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PubMed1993

Improved repeatability of 12-lead ECG analysis using continuous scoring techniques.

This study describes a method for improving the day-to-day and minute-to-minute repeatability of the deterministic computer-assisted diagnosis of left ventricular hypertrophy. Conventional upper limits of normal for many age-dependent electrocardiographic parameters have been replaced by continuous equations, thereby, eliminating points of discontinuity that can contribute to lack of repeatability. Estimates of the normal amounts of variability present in many electrocardiographic parameters that are used in the diagnosis of left ventricular hypertrophy are calculated. These estimates are then used together with a smoothed version of a score function to form the basis of the new technique. The implementation of smoothing techniques enhances the repeatability of the Glasgow electrocardiographic analysis program. With respect to the electrocardiographic diagnosis of left ventricular hypertrophy, these methods eliminate 44% of the day-to-day and 50% of the minute-to-minute inconsistencies in computer reports.

Adult↗
PubMed2002

Single-species models of the Allee effect: extinction boundaries, sex ratios and mate encounters.

We critically review and classify models of single-species population dynamics subject to the demographic Allee effect with emphasis on non-spatial, deterministic approach. Inclusion of spatial movement and stochastic phenomena does not substantially change the behaviour; stochasticity only "blurs" step-like character of the Allee effect into a sigmoidal form. The outcome of all non-spatial, deterministic models is either unconditional extinction, extinction-survival scenario (ES), or unconditional survival. Three major model classes are recognized: (1) one-dimensional heuristic models, (2) one-dimensional models with mating probability and fixed sex ratio, and (3) two-sex models with variable adult sex ratio. Each class is characterized by the shape of extinction boundary which separates extinction from survival in the ES scenario. The latter two classes may give better predictions of extinction thresholds than heuristic models but require specific information and are data intensive. In one-dimensional models with fixed sex ratio, population cannot survive if density/number of males decreases below some threshold while there is no such restriction on females. Individual-based models seem to be most capable of explaining mechanisms leading to the Allee effect.

Animals↗
PubMed2003

DTI mapping of human brain connectivity: statistical fibre tracking and virtual dissection.

Several approaches have been used to trace axonal trajectories from diffusion MRI data. If such techniques were first developed in a deterministic framework reducing the diffusion information to one single main direction, more recent approaches emerged that were statistical in nature and that took into account the whole diffusion information. Based on diffusion tensor MRI data coming from normal brains, this paper presents how brain connectivity could be modelled globally by means of a random walk algorithm. The mass of connections thus generated was then virtually dissected to uncover different tracts. Corticospinal, corticobulbar, and corticothalamic tracts, the corpus callosum, the limbic system, several cortical association bundles, the cerebellar peduncles, and the medial lemniscus were all investigated. The results were then displayed in the form of an in vivo brain connectivity atlas. The connectivity pattern and the individual fibre tracts were then compared to known anatomical data; a good matching was found.

Algorithms↗
PubMed2003

Extraction of periodic multivariate signals: mapping of voltage-dependent dye fluorescence in the mouse heart.

In many experimental circumstances, heart dynamics are, to a good approximation, periodic. For this reason, it makes sense to use high-resolution methods in the frequency domain to visualize the spectrum of imaging data of the heart and to estimate the deterministic signal content and extract the periodic signal from background noise in experimental data. In this paper, we describe the first application of a new method that we call cardiac rhythm analysis which uses a combination of principal component analysis and multitaper harmonic analysis to extract periodic, deterministic signals from high-resolution imaging data of cardiac electrical activity, We show that this method significantly increases the signal-to-noise ratio of our recordings, allowing for better visualization of signal dynamics and more accurate quantification of the properties of electrical conduction. We visualize the spectra of three cardiac data sets of mouse hearts exhibiting sinus rhythm, paced rhythm and monomorphic tachycardia. Then, for pedagogical purposes, we investigate the tachycardia more closely, demonstrating the presence of two distinct periodicities in the re-entrant tachycardia. Analysis of the tachycardia shows that cardiac rhythm analysis not only allows for better visualization of electrical activity, but also provides new opportunities to study multiple periodicities in signal dynamics.

Action Potentials↗
PubMed1999

Thermodynamically reversible generalization of diffusion limited aggregation.

