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PubMed2006

Biological responses to environmental forcing: the linear tracking window hypothesis.

Determining the relative contributions of intrinsic and extrinsic processes to the regulation of biological populations has been a recurrent ecological issue. Recent discussions concerning ecosystem "regime shifts" again raise the question of whether population fluctuations are mainly controlled by external forcing. Results of nonlinear time series analyses indicate that pelagic populations typically do not passively track stochastic environmental variables. Rather, population dynamics are better described as nonlinear amplification of physical forcing by biological interactions. However, we illustrate that in some cases populations do show linear tracking of the physical environment. To explain why population dynamics can sometimes be linear, we propose the linear tracking window hypothesis: populations are most likely to track the stochastic environmental forcing when their generation time matches the characteristic time scale of the environmental signal. While our observations follow this hypothesis well, our results indicate that the linear tracking window is a necessary but not a sufficient condition.

Animals↗

PubMed2003

Discerning nonstationarity from nonlinearity in seizure-free and preseizure EEG recordings from epilepsy patients.

A number of recent studies indicate that nonlinear electroencephalogram (EEG) analyses allow to define a state predictive of an impending epileptic seizure. In this paper, we combine a method for detecting nonlinear determinism with a novel test for stationarity to characterize EEG recordings from both the seizure-free interval and the preseizure phase. We discuss differences between these periods, particularly an increased occurrence of stationary, nonlinear segments prior to seizures. These differences seem most prominent for recording sites within the seizure-generating area and for EEG segments less than one minute's length.

Electroencephalography↗

PubMedDate not supplied

Linear and nonlinear measures and seizure anticipation in temporal lobe epilepsy.

In a recent paper, we showed that the value of a nonlinear quantity computed from scalp electrode data was correlated with the time to a seizure in patients with temporal lobe epilepsy. In this paper we study the relationship between the linear and nonlinear content and analyses of the scalp data. We do this in two ways. First, using surrogate data methods, we show that there is important nonlinear structure in the scalp electrode data to which our methods are sensitive. Second, we study the behavior of some simple linear metrics on the same set of scalp data to see whether the nonlinear metrics contain additional information not carried by the linear measures. We find that, while the nonlinear measures are correlated with time to seizure, the linear measures are not, over the time scales we have defined. The linear and nonlinear measures are themselves apparently linearly correlated, but that correlation can be ascribed to the influence of a small set of outliers, associated with muscle artifact. A remaining, more subtle relation between the variance of the values of a nonlinear measure and the expectation value of a linear measure persists. Implications of our observations are discussed.

Electroencephalography↗

PubMedDate not supplied

Sensitivity analysis for evaluating nonlinear models of lung mechanics.

We present a combined theoretical and numerical procedure for sensitivity analyses of lung mechanics models that are nonlinear in both state variables and parameters. We apply the analyses to a recently proposed nonlinear lung model which incorporates a wide range of potential nonlinear identification conditions including nonlinear viscoelastic tissues, airway inhomogeneities via a parallel airway resistance distribution function, and a nonlinear block-structure paradigm. Additionally, we examine a system identification procedure which fits time- and frequency-domain data simultaneously. Model nonlinearities motivate sensitivity analyses involving numerical approximation of sensitivity coefficients. Examination of the normalized sensitivity coefficients provides direct insight on the relative importance of each model parameter, and hence the respective mechanism. More formal quantification of parameter uniqueness requires approximation of the paired and multidimensional parameter confidence regions. Combined with parameter estimation, we use the sensitivity analyses to justify tissue nonlinearities in modeling of lung mechanics for healthy and airway constricted conditions, and to justify both airway inhomogeneities and tissue nonlinearities during bronchoconstriction. The tools in this paper are general and can be applied to a wide class of nonlinear models.

Airway Resistance↗

PubMed2003

Parametric processes of a strong laser in partially ionized plasmas.

The effects of the nonlinear polarization in a partially ionized plasma on the parametric processes of a strong laser are discussed. The nonlinear mode coupling equations and the linear growth rate of stimulated Raman scattering (SRS) and stimulated Brillouin scattering (SBS) are derived. The numerical analyses for the nonlinear evolutions of SRS and SBS processes are given. Various effects of the second and the third order nonlinear susceptibilities on the SRS and SBS processes are discussed. The nonlinear evolutions of SRS and SBS processes are affected more efficiently than their linear growth rates by the nonlinear susceptibility.

Journal Article↗

PubMed1999

A biomechanical study of posterolateral lumbar fusion using a three-dimensional nonlinear finite element method.

