Nonlinear identification of the total baroreflex arc

Input-size dependence of the baroreflex neural arc transfer characteristics during Gaussian white noise inputs

Although Gaussian white noise (GWN) inputs offer a theoretical framework for identifying higher-order nonlinearity, an actual application to the data of the neural arc of the carotid sinus baroreflex did not succeed in fully predicting the well-known sigmoidal nonlinearity. In the present study, we assumed that the neural arc can be approximated by a cascade of a linear dynamic (LD) component and a nonlinear static (NS) component. We analyzed the data obtained using GWN inputs with a mean of 120 mmHg and standard deviations (SDs) of 10, 20, and 30 mmHg for 15 min each in anesthetized rats (n = 7). We first estimated the linear transfer function from carotid sinus pressure to sympathetic nerve activity (SNA) and then plotted the measured SNA against the linearly predicted SNA. The predicted and measured data pairs exhibited an inverse sigmoidal distribution when grouped into 10 bins based on the size of the linearly predicted SNA. The sigmoidal nonlinearity estimated via the LD-NS model showed a midpoint pressure (104.1 ± 4.4 mmHg for SD of 30 mmHg) lower than that estimated by a conventional stepwise input (135.8 ± 3.9 mmHg, P < 0.001). This suggests that the NS component is more likely to reflect the nonlinearity observed during pulsatile inputs that are physiological to baroreceptors. Furthermore, the LD-NS model yielded higher R2 values compared with the linear model and the previously suggested second-order Uryson model in the testing dataset.NEW & NOTEWORTHY We examined the input-size dependence of the baroreflex neural arc transfer characteristics during Gaussian white noise inputs. A linear dynamic-static nonlinear model yielded higher R2 values compared with a linear model and captured the well-known sigmoidal nonlinearity of the neural arc, indicating that the nonlinear dynamics contributed to determining sympathetic nerve activity. Ignoring such nonlinear dynamics might reduce our ability to explain underlying physiology and significantly limit the interpretation of experimental data.

Linear and nonlinear identification of the carotid sinus baroreflex in the very low-frequency range

Since the arterial baroreflex system is classified as an immediate control system, the focus has been on analyzing its dynamic characteristics in the frequency range between 0.01 and 1 Hz. Although the dynamic characteristics in the frequency range below 0.01 Hz are not expected to be large, actual experimental data are scant. The aim was to identify the dynamic characteristics of the carotid sinus baroreflex in the frequency range down to 0.001 Hz. The carotid sinus baroreceptor regions were isolated from the systemic circulation, and carotid sinus pressure (CSP) was changed every 10 s according to Gaussian white noise with a mean of 120 mmHg and standard deviation of 20 mmHg for 90 min in anesthetized Wistar‐Kyoto rats (n = 8). The dynamic gain of the linear transfer function relating CSP to arterial pressure (AP) at 0.001 Hz tended to be greater than that at 0.01 Hz (1.060 ± 0.197 vs. 0.625 ± 0.067, p = 0.080), suggesting that baroreflex control was largely maintained at 0.001 Hz. Regarding nonlinear analysis, a second‐order Uryson model predicted AP with a higher R² value (0.645 ± 0.053) than a linear model (R² = 0.543 ± 0.057, p = 0.025) or a second‐order Volterra model (R² = 0.589 ± 0.055, p = 0.045) in testing data. These pieces of information may be used to create baroreflex models that can add a component of autonomic control to a cardiovascular digital twin for predicting acute hemodynamic responses to treatments and tailoring individual treatment strategies.