We introduce a lattice gas model of cluster growth via the diffusive aggregation of particles in a closed system obeying a local, deterministic, microscopically reversible dynamics. This model roughly corresponds to placing the irreversible diffusion limited aggregation model (DLA) in contact with a heat bath. Particles release latent heat when aggregating, while singly connected cluster members can absorb heat and evaporate. The heat bath is initially empty, hence we observe the flow of entropy from the aggregating gas of particles into the heat bath, which is being populated by diffusing heat tokens. Before the population of the heat bath stabilizes, the cluster morphology (quantified by the fractal dimension) is similar to a standard DLA cluster. The cluster then gradually anneals, becoming more tenuous, until reaching configurational equilibrium when the cluster morphology resembles a quenched branched random polymer. As the microscopic dynamics is invertible, we can reverse the evolution, observe the inverse flow of heat and entropy, and recover the initial condition. This simple system provides an explicit example of how macroscopic dissipation and self-organization can result from an underlying microscopically reversible dynamics. We present a detailed description of the dynamics for the model, discuss the macroscopic limit, and give predictions for the equilibrium particle densities obtained in the mean field limit. Empirical results for the growth are then presented, including the observed equilibrium particle densities, the temperature of the system, the fractal dimension of the growth clusters, scaling behavior, finite size effects, and the approach to equilibrium. We pay particular attention to the temporal behavior of the growth process and show that the relaxation to the maximum entropy state is initially a rapid nonequilibrium process, then subsequently it is a quasistatic process with a well defined temperature.

Journal Article↗
PubMed2003

Deterministic extinction effect of parasites on host populations.

Experimental studies have shown that parasites can reduce host density and even drive host population to extinction. Conventional mathematical models for parasite-host interactions, while can address the host density reduction scenario, fail to explain such deterministic extinction phenomena. In order to understand the parasite induced host extinction, Ebert et al. (2000) formulated a plausible but ad hoc epidemiological microparasite model and its stochastic variation. The deterministic model, resembles a simple SI type model, predicts the existence of a globally attractive positive steady state. Their simulation of the stochastic model indicates that extinction of host is a likely outcome in some parameter regions. A careful examination of their ad hoc model suggests an alternative and plausible model assumption. With this modification, we show that the revised parasite-host model can exhibit the observed parasite induced host extinction. This finding strengthens and complements that of Ebert et al. (2000), since all continuous models are likely break down when all population densities are small. This extinction dynamics resembles that of ratio-dependent predator-prey models. We report here a complete global study of the revised parasite-host model. Biological implications and limitations of our findings are also presented.

Animals↗
PubMed2005

Metapopulation persistence in heterogeneous landscapes: lessons about the effect of stochasticity.

This article addresses an important aspect of the analysis of metapopulation persistence. It highlights some consequences of ignoring and including stochasticity in the sequence of extinction and colonization events. The results are based on a comparative analysis of the outcomes of two (one deterministic, one stochastic) spatially realistic metapopulation models and a search for common effects and differences. One key result of the article is that, under certain conditions, there are extra effects of the landscape structure (number and configuration of patches, patch size distribution) on metapopulation persistence if stochasticity is included. In these cases, ignoring or including stochasticity can change conclusions about the persistence status but also ranking orders, relative results, and qualitative trends. A list of conditions is provided under which including stochasticity is vital to prevent counterproductive conclusions about metapopulation persistence. The results of the overall study are condensed in five lessons about the effect of stochasticity. A number of implications for ecological theory and conservation management are discussed. The study demonstrates the potential of three recently published approximation formulas (metapopulation capacity lambdaM, mean lifetime Tm, and effective number of patches N) to serve as tools for ecological analysis and thinking.

Environment↗
PubMed1987

The fractal dimension of a test signal: implications for system identification procedures.

The experimental identification of a non-linear biologic transducer is often approached via consideration of its response to a stochastic test ensemble, such as Gaussian white noise (Marmarelis and Marmarelis 1978). In this approach, the input-output relationship a deterministic transducer is described by an orthogonal series of functionals. Laboratory implementation of such procedures requires the use of a particular test signal drawn from the idealized stochastic ensemble; the statistics of the particular test signal necessarily deviate from the statistics of the ensemble. The notion of a fractal dimension (specifically the capacity dimension) is a means to characterize a complex time series. It characterizes one aspect of the difference between a specific example of a test signal and the test ensemble from which it is drawn: the fractal dimension of ideal Gaussian white noise is infinite, while the fractal dimension of a particular test signal is finite. This paper shows that the fractal dimension of a test signal is a key descriptor of its departure from ideality: the fractal dimension of the test signal bounds the number of terms that can reliably be identified in the orthogonal functional series of an unknown transducer.

