Index of content:
Volume 1, Issue 3, October 1991
1(1991); http://dx.doi.org/10.1063/1.165836View Description Hide Description
Complex rhythms are observed in the physiological systems that control and carry out vital bodily functions.Theoretical approaches to analyze the physiological systems include control theory and computation theory. Complementary to these approaches is nonlinear dynamics, which offers ways to classify both normal and abnormal dynamics, and to analyze bifurcations occurring in physiological dynamics.
1(1991); http://dx.doi.org/10.1063/1.165837View Description Hide Description
Heart rate oscillates on several different time scales and has long‐term variability in the form of 1/fnoise. The physiological control of heart rate is briefly reviewed, and several typical patterns of heart rate variability, in health and sickness, are described. Considered briefly are some possible dynamical mechanisms for heart rate variability.
1(1991); http://dx.doi.org/10.1063/1.165838View Description Hide Description
Studies of heart rate variability in people who faint may yield insights into normal physiologic mechanisms which probably are dynamic. These insights might be gained because fainting appears to be due to a breakdown of these mechanisms. Tilt table testing reliably induces fainting in patients with a history of fainting and can be used to study these mechanisms. During tilt tests ending in fainting heart rate changes markedly, with a loss of high‐frequency components on power spectral analysis and a progressive slowing of overall sinus node discharge. These changes appear to be due to changes in efferent vagal nerve traffic. Several possible mechanisms of these changes in heart rate variability are discussed.
1(1991); http://dx.doi.org/10.1063/1.165839View Description Hide Description
Cheyne–Stokes respiration, a breathing pattern found in patients with heart failure, is characterized by periodic changes in ventilation. This pattern of breathing is also associated with oscillations in the arousal state, blood oxygen level, carbon dioxide blood level, and the blood pressure. Although originally described as an irregular breathing pattern or an unstable breathing pattern, Cheyne–Stokes respiration may be quite stable for prolonged periods of time. This breathing pattern may represent a clinical disorder in which disease results in a low‐frequency oscillation of the system. Treatment that either reduces or abolishes the oscillation results in clinical improvement because of reduced oscillation of the systems whose function is linked to the changes in ventilation.
1(1991); http://dx.doi.org/10.1063/1.165840View Description Hide Description
Menopausal hot flashes are episodes of flushing, increased heart rate, skinblood flow and skin temperature, and a sensation of heat. The thermoregulatory and cardiovascular concomitants of hot flashes are associated with peaks in the levels of various hormones and neurotransmitters in the peripheral circulation. Although hot flashes affect about 75% of women, and are the primary reason that women at menopause seek medical attention, the mechanism of hot flashes is still not understood. Hot flashes vary in frequency and intensity both within and between individuals, and have been thought of as occurring randomly. Yet, some women report that their hot flashes are worse at a particular time of day or year. Initial examination of subjects’ recordings of their hot flashes showed diurnal patterns of hot flash occurrence. There also seems to be a diurnal rhythm of hot flash intensity. Continuous physiological monitoring of hot flashes is facilitating the analysis of these patterns, which is revealing circadian and ultradian periodicities. The occurrence of hot flashes can be modulated by external and internal factors, including ambient temperature and fever. Rhythms of thermoregulatory and endocrine functions also may influence hot flash patterns. Examination of the interrelationships between the various systems of the body involved in hot flashes, and a multidisciplinary approach to the analysis of hot flash patterns, will aid our understanding of this complex phenomenon.
1(1991); http://dx.doi.org/10.1063/1.165841View Description Hide Description
Experimental observations of movement disorders including tremor and voluntary microdisplacements recorded in patients with Parkinson’s disease (PD) during a simple visuomotor tracking task are analyzed. The performance of patients with PD having a very large amplitude tremor is characterized either by the intermittent appearance of transient dynamics or by the presence of sudden transitions in the amplitude or frequency of the signal. The need to develop new tools to characterize changes in dynamics (i.e., transitions) and to redefine neurological degeneration, such as Parkinson’s disease, in terms of qualitative changes in oscillatory behaviors is emphasized.
1(1991); http://dx.doi.org/10.1063/1.165842View Description Hide Description
Virtually all members of the animal kingdom experience a relentless and powerful cycling of states of being: wakefulness, rapid eye movement sleep, and nonrapid eye movement sleep. Each of these states is composed of a number of physiologic variables generated in a variety of neural structures. The predictable oscillations of these states are driven by presumed neural pacemakers which are entrained to the 24 h geophysical environment by the light/dark cycle. Experiments in nature have indicated that wake/sleep rhythm perturbations may occur either involving desynchronization of the basic 24 h wake/sleep cycle within the geophysical 24 h cycle (circadian rhythm disturbances) or involving the rapid oscillation or incomplete declaration of state (such as narcolepsy). The use of phase spaces to describe states of being may be of interest in the description of state determination in both illness and health. Some fascinating clinical and experimental phenomena may represent bifurcations in the sleep/wake control system.
