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PubMed1992

Automated capillary electrophoresis applied to therapeutic drug monitoring.

Chromatographic separations in conjunction with physical chemical detection methods can provide extremely accurate and highly precise measurements of drugs in biological matrices. Immunochemical methods for drug analyses, on the other hand, although usually fully automated, often lack accuracy, may be subject to matrix interference effects, and frequently exhibit nonlinearities that contribute to suboptimal analytical results. Automated capillary electrophoresis (CE) promises the high accuracy and precision of physical methods with no operator intervention once the sample is loaded into the sample cup. A clean-up step is necessary for the analysis of drugs in biological matrices, but that could also be fully automated. Reagent costs per test with CE approach zero, because of the use of extremely small volumes of buffers, standards, and controls. We present data supporting CE as an alternative separation strategy for 28 commonly used therapeutic drugs. These can be resolved in less than 16 min with an optimized micelle-based buffer system.

Anticonvulsants↗

PubMed2002

Oscillations and noise: inherent instability of pressure support ventilation?

Pressure support ventilation (PSV) is almost universally employed in the management of actively breathing ventilated patients with acute respiratory failure. In this partial support mode of ventilation, a fixed pressure is applied to the airway opening, and flow delivery is monitored by the ventilator. Inspiration is terminated when measured inspiratory flow falls below a set fraction of the peak flow rate (flow cutoff); the ventilator then cycles to a lower pressure and expiration commences. We used linear and nonlinear mathematical models to investigate the dynamic behavior of pressure support ventilation and confirmed the predicted behavior using a test lung. Our mathematical and laboratory analyses indicate that pressure support ventilation in the setting of airflow obstruction can be accompanied by marked variations in tidal volume and end-expiratory alveolar pressure, even when subject effort is unvarying. Unstable behavior was observed in the simplest plausible linear mathematical model and is an inherent consequence of the underlying dynamics of this mode of ventilation. The mechanism underlying the observed instability is "feed forward" behavior mediated by oscillatory elevation in end-expiratory pressure. In both mathematical and mechanical models, unstable behavior occurred at impedance values and ventilator settings that are clinically realistic.

Adult↗

PubMed2004

Deterministic nonlinear characteristics of in vivo blood flow velocity and arteriolar diameter fluctuations.

We have performed a nonlinear analysis of fluctuations in red cell velocity and arteriolar calibre in the mesenteric bed of the anaesthetized rat. Measurements were obtained under control conditions and during local superfusion with NG-nitro-L-arginine (L-NNA, 30 microM) and tetrabutylammonium (TBA, 0.1 mM), which suppress NO synthesis and block Ca2+ activated K+ channels (KCa), respectively. Time series were analysed by calculating correlation dimensions and largest Lyapunov exponents. Both statistics were higher for red cell velocity than diameter fluctuations, thereby potentially differentiating between global and local mechanisms that regulate microvascular flow. Evidence for underlying nonlinear structure was provided by analysis of surrogate time series generated from the experimental data following randomization of Fourier phase. Complexity indices characterizing time series under control conditions were in general higher than those derived from data obtained during superfusion with L-NNA and TBA.

Animals↗

PubMed1995

Nonlinear changes in brain's response in the event of injury as detected by adaptive coherence estimation of evoked potentials.

Injury-related changes in evoked potentials are studied with the aid of the coherence function, which effectively measures the degree of linear association between a pair of signals recorded during normal and abnormal states of the brain. The performance of an adaptive algorithm for estimating coherence function is studied, and the effects of additive noise on the estimated coherence function is discussed. Further, a linearity index is formulated and, through analysis and simulations, the index is shown to respond in a predictable manner to increasing nonlinearity while maintaining the robustness to the observation noise. Somatosensory evoked potentials are shown to be sensitive to injury resulting from acute cerebral hypoxia. We analyze the somatosensory evoked potentials recorded from anesthetized cats during inhalation of 8-9% oxygen gas mixtures and during recovery with 100% oxygen. Analyses of the experimental data show a very sharp drop in the magnitude coherence estimates during hypoxic injury and a corresponding rapid decline in the linearity index at the very early stages of the hypoxic injury. Thus, injury may lead to nonlinearities in the electrical response of the brain, and such measurements analyzed by the adaptive coherence estimation method may be used for diagnostic purposes.

Algorithms↗

PubMed2004

Bayesian analysis of two-level nonlinear structural equation models with continuous and polytomous data.

Two-level structural equation models with mixed continuous and polytomous data and nonlinear structural equations at both the between-groups and within-groups levels are important but difficult to deal with. A Bayesian approach is developed for analysing this kind of model. A Markov chain Monte Carlo procedure based on the Gibbs sampler and the Metropolis-Hasting algorithm is proposed for producing joint Bayesian estimates of the thresholds, structural parameters and latent variables at both levels. Standard errors and highest posterior density intervals are also computed. A procedure for computing Bayes factor, based on the key idea of path sampling, is established for model comparison.

