A nonlinear model for vasoconstriction

The control of blood pressure is a complex mixture of neural, hormonal and intrinsic interactions at the level of the heart, kidney and blood vessels. While experimental approaches to understanding these interactions remain useful, it remains difficult to conduct experiments to quantify these interactions as the number of parameters increases. Thus modelling approaches can offer considerable assistance. Typical mathematical models which describe the ability of the blood vessels to change their diameter (vasoconstriction) assume linearity of operation. However, due to the interaction of multiple vasocontrictive and vasodilative effectors, there is a significant nonlinear response to the in uence of neural factors, particularly at higher levels of nerve activity (often seen in subjects with high blood pressure) which leads to low blood ow rates. This paper proposes a nonlinear mathematical model for the relationship between neural in uences (sympathetic nerve activity (SNA) and blood ow, using a feedback path to model the predominently nonlinear effect of local vasoactive modulators such as Nitric Oxide, which oppose the action of SNA. The model, the structure of which is motivated by basic physiological principles, is parameterised using a numerical optimisation method using open-loop data collected from rabbits. The model responses are shown to be in good agreement with the experimental data

Dynamic relationship between sympathetic nerve activity and renal blood flow: a frequency domain approach

Blood pressure displays an oscillation at 0.1 Hz in humans that is well established to be due to oscillations in sympathetic nerve activity (SNA). However, the mechanisms that control the strength or frequency of this oscillation are poorly understood. The aim of the present study was to define the dynamic relationship between SNA and the vasculature. The sympathetic nerves to the kidney were electrically stimulated in six pentobarbital-sodium anesthetized rabbits, and the renal blood flow response was recorded. A pseudo-random binary sequence (PRBS) was applied to the renal nerves, which contains equal spectral power at frequencies in the range of interest (<1 Hz). Transfer function analysis revealed a complex system composed of low-pass filter characteristics but also with regions of constant gain. A model was developed that accounted for this relationship composed of a 2 zero/4 pole transfer function. Although the position of the poles and zeros varied among animals, the model structure was consistent. We also found the time delay between the stimulus and the RBF responses to be consistent among animals (mean 672 ± 22 ms). We propose that the identification of the precise relationship between SNA and renal blood flow (RBF) is a fundamental and necessary step toward understanding the interaction between SNA and other physiological mediators of RBF

Deterministic Chaos in Blood Pressure Signals During Different Physiological Conditions

Several coupled and nonlinear controlling mechanisms are involved in the regulation of blood pressure. The possible presence of chaos in physiological signals has been the subject of some research. In this study, blood pressure signals were analysed using a range of nonlinear time series analysis techniques. Individual effectors of blood pressure were either experimentally removed or enhanced, so that the controlling mechanisms that are responsible for the chaotic nature of the signals may be identified by chaotic analysis of the signals. The level of chaos varied across the different experimental conditions, showing a distinct decrease from control conditions to all other experimental conditions

Deterministic Chaos in Blood Pressure Signals During Different Physiological Conditions

Several coupled and nonlinear controlling mechanisms are involved in the regulation of blood pressure. The possible presence of chaos in physiological signals has been the subject of some research. In this study, blood pressure signals were analysed using a range of nonlinear time series analysis techniques. Individual effectors of blood pressure were either experimentally removed or enhanced, so that the controlling mechanisms that are responsible for the chaotic nature of the signals may be identified by chaotic analysis of the signals. The level of chaos varied across the different experimental conditions, showing a distinct decrease from control conditions to all other experimental conditions

Dynamic baroreflex control of blood pressure: influence of the heart vs. peripheral resistance

The aim in the present experiments was to assess the dynamic baroreflex control of blood pressure, to develop an accurate mathematical model that represented this relationship, and to assess the role of dynamic changes in heart rate and stroke volume in giving rise to components of this response. Patterned electrical stimulation [pseudo-random binary sequence (PRBS)] was applied to the aortic depressor nerve (ADN) to produce changes in blood pressure under open-loop conditions in anesthetized rabbits. The stimulus provided constant power over the frequency range 0–0.5 Hz and revealed that the composite systems represented by the central nervous system, sympathetic activity, and vascular resistance responded as a second-order low-pass filter (corner frequency ≈0.047 Hz) with a time delay (1.01 s). The gain between ADN and mean arterial pressure was reasonably constant before the corner frequency and then decreased with increasing frequency of stimulus. Although the heart rate was altered in response to the PRBS stimuli, we found that removal of the heart's ability to contribute to blood pressure variability by vagotomy and β1-receptor blockade did not significantly alter the frequency response. We conclude that the contribution of the heart to the dynamic regulation of blood pressure is negligible in the rabbit. The consequences of this finding are examined with respect to low-frequency oscillations in blood pressure