The total baroreflex arc [the open-loop system relating carotid sinus pressure (CSP) to arterial pressure (AP)] is known to exhibit nonlinear behaviors. However, few studies have quantitatively characterized its nonlinear dynamics. The aim of this study was to develop a nonlinear model of the sympathetically mediated total arc without assuming any model form. Normal 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, and the AP and sympathetic nerve activity (SNA) were measured. CSP was perturbed using a Gaussian white noise signal. A second-order Volterra model was developed by applying nonparametric identification to the measurements. The second-order kernel was mainly diagonal, but the diagonal differed in shape from the first-order kernel. Hence, a reduced second-order model was similarly developed comprising a linear dynamic system in parallel with a squaring system in cascade with a slower linear dynamic system. This "Uryson" model predicted AP changes 12% better (P < 0.01) than a linear model in response to new Gaussian white noise CSP. The model also predicted nonlinear behaviors, including thresholding and mean responses to CSP changes about the mean. Models of the neural arc (the system relating CSP to SNA) and peripheral arc (the system relating SNA to AP) were likewise developed and tested. However, these models of subsystems of the total arc showed approximately linear behaviors. In conclusion, the validated nonlinear model of the total arc revealed that the system takes on an Uryson structure.

Objective Most automatic cuff blood pressure (BP) measurement devices are based on oscillometry. These devices estimate BP from the envelopes of the cuff pressure oscillations using fixed ratios. The values of the fixed ratios represent population averages, so the devices may only be accurate in subjects with normal BP levels. The objective was to develop and demonstrate the validity of a patient-specific oscillometric BP measurement method. Methods The idea of the developed method was to represent the cuff pressure oscillation envelopes with a physiologic model and then estimate the patient-specific parameters of the model, which includes BP levels, by optimally fitting it to the envelopes. The method was investigated against gold standard reference BP measurements from 57 patients with widely varying pulse pressures. A portion of the data was used to optimize the patient-specific method and a fixed-ratio method, while the remaining data were used to test these methods and a current office device. Results The patient-specific method yielded BP root-mean-square-errors ranging from 6.0 to 9.3 mmHg. On average, these errors were nearly 40% lower than the errors of each existing method. Conclusion The patient-specific method may improve automatic cuff BP measurement accuracy. Significance A patient-specific oscillometric BP measurement method was proposed and shown to be more accurate than the conventional method and a current device.

. 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 Ͻ 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 [Ϫ0.38 Ϯ 0.04 (unitless) vs. Ϫ0.22 Ϯ 0.03, P Ͻ 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. arterial baroreflex; Gaussian white noise; system identification; nonlinear model; hypertension THE CAROTID SINUS BAROREFLEX plays a central role in maintaining arterial pressure (AP) in the face of fast-acting, exogenous disturbances and may also contribute to long-term AP regulation (7,20,21). This system responds to increases in carotid sinus pressure (CSP) by decreasing efferent sympathetic nerve activity (SNA), which, in turn, decreases AP. We refer to the aggregate, open-loop system relating CSP to AP as the total baroreflex arc, the "controller" subsystem relating CSP to SNA as the neural arc, and the "effector" subsystem relating SNA to AP as the peripheral arc.We and others have identified the linear dynamics of the three baroreflex arcs in the form of transfer functions (i.e., gain and phase as a function of frequency) (3-5, 16). These linear models can capture the dynamic behavior of the systems to a significant extent. We previously showed that the linear dynamics of the total arc are preserved in spontaneously hypertensive rats (SHR) despite resetting of mean AP (4). However, the nonlinear dynamics of this system, which have been less investigated, could possibly respond differently to the chronic hypertension model.In a recent study (9), we employed the Gaussian white noise approach for nonlinear system identification to develop a second-order, nonlinear dynamic model of the total arc in normotensive Wistar-Kyoto rats (WKY). The model predicted AP 12% better than a linear dynamic model in response to new Gaussian w...

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 R 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 R values for the best third-order Uryson model were 0.71 ± 0.03 and 0.73 ± 0.03. These R 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.

-The cardiopulmonary baroreflex responds to an increase in central venous pressure (CVP) by decreasing total peripheral resistance and increasing heart rate (HR) in dogs. However, the direction of ventricular contractility change is not well understood. The aim was to elucidate the cardiopulmonary baroreflex control of ventricular contractility during normal physiological conditions via a mathematical analysis. Spontaneous beat-to-beat fluctuations in maximal ventricular elastance (E max), which is perhaps the best available index of ventricular contractility, CVP, arterial blood pressure (ABP), and HR were measured from awake dogs at rest before and after ␤-adrenergic receptor blockade. An autoregressive exogenous input model was employed to jointly identify the three causal transfer functions relating beat-to-beat fluctuations in CVP to E max (CVP ¡ Emax), which characterizes the cardiopulmonary baroreflex control of ventricular contractility, ABP to E max, which characterizes the arterial baroreflex control of ventricular contractility, and HR to E max, which characterizes the force-frequency relation. The CVP ¡ E max transfer function showed a static gain of 0.037 Ϯ 0.010 ml Ϫ1 (different from zero; P Ͻ 0.05) and an overall time constant of 3.2 Ϯ 1.2 s. Hence, E max would increase and reach steady state in ϳ16 s in response to a step increase in CVP, without any change to ABP or HR, due to the cardiopulmonary baroreflex. Following ␤-adrenergic receptor blockade, the CVP ¡ E max transfer function showed a static gain of 0.0007 Ϯ 0.0113 ml Ϫ1 (different from control; P Ͻ 0.10). Hence, E max would change little in steady state in response to a step increase in CVP. Stimulation of the cardiopulmonary baroreflex increases ventricular contractility through ␤-adrenergic receptor system mediation.beat-to-beat variability; cardiopulmonary baroreflex; maximal ventricular elastance; system identification; ventricular contractility THE BAROREFLEX SYSTEMS ARE primarily responsible for maintaining blood pressure in the short term (seconds to minutes) and also appear to contribute to longer-term blood pressure regulation (29,30). It is well known that the arterial baroreflex senses arterial blood pressure (ABP) via stretch receptors lying in the carotid sinus and aortic arch and buffers an increase in ABP by decreasing, for example, total peripheral resistance (TPR), heart rate (HR), and ventricular contractility. The sensory receptors of the cardiopulmonary baroreflex are more complex, residing mainly in the cardiac chambers but also in the pulmonary vessels (5). These receptors have been shown to be responsive to both central venous pressure (CVP) (7,25) and left atrial pressure (LAP) (10, 21), which often change in parallel. The cardiopulmonary baroreflex responds to a change in these pressures by inducing an opposite change in TPR (1,16,25). An increase in the preload pressures also leads to an increase in HR (i.e., Bainbridge effect) in dogs (3), but an opposite change may occur in humans (7).However, the cardiopulmon...