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PubMed1998

Global asymptotic stability of bone remodeling theories: a new approach based on non-linear dynamical systems analysis.

Mathematical tools for the analysis of nonlinear dynamical systems are applied to the study of stability of bone remodeling theories. As a practical application, the same problem studied by Harrigan and Hamilton (1992) and Cowin et al. (1994b) is analysed using these tools, and their findings on the necessary and sufficient conditions to ensure local asymptotic stability are easily confirmed. Using a general approach based on Lyapunov's method the same condition has been found to be necessary and sufficient also for the global asymptotic stability, thus confirming a result obtained by Harrigan and Hamilton (1994) by variational methods applied to finite-element models. The proof is based on the discretization of the spatial domain but the results for the continuum can be easily extrapolated.

Animals↗

PubMed1984

The transducer and encoder of frog muscle spindles are essentially nonlinear. Physiological conclusions from a white-noise analysis.

Nonlinear second order white-noise analysis has been applied to the isolated frog muscle spindle. Power (delta 2) of the Gaussian white noise (GWN) and the average prestretch level L were varied and the response of both the isolated receptor potential (transducer) and the action potential (encoder) level were analysed. The standard white-noise method is briefly presented. Particular emphasis, however, is put on the limitations in the range of validity of the method and, consequently, on the use and interpretation of the kernels as a Wiener model. Conclusions in the present paper are within this frame and are mainly of qualitative nature. The analysis reveals that the nonlinear contributions of the model are essential for approximating physiological results, thus ruling out purely linear modelling for this receptor organ. The dependence of the transducer kernels on delta are compatible with the behaviour of a rectifier. Rectification is represented by the lack of hyperpolarization within the isolated receptor potential and is enhanced by the substantial memory in the linear and nonlinear kernels as demonstrated by their extent in time. This is equivalent to low power in high frequencies of the response. Obviously, the hyperpolarizing potentials following each spike counteract the long transducer memory. At the encoder level the memory of the system is strongly reduced. This is achieved by using predominantly high frequency components of the receptor potential for triggering the process of impulse generation, and by the precise coupling and high frequency content of the impulses. This coupling precision is possible because of the sensitivity of the spike-generating mechanism to steep rising transients of the receptor potential and also owing to the reduction in transducer memory by the hyperpolarizing afterpotentials. The preference given to the high frequency components is also read from the structure of the second order transducer kernel and from both the linear and the second order encoder kernels, which allows the most effective input waveform for triggering action potentials to be determined. When the operating point is changed to higher prestretch values, kernel heights increase strongly implying higher response strength of the muscle spindle.(ABSTRACT TRUNCATED AT 400 WORDS)

Animals↗

PubMed2005

Nonlinear relationships between weekly walking distance and adiposity in 27,596 women.

INTRODUCTION/PURPOSE: Data from vigorously active women (runners) suggested that declines in adiposity with weekly running distance were nonlinear and dependent on whether the women are relatively lean or fat. The purpose of the current study is to assess the cross-sectional relationship between the amount of moderate-intensity physical activity (walking distance) and indicators of adiposity. METHODS: Cross-sectional analyses (i.e., quadratic polynomial regression, regression for percentiles of adiposity) of body mass index (BMI), body circumferences, and bra cup sizes in 27,596 women. RESULTS: The estimated percent reductions between walking 40-50 km.wk(-1) and <10 km.wk(-1) were greatest for BMI, intermediate for waist circumference and cup size, and least for hip and chest circumferences. The relationships of walking distance to BMI and body circumferences were all nonlinear (convex). In addition, the inverse relationship between weekly walking distance and adiposity was greatest at the highest percentile of BMI, body circumferences, and cup size, and least at the lowest percentiles. Thus, the decline in adiposity per kilometer per week increment in walking distance was greatest in overweight mostly sedentary women and least in lean active women. The decline in BMI per kilometer per week of exercise was greater in the walkers than previously reported for runners. However, based on the relationships between walking distance and percentiles of the BMI distribution reported here, we show that the majority of this difference is attributable to the leanness of the runners and greater fatness of the walker. CONCLUSION: These data suggest that in women the greatest benefit of walking may be among the most obese and that at higher weekly distances the declines in weight associated with walking diminish. Whether these relationships are causal remains to be determined.

