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

Abstract

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.

Aortic depressor nerve stimulation does not impede the dynamic characteristics of the carotid sinus baroreflex in normotensive or spontaneously hypertensive rats

“…Second, the hypotensive effect attained by the ADN stimulation was statistically significant but relatively small in magnitude. This may be because the perturbation with GWN alone has a significant hypotensive effect, as shown in a previous study (19). When we analyzed previously obtained data, mean AP during the GWN input (the mean of 120 mmHg and the SD of 20 mmHg) was significantly lower than that during a static input at 120 mmHg (95.2 Ϯ 8.6 vs. 107.3 Ϯ 11.6 mmHg, n ϭ 8, P ϭ 0.010).…”

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

“…Limitations. First, the derivative-sigmoidal model may not be unique for explaining dynamic nonlinear characteristics of the carotid sinus baroreflex, as evidenced by the analysis based on the Volterra series (17)(18)(19) and, therefore, may not necessarily represent the true mechanism. However, the derivativesigmodal model aids intuitive understanding of how the dy-namic linear characteristics, coupled with the nonlinear sigmoidal transform, can produce a directional rate sensitivity of the arterial baroreflex function.…”

Linear and Nonlinear Analysis of the Carotid Sinus Baroreflex Dynamic Characteristics

“…Since the static input-output relationship of the total re ex arc reveals a sigmoidal nonlinearity [30], kernels of third or higher order will be required to fully describe the barore ex-mediated AP response. We examined whether inclusion of the third order kernel improved the AP prediction during Gaussian white noise CSP input [31]. However, the r 2 values between the model-predicted and measured AP did not improve compared with the second order Uryson model.…”