Biomechanical analyses under compressive load, flexion, and extension torque were performed, using a nonlinear three-dimensional finite element method, to evaluate stability in posterolateral fusion. Effects of facet fusion and disc denucleation on posterolateral fusion were also examined. Using an initially prepared L4-5 motion segment model, we prepared a denucleation model, posterolateral fusion models classified by presence or absence of denucleation and facet fusion, and an interbody fusion model. In the denucleation model, rigidity was less than in the normal model, and maximum rigidity was analyzed for the interbody fusion model. The effect of denucleation on posterolateral fusion was also analyzed. Taking into account the instability of the anterior elements, including the intervertebral disc, appears to be clinically important. In the posterolateral fusion model under compressive load, the axis of rotation moved principally toward the fusion mass, and axial displacement and flexion rotation were induced. Sagittal rotation angles under flexion and extension torque were 1.5 degrees -2.3 degrees at a maximum moment of 15 N-m, demonstrating elasticity of posterolateral fusion. When combined with facet fusion, posterolateral fusion yielded increase of load transfer across the lamina and decrease of rotation angle of about 10% under flexion-extension torque. Adjunctive clinical use of facet fusion should permit more solid posterolateral fusion.

Biomechanical Phenomena↗

PubMed2000

Ethanol pharmacokinetics in white women: nonlinear model fitting versus zero-order elimination analyses.

BACKGROUND: Studies have shown repeatedly that ethanol pharmacokinetics are not linear, yet most researchers still determine ethanol elimination by linear, zero-order kinetics. The goals of the present work were to: (1) fit four nonlinear pharmacokinetic models to mean breath alcohol concentration (BrAC)-time data of 27 women and determine the best-fit model; (2) fit the determined best-fit model to individual BrAC data and estimate the pharmacokinetic parameters; and (3) compare the method of nonlinear model fitting with the classical zero-order elimination method and determine in which cases the classical approach is justified. METHODS: Twenty-seven healthy white women ingested four drinks (total of 0.67 g x kg(-1)) of ethanol on two test days. Approximately 24 breath ethanol samples (for pharmacokinetic analyses) and one blood sample (for hormonal markers) were taken per day. Pharmacokinetic model evaluation was based on the coefficient of variation, the weighted residual sum of squares, and the sequence of the weighted residuals. Because hormonal changes across the menstrual cycle did not significantly influence ethanol pharmacokinetics, data from the two test days were pooled. RESULTS: The best-fit model was a one-compartment open model with first-order absorption and sequential first-order elimination, followed by Michaelis-Menten elimination kinetics. Fitting this model to the individual BrAC data yielded mean ka = 0.062 hr(-1), Vd = 0.457 L x kg(-1), ke = 0.011 hr(-1), Vmax = 0.136 g x L(-1) x hr(-1), and Km = 0.096 g x L(-1). For the classical analyses, mean time to peak BrAC = 1.83 hr, disappearance rate = 0.179 g x L(-1) x hr(-1), and area under the blood ethanol-time curve (AUC) = 2.884 g x L(-1) x hr. Correlational analyses showed that more frequent drinkers eliminated ethanol significantly faster and reached significantly lower AUC than less frequent drinkers. CONCLUSIONS: After multiple dose ingestion in white women, classical zero-order elimination analyses can be applied only to a limited portion of the descending BrAC-time curve. They seem justified and practical from 0.5 hr after peak BrAC until BrAC reaches 0.2 g x L(-1). To describe ethanol pharmacokinetics across the entire BrAC-time curve, however, sophisticated nonlinear model fitting is required.

Adult↗

PubMed2001

Variability of the electric organ discharge interval duration in resting Gymnotus carapo.

We recorded the electric organ discharges of resting Gymnotus carapo specimens. We analyzed the time series formed by the sequence of interdischarge intervals. Nonlinear prediction, false nearest neighbor analyses, and comparison between the performance of nonlinear and linear autoregressive models fitted to the data indicated that nonlinear correlations between intervals were absent, or were present to a minor extent only. Following these analyses, we showed that linear autoregressive models with combined Gaussian and shot noise reproduced the variability and correlations of the resting discharge pattern. We discuss the implications of our findings for the mechanisms underlying the timing of electric organ discharge generation. We also argue that autoregressive models can be used to evaluate the changes arising during a wide variety of behaviors, such as the modification in the discharge intervals during interaction between fish pairs.

Animals↗

PubMed1994

Analysis of role of bone compliance on mechanics of a lumbar motion segment.

