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PubMed1994

A characterization of the blood lead concentrations in Saudi Arabian children.

The results presented in this paper are those derived from an extensive analysis of lead in 1047 children aged 2 months to 16 years attending as outpatients at a reference hospital, taking cases from all parts of the Kingdom of Saudi Arabia. Since the distribution of blood lead data in the sample suggested the existence of two mixed sub groups among the studied children, a non-linear mathematical model was used fit to the data. More than 20% of the children had blood lead concentrations above 0.608 mumol/L (12.59 micrograms/dL).

Adolescent↗
PubMed1998

Evaluation of the accuracy of solid implant casts.

PURPOSE: Materials used to fabricate the most dimensionally accurate implant casts have not been identified experimentally. The purpose of this investigation was to examine the dimensional accuracy of implant casts fabricated with different materials. Measurements of linear horizontal dimensional change and strain produced on a master framework were evaluated and correlated. MATERIALS AND METHODS: A master framework was fabricated to fit an aluminum five-implant model. Forty polyether implant impressions of the aluminium model were randomly grouped and poured in either Vel-mix, Die Keen, Resin Rock, or Low Fusing Alloy. A digital veneer caliper was used to measure linear distance between the most distal abutments on each of the experimental implant casts and the master model. In addition, strain values were recorded from strain gauges bonded in the mesiodistal axis of the framework, which was secured by prosthetic retaining screws torqued to 10 Ncm. RESULTS: A one-way ANOVA showed a significant difference among the four die materials in dimensional change of the experimental casts (p = .0001). A post-hoc Duncan's multiple-range test (p < .05) showed that casts fabricated with Low Fusing Alloy had the least linear dimensional change from the master cast, but the material exhibited the greatest dimensional variability. A MANOVA (Wilks' Lambda) showed significant differences in strain on the framework based upon die material (p = .015). A post-hoc Duncan's multiple-range test (p < .05) showed that Resin Rock casts induced significantly less strain on the framework than the other materials. Negligible correlation was found between the linear horizontal dimensional change and the total absolute strain on the framework. CONCLUSION: Experimental implant casts made of Resin Rock minimized strain on the master framework and decreased the amount of framework distortion on casts of this material. Low Fusing Alloy yielded accurate casts, but highly variable linear dimensional changes in the horizontal dimension may preclude its clinical benefit.

Analysis of Variance↗
PubMed2006

Assessment and mathematical modeling of glucose turnover and insulin sensitivity in lean and obese cats.

Insulin sensitivity (SI) of glucose disposal can be quantified with the euglycemic hyperinsulinemic clamp (EHC) with tracer glucose infusion. True steady state is, however, difficult to achieve, and non-steady state analysis of EHC data is preferred. This analysis requires information on glucose kinetics that can be obtained from bolus injection of cold and tracer glucose. The aim of this study was to assess glucose kinetics in cats. Mathematical modeling and non-steady state analysis was applied to assess effects of obesity on glucose turnover, glycolysis/glycogen synthesis, SI, and inhibition of endogenous glucose production (EGP) in lean cats (L) and obese cats (O). D-[3-(3)H]-glucose kinetics and 3H-H2O production were analyzed in 4 L and 4 O with three-compartment modeling. Frequently sampled insulin-modified intravenous glucose tolerance tests (FSIGT) with minimal model analysis were performed in 5L and 3 O to assess glucose kinetics and SI. EHC was performed in 10 L and 10 O with primed-constant infusion of 3H-glucose. Data were analyzed with a modified minimal model segregating suppression of EGP by insulin using a non-linear mixed-effects population approach. FSIGT provided estimates of SI, glucose effectiveness SG, and distribution volume. EHC provided estimates of SI, SG, glycolysis, and suprabasal insulin concentration for 50% EGP inhibition. Obesity appears to affect glucose distribution but not utilization at basal insulin, and reduces SI estimated by FSIGT and EHC. Differences in SI between FSIGT and EHC depend on different descriptions of EGP inhibition by insulin. Finally, glucose disposal at basal insulin appears to occur entirely through glycolysis, whereas significant amounts of glucose are sequestrated from oxidation during EHC.

Animals↗
PubMed2005

Optical nonlinear response function with linear and diagonal quadratic electron-vibration coupling in mixed quantum-classical systems.

While an optical linear response function of linearly and quadratically coupled mixed quantum-classical condensed-phase systems was derived by Toutounji [J. Chem. Phys. 121, 2228 (2004)], the corresponding analytical optical line shape is derived. The respective nonlinear correlation functions are also derived. Model calculations involving photon-echo, pump-probe, and hole-burning signals of model systems with both linear and quadratic coupling are provided. Hole-burning formula of Hayes-Small is compared to that of Mukamel in mixed quantum-classical systems.

Journal Article↗
PubMed2004

Development of a model based on body composition to predict drug kinetics-1 evaluation in healthy volunteers.

