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Random walks, random sequences, and nonlinear dynamics in human optokinetic nystagmus.

Optokinetic nystagmus (OKN) is a reflexive eye movement with target-following slow phases (SP) alternating with oppositely directed fast phases (FP). We measured the following from OKN in three humans: FP beginning and ending positions, amplitudes, and intervals and SP amplitudes and velocities. We sought to predict future values of each parameter on the basis of past values, using state-space representation of the sequence (time-delay embedding) and local second-order approximation of trajectories. Predictability is an indication of determinism: this approach allows us to investigate the relative contributions of random and deterministic dynamics in OKN. FP beginning and ending positions showed good predictability, but SP velocity was less predictable. FP and SP amplitudes and FP intervals had little or no predictability. FP beginnings and endings were as predictable as randomized versions that retain linear autocorrelation; this is typical of random walks. Predictability of FP intervals did not change under random rearrangement, which is characteristic of a random process. Only linear determinism was demonstrated; nonlinear interactions may exist that would not be detected by our present approach.

Humans↗

Circadian rhythms of plasma renin activity and aldosterone: changes related to age, sex, recumbency and sodium restriction. Chronobiologic specification for reference values.

Plasma renin activity (PRA) and aldosterone (PA) levels are characterized by a circadian rhythmicity (CR). The present study revealed that this rhythmicity is influenced by several factors including posture, sodium intake and age. Time-qualified PRA and PA reference intervals can reduce the incidence of false positives and false negatives in a diagnostic work-up. The circadian rhythmicity of PRA and PA have been quantified in relation to posture, sodium intake and age. The cosinor procedure has been applied to quantify the properties of the circadian rhythmicity under these conditions. Chronograms and circadian parameters can be used to optimize the use of PRA and PA measurements in clinical practice. The chronobiological specification of reference values for PRA and PA is of valuable importance since the assessment of PRA and PA circadian rhythmicity has a diagnostic interest for a certain type of clinical disorder. It should be noted that several studies have described circannual variations for renin and aldosterone. The next step in the optimation of laboratory time-qualified reference values is the assessment of changes induced by the deterministic factors on a circannual domain.

Adult↗

Semi-automatic level-set based segmentation and stenosis quantification of the internal carotid artery in 3D CTA data sets.

We present a new level-set based method to segment and quantify stenosed internal carotid arteries (ICAs) in 3D contrast-enhanced computed tomography angiography (CTA). Within these data sets it is a difficult task to evaluate the degree of stenoses deterministically even for the experienced physician because the actual vessel lumen is hardly distinguishable from calcified plaque and there is no sharp border between lumen and arterial wall. According to our knowledge no commercially available software package allows the detection of the boundary between lumen and plaque components. Therefore in the clinical environment physicians have to perform the evaluation manually. This approach suffers from both intra- and inter-observer variability. The limitation of the manual approach requires the development of a semi-automatic method that is able to achieve deterministic segmentation results of the internal carotid artery via level-set techniques. With the new method different kinds of plaques were almost completely excluded from the segmented regions. For an objective evaluation we also studied the method's performance with four different phantom data sets for which the ground truth of the degree of stenosis was known a priori. Finally, we applied the method to 10 ICAs and compared the obtained segmentations with manual measurements of three physicians.

Algorithms↗

Lung function interpolation by means of neural-network-supported analysis of respiration sounds.

Respiration sounds of individual asthmatic patients were analysed in the scope of the development of a method for computerised recognition of the degree of airways obstruction. Respiration sounds were recorded during laboratory sessions of allergen provoked airways obstruction, during several stages of advancing obstruction. The technique of artificial neural networks was applied for relating sound spectra and simultaneously measured lung function values (spirometry parameter FEV(1)). The ability of feedforward neural networks was tested to interpolate obstruction levels of FEV(1)-classes of which no members were included in the set used for training a network. In this way, a situation was simulated of an existing network recognising a new asthmatic attack under the same physiological conditions. It appeared to be possible to interpolate FEV(1) values, and it is concluded that a deterministic relationship exists between sound spectra and lung function parameter FEV(1). Variance optimisation appeared to be important in optimising the neural network configuration.

Asthma↗

Temporal organization of atrial activity and irregular ventricular rhythm during spontaneous atrial fibrillation: an in vivo study in the horse.

