The baroreflex is one of the most important regulatory mechanisms of blood pressure in the body, and the total baroreflex arc is defined to be the open-loop system relating carotid sinus pressure (CSP) to arterial pressure (AP). This system is known to exhibit nonlinear behaviors. However, few studies have quantitatively characterized its nonlinear dynamics. The aim of this thesis was to develop a nonlinear model of the sympathetically-mediated total arc without assuming any model form in both healthy and hypertensive rats. 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. 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 conventional linear dynamic 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. Spontaneously hypertensive rats were studied under the same protocol. The second-order kernel in these rats was also mainly diagonal and follows the Uryson model. 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 to 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 (e.g., gain of -0.38±0.04 (unitless) for hypertensive rats versus -0.22±0.03 for normotensive rats; 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 spontaneously hypertensive rats than normotensive rats. The importance of higher-order nonlinear dynamics was also assessed 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 several nonparametric and parametric identification methods. The R2 values between the measured AP and AP predicted by both the best third-order Volterra and the third-order Uryson model in response to new Gaussian white noise CSP were not statistically different from the corresponding values for the previously established second-order Uryson model neither in normotensive nor in hypertensive rats. Further, none of the third-order models were able to predict important 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 and the nonlinear part of this model showed significant changes in hypertensive rats compared to normotensive rats.
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