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PubMed2004

Structural modeling of dynamic changes in memory and brain structure using longitudinal data from the normative aging study.

This is an application of new longitudinal structural equation modeling techniques to time-dependent associations of memory and brain structure measurements. There were 225 participants aged 30-80 years at baseline who were measured again after a 7-year interval on both the lateral ventricular size and Wechsler memory score. Multiple regression analyses show nonlinear associations with age but no relationships among longitudinal changes. Mixed-effects latent growth curve analyses and analyses based on latent difference scores indicate that longitudinal changes in both variables are reasonably well described by an exponential or dual change model. Bivariate dynamic structural equation modeling analyses indicate age-lagged changes operate in a coupled-over-time fashion, with the brain measure (lateral ventricular size) as a leading indicator in time of memory (Wechsler memory score) declines.

Adult↗

PubMed2005

Nonlinear multivariate models of successional change in community structure using the von Bertalanffy curve.

von Bertalanffy curves were used to describe the nonlinear relationship between assemblages inhabiting holdfasts of the kelp Ecklonia radiata and the volume of the holdfast. This was done using nonlinear canonical analyses of principal coordinates (NCAP). The volume of the holdfast is a proxy for the age of the plant and, thus, the canonical axis is a proxy for succession in the marine invertebrate community inhabiting the holdfast. Analyses were done at several different taxonomic resolutions on the basis of various dissimilarity measures. Assemblages in relatively large holdfasts demonstrated ongoing variation in community structure with increasing volume when the dissimilarity used was independent of sample size. Smaller holdfasts had proportionately greater abundances of ophiuroids and encrusting organisms (bryozoans, sponges, ascidians), while larger holdfasts were characterised by proportionately greater abundances of crustaceans, polychaetes and molluscs. Such linear and nonlinear multivariate models may be applied to analyse system-level responses to the growth of many habitat-forming organisms, such as sponges, coral reefs, coralline algal turf or forest canopies.

Animals↗

PubMed2006

Nonlinear finite element model predicts vertebral bone strength and fracture site.

STUDY DESIGN: A study on computed tomography (CT)-based finite element (FE) method that predicts vertebral strength and fracture site using human cadaveric specimens. OBJECTIVE: To evaluate the accuracy of the nonlinear FE method by comparing the predicted data with those of mechanical testing. SUMMARY OF BACKGROUND DATA: FE methods may predict vertebral strength and fracture site but the prediction has been difficult because of a complex geometry, elastoplasticity, and thin cortical shell of the vertebra. METHODS: FE models of the 12 thoracolumbar vertebral specimens were constructed. Nonlinear FE analyses were performed, and the yield load, the fracture load, the sites where elements failed, and the distribution of minimum principal strain were evaluated. A quasi-static uniaxial compression test for the same specimens was conducted to verify these analyses. RESULTS: The yield loads, fracture loads, minimum principal strains, and fracture sites of the FE prediction significantly correlated with those measured. CONCLUSIONS: Nonlinear FE model predicted vertebral strength and fracture site accurately.

Adult↗

PubMed2005

An introduction to Bayesian hierarchical models with an application in the theory of signal detection.

Although many nonlinear models of cognition have been proposed in the past 50 years, there has been little consideration of corresponding statistical techniques for their analysis. In analyses with nonlinear models, unmodeled variability from the selection of items or participants may lead to asymptotically biased estimation. This asymptotic bias, in turn, renders inference problematic. We show, for example, that a signal detection analysis of recognition memory data leads to asymptotic underestimation of sensitivity. To eliminate asymptotic bias, we advocate hierarchical models in which participant variability, item variability, and measurement error are modeled simultaneously. By accounting for multiple sources of variability, hierarchical models yield consistent and accurate estimates of participant and item effects in recognition memory. This article is written in tutorial format; we provide an introduction to Bayesian statistics, hierarchical modeling, and Markov chain Monte Carlo computational techniques.

Bayes Theorem↗

PubMed2004

Evaluation of different measures of functional connectivity using a neural mass model.

