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PubMed2002

Pathological tremors as diffusional processes.

Two types of pathological tremors, essential and Parkinsonian, are studied using dynamical systems theory. It is shown that pathological tremors can be characterized as diffusional processes. The time-scale range for the diffusional scaling law to be valid starts from about one to several tens of the mean oscillation period. This time-scale range contrasts sharply with the predictable time scale for deterministic chaos, which is usually only a small fraction of the mean oscillation period. The diffusions in pathological tremors are usually anomalous. A number of quantities are designed to characterize the diffusions in the tremor. Their relevance to potential clinical applications is discussed. It is argued that in order to discriminate between Parkinsonian and essential tremors, quantities not of purely dynamical origin may be more useful, since purely dynamical quantities emphasize more the dynamical similarities between the two types of tremors.

Essential Tremor↗
PubMed1995

The D-1 dopamine receptor: past, present and future an idiosyncratic review.

1. Key events in the experimental investigation of the D-1 dopamine receptor are reviewed. 2. The efficacy of D-1 receptor agonists in the treatment of experimental parkinsonism in MPTP-treated primates is demonstrated. The diminished dyskinetic liability of D-1 agonists is discussed. 3. The significance of the dopa-induced dyskinesias is discussed from the perspective of deterministic chaos. The unpredictibility and irreproducibility of dyskinetic movements is highlighted and compared with features of the logistic equation. 4. The authors propose that the dopa-induced dyskinesias should be considered to be a manifestation of a chaotic process within the basal ganglia. The loss of the dopaminergic innervation and the subsequent repeated exposure to dopamine (derived from the exogenous dopa administered to the subjects) alters the response properties of the basal ganglia circuitry so that stimulation of dopamine receptors now elicits the dyskinetic movements.

Animals↗
PubMed2002

Advances in space radiation shielding codes.

Early space radiation shield code development relied on Monte Carlo methods and made important contributions to the space program. Monte Carlo methods have resorted to restricted one-dimensional problems leading to imperfect representation of appropriate boundary conditions. Even so, intensive computational requirements resulted and shield evaluation was made near the end of the design process. Resolving shielding issues usually had a negative impact on the design. Improved spacecraft shield design requires early entry of radiation constraints into the design process to maximize performance and minimize costs. As a result, we have been investigating high-speed computational procedures to allow shield analysis from the preliminary concept to the final design. For the last few decades, we have pursued deterministic solutions of the Boltzmann equation allowing field mapping within the International Space Station (ISS) in tens of minutes using standard Finite Element Method (FEM) geometry common to engineering design methods. A single ray trace in such geometry requires 14 milliseconds and limits application of Monte Carlo methods to such engineering models. A potential means of improving the Monte Carlo efficiency in coupling to spacecraft geometry is given.

Cosmic Radiation↗
PubMed1993

Time series analysis of complex dynamics in physiology and medicine.

A variety of mathematical methods have been developed to characterize complex rhythms that are observed in physiological systems. These methods include classical techniques such as the mean, standard deviation, and power spectrum, as well as newer methods suggested by nonlinear dynamics including the dimension, Lyapunov number, and entropy. This paper reviews the various ways in which these measures have been applied to analyze physiological dynamics with emphasis on the potential advantages and pitfalls of the various approaches. We conclude that these methods may be useful to help characterize complex time series, but only rarely is it possible to use these methods to establish deterministic chaos in a given time series.

Animals↗
PubMed1997

Stochastic seasonality and nonlinear density-dependent factors regulate population size in an African rodent.

Ecology has long been troubled by the controversy over how populations are regulated. Some ecologists focus on the role of environmental effects, whereas others argue that density-dependent feedback mechanisms are central. The relative importance of both processes is still hotly debated, but clear examples of both processes acting in the same population are rare. Key-factor analysis (regression of population changes on possible causal factors) and time-series analysis are often used to investigate the presence of density dependence, but such approaches may be biased and provide no information on actual demographic rates. Here we report on both density-dependent and density-independent effects in a murid rodent pest species, the multimammate rat Mastomys natalensis (Smith, 1834), using statistical capture-recapture models. Both effects occur simultaneously, but we also demonstrate that they do not affect all demographic rates in the same way. We have incorporated the obtained estimates of demographic rates in a population dynamics model and show that the observed dynamics are affected by stabilizing nonlinear density-dependent components coupled with strong deterministic and stochastic seasonal components.

