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PubMed2005

Interpreting spatial and temporal neural activity through a recurrent neural network brain-machine interface.

We propose the use of optimized brain-machine interface (BMI) models for interpreting the spatial and temporal neural activity generated in motor tasks. In this study, a nonlinear dynamical neural network is trained to predict the hand position of primates from neural recordings in a reaching task paradigm. We first develop a method to reveal the role attributed by the model to the sampled motor, premotor, and parietal cortices in generating hand movements. Next, using the trained model weights, we derive a temporal sensitivity measure to asses how the model utilized the sampled cortices and neurons in real-time during BMI testing.

Algorithms↗

PubMed2004

Prediction and identification using wavelet-based recurrent fuzzy neural networks.

This paper presents a wavelet-based recurrent fuzzy neural network (WRFNN) for prediction and identification of nonlinear dynamic systems. The proposed WRFNN model combines the traditional Takagi-Sugeno-Kang (TSK) fuzzy model and the wavelet neural networks (WNN). This paper adopts the nonorthogonal and compactly supported functions as wavelet neural network bases. Temporal relations embedded in the network are caused by adding some feedback connections representing the memory units into the second layer of the feedforward wavelet-based fuzzy neural networks (WFNN). An online learning algorithm, which consists of structure learning and parameter learning, is also presented. The structure learning depends on the degree measure to obtain the number of fuzzy rules and wavelet functions. Meanwhile, the parameter learning is based on the gradient descent method for adjusting the shape of the membership function and the connection weights of WNN. Finally, computer simulations have demonstrated that the proposed WRFNN model requires fewer adjustable parameters and obtains a smaller rms error than other methods.

Algorithms↗

PubMed2006

Population pharmacokinetic/pharmacodynamic (PK/PD) modelling of the hypothalamic-pituitary-gonadal axis following treatment with GnRH analogues.

AIMS: To develop a population pharmacokinetic/pharmacodynamic (PK/PD) model of the hypothalamic-pituitary-gonadal (HPG) axis describing the changes in luteinizing hormone (LH) and testosterone concentrations following treatment with the gonadotropin-releasing hormone (GnRH) agonist triptorelin and the GnRH receptor blocker degarelix. METHODS: Fifty-eight healthy subjects received single subcutaneous or intramuscular injections of 3.75 mg of triptorelin and 170 prostate cancer patients received multiple subcutaneous doses of degarelix of between 120 and 320 mg. All subjects were pooled for the population PK/PD data analysis. A systematic population PK/PD model-building framework using stochastic differential equations was applied to the data to identify nonlinear dynamic dependencies and to deconvolve the functional feedback interactions of the HPG axis. RESULTS: In our final PK/PD model of the HPG axis, the half-life of LH was estimated to be 1.3 h and that of testosterone 7.69 h, which corresponds well with literature values. The estimated potency of LH with respect to testosterone secretion was 5.18 IU l(-1), with a maximal stimulation of 77.5 times basal testosterone production. The estimated maximal triptorelin stimulation of the basal LH pool release was 1330 times above basal concentrations, with a potency of 0.047 ng ml(-1). The LH pool release was decreased by a maximum of 94.2% by degarelix with an estimated potency of 1.49 ng ml(-1). CONCLUSIONS: Our model of the HPG axis was able to account for the different dynamic responses observed after administration of both GnRH agonists and GnRH receptor blockers, suggesting that the model adequately characterizes the underlying physiology of the endocrine system.

Dose-Response Relationship, Drug↗

PubMed2006

A novel technique to evaluate fluctuations of mood: implications for evaluating course and treatment effects in bipolar/affective disorders.