INTRODUCTION: Atrial fibrillation (AF) is common in healthy horses. We studied the temporal organization of AF to test the hypothesis that the arrhythmia is governed by a high degree of periodicity and therefore is not random in the horse. Further, we surmised that concealed conduction of AF impulses in the AV node results in an inverse relationship between AF frequency and ventricular frequency. METHODS AND RESULTS: Fast Fourier transform (FFT) analysis of atrial activity was done on signal-averaged ECGs (n = 11) and atrial electrograms (n = 3) of horses with AF at control (C), after quinidine sulfate (22 mg/kg by mouth every 2 hours) at 50% time to conversion (T50), and immediately before conversion (T90) to sinus rhythm. FFT always revealed a single dominant frequency peak. The mean dominant frequency decreased until conversion (C = 6.84 +/- 0.85 Hz, T50 = 4.87 +/- 1.5 Hz, T90 = 3.41 +/- 1.18 Hz; P < 0.001). Mean AA intervals (n = 500) gradually increased after quinidine. Mean RR intervals (n = 500), standard deviation of the mean (SDM), Poincaré plots, and serial autocorrelograms (SACs) of 500 RR intervals were measured at C and T90 to determine the ventricular response to AF and quinidine-induced changes in the variability of the ventricular response. Mean RR interval and SDM were reduced after quinidine (C = 1431 +/- 266 msec and 695 +/- 23 msec; T90 = 974 +/- 116 msec and 273 +/- 158 msec, respectively; P < 0.01). Poincaré plots and SAC at C and at T90 revealed a significant correlation of consecutive RR intervals typical of a system with a deterministic behavior. At T90, the variability of RR intervals was reduced and the overall periodicity of RR intervals was increased after quinidine administration. CONCLUSION: In the horse, AF is a complex arrhythmia characterized by a high degree of underlying periodicity. The inverse AA-to-RR interval relationship and reduced variability of RR intervals after quinidine suggest that the ventricular response during AF results from rate-dependent concealment of AF wavelets bombarding the AV node, which nevertheless results in a significant degree of short-term predictability of beat-to-beat changes in RR intervals.

Animals↗

Stochastic vs. deterministic uptake of dodecanedioic acid by isolated rat livers.

Deterministic and stochastic differential equations models of the uptake of dodecanedioic acid (C12) are fitted to experimental data obtained on nine isolated, perfused rat livers. 11500 mug of C12 were injected as a bolus into the perfusing liver solution. The concentrations of C12 in perfusate samples taken over 2 h from the beginning of the experiments were analyzed by High Performance Liquid Chromatography (HPLC). A two-compartment deterministic model is studied. To include spontaneous erratic variations in the metabolic processes the parameter for the uptake rate is randomized to obtain a stochastic differential equations model. Parameters are estimated in a two-step procedure: first, parameters in the drift part are estimated by least squares; then, the diffusion parameter is estimated using Monte-Carlo simulations to approximate the unknown likelihood function. Parameter estimation is carried out over a wide range of reasonable measurement error variances to check robustness of estimates. It is concluded that the kinetics of dodecanedioic acid, in the experimental conditions discussed, is well approximated by a model including spontaneous erratic variations in the liver uptake rate.

Algorithms↗

Genetic modifiers of APOE-&#x3b5;4-associated cognitive decline.

The APOE-&#x3b5;4 allele is the strongest genetic risk factor for late-onset Alzheimer's disease. However, APOE-&#x3b5;4 is not deterministic, highlighting the need to identify additional genetic and environmental factors. APOE-&#x3b5;4 has been linked to accelerated cognitive decline, so we sought to investigate genetic factors that modify APOE-&#x3b5;4-associated cognitive decline. We conduct cross-ancestry APOE-&#x3b5;4-stratified and interaction GWAS using harmonized cognitive data from 32,778 participants, including 29,354 non-Hispanic White and 3,424 non-Hispanic Black individuals. Our primary outcome is late-life cognition, measured using harmonized composite scores for memory, executive function, and language, modeled as continuous traits reflecting both normative cognitive aging and disease-related decline. We identify two genome-wide significant loci in APOE-&#x3b5;4 carriers, reaching genome-wide significance for executive function. These loci also demonstrate nominal associations across the other domains, suggesting broad effects on cognition. In non-carriers, we identify a genome-wide significant association at ITGB8 restricted to executive function, and another locus associated with language. We further link these loci to SEMA6D, GRIN3A, and ITGB8 through expression and methylation databases. Post-GWAS analyses implicate additional genes including SLCO1A2, and DNAH11. Genetic correlation analyses reveal differences by APOE-&#x3b5;4 status for immune-related traits, suggesting immune-related predispositions may exacerbate cognitive risk in APOE-&#x3b5;4 carriers.