Africa↗
PubMed1993

Recurrence plots of neuronal spike trains.

The recently developed qualitative method of diagnosis of dynamical systems-recurrence plots-has been applied to the analysis of dynamics of neuronal spike trains recorded from cerebellum and red nucleus of anesthetized cats. Recurrence plots revealed robust and common changes in the similarity structure of interspike interval sequences as well as significant deviations from randomness in serial ordering of intervals. Recurring episodes of alike, quasi-deterministic firing patterns suggest the spontaneous modulation of the dynamical complexity of the trajectories of observed neurons. These modulations are associated with changing dynamical properties of a neuronal spike-train-generating system. Their existence is compatible with the information processing paradigm of attractor neural networks.

Action Potentials↗
PubMed1980

System-theoretical analysis of the Clare Bishop Area in the cat.

The Clare Bishop Area (CBA) is a retinotopically organized cortical area in the cat brain connected to a great variety of visual areas in a very complex way (Fig. 1). Experimental analysis is difficult because of the following aspects: 1. As the distance from the retina increases, the signal combinations necessary to analyse the system become more and more specific. 2. Feedback loops cannot be opened, so an unequivocal identification of CBA cell properties is impossible. 3. The nonlinear character seems to have a great influence on signal processing. To circumvent these problems, specific signal combinations leading to a separation of input subsystems have been developed (Hoffmann and v. Seelen, 1979). On grounds of practical experience and theoretic considerations, the signal combinations are usually restricted to combinations of deterministic and stochastic signals when analysing the CBA. The different methods of measurement are applied successively, the linearizing ones being used first so that a rough classification is possible. If the nonlinear features of the system have little efect, they can be linearized in the theoretical description, if not, a model consisting of a sequence of a linear dynamic system and a nonlinear one with a static, polynomial feature must be used for analysis by parameter estimation. The experimental part of this publication deals with the determination of a number of cell properties. Some hypotheses on the function of the CBA are tested. THe results lead to the conclusion that further experiments, such as are discussed below, are necessary in the input subsystems, area 18 and 19. The experimental results of some other authors (Hubel and Wiesel, 1969; Turlejski, 1975; Turlejski and Michalski, 1975; Smith and Bauman, 1979; SPera and Bauman, 1979) are confirmed by the implicaions of the present results.

Animals↗
PubMed1989

Optimal input design: case study of the metabolic process.

An optimal input of nutrients into the metabolic process of the individual subject so as to effect desired therapeutic results is particularly important for the critically ill. A patient-related, individualized nutrients optimization procedure is proposed here. The procedure is applicable to any time-invariant and deterministic metabolic model that is bound by one or more quantitative limiting criteria. As a case in hand, the procedure is used to optimize the individual metabolic needs of critically ill patients. The results indicate that, given a proper metabolic model, the patient may be treated on an individual appropriateness basis rather than on the traditional statistical intuitive approach.

Critical Care↗
PubMed2001

Extinctions in the random replicator model.

The statistical properties of an ecosystem composed of species interacting via pairwise, random interactions and deterministic, concentration limiting self-interactions are studied analytically with tools of equilibrium statistical mechanics of disordered systems. Emphasis is given to the effects of externally induced extinction of a fixed fraction of species at the outset of the evolutionary process. The manner the ecosystem copes with the initial extinction event depends on the degree of competition among the species as well as on the strength of that event. For instance, in the regime of high competition the ecosystem diversity, given by the fraction of surviving species, is practically insensitive to the strength of the initial extinction provided it is not too large, while in the less competitive regime the diversity decreases linearly with the size of the event. In the case of large extinction events we find that no further biotic extinctions take place and, furthermore, that rare species become very unlikely to be found in the ecosystem at equilibrium. In addition, we show that the reciprocal of the Edwards-Anderson order parameter yields a good measure of the diversity of the model ecosystem.

