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A nonparametric comparison of monomolecular growth curves: application to western painted turtle data.

Intractable distributional assumptions are generated in parametric analyses comparing groups of subjects described by nonlinear growth models. The distributional situation becomes more complex when pointwise mean curves best describe group growth (instead of curves based on mean parameters). An interval specific randomization test is developed to handle monomolecular growth models. The need for the technique was motivated by a study describing longitudinal growth data from the annuli on abdominal scutes of groups of western painted turtles. The analyses indicate that female turtles grow larger than male through the first seven years of life. The analytical procedures developed for these turtles are useful in the description and analyses of many other growth processes.

Animals↗

Biomechanical comparisons of three different tibial tunnel directions in posterior cruciate ligament reconstruction.

PURPOSE: To investigate the effects of 3 different tunnel directions on the outcomes of posterior cruciate ligament (PCL) reconstruction surgery based on the forces exerted on the replacement ligament from a biomechanical point of view. The 3 tunnel directions in the proximal tibia are medial, central, and lateral. TYPE OF STUDY: Biomechanical study. METHODS: The forces exerted on the replaced PCL were calculated using finite element analyses as well as measurements from 6 cadavers. The results of the 3 surgical approaches were then compared. In the finite element analyses, the replaced ligament was assumed to have nonlinear elastic as well as viscoelastic properties. To simulate the overload in exercise, the femur was forced to move in the anterior direction abruptly while the tibia was held. From numerical analyses, the resultant forces, von Mises stresses, and maximum shear stresses on the replacement PCLs were calculated and compared. In the cadaveric study, a pressure-sensitive thin film was inserted between the replacement PCL and the killer turn area of the tibia. The color changes in films were evaluated using digital image processing in each case. RESULTS: The medial approach showed remarkably higher stresses and forces on the interface between the replaced PCL and the killer turn in both the numerical and cadaveric study. In contrast, the lateral approach showed the lowest stresses. CONCLUSIONS: The numerical and cadaveric studies indicate that the lateral approach is highly promising compared with the other approaches. CLINICAL RELEVANCE: The lateral approach has been shown to minimize stress concentration around the killer turn during in vitro experiments and a computer simulation of PCL reconstruction for long-term stability. The lateral approach technique appears to provide a promising clinical outcome in patients undergoing PCL reconstruction.

Arthroscopy↗

Biological populations with nonoverlapping generations: stable points, stable cycles, and chaos.

Some of the simplest nonlinear difference equations describing the growth of biological populations with nonoverlapping generations can exhibit a remarkable spectrum of dynamical behavior, from stable equilibrium points, to stable cyclic oscillations between 2 population points, to stable cycles with 4, 8, 16, . . . points, through to a chaotic regime in which (depending on the initial population value) cycles of any period, or even totally aperiodic but boundedpopulation fluctuations, can occur. This rich dynamical structure is overlooked in conventional linearized analyses; its existence in such fully deterministic nonlinear difference equations is a fact of considerable mathematical and ecological interest.

Ecology↗

Double-stranded helices and molecular zippers assembled from single-stranded coordination polymers directed by supramolecular interactions.

Using three nonlinear dicarboxylates, isophthalate (ipa), 4,4'-oxybis(benzoate) (oba), and ethylenedi(4-oxybenzoate) (eoba), we have prepared five neutral infinite copper(II) dicarboxylate coordination polymers containing lateral aromatic chelate ligands, namely [Cu(ipa)(2,2'-bpy)]n.2nH2O (1), [Cu2(ipa)2(phen)2H2O]n (2), [Cu(oba)(phen)]n (3), [Cu(oba)(2,2'-bpy)]n (4), and [Cu(eoba)(phen)]n (5; 2,2'-bpy = 2,2'-bipyridine, phen = 1,10-phenanthroline) by hydrothermal synthesis. X-ray single-crystal structural analyses of these complexes reveal that the nonlinear flexible or V-shaped dicarboxylates can induce the helicity or flexuousity of the polymeric chains and aromatic chelate ligands are important in providing potential supramolecular recognition sites for pi-pi aromatic stacking interactions. An appropriate combination of the bridging dicarboxylate and aromatic chelate can induce a pair of single-stranded helical or flexuous chains to generate a double-stranded helix or molecular zipper through supramolecular interactions, respectively.

Journal Article↗

Heart rate dynamics in low risk human fetuses.

