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PubMed2004

Dimensional complexity of the neuronal activity in a rat model of depression.

The Flinders sensitive line of rats is a widely accepted and validated model of depression. These rats demonstrate abnormalities in limbic dopamine neurotransmission, suggesting disturbed neuronal activity in the ventral tegmental area. Interspike interval time-series were recorded from the ventral tegmental area of control Sprague-Dawley and Flinder sensitive line rats. These data were analyzed using standard measures (mean firing rate, bursting activity and spectral analysis) as well as the pointwise correlation dimension, a nonlinear measurement characterizing the complexity degree of dynamic systems. Pointwise correlation dimension, but not standard analysis revealed a significant difference between the animal lines. Our results suggest that nonlinear analyses can detect dysregulation of the mesolimbic dopaminergic system and shed light on the pathophysiology of depression.

Action Potentials↗

PubMed2006

Evaluation of Goldmann applanation tonometry using a nonlinear finite element ocular model.

Goldmann applanation tonometry (GAT) is the internationally accepted standard for intra-ocular pressure (IOP) measurement, which is important for the diagnosis of glaucoma. The technique does not consider the effect of the natural variation in the corneal thickness, curvature and material properties. As these parameters affect the structural resistance of the cornea, their variation is expected to lead to inaccuracies in IOP determination. Numerical Analysis based on the finite element method has been used to simulate the loading conditions experienced in GAT and hence assess the effect of variation in corneal parameters on GAT IOP measurements. The analysis is highly nonlinear and considers the hyper-elastic J-shaped stress-strain properties of corneal tissue observed in laboratory tests. The results reveal a clear association between both the corneal thickness and material properties, and the measured IOP. Corneal curvature has a considerably lower effect. Similar trends have been found from analysis of clinical data involving 532 patients referred to the Glaucoma Unit at Moorfields Hospital, and from earlier mathematical analyses. Nonlinear modelling is shown to trace the behaviour of the cornea under both IOP and tonometric pressure, and to be able to provide additional, and potentially useful, information on the distribution of stress, strain, contact pressure and gap closure.

Biomedical Engineering↗

PubMed2000

The role of the thalamic reticular neurons in alpha- and gamma-oscillations in neocortex: a mechanism for selective perception and stimulus binding.

The long-term objective is to understand how large masses of neurons in the brain process information during various learning and memory paradigms. Both time- and space-dependent processes have been identified in animals through computer-based analytic quantifications of event-related extracellular potentials. New nonlinear analyses have been introduced that presume that the fine-grain variation in the signal is determined and patterned in phase-space. Some neurons in the primary visual cortex manifest gamma-band oscillations. These cells show both a nonspecific phase-alignment (response synchrony) and a specific tuning (orientation tuning) when stimuli are presented to their receptive fields. This dual regulation of the sensory cells is proposed to underlie stimulus binding, a theoretical mechanism for "object" perception. Nonlinear analytic results from gamma-activities in a simple model neuropil (olfactory bulb) suggest that neuroplasticity may arise through self-organization, a process in which a nonlinear change in the dynamics of the oscillatory field potentials is the hallmark. This self-organization may follow simple dynamical laws in which global cooperativity among the neurons is transiently brought about that, over trials, results in enduring changes in the nonlinear dynamics of some neurons. In conclusion, the sculpturing of the synaptic throughput in the sensory cortex (stimulus binding) may be associated with the irregular phases of the gamma-activities and may result from both specific and nonspecific systems operating together in a nonlinear self-organizing manner.

Alpha Rhythm↗

PubMed2004

Impairment of cardiovascular autonomic control in patients early after cardiac surgery.

OBJECTIVE: Impairment of the baroreceptor reflex activity reflects an alteration of the autonomous regulation of the cardiovascular system and has proven to predict fatal outcome in patients after acute myocardial infarction. The following study was performed to analyse the baroreceptor sensitivity, heart rate variability and blood pressure variability in patients early after coronary surgery. METHODS: Twenty-five male patients undergoing coronary artery bypass were examined in a prospective study; normal values were obtained from healthy volunteers. Arterial pressure signals were recorded from a radial artery catheter for 30 min preoperatively and in short intervals after surgery. Mechanical manipulations and pharmacological interventions were avoided during the sampling periods. Baroreflex function was calculated according to the dual sequence method, heart rate variability and blood pressure variability were calculated including nonlinear methods. RESULTS: Initial values of the patients did not differ from healthy volunteers. The strength of baroreflex sensitivity (increase in blood pressure causing a synchronous decrease of heart rate) is low 2 h postoperatively. The number of delayed tachycardic changes of heart rate, which are caused by sympathetic activation, is only moderately reduced as compared to values obtained from healthy volunteers. Heart rate variability is widely unchanged as compared to preoperative values; blood pressure variability showed an increase of low-frequency components, again indicating sympathetic predominance. Nonlinear analyses revealed reduced system complexity at the beginning of the postoperative course. CONCLUSION: Obviously, there is a vagal suppression 20 h after surgery, while the sympathetic tonus works in a normal range. This unbalanced interaction of the autonomous systems is similar to findings in patients after myocardial infarction. The predictive value of these markers has to be elucidated in further clinical studies.