We use a neural mass model to address some important issues in characterising functional integration among remote cortical areas using magnetoencephalography or electroencephalography (MEG or EEG). In a previous paper [Neuroimage (in press)], we showed how the coupling among cortical areas can modulate the MEG or EEG spectrum and synchronise oscillatory dynamics. In this work, we exploit the model further by evaluating different measures of statistical dependencies (i.e., functional connectivity) among MEG or EEG signals that are mediated by neuronal coupling. We have examined linear and nonlinear methods, including phase synchronisation. Our results show that each method can detect coupling but with different sensitivity profiles that depended on (i) the frequency specificity of the interaction (broad vs. narrow band) and (ii) the nature of the coupling (linear vs. nonlinear). Our analyses suggest that methods based on the concept of generalised synchronisation are the most sensitive when interactions encompass different frequencies (broadband analyses). In the context of narrow-band analyses, mutual information was found to be the most sensitive way to disclose frequency-specific couplings. Measures based on generalised synchronisation and phase synchronisation are the most sensitive to nonlinear coupling. These different sensitivity profiles mean that the choice of coupling measures can have dramatic effects on the cortical networks identified. We illustrate this using a single-subject MEG study of binocular rivalry and highlight the greater recovery of statistical dependencies among cortical areas in the beta band when mutual information is used.

Beta Rhythm↗

PubMed2003

On the importance of geometric nonlinearity in finite-element simulations of trabecular bone failure.

The finite element method, which has been successfully applied to studies of the elastic properties of trabecular bone, is now being used to simulate its failure. These simulations have used a geometrically linear (linear kinematic) approximation to the total stiffness matrix; nonlinear terms in the total stiffness matrix have been excluded from the computation in order to achieve efficiency. Because trabecular bone appears to be a slender (i.e., geometrically nonlinear) structure, we studied the validity of the linear kinematic approximation for simulating its failure. Two cases, designed to bracket the extremes of stability behavior, were explored: a single representative spicule of trabecular bone (case 1) and a volume of trabecular bone consisting of relatively low aspect ratio members (case 2). For case 1, geometrically linear (GL) and nonlinear (GNL) analyses were performed with two different materials models: a plastic damage model and a brittle damage model. When GNL terms were included in the total stiffness matrix, we found that load-path bifurcation preceded tissue failure regardless of the form of the damage model. This bifurcation was the result of a complex coupling between material yield and structural instability. The nature of this coupling was highly sensitive to the form of the damage model. None of these behaviors was observed in the linear analyses, where failure was insensitive to the form of the damage model and where structural instabilities were prevented from occurring. For case 2, compressive loading of a volume of trabecular bone, geometric nonlinear effects were pronounced. There was a bifurcation in load response that resulted in large apparent strain to failure. The GL simulations, on the other hand, precluded this bifurcation. We hypothesize that trabecular bone is a geometric nonlinear structure; nonlinear terms must be included in the total stiffness matrix to accurately simulate its failure.

Biomechanical Phenomena↗

PubMed1987

Functional residual capacity in healthy preschool children lying supine.

Functional residual capacity (FRC) was measured by the closed-circuit helium dilution method in 41 supine healthy children 1 month to 8 yr of age. In 20 children, the measurement was carried out while they were awake, and in the others, who were less cooperative, testing was done during ketamine anesthesia before elective surgery. There was no significant difference in the FRC values between these groups, and they were subsequently analyzed as a single group. For males and females separately and combined, FRC correlated significantly with height, age, and weight, both with linear and nonlinear regression analyses. No significant difference between the sexes was found. The best correlation of FRC was with height; the linear equation being FRC (ml) = -457.3 + 8.8 X height (cm) (r2 = 0.662), and the nonlinear equation being FRC (ml) = 0.0052 X [height (cm)]2.44 (r2 = 0.827).

Child↗

PubMedDate not supplied

Changes in metacarpal bone mineral density with age and menopause using computed X-ray densitometry in Japanese women: cross-sectional and longitudinal study.

