A dissertation submitted to the Faculty of Engineering and the Built Environment, University of Witwatersrand in fulfilment of the requirements for the degree of Master of Science in Engineering. 2017 / The baroreceptor is a stretch receptor which detects changes in pressure in arterial blood vessels. Baroreceptor nerves inform the brainstem of changes in blood pressure, which then influences sympathetic and parasympathetic nervous activity to counteract that change. Due to the relationship between essential hypertension, sympathetic nervous activity and the baroreflex, there is some debate in the literature about whether the baroreflex can act as a long-term controller of blood pressure. This debate has increased in recent years, due to the high prevalence of essential hypertension in all societies and the introduction of new technologies to counteract drug-resistance hypertension. The baroreflex has become a source of debate due to the complex physiological feedback control that regulates blood pressure and due to new stimulating electrical devices, which have shown promising results in reducing drug-resistant essential hypertension. system. This is done through a literature survey extending through experimental and modelling research, where selected mathematical models of the baroreceptor are then analysed and simulated to find the best performing model, so that they may be simulated for an extended frequency response than what would be experimentally possible. The purpose of this investigation is to determine, through simulation, what the sensor static and dynamic characteristics are. Through this characterisation of the sensor behaviour of the baroreceptor in the baroreflex control loop, it is then possible to infer whether the baroreflex can act as a long-term controller of blood pressure. An overview of experimental and analytical investigations on the baroreceptor over the last 70 years is summarised. This overview includes mathematical models, which predict experimental results. A subset of four models from Srinivasen et al., Bugenhagen et al., Beard et al. and Mahdi et al. are selected. These models are implemented in MATLAB and Simulink. The parameters and experimental conditions are integrated into the Simulink models, and the simulated results are compared to the reported experimental data. In this way, each mathematical model is evaluated using secondary data for its ability to simulate the expected behaviour. Thereafter, all simulated models are compared under the same input conditions (a 0-230 mmHg step input over 12 s). These results are used to select the best performing models, based on how well they were parameterised and validated for experimental tests. The best performing models are those of Beard et al. and Bugenhagen et al. They are tested for a wide range of artificial inputs at different frequencies, with sinusoidal inputs which have periods that range from 0.1 s to 10 days and have a 100 mmHg operating point with a 1 mmHg peak amplitude. All modelling techniques studied show that the baroreceptor firing response resets due to the rate of change in strain in the visco-elastic arterial wall. Both tested model frequency responses, although parameterised for different species and for different major vessels, show high sensitivity to inputs in range from 1 s to 1 min 36 s (0.01 Hz 1Hz), and very low sensitivity for changes that are longer than 16 min 36s (0.001 Hz). This extrapolated simulation suggests a zero gain near DC. The simulated frequency response of the best performing baroreceptor models, which were validated against short-term experimental data, indicate that the baroreceptor is only able to sense changes that happen in less than 1 min 16s. The critical analysis of all the simulated baroreceptor models show that this characteristic of the baroreceptor is caused by the visco-elastic layers of the arterial wall, and is likely in all baroreceptors regardless of type or species. It also indicates that under electrical stimulation of the baroreceptor, the input signal from the electrical device bypasses the baroreceptor nerve ending (which is embedded in the arterial wall) and that the electrical signal of the baroreceptor is bypassed by the new stimulated electrical signal of the device. Furthermore, if the sensor can only detect short-term changes, then it is unlikely that the baroreceptor can inform the brainstem on longterm changes to mean arterial blood pressure. Therefore, based on the models examined in this study, this suggests that the baroreceptor is unlikely to be involved in long-term blood pressure control. This analysis of the best performing model is presented to show the limitations of the baroreflex in long term control of blood pressure. It serves as a simulated experiment to rationalise the contentious debate around the role of the baroreflex in long term blood pressure control, and to allow for future improvements that can be made on the baroreceptor model to allow for more extended modelling on sor characteristics. An improvement that could be applied to the best performing baroreceptor models, implemented in this study, is to examine the effects of ageing and inter-species variability on carotid sinus dimensions and visco-elastic wall properties. / CK2018

This dissertation develops uncertainty quantification methodologies for modeling, response analysis and optimization of diverse dynamical systems. Two distinct application platforms are considered pertaining to engineering dynamics and precision medicine. First, the recently developed Wiener path integral (WPI) technique for determining, accurately and in a computationally efficient manner, the stochastic response of diverse dynamical systems is employed for solving a high-dimensional, nonlinear system of stochastic differential equations governing the dynamics of a representative model of electrostatically coupled micromechanical oscillators. Compared to alternative modeling and solution treatments in the literature, the current development exhibits the following novelties: a) typically adopted linear, or higher-order polynomial, approximations of the nonlinear electrostatic forces are circumvented; and b) stochastic modeling is employed, for the first time, by considering a random excitation component representing the effect of diverse noise sources on the system dynamics. Further, the WPI technique is enhanced and extended based on a Bayesian compressive sampling (CS) treatment. Specifically, sparse expansions for the system response joint PDF are utilized. Next, exploiting the localization capabilities of the WPI technique for direct evaluation of specific PDF points leads to an underdetermined linear system of equations for the expansion coefficients. Furthermore, relying on a Bayesian CS solution formulation yields a posterior distribution for the expansion coefficient vector. In this regard, a significant advantage of the herein-developed methodology relates to the fact that the uncertainty of the response PDF estimates obtained by the WPI technique is quantified. Also, an adaptive scheme is proposed based on the quantified uncertainty of the estimates for the optimal selection of PDF sample points. This yields considerably fewer boundary value problems to be solved as part of the WPI technique, and thus, the associated computational cost is significantly reduced. Second, modeling and analysis of the physiological mechanism of dynamic cerebral autoregulation (DCA) is pursued based on the concept of diffusion maps. Specifically, a state-space description of DCA dynamics is considered based on arterial blood pressure (ABP), cerebral blood flow velocity (CBFV), and their time derivatives. Next, an eigenvalue analysis of the Markov matrix of a random walk on a graph over the dataset domain yields a low-dimensional representation of the intrinsic dynamics. Further dimension reduction is made possible by accounting only for the two most significant eigenvalues. The value of their ratio indicates whether the underlying system is governed by active or hypoactive dynamics, indicating healthy or impaired DCA function, respectively. The reliability of the technique is assessed by considering healthy individuals and patients with unilateral carotid artery stenosis or occlusion. It is shown that the proposed ratio of eigenvalues can be used as a reliable and robust biomarker for assessing how active the intrinsic dynamics of the autoregulation is and for indicating healthy versus impaired DCA function. Further, an alternative joint time-frequency analysis methodology based on generalized harmonic wavelets is utilized for assessing DCA performance in patients with preeclampsia within one week postpartum, which is associated with an increased risk for postpartum maternal cerebrovascular complications. The results are compared with normotensive postpartum individuals and healthy non-pregnant female volunteers and suggest a faster, but less effective response of the cerebral autoregulatory mechanism in the first week postpartum, regardless of preeclampsia diagnosis.