Aged↗

PubMed2003

Low-order chaos in sympathetic nerve activity and scaling of heartbeat intervals.

The mechanism of 1/f scaling of heartbeat intervals remains unknown. We recorded heartbeat intervals, sympathetic nerve activity, and blood pressure in conscious rats with normal or high blood pressure. Using nonlinear analyses, we demonstrate that the dynamics of this system of three variables is low-order chaos, and that sympathetic nerve activity leads to heartbeat interval and blood pressure changes. It is suggested that impaired regulation of blood pressure by sympathetic nerve activity is likely to cause experimentally observable steeper scaling of heartbeat intervals in hypertensive (high blood pressure) rats.

Algorithms↗

PubMedDate not supplied

Detection of hemodynamic turbulence in experimental stenosis: an in vivo study in the rat carotid artery.

In a previous study, we have demonstrated that turbulences in arteries less than 1.5 mm in diameter perfused ex vivo by an oscillated flow can be determined using nonlinear mathematical models. The hypothesis tested here was that nonlinear analyses enable the in vivo detection of turbulences in blood flow in vessels with dimensions affected by microsurgery. Twenty Wistar male rats were studied. After an intraperitoneal anesthesia (50 mg/kg sodium pentobarbital), each right carotid artery was dissected and a transit time flowmeter was used to measure blood flow. Arteries were studied in control conditions and graded stenoses, which were performed by a collar system and progressively increased from 0 to 95%. For each flow signal, time delay, false-nearest neighbors, correlation dimension and the largest Lyapunov exponent were computed to characterize the level of turbulence. The level of turbulence was highly correlated with the degree of stenosis induced (p < 0.001). The correlation dimensions of all the flow signals varied between 3 and 5, thus implying that more than three independent noninteger control variables were necessary to account for the complexity of rat carotid artery dynamics. Turbulence flow significantly increased in arteries with 40-95% stenosis. Nonlinear analysis may be useful to determine the turbulence level of an in vivo flow in arteries less than 1.5 mm in diameter and might be clinical useful for turbulence detection after microsurgery.

Algorithms↗

PubMed2003

Further evidence for the dynamic stability of intracranial saccular aneurysms.

It has long been thought that intracranial saccular aneurysms enlarge and rupture because of mechanical instabilities. Recent nonlinear analyses suggest, however, that at least certain sub-classes of aneurysms do not exhibit quasi-static limit point instabilities or dynamic instabilities in response to periodic loading, and consequently, that the natural history of these lesions is likely governed by growth and remodeling processes. In this paper, we present additional results that support the finding that one particular sub-class of saccular aneurysms is dynamically stable. Specifically, we extended recent results of Shah and Humphrey, which are based on the assumption that some saccular aneurysms can be modeled as spherical elastic membranes surrounded by a viscous cerebrospinal fluid, to account for a viscohyperelastic behavior of the aneurysm. It is shown that inclusion of a "short-term" viscoelastic contribution to the mechanical behavior of an aneurysm serves to increase its dynamic stability against various disturbances.

Aneurysm, Ruptured↗

PubMed1994

A nonlinear dynamical (chaos) approach to the analysis of broiler growth.

Mathematical chaos has been observed in a number of biological areas, suggesting that order can be found in systems previously described as random. Nonlinear analyses were conducted to determine whether periodicity or chaos was evident in the growth responses of broiler chickens. Analyses of the absolute growth rate and growth rate acceleration were conducted for four lines of broilers selected at 14 or 42 d for high or low growth rates (Experiment 1) and for a commercial broiler strain (Experiment 2). Resulting Lyapunov exponents (LE) and correlation dimensions (CD) were statistically evaluated. Time series and return map graphics were analyzed. In both experiments, independence of day-to-day growth responses was indicated by low r2 values. In Experiment 1, there were significant differences between lines in growth rate (low, 9.1 +/- .3; high, 12.9 +/- .5 g/d) and the standard deviation of growth rate (low, 5.8 +/- .2; high 7.3 +/- .3 g/d). There were no significant differences for LE or CD values between lines or day of selection. In general, the positive LE, noninteger values of CD, and return map graphics in both experiments suggested the presence of chaotic dynamics. Evaluation of mathematical chaos in broiler growth may give insight into the dynamics and modeling of growth and diseases associated with growth.