Animals↗
PubMed2001

Stochasticity in transcriptional regulation: origins, consequences, and mathematical representations.

Transcriptional regulation is an inherently noisy process. The origins of this stochastic behavior can be traced to the random transitions among the discrete chemical states of operators that control the transcription rate and to finite number fluctuations in the biochemical reactions for the synthesis and degradation of transcripts. We develop stochastic models to which these random reactions are intrinsic and a series of simpler models derived explicitly from the first as approximations in different parameter regimes. This innate stochasticity can have both a quantitative and qualitative impact on the behavior of gene-regulatory networks. We introduce a natural generalization of deterministic bifurcations for classification of stochastic systems and show that simple noisy genetic switches have rich bifurcation structures; among them, bifurcations driven solely by changing the rate of operator fluctuations even as the underlying deterministic system remains unchanged. We find stochastic bistability where the deterministic equations predict monostability and vice-versa. We derive and solve equations for the mean waiting times for spontaneous transitions between quasistable states in these switches.

Feedback, Physiological↗
PubMed2000

Pharmacokinetic variability and therapeutic drug monitoring actions at steady state.

PURPOSE: To develop a mathematical model for therapeutic drug monitoring and to assess the kinetic relationships between the intensity of corrective action and the approach of drug concentrations to target values. METHODS: A mathematical model that succinctly accounts for the corrective actions and the variability inherent in the pharmacokinetics was used. RESULTS: The validity of the variability term was tested using experimental data for steady state concentrations of the drug procainamide. The approach of the monitored process to the target value followed exponential kinetics and an analytical expression for dependence the variance with time and various dosing parameters was derived. The variance of the drug concentration depends critically on a single non-dimensional parameter containing the rate constant for the therapeutic corrective actions and a coefficient describing the variance rate. When the rate constant for the therapeutic corrective actions was less than this critical value, the variance increased indefinitely. CONCLUSIONS: From a dosing standpoint, large variances in drug concentrations are undesirable because some patients will be overdosed or underdosed. Since deterministic models cannot provide analytical solutions for the moments of drug concentration distribution functions, stochastic models can be used to provide useful insights into the design of therapeutic regimens.

Algorithms↗
PubMed1994

Artificial neural networks for the diagnosis of atrial fibrillation.

Different forms of artificial intelligence have been applied to pattern recognition in medicine. Recently, however, a relatively new technique involving software-based neural networks has become more readily available. Deterministic logic is currently applied to rhythm analysis in computer-assisted ECG interpretation methods developed in the University of Glasgow. The aim of the present study is to compare an artificial neural network with deterministic logic for separating sinus rhythm (SR) with supraventricular extrasystoles (SVEs) and/or ventricular extra-systoles (VEs) from atrial fibrillation (AF) at a particular point in the diagnostic logic of the Glasgow Program. A total of 2363 ECGs with 1495 AF and 868 SR + (SVEs and/or VEs) are used for training and testing a variety of neural networks, and the optimum design is selected. Methods for combining the results of the neural-network classification and the deterministic interpretation are also developed. A further 717 ECGs are used to test the selected network. The results show that the use of an artificial neural network can improve the sensitivity of reporting AF from 88.5% using the deterministic approach to 92%, without sacrificing specificity (92.3%).

Atrial Fibrillation↗
PubMed1988

Ventricular fibrillation-defibrillation in the toad Bufo paracnemis.

Fibrillation is more likely to occur in animals showing a high degree of cellular differentiation. Lower species, with cardiac tissue histologically and electrophysiologically more uniform, very rarely, if ever, can fall into this uncoordinated activity. We describe experiments during which two specimens of the South American toad, Bufo paracnemis (body weights, 363 g and 297 g; ventricular weights, 1.8 g and 1.4 g, respectively), were repeatedly fibrillated and defibrillated almost at will. However, we failed when we tried a series of experiments in a given number of animals. Over a total of 16 fibrillation-defibrillation episodes, a fibrillation threshold of about 3.8 mA/g was estimated. The lowest defibrillation values were, respectively, 43 mA/g and 507 mA/g, using rectangular pulses (less than 7 msec pulses width). There were also a few spontaneous reversals before and after defibrillation shocks. These cases point to our still poor understanding of the mechanisms involved in the process. It is suggested that reentry or multiple ectopic foci might not be the basic mechanisms, as traditionally accepted. Rather, it might well be a new behavior of the cells or group of cells like that predicted by the theory of deterministic chaos.