OBJECTIVES: Several psychiatric conditions are associated with frequent fluctuations of affect. In this study, we propose a new technique to uniformly score depression and mania objectively and use a new mathematical technique to model the frequent fluctuations in mood using simulated data. Our main aim is to examine the usefulness of this measure for evaluating treatment effects or course of illness, especially in bipolar or unipolar affective illness to quantify mood fluctuations. METHODS: We use a prototypical model, which takes into account the mean, the standard deviation (SD) and the coefficient of variation (CV = SD*100/mean) of the mood scores of the subjects over a user-defined period. We utilize simulated data of subjects for euthymia, minor depression, minor mania, severe depression, severe mania and cyclic bipolar illness (manic depression, MDP). We propose an objective method to quantify the mood of the subjects at weekly intervals (the interval can be user-defined) using a scale of 1-9 (1-4 = degrees of depression, 5 = euthymia, 6-9 = degrees of mania). These scores can be sampled according to the convenience and feasibility of the measurements, which can be derived from various clinical scales or by observation of the subjects in hospitals or other environments. We derive a new mathematical technique to arrive at a normalized measure for each of these conditions of simulated data in addition to the mean, SD and approximate entropy (ApEn). RESULTS: We utilize three sets of data, one to train the model to classify the condition of the subjects and the other two to test the reliability of the technique. We are able to successfully classify the condition of the subjects over a 52-timepoint period (length can be days or weeks depending upon the sampling rate). The New Index (NI) correlates significantly only with the mean (r(2) = 0.78), but not with the SD or ApEn score. CONCLUSIONS: These results indicate that it may be beneficial to reduce data according to the techniques we propose so that there is greater uniformity within which to compare future studies to evaluate treatment effects, not only in rapid-cycling MDP but also in other affective disorders. This method may be suitable for the meta-analysis of several studies, although different scales have been used in each of those studies. Our measure derived from simulated data has shown sufficient deviation of all the abnormal states from the euthymic state. The advantages and pitfalls of these techniques are further discussed to evaluate affect in various disorders. However, future prospective studies must address the importance of this measure in comparison with mean, SD and ApEn scores or other nonlinear measures of these time series. We are evaluating other nonlinear dynamic models, which may provide a continuous measure with which to identify different degrees of fluctuation of mood.

Affect↗

PubMed2005

Heart rate variability in young patients with diabetes mellitus and healthy subjects explored by Poincaré and sequence plots.

Autonomic neuropathy is a common complication of the diabetes mellitus (DM). The significance of its early diagnosis is very high because the mortality of the patients with this complication is elevated. Considering the effort to apply new mathematical methods to cardiac dysregulation diagnosis, the major aim of the study was to ascertain which of the new heart rate variability (HRV) parameters are different in young patients with DM type 1 compared with control group. The next aim was to assess the HRV changes during prolonged (40 min) supine rest. The heart rate was continuously recorded during supine rest in 17 young patients with DM type 1 (10 women, 7 men) aged 22.4 +/- 1.0 years (mean +/- SEM). The control group consisted of 17 healthy matched probands. The HRV (time/frequency domains, Poincare and sequence plots, sample entropy) was analysed in two intervals - T1 starting at fifth minute and T2 starting at 30th minute of supine rest. The major results of our study are: the reduced Poincare plot pattern measures in the young DM group; the lower percentage of points in the third quadrant of sequence plot (this parameter was not correlated with the mean heart rate) and significant changes in HRV during supine rest in DM group (in contrast to control subjects). In conclusion, HRV parameters based on nonlinear dynamics were able to distinguish cardiac dysregulation in young patients with DM from the control group. The percentage of points in the third quadrant of sequence plot provides information that is not dependent on mean heart rate. Poincare and sequence plots, together with the rate of HRV changes during supine rest, can provide clinically relevant information usable in diagnosis of the cardiac dysregulation.

Adolescent↗

PubMed1992

Phase plane plot of electrograms as a marker of ventricular electrical instability during acute ischemia: initial experimental results and potential clinical applications.

We used a phase plane plots method (a plot of voltage [V(t)] vs rate of change of voltage [dV/dt]) derived from nonlinear dynamics to transform a sinus rhythm strip into a geometric form. The geometric form thus obtained detects variations in the ECG over time and therefore may aid in identifying patterns of vulnerability to ventricular fibrillation (VF). The trajectories of consecutive ventricular depolarizations and repolarizations of sinus rhythm in dogs that evolve to VF showed characteristic differential band thickening (inhomogeneities) that were absent in the dogs that did not develop VF. This method of analysis can be a useful complementary tool to detect cardiac electrical instability, and with simple hardware, can easily be displayed in real time.

