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PubMed2001

Patterns of change in family-based aggression prevention.

Patterns of change on three intervention targets were examined in 151 families that participated in a family intervention designed to reduce and prevent children's aggressive behavior. Measures of parents' alliance and parenting skills and children's aggressive behavior were obtained at five times during the intervention. Three cluster analyses were conducted to identify patterns of change on each target. Linear and nonlinear patterns of improvement as well as two distinct patterns of no change were obtained. The patterns were differentiated by net improvement, overall level of skill, and trajectory of change. Family characteristics also differentiated the patterns and relations were found among patterns across intervention targets. The clinical implications of these findings are discussed.

Aggression↗

PubMed2000

Relationship between skin color and blood pressure in egyptian adults: results from the national hypertension project.

In many, but not all societies, dark skin color is associated with high blood pressure. Whether the association between skin color and blood pressure is independent of known determinants of blood pressure remains controversial. We examined the association between skin color and blood pressure in 835 Egyptian adults (370 men and 465 women) participating in the National Hypertension Project, a national survey of hypertension prevalence and blood pressure-related complications conducted in Egypt during 1991-1993. Skin color was assessed by measuring the concentration of cutaneous melanin in an unexposed area with the use of reflectance spectrophotometry. Higher concentrations of melanin were associated with lower body mass index, less education, manual labor (among men), and a lower urinary sodium-to-potassium ratio (among women). In multivariate regression analyses adjusted for age, body mass index, and education, there was a significant nonlinear association between blood pressure and skin color among women; in the lower to intermediate range of skin pigmentation, both systolic and diastolic blood pressures were higher in women with greater concentrations of cutaneous melanin. In men, blood pressure was not associated with skin color. When we used a subjective assessment of skin color, there was no significant difference in blood pressure between black-skinned Egyptians (predominantly of Nubian descent) and fair-skinned Egyptians for either gender. While the significant relationship in women appeared to be independent of known risk factors for hypertension, residual confounding may explain the association.

Adult↗

PubMed2004

Race is not associated with nevirapine pharmacokinetics.

The effect of race on the pharmacokinetics of nevirapine was investigated in a nonselected population. Included patients were ambulatory HIV-1-infected patients from the outpatient clinics of the Academic Medical Center and the Slotervaart Hospital, Amsterdam, The Netherlands. All patients were using nevirapine as part of their antiretroviral regimen and had at least one plasma concentration available for analysis. From the included patients, gender, age, race, hepatitis C status, baseline ASAT value, and body weight were obtained. The nonlinear mixed-effect modeling program (NONMEM) version V 1.1 was used for all analyses. Population pharmacokinetic parameters [clearance (CL/F), volume of distribution (V/F), absorption rate constant (ka)] and interindividual (IIV) and interoccasion variability (IOV) were estimated. The influence of race on the CL/F of nevirapine was tested as Negroid race versus the other races, Asian race versus the other races, and the Negroid and the Asian races as separate variables versus the Caucasian race. A database of 1732 nevirapine plasma concentrations of 383 HIV-1-infected individuals collected during 1186 outpatient clinic visits was available for this analysis. The conclusion of this study is that race is not associated with the pharmacokinetics of nevirapine, and thus requires no dose adaptations.

Adult↗

PubMed2005

Nonlinear dynamical analysis of noisy time series.

Empirical time series in the life sciences are often nonstationary and have small signal-to-noise ratios, making it difficult to accurately detect and characterize dynamical structure. The usual response to high noise is averaging, but time domain averaging is inappropriate, especially when the dynamics are nonlinear. We review alternative delay-space averaging methods based on the topology and short-term predictability of nonlinear dynamics and illustrate their application using the TISEAN software (Hegger, Kantz & Schreiber, 1999). The methods were applied to a Lorenz series, which resembles the dynamics found by Kelly, Heathcote, Heath and Longstaff (2001) in series of decision times. The Lorenz series was corrupted with up to 80% additive Gaussian noise, a lower signal-to-noise ratio than has been used in any previous test of these methods, but consistent with Kelly et al.'s data. Prediction methods performed the best for detecting nonstationarity and nonlinear dynamics, and optimal predictability provided an objective criterion for setting the parameters required by the analyses. Local linear filtering methods performed best for characterization, producing informative plots that revealed the nature of the underlying dynamics. These results suggest that a methodology based on delay-space averaging and prediction could be useful with noisy empirical data series.