Humans↗

Approaches to establishing reference levels in interventional radiology.

Reference levels in radiodiagnostics are a requirement stated by the Council Directive 97/43/EURATOM. Reference levels are also relevant for interventional procedures, in accordance with this Directive, which claims special attention to quality assurance programmes, including quality control and patient dose evaluations for special practices such as interventional radiology, to assess the convenience of corrective action depending on the measured doses. The present paper addresses a method of establishing reference levels in interventional radiology, in the framework of optimisation, discussing the ways of putting forward values with a degree of tolerance, to allow for procedure complexity, depending on patient pathology. The need for several estimators used together, namely fluoroscopy time, total number of images per procedure and dose-area product, is also emphasised, proposing a further skin dose estimate in case of risk of deterministic effects. Finally, a brief summary of principles is given for the correct management of reference levels in interventional radiology.

European Union↗

The Lyapunov exponent of heart rate dynamics as a sensitive marker of central autonomic organization: an exemplary study of early multiple sclerosis.

In a study of central autonomic dynamics in early multiple sclerosis, we measured the temporal oscillations of the momentary heart rate (heart rate dynamics). 11 young patients suffering from relapsing remitting definite multiple sclerosis in relapse-free and early stages of illness and 11 healthy controls were examined under vagotonic and sympathicotonic conditions. The temporal structure of the heart rate dynamics was operationalized phase-space analytically through the estimation of the largest Lyapunov exponent. Positive Lyapunov exponents were found in all participants under all conditions indicating deterministically chaotic heart rate oscillations. The variance analysis of these exponents detected no significant effect of sympathetic or vagal activity (experimental condition) but a significant group difference (p < .02). The multiple sclerosis patients were characterized by significantly lower Lyapunov exponents than the healthy controls. This finding suggests a more stable and thus less adaptive central-autonomic organization in early multiple sclerosis.

Adolescent↗

Modelling the propagation of terahertz radiation through a tissue simulating phantom.

Terahertz (THz) frequency radiation, 0.1 THz to 20 THz, is being investigated for biomedical imaging applications following the introduction of pulsed THz sources that produce picosecond pulses and function at room temperature. Owing to the broadband nature of the radiation, spectral and temporal information is available from radiation that has interacted with a sample; this information is exploited in the development of biomedical imaging tools and sensors. In this work, models to aid interpretation of broadband THz spectra were developed and evaluated. THz radiation lies on the boundary between regions best considered using a deterministic electromagnetic approach and those better analysed using a stochastic approach incorporating quantum mechanical effects, so two computational models to simulate the propagation of THz radiation in an absorbing medium were compared. The first was a thin film analysis and the second a stochastic Monte Carlo model. The Cole-Cole model was used to predict the variation with frequency of the physical properties of the sample and scattering was neglected. The two models were compared with measurements from a highly absorbing water-based phantom. The Monte Carlo model gave a prediction closer to experiment over 0.1 to 3 THz. Knowledge of the frequency-dependent physical properties, including the scattering characteristics, of the absorbing media is necessary. The thin film model is computationally simple to implement but is restricted by the geometry of the sample it can describe. The Monte Carlo framework, despite being initially more complex, provides greater flexibility to investigate more complicated sample geometries.

Diagnostic Imaging↗

Transition from stochastic to deterministic behavior in calcium oscillations.