Bayes Theorem↗

PubMed2003

Self-organization and complexity: a new age for theory, computation and experiment.

I first describe the notion of self-organization as a property of far-from-equilibrium nonlinear dissipative dynamical systems. Rather than describing such complex systems at a purely phenomenological level, however, I focus attention on the emergent nature of this complexity, by analysing a few examples of physical and physicochemical systems with simple underlying microscopic dynamics yet complex, self-organizing macroscopic properties. These include several mesoscopic models of fluid dynamics as well as a modern approach to nucleation and growth phenomena. Finally, I discuss how the advent of computational grids is set to provide a major boost to the study of such complex, self-organizing systems.

Adaptation, Physiological↗

PubMed2001

A new approach to analysing texture-defined motion.

It has been widely accepted that standard low-level computational approaches to motion processing cannot extract texture-defined motion without applying some pre-processing nonlinearity. This has motivated accounts of motion perception in which luminance- and texture-defined motion are processed by separate mechanisms. Here, we introduce a novel method of image description where motion sequences may be described in terms of their local spatial and temporal gradients. This allows us to assess the local velocity information available to standard low-level motion mechanisms. Our analysis of several texture-motion stimuli shows that the information indicating correct texture-motion velocity and/or direction is present in the raw luminance measures. This raises the possibility that luminance-motion and texture-motion may be processed by the same cortical mechanisms. Our analysis offers a way of looking at texture-motion processing that is, to our knowledge, new and original.

Electrophysiology↗

PubMedDate not supplied

Nonlinear least-squares regression analysis by a simplex method using differential equations containing Michaelis-Menten type rate constants.

Computer curve fittings were carried out to observed data as well as theoretically generated plasma concentrations of several drugs, using differential equations which contained nonlinear Michaelis-Menten type rate constants to discuss problems of initial parameter estimation in pharmacokinetic analysis. Calculation based on two different algorithms, each carried out by using SIMP (simplex method) and NONLIN (modified Gauss-Newton method) produced similar results. However, occasional divergence or unreasonable solutions occurred in a later case, when assumed values of Km and Vmax were used as initial parameters. A combined use of SIMP and NONLIN in which calculated values by SIMP were used as initial values for NONLIN, was shown to be effective to analyse plasma concentration data of indocyanine green bearing difficulty in estimating initial values. It is suggested that the successive method is useful for the curve fitting of plasma concentration with nonlinear pharmacokinetic rate processes.

Models, Statistical↗

PubMed1999

Synchronization in chaotic Hamiltonian systems and a geophysical application.

This paper addresses the question of the rate of synchronization of two identical systems as a function of the inserting time interval Delta t between inserted variables of the driving system in the role of the same variables of the driven system in a simplified Hamiltonian system and its application to a simplified geophysical model. We start by analyzing the synchronization in a simplified two-degree Hamiltonian system. The synchronization rate turns out to be a decreasing function of the inserting time interval Delta t up to a certain limit Delta t(o) where the process reverses and the synchronization rate becomes slower as the inserting frequency decreases. The key point of the analysis uses a second-order Taylor expansion of the system resolvent which indicates that synchronization rate is basically of order O(Delta t(2)) for small Delta t. The study is then extended to include a simplified geophysical system. A nonlinear one-dimensional shallow-water model on a periodic domain meant to represent a latitudinal circle around 45 degrees N is used. It is found that when the zonal wind is inserted, the maximum synchronization rate is obtained when the inserting time interval is approximately 4 h. When the meridional wind is inserted, it is obtained at slightly less than 4 h. It is shown, in particular, that the synchronization rate depends on the latitude (or the Coriolis parameter). A low-order simplified dynamical system derived from the one-dimensional shallow-water model is used to show that this optimum time interval Delta t(o) when the zonal wind and the geopotential, for example, are inserted varies approximately as square root of [2]/2 Omega sin phi to accuracy O(Delta t(3)). Analyses performed with a linear version of the shallow-water model reveal that this latter can be used to explain the observed convergence behavior in the nonlinear model. The only point is the choice of the stationary state for linearization purposes. It is then suggested that in more complicated geophysical systems, the closest stationary state to the climatology can be used to estimate the crossover point Delta t(o).

Journal Article↗

PubMed2000

Further analysis of the size and shape of cells obtained by impression cytology from the exposed portion of the human bulbar conjunctiva.