Animals↗

PubMed2003

Comparing linear and nonlinear mixed model approaches to cosinor analysis.

The cosinor model, used for variables governed by circadian and other biological rhythms, is a nonlinear model in the amplitude and acrophase parameters that has a linear representation upon transformation. With linear cosinor analysis, amplitude and acrophase for each harmonic can be computed as nonlinear functions of the estimated linear regression coefficients. Here a flexible mixed model approach to cosinor analysis is considered, where the fixed effect parameters may enter nonlinearly as acrophase and amplitude for each harmonic or linearly after transformation to regression coefficients. In addition, the random effects may enter nonlinearly as subject-specific deviations from the acrophases and amplitudes or linearly as subject-specific deviations from the regression coefficients. It is also possible for the fixed effects to enter nonlinearly while the random effects enter linearly. Additionally, we evaluate whether including higher order linear harmonic terms as random effects, that is, Rao-Khatri 'covariance adjustment', improves precision. Applying the delta method to nonlinear functions of the parameters from linear mixed cosinor models to obtain approximate variances produces results that are often identical to results from nonlinear mixed models. Consequently, traditional linear cosinor analysis can often be used to estimate and compare the nonlinear parameters of interest, that is, amplitudes and acrophases, via the delta method. This is advantageous since the nonlinear mixed model may have convergence difficulties for more complex models. However, for some multiple-group analyses, the linear cosinor transformation should not be used and we clarify when the two methods are equivalent and when they differ.

Circadian Rhythm↗

PubMed1994

The ecological effects of individual exposures and nonlinear disease dynamics in populations.

To describe causally predictive relationships, model parameters and the data used to estimate them must correspond to the social context of causal actions. Causes may act directly upon the individual, during a contact between individuals, or upon a group dynamic. Assuming that outcomes in different individuals are independent puts the causal action directly upon individuals. Analyses making this assumption are thus inappropriate for infectious diseases, for which risk factors alter the outcome of contacts between individuals. Transmission during contact generates nonlinear infection dynamics. These dynamics can so attenuate exposure-infection relationships at the individual level that even risk factors causing the vast majority of infections can be missed by individual-level analyses. On the other hand, these dynamics amplify causal associations between exposure and infection at the ecological level. The amplification and attenuation derive from chains of transmission initiated by exposed individuals but involving unexposed individuals. A study of household exposure to the only vector of dengue in Mexico illustrates the phenomenon. An individual-level analysis demonstrated almost no association between exposure and infection. Ecological analysis, in contrast, demonstrated a strong association. Transmission models that are devoid of any sources of the ecological fallacy are used to illustrate how nonlinear dynamics generate such results.

Dengue↗

PubMed1994

Non-linear regression models to estimate the size of DNA fragments.

The least-squares, hyperbolic regression model is frequently used to estimate the size of unknown DNA fragments. This model avoids problems associated with semilog-plot interpolation, is computationally easy to use and provides an excellent fit to many experimental data sets. However, the methods commonly used to solve the hyperbolic regression model perform an inappropriate linearization of the original non-linear model. In this note, we describe advantages offered by standard, non-linear regression techniques, and provide computer code for a common statistical package to do these analyses.

Algorithms↗

PubMed1992

Reassessing benzene cancer risks using internal doses.

