Consideration on parameter determination of a new model describing dynamic vagal heart rate control in rats

Dynamic accentuated antagonism of heart rate control during different levels of vagal nerve stimulation intensity in rats

Accentuated antagonism refers to a phenomenon in which the vagal effect on heart rate (HR) is augmented by background sympathetic tone. The dynamic aspect of accentuated antagonism remains to be elucidated during different levels of vagal nerve stimulation (VNS) intensity. We performed VNS on anesthetized rats (n = 8) according to a binary white noise signal with a switching interval of 500 ms at three different stimulation rates (low-intensity: 0-10 Hz, moderate-intensity: 0-20 Hz, and high-intensity: 0-40 Hz). The transfer function from VNS to HR was estimated with and without concomitant tonic sympathetic nerve stimulation (SNS) at 5 Hz. The asymptotic low-frequency (LF) gain (in beats/min/Hz) of the transfer function increased with SNS regardless of the VNS rate [low-intensity: 3.93 ± 0.70 vs. 5.82 ± 0.65 (P = 0.021), moderate-intensity: 3.87 ± 0.62 vs. 5.36 ± 0.53 (P = 0.018), high-intensity: 4.77 ± 0.85 vs. 7.39 ± 1.36 (P = 0.011)]. Moreover, SNS slightly increased the ratio of high-frequency (HF) gain to the LF gain. These effects of SNS were canceled by the pretreatment of ivabradine, an inhibitor of hyperpolarization-activated cyclic nucleotide-gated channels, in another group of rats (n = 6). Although background sympathetic tone antagonizes the vagal effect on mean HR, it enables finer HR control by increasing the dynamic gain of the vagal HR transfer function regardless of VNS intensity. When interpreting the HF component of HR variability, the augmenting effect from background sympathetic tone needs to be considered.

Contrasting open-loop dynamic characteristics of sympathetic and vagal systems during baroreflex-mediated heart rate control in rats

Although heart rate (HR) is governed by the sympathetic and parasympathetic nervous systems, a head-to-head comparison of the open-loop dynamic characteristics of the total arc from a baroreceptor pressure input to the HR response has yet to be performed. We estimated the transfer function from carotid sinus pressure input to the HR response ( HCSP→HR) before and after bilateral vagotomy ( n = 7) as well as before and after the administration of a β-blocker propranolol ( n = 8) in anesthetized male Wistar-Kyoto rats. The carotid sinus pressure was perturbed according to a Gaussian white noise signal so that the input power spectra were relatively flat between 0.01 and 1 Hz. The gain plot of HCSP→HR was V-shaped. Vagotomy reduced the dynamic gain at 1 Hz (0.0598 ± 0.0065 to 0.0025 ± 0.0004 beats·min−1·mmHg−1, P < 0.001) but not at 0.01 or 0.1 Hz. β-Blockade reduced the dynamic gain at 0.01 Hz (0.247 ± 0.069 to 0.077 ± 0.017 beats·min−1·mmHg−1, P = 0.020) but not at 0.1 or 1 Hz. We also estimated the efferent limb transfer function from electrical vagal efferent stimulation to the HR response ( HVN→HR) under β-blockade conditions. We associated the model parameters of HVN→HR with the mean HR and the standard deviation of HR so that HVN→HR could be estimated based only on the HR data. We finally estimated the neural arc transfer function from a pressure input to efferent vagal nerve activity by dividing HCSP→HR by HVN→HR. The mathematically determined vagal neural arc showed derivative characteristics with its phase near zero radians at the lowest frequency.

Intravenous ivabradine augments the dynamic heart rate response to moderate vagal nerve stimulation in anesthetized rats

Ivabradine is a selective bradycardic agent that reduces the heart rate (HR) by inhibiting the hyperpolarization-activated cyclic nucleotide-gated channels. Although its cardiovascular effect is thought to be minimal except for inducing bradycardia, ivabradine could interact with cardiovascular regulation by the autonomic nervous system. We tested whether ivabradine modifies dynamic characteristics of peripheral vagal HR control. In anesthetized Wistar-Kyoto rats ( n = 7), the right vagal nerve was sectioned and stimulated for 10 min according to a binary white noise sequence with a switching interval of 500 ms. The efferent vagal nerve stimulation (VNS) trials were performed using three different rates (10, 20, and 40 Hz), and were designated as V0–10, V0–20, and V0–40, respectively. The transfer function from the VNS to the HR was estimated before and after the intravenous administration of ivabradine (2 mg/kg). Ivabradine increased the asymptotic dynamic gain in V0–20 [from 3.88 (1.78–5.79) to 6.62 (3.12–8.31) beats·min−1·Hz−1, P < 0.01, median (range)] but not in V0–10 or V0–40. Ivabradine increased the corner frequency in V0–10 [from 0.032 (0.026–0.041) to 0.064 (0.029–0.090) Hz, P < 0.01] and V0–20 [from 0.040 (0.037–0.056) to 0.068 (0.051–0.100) Hz, P < 0.01] but not in V0–40. In conclusion, ivabradine augmented the dynamic HR response to moderate VNS. At high VNS, however, ivabradine did not significantly augment the dynamic HR response, possibly because ivabradine reduced the baseline HR and limited the range for the bradycardic response to high VNS.

NEW & NOTEWORTHY Ivabradine is considered to be a pure bradycardic agent that has little effect on cardiovascular function except inducing bradycardia. The present study demonstrated that ivabradine interacts with the dynamic vagal heart rate control in a manner that augments the heart rate response to moderate-intensity efferent vagal nerve stimulation.

Recursive identification of an arterial baroreflex model for the evaluation of cardiovascular autonomic modulation

The evaluation of the time-varying vagal and sympathetic contributions to heart rate remains a challenging task because the observability of the baroreflex is generally limited and the time-varying properties are difficult to take into account, especially in non-stationnary conditions. The objective is to propose a model-based approach to estimate the autonomic modulation during a pharmacological challenge. A recursive parameter identification method is proposed and applied to a mathematical model of the baroreflex, in order to estimate the time-varying vagal and sympathetic contributions to heart rate modulation during autonomic maneuvers. The model-based method was evaluated with data from five newborn lambs, which were acquired during injection of vasodilator and vasoconstrictor drugs, on normal conditions and under beta-blockers, so as to quantify the effect of the pharmacological sympathetic blockade on the estimated parameters. After parameter identification, results show a close match between experimental and simulated signals for the five lambs, as the mean relative root mean squared error is equal to 0.0026 (± 0.003). The error, between simulated and experimental signals, is significantly reduced compared to a batch identification of parameters. The model-based estimation of vagal and sympathetic contributions were consistent with physiological knowledge and, as expected, it was possible to observe an alteration of the sympathetic response under beta-blockers. The simulated vagal modulation illustrates a response similar to traditional heart rate variability markers during the pharmacological maneuver. The model-based method, proposed in the paper, highlights the advantages of using a recursive identification method for the estimation of vagal and sympathetic modulation.