Animals↗

PubMed2000

Recurrent patterns of atrial depolarization during atrial fibrillation assessed by recurrence plot quantification.

The aim of this study was to determine the presence of organization of atrial activation processes during atrial fibrillation (AF) by assessing whether the activation sequences are wholly random or are governed by deterministic mechanisms. We performed both linear and nonlinear analyses based on the cross correlation function (CCF) and recurrence plot quantification (RPQ), respectively. Recurrence plots were quantified by three variables: percent recurrence (PR), percent determinism (PD), and entropy of recurrences (ER). We recorded bipolar intra-atrial electrograms in two atrial sites during chronic AF in 19 informed subjects, following two protocols. In one, both recording sites were in the right atrium; in the other protocol, one site was in the right atrium, the other one in the left atrium. We extracted 19 episodes of type I AF (Wells' classification). RPQ detected transient recurrent patterns in all the episodes, while CCF was significant only in ten episodes. Surrogate data analysis, based on a cross-phase randomization procedure, decreased PR, PD, and ER values. The detection of spatiotemporal recurrent patterns together with the surrogate data results indicate that during AF a certain degree of local organization exists, likely caused by deterministic mechanisms of activation.

Adult↗

PubMed1992

Chaotic dynamics in autonomic nervous system activity of a patient during a psychotherapy session.

Chaos theory and nonlinear dynamical modeling have been applied successfully in a variety of scientific fields ranging from the physical sciences to population biology. More recently, investigators have modeled long-term psychological processes by applying this paradigm to subjective measures. Yet, mathematically rigorous dynamical modeling of transient psychodynamic processes remains uncharted. Human behaviors and intrapsychic processes often defy prediction, yet psychodynamic theory views these as fundamentally deterministic. We postulate that a nonlinear dynamical analysis of mental states and mental control processes may help reconcile the paradox that seemingly random mental states are thought ultimately to result from deterministic, rather than stochastic, psychological processes. As an initial empirical approach, we examined spontaneously occurring autonomic activity of a patient during 1 hr of psychotherapy and illustrate that cardiac responses associated with psychologically meaningful events possess nonlinear characteristics indicative of chaos. Such nonlinear analyses may shed light on fundamental issues of psychological functioning.

Adult↗

PubMed2006

Discrete bandwidth visual feedback increases structure of output as compared to continuous visual feedback in isometric force control tasks.

BACKGROUND: Performance variability measures provide a partial picture of force control ability. Nonlinear analyses can reveal important information related to the randomness and complexity of the data, providing a more complete picture of the physiological process. METHODS: We investigated the effects of visual feedback on the structure and performance of the force output from isometric force control tasks. Twelve young volunteers completed isometric force control tasks using two types of visual feedback: discrete bandwidth (+/-4% maximal voluntary contraction) and continuous line matching. We determined force signal variability (standard deviation), self-similarity (fractal dimension), and complexity (approximate entropy). Analyses of variance (feedback x muscle group x force level) were conducted and P values less than 0.05 were considered significant. FINDINGS: The force signal in discrete bandwidth feedback, compared to continuous line matching, had significantly a higher standard deviation (P=.000): 2.18 Nm (SD 1.98) vs. 0.99 Nm (SD 0.91); lower fractal dimension (P=.000): 1.07 (SD 0.04) vs. 1.16 (SD 0.04); and lower approximate entropy (P=.000): 0.12 (SD 0.07) vs. 0.26 (SD 0.09). INTERPRETATION: The greater self-similarity (lower fractal dimension) and greater regularity (lower approximate entropy) of the discrete bandwidth, compared to the continuous line matching, may indicate a process that required more kinesthetic (intrinsic) feedback to modulate force. Clinicians may choose to employ visual feedback paradigms that target the use of intrinsic feedback during rehabilitation. Discrete bandwidth feedback may be useful for delineating impairments in motor skill and measuring outcomes of intervention programs.

Adult↗

PubMed2002

A low-noise flexible integrated system for recording and analysis of multiple electrical signals during sleep-wake states in rats.