Evaluation of nonlinear heart rate (HR) dynamics has received considerable attention in the pediatric literature because such analyses not only provide insight into underlying control mechanisms, but may also help to differentiate between normal and abnormal infants. The purpose of this study was to determine, in eight low risk human fetuses, if nonlinear HR dynamics could be identified by analyzing the dispersion of interbeat intervals at slow (Ds) and fast (Df) HRs. The fetal cardiac electrical signal was captured transabdominally at a resolution of +/- 1 ms. To test the null hypothesis, that the time series is the result of a linear stochastic process, Ds and Df for the original time series were compared with the values calculated for three linear models. The linear models were constructed to preserve the major statistical properties of the original time series, including the mean, SD, and the Fourier power spectrum. For each fetus, there was no evidence of nonlinear cardiac dynamics based on analyses of Ds and Df. In contrast, the distribution of adjacent R-R intervals and the pattern of change across three successive interbeat intervals both revealed significant nonlinearities in HR control in each fetus. If the difference between normal and abnormal infants is the result of aberrant control of nonlinear processes, then our findings indicate that parameters which describe the nonlinearity may be more useful then Ds and Df in assigning a risk status.

Apgar Score↗

The effects of occupation-based social position on mortality in a large American cohort.

OBJECTIVES: Four occupation-based measures were used to derive estimates of social position's effect on all-cause mortality among men and women in a large national cohort. METHODS: The National Longitudinal Mortality Study provided information on principal occupation and 9-year follow-up for 229,851 persons aged 25 through 64 years. Cox's proportional hazards model was used to estimate the age-adjusted risk of death relative to six ordinal categories of social position. The Slope Index of Inequality described average change in death rates across categories. RESULTS: Risk of death was consistently elevated among persons at lower positions in the social hierarchy. Estimates comparing lowest with highest categories varied within a narrow range (1.47-1.92 for men and 1.23-1.55 for women). However, several discrepancies among analyses were noted. The analysis by US census groups revealed nonlinear associations, whereas those using other scales found incremental increases in risk. Effect modification by sex was observed for analyses by two of the four measures. Race/ ethnicity did not modify the underlying association between variables. CONCLUSIONS: Our analysis complements previous findings and supports, with few qualifications, the interchangeability of occupation-based measures of social position in mortality studies. Explanations for why relative risk estimates were modified by sex are offered.

Adult↗

Reassessing benzene risks using internal doses and Monte-Carlo uncertainty analysis.

Human cancer risks from benzene have been estimated from epidemiological data, with supporting evidence from animal bioassay data. This article reexamines the animal-based risk assessments using physiologically based pharmacokinetic (PBPK) models of benzene metabolism in animals and humans. Internal doses (total benzene metabolites) from oral gavage experiments in mice are well predicted by the PBPK model. Both the data and the PBPK model outputs are also well described by a simple nonlinear (Michaelis-Menten) regression model, as previously used by Bailer and Hoel [Metabolite-based internal doses used in risk assessment of benzene. Environ Health Perspect 82:177-184 (1989)]. Refitting the multistage model family to internal doses changes the maximum-likelihood estimate (MLE) dose-response curve for mice from linear-quadratic to purely cubic, so that low-dose risk estimates are smaller than in previous risk assessments. In contrast to Bailer and Hoel's findings using interspecies dose conversion, the use of internal dose estimates for humans from a PBPK model reduces estimated human risks at low doses. Sensitivity analyses suggest that the finding of a nonlinear MLE dose-response curve at low doses is robust to changes in internal dose definitions and more consistent with epidemiological data than earlier risk models. A Monte-Carlo uncertainty analysis based on maximum-entropy probabilities and Bayesian conditioning is used to develop an entire probability distribution for the true but unknown dose-response function. This allows the probability of a positive low-dose slope to be quantified: It is about 10%. An upper 95% confidence limit on the low-dose slope of excess risk is also obtained directly from the posterior distribution and is similar to previous q1* values. This approach suggests that the excess risk due to benzene exposure may be nonexistent (or even negative) at sufficiently low doses. Two types of biological information about benzene effects--pharmacokinetic and hematotoxic--are examined to test the plausibility of this finding. A framework for incorporating causally relevant biological information into benzene risk assessment is introduced, and it is shown that both pharmacokinetic and hematotoxic models appear to be consistent with the hypothesis that sufficiently low concentrations of inhaled benzene do not create and excess risk.

Administration, Oral↗

A pharmacokinetic/pharmacodynamic model for a platelet activating factor antagonist based on data arising from Phase I studies.

