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PubMed1983

Ultrasound velocity in fixed human liver: empirical anova and regression modelling on histologically assessed abnormalities.

Anova and "dummy variables" least squares regression methods are used to investigate the dependence of ultrasound propagation velocity on the presence or absence of fat and on the rank ordered level of cirrhosis in fixed human liver. Cirrhosis is found to affect velocity in a nonlinear fashion, while fat depresses the velocities toward lower values. Quantifications of these effects and statistical analyses of their magnitudes are presented. The results represent a contribution toward the empirical understanding of the effects of tissue abnormalities on the velocity of ultrasound propagation in fixed human tissues.

Analysis of Variance↗

PubMed2005

A unified cosolvency model for calculating solute solubility in mixed solvents.

Organic solvents are amongst the most powerful solubilization agents for a large number of water-insoluble drugs. A number of equations has been reported for mathematical representation of solute solubility in mixed solvents. The question is then posed--is there a mathematical difference between these models? To address this point, it has been demonstrated that all cosolvency models could be made equivalent by using algebraic manipulations. In order to familiarize the readers with the available cosolvency models, they are briefly reviewed. The models can be divided into two mathematical categories, i.e. linear and non-linear models. The linear models include: the log-linear, extended Hildebrand solubility approach, excess free energy equations, combined nearly ideal binary solvent/Redlich-Kister equation and Margule equations which can be converted to a general single model which expresses the logarithm of mole fraction solubility of a solute as a power series of volume fraction of the cosolvent. The non-linear models include the mixture response surface methods, two step solvation model and modified Wilson model which can be converted to a non-linear general form. Also, it has been shown that both the general single model and a non-linear general model are mathematically identical. To show the applicability of the models on real experimental data, 35 data sets have been collected from the literature. Both linear and nonlinear models produced comparable accuracies when an equal number of constant terms was employed in numerical analyses.

Models, Chemical↗

PubMed2004

Initial years of recreational artistic gymnastics training improves lumbar spine bone mineral accrual in 4- to 8-year-old females.

UNLABELLED: Gymnasts' bone mineral characteristics are generally not known before starting their sport. Prepubertal females who enrolled in beginning artistic gymnastics (n = 65) had lower bone mineral than controls (n = 78). However, 2 years of gymnastics participation versus no participation led to a significantly greater accrual of forearm bone area and lumbar spine areal BMD. INTRODUCTION: The skeletal response to exercise in children compared with adults is heightened because of the high bone turnover rate and the ability of bone to change its size and shape. Whereas child gymnasts generally have greater rates of bone mineral accrual compared with nongymnasts, it is unknown if some of these skeletal advantages are present before the onset of training or are caused entirely by training. MATERIALS AND METHODS: Changes in bone area (BA; cm2), BMC (g), and areal BMD (aBMD; g/cm2) over 24 months were examined in prepubertal females, 4-8 years of age, who selected to perform recreational gymnastics (GYM; n = 65), nongymnastic activities, or no organized activity (CON; n = 78). Participants had essentially no lifetime history of organized athletic participation (< 12 weeks). Pubertal maturation was assessed annually by a physician. Total body, lumbar spine, total proximal femur, and forearm BA, BMC, and aBMD were measured every 6 months using DXA (Hologic QDR-1000W). Independent samples t-tests determined baseline group differences. Nonlinear mixed effects models were used to model 24-month changes in bone data. In subset analyses, high-level gymnasts advancing to competition (HLG; n = 9) were compared with low-level nonadvancing gymnasts (LLG; n = 56). RESULTS: At baseline, GYM were shorter, lighter, and had lower BA, BMC, and aBMD compared with CON (p < 0.05), whereas HLG did not differ significantly in these measurements compared with LLG (p > 0.05). Controlling for differences in race, baseline measures of body mass, height, and calcium intake, and change in breast development beyond stage II at 24 months, GYM had greater long-term (asymptotic) mean responses for total body aBMD and forearm BMC (p < 0.04) and greater rates of increase in the mean responses of lumbar spine aBMD and forearm BA compared with CON over 24 months. Over time, forearm BA increased to a greater extent in HLG compared with LLG (p < 0.01). CONCLUSIONS: Females participating in recreational gymnastics initiated during childhood have enhanced bone mineral gains at the total body, lumbar spine, and forearm over 24 months. Higher-level training promotes additional gains in forearm BA.