Adipose Tissue↗

PubMedDate not supplied

Epidemiological studies of acute ozone exposures and mortality.

Many, but not all, observational epidemiological studies of ozone (O(3)) air pollution have yielded significant associations between variations in daily ambient concentrations of this pollutant and a wide range of adverse health outcomes. We evaluate some past epidemiological studies that have assessed the short-term association of O(3) with mortality, and investigate one possible reason for variations in their O(3) effect estimate, i.e., differences in their approaches to the modeling of weather influences on mortality. For all of the total mortality-air pollution time-series studies considered, the combined analysis yielded a relative risk, RR=1.036 per 100-ppb increase in daily 1-h maximum O(3) (95% CI: 1.023-1.050). However, the subset of studies that specified the nonlinear nature of the temperature-mortality association yielded a combined estimate of RR=1.056 per 100 ppb (95% CI: 1.032-1.081). This indicates that past time-series studies using linear temperature-mortality specifications have underpredicted the premature mortality effects of O(3) air pollution. For Detroit, MI, an illustrative analysis of daily total mortality during 1985-1990 also indicated that the model weather specification choice can influence the O(3) health effects estimate. Results were intercompared for alternative weather specifications. Nonlinear specifications of temperature and relative humidity (RH) yielded lower intercorrelations with the O(3) coefficient, and larger O(3) RR estimates, than a base model employing a simple linear spline of hot and cold temperature. We conclude that, unlike for particulate matter (PM) mass, the mortality effect estimates derived by time-series analyses for O(3) can be sensitive to the way that weather is addressed in the model. The same may well also be true for other pollutants with largely temperature-dependent formation mechanisms, such as secondary aerosols. Generally, we find that the O(3)-mortality effect estimate increases in size and statistical significance when the nonlinearity and the humidity interaction of the temperature-health effect association are incorporated into the model weather specification. We recommend that a minimization of the intercorrelations of model coefficients be considered (along with other critical factors such as goodness of fit, autocorrelation, and overdispersion) when specifying such a model, especially when individual coefficients are to be interpreted for risk estimation.

Air Pollutants↗

PubMed1999

Quantitative measure of complexity of EEG signal dynamics.

Since electroencephalographic (EEG) signal may be considered chaotic, Nonlinear Dynamics and Deterministic Chaos Theory may supply effective quantitative descriptors of EEG dynamics and of underlying chaos in the brain. We have used Karhunen-Loeve decomposition of the covariance matrix of the EEG signal to analyse EEG signals of 4 healthy subjects, under drug-free condition and under the influence of Diazepam. We found that what we call KL-complexity of the signal differs profoundly for the signals registered in different EEG channels, from about 5-8 for signals in frontal channels up to 40 and more in occipital ones. But no consistency in the influence of Diazepam administration on KL-complexity is observed. We also estimated the embedding dimension of the EEG signals of the same subjects, which turned to be between 7 and 11, so endorsing the presumption about existence of low-dimensional chaotic attractor. We are sure that nonlinear time series analysis can be used to investigate the dynamics underlying the generation of EEG signal. This approach does not seem practical yet, but deserves further study.

Adult↗

PubMed2004

On atomic force microscopy and the constitutive behavior of living cells.

Atomic force microscopy (AFM) is one of many new technologies available to study the mechanical properties and mechanobiological responses of living cells. Despite the widespread usage of this technology, there has been little attempt to develop new theoretical frameworks to interpret the associated data. Rather, most analyses rely on the classical Hertz solution for the indentation of an elastic half-space within the context of linearized elasticity. In contrast, we propose a fully nonlinear, constrained mixture model for adherent cells that allows one to account separately for the contributions of the three primary structural constituents of the cytoskeleton. Moreover, we extend a prior solution for a small indentation superimposed on a finite equibiaxial extension by incorporating in this mixture model for the special case of an initially random distribution of constituents (actin, intermediate filaments, and microtubules). We submit that this theoretical framework will allow an improved interpretation of indentation force-depth data from a sub-class of atomic force microscopy tests and will serve as an important analytical check for future finite element models. The latter will be necessary to exploit further the capabilities of both atomic force microscopy and nonlinear mixture theories for cell behavior.