BACKGROUND: Bone mineral density (BMD) loss with age and menopause is widely accepted in elderly women. However, only a few studies have utilized a multiple regression model that includes physical characteristics to assess comprehensive lifetime changes in BMD. OBJECTIVE: A prospective study was conducted to characterize the normal patterns in metacarpal BMD changes in Japanese women, and to assess the applicability of a fitting model using cross-sectional data compared with longitudinal variability. SUBJECTS AND METHODS: The study consisted of 5422 healthy women in cross-sectional data and a 1-year follow-up of 359 women. The metacarpal BMD was measured by computed X-ray densitometry. Multiple linear and nonlinear regression analyses were performed in cross-sectional subjects. Nonparametric analysis was used to compare percentage rates of BMD changes between actual and estimated values. RESULTS: The cross-sectional data showed that the best-fit equation was a nonlinear change model using the variables of age and height in premenopausal women, and years since menopause (YSM), age and height in postmenopausal women. The results of longitudinal data indicated the following. In premenopausal women, the actual BMD changes were greater in the 30-39 age group than the 20-29 age group and were less in the 50-59 group than the 40-49 group. The rates of annual change in BMD between the actual value and estimated value by change model were very similar. In postmenopausal women, the actual changes in BMD indicated that the rapid rate of reduction observed was over 3% at 0-5 YSM and 1.5% at 6-10 YSM, and thereafter showed a slower rate of decline at 11 YSM. The change model represented the trend of actual change in BMD for postmenopausal women, whereas the rates of estimated BMD loss underestimated the actual changes at 1-10 YSM. CONCLUSION: The change model for premenopausal women using cross-sectional data is beneficial in evaluating the actual metacarpal BMD variability, whereas that for postmenopausal women is insufficient in estimating the longitudinal BMD variability.

Adult↗

PubMed1999

The pharmacokinetic modelling of GI198745 (dutasteride), a compound with parallel linear and nonlinear elimination.

AIMS: To characterize the pharmacokinetics of the dual 5alpha-reductase inhibitor GI198745 (dutasteride) to allow for more accurate predictions of GI198745 concentrations after different dosing schedules. METHODS: In this randomized, single-blind, parallel group study, 32 healthy male volunteers received single oral doses of GI198745 ranging from 0.01 to 40 mg. Data were analysed by nonlinear mixed effects modelling using NONMEM where both linear and nonlinear pharmacokinetic models were examined. RESULTS: The time course of GI198745 serum concentrations indicated concentration dependent elimination, with the apparent half-life increasing with dose. Data were best described by a two-compartment model with first order absorption and parallel linear and nonlinear elimination pathways. Drug absorption was rapid, and was followed by a short distribution phase. A high volume of distribution (511 l) and a low linear clearance (0.58 l h(-1)) combined to give a half-life of up to 5 (1-7) weeks at high concentrations. As concentrations declined towards Km (0.96 ng ml(-1)), the proportion eliminated by the relatively rapid saturable elimination pathway, with a maximum clearance of 6.2 l h(-1), increased and the half-life reduced to about 3 days. The estimated inter individual variability for the linear clearance was high (CV = 70%). CONCLUSIONS: G1198745 pharmacokinetics are well described by a pharmacokinetic model with parallel linear and nonlinear elimination. Simulations using this model show that at daily doses of 0.1 mg the steady state drug concentrations, and the rate at which these are achieved, are mainly influenced by the nonlinear pathway, while at daily doses above 1 mg they are almost entirely influenced by the linear pathway.

Adult↗

PubMed2005

Electric-field-induced patterns in thin polymer films: weakly nonlinear and fully nonlinear evolution.