A large deformation elasto-static finite element formulation is developed and used for the determination of the role of bone compliance in mechanics of a lumbar motion segment. This is done by simulating each vertebra as a deformable body with realistic material properties, as a deformable body with stiffer or softer mechanical properties, as a single rigid body, or finally as two rigid bodies attached by deformable beams. The single loadings of axial compression, flexion moment, extension moment, and axial torque are considered. The results indicate the marked effect of alteration in bone material properties on biomechanics of lumbar segments specially under larger loads. The biomechanical studies of the lumbar spine should, therefore, be performed and evaluated in the light of such dependency. A model for bony vertebrae is finally proposed that preserves both the accuracy and the cost-efficiency in nonlinear finite element analyses of spinal multi-motion segment systems.

Biomechanical Phenomena↗

PubMed2004

Evaluation of combination chemotherapy: integration of nonlinear regression, curve shift, isobologram, and combination index analyses.

Isobologram and combination index (CI) analyses are the two most popular methods for evaluating drug interactions in combination cancer chemotherapy. As the commonly used CI-based software program uses linear regression, our first objective was to evaluate the effects of logarithmic data transformation on data analysis and conclusions. Monte-Carlo simulations were conducted with experimentally relevant parameter values to generate error-containing effect or concentration-effect data of single agents and combinations. The simulated data were then analyzed with linear and nonlinear regression. The results showed that data transformation reduced the accuracy and precision of the regression-derived IC(50), curve shape parameter and CI values. Furthermore, as neither isobologram nor CI analyses provide output of concentration-effect curves for investigator evaluation, our second objective was to develop a method and the associated computer program/algorithm to (a) normalize drug concentrations in IC(50) equivalents and thereby enable simultaneous presentation of the curves for single agents and combinations in a single plot for visual inspection of potential curve shifts, (b) analyze concentration-effect data with nonlinear regression, and (c) use the curve shift analysis simultaneously with isobologram and CI analyses. The applicability of this method was shown with experimentally obtained data for single agent doxorubicin and suramin and their combinations in cultured tumor cells. In summary, this method, by incorporating nonlinear regression and curve shift analysis, although retaining the attractive features of isobologram and CI analyses, reduced the potential errors introduced by logarithmic data transformation, enabled visual inspection of data variability and goodness of fit of regression analysis, and simultaneously provided information on the extent of drug interaction at different combination ratios/concentrations and at different effect levels.

Animals↗

PubMed1990

Numerical 3D-stimulation of pulsatile wall shear stress in an arterial T-bifurcation model.

The structure of pulsatile blood flow and wall shear stress in a 90 degrees T-bifurcation model is analysed numerically. The nonlinear Navier-Stokes equations for time-dependent incompressible Newtonian fluid flow are approximated using a newly developed pressure correction, finite element method. The wall shear stress is calculated from the finite element velocity field. The investigation shows viscous flow phenomena such as flow separation and stagnation and the distribution of high and low wall shear stress during the pulse cycle. Furthermore, the effect of a sharp corner at the bifurcation edge on the wall shear stress is analysed. Detailed local flow investigation is required to examine fluid dynamic contribution to the development of arterial diseases such as atherosclerosis and thrombosis.

Arteries↗

PubMed2000

Race and sex influence clearance of nifedipine: results of a population study.

OBJECTIVE: To estimate oral clearance of nifedipine and to determine demographic and clinical covariates that affect nifedipine clearance in a clinical population. METHODS: Apparent oral clearance of nifedipine and protein binding were measured in 226 patients receiving sustained-release nifedipine formulations for hypertension and coronary artery disease (black men, n = 111; black women, n = 27; white men, n = 64; white women, n = 24). Mean age +/- SD was 71 +/- 11 years, and mean weight was 86 +/- 17 kg. Nifedipine concentrations were analyzed by HPLC, protein binding was measured by equilibrium dialysis, clearance and covariate effects were estimated by a nonlinear mixed effects population model, and statistical analyses were performed by a nonlinear mixed-effects model (clearance) and ANOVA (protein binding). RESULTS: Clearance was significantly slower in black subjects (8.9 +/- 0.7 mL/min/kg; mean +/- SE) compared with white subjects (11.6 +/- 0.8 mL/min/kg; P = .00004) and in men compared with women (9.3 +/- 0.6 versus 12.1 +/- 1.5 mL/min/kg; P = .0021). Reported alcohol use (alcohol, 8.6 +/- 1.1 versus no alcohol, 10.8 +/- 0.6 mL/min/kg; P = .0002) and smoking status (smoker, 8.8 +/- 2.0 versus nonsmoker, 10.2 +/- 0.6 mL/min/kg; P = .0362) also affected nifedipine clearance. Race and sex had no effect on protein binding of nifedipine (P = .29 and P = .44, respectively). No effects of age, stable coronary artery disease, or reported intake of beta-blockers on nifedipine clearance were detected in this primarily elderly population with hypertension. CONCLUSIONS: The data suggest that race, sex, and environmental factors are identifiable sources of interindividual variation in the oral clearance of nifedipine, a CYP3A substrate. Our experience also suggests that data from clinical populations may be biased with regard to age, sex, and formulation selection, and covariates may not be independently distributed, which can limit analyses.