Animals↗

PubMed1996

Variability of ventricular premature complexes and mortality risk.

A method using a parameter from the field of nonlinear dynamics to quantify the variability of ventricular premature complexes (VPCs) is presented. One hundred patients with coronary artery disease and > or = 10 VPCs/hour were included in the study. The RR intervals were plotted in a three-dimensional artificial phase space, and the structures in phase space were quantified by the local scaling indices, alpha. In the frequency distribution histogram, n(alpha), for each patient, the maximum of the ventricular ectopies alpha VPC, adjusted to the VPC frequency, was assessed; alpha VPC was used as the risk indicator. Endpoints were total mortality and sudden cardiac death. During follow-up (mean 3.1 years), 28 out of 100 patients died, 16 suddenly; alpha VPC had a significant prognostic impact and was independent from other risk indicators, such as left ventricular ejection fraction (LVEF). Patients who died during follow-up were characterized by a high alpha VPC. The optimal discrimination of high risk patients and low risk patients occurred at alpha VPC = 3.0. After 4 years, the survival rate of patients with a alpha VPC > 3.0 was 59%, in contrast to 97% in patients with alpha VPC < or = 0.3. As to the sudden death mortality, the survival rates were 74% and 97%, respectively. The difference between the groups were significant for both endpoints. Patients with an increased VPC variability (i.e., alpha VPC > 3.0) were at enhanced risk of sudden death and total mortality risk; alpha VPC was independent from other risk indicators such as the LVEF or heart rate variability parameters.

Adolescent↗

PubMed2000

Scaling structure of electrocardiographic waveform during prolonged ventricular fibrillation in swine.

Ventricular fibrillation (VF) is the most common arrhythmia causing sudden cardiac death. However, the likelihood of successful defibrillation declines with increasing duration of VF. Because the morphology of the electrocardiogram (ECG) waveform during VF also changes with time, this study examined a new measure that describes the VF waveform and distinguishes between early and late VF. Surface ECG recordings were digitized at 200 samples/s from nine swine with induced VF. A new measure called the scaling exponent was calculated by examining the power-law relationship between the summation of amplitudes of a 1,024-point (5.12 second) waveform segment and the time scale of measurement. The scaling exponent is a local estimate of the fractal dimension of the ECG waveform. A consistent power-law relationship was observed for measurement time scales of 0.005-0.040 seconds. Calculation of the scaling exponent produced similar results between subjects, and distinguished early VF (< 4-minute duration) from late VF (> or = 4-minute duration). The scaling exponent was dependent on the order of the data, supporting the hypothesis that the surface ECG during VF is a deterministic rather than a random signal. The waveform of VF results from the interaction of multiple fronts of depolarization within the heart, and may be described using the tools of nonlinear dynamics. As a quantitative descriptor of waveform structure, the scaling exponent characterizes the time dependent organization of VF.

Animals↗

PubMedDate not supplied

Cultural competence: an evolutionary perspective.

PROBLEM: The need for conceptual clarity, which is essential for effective communication related to cultural competence. Practice, education, administration, and research are identified. METHODS: Rodgers' (2000) method of concept analysis. FINDINGS: Attributes of cultural competence were identified as cultural awareness, cultural knowledge, cultural understanding, cultural sensitivity, and cultural skill. CONCLUSIONS: Cultural competence can best be identified as a nonlinear dynamic process that is never ending and ever expanding. It is built on increases in knowledge and skill development related to its attributes.

Cultural Evolution↗

PubMed2001

New data and tools for integrating discrete and continuous population modeling strategies.

Realistic population models have interactions between individuals. Such interactions cause populations to behave as systems with nonlinear dynamics. Much population data analysis is done using linear models assuming no interactions between individuals. Such analyses miss strong influences on population behavior and can lead to serious errors--especially for infectious diseases. To promote more effective population system analyses, we present a flexible and intuitive modeling framework for infection transmission systems. This framework will help population scientists gain insight into population dynamics, develop theory about population processes, better analyze and interpret population data, design more powerful and informative studies, and better inform policy decisions. Our framework uses a hierarchy of infection transmission system models. Four levels are presented here: deterministic compartmental models using ordinary differential equations (DE); stochastic compartmental (SC) models that relax assumptions about population size and include stochastic effects; individual event history models (IEH) that relax the SC compartmental structure assumptions by allowing each individual to be unique. IEH models also track each individual's history, and thus, allow the simulation of field studies. Finally, dynamic network (DNW) models relax the assumption of the previous models that contacts between individuals are instantaneous events that do not affect subsequent contacts. Eventually it should be possible to transit between these model forms at the click of a mouse. An example is presented dealing with Cryptosporidium. It illustrates how transiting model forms helps assess water contamination effects, evaluate control options, and design studies of infection transmission systems using nucleotide sequences of infectious agents.