Closed-Loop Identification of Baroreflex Properties in the Frequency Domain

The arterial baroreflex system plays a key role in maintaining the homeostasis of arterial pressure (AP). Changes in AP affect autonomic nervous activities through the baroreflex neural arc, whereas changes in the autonomic nervous activities, in turn, alter AP through the baroreflex peripheral arc. This closed-loop negative feedback operation makes it difficult to identify open-loop dynamic characteristics of the neural and peripheral arcs. Regarding sympathetic AP controls, we examined the applicability of a nonparametric frequency-domain closed-loop identification method to the carotid sinus baroreflex system in anesthetized rabbits. This article compares the results of an open-loop analysis applied to open-loop data, an open-loop analysis erroneously applied to closed-loop data, and a closed-loop analysis applied to closed-loop data. To facilitate the understanding of the analytical method, sample data files and sample analytical codes were provided. In the closed-loop identification, properties of the unknown central noise that modulated the sympathetic nerve activity and the unknown peripheral noise that fluctuated AP affected the accuracy of the estimation results. A priori knowledge about the open-loop dynamic characteristics of the arterial baroreflex system may be used to advance the assessment of baroreflex function under closed-loop conditions in the future.

Vascular resistance arm of the baroreflex: methodology and comparison with the cardiac chronotropic arm

Baroreflex response consists of cardiac chronotropic (effect on heart rate), cardiac inotropic (on contractility), venous (on venous return) and vascular (on vascular resistance) arms. Because of the simplicity of its measurement, the cardiac chronotropic arm is most often analyzed. The aim was to introduce a method to assess the vascular baroreflex arm and to characterize its changes during stress. We evaluated the effect of orthostasis and mental arithmetics (MA) in 39 (22 women, 17 men; median age: 18.7 yr) and 36 (21 women, 15 men; 19.2 yr) healthy volunteers, respectively. We recorded systolic (SBP) and mean (MBP) blood pressure by volume-clamp method and R-R interval (RR) by ECG. Cardiac output (CO) was recorded by impedance cardiography. From MBP and CO, peripheral vascular resistance (PVR) was calculated. The directional spectral coupling and gain of cardiac chronotropic (SBP to RR) and vascular (SBP to PVR) arms were quantified. The strength of the causal coupling from SBP to PVR was significantly higher than that of SBP to RR coupling over the whole protocol (P < 0.001). Along both arms, the coupling was higher during orthostasis compared with the supine position (P < 0.001 and P = 0.006); no MA effect was observed. No significant changes in the spectral gain (ratio of RR or PVR change to a unit SBP change) across all phases were found (0.111 ≤ P ≤ 0.907). We conclude that changes in PVR are tightly coupled with SBP oscillations via the baroreflex, providing an approach for baroreflex vascular arm analysis with the potential to reveal new aspects of blood pressure dysregulation.NEW & NOTEWORTHY Baroreflex response consists of several arms, but the cardiac chronotropic arm (blood pressure changes evoking heart rate response) is usually analyzed. This study introduces a method to assess the vascular baroreflex arm with the continuous noninvasive measurement of peripheral vascular resistance as an output considering causality in the interaction between oscillations and slower dynamics of vascular tone changes. We conclude that although vascular baroreflex arm involvement becomes dominant during orthostasis, gain of this interaction is relatively stable.

System dynamics of active and passive postural changes: Insights from principal dynamic modes analysis of baroreflex loop

The baroreflex being a key modulator of cardiovascular control ensures adequate blood pressure regulation under orthostatic stress which otherwise may cause severe hypotension. Contrary to conventional baroreflex sensitivity indices derived across a-priori traditional frequency bands, the present study is aimed at proposing new indices for the assessment of baroreflex drive which follows active (supine to stand-up) and passive (supine to head-up tilt) postural changes. To achieve this, a novel system identification approach of principal dynamic modes (PDM) was utilized to extract data-adaptive frequency components of closed-loop interactions between beat-to-beat interval and systolic blood pressure recorded from 10 healthy humans. We observed that the gain of low-pass global PDM of cardiac arm (:feedback reflex loop, mediated by pressure sensors to adjust heart rate in response to arterial blood pressure), and 0.2 Hz global PDM of mechanical arm (:feed-forward pathways, originating changes in arterial blood pressure in response to heart rate variations) may function as potential markers to distinguish active and passive orthostatic tests in healthy subjects.