A nonlinear mixed-effects modelling approach was used to analyse pharmacokinetic and pharmacodynamic data from two Phase I studies of a platelet activating factor (PAF) antagonist under development for the treatment of seasonal allergic rhinitis. Data for single-dose (8 subjects) and multiple-dose (9 subjects) administration were available for analysis with a program based on an EM algorithm. Pharmacokinetic analyses of plasma drug concentrations were performed using a biexponential model with first-order absorption. PAF response data were modelled with a hyperbolic Emax model. The drug showed nonlinear pharmacokinetics, with the clearance decreasing from 46.0 to 27.1 L h(-1) over a dose range of 160-480 mg. There was an apparent dose dependency within the C50 (concentration producing 50% of the maximum effect) but at higher doses most of the data was above the estimated C50 and when the data was analysed simultaneously a value of 17.57 ng mL(-1) was obtained for C50, with considerable intersubject variability (103%). Consistent results were obtained from the two studies and the population and individual pharmacodynamic parameter estimates from the analyses provided predicted responses that were in good agreement with the observed data. The results were used to simulate a 320-mg twice-daily dosing regimen.

Administration, Oral↗

Using genetic programming to discover nonlinear variable interactions.

Psychology has to deal with many interacting variables. The analyses usually used to uncover such relationships have many constraints that limit their utility. We briefly discuss these and describe recent work that uses genetic programming to evolve equations to combine variables in nonlinear ways in a number of different domains. We focus on four studies of interactions from lexical access experiments and psychometric problems. In all cases, genetic programming described nonlinear combinations of items in a manner that was subsequently independently verified. We discuss the general implications of genetic programming and related computational methods for multivariate problems in psychology.

Adult↗

Chaos and spectral analyses of heart rate variability during head-up tilting in essential hypertension.

To investigate nonlinear and linear components of heart rate variability (HRV) in essential hypertension (EHT), we analyzed HRV by chaos and spectral analyses in patients with EHT (n = 18) and normotensives (n = 10) during head-up tilting. We used the correlation dimension (CD) and Lyapunov exponents as the parameters of chaos. The CD, an index of complexity, was lower at rest in EHT group than in normotensives, and did not change in EHT group in response to head-up tilting, but decreased in normotensives. Head-up tilting did not change the Lyapunov exponents, an index of sensitive dependence on initial condition, a hallmark of chaos, in both groups. In the spectral analysis, the normalized high-frequency component (%HF) was decreased in EHT group at rest, and head-up tilting increased the low- to high-frequency ratio (L/H) and reduced the %HF in both groups. The CD and Lyapunov exponents at rest were correlated with the %HF and L/H. These results suggest that chaos analysis can assess the different aspect of HRV from spectral analysis and that nonlinear components of HRV may be associated with hypertension through an impaired dynamic regulation of HRV.

Adult↗

Cartilage interstitial fluid load support in unconfined compression.

Under physiological conditions of loading, articular cartilage is subjected to both compressive strains, normal to the articular surface, and tensile strains, tangential to the articular surface. Previous studies have shown that articular cartilage exhibits a much higher modulus in tension than in compression, and theoretical analyses have suggested that this tension-compression nonlinearity enhances the magnitude of interstitial fluid pressurization during loading in unconfined compression, above a theoretical threshold of 33% of the average applied stress. The first hypothesis of this experimental study is that the peak fluid load support in unconfined compression is significantly greater than the 33% theoretical limit predicted for porous permeable tissues modeled with equal moduli in tension and compression. The second hypothesis is that the peak fluid load support is higher at the articular surface side of the tissue samples than near the deep zone, because the disparity between the tensile and compressive moduli is greater at the surface zone. Ten human cartilage samples from six patellofemoral joints, and 10 bovine cartilage specimens from three calf patellofemoral joints were tested in unconfined compression. The peak fluid load support was measured at 79 +/- 11% and 69 +/- 15% at the articular surface and deep zone of human cartilage, respectively, and at 94 +/- 4% and 71 +/- 8% at the articular surface and deep zone of bovine calf cartilage, respectively. Statistical analyses confirmed both hypotheses of this study. These experimental results suggest that the tension-compression nonlinearity of cartilage is an essential functional property of the tissue which makes interstitial fluid pressurization the dominant mechanism of load support in articular cartilage.

Adult↗

Time-resolved fluorescence investigation of membrane cholesterol heterogeneity and exchange.