Human cancer risks from benzene exposure have previously been estimated by regulatory agencies based primarily on epidemiological data, with supporting evidence provided by animal bioassay data. This paper reexamines the animal-based risk assessments for benzene using physiologically-based pharmacokinetic (PBPK) models of benzene metabolism in animals and humans. It demonstrates that internal doses (interpreted as total benzene metabolites formed) from oral gavage experiments in mice are well predicted by a PBPK model developed by Travis et al. Both the data and the model outputs can also be accurately described by the simple nonlinear regression model total metabolites = 76.4x/(80.75 + x), where x = administered dose in mg/kg/day. Thus, PBPK modeling validates the use of such nonlinear regression models, previously used by Bailer and Hoel. An important finding is that refitting the linearized multistage (LMS) model family to internal doses and observed responses changes the maximum-likelihood estimate (MLE) dose-response curve for mice from linear-quadratic to cubic, leading to low-dose risk estimates smaller than in previous risk assessments. This is consistent with the conclusion for mice from the Bailer and Hoel analysis. An innovation in this paper is estimation of internal doses for humans based on a PBPK model (and the regression model approximating it) rather than on interspecies dose conversions. Estimates of human risks at low doses are reduced by the use of internal dose estimates when the estimates are obtained from a PBPK model, in contrast to Bailer and Hoel's findings based on interspecies dose conversion. Sensitivity analyses and comparisons with epidemiological data and risk models suggest that our finding of a nonlinear MLE dose-response curve at low doses is robust to changes in assumptions and more consistent with epidemiological data than earlier risk models.

Animals↗

PubMed1999

Nonlinear curve fitting for bioelectrical impedance data analysis: a minimum ellipsoid volume method.

Bioelectrical impedance spectroscopy has become a widely used method with various applications in physiological and clinical investigations. Its measurement results are often analysed using the Cole-Cole model in an attempt to relate its parameters to structural or physiological characteristics of the studied object. The model parameter values are usually assessed by nonlinear curve fitting based on the least mean square method. A new approach is proposed, leading to better accuracy. It is based on the notion that the difference between measured and model parameter values is randomly distributed with zero mean. The values of the unknown parameters are then deduced by minimizing the covariance matrix determinant. This method can be considered as a minimization of the volume of an ellipsoid, or ajoint minimization of two regressions having the same argument and common parameters.

Electric Impedance↗

PubMed1994

Simulations of X and Y retinal ganglion cell behavior with a nonlinear push-pull model of spatiotemporal retinal processing.

This article describes a nonlinear model of neural processing in the vertebrate retina, comprising model photoreceptors, model push-pull bipolar cells, and model ganglion cells. Previous analyses and simulations have shown that with a choice of parameters that mimics beta cells, the model exhibits X-like linear spatial summation (null response to contrast-reversed gratings) in spite of photoreceptor nonlinearities; on the other hand, a choice of parameters that mimics alpha cells leads to Y-like frequency doubling. This article extends the previous work by showing that the model can replicate qualitatively many of the original findings on X and Y cells with a fixed choice of parameters. The results generally support the hypothesis that X and Y cells can be seen as functional variants of a single neural circuit. The model also suggests that both depolarizing and hyperpolarizing bipolar cells converge onto both ON and OFF ganglion cell types. The push-pull connectivity enables ganglion cells to remain sensitive to deviations about the mean output level of nonlinear photoreceptors. These and other properties of the push-pull model are discussed in the general context of retinal processing of spatiotemporal luminance patterns.

Adaptation, Physiological↗

PubMed2002

Quantitative analyses of anaerobic wastewater treatment processes: identifiability and parameter estimation.

We investigated the problem of identifying the parameters of a nonlinear fifth order model describing the population dynamics of two main bacterial groups in an anaerobic wastewater treatment process. In addition to addressing problems concerning structural and practical identifiability, we also analyzed how mathematical descriptions of bacterial population dynamics can model real data. Using three data sets recorded under different experimental conditions, we estimated important biochemical parameters and demonstrated that our model could describe the data successfully. Parameters, which are simultaneously determined using information from all three experiments, have more reliable estimates. We conclude that, after appropriate estimation, this model can be used for optimization and the control of continuous processes.

Anaerobiosis↗

PubMed2004

Determination of dissociation constants for a heparin-binding domain of amyloid precursor protein and heparins or heparan sulfate by affinity capillary electrophoresis.