A thin polymer melt on a substrate can be unstable to an electric field normal to the interface, a phenomenon that can be harnessed as a patterning technique with a range of potential applications. Motivated by the variety of patterns observed in experiments for polymers under both unpatterned and patterned masks, we describe here, from theoretical and numerical analyses, how nonlinear effects govern the growth of the instability and determine the final patterns. In particular, we discuss the nonlinear growth in terms of interactions among different Fourier modes and show that the second- and third-order nonlinearities favor the growth of hexagonal patterns under a featureless mask, in agreement with experimental observations. Also, numerical simulations based on the fully nonlinear model validate the prediction of the weakly nonlinear analysis: hexagonal patterns do emerge under an unpatterned mask. Furthermore, in one-dimensional simulations, we demonstrate the energetic evolution of this patterning process and reveal several "kinetically stable structures" along the path to the thermodynamically stable state. Two-dimensional simulations allow us to study the effects of both mask patterns and the initial film thickness. Generally, patterns on the mask guide the growth such that the pattern conforms to the geometric shapes. Interestingly, a small cylindrical protrusion at the center of the mask can produce exactly the same pattern as a large, flat, circular protrusion. The initial film thickness or the thickness ratio of the polymer layer to the air gap plays an important role in determining the final pattern formed. Finally, we demonstrate, by two simple examples, that the simulations can provide insights on "smart" mask designs for producing large areas of well-ordered patterns.

Journal Article↗

PubMed1992

Cultured Müller cells have high levels of epidermal growth factor receptors.

High levels of epidermal growth factor (EGF)-receptors have been reported in membrane homogenates of bovine retinas, but the biologic function and tissue target of EGF in the retina have not been established fully. Because EGF participation has been suggested in the mechanisms of wound healing and Müller cells undergo changes after retinal injury, the authors studied EGF receptor expression and functional role of this substance in cultured Müller cells. These cells (isolated from normal rats) were tested for the glial cell markers: vimentin, S-100 protein, and carbonic anhydrase C. These markers were found to be positive through all passages used in the experiments. The 125I-EGF binding in Müller cells was highly specific, concentration dependent, and saturable. Compared with 3T3 fibroblasts, Müller cells bound threefold more EGF. Binding kinetics and Scatchard analyses showed the higher level of binding was related to the greater number of receptors on these cells (Müller cells, 2.4 x 10(5) receptors/cell; 3T3 fibroblasts, 7.1 x 10(4) receptors/cell) rather than a change in affinity of the receptors to bind the ligand. Nonlinear-regression analyses suggested the presence of two classes of affinity sites. The high level of EGF-receptor expression in Müller cells was confirmed by western blot analyses that showed increased reactivity of the approximately 170-kilodalton receptor band to a monoclonal anti-EGF receptor antibody. Moreover, EGF treatment of Müller cells resulted in two- to threefold increase in DNA synthesis, as evidenced by 3H-thymidine uptake studies. These findings support a functional role for EGF in Müller cell proliferation in retinal disease.

3T3 Cells↗

PubMed2004

Nonlinear breathing modes due to a defect in a DNA chain.

Recent molecular-dynamics simulations of a DNA duplex containing the 'rogue' base difluorotoluene (F) in place of a thymine (T) base show that breathing events can occur on the nanosecond time-scale, whereas breathing events in a normal DNA duplex take place on the microsecond time-scale. The main aim of this paper is to analyse a nonlinear Klein-Gordon lattice model of the DNA duplex, including both nonlinear interactions between opposing bases and a defect in the interaction at one lattice site, each of which can cause localization of energy. Solutions for a breather mode either side of the defect are derived using multiple-scales asymptotics and are pieced together across the defect to form a solution which includes the effects of the nonlinearity and the defect. We consider defects in the inter-chain interactions and in the along-chain interactions. In most cases we find in-phase breather modes and/or out-of-phase breather modes, with one case displaying a shifted mode.

Base Pair Mismatch↗

PubMed2026

Association between hepatic steatosis index and female infertility: a cross-sectional study using NHANES 2013-2018.

Female infertility is a major reproductive health concern. Hepatic steatosis index (HSI), a non-invasive marker of liver-related metabolic burden, has not been well studied in relation to infertility across its distribution. We analyzed women aged 20-49 years from three NHANES cycles (2013-2018). HSI was examined as both a continuous variable and in quartiles, and restricted cubic spline models were used to assess potential nonlinearity. Sensitivity analyses using alternative infertility definitions and exploratory interaction analyses were also performed. Among 3,007 women, 416 (13.8%) were classified as having infertility. In the fully adjusted model, women in the highest HSI quartile had higher odds of infertility than those in the lowest quartile (OR 1.66, 95% CI 1.08-2.57; P = 0.031), with a significant trend across quartiles (P for trend = 0.010). Restricted cubic spline analysis showed a nonlinear association between HSI and infertility (P for overall association = 0.005), which was more evident at higher HSI levels. Higher HSI was associated with greater odds of infertility among reproductive-aged women.