Aged↗

PubMed1999

A method of graphically analyzing substrate-inhibition kinetics.

A model of substrate inhibition for enzyme catalysis was extended to describe the kinetics of photosynthetic production of ethylene by a recombinant cyanobacterium, which exhibits light-inhibition behavior similar to the substrate-inhibition behavior in enzyme reactions. To check the validity of the model against the experimental data, the model equation, which contains three kinetic parameters, was transformed so that a linear plot of the data could be made. The plot yielded reasonable linearity, and the parameter values could be estimated from the plot. The linear-plot approach was then applied to other inhibition kinetics including substrate inhibition of enzyme reactions and inhibitory growth of bacteria, whose analyses would otherwise require nonlinear least-squares fits or data measured in constrained ranges. Plots for three totally different systems all showed reasonable linearity, which enabled visual validation of the assumed kinetics. Parameter values evaluated from the plots were compared with results of nonlinear least-squares fits. A normalized linear plot for all the results discussed in this work is also presented, where dimensionless rates as a function of dimensionless concentration lie in a straight line. The linear-plot approach is expected to be complementary to nonlinear least-squares fits and other currently used methods in analyses of substrate-inhibition kinetics. Copyright 1999 John Wiley & Sons, Inc.

Journal Article↗

PubMed1993

The relation between head size and auditory brain-stem response interpeak latency maturation.

In developmental populations, duration of auditory brain-stem response (ABR) I-III, III-V, and I-V vary substantially across individuals, particularly among preterm infants. Adult ABR interpeak latency has a strong correlation with brain-stem size and weaker correlation with head size. To determine if head size might contribute to this increased interpeak latency variability among infants, ABR data were normalized based on head circumference. Normalization by head circumference did not reduce interpeak variability. Further analyses revealed a negative correlation between interpeak latency and head circumference that varied as a function of age. Before 42 weeks conceptional age (CA), a significant relation exists between increased head circumference and decreased duration of the III-V and I-V intervals, but not the I-III interval. For infants older than 42 weeks CA, there was a significant relation between increased head circumference and decreased duration for the I-III intervals but not the III-V and I-V intervals. An age-dependent correlation between decreasing interpeak latency and increasing head circumference suggests that improved neural transmission through the auditory nerve and brain-stem pathway offset or even overcompensate for developmental lengthening of the sensory pathway. Also, developmental time constants obtained from nonlinear curve fit analyses were shorter for normalized than non-normalized data, particularly for the I-V interval. Therefore, correction of ABR data for the length of the sensory pathway may be important to estimate accurately maturation rate for developmental populations.

Acoustic Stimulation↗

PubMed1996

Influence of size, shape and properties on the mechanics of axisymmetric saccular aneurysms.

Rupture of intracranial saccular aneurysms is the most common cause of spontaneous subarachnoid hemorrhage which, despite advances in neurosurgery, continues to result in significant morbidity and mortality. Currently, the decision to treat a diagnosed, unruptured aneurysm is based primarily on the maximum dimension of the lesion even though there is controversy over the 'critical size' (e.g. many 'large' lesions do not rupture whereas some 'small' ones do). There is a need, therefore, for improved predictors of the rupture-potential of these lesions. In this paper, we show that it is highly unlikely that saccular aneurysms expand or rupture due to a limit point instability, and suggest that a rupture-criterion should be based on local multiaxial states of stress or strain. Moreover, our results from nonlinear finite element analyses reveal important roles of lesion shape, material properties, and loading conditions, not just size, in governing the distributions of stress and strain within a sub-class of axisymmetric saccular aneurysms. For example, we find that maximum biaxial stresses and strains are most often at the fundus, where rupture tends to occur, and that maximum stresses increase markedly with increases in lesion size, the ratio of neck diameter to lesion height, and the distending transmural pressure.

Aneurysm, Ruptured↗

PubMed2001

Bouncing a ball: tuning into dynamic stability.