Dynamic affinity capillary electrophoresis (ACE) was used for determining the binding constants between heparin-like glycosaminoglycans and the (96-110) heparin-binding domain of amyloid precursor protein (APP). The migration time shift of the (96-110) APP peptide was monitored as the concentration of heparin was increased in the background electrolyte. The compounds investigated included low-molecular-weight heparin, porcine mucosa heparin, and heparan sulfate. Change in mobility as a function of glycosaminoglycan concentration was plotted using both linear regression (Scatchard analysis) and nonlinear regression. Dissociation constants (K(d)) were determined and compared for both sets of analyses with the low-molecular-weight heparin giving the most reproducible results and best fit with a K(d) value of 3.9 microM.

Amyloid beta-Protein Precursor↗

PubMed2001

Convergence of the Integration Dynamics of the Construction-Integration Model.

The connectionist network corresponding to the nonlinear integration dynamical system associated with Kintsch's construction-integration (CI) model is analysed with linear algebra tools. This addresses some theoretical questions raised and left unanswered by Rodenhausen (1992, Psychological Review 99, 547-549). A mathematical characterization for equilibrium points, which allows an a priori enumeration of all possible asymptotic states for the integration dynamical system, given a connectivity matrix, is given. The dynamics of convergence of the integration dynamical system is characterized in some detail as well. This provides a tool for understanding CI simulations and helps in particular to let us know to what extent the outcome will depend on the initial conditions. The criteria also provide a new mathematical analysis which allows for the explicit calculation of asymptotic states of the integration process without requiring computer simulation experiments. The new mathematical analysis should facilitate comparisons of the model's predictions with behavioural data. Copyright 2001 Academic Press.

Journal Article↗

PubMed1983

Dynamics of human neutrophil receptors for the chemoattractant fmet-leu-phe.

Neutrophils contain an intracellular pool of binding sites for the chemoattractant fmet-leu-phe with the same density as specific granules. This pool of receptors appears to be translocated to the plasma membrane during degranulation and may be important for receptor renewal during chemotaxis. Scatchard analyses of fmet-leu-phe binding to neutrophils and isolated plasma membranes are nonlinear and calculated Hill coefficients of binding to these fractions were about 0.67, suggesting negative cooperativity and/or heterogeneity of receptors. Some of the features of the nonlinear Scatchard curves may reflect heterogeneity of binding among cells since binding of fmet-leu-phe-lys-fluorescein to cells is heterogeneous when simultaneously monitored in the fluorescence activated cell sorter with a fluorescent probe of membrane potential. Following addition of a chemoattractant cells showing a depolarization have more chemoattractant associated with them than cells showing no change of membrane potential or a hyperpolarization. The cell associated chemoattractant is largely in a displaceable pool on the cells showing depolarization while it is in a nondisplaceable pool in the cells that either do not respond or show a hyperpolarization. Studies of the adaptation of human neutrophils responsiveness to fmet-leu-phe elicited membrane potential changes indicate that fmet-leu-phe stimulated decreases in receptor affinity accompany such adaptation. This decreased affinity appears to involve heterogeneity and/or negative cooperative interaction of receptors. The dynamics of chemoattractant receptors that have been reviewed provide further insights for studying the concepts behind the spatial and temporal mechanisms by which cells respond and adapt to a gradient of chemoattractant.

Adaptation, Physiological↗

PubMed1997

Effects of aging on the cerebral distribution of technetium-99m hexamethylpropylene amine oxime in healthy humans.