The fluorescent sterol delta 5,7,9(11),22-ergostatetraen-3 beta-ol (dehydroergosterol) was investigated as a cholesterol analogue to examine sterol domains in and spontaneous exchange of sterol between 1-palmitoyl-2-oleoylphosphatidylcholine (POPC) small unilamellar vesicles (SUV). Fluorescence lifetime, acrylamide quenching analyses, and intermembrane exchange kinetics were consistent with the presence of at least two sterol domains in POPC. Fluorescence lifetime was determined by phase and modulation fluorescence spectroscopy and analyzed by nonlinear least-squares as well as continuous distributional analyses. Both methods demonstrated that pure dehydroergosterol in POPC SUV had two lifetime components (C) and fractional intensities (F) near C1 = 0.851 ns (F1 0.96) and C2 = 2.668 ns (F2 0.004). In contrast to component C1, the center of lifetime distribution, fractional intensity, and peak width of dehydroergosterol lifetime component C2 was dependent on the polarity of the medium and vesicle curvature. The sterol domain corresponding to dehydroergosterol component C2 was preferentially quenched by acrylamide. Acrylamide quenching of dehydroergosterol fluorescence demonstrated that the two lifetime components of dehydroergosterol were not due to transbilayer sterol domains with different lifetimes. In a spontaneous exchange assay not requiring separation of donor and acceptor SUV, the lifetime component C2, but not C1, shifted to a shorter lifetime with altered distributional width. The kinetics of these lifetime and distributional width changes best fitted a two-exponential function, with a fast exchange rate constant K1 = 0.0325 min-1, t1/2 = 21.3 min, and a slow rate constant k2 = 0.00275 min-1, t1/2 = 261 min. The fast exchanging pool correlates with the longer lifetime component C2. These kinetics were confirmed both by dehydroergosterol exchange measured with fluorescence intensity and by [3H]cholesterol exchange. In summary, lifetime, distributional width, acrylamide quenching, and classical exchange assay data are consistent with the presence of at least two pools of sterol in POPC SUV.

Cholesterol↗

Converging evidence suggests that monoamine neurotransmitter turnover in human adults is associated with their season of birth.

Separate studies on adults, including those in suicidology and another regarding personality in the general population, have indicated associations with their season of birth. We analyse each of these studies by multiple nonlinear regression employing a cosine function for the month of birth, and compare these studies regarding the birth months giving the maxima and minima. The method of suicide in suicide studies shows a significant month-of-birth variation similar to that for the serotonin metabolite 5-HIAA in the separate study on cerebrospinal fluid, with a peak around the birth month September and a nadir around birth in March. When comparing the personality study with the study on cerebrospinal fluid, the trait novelty seeking varies similar to that for the dopamine metabolite HVA or the norepinephrine metabolite MHPG, and the trait reward dependence varies similar to that for HVA. The trait self-transcendence varies similar to the ratio of the dopamine and serotonin metabolites. Dopamine turnover in adults thus shows a peak around the birth months November-December, and a nadir around the birth months May-June, suggesting a possible involvement of the length of photoperiod during their perinatal period. These results provide strong evidence for the influence of season of birth on adult monoamine neurotransmitter turnover, and give further support for the monoaminergic modulation of the temperament and character traits.

Adult↗

Perl-speaks-NONMEM (PsN)--a Perl module for NONMEM related programming.

The NONMEM program is the most widely used nonlinear regression software in population pharmacokinetic/pharmacodynamic (PK/PD) analyses. In this article we describe a programming library, Perl-speaks-NONMEM (PsN), intended for programmers that aim at using the computational capability of NONMEM in external applications. The library is object oriented and written in the programming language Perl. The classes of the library are built around NONMEM's data, model and output files. The specification of the NONMEM model is easily set or changed through the model and data file classes while the output from a model fit is accessed through the output file class. The classes have methods that help the programmer perform common repetitive tasks, e.g. summarising the output from a NONMEM run, setting the initial estimates of a model based on a previous run or truncating values over a certain threshold in the data file. PsN creates a basis for the development of high-level software using NONMEM as the regression tool.

Computer Simulation↗

Radioisotope tracer study in a sludge hygienization research irradiator (SHRI).