PURPOSE: To assess whether the size of the cells obtained by conjunctival impression cytology can be quantitatively assessed by measurement of the longest dimension of the cells. METHODS: Under topical benoxinate anaesthesia, cells were removed from the normally exposed nasal bulbar conjunctival surface using a 0.4 micron pore diameter filter (Biopore filter; type Millcell-CM). The filters were stained with haematoxylin after ethanol denaturation, photographed at 40 x magnification, and 35 mm slides prepared. An optical overlay method was used to outline the borders of sets of 30-35 contiguous cells on each image. The cell area, longest and shortest dimensions were measured by planimetry to an accuracy of +/- 3%. RESULTS: Analyses of 20 sets of samples, from individuals aged 21 to 48 years and without clinically significant ocular surface disease, revealed a median cell area of 133 micron 2 (n = 621, range 46-1602 micron 2; average 212 micron 2), a median longest dimension of 13.9 microns (range 6.6-68.8 microns; average 16.9 microns) and a shorter dimension of 10.0 microns (range 4.7-43.0 microns; average 11.9 microns); the distributions of values indicated bimodality. Most cells had a long:short ratio (L:S ratio) value between 1.00 and 1.80, but 11.9 +/- 6.1% of the cells had L:S ratios between 1.80 and 4.60. The overall relationship between the longest dimension and the area of the cells was nonlinear, with cells having larger L:S ratios having disproportionately smaller areas. CONCLUSIONS: The superficial conjunctival cells are small, and their longest dimensions are systematically related to area. Analyses of cell shape indicate further possible ways of identifying different cells on the bulbar conjunctiva. Compared to literature values, there is a substantial overlap in longest dimensions of the conjunctival cells with those of cells that can be collected off the corneal surface. This means that superficial conjunctival and corneal cells cannot be distinguished simply on the basis of measurements of the long dimension.

Adult↗

PubMed1995

A new method to explore the distribution of interindividual random effects in non-linear mixed effects models.

This article presents a new approach for exploring the distribution of interindividual random effects in nonlinear mixed effect models. The approach introduces a spline function, which transforms an assumed normally distributed interindividual random effect to an arbitrary distribution approximating that of the data. The performance of this tool is illustrated using simulated pharmacokinetic data with non-normally distributed random effects. Results of the analyses of two real kinetic data sets are also presented.

Biometry↗

PubMed1993

Statistical considerations for cross-sectional data relating to tracheal reconstruction over time.

Complementary statistical analyses are performed on data concerning tracheal reconstruction in rats. The principal response criterion is vessel area as defined by the area of a graft onto the trachea covered by blood vessels. Postoperatively, this vessel area changes in a nonlinear fashion over time. Starting at 0% immediately postoperation, the vessel area increases to a peak and then sharply decreases to a certain level at which it remains. A total of 64 independently observed cross-sectional pairs (postop day, vessel area) are distributed among four treated groups. Analysis consists of two-way analysis of variance and piecewise linear regression under the usual assumptions of normality and variance homogeneity. Other analyses that relax these assumptions are also considered; treatment differences are established by nonparametric tests, and a quasi-likelihood analysis of the piecewise linear regression model is applied under the assumption of a binomial-like variance function. The resulting fit of the normal-theory-based piecewise linear model is compared to that of a nonlinear model whose shape is that of a gamma function integrand.

Analysis of Variance↗

PubMed2005

Whole-brain morphometric study of schizophrenia revealing a spatially complex set of focal abnormalities.

CONTEXT: Neuroanatomic abnormalities in schizophrenia may underlie behavioral manifestations. Characterization of such abnormalities is required for interpreting functional data. Frontotemporal abnormalities have been documented by using predetermined region-of-interest approaches, but deformation-based morphometry permits examination of the entire brain. OBJECTIVES: To perform whole-brain analyses of structural differences between patients with schizophrenia and controls, to examine sex and medication effects, and to apply a high-dimensional nonlinear pattern classification technique to quantify the degree of separation between patients and controls, thereby testing the potential of this new technique as an aid to diagnostic procedures. DESIGN: Whole-brain morphologic analysis using high-dimensional shape transformations. SETTING: Schizophrenia Research Center, University of Pennsylvania Medical Center. PARTICIPANTS: Neuroleptic-naïve and previously treated patients with DSM-IV schizophrenia (n = 69) and sociodemographically matched controls (n = 79). MAIN OUTCOME MEASURES: Gray matter, white matter, and ventricular cerebrospinal fluid volumes in the brain. RESULTS: Magnetic resonance images showed reduced gray matter and increased ventricular cerebrospinal fluid volumes in patients with schizophrenia in the whole brain and in specific foci: the hippocampus and adjacent white matter, the cingulate and orbitofrontal cortex, the frontotemporal and parietotemporal areas, and the occipital areas near the lingual gyrus. The classifier had a mean classification accuracy of 81.1% for men and women combined (82% for women and 85% for men, when each group was treated separately), determined via cross-validation. CONCLUSIONS: This study confirms previous findings of reduced frontotemporal volumes and suggests new hypotheses, especially involving occipital association and speech production areas. It also suggests finer localization of volume reduction in the hippocampus and other limbic structures and in the frontal lobe. Pattern classification showed high sensitivity and specificity for the diagnosis of schizophrenia, suggesting the potential utility of magnetic resonance imaging as a diagnostic aid.