Wavelet decomposition analysis is a clinically relevant strategy to evaluate cerebrovascular buffering of blood pressure after spinal cord injury

The capacity of the cerebrovasculature to buffer changes in blood pressure (BP) is crucial to prevent stroke, the incidence of which is three- to fourfold elevated after spinal cord injury (SCI). Disruption of descending sympathetic pathways within the spinal cord due to cervical SCI may result in impaired cerebrovascular buffering. Only linear analyses of cerebrovascular buffering of BP, such as transfer function, have been used in SCI research. This approach does not account for inherent nonlinearity and nonstationarity components of cerebrovascular regulation, often depends on perturbations of BP to increase the statistical power, and does not account for the influence of arterial CO₂ tension. Here, we used a nonlinear and nonstationary analysis approach termed wavelet decomposition analysis (WDA), which recently identified novel sympathetic influences on cerebrovascular buffering of BP occurring in the ultra-low-frequency range (ULF; 0.02-0.03Hz). WDA does not require BP perturbations and can account for influences of CO₂ tension. Supine resting beat-by-beat BP (Finometer), middle cerebral artery blood velocity (transcranial Doppler), and end-tidal CO₂ tension were recorded in cervical SCI ( n = 14) and uninjured ( n = 16) individuals. WDA revealed that cerebral blood flow more closely follows changes in BP in the ULF range ( P = 0.0021, Cohen's d = 0.89), which may be interpreted as an impairment in cerebrovascular buffering of BP. This persisted after accounting for CO₂. Transfer function metrics were not different in the ULF range, but phase was reduced at 0.07-0.2 Hz ( P = 0.03, Cohen's d = 0.31). Sympathetically mediated cerebrovascular buffering of BP is impaired after SCI, and WDA is a powerful strategy for evaluating cerebrovascular buffering in clinical populations.

Effects of different input pressure waveforms on the carotid sinus baroreflex-mediated sympathetic arterial pressure response in rats

Although the pulsatility of an input pressure is an important factor that determines the arterial baroreflex responses, whether the difference in the input waveforms can meaningfully affect the baroreflex function remains unknown. This study aimed to compare baroreflex responses between two distinct pressure waveforms: a forward saw wave (FSW) and a backward saw wave (BSW). In seven anesthetized rats, carotid sinus pressure was exposed to the FSW or the BSW with a mean of 120 mmHg, pulse pressure of 40 mmHg, and pulse frequency of 1 Hz. Changes in efferent sympathetic nerve activity (SNA) and arterial pressure (AP) during six consecutive saw wave trials (FSW1, BSW1, FSW2, BSW2, FSW3, and BSW3) were examined. The steady-state SNA value during FSW1 was 91.1 ± 1.9%, which was unchanged during FSW2 and FSW3 but significantly increased during BSW1 (106.6 ± 3.4%, P < 0.01), BSW2 (110.6 ± 2.5%, P < 0.01), and BSW3 (111.6 ± 2.3%, P < 0.01). The steady-state AP value during FSW1 was 98.2 ± 8.1 mmHg, which was unchanged during FSW2 and FSW3 but significantly increased during BSW1 (106.7 ± 7.4 mmHg, P < 0.01), BSW2 (105.6 ± 7.8 mmHg, P < 0.01), and BSW3 (103.8 ± 7.2 mmHg, P < 0.05). In conclusion, the FSW was more effective than the BSW in reducing mean SNA and AP. The finding could be applied to designing an artificial pulsatile pressure such as that generated by left ventricular assist devices.

NEW & NOTEWORTHY This study examined whether the waveforms of an input pressure alone can affect the baroreflex function by using a forward saw wave and a backward saw wave with the same mean pressure, pulse pressure, and pulse frequency. The forward saw wave was more effective than the backward saw wave in reducing sympathetic nerve activity and arterial pressure. The finding could be applied to designing an artificial pulsatile pressure such as that generated by left ventricular assist devices.