Data Interpretation, Statistical↗

PubMed1990

A dynamic finite element analysis of impulsive loading of the extension-splinted rabbit knee.

A dynamic nonlinear finite element model was developed to study juxtarticular stresses in the splinted rabbit knee, an established laboratory model for creating osteoarthrosis due to impulsive loading. Plane strain finite element results were validated by comparison with corresponding experimental data. Parametric effects studied included the input tibial displacement speed, the local bone density distribution, and the modulus of cartilage and subchondral bone. While the computed resultant contact force magnitude was sensitive to a number of model parameters, the stress patterns, when normalized to a given resultant force magnitude, were not. Despite comparable force peaks, the finite element results showed approximately six-fold higher effective strain rate levels for a severely impulsive loading protocol known to induce rapid osteoarthrosis, versus those for a mildly impulsive loading protocol not usually associated with cartilage damage. A propensity for elevated shear in the deep cartilage layer near the contact periphery, observed in nearly all computed stress distributions, is consistent with previous experimental findings of fissuring at that level in the impulsively loaded rabbit knee.

Animals↗

PubMed2002

Representations of sound that are insensitive to spectral filtering and parametrization procedures.

This paper describes representations of time-dependent signals that are invariant under any invertible signal distortion. Such a representation can be created by rescaling the signal in a nonlinear dynamic manner that is determined by recently encountered signal levels. Information that is encoded in such representations will be faithfully communicated in the presence of severe signal distortions, which may originate in the transmitter, receiver, or the channel between them. As in speech communication, the receiver is "blind" and need not characterize the form of the signal distortion, which remains unknown. The method is applied to analytical examples, acoustic waveforms of human speech, and the short-term Fourier spectra of a bird song. The results suggest that the rescaled representation of a sound is insensitive to the way its spectra have been filtered and parametrized, as long as those processes do not obliterate the differences between the various spectra in the sound. Finally, the possible "speaker" independence of these representations is explored in the context of a simple linear prediction model of vocal tracts with a single degree of freedom.

Acoustics↗

PubMed2002

Chaotic vibration induced by turbulent noise in a two-mass model of vocal folds.

The contribution of turbulent noise was modeled in symmetric vocal folds. A two-mass model was used to simulate irregular vocal fold vibrations. The threshold values of system parameters to produce irregular vibrations were decreased as a result of turbulent airflow. Periodic vibrations were then driven into the regions of irregular vibrations. Using nonlinear dynamics including Poincaré map and Lyapunov exponents, irregular vibrations were demonstrated as chaos. For the deterministic vocal-fold model with noise free and steady airflow, a fine period-doubling bifurcation cascade was shown in a bifurcation diagram. However, turbulent noise added to the vocal-fold model would induce chaotic vibrations, broaden the regions of irregular vocal fold vibrations, and inhibit the fine period-doubling bifurcations in the bifurcation diagrams. The perturbations from neurological and biomechanical effects were simulated as a random variation of the vocal fold stiffness. Turbulent noise as an external random source, as well as random stiffness perturbation as an internal random source, played important roles in the presence of irregular vocal fold vibrations.

Humans↗

PubMed2003

Delayed models for simplified musical instruments.

