Two healthy volunteer subjects, ages 20 and 32, gave written consent to participate in this study approved by the Massachusetts General Hospital (MGH). Any subject whose medical evaluation did not allow him or her to be classified as American Society of Anesthesiologists Physical Status I was excluded from the study. Intravenous and arterial lines were placed in each subject. Propofol was infused intravenously using a previously validated computer-controlled delivery system running STANPUMP [14
] connected to a Harvard 22 syringe pump (Harvard Apparatus, Holliston, MA). Five effect-site target concentrations (0-4 mcg/ml) were each maintained for 15 minutes respectively. In subject 2, an additional effect-site target concentration of 5 mcg/ml was administered. Capnography, pulse oximetry, ECG, and arterial BP (P1) were recorded and (sampling rate 1 kHz) and monitored continuously by an anesthesiologist throughout the study. Bag-mask ventilation with 30% oxygen was administered as needed in the event of propofol-induced apnea. Because propofol is a potent peripheral vasodilator, phenylephrine was administered intravenously to maintain mean arterial BP within 20% of the baseline value [12
In the present experiment, systolic BP (SBP) value was used for baroreflex evaluation. For the linear model (2
), the bivariate orders p
were fitted from 2 to 8 and the optimal order was chosen according to the Akaike information criterion
(AIC). For the bilinear model (3
), the order r=2
was chosen empirically to avoid demanding computation burden, and the initial hij
was estimated by fitting the residual error via least-squares. Upon estimating the CIF, the goodness-of-fit of the probabilistic heartbeat model is evaluated with the Kolmogorov-Smirnov
(KS) test [3
]. For all of data fitted here, our model achieves fairly satisfactory goodness-of-fit: among a total of 11 epochs (5 in subject 1 plus 6 in subject 2), the linear model is able to reach 95% confidence bounds in KS test for 8 epochs.
For each subject, we first examine the mean statistics of baroreflex gain (LF and HF) during each epoch (15 min each, upon reaching the steady state). Specifically, during the steady state we observed a clear reduction of baroreflex gain at HF from control baseline to the start of anesthesia (level 1), and it continued to decrease as the level of the drug concentration increased. This observation is also consistent with some published results in the literature [5
]. For HR and HRV, upon the induction of general anesthesia, we observed an opposite trend between two subjects (for subject 1, HR increased and HRV slightly decreased). Results from two subjects across all 11 epochs are summarized in .
Summarized estimated mean statistics for two subjects
Furthermore, to evaluate the tracking performance of point process filter, we also examine its performance during transient dynamics. We use subject 1 to illustrate this point in . As seen, the baroreflex responses were triggered by injections of drug around 1890 s, which is accompanied by a drop in the baroreflex gain (about 55%), and the point process filter quickly captures the change. Meanwhile, the instantaneous cross-spectrum (or coherence) between SBP and RR shows that these two series are strongly correlated at the HF range, first staying around 0.3 Hz at the conscious baseline and then shifting around 0.25 Hz at level-1 of drug concentration (now shown here).
Figure 2 A snapshot of estimated dynamic statistical indices ranging from the baseline to level-1 (subject 1). The dashed line marks the start of anesthesia at level-1, and the blank region represents the transient period after the baseline (where SBP measures (more ...)
Next, we also investigate the role of nonlinearity that is played by the bilinear model before and during general anesthesia. Specifically, we compare the mean ratio statistic between the conscious baseline and the level-1 drug concentration, and the result is listed in . For both subjects, the ρ
value (LF and HF) is significantly greater in the conscious baseline condition (P
<0.01, Mann-Whitney test), which suggests that the bilinear interaction between BP and RR became more active during general anesthesia, where the parasympathetic activity is suppressed or attenuated [10
] (this phenomenon is also consistent with our observations in another experimental protocol [7
]). Meanwhile, the reduction of mean coherence (see ) during anesthesia also suggests that the BP-RR relation might have either nonlinear components, or two signals are (relatively) less linearly correlated.
Comparison of mean HR, SBP, coherence, and ρ-value