Mathematics↗
PubMed2004

Interpretation and optimization of the dissolution specifications for a modified release product with an in vivo-in vitro correlation (IVIVC).

This article considers the in vivo significance attached to in vitro dissolution testing. Almost invariably, the in vitro dissolution test is interpreted in terms of bioequivalence. The literature that describes methods for setting in vitro dissolution specifications is reviewed. The most common interpretation of these specifications is a deterministic one, that is, those batches passing the dissolution specifications would be bioequivalent with the reference if tested in vivo and those failing the dissolution specifications would not be bioequivalent if tested in vivo. Due to random variation, the deterministic interpretation is not appropriate. Instead, we need to consider the conditional probability that a batch that has passed the in vitro dissolution test would demonstrate bioequivalence if tested in vivo, and that a batch known to have failed the in vitro dissolution test would demonstrate bioinequivalence if tested in vivo. One way to estimate these probabilities is by means of a simulated experiment in which the production and testing (in vivo and in vitro) of a large number of batches is computer simulated. Such a simulation can only be performed if the relationship between the in vitro dissolution characteristics and the in vivo performance of the product has been modeled. These models are generally referred to as in vivo-in vitro correlations (IVIVC). The results of one such experiment are described. The above-mentioned conditional probabilities are shown to depend on the choice of dissolution specifications. This result leads to the notion of optimal dissolution specifications. However, both of the conditional probabilities cannot be maximized simultaneously. The probability of making a correct decision on the basis of the in vitro dissolution test is introduced as a possible optimality criterion. This probability is a linear combination of the two conditional probabilities of interest. Using this criterion, the optimal dissolution specifications can be found by searching over the multidimensional space defined by the half width of each interval used in the specifications to find the combination that maximizes this probability. This process is demonstrated using the Nelder-Mead search routine. The choice of dissolution specifications has profound implications for the routine production of the product because if the specifications were very narrow the probability of a batch passing would be low, resulting in a low hit rate. The same computer program used to perform the simulation experiment can be used to estimate the hit rate. Furthermore, it can be used to explore the magnitude of changes required in the parameters describing the test product (particularly variability) to increase a low hit rate to an acceptable level.

Biological Availability↗
PubMed1996

Mechanochemical coupling of the motion of molecular motors to ATP hydrolysis.

The typical biochemical paradigm for coupling between hydrolysis of ATP and the performance of chemical or mechanical work involves a well-defined sequence of events (a kinetic mechanism) with a fixed stoichiometry between the number of ATP molecules hydrolyzed and the turnover of the output reaction. Recent experiments show, however, that such a deterministic picture of coupling may not be adequate to explain observed behavior of molecular motor proteins in the presence of applied forces. Here we present a general model in which the binding of ATP and release of ADP serve to modulate the binding energy of a motor protein as it travels along a biopolymer backbone. The mechanism is loosely coupled--the average number of ATPs hydrolyzed to cause a single step from one binding site to the next depends strongly on the magnitude of an applied force and on the effective viscous drag force. The statistical mechanical perspective described here offers insight into how local anisotrophy along the "track" for a molecular motor, combined with an energy-releasing chemical reaction to provide a source of nonequilibrium fluctuations, can lead to macroscopic motion.

Adenosine Triphosphate↗
PubMed2001

Nonlinear dynamics of heart rate variability in cocaine-exposed neonates during sleep.

The aim of this study was to determine the effects of prenatal cocaine exposure (PCE) on the dynamics of heart rate variability in full-term neonates during sleep. R-R interval (RRI) time series from 9 infants with PCE and 12 controls during periods of stable quiet sleep and active sleep were analyzed using autoregressive modeling and nonlinear dynamics. There were no differences between the two groups in spectral power distribution, approximate entropy, correlation dimension, and nonlinear predictability. However, application of surrogate data analysis to these measures revealed a significant degree of nonlinear RRI dynamics in all subjects. A parametric model, consisting of a nonlinear delayed-feedback system with stochastic noise as the perturbing input, was employed to estimate the relative contributions of linear and nonlinear deterministic dynamics in the data. Both infant groups showed similar proportional contributions in linear, nonlinear, and stochastic dynamics. However, approximate entropy, correlation dimension, and nonlinear prediction error were all decreased in active versus quiet sleep; in addition, the parametric model revealed a doubling of the linear component and a halving of the nonlinear contribution to overall heart rate variability. Spectral analysis indicated a shift in relative power toward lower frequencies. We conclude that 1) RRI dynamics in infants with PCE and normal controls are similar; and 2) in both groups, sympathetic dominance during active sleep produces primarily periodic low-frequency oscillations in RRI, whereas in quiet sleep vagal modulation leads to RRI fluctuations that are broadband and dynamically more complex.