Nonlinear identification of the total baroreflex arc: higher-order nonlinearity

The total baroreflex arc is the open-loop system relating carotid sinus pressure (CSP) to arterial pressure (AP). The nonlinear dynamics of this system were recently characterized. First, Gaussian white noise CSP stimulation was employed in open-loop conditions in normotensive and hypertensive rats with sectioned vagal and aortic depressor nerves. Nonparametric system identification was then applied to measured CSP and AP to establish a second-order nonlinear Uryson model. The aim in this study was to assess the importance of higher-order nonlinear dynamics via development and evaluation of a third-order nonlinear model of the total arc using the same experimental data. Third-order Volterra and Uryson models were developed by employing nonparametric and parametric identification methods. The R² values between the AP predicted by the best third-order Volterra model and measured AP in response to Gaussian white noise CSP not utilized in developing the model were 0.69 ± 0.03 and 0.70 ± 0.03 for normotensive and hypertensive rats, respectively. The analogous R² values for the best third-order Uryson model were 0.71 ± 0.03 and 0.73 ± 0.03. These R² values were not statistically different from the corresponding values for the previously established second-order Uryson model, which were both 0.71 ± 0.03 (P > 0.1). Furthermore, none of the third-order models predicted well-known nonlinear behaviors including thresholding and saturation better than the second-order Uryson model. Additional experiments suggested that the unexplained AP variance was partly due to higher brain center activity. In conclusion, the second-order Uryson model sufficed to represent the sympathetically mediated total arc under the employed experimental conditions.

Nonlinear identification of the total baroreflex arc: chronic hypertension model

The total baroreflex arc is the open-loop system relating carotid sinus pressure (CSP) to arterial pressure (AP). Its linear dynamic functioning has been shown to be preserved in spontaneously hypertensive rats (SHR). However, the system is known to exhibit nonlinear dynamic behaviors. The aim of this study was to establish nonlinear dynamic models of the total arc (and its subsystems) in hypertensive rats and to compare these models with previously published models for normotensive rats. Hypertensive rats were studied under anesthesia. The vagal and aortic depressor nerves were sectioned. The carotid sinus regions were isolated and attached to a servo-controlled piston pump. AP and sympathetic nerve activity were measured while CSP was controlled via the pump using Gaussian white noise stimulation. Second-order, nonlinear dynamics models were developed by application of nonparametric system identification to a portion of the measurements. The models of the total arc predicted AP 21-43% better (P < 0.005) than conventional linear dynamic models in response to a new portion of the CSP measurement. The linear and nonlinear terms of these validated models were compared with the corresponding terms of an analogous model for normotensive rats. The nonlinear gains for the hypertensive rats were significantly larger than those for the normotensive rats [-0.38 ± 0.04 (unitless) vs. -0.22 ± 0.03, P < 0.01], whereas the linear gains were similar. Hence, nonlinear dynamic functioning of the sympathetically mediated total arc may enhance baroreflex buffering of AP increases more in SHR than normotensive rats.

Open-loop static and dynamic characteristics of the arterial baroreflex system in rabbits and rats

The arterial baroreflex system is the most important negative feedback system for stabilizing arterial pressure (AP). This system serves as a key link between the autonomic nervous system and the cardiovascular system, and is thus essential for understanding the pathophysiology of cardiovascular diseases and accompanying autonomic abnormalities. This article focuses on an open-loop systems analysis using a baroreceptor isolation preparation to identify the characteristics of two principal subsystems of the arterial baroreflex system, namely, the neural arc from pressure input to efferent sympathetic nerve activity (SNA) and the peripheral arc from SNA to AP. Studies on the static and dynamic characteristics of the two arcs under normal physiological conditions and also under various interventions including diseased conditions are to be reviewed. Quantitative understanding of the arterial baroreflex function under diseased conditions would help develop new treatment strategies such as electrical activation of the carotid sinus baroreflex for drug-resistant hypertension.