1(1991); http://dx.doi.org/10.1063/1.165843View Description Hide Description
Gastric and small intestinal myoelectric and motor activity is divided into two main patterns, fed and fasted. During fasting, the predominant pattern of activity is the migrating myoelectric complex (MMC), a cyclically occurring pattern of electric and mechanical activity that is initiated in the stomach and duodenum almost simultaneously and, from there, propagates the length of the small intestine. Cyclic motor activity also occurs in the lower esophageal sphincter, the gallbladder, and the sphincter of Oddi with a duration that is related to the MMC in the small intestine. Of the possible mechanisms for initiation of the MMC in the small intestine (extrinsic neural control, intrinsic neural control, and hormonal control), intrinsic neural control via a series of coupled is the most likely. The keep this sentence in! hormone motilin also plays a role in the initiation of MMCs. After a meal, in man the MMC is disrupted and replaced by irregular contractions. The physiologic role of the MMC is to clear the stomach and small intestine of residual food, secretions, and desquamated cells and propel them to the colon. Disruption of the MMC cycle is associated with bacterial overgrowth in some patients, an observation that supports the proposed cleansing function of the MMC cycle.
1(1991); http://dx.doi.org/10.1063/1.165844View Description Hide Description
Spiral waves in diverse excitable media exhibit strikingly variegated behavior. Mechanistic interpretations of excitability in laboratory systems are commonly tested by comparing the wavelength, period, and meander patterns of the model’s spiral waves with laboratory observations, but models seem seldom to be rejected by such tests. The reason may be that almost any excitable medium behaves in many respects like almost any other, if its parameters are properly adjusted within a reasonable range. What generalizations can be made about ‘‘excitable media’’ in the absence of more specifications? It would be useful to distinguish such generic features from idiosyncrasies of specific models. The range of behavioral flexibility of the FitzHugh–Nagumo excitable medium is explored by varying two of its parameters and comparing the results with other excitable media to suggest a generic pattern of parameter dependence. The results exhibit the remarkable diversity of rotor behavior in a single model and provide a database for quantitative testing of mathematical generalizations.
1(1991); http://dx.doi.org/10.1063/1.165845View Description Hide Description
In the case of a benign but very active cardiac arrhythmia often observed in healthy subjects, the behavior of the ventricular extrasystoles during long‐term electrocardiographic recording was carefully scrutinized using the facilities of complex computerized programs of analysis. The presence or the absence of the extrasystoles, their distribution with respect to the normal beats, their time relationships, and the existence or the absence of a repetitive activity after the initial extrasystole follow complex, interactive rules that essentially depend on two determinants: the cardiac frequency as such (rate‐dependence) and the autonomic nervous system (adrenergic dependence). It can be concluded, at variance from the random distribution suggested by a superficial examination, that an in‐depth study allows the complex rules conditioning the various types and patterns of extrasystoles to be unearthed. Precise quantitative regularities underly the dynamics, and observing such rules gives the cardiologist hopes that one might distinguish various physiological mechanisms from a careful consideration of the dynamics. Collaboration of cardiologists and nonlinear dynamicists is needed to understand the origin of complex cardiac rhythms and to sort out the roles of chance and determinism in their genesis.
1(1991); http://dx.doi.org/10.1063/1.165860View Description Hide Description
A particularly simple chaotic nonequilibrium open system with two Cartesian degrees of freedom, characterized by two distinct temperatures T x and T y , is introduced. The two temperatures are maintained by Nosé–Hoover canonical‐ensemble thermostats. Both the equilibrium (no net heat transfer) and nonequilibrium (dissipative) Lyapunov spectra are characterized for this simple system.
1(1991); http://dx.doi.org/10.1063/1.165846View Description Hide Description
For a class of piecewise monotone locally noncontracting maps f:X→X with small ‘‘traps’’ Y ε⊆X (diam(Y ε)≤ε), the existence of smooth conditionally f‐invariant measures με are proved, corresponding to a limit as n→∞ conditional probabilities that f n+1 x∈X\Y ε if x,fx,...,f nx ∈X\Y ε and the point x is chosen at random. Also proven is the convergence of με to smooth f‐invariant measures as ε→0. By means of this construction, the numerical phenomenon of the convergence of histograms of trajectories of maps with marginal singularities to densities of nonfinite smooth invariant measures in the computer modeling was investigated.
1(1991); http://dx.doi.org/10.1063/1.165847View Description Hide Description
Kramers’ 1940 paper and its successive elaborations have extensively explored the transition rate between two stable situations, that is, in the language of system dynamics, the transition between the basins of attraction of two stable fixed point attractors. In a nonequilibrium system some of the above conditions may be violated, either because one of the two fixed points is unstable, as in the case of transient phenomena, or because both fixed points are unstable, as in the case of heteroclinic chaos, or because the attractors are more complex than fixed points, as in a chaotic dynamics where two or more strange attractors coexist. Furthermore, there is recent experimental evidence of space‐time complexity consisting in the alternate or simultaneous oscillation of many modes, each one with its own (possibly chaotic) dynamics. In all the above cases, coexistence of many alternative paths implies a choice, either due to noise or self‐triggered by the same interacting degrees of freedom. A review of the above phenomena in the case of nonequilibrium optical systems is here presented, with the aim of stimulating theoretical investigation on these novel rate processes.