Animals↗
PubMed1979

A mathematical model for the 1973 cholera epidemic in the European Mediterranean region.

For the cholera epidemic that occurred in the European Mediterranean region in the summer of 1973, a simple deterministic mathematic model is proposed; it consists of a system of two ordinary differential equations which concern the evolution of the human infective population in a town community and of bacteria population in the sea. It is conjectured that the infection process obeys a non linear saturation-type law. A phase space analysis is performed for the system of equations. Conclusions are drawn which concern the evolution of the epidemic and which suggest some indications for the selection of public health policies. The validity of the model is compared with the available data for the town of Bari (Italy).

Cholera↗
PubMed1996

A mathematical model for fibro-proliferative wound healing disorders.

The normal process of dermal wound healing fails in some cases, due to fibro-proliferative disorders such as keloid and hypertrophic scars. These types of abnormal healing may be regarded as pathologically excessive responses to wounding in terms of fibroblastic cell profiles and their inflammatory growth-factor mediators. Biologically, these conditions are poorly understood and current medical treatments are thus unreliable. In this paper, the authors apply an existing deterministic mathematical model for fibroplasia and wound contraction in adult mammalian dermis (Olsen et al., J. theor. Biol. 177, 113-128, 1995) to investigate key clinical problems concerning these healing disorders. A caricature model is proposed which retains the fundamental cellular and chemical components of the full model, in order to analyse the spatiotemporal dynamics of the initiation, progression, cessation and regression of fibro-contractive diseases in relation to normal healing. This model accounts for fibroblastic cell migration, proliferation and death and growth-factor diffusion, production by cells and tissue removal/decay. Explicit results are obtained in terms of the model processes and parameters. The rate of cellular production of the chemical is shown to be critical to the development of a stable pathological state. Further, cessation and/or regression of the disease depend on appropriate spatiotemporally varying forms for this production rate, which can be understood in terms of the bistability of the normal dermal and pathological steady states-a central property of the model, which is evident from stability and bifurcation analyses. The work predicts novel, biologically realistic and testable pathogenic and control mechanisms, the understanding of which will lead toward more effective strategies for clinical therapy of fibro-proliferative disorders.

Adult↗
PubMed1995

Application of the correlation integral to respiratory data of infants during REM sleep.

Non-linear time sequence analysis has been performed on infant sleep measurement data in order to obtain more information about the respiratory processes. As a first step, respiration data during REM sleep were analysed with methods from non-linear dynamics, especially, the correlation integral and the slope of its log-log plot, representing the correlation dimension. Before calculation of the correlation integral, a special kind of filtering has to be applied to the data. This filtering algorithm is a state space and singular value decomposition-based noise reduction method, and it is used to separate the noise and signal subspaces. The dynamics of a signal (in our case data from the respiratory process) and its degrees of freedom can be characterised by the correlation integral and by the correlation dimension, respectively. The main result of this study is that the highly irregular-looking breathing patterns during REM sleep could be described by a deterministic system, and finally the physiological significance of this finding is discussed.

Electroencephalography↗
PubMed1974

A note on the balance between random sampling and population size. (On the 30th anniversary of G. Malécot's paper).

Wright's model for the effects of random fluctuations in gene frequency in a population of fixed size is generalized to randomly fluctuating population size, and treated from the viewpoint of G. Malécot, using a martingale convergence theorem. The gene frequency approaches a limit, whose value depends on the actual realization, or history, of the process; that is, convergence is with probability one (or: almost surely) in statistical language. The limit does not necessarily represent a state of fixation of either allele; in particular, the limiting probability distribution is not necessarily trivial. For the special case of deterministically varying population size, a necessary and sufficient condition for such non-triviality is given.

Alleles↗