to quantifying BRS by estimating the baroreflex gain with a closed-loop system identification approach.6, 38, 2, 3, 29, 30
In this paper, we extend the point process model of the heartbeat interval to include BP as a covariate, allowing for a dynamic assessment of the baroreflex gain within the feedback BP→RR transfer function. At the same time, a discrete-time RLS filter is used to track the parameters for estimating the RR→BP frequency response in the feedforward cardiovascular pathway. This two-filter estimation structure provides a direct assessment of the baroreflex control of heart rate, as well as an instantaneous quantification of beat-to-beat cardiovascular variability, in an online fashion.14
It is noted that the main focus of this paper is to illustrate the strength of the point process method as potential application in clinical anesthesiology, a thorough and systematic comparison between our method and other linear/nonlinear ARX methods is beyond the scope of the current paper. Nevertheless, as an illustration, we compare the tracking performance of the point process filter and the standard RLS filter in analyzing known transient dynamics of BRS. Another important issue of cardiovascular modeling is goodness-of-fit. The current point process approach provides a rigorous statistical framework for model evaluation, which is not available for the standard linear/nonlinear AR or ARX type methods (based on R-R intervals).
In healthy subjects, the heartbeat interval dynamics are known to be nonlinear or even possibly chaotic.45, 48
In a previous investigation,18
, we have modeled the nonlinear heartbeat dynamics within the point process framework using the beat intervals alone. In the present study, in order to characterize a potential nonlinear interaction between the beat intervals and blood pressure measures, we model the heartbeat interval mean using a bilinear system. The use of the bilinear system identification also allows us to estimate the dynamic cross-bispectrum between the R-R and BP series, as well as the power ratio between the cross-spectrum and cross-bispectrum. We apply our point process model to experimental physiological recordings of eleven healthy subjects during induction of propofol anesthesia,51
and we conduct quantitative assessment of baroreflex control during both transient periods as anesthesia is initiated, and performing statistical analyses on steady-state epochs before and after propofol administration.