Simulation and modeling is becoming more and more important when studying complex biochemical systems. Most often, ordinary differential equations are employed for this purpose. However, these are only applicable when the numbers of participating molecules in the biochemical systems are large enough to be treated as concentrations. For smaller systems, stochastic simulations on discrete particle basis are more accurate. Unfortunately, there are no general rules for determining which method should be employed for exactly which problem to get the most realistic result. Therefore, we study the transition from stochastic to deterministic behavior in a widely studied system, namely the signal transduction via calcium, especially calcium oscillations. We observe that the transition occurs within a range of particle numbers, which roughly corresponds to the number of receptors and channels in the cell, and depends heavily on the attractive properties of the phase space of the respective systems dynamics. We conclude that the attractive properties of a system, expressed, e.g., by the divergence of the system, are a good measure for determining which simulation algorithm is appropriate in terms of speed and realism.

Adenosine Triphosphate↗

Stochastic resonance on a circle without excitation: physical investigation and peak frequency formula

In this article the existence of stochastic resonance (SR) without external force in a simplified circular system for different values of the control parameter b is considered. The average power spectra are calculated as well as the signal-to-noise ratio as a measure for stochastic resonance. It is shown that in the monostable and semistable (b<1 and b=1) cases coherent oscillations occur and SR exists. For the case b>1, the system is oscillatory and noise plays only a destructive role; therefore no SR occurs. The rotation number of the system is calculated and compared to the peak frequency of the power spectrum. Although the coincidence in the noisy case is not as good as that in the deterministic case, we can derive an empirical formula between the peak frequency of the power spectrum and the rotation number of the system, which is in good agreement with results of numerical simulations.

Journal Article↗

Aminoglycoside nephrotoxicity: modeling, simulation, and control.

The main constraints on the administration of aminoglycosides are the risks of nephrotoxicity and ototoxicity, which can lead to acute, renal, vestibular, and auditory toxicities. In the present study we focused on nephrotoxicity. No reliable predictor of nephrotoxicity has been found to date. We have developed a deterministic model which describes the pharmacokinetic behavior of aminoglycosides (with a two-compartment model), the kinetics of aminoglycoside accumulation in the renal cortex, the effects of aminoglycosides on renal cells, the resulting effects on renal function by tubuloglomerular feedback, and the resulting effects on serum creatinine concentrations. The pharmacokinetic parameter values were estimated by use of the NPEM program. The estimated pharmacodynamic parameter values were obtained after minimization of the least-squares objective function between the measured and the calculated serum creatinine concentrations. A simulation program assessed the influences of the dosage regimens on the occurrence of nephrotoxicity. We have also demonstrated the relevancy of modeling of the circadian rhythm of the renal function. We have shown the ability of the model to fit with 49 observed serum creatinine concentrations for a group of eight patients treated for endocarditis by comparison with 49 calculated serum creatinine concentrations (r(2) = 0.988; P < 0.001). We have found that for the same daily dose, the nephrotoxicity observed with a thrice-daily administration schedule appears more rapidly, induces a greater decrease in renal function, and is more prolonged than those that occur with less frequent administration schedules (for example, once-daily administration). Moreover, for once-daily administration, we have demonstrated that the time of day of administration can influence the incidence of aminoglycoside nephrotoxicity. The lowest level of nephrotoxicity was observed when aminoglycosides were administered at 1:30 p.m. Clinical application of this model might make it possible to adjust aminoglycoside dosage regimens by taking into account both the efficacies and toxicities of the drugs.

Adult↗

Is there chaos in the brain? I. Concepts of nonlinear dynamics and methods of investigation.

In the light of results obtained during the last two decades in a number of laboratories, it appears that some of the tools of nonlinear dynamics, first developed and improved for the physical sciences and engineering, are well-suited for studies of biological phenomena. In particular it has become clear that the different regimes of activities undergone by nerve cells, neural assemblies and behavioural patterns, the linkage between them, and their modifications over time, cannot be fully understood in the context of even integrative physiology, without using these new techniques. This report, which is the first of two related papers, is aimed at introducing the non expert to the fundamental aspects of nonlinear dynamics, the most spectacular aspect of which is chaos theory. After a general history and definition of chaos the principles of analysis of time series in phase space and the general properties of chaotic trajectories will be described as will be the classical measures which allow a process to be classified as chaotic in ideal systems and models. We will then proceed to show how these methods need to be adapted for handling experimental time series; the dangers and pitfalls faced when dealing with non stationary and often noisy data will be stressed, and specific criteria for suspecting determinism in neuronal cells and/or assemblies will be described. We will finally address two fundamental questions, namely i) whether and how can one distinguish, deterministic patterns from stochastic ones, and, ii) what is the advantage of chaos over randomness: we will explain why and how the former can be controlled whereas, notoriously, the latter cannot be tamed. In the second paper of the series, results obtained at the level of single cells and their membrane conductances in real neuronal networks and in the study of higher brain functions, will be critically reviewed. It will be shown that the tools of nonlinear dynamics can be irreplaceable for revealing hidden mechanisms subserving, for example, neuronal synchronization and periodic oscillations. The benefits for the brain of adopting chaotic regimes with their wide range of potential behaviours and their aptitude to quickly react to changing conditions will also be considered.