Biomechanical Phenomena↗

PubMed1995

Carrier-mediated transport can obey fractal kinetics.

A model based on the fractal methodology is proposed for the kinetic study of carrier-mediated transport under heterogeneous conditions, i.e., when the drug-carrier interaction occurs at an interface with an effective dimensionality smaller than the embedding dimension of d = 2. A model equation is derived for the flux, based on a similar approach for an analogous equation for enzyme kinetics. It is shown that the total flux-solute concentration plots are curvilinear when the fractal dimension is smaller than unity while they become biexponential, with ascending and descending limbs, when the fractal dimension D is in the range 1 < D < 2. Nonlinear Lineweaver-Burk plots are obtained when this fractal kinetics approach is used. Good fittings are obtained when the fractal model is applied to literature data previously analysed with a combined transport mechanism, revealing experimental systems that display a D value in the range 1 < D < 2. It is suggested that transport studies should be carried out at a wider working solute concentration range and various agitation and incubation conditions in order to derive definite conclusions for the transport pathways.

Animals↗

PubMed1995

Role of smoking in the U-shaped relation of cholesterol to mortality in men. The Framingham Study.

Elevated mortality has been reported at extremes of the serum total cholesterol distribution, with increased coronary mortality reported at high total cholesterol levels and increased cancer and non-cardiovascular/non-cancer mortality at low total cholesterol levels. The authors used data collected on 1,959 males aged 35-69 years from the fourth Framingham Study examination to analyze the relations between total serum cholesterol levels and 409 coronary deaths, 325 cancer deaths, and 534 other deaths for a 32-year follow-up. Age- and risk factor-adjusted Cox regressions were computed. Nonlinear (U-shaped) relations were investigated with the use of quadratic regression and with dummy variables using the 160-199 mg/dl group as the comparison group. Subset analyses investigated the relation in smokers and men who drank > or = 14 alcoholic drinks per week. All analyses were repeated removing those with existing cardiovascular disease and cancer and those who died during the first 5 years of follow-up. A significant U-shaped relation with all-cause mortality was noted, as were an inverse relation to cancer mortality and a monotonic increasing relation with coronary disease mortality. In subset analyses, the association of low serum cholesterol (< 160 mg/dl) with cancer mortality was observed in men who smoked cigarettes. Compared with the 160-199 mg/dl group, the relative risk was 3.72 (p = 0.0001, 95% confidence interval 1.91-7.25). Studies of the relation of low total serum cholesterol levels, cigarette smoking, and cancer are needed.

Adult↗

PubMedDate not supplied

A practical method of predicting client revisit intention in a hospital setting.

Data mining (DM) models are an alternative to traditional statistical methods for examining whether higher customer satisfaction leads to higher revisit intention. This study used a total of 906 outpatients' satisfaction data collected from a nationwide survey interviews conducted by professional interviewers on a face-to-face basis in South Korea, 1998. Analyses showed that the relationship between overall satisfaction with hospital services and outpatients' revisit intention, along with word-of-mouth recommendation as intermediate variables, developed into a nonlinear relationship. The five strongest predictors of revisit intention were overall satisfaction, intention to recommend to others, awareness of hospital promotion, satisfaction with physician's kindness, and satisfaction with treatment level.

Adult↗

PubMed2004

Statistical analyses of repeated measures in physiological research: a tutorial.