Absorptiometry, Photon↗

PubMed2000

Comparison of pharmacokinetics of fentanyl after intravenous and transdermal administration in cats.

OBJECTIVE: To compare pharmacokinetic and pharmacodynamic characteristics of fentanyl citrate after IV or transdermal administration in cats. ANIMALS: 6 healthy adult cats with a mean weight of 3.78 kg. PROCEDURE: Each cat was given fentanyl IV (25 mg/cat; mean +/- SD dosage, 7.19 +/- 1.17 mg/kg of body weight) and via a transdermal patch (25 microg of fentanyl/h). Plasma concentrations of fentanyl were measured by use of radioimmunoassay. Pharmacokinetic analyses of plasma drug concentrations were conducted, using an automated curve-stripping process followed by nonlinear, least-squares regression. Transdermal delivery of drug was calculated by use of IV pharmacokinetic data. RESULTS: Plasma concentrations of fentanyl given IV decreased rapidly (mean elimination half-life, 2.35 +/- 0.57 hours). Mean +/- SEM calculated rate of transdermal delivery of fentanyl was 8.48 +/- 1.7 mg/h (< 36% of the theoretical 25 mg/h). Median steady-state concentration of fentanyl 12 to 100 hours after application of the transdermal patch was 1.58 ng/ml. Plasma concentrations of fentanyl < 1.0 ng/ml were detected in 4 of 6 cats 12 hours after patch application, 5 of 6 cats 18 and 24 hours after application, and 6 of 6 cats 36 hours after application. CONCLUSIONS AND CLINICAL RELEVANCE: In cats, transdermal administration provides sustained plasma concentrations of fentanyl citrate throughout a 5-day period. Variation of plasma drug concentrations with transdermal absorption for each cat was pronounced. Transdermal administration of fentanyl has potential for use in cats for long-term control of pain after surgery or chronic pain associated with cancer.

Administration, Topical↗

PubMed2003

Analyses of circular dichroism spectra of membrane proteins.

Circular dichroism (CD) spectroscopy is a valuable technique for the determination of protein secondary structures. Many linear and nonlinear algorithms have been developed for the empirical analysis of CD data, using reference databases derived from proteins of known structures. To date, the reference databases used by the various algorithms have all been derived from the spectra of soluble proteins. When applied to the analysis of soluble protein spectra, these methods generally produce calculated secondary structures that correspond well with crystallographic structures. In this study, however, it was shown that when applied to membrane protein spectra, the resulting calculations produce considerably poorer results. One source of this discrepancy may be the altered spectral peak positions (wavelength shifts) of membrane proteins due to the different dielectric of the membrane environment relative to that of water. These results have important consequences for studies that seek to use the existing soluble protein reference databases for the analyses of membrane proteins.

Animals↗

PubMed1998

Use of the bispectrum to analyse properties of the human electrocardiograph.

The bispectrum and bicoherence spectrum have been shown to be powerful techniques for identifying different types of nonlinear system responses. This paper presents an introduction to bispectral techniques applied to biomedical signals and examines the bispectral properties of the human electrocardiograph (ECG). The bispectrum proves to be an effective tool for representing and distinguishing different ECG response types. Bispectral ECG analysis is non-invasive and may prove to be a useful discriminant diagnostic.

Electrocardiography↗

PubMed2001

A possible role of the striatum in linear and nonlinear category learning: evidence from patients with Huntington's disease.

Linear and nonlinear categorization rule learning was examined in patients with Huntington's disease (HD) and a group of controls using the perceptual categorization task. Participants learned to categorize simple line stimuli into 1 of 2 categories over 600 trials. In addition to traditional measures of accuracy, quantitative model-based analyses were applied to each participant's data to characterize better the nature of any observed deficits. In the linear rule condition, HD patients displayed an early-training deficit relative to controls, whereas later in training the HD patients were not statistically different from controls. In the nonlinear rule condition, HD patients displayed both an early- and late-training deficit. The quantitative model-based analyses revealed that the HD patients' deficits in the linear condition were due to an impairment in learning the experimenter-defined rule and not in applying a learned rule inconsistently. In the nonlinear condition, in contrast, the HD patients' deficits were due to an impairment in learning the experimenter-defined rule and in applying a learned rule inconsistently. Overall, these results suggest that HD can result in a deficit in learning both linear and nonlinear categorization rules.