Most musical instruments contain, at their very basis, a continuous vibrating element (string or air column) which can be treated as a one-dimensional system. Its oscillation is obtained either through an initial condition or by means of a continuous energy input through a nonlinear device. In both cases and as a first approach, the excitation can be localized at one single point, and the continuous system can be considered as a linear one. The coupling between these two elements is often represented through a convolution integral. This convolution will be rewritten here in a way that different phenomena taking place in the continuous element (internal losses, radiation at the ends...) are separated. Different choices in the formulation of these processes and some mathematical manipulation will lead to either algebraic iterative or delayed differential equations. These equations are valid for any form of energy input. Once this energy input is defined, they can be used to simulate the behavior of different instruments in a more efficient way than that of traditional convolution. Moreover, these equations allow an analytical analysis of possible regimes using the tools of nonlinear dynamical systems (NLDS). The case of woodwinds will be emphasized throughout the paper, while that of strings will be presented briefly for the sake of completeness.

Journal Article↗

PubMed1995

Bifurcations in an asymmetric vocal-fold model.

A two-mass model of vocal-fold vibrations is analyzed with methods from nonlinear dynamics. Bifurcations are located in parameter planes of physiological interest (subglottal pressure, stiffness of the folds). It is shown that a sufficiently large tension imbalance of the left and right vocal fold induces bifurcations to subharmonic regimes, toroidal oscillations, and chaos. The corresponding attractors are characterized by phase portraits, spectra, and next-maximum maps. The relevance of these simulations for voice disorders such as laryngeal paralysis is discussed.

Humans↗

PubMed1999

Perturbation-free measurement of the harmonics-to-noise ratio in voice signals using pitch synchronous harmonic analysis.

The measurement of the harmonics-to-noise ratio (HNR) in speech signals gives an indication of the aperiodicity of the speech waveform. This may be due to the presence of jitter, shimmer, additive noise, waveshape change, or some unknown combination of these factors. In order to estimate the HNR as a measure of the additive noise component only, the contaminating effects of the other contributory components must first be removed. A pitch synchronous harmonic analysis is proposed to overcome this problem. The procedure takes advantage of the time scale compression-frequency expansion property of the Fourier series in order to eliminate jitter and shimmer. Successive spectra are added by harmonic number as opposed to frequency location, and perturbation is removed due to the fact that the relative heights of the harmonic components remain the same for scaled signals. The technique is examined on synthetically generated voice signals. A discussion of the results is given in terms of human voice signals, characterization of jitter, vocal tract filtering effects, perturbation mechanisms, nonlinear dynamics, and the possibility of developing the method for use with inverse filtering strategies.

Humans↗

PubMed1999

On pitch jumps between chest and falsetto registers in voice: data from living and excised human larynges.

The paper offers a new concept of studying abrupt chest-falsetto register transitions (jumps) based on the theory of nonlinear dynamics. The jumps were studied in an excised human larynx and in three living subjects (one female and two male). Data from the excised larynx revealed that a small and gradual change in tension of the vocal folds can cause an abrupt change of register and pitch. This gives evidence that the register jumps are manifestations of bifurcations in the vocal-fold vibratory mechanism. A hysteresis was observed; the upward register jump occurred at higher pitches and tensions than the downward jump. Due to the hysteresis, the chest and falsetto registers can be produced with practically identical laryngeal adjustments within a certain range of longitudinal tensions. The magnitude of the frequency jump was measured as the "leap ratio" F0F:F0C (fundamental frequency of the falsetto related to that of the chest register) and alternatively expressed as a corresponding musical interval, termed the "leap interval." Ranges of this leap interval were found to be different for the three living subjects (0-5 semitones for the female, 5-10 and 10-17 for the two males, respectively). These differences are considered to reflect different biomechanical properties of the vocal folds of the examined subjects. A small magnitude of the leap interval was associated with a smooth chest-falsetto transition in the female subject.

Adult↗

PubMed2004

Physiological complexity, aging, and the path to frailty.

Healthy physiological processes require the complex interaction of multiple control systems operating over multiple time scales. The output of these processes (for example, heart rate, blood pressure, hormonal rhythms, or postural sway) demonstrates complex variability that can be quantified using the concept of fractals, derived from the field of nonlinear dynamics. Complex physiological dynamics enable an organism to rapidly respond to the internal and external perturbations of everyday life. Aging and disease are associated with a loss of complexity in the dynamics of many physiological systems. This loss of complexity may reduce the ability to adapt to stress and lead to the syndrome of frailty.

Aged↗