Oscillation and Chaos in Physiological Control Systems

Abstract

First-order nonlinear differential-delay equations describing physiological control systems are studied. The equations display a broad diversity of dynamical behavior including limit cycle oscillations, with a variety of wave forms, and apparently aperiodic or "chaotic" solutions. These results are discussed in relation to dynamical respiratory and hematopoietic diseases.

A Model of the Effects of Fluid Variation due to Body Position on Cheyne–Stokes Respiration

“…Since the amount of CO 2 in moles leaving the blood equals the amount in moles entering the alveoli, we can eliminateṅ between (29) and (30) and finḋ Total neck, chest, abdomen, and leg volumes are measured using bioelectrical impedance for each subject and recorded [37]. Results are displayed in Table 6.4.…”

“…It is a measure of how sensitive the chemoreceptors are to changes in CO 2 concentrations. A Hill function is used as the control to model the response of the chemoreceptors, as it is the best representation of human respiratory response [15,22,25,29]. Little is known about the actual value of the gain, however it can be predicted from the control function, as it is the slope.…”

“…Hopf bifurcation theory, which include [6,15,29]. The first model ever to use Hopf bifurcation to explain the onset of this disease was constructed by Mackey and Glass in 1977 [29].…”

“…The first model ever to use Hopf bifurcation to explain the onset of this disease was constructed by Mackey and Glass in 1977 [29]. They constructed a model of a physiological system using a first-order delay-differential equation.…”

Modeling Alveolar Volume Changes During Periodic Breathing in Heterogeneously Ventilated Lungs

“…14 Periodic breathing, while observed in healthy subjects during sleep, acclimatization to high altitudes, and in those under anesthesia, is also associated with a number of pathological problems, such as heart failure, stroke, and neurological disease. 22 A number of mathematical models have been developed to study periodic breathing, 1,4,7,8,18,24 many of which derive from the general Grodins model for cardiorespiratory control, 10 which is a compartment model based on the hypothesis that the periodicities associated with ventilation are the result of feedback delays. These delays arise due to the physical distance that the blood has to travel from the lungs to the chemoreceptors which act to coordinate ventilatory response, causing them to react to past conditions.…”