Adult↗

PubMed2004

Multibody dynamic simulation of knee contact mechanics.

Multibody dynamic musculoskeletal models capable of predicting muscle forces and joint contact pressures simultaneously would be valuable for studying clinical issues related to knee joint degeneration and restoration. Current three-dimensional multibody knee models are either quasi-static with deformable contact or dynamic with rigid contact. This study proposes a computationally efficient methodology for combining multibody dynamic simulation methods with a deformable contact knee model. The methodology requires preparation of the articular surface geometry, development of efficient methods to calculate distances between contact surfaces, implementation of an efficient contact solver that accounts for the unique characteristics of human joints, and specification of an application programming interface for integration with any multibody dynamic simulation environment. The current implementation accommodates natural or artificial tibiofemoral joint models, small or large strain contact models, and linear or nonlinear material models. Applications are presented for static analysis (via dynamic simulation) of a natural knee model created from MRI and CT data and dynamic simulation of an artificial knee model produced from manufacturer's CAD data. Small and large strain natural knee static analyses required 1 min of CPU time and predicted similar contact conditions except for peak pressure, which was higher for the large strain model. Linear and nonlinear artificial knee dynamic simulations required 10 min of CPU time and predicted similar contact force and torque but different contact pressures, which were lower for the nonlinear model due to increased contact area. This methodology provides an important step toward the realization of dynamic musculoskeletal models that can predict in vivo knee joint motion and loading simultaneously.

Computer Simulation↗

PubMed1995

Quantification of the static load component in muscle work using nonlinear filtering of surface EMG.

Prolonged static strain on the muscles of the neck-shoulder region is believed to be linked to the development of musculoskeletal problems. To quantify the static strain on the basis of EMG, the level as well as the duration of the muscle load should be analysed on temporal basis. In this paper, some methods for the temporal analysis of EMG recordings are proposed with an aim of quantifying the long-term static strain on the muscle. The use of nonlinear median prefilters for decomposing the EMG activity according both to amplitude level and duration of the activity at different levels is proposed. The prefiltering methods were also evaluated using laboratory studies. The main aim of the studies was to compare the estimation errors between EMG and force for different types of prefilters especially when the static load component was analysed. The average estimation error for sequences having a duration longer than 1 s was found to be 8% of MVC in the case of trapezius muscle and 14% of MVC in the case of biceps brachii muscle. Linear relation was found on the basis of linear least squares curve fitting to give the largest correlation coefficients between EMG and force, when the static load component was analysed.

Adult↗

PubMed1979

A nonlinear model for studying oscillations in the blood pressure control system.

The idea that physiological systems sometimes include oscillations as part of their control function is a relatively new idea; the paper discusses the role of such oscillations in the regulation of arterial blood pressure and how they can be studied by modelling techniques. A nonlinear model is proposed which can be related directly to the physiology. This is seen as an important step because mainly previous studies of biological oscillations have used lumped equations, e.g. the Van der Pol equation, which do not possess the property. On the basis of the model, the oscillatory behaviour of the blood pressure control system is analysed by the application of the dual input describing function technique, a powerful analytical method which has wide application to the study of nonlinear oscillatory phenomena in physiology. The final section of the paper considers the digital simulation of the model by Z transform techniques and how the simulation can be used to study the interaction of respiratory and blood pressure control systems.

Blood Pressure↗

PubMed2003

Forcing function effects on nonlinear trajectories: identifying very local brain dynamics.

Effects of imposing a sinusoidal acoustic and visual forcing function at various frequencies onto an EEG process are examined in terms of various indices of the nonlinear dynamics. Conjoint use of four methods of data analysis; Lyapunov exponents, the entropic analogue of the Schwarzian derivative, surrogate distributions, and higher-order kernel analyses in the time domain, is illustrated. Local epochs with unstable dynamics are identifed on very short series.

Auditory Perception↗

PubMed2005

The role of nonlinear factor-to-indicator relationships in tests of measurement equivalence.