Humans↗

PubMed1991

The end-systolic pressure-volume relationship in the newborn lamb: effects of loading and inotropic interventions.

Indices of global systolic performance of the newborn left ventricle exceed those of the adult, despite isolated tissue studies showing immature contractile mechanisms. To evaluate contractility in situ, we investigated the end-systolic pressure-volume relationship (ESPVR) by the conductance technique in nine newborn lambs. After percutaneous placement of catheters, we generated ESPVR by inferior vena cava occlusion, aortic occlusion, and volume infusion in two control states, during three levels of dobutamine infusion, and after propranolol. We performed linear and nonlinear regression analyses of the end-systolic points and derived the slope (Ees) and volume at 14 kPa pressure. We found that reliable ESPVR could be obtained in almost all inferior vena cava and aortic occlusions (50 of 51 in each), but in only 18 of 27 volume infusions. Overall, linear regressions adequately defined the ESPVR (75 of 102 were not statistically different than nonlinear regressions; of those different, the mean linear R2 was 0.934 +/- 0.048). By multiple regression analysis, neither Ees nor volume at 14 kPa significantly changed with dobutamine, but both changed after propranolol (23% less than control and 54% greater, respectively), supporting previous studies showing a limited contractile reserve in the newborn secondary to high resting beta-adrenergic tone. Neither Ees nor volume at 14 kPa was different between control states. However, Ees was 25% less steep when generated by inferior vena cava than by aortic occlusion. We conclude that the ESPVR can be generated reliably and reproducibly in the newborn lamb and is relatively linear and sensitive to changes in contractility, but that it is also sensitive to the technique of load intervention.

Animals↗

PubMed1996

Discrimination of sleep stages: a comparison between spectral and nonlinear EEG measures.

During recent years, methods from nonlinear dynamics were introduced into the analysis of EEG signals. Although from a theoretical point of view nonlinear measures quantify properties being independent from conventional spectral measures, it is a crucial question whether in practice nonlinear EEG measures yield additional information, which is not redundant to the information gained by spectral analysis. Therefore, we compared the ability of several spectral and nonlinear measures to discriminate different sleep stages. We evaluated spectral measures (relative delta power, spectral edge, spectral entropy and first spectral moment), and nonlinear measures (correlation dimension D2, largest Lyapunov exponent LI, and approximated Kolmogorof entropy K2), and additionally the stochastic time domain based measure entropy of amplitudes. For 12 healthy subjects these measures were calculated from sleep EEG segments of 2:44 min duration, each segment unambiguously corresponding to one of the sleep stages I, II, SWS and REM. Results were statistically evaluated by multivariate and univariate analyses of variance and by discriminant analyses. Generally, nonlinear measures (D2 and L1) performed better in discriminating sleep stages I and II, whereas spectral measures showed advantages in discriminating stage II and SWS. Combinations of spectral and nonlinear measures yielded a better overall discrimination of sleep stages than spectral measures alone. The best overall discrimination was reached even without inclusion of any of the spectral measures. It can be concluded that nonlinear measures yield additional information, which improves the ability to discriminate sleep stages and which may in general improve the ability to distinguish different psychophysiological states. This confirms the importance and practical reliability of the application of nonlinear methods to EEG analysis.

Adult↗

PubMed2002

In vitro interactions between a potential muscle relaxant E2101 and human cytochromes P450.