Cocaine↗
PubMed1996

Synchronized chaos in local cortical circuits.

Neurons in cortical slices emit spikes or bursts of spikes regularly in response to a suprathreshold current injection. This is in marked contrast to the behavior of cortical neurons in-vivo, whose response to electrical or sensory input displays a strong degree of irregularity. Correlation measurements show significant degree of synchrony in the temporal fluctuations of neuronal activities in cortex. We explore the hypothesis that these phenomena are the result of the synchronized chaos generated by the deterministic dynamics of local cortical networks. A model of a "hypercolumn" in the visual cortex is studied. It consists of two populations of neurons, one inhibitory and one excitatory. The dynamics of the neurons is based on a Hodgkin-Huxley type model with several cellular and synaptic conductances. The pattern of connectivity is correlated with the internal organization of hypercolumns in orientation columns. Numerical simulations of the model show that in an appropriate parameter range, the network settles in a synchronous chaotic state, characterized by a strong temporal variability of the neural activity which is correlated across the hypercolumn. Strong inhibitory feedback is essential for the stabilization of this state. Auto-correlation and cross-correlation functions of neuronal spike trains are computed, and analyzed. The relation between the results of the model and experiments in visual cortex is discussed.

Animals↗
PubMed1993

A reduction in the correlation dimension of heartbeat intervals precedes imminent ventricular fibrillation in human subjects.

Reduced reflexive control of heartbeat intervals occurs with advanced heart disease and is an independent risk factor for mortality. Based on a previous study of experimental myocardial infarction in pigs, we hypothesized that a deterministic measure of heartbeat dynamics, the correlation dimension of R-R intervals (D2), may be a better predictor of risk than a stochastic measure, such as the standard deviation (SD). We determined the point estimates of the heartbeat D2 (i.e., PD2s) in Holter electrocardiographic recordings from 11 high-risk patients who manifested ventricular fibrillation (VF) during the recording and in high-risk controls having only nonsustained ventricular tachycardia (14 patients) or premature ventricular complexes (13 patients). We found that PD2 reduction (i.e., PD2s < 1.2) precedes lethal arrhythmias by hours, but is not reduced in high-risk controls (p < 0.001; sensitivity, 91%; specificity, 85%). Heartbeat SD did not discriminate among the patients. Thus PD2 of heartbeat intervals may provide an important diagnostic test and early warning sign of VF.

Algorithms↗
PubMed2004

Dose quantities in radiation protection and their limitations.

For more than 50 years the quantity absorbed dose has been the basic physical quantity in the medical applications of ionising radiation as well as radiological protection against harm from ionising radiation. In radiotherapy relatively high doses are applied (to a part of the human body) within a short period and the absorbed dose is mainly correlated with deterministic effects such as cell killing and tissue damage. In contrast, in radiological protection one is dealing with low doses and low dose rates and long-term stochastic effects in tissue such as cancer induction. The dose quantity (absorbed dose) is considered to be correlated with the probability of cancer incidence and thus risk induced by exposure. ICRP has developed specific dosimetric quantities for radiological protection that allow the extent of exposure to ionising radiation from whole and partial body external radiation as well as from intakes of radionuclides to be taken into account by one quantity. Moreover, radiological protection quantities are designed to provide a correlation with risk of radiation induced cancer. In addition, operational dose quantities have been defined for use in measurements of external radiation exposure and practical applications. The paper describes the concept and considerations underlying the actual system of dose quantities, and discusses the advantage as well as the limitations of applicability of such a system. For example, absorbed dose is a non-stochastic quantity defined at any point in matter. All dose quantities in use are based on an averaging procedure. Stochastic effects and microscopic biological and energy deposition structures are not considered in the definition. Absorbed dose is correlated to the initial very short phase of the radiation interaction with tissue while the radiation induced biological reactions of the tissue may last for minutes or hours or even longer. There are many parameters other than absorbed dose that influence the process of cancer induction, which may influence the consideration of cells and/or tissues at risk which are most important for radiological protection.