Experimental designs involving repeated measurements on experimental units are widely used in physiological research. Often, relatively many consecutive observations on each experimental unit are involved and the data may be quite nonlinear. Yet evidently, one of the most commonly used statistical methods for dealing with such data sets in physiological research is the repeated-measurements ANOVA model. The problem herewith is that it is not well suited for data sets with many consecutive measurements; it does not deal with nonlinear features of the data, and the interpretability of the model may be low. The use of inappropriate statistical models increases the likelihood of drawing wrong conclusions. The aim of this article is to illustrate, for a reasonably typical repeated-measurements data set, how fundamental assumptions of the repeated-measurements ANOVA model are inappropriate and how researchers may benefit from adopting different modeling approaches using a variety of different kinds of models. We emphasize intuitive ideas rather than mathematical rigor. We illustrate how such models represent alternatives that 1) can have much higher interpretability, 2) are more likely to meet underlying assumptions, 3) provide better fitted models, and 4) are readily implemented in widely distributed software products.

Animals↗

PubMed1998

[Occupational problems from exposure to roentgen rays].

The authors analysed methodological problems concerning the use of film dosimetry in the evaluation of annual doses received by workers exposed to X-radiation. This is mainly related to nonlinearity of the optical density of films dependent on the dose and the photon energy. The set of four filters solved these problems. The evaluation of occupational exposure among workers being in contract with X-radiation sources in 1996 as well as the analysis of data on occupational exposure followed since 1966 are presented.

Film Dosimetry↗

PubMed2005

Synthesis, spectroscopic and nonlinear optical properties of multiple [60]fullerene-oligo(p-phenylene ethynylene) hybrids.

A series of multiple [60]fullerene terminated oligo(p-phenylene ethynylene) (OPE) hybrid compounds has been synthesized through a newly developed in situ ethynylation method. Structural and magnetic shielding properties of the highly unsaturated carbon-rich C(60) and OPE scaffolds were characterized by 1D and 2D NMR spectroscopic analyses. Electronic interactions between the [60]fullerenes and the OPE backbones were investigated by UV/Vis spectroscopic and cyclic voltammetry (CV) experiments. Our studies clearly show that although the multiple [60]fullerene groups are connected via pi-conjugated OPE frameworks, they present diminutive electronic interactions in the ground state, and the electronic behavior of the [60]fullerene cages are only affected by the OPE backbones through modest inductive effects. Interestingly, sizable third-order nonlinear optical (NLO) responses (gamma) and enhanced two-photon absorption (TPA) cross-sections (sigma((2))) were determined for the multifullerene-OPE hybrid 31 relative to its OPE precursor from differential optical Kerr effect (DOKE) experiments. Such enhanced NLO performance is presumably due to the occurrence of periconjugation and/or charge transfer effects in the excited state. In addition, comparatively strong excited-state absorption was observed and characterized for OPE pentamer 12. Thus, the use of such fullerene-derivatized conjugated oligomers aids the quest for molecules with large third-order NLO and TPA properties.

Fullerenes↗

PubMed2003

How much information is associated with a particular stimulus?

Although the Shannon mutual information can be used to reveal general features of the neural code, it cannot directly address which symbols of the code are significant. Further insight can be gained by using information measures that are specific to particular stimuli or responses. The specific information is a previously proposed measure of the amount of information associated with a particular response; however, as I show, it does not properly characterize the amount of information associated with particular stimuli. Instead, I propose a new measure: the stimulus-specific information (SSI), defined to be the average specific information of responses given the presence of a particular stimulus. Like other information theoretic measures, the SSI does not rely on assumptions about the neural code, and is robust to non-linearities of the system. To demonstrate its applicability, the SSI is applied to data from simulated visual neurons, and identifies stimuli consistent with the neuron's linear kernel. While the SSI reveals the essential linearity of the visual neurons, it also successfully identifies the well-encoded stimuli in a modified example where linear analysis techniques fail. Thus, I demonstrate that the SSI is an appropriate measure of the information associated with particular stimuli, and provides a new unbiased method of analysing the significant stimuli of a neural code.

Action Potentials↗

PubMed2005

Importance of unburned coal carbon, black carbon, and amorphous organic carbon to phenanthrene sorption in sediments.