A low-noise flexible system for the simultaneous recording and analysis of several electrical signals (EEG, ECG, EMG, and diaphragm EMG) from the same rat was constructed for studying changes in physiological functions during the sleep-wake cycle. The hardware in the system includes a multichannel amplifier, a video camera, a timer code generator, and a PC. A miniature buffer headstage with high-input impedance connected to a 6-channel amplifier was developed. All electrical activities devoid of 60 Hz interference could be consistently recorded by our low-cost amplifier with no shielding treatment. The analytical software was established in the LabVIEW environment and consisted of three major frames: temporal, spectral, and nonlinear analyses. These analytical tools demonstrated several distinct utilities. For example, the sleep-wake states could be successfully distinguished by combining temporal and spectral analyses. An obvious theta rhythm during rapid-eye-movement sleep (REMS) was recorded from parietal to occipital cortical areas but not from the frontal area. In addition, two types of sleep apnea with/without cardiac arrhythmias were observed under REMS condition. Moreover, the evoked potentials of the primary somatosensory cortex elicited by innocuous electrical pulses were modulated by vigilant states, especially under a slow-wave sleep state. These results show that our system delivers high-quality signals and is suitable for sleep investigations. The system can be easily expanded by combining other recording devices, like a plethysmograph. This compact system can also be easily modified and applied to other related physiological or pharmacological studies.

Animals↗

PubMed2002

Temporal patterns of atrial arrhythmia recurrences in patients with implantable defibrillators: implications for assessing antiarrhythmic therapies.

INTRODUCTION: The statistical measures commonly used to assess therapies for recurrent atrial arrhythmias (such as time to first recurrence) often assume a uniformly random pattern of arrhythmic events over time. However, the true temporal pattern of atrial arrhythmia recurrences is unknown. The aim of this study was to use linear and nonlinear analyses to characterize the temporal pattern of atrial arrhythmia recurrences in patients with implantable cardioverter defibrillators. METHODS AND RESULTS: The time and date of atrial tachyarrhythmias recorded in 65 patients with combined atrial and ventricular defibrillators were used to construct a probability density function (PDF) and a model of a Poisson distribution of arrhythmic events for each patient. Average patient age was 66 +/- 10 years and follow-up was 7.8 +/- 4.8 months. A total of 10,759 episodes of atrial tachyarrhythmias were analyzed (range 43 to 618 episodes per patient). The PDF fit a power law distribution for all 65 patients, with an average r2 = 0.89 +/- 0.08. The PDF distribution differed significantly from the model Poisson distribution in 47 of 65 patients (P = 0.0002). Differences from the Poisson distribution were noted for patients both taking (30/43 patients; P < or = 0.015) and not taking (17/22 patients; P < or = 0.017) antiarrhythmic drugs. Median time between atrial arrhythmia detections for all 65 patients was 10.8 minutes. CONCLUSION: In implantable cardioverter defibrillator patients, the temporal pattern of frequent recurrences of atrial tachyarrhythmias usually is characterized by a power law distribution. The unique statistical properties of this type of distribution should be considered in designing outcome measures for treatment of atrial tachyarrhythmias.

Adult↗

PubMed2006

A finite element model for investigating effects of aerial architecture on tree oscillations.

A finite element model was developed to study the influence of aerial architecture on the structural dynamics of trees. The model combines a complete description of the axes of the aerial architecture of the plant with numerical techniques suitable for dynamic nonlinear analyses. Trees were modeled on the basis of morphological measurements that were previously made on three 4-year-old Pinus pinaster Ait. saplings originating from even-aged stands. Calculated and measured oscillations were compared to evaluate model behavior. The computations allowed the characteristics of the fundamental mode of vibration to be estimated with satisfactory accuracy. Inclusion of a topological description of the aerial system in a mechanical model provided insight into the effect of tree architecture on tree dynamic behavior. Simplifications of the branching pattern in the model led to overestimations of the natural swaying frequency of saplings by 10 to 20%. Inadequate values of stem and root anchorage stiffness resulted in errors of 10 to 20%. Modeling results indicated that aerodynamic drag of needles is responsible for 80% of the damping in the studied trees. Additionally, damping of stem movement is reduced by one half when branch oscillations are not considered. It appears that the efficiency of the dissipative mechanisms depends directly on crown topology.

Biomechanical Phenomena↗

PubMed2004

Diagnosis of pneumonia with an electronic nose: correlation of vapor signature with chest computed tomography scan findings.