Dose-Response Relationship, Radiation↗
PubMed2003

Frequency and phase synchronization in stochastic systems.

The phenomenon of frequency and phase synchronization in stochastic systems requires a revision of concepts originally phrased in the context of purely deterministic systems. Various definitions of an instantaneous phase are presented and compared with each other with special attention paid to their robustness with respect to noise. We review the results of an analytic approach describing noise-induced phase synchronization in a thermal two-state system. In this context exact expressions for the mean frequency and the phase diffusivity are obtained that together determine the average length of locking episodes. A recently proposed method to quantify frequency synchronization in noisy potential systems is presented and exemplified by applying it to the periodically driven noisy harmonic oscillator. Since this method is based on a threshold crossing rate pioneered by Rice the related phase velocity is termed the Rice frequency. Finally, we discuss the relation between the phenomenon of stochastic resonance and noise-enhanced phase coherence by applying the developed concepts to the periodically driven bistable Kramers oscillator.

Models, Theoretical↗
PubMed2000

An iterative approach to the beam hardening correction in cone beam CT.

In computed tomography (CT), the beam hardening effect has been known to be one of the major sources of deterministic error that leads to inaccuracy and artifact in the reconstructed images. Because of the polychromatic nature of the x-ray source used in CT and the energy-dependent attenuation of most materials, Beer's law no longer holds. As a result, errors are present in the acquired line integrals or measurements of the attenuation coefficients of the scanned object. In the past, many studies have been conducted to combat image artifacts induced by beam hardening. In this paper, we present an iterative beam hardening correction approach for cone beam CT. An algorithm that utilizes a tilted parallel beam geometry is developed and subsequently employed to estimate the projection error and obtain an error estimation image, which is then subtracted from the initial reconstruction. A theoretical analysis is performed to investigate the accuracy of our methods. Phantom and animal experiments are conducted to demonstrate the effectiveness of our approach.

Algorithms↗
PubMed1995

Spatial heterogeneity, nonlinear dynamics and chaos in infectious diseases.

There is currently considerable interest in the role of nonlinear phenomena in the population dynamics of infectious diseases. Childhood diseases such as measles are particularly well documented dynamically, and have recently been the subject of analyses (of both models and notification data) to establish whether the pattern of epidemics is chaotic. Though the spatial dynamics of measles have also been extensively studied, spatial and nonlinear dynamics have only recently been brought together. The present review concentrates mainly on describing this synthesis. We begin with a general review of the nonlinear dynamics of measles models, in a spatially homogeneous environment. Simple compartmental models (specifically the SEIR model) can behave chaotically, under the influence of strong seasonal 'forcing' of infection rate associated with patterns of schooling. However, adding observed heterogeneities such as age structure can simplify the deterministic dynamics back to limit cycles. By contrast all current strongly seasonally forced stochastic models show large amplitude irregular fluctuations, with many more 'fadeouts' of infection that is observed in real communities of similar size. This indicates that (social and/or geographical) spatial heterogeneity is needed in the models. We review the exploration of this problem with nonlinear spatiotemporal models. The few studies to date indicate that spatial heterogeneity can help to increase the realism of models. However, a review of nonlinear analyses of spatially subdivided measles data show that more refinements of the models (particularly in representing the impact of human demographic changes on infection dynamics) are required. We conclude with a discussion of the implication of these results for the dynamics of infectious diseases in general and, in particular, the possibilities of cross fertilization between human disease epidemiology and the study of plant and animal diseases.

Communicable Diseases↗
PubMed2004

Complexity quantification of dense array EEG using sample entropy analysis.

In this paper, a time series complexity analysis of dense array electroencephalogram signals is carried out using the recently introduced Sample Entropy (SampEn) measure. This statistic quantifies the regularity in signals recorded from systems that can vary from the purely deterministic to purely stochastic realm. The present analysis is conducted with an objective of gaining insight into complexity variations related to changing brain dynamics for EEG recorded from the three cases of passive, eyes closed condition, a mental arithmetic task and the same mental task carried out after a physical exertion task. It is observed that the statistic is a robust quantifier of complexity suited for short physiological signals such as the EEG and it points to the specific brain regions that exhibit lowered complexity during the mental task state as compared to a passive, relaxed state. In the case of mental tasks carried out before and after the performance of a physical exercise, the statistic can detect the variations brought in by the intermediate fatigue inducing exercise period. This enhances its utility in detecting subtle changes in the brain state that can find wider scope for applications in EEG based brain studies.

Adult↗