The aim of this paper was to estimate the contribution to total phenanthrene sorption from unburned coal and black carbon (BC; soot and charcoal) in sediment. We determined sorption isotherms for five Argonne Premium Coal standards over a wide concentration interval (0.01-10 000 ng/L). The coals showed strong and nonlinear sorption (carbon-normalized K(F) = 5.41-5.96; nF = 0.68-0.82). Coal sorption appeared to become more nonlinear with increasing coal maturity. The coal's specific surface area appeared to influence K(F). On the basis of the current coal sorption observations combined with earlier petrographic analyses and BC sorption experiments, we calculated for one particular sediment that coal, BC, and "other" OC were all important to PHE sorption in the environmentally relevant nanogram per liter range. This indicates that it is important to consider strong sorption to coal in the risk assessment of coal-impacted geosorbents (e.g., river beds) where coal is mined/shipped and manufactured gas plant sites.

Adsorption↗

PubMed2000

Slow dynamics of equilibrium density fluctuations in suspensions of colloidal hard spheres near the glass transition

A mean-field theory for the dynamics of equilibrium suspensions of colloidal hard spheres near the glass transition is presented based on the standpoint recently proposed by the present author. It is shown that although the relative magnitude of the density fluctuations to the mean equilibrium density is small even near the glass transition, they are described by a nonlinear stochastic equation which originates from the long-range hydrodynamic interactions between particles. A nonlinear mean-field equation for the particle mean-square displacement is then derived. This equation is used to analyze the recent experimental data for equilibrium colloidal suspensions. Analyses show that no divergence of the alpha- and beta-relaxation times is found in the experimental data, although the dynamic properties of the colloidal liquid exhibit a drastic slowing down in the so-called supercooled region.

Journal Article↗

PubMed1980

Relationship between plasma osmolality and plasma vasopressin in human subjects.

The relationship between plasma osmolality (pOsm) and plasma vasopressin (pAVP) was studied in 13 human subjects during dehydration. The fit of linear, log-linear, parabolic, and exponential models was tested. For all of the data, the nonlinear models had the best fit. However, when individual differences in either gain or threshold were allowed for, the linear models were better than log-linear models. Finally, analyses were made with individual data points. Linear models had the best fit in half of the subjects, whereas for the others the parabolic model gave the best fit. For those subjects investigated in the low range of the osmoregulatory curve, a linear relationship was found, whereas, for those having the most pronounced increase in pOsm, the most significant improvement was found with the parabolic model. This finding indicates that the relationship is not stable during dehydration in the whole range and that hypovolemia probably can influence the secretion rate and/or metabolic clearance rate and thereby the relationship.

Adolescent↗

PubMed2006

Psychological distress and mortality: are women more vulnerable?

Does psychological distress increase mortality risk? If it does, are women more vulnerable than men to the effect of distress on mortality? Drawing from cumulative disadvantage theory, these questions are addressed with data from a 20-year follow-up of a national sample of adults ages 25-74. Event history analyses were performed to examine mortality from general and specific causes for men and women. Findings reveal that the effect of psychological distress on all-cause mortality was nonlinear for men. Moderate amounts of distress were associated with lower mortality risk, but high levels of distress raised men's mortality risk. Moreover the curvilinear relationship between distress and mortality varied by cause of death for men and women. Men with high levels of psychological distress were more vulnerable to ischemic heart disease mortality. Women with high levels of distress were more vulnerable to cancer mortality.

Adult↗

PubMed1999

Temporal properties of the hemodynamic response in functional MRI.

Today, most studies of cognitive processes using functional magnetic resonance imaging (fMRI) adopt an event-related experimental design. Highly flexible stimulation settings require new statistical models where not only the activation amount, but also the time course of the measured hemodynamic response is analyzed. It is possible to obtain statistically valid descriptions of single hemodynamic responses from a robust nonlinear estimation procedure. Focus is placed on the temporal behaviour of the hemodynamic response: relative temporal order, changes induced by modification of the experimental context, and interindividual differences. Example analyses from recent fMRI studies underline the usefulness of this approach.

Adult↗