Measurement invariance is a necessary condition for the evaluation of factor mean differences over groups or time. This article considers the potential problems that can arise for tests of measurement invariance when the true factor-to-indicator relationship is nonlinear (quadratic) and invariant but the linear factor model is nevertheless applied. The factor loadings and indicator intercepts of the linear model will diverge across groups as the factor mean difference increases. Power analyses show that even apparently small quadratic effects can result in rejection of measurement invariance at moderate sample sizes when the factor mean difference is medium to large. Recommendations include the identification of nonlinear relationships using diagnostic plots and consideration of newly developed methods for fitting nonlinear factor models.

Analysis of Variance↗

PubMed1998

Sedimentation analysis of noninteracting and self-associating solutes using numerical solutions to the Lamm equation.

The potential of using the Lamm equation in the analysis of hydrodynamic shape and gross conformation of proteins and reversibly formed protein complexes from analytical ultracentrifugation data was investigated. An efficient numerical solution of the Lamm equation for noninteracting and rapidly self-associating proteins by using combined finite-element and moving grid techniques is described. It has been implemented for noninteracting solutes and monomer-dimer and monomer-trimer equilibria. To predict its utility, the error surface of a nonlinear regression of simulated sedimentation profiles was explored. Error contour maps were calculated for conventional independent and global analyses of experiments with noninteracting solutes and with monomer-dimer systems at different solution column heights, loading concentrations, and centrifugal fields. It was found that the rotor speed is the major determinant for the shape of the error surface, and that global analysis of different experiments can allow substantially improved characterization of the solutes. We suggest that the global analysis of the approach to equilibrium in a short-column sedimentation equilibrium experiment followed by a high-speed short-column sedimentation velocity experiment can result in sedimentation and diffusion coefficients of very high statistical accuracy. In addition, in the case of a protein in rapid monomer-dimer equilibrium, this configuration was found to reveal the most precise estimate of the association constant.

Biophysical Phenomena↗

PubMed2001

Estimation of leaf nitrogen content from spectral characteristics of rice canopy.

Ground-based remotely sensed reflectance spectra of hyperspectral resolution were monitored during the growing period of rice under various nitrogen application rates. It was found that reflectance spectrum of rice canopy changed in both wavelength and reflectance as the plants developed. Fifteen characteristic wavebands were identified from the apparent peaks and valleys of spectral reflectance curves, in accordance with the results of the first-order differentiation, measured over the growing season of rice. The bandwidths and center wavelengths of these characteristic wavebands were different among nitrogen treatments. The simplified features by connecting these 15 characteristic wavelengths may be considered as spectral signatures of rice canopy, but spectral signatures varied with developmental age and nitrogen application rates. Among these characteristic wavebands, the changes of the wavelength in band 11 showed a positive linear relationship with application rates of nitrogen fertilizer, while it was a negative linear relationship in band 5. Mean reflectance of wavelengths in bands 1, 2, 3, 5, 11, and 15 was significantly correlated with application rates. Reflectance of these six wavelengths changed nonlinearly after transplanting and could be used in combination to distinguish rice plants subjected to different nitrogen application rates. From the correlation analyses, there are a variety of correlation coefficients for spectral reflectance to leaf nitrogen content in the range of 350-2400 nm. Reflectance of most wavelengths exhibited an inverse correlation with leaf nitrogen content, with the largest negative value (r = -0.581) located at about 1376 nm. Changes in reflectance at 1376 nm to leaf nitrogen content during the growing period were closely related and were best fitted to a nonlinear function. This relationship may be used to estimate and to monitor nitrogen content of rice leaves during rice growth. Reflectance of red light minimum and near-infrared peak and leaf nitrogen content were correlated nonlinearly.

Agriculture↗

PubMed2003

Effect of imipramine on linear and nonlinear measures of heart rate variability in children.