Some brain functions decline at a linear rate throughout adulthood. Others remain relatively stable until very late in the life cycle. This study characterized the effects of aging on the regional cerebral distribution of hexamethylpropylene amine oxime (HMPAO) in healthy human volunteers. The sample consisted of 26 men and 18 women with a mean age of 41.6+/-14.9 years (range: 19-73). Their past medical histories, physical examinations, and laboratory screening tests were normal. Single-photon emission tomography (SPET) scans of the brain were performed with a standardized acquisition and processing protocol on a triple-headed camera equipped with fan beam collimators. A 3-D restorative filter and a correction for uniform attenuation were applied before the images were reinterpolated in planes parallel to the line connecting the frontal and occipital poles. Mean counts per pixel were measured in multiple regions of interest (ROIs) within each hemisphere by custom fitting a set of templates to the images. The mean activity in each ROI was compared with the mean activity per pixel in the whole brain. Regression analyses were used to relate the activity ratios to age with both linear and nonlinear models. The relative concentration of radioactivity decreased significantly with age in most, but not all, gray matter structures. It increased in the white matter regions. The nonlinear model of aging fit the data significantly better than a straight line did. Most of the changes with age occurred during young adulthood. No further changes were detectable after the onset of middle age. The median breakpoint age at which the rate of change became negligible was 36.6 years. Aging significantly affects the relative uptake of HMPAO in healthy humans. It decreases in many gray matter regions and increases in most white matter regions. However, the changes do not appear to be linear. Most seem to occur during young adulthood before people reach their late thirties. The distribution then appears to remain relatively stable throughout middle age.

Adult↗

PubMed2004

Compact program resolves overlapping voltammetric peaks.

A simple self-contained program designed to separate overlapping peaks from electrochemical analyses is presented. Combining an original interactive way to define initial parameter estimates with nonlinear curve fitting based on the simplex method of optimization, it allows the user to resolve voltammograms consisting of 2 to 5 analytical peaks raised on a straight base line. The program provides highly intuitive interface, easy operation, and straightforward result documentation. A free package including the program, three data files and user instructions is available on request.

Journal Article↗

PubMed1984

Application of Taylor's hypothesis to an unsteady convective field for the spectral analysis of turbulence in the aorta.

Two types of unsteadiness must be considered when spectral analysis is applied to unsteady turbulence such as that found in the aorta. Firstly, the statistical properties of the turbulence itself change in time and so the definition of spectral density must be reconsidered. Secondly, the turbulent velocity fluctuations, whether they are steady or unsteady, are carried by an unsteady convective velocity which alters their properties as seen by a stationary observer. In the present study, unsteadiness of turbulence in the latter sense is discussed by applying Taylor's hypothesis of 'frozen turbulence' to turbulence with an unsteady convective velocity. If both a 'frozen' pattern of turbulence and a constant convective velocity are assumed, measured frequency spectra can be easily transformed into wavenumber (spatial) spectra, usually as a trivial part of normalisation. In the case of unsteady turbulence, however, the convection velocity is no longer constant and the conventional method can not be used. A new method of estimating the spatial properties of unsteady turbulence is proposed in which the temporal fluctuations of the turbulent velocity are transformed into spatial fluctuations using a nonlinear transformation based upon the unsteady convective velocity. The transformed data are then Fourier analysed to yield a wavenumber spectrum directly. The proposed method is applied to data obtained in the canine ascending aorta. Spectra calculated by the proposed method differ significantly from those obtained by the conventional method, particularly in the high wavenumber (or frequency) range. This difference is discussed as an 'aliasing' phenomenon that has also been known in steady turbulence.

Animals↗

PubMed1996

Restraint, dieting, and the continuum model of bulimia nervosa.

The authors evaluated the continuity model of bulimia nervosa, which suggests that bulimia results from extreme weight concern and dieting practices. Individuals with bulimia, current dieters, restrained nondieters, and unrestrained nondieters were compared on measures of general psychopathology, eating-disorder-specific psychopathology, and overeating. Multiple methods, including questionnaires, clinical interviews, and food records, were used to collect data. The continuity and discontinuity models were tested with trend and regression analyses. The results of most analyses were consistent with the continuity perspective. However, binge eating behaviour exhibited a clear nonlinear trend, which occurred because binge eating was common in bulimic individuals but virtually non-existent in the other 3 groups. Current dieters scored higher than restrained nondieters on restraint/ weight concern, but not on psychopathology or binge eating. Overall, the results suggest that "normal" dieting is associated with psychological, but not consummatory, symptoms of bulimia.

Adult↗