Adult↗

PubMed1994

Sensitivity functions of a human head movement model.

With time as the criterion to be optimized, the divergences from optimal head movements show systematic differences of their control signal variables with respect to single behaviours. To clarify these relationships, this study uses manipulation and mathematical analysis of the 6th order nonlinear head movement model, i.e. the threefold approach of sensitivity analysis. In addition to sensitivity coefficients, graphs and trajectories sensitivity functions have been analysed. This is the sensitivity of a nominal head movement to changes of the model parameters during the time course of the movement. This demonstrated both the specific change of the visco-inertial properties of the head movement model during the movement and also the potential pathological deficits that may occur.

Computer Simulation↗

PubMed2000

Gigantic optical nonlinearity in one-dimensional Mott-Hubbard insulators

The realization of all-optical switching, modulating and computing devices is an important goal in modern optical technology. Nonlinear optical materials with large third-order nonlinear susceptibilities (chi(3)) are indispensable for such devices, because the magnitude of this quantity dominates the device performance. A key strategy in the development of new materials with large nonlinear susceptibilities is the exploration of quasi-one-dimensional systems, or 'quantum wires'--the quantum confinement of electron-hole motion in one-dimensional space can enhance chi(3). Two types of chemically synthesized quantum wires have been extensively studied: the band insulators of silicon polymers, and Peierls insulators of pi-conjugated polymers and platinum halides. In these systems, chi(3) values of 10(-12) to 10(-7) e.s.u. (electrostatic system of units) have been reported. Here we demonstrate an anomalous enhancement of the third-order nonlinear susceptibility in a different category of quantum wires: one-dimensional Mott insulators of 3d transition-metal oxides and halides. By analysing the electroreflectance spectra of these compounds, we measure chi(3) values in the range 10(-8) to 10(-5) e.s.u. The anomalous enhancement results from a large dipole moment between the lowest two excited states of these systems.

Journal Article↗

PubMed2006

Automated sonographic evaluation of testicular perfusion.

Contrast-enhanced ultrasound (US) imaging is potentially applicable to the investigation of vascular disorders of the testis. We investigated the ability of two automated computer algorithms to analyse contrast-enhanced pulse inversion US data in a rabbit model of unilateral testicular ischaemia and to correctly determine relative testicular perfusion: nonlinear curve fitting of the US backscatter intensity as a function of time; and spectral analysis of the intensity time trace. We compared (i) five metrics based on the algorithmic data to testicular perfusion ratios obtained with radiolabelled microspheres, a reference standard; (ii) qualitative assessment of the US images by two independent readers blinded to the side of the experimental and control testes to the radiolabelled microsphere perfusion ratios; and (iii) results of the algorithmically-derived metrics to the qualitative assessments of the two readers. For the curve fit method, the algorithmically-derived metrics agreed with the reference standard in 54% to 68% of all cases. For the spectral method, the results agreed in 70% of all cases. The two readers agreed with the reference standard in 40% and 35% of all cases, respectively. These results suggest that automated methods of analysis may provide useful information in the assessment of testicular perfusion.

Algorithms↗

PubMed1994

Resonance in a model of a mammalian neuron.

In this paper we show that for a small range of voltages the model described in the previous paper (Hindmarsh & Rose Phil. Trans. R. Soc. Lond. B 346, 129-150 (1994a)) will generate damped oscillations in response to a negative current pulse. As a consequence the cell has the property that it can be driven into bursting by periodic sinusoidal inputs close to the resonant frequency. The main objective of this paper is to analyse this resonant behaviour using the model of the model introduced in the previous paper. We derive analytical expressions which closely approximate the nonlinear resonance observed in the physiological model driven by a periodic sinusoidal input. This leads to the conclusion that resonance could play a role in synaptic transmission at relay nuclei in the mammalian brain.

Animals↗

PubMed2005

Stabilization of interchange modes in mirror plasmas by a nonlinear rf-plasma wave coupling process.

Experimental and theoretical studies are made of the consequences of a nonlinear coupling process between pump rf waves and interchange modes in mirror plasmas. It is demonstrated that the interchange-stable operation window exists depending on the applied rf power and gamma=omega(0)/Omega(i), where omega(0) (Omega(i)) is the angular frequency of the applied rf wave (ion cyclotron frequency). Results are shown that the nonlinear wave coupling process gives rise to the operation window near the resonance (gamma approximately equal to 1), which is elucidated by theoretical analyses combined with full rf wave simulations.

Journal Article↗