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.

Patient-Specific Oscillometric Blood Pressure Measurement.

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 an 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.

Nonlinear identification of the total baroreflex arc.

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.

Stimulation of the cardiopulmonary baroreflex enhances ventricular contractility in awake dogs: a mathematical analysis study.

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 (Emax), 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 ß-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 Emax (CVP → Emax), which characterizes the cardiopulmonary baroreflex control of ventricular contractility, ABP to Emax, which characterizes the arterial baroreflex control of ventricular contractility, and HR to Emax, which characterizes the force-frequency relation. The CVP → Emax transfer function showed a static gain of 0.037 ± 0.010 ml(-1) (different from zero; P < 0.05) and an overall time constant of 3.2 ± 1.2 s. Hence, Emax would increase and reach steady state in ∼16 s in response to a step increase in CVP, without any change to ABP or HR, due to the cardiopulmonary baroreflex. Following ß-adrenergic receptor blockade, the CVP → Emax transfer function showed a static gain of 0.0007 ± 0.0113 ml(-1) (different from control; P < 0.10). Hence, Emax would change little in steady state in response to a step increase in CVP. Stimulation of the cardiopulmonary baroreflex increases ventricular contractility through ß-adrenergic receptor system mediation.

Emax monitoring by aortic pressure waveform analysis.

Emax- the maximal left ventricular elastance- is perhaps the best available scalar index of contractility. However, the conventional method for its measurement involves obtaining multiple ventricular pressure-volume loops at different loading conditions and is thus impractical. We previously proposed a more practical technique for tracking Emax from just a single beat of an aortic pressure waveform based on a lumped parameter model of the left ventricle and arteries. Here, we tested the technique against the conventional Emax measurement method in animals during inotropic interventions. Our results show that the estimated Emax changes corresponded fairly well to the reference changes, with a correlation coefficient of 0.793. With further development and testing, the technique could ultimately permit continuous and less invasive monitoring of Emax.

Cardiac output monitoring by long time interval analysis of a radial arterial blood pressure waveform with correction for arterial compliance changes using pulse transit time.

We previously developed a technique for estimating relative cardiac output (CO) change by long time interval analysis of a radial arterial blood pressure waveform. This technique analyzes the slow, beat-to-beat changes in the waveform to circumvent the confounding wave reflections but assumes constant arterial compliance (AC). Here, we sought to correct the CO estimates of the technique for potential AC changes using pulse transit time--a conveniently measured index of AC. For proof-of-concept, we compared the original and corrected techniques using invasive swine hemodynamic data. The corrected technique reduced the overall calibrated CO estimation error by 18% relative to the original technique.