OBJECTIVES/HYPOTHESIS: The electronic nose is a sensor of volatile molecules that is useful in the analysis of expired gases. The device is well suited to testing the breath of patients receiving mechanical ventilation and is a potential diagnostic adjunct that can aid in the detection of patients with ventilator-associated pneumonia. STUDY DESIGN: A prospective study. METHODS: We performed a prospective study of patients receiving mechanical ventilation in a surgical intensive care unit who underwent chest computed tomography (CT) scanning. A single attending radiologist reviewed the chest CT scans, and imaging features were recorded on a standardized form. Within 48 hours of chest CT scan, five sets of exhaled gas were sampled from the expiratory limb of the ventilator circuit. The gases were assayed with a commercially available electronic nose. Both linear and nonlinear analyses were performed to identify correlations between imaging features and the assayed gas signatures. RESULTS: Twenty-five patients were identified, 13 of whom were diagnosed with pneumonia by CT scan. Support vector machine analysis was performed in two separate analyses. In the first analysis, in which a training set was identical to a prediction set, the accuracy of prediction results was greater than 91.6%. In the second analysis, in which the training set and the prediction set were different, the accuracy of prediction results was at least 80%, with higher accuracy depending on the specific parameters and models being used. CONCLUSION: The electronic nose is a new technology that continues to show promise as a potential diagnostic adjunct in the diagnosis of pneumonia and other infectious diseases.

Adult↗

PubMed2004

Adaptive control of unknown unstable steady states of dynamical systems.

A simple adaptive controller based on a low-pass filter to stabilize unstable steady states of dynamical systems is considered. The controller is reference-free; it does not require knowledge of the location of the fixed point in the phase space. A topological limitation similar to that of the delayed feedback controller is discussed. We show that the saddle-type steady states cannot be stabilized by using the conventional low-pass filter. The limitation can be overcome by using an unstable low-pass filter. The use of the controller is demonstrated for several physical models, including the pendulum driven by a constant torque, the Lorenz system, and an electrochemical oscillator. Linear and nonlinear analyses of the models are performed and the problem of the basins of attraction of the stabilized steady states is discussed. The robustness of the controller is demonstrated in experiments and numerical simulations with an electrochemical oscillator, the dissolution of nickel in sulfuric acid; a comparison of the effect of using direct and indirect variables in the control is made. With the use of the controller, all unstable phase-space objects are successfully reconstructed experimentally.

Journal Article↗

PubMed1995

Application of linear and nonlinear time series modeling to heart rate dynamics analysis.

The linear autoregressive (AR) model is often used to investigate the pathophysiologic mechanisms controlling heart rate (HR) dynamics. This study implemented parametric models new to this field to determine if a more appropriate HR dynamics modeling structure exists. The linear AR and autoregressive-moving average (ARMA) models, and the nonlinear polynomial autoregressive (PAR) and bilinear (BL) models were fit to instantaneous HR time series obtained from nine subjects in the supine position. Model orders were determined by the Akaike Information Criteria (AIC). Model residual variance was used as the primary intermodel comparison criterion, with significance evaluated by a chi 2 distributed statistic. The BL model best represented the HR dynamics, as its residual variance was significantly (p < 0.05) smaller than that of the corresponding AR model for nine out of nine data sets. In all cases, the BL model had a smaller residual variance than either the ARMA or PAR models. The bilinear model was ineffective at data forecasting, however, we show that this cannot reflect BL model validity because poor prediction is inherent to the BL model structure. The apparent superiority of the nonlinear bilinear model suggests that future heart rate dynamics studies should put greater emphasis on nonlinear analyses.

Adult↗

PubMed1992

Dose-dependent inhibition in plasma protein binding of valproic acid during continued treatment in guinea-pigs.

Plasma protein binding of valproic acid over a wide range of steady-state plasma concentration (11.3 +/- 2.6-1303.0 +/- 122.9 micrograms mL-1: s.e.m., n = 5) in guinea-pigs has been studied. Valproic acid was given by intravenous constant infusion. At steady-state the plasma protein binding of valproic acid was analysed. Nonlinear binding was observed. Unbound fraction (fu) of valproic acid increased from 25 to 95% with the increase of steady-state plasma concentration (Css). The plasma protein-bound drug concentration (Cb) of valproic acid increased initially with Css but decreased after the Css exceeded 345.0 micrograms mL-1, where the Cb was 152.5 +/- 26.8 micrograms mL-1. At a Css of 1303.3 +/- 122.9 micrograms mL-1 the Cb was significantly (P less than 0.05) decreased to 72.8 +/- 20.2 micrograms mL-1. Binding characteristics of valproic acid in-vitro were studied using drug-free guinea-pig plasma with added valproic acid (10-1000 micrograms mL-1). The binding behaviour was also nonlinear in-vitro. The fu increased from 14 to 79% with the increase of valproate concentrations. No decrease in Cb was observed throughout the range. The study demonstrated that binding characteristics of valproic acid in-vivo and in-vitro are not parallel. The results suggest that valproic acid may produce or induce plasma protein binding competitors; metabolites of valproic acid may be implicated.

Animals↗