Rhythmically bouncing a ball with a racket was investigated and modeled with a nonlinear map. Model analyses provided a variable defining a dynamically stable solution that obviates computationally expensive corrections. Three experiments evaluated whether dynamic stability is optimized and what perceptual support is necessary for stable behavior. Two hypotheses were tested: (a) Performance is stable if racket acceleration is negative at impact, and (b) variability is lowest at an impact acceleration between -4 and -1 m/s2. In Experiment 1 participants performed the task, eyes open or closed, bouncing a ball confined to a 1-dimensional trajectory. Experiment 2 eliminated constraints on racket and ball trajectory. Experiment 3 excluded visual or haptic information. Movements were performed with negative racket accelerations in the range of highest stability. Performance with eyes closed was more variable, leaving acceleration unaffected. With haptic information, performance was more stable than with visual information alone.

Adult↗

PubMed2005

Evolving concepts on the pathophysiology of absence seizures: the cortical focus theory.

Four main theories on the pathophysiology of generalized absence seizures have been proposed. The "centrencephalic" theory, proposed in 1954, suggested that discharges originate from a deep-seated diffusely projecting subcortical pacemaker in the midline thalamus. This concept was refined in 1991 with the "thalamic clock" theory, implying that the reticular thalamic nucleus contains the pacemaker cells for the thalamic clock, imposing its rhythm to the cortex. According to other investigators, however, the cortex seems to play a leading role. They suggested that spike-wave discharges have a focal onset in the cortex and are generalized through a rapid propagation. In the "corticoreticular" theory, postulated in 1968, spike-wave discharges are linked to the thalamocortical mechanisms that generate spindles. Rhythmic spindle oscillations generated in the thalamus are transformed into spike-wave discharges when the cortex is hyperexcitable. A 2002 study confirmed in epileptic rats that a functionally intact thalamocortical network is required for the generation of spike-wave discharges. The corticothalamic interrelationships were investigated by means of nonlinear association signal analyses of multiple spike-wave discharges. This showed a consistent focus within the perioral region of the somatosensory cortex. From this focus, seizure activity generalizes rapidly over the cortex. During the first cycles of the seizure the cortex drives the thalamus, while thereafter cortex and thalamus drive each other, thus amplifying and maintaining the rhythmic discharge. In this way the "cortical focus" theory for generalized absence epilepsy bridges cortical and thalamic theories.

Animals↗

PubMed2002

Relationship between changes in hemoglobin level and quality of life during chemotherapy in anemic cancer patients receiving epoetin alfa therapy.

BACKGROUND: Hemoglobin increases have been associated with quality of life (QOL) improvements in anemic cancer patients treated with epoetin alfa, but intervention generally has been reserved for symptomatic anemia or hemoglobin < 10 g/dL. Relationships among hemoglobin, functional status, and patient reported QOL have not been well characterized. METHODS: Data from two open-label, community-based trials of epoetin alfa therapy that enrolled 4382 anemic cancer patients undergoing chemotherapy were used to evaluate the relationship between hemoglobin changes and QOL changes. The authors measured QOL using the Linear Analog Scale Assessment (LASA) and the more detailed, disease-specific Functional Assessment of Cancer Therapy-Anemia (FACT-An) instrument. Analyses were performed to determine the incremental change in QOL associated with hemoglobin increases (1 g/dL increments). RESULTS: Cross-sectional analyses showed a nonlinear relationship and significant positive correlation between high hemoglobin levels and high LASA and FACT-An scores (r = 0.25 and 0.29, respectively, P < 0.01). Patients with hemoglobin increases of > or = 2 g/dL reported statistically significant improvements in five FACT-An items selected a priori specifically to reflect functional capacity. An incremental analysis used regression methods to identify the longitudinal relationship between incremental changes in hemoglobin and QOL scores. This relationship was found to be nonlinear, with the maximum QOL gain occurring at a hemoglobin level of 12 g/dL (range, 11-13 g/dL). Patients with low baseline QOL scores and longer time periods between baseline and final QOL assessments experienced significantly (P < 0.05) greater increases in overall QOL. Progressive disease at baseline, change in disease status from baseline to end of study, and increase in self-reported pain or nausea all had significant (P < 0.05) negative effects on QOL scores. CONCLUSIONS: A direct relationship exists between hemoglobin increases during epoetin alfa therapy and corresponding QOL improvements in cancer patients receiving chemotherapy across the clinically relevant hemoglobin range of 8-14 g/dL. These data suggest that the maximal incremental gain in QOL occurs when hemoglobin is in the range of 11-13 g/dL.

Anemia↗