Animals↗

Chapter three: methodology of exposure modeling.

In this chapter, the concept of exposure assessment and its evolution is introduced, and evaluated by critically appraising the pertinent literature as it applies to exposures to Particulate Matter (PM). Exposure measurement or estimation methodologies and models are reviewed. Three exposure/measurement methodologies are assessed. Estimation methods focus on source evaluation and attribution, sources include those outdoors and indoors as well as in occupational and in-transit environments. Fate and transport models and their inputs are addressed to estimate concentrations outdoors and indoors; source attribution techniques help focus on the contributing sources. Activity pattern techniques are also reviewed and their use in exposure models to estimate inhalation exposure to PM is presented. Deterministic, regression and other stochastic models of exposure to PM are reviewed and evaluated. Strengths, limitations, assumptions and affirmations of the use of exposure assessment as an integral component of risk assessment and risk management are discussed in the conclusions and discussions section of this work.

Air Pollutants↗

Non-linear prediction for oesophageal voice analysis.

Herein, non-linear prediction methods are applied to oesophageal voice analysis. The research aims to investigate normal and pathological subjects, in order to improve knowledge of the oesophageal voice behaviour. Analysis is performed in the reconstructed phase space, using both non-linear prediction with local linear approximation and the S-Map method. Preliminary results seem to confirm that in normal subjects a non-linear stable deterministic behaviour takes place, while in pathological subjects the non-linear contribution reduces while the time series becomes unstable.

Adult↗

Distinguishing random environmental fluctuations from ecological catastrophes for the North Pacific Ocean.

The prospect of rapid dynamic changes in the environment is a pressing concern that has profound management and public policy implications. Worries over sudden climate change and irreversible changes in ecosystems are rooted in the potential that nonlinear systems have for complex and 'pathological' behaviours. Nonlinear behaviours have been shown in model systems and in some natural systems, but their occurrence in large-scale marine environments remains controversial. Here we show that time series observations of key physical variables for the North Pacific Ocean that seem to show these behaviours are not deterministically nonlinear, and are best described as linear stochastic. In contrast, we find that time series for biological variables having similar properties exhibit a low-dimensional nonlinear signature. To our knowledge, this is the first direct test for nonlinearity in large-scale physical and biological data for the marine environment. These results address a continuing debate over the origin of rapid shifts in certain key marine observations as coming from essentially stochastic processes or from dominant nonlinear mechanisms. Our measurements suggest that large-scale marine ecosystems are dynamically nonlinear, and as such have the capacity for dramatic change in response to stochastic fluctuations in basin-scale physical states.

Animals↗

A cost-effectiveness analysis of n-3 PUFA (Omacor) treatment in post-MI patients.

This study evaluates the cost-effectiveness of Omacor treatment as a standard prevention measure post-MI in the UK. A cost-effectiveness model was developed based on the GISSI-P trial, combining a survival and a Markov model, over a lifetime period. The base case results for Omacor, at 4 years and over a lifetime, respectively, were: cost [corrected] per QALY gained: pound15,189 and 3,723; [corrected] cost per life years gained (LYG): pound12,011 and pound2,812 [corrected] The cost per death avoided at 4 years was pound31,786. Deterministic and probabilistic sensitivity analyses did not change the base case results substantially. The use of Omacor as a standard post-MI prevention treatment seems warranted in the UK, both on the basis of its efficacy, which is in addition to other prophylactic treatments as evidenced by the results of the GISSI-P trial, and on cost-effectiveness grounds - both at 4 years and over a lifetime's time-horizon, using the current cost-effectiveness thresholds.

Aged↗