We investigated the effects of treatment with the tricyclic antidepressant (TCA) imipramine in eight children in supine and standing postures. We used 256 seconds of real-time data for the analyses. Spectral analysis showed a significant decrease of high-frequency (HF) power (0.15-0.5 Hz), especially in the standing posture. Low frequency (LF) HF ratios were significantly higher in the standing posture after treatment, suggesting increased sympathovagal interaction. We also obtained the nonlinear measures of fractal dimension (FD), and approximate entropy (APEN). Although the FD of heart rate was significantly lower in the standing posture, APEN was significantly decreased after treatment in either posture and was the most sensitive measure in this study. These findings suggest a decreased cardiac vagal function with a relative increase in sympathetic responsiveness, which may in part be related to the cardiotoxicity of these drugs. These findings are discussed in relation to the cardiovascular side effects of TCAs.

Adolescent↗

PubMed1990

Coding of spectral fine structure in the auditory nerve. II: Level-dependent nonlinear responses.

Phase-locked discharge patterns of single cat auditory-nerve fibers were analyzed in response to complex tones centered at fiber characteristic frequency (CF). Signals were octave-bandwidth harmonic complexes defined by a center frequency F and an intercomponent spacing factor N, such that F/N was the fundamental frequency. Parameters that were manipulated included the phase spectrum, the number of components, and the intensity of the center component. Analyses employed Fourier transforms of period histograms to assess the degree to which responses were synchronized to the frequencies present in the acoustic stimulus. Several nonlinearities were observed in the response as intensity was varied between threshold and 80-90 dB SPL. Response nonlinearities were strong for all signals except those with random phase spectra. The most commonly observed nonlinearity was an emphasis of one or more stimulus components in the response. The degree of nonlinearity usually increased with intensity and signal complexity and decreased with fiber frequency selectivity. Half-wave rectification introduced synchronization to the missing fundamental. The strength of the response at the fundamental was related to stimulus crest factor. Signals with low center frequencies and high crest factors often elicited instantaneous discharge rates at the theoretical maximum of pi CF. This suggests that the probability of spike generation approaches one during high-amplitude waveform segments. Response nonlinearity was interpreted as arising from three sources, namely, cochlear mechanics, compression of instantaneous discharge rate, and saturation of average discharge rate. At near-threshold intensities, fibers with high spontaneous rates exhibited responses that were linear functions of stimulus waveshape, whereas fibers with low spontaneous spike rates produced responses that were best described in terms of an expansive nonlinearity.

Animals↗

PubMed1999

Power of univariate and multivariate analyses of repeated measurements in controlled clinical trials.

The power of univariate and multivariate tests of significance is compared in relation to linear and nonlinear patterns of treatment effects in a repeated measurement design. Bonferroni correction was used to control the experiment-wise error rate in combining results from univariate tests of significance accomplished separately on average level, linear, quadratic, and cubic trend components. Multivariate tests on these same components of the overall treatment effect, as well as a multivariate test for between-groups difference on the original repeated measurements, were also evaluated for power against the same representative patterns of treatment effects. Results emphasize the advantage of parsimony that is achieved by transforming multiple repeated measurements into a reduced set of mean ngful composite variables representing average levels and rates of change. The Bonferroni correction applied to the separate univariate tests provided experiment-wise protection against Type I error, produced slightly greater experiment-wise power than a multivariate test applied to the same components of the data patterns, and provided substantially greater power than a multivariate test on the complete set of original repeated measurements. The separate univariate tests provide interpretive advantage regarding locus of the treatment effects.

Analysis of Variance↗

PubMed2005

A unifying explanation of primary generalized seizures through nonlinear brain modeling and bifurcation analysis.

The aim of this paper is to explain critical features of the human primary generalized epilepsies by investigating the dynamical bifurcations of a nonlinear model of the brain's mean field dynamics. The model treats the cortex as a medium for the propagation of waves of electrical activity, incorporating key physiological processes such as propagation delays, membrane physiology, and corticothalamic feedback. Previous analyses have demonstrated its descriptive validity in a wide range of healthy states and yielded specific predictions with regards to seizure phenomena. We show that mapping the structure of the nonlinear bifurcation set predicts a number of crucial dynamic processes, including the onset of periodic and chaotic dynamics as well as multistability. Quantitative study of electrophysiological data supports the validity of these predictions. Hence, we argue that the core electrophysiological and cognitive differences between tonic-clonic and absence seizures are predicted and interrelated by the global bifurcation diagram of the model's dynamics. The present study is the first to present a unifying explanation of these generalized seizures using the bifurcation analysis of a dynamical model of the brain.

Action Potentials↗