A radioisotope tracer study has been carried out in a batch type sludge hygienization research irradiator with flow from top to bottom, the objective being to measure flow rate, circulation and mixing times and to investigate the hydrodynamic behaviour of the irradiator for identifying the cause(s) of malfunction. A stimulus-response technique with NH4(82)Br as a tracer was used to measure the above parameters. Experiments were carried out at three different flow rates, i.e 1.0, 0.64 and 0.33 m3/min. Three combined models based on a set of differential equations are proposed and used to simulate the measured tracer concentration curves. The obtained parameters were used to estimate dead volume and analyse hydrodynamic behaviour of the irradiator. The nonlinear regression problem of model parameter estimation was solved using the Marquardt-Levenberg method. The measured flow rate was found to be in good agreement with the values shown by the flow meter. The circulation times were found to be half of the mixing times. A simple approach for estimation of dose based on a known vertical dose-rate profile inside the irradiator is presented. About one-fourth of the volume of the irradiator was found to be dead at lower flow rates and this decreased with increase in flow rate. At higher flow rates, a semi stagnant volume was found with slow exchange of flow between the active and dead volumes.

Bromine Radioisotopes↗

Ab initio molecular-dynamics study of supercritical carbon dioxide.

Car-Parrinello molecular-dynamics simulations of supercritical carbon dioxide (scCO(2)) have been performed at the temperature of 318.15 K and at the density of 0.703 g/cc in order to understand its microscopic structure and dynamics. Atomic pair correlation functions and structure factors have been obtained and good agreement has been found with experiments. In the supercritical state the CO(2) molecule is marginally nonlinear, and thus possesses a dipole moment. Analyses of angle distributions between near neighbor molecules reveal the existence of configurations with pairs of molecules in the distorted T-shaped geometry. The reorientational dynamics of carbon dioxide molecules, investigated through first- and second-order time correlation functions, exhibit time constants of 620 and 268 fs, respectively, in good agreement with nuclear magnetic resonance experiments. The intramolecular vibrations of CO(2) have been examined through an analysis of the velocity autocorrelation function of the atoms. These reveal a red shift in the frequency spectrum relative to that of an isolated molecule, consistent with experiments on scCO(2). The results have also been compared to classical molecular-dynamics calculations employing an empirical potential.

Journal Article↗

The cyclin-dependent kinases cdk2 and cdk5 act by a random, anticooperative kinetic mechanism.

cdk2.cyclin E and cdk5.p25 are two members of the cyclin-dependent kinase family that are potential therapeutic targets for oncology and Alzheimer's disease, respectively. In this study we have investigated the mechanism for these enzymes. Kinases catalyze the transfer of phosphate from ATP to a protein acceptor, thus utilizing two substrates, ATP and the target protein. For a two-substrate reaction, possible kinetic mechanisms include: ping-pong, sequential random, or sequential ordered. To determine the kinetic mechanism of cdk2.GST-cyclin E and cdk5.GST-p25, kinase activity was measured in experiments in which concentrations of peptide and ATP substrates were varied in the presence of dead-end inhibitors. A peptide identical to the peptide substrate, but with a substitution of valine for the phosphoacceptor threonine, competed with substrate with a K(i) value of 0.6 mm. An aminopyrimidine, PNU 112455A, was identified in a screen for inhibitors of cdk2. Nonlinear least squares and Lineweaver-Burk analyses demonstrated that the inhibitor PNU 112455A was competitive with ATP with a K(i) value of 2 microm. In addition, a co-crystal of PNU 112455A with cdk2 showed that the inhibitor binds in the ATP binding pocket of the enzyme. Analysis of the inhibitor data demonstrated that both kinases use a sequential random mechanism, in which either ATP or peptide may bind first to the enzyme active site. For both kinases, the binding of the second substrate was shown to be anticooperative, in that the binding of the first substrate decreases the affinity of the second substrate. For cdk2.GST-cyclin E the kinetic parameters were determined to be K(m, ATP) = 3.6 +/- 1.0 microm, K(m, peptide) = 4.6 +/- 1.4 microm, and the anticooperativity factor, alpha = 130 +/- 44. For cdk5.GST-p25, the K(m, ATP) = 3.2 +/- 0.7 microm, K(m, peptide) = 1.6 +/- 0.3 microm, and alpha = 7.2 +/- 1.8.

Adenosine Triphosphate↗

The relationship between club drug use and other drug use: a survey of New York City middle school students.

In order to explore the relationship between use of club drugs (crystal methamphetamine, ecstasy, GHB, ketamine), and use of other drugs, survey data collected from 23,780 middle school students in New York City during 2002-2003 was examined. Results of HGLM analyses (a generalization of HLM to accommodate nonlinear outcomes), controlling for the effect of school, indicate that Black students are less likely than White students to use club drugs depending on the timeframe of use. The use of alcohol and/or marijuana predict club drug use regardless of the timeframe of use, and lifetime cigarette use predicts lifetime club drug use. Recommendations for future research and prevention efforts are discussed.

Adolescent↗