E2101 or N-methyl-[1-[1-(2-fluorophenethyl)piperidine-4-yl]-1H-indol-6-yl] acetamide, an antagonist of 5-hydroxytryptamine receptor subtypes 1A and 2, is currently under development for the potential treatment of skeletal muscle associated spasticity. Here we characterized the in vitro metabolism of E2101 using human liver enzymes including human liver microsomal preparations, human liver S9 fractions, and individual forms of recombinant cytochromes P450 (P450s). Our results showed that E2101 was metabolized by P450s to form monohydroxylated (M1 and M2), dihydroxylated (M3), and N-dealkylated metabolites (M4). The structures of these major microsomal metabolites were proposed based on LC/MS/MS analyses. All four metabolites, M1-M4, were formed by CYP3A4. Metabolites, M1, M2, and M4, were also formed by CYP2C19 and M2 and M3 by CYP2D6. The potential P450 inhibition and induction of E2101 were also evaluated. E2101 was determined to be a competitive inhibitor of CYP2C19 and CYP2D6 with K(i) of 15 and 48 microM, respectively, as determined by both Dixon plots and simultaneously nonlinear regression analyses. Induction of major P450 expression was not detected immunochemically after 72-h exposure to 10 or 50 microM E2101 in primary hepatocyte cultures obtained from three subjects. Taken together, E2101 is expected to metabolically interact with major human P450 enzymes including CYP2C19, CYP2D6, and CYP3A4, and a low risk of drug-drug interaction would be anticipated in clinical studies.

Acetamides↗

PubMed2003

Characterisation of the human liver in vitro metabolic pattern of artemisinin and auto-induction in the rat by use of nonlinear mixed effects modelling.

AIMS: The aims of the study were to characterise the metabolic pattern of artemisinin in human and rat liver microsomes and to assess the magnitude of auto-induction in the rat. METHODS: (14)C-artemisinin was incubated with human liver microsomes and with liver microsomes from rats pretreated with oral artemisinin or placebo. The metabolic fate of (14)C-artemisinin in microsomes from human B-lymphoblastoid cell lines transformed with CYP2A6, CYP2B6 and CYP3A4 was also investigated. The human liver microsome data and the rat liver microsomes data were analysed by nonlinear mixed effects modelling and naïve pooling using NONMEM, respectively. RESULTS: Four metabolites were radiometrically detected in experiments with rat liver microsomes. The model that best described the data involved three primary metabolites of which one metabolite was further metabolised to a secondary metabolite. The formation of the four metabolites was induced 2.8, 7.2, 4.8 and 2.5-fold, respectively, in liver microsomes from rats pre-treated with artemisinin. Three metabolites were formed in human liver microsomes; having the same retention times as three of the metabolites formed in the rat. The final model consisted of two primary metabolites and a secondary metabolite with CYP2B6 and CYP2A6 influencing the formation rates of the major and minor primary metabolites, respectively. CONCLUSIONS: CYP2B6 and CYP2A6 activities described variability in the formation of the major and minor primary metabolites, respectively, in human liver microsomes. All artemisinin metabolic pathways in rat liver microsomes were induced in artemisinin pretreated animals. We suggest modelling as a method for the discrimination and detection of more complex metabolic patterns from in vitro metabolism rate data.

Animals↗

PubMed2001

Modeling of chaotic vibrations in symmetric vocal folds.

The chaos mechanism of above-range phonation was examined in symmetrically modeled vocal folds by using the traditional two-mass model assumption. The Poincaré map technique was used to display chaotic attractors. This method provided an effective description of irregular vocal-fold movements. The power spectrum, Lyapunov exponent, and Kaplan-Yorke dimension were employed to describe chaotic vibrations in the vocal-fold model. These nonlinear dynamic analyses suggested that, for the positive Lyapunov exponent, chaotic attractors contribute to irregular vocal-fold vibrations. Descriptions of complicated irregular vibrations of the vocal fold yielded evidence of chaos. To investigate the effects of independent parameters such as subglottal pressure, coupling stiffness, and phonation neutral area, bifurcation diagrams based on the Poincaré map were discussed. The results confirmed that the dynamics of the two-mass model was strongly influenced by independent parameters. Nonlinear dynamic methods were expected to provide useful information for better understanding of irregular vocal-fold vibrations as well as of the dynamic mechanism of above-range phonation in excised larynx experimentation.

Humans↗