A kinetic model for widely used drugs, based on body composition analysis, was developed and evaluated in young and elderly healthy individuals. Body composition was studied by body impedance analysis (BIA). Antipyrine, amlodipine, digoxin and tobramycin kinetics, liver microsomal activity enzyme (lidocaine/MEGX test), and appropriate clinical and laboratory tests were carried out. Major variables (V(d), AUC, t(1/2), C(max), Cl) for these drugs were calculated, and the possible relationships with the other clinical and biochemical data were analyzed by the Pearson's moment correlation, forecasting models being then obtained by a multiple linear regression method. Major kinetic parameters, particularly for the mixed elimination drugs (liver/renal), i.e. digoxin and amlodipine, proved to be well correlated to data collected during the study, in particular with body structure parameters. Results were less satisfactory in the case of the mainly renally handled tobramycin. Mathematical models to forecast the kinetic behaviors of the three chosen drugs, using readily accessible data, showed both in the young and the elder, as well as in the whole examined population, very satisfactory correlations in the case of digoxin (R(2) ranging from 0.89 to 0.85) and amlodipine (R(2) between 0.81 and 0.91), less satisfactory (with a wide range of R(2), from 0.65 to 0.94), in the case of tobramycin.

Adult↗
PubMed2004

A mixed integer linear programming (MILP) framework for inferring time delay in gene regulatory networks.

In this paper, an optimization based modeling and solution framework for inferring gene regulatory networks while accounting for time delay is described. The proposed framework uses the basic linear model of gene regulation. Boolean variables are used to capture the existence of discrete time delays between the various regulatory relationships. Subsequently, the time delay that best fits the expression profiles is inferred by minimizing the error between the predicted and experimental expression values. Computational experiments are conducted for both in numero and real expression data sets. The former reveal that if time delay is neglected in a system a priori known to be characterized with time delay then a significantly larger number of parameters are needed to describe the system dynamics. The real microarray data example reveals a considerable number of time delayed interactions suggesting that time delay is ubiquitous in gene regulation. Incorporation of time delay leads to inferred networks that are sparser. Analysis of the amount of variance in the data explained by the model and comparison with randomized data reveals that accounting for time delay explains more variance in real rather than randomized data.

Computational Biology↗
PubMed2003

A simple model illustrating the role of turbulence on phytoplankton blooms.

The problem of the vertical distribution of phytoplankton is considered in the presence of gravitational settling, turbulent mixing, population growth due to cell division and a constant rate of loss due to predation and natural death. Nutrients are assumed to be plentiful so that the production rate depends only on the light available for photosynthesis. The non-linear saturation of plankton growth is modeled by allowing the attenuation rate of light to be a linear function of the plankton density. The turbulent diffusivity is assumed constant which corresponds to a mixed layer depth very much greater than the depth of light penetration (euphotic depth). It is shown that an exact analytical solution of this non-linear problem is possible for an idealized model in which the functional dependence of production on light intensity is assumed to be a step function. Non-zero solutions are shown to exist only if the parameters characterizing the system are above a certain critical curve in a two dimensional parameter space. Numerical simulations using functional forms of the production curve that resemble the measured photosynthetic response of plankton, show, that the qualitative behavior of the system is similar to that of the idealized model presented. Comparisons are made with other analytical approaches to the problem.

Computer Simulation↗
PubMed1995

Development of limited sampling strategies for characteristics of a pharmacokinetic profile.

New approaches for empirical and model-based development of constrained, limited sampling strategies for the estimation of one or more characteristics of a pharmacokinetic (PK) profile are evaluated. The methods (i) permit a specification of an overall risk function weighted by each estimation objective, (ii) require only a few sampling times for each of one or more new individuals, (iii) permit tight time constraints, such as those imposed by outpatients, and (iv) recognize variations across individuals, but determine optimal sampling times that are the same for all individuals. The methods are applied to a 4-way crossover pharmacokinetic study of two formulations of cyclosporin G, under fed and fasted conditions, in renal transplant patients. This application used average percentage absolute error for estimating AUC and Cmax with an overall risk function that first put all weight on the error for estimating AUC and second put equal weights on the errors for estimating AUC and Cmax. Empirical and model-based methods identified constrained, 3-point designs with acceptable precision for estimating either AUC alone or AUC and Cmax simultaneously. Model-based sampling times were obtained by software for minimizing a general objective function subject to linear constraints where the objective function was evaluated by computer-intensive sampling under a nonlinear mixed-effects model. The model-based approach permitted a direct comparison of the precision of limited and full sampling strategies.

Cyclosporine↗
PubMed2001

Integrated self-calibration via electrokinetic solvent proportioning for microfluidic immunoassays.

On-board generation of a set of calibration standards was demonstrated within a microfluidic device designed to perform immunoassay. Electrokinetic flow was used to proportionally mix the antibody (Ab) to bovine serum albumin (BSA) and a diluting buffer, to provide varying Ab concentrations for downstream mixing with fluorescently labeled BSA (BSA*). Mixing ratios were determined from electrical impedance modeling of the fluidic network using P-SPICE software, and peak heights for the labeled species were analyzed relative to the concentration calculated from the model. For dilution and separation of fluorescently labeled amino acids, a linear calibration curve was obtained for mixing ratios of 0.118 to 7.46. A linear calibration curve was obtained for the immunoassay calibration using dilution ratios between 0.197 and 5.077. Deviations were observed at larger extremes, possibly due to leakage effects at intersections. Peak height reproducibility was +/- 3% for the immunoassay, using diluted monoclonal Ab in mouse ascites fluid as the analyte. Recovery for on-chip calibration was 92 +/- 6% versus calibrants prepared off-chip, indicating a small bias.

Amino Acids↗
PubMedDate not supplied

Optimal design of protein production plants with time and size factor process models.

In this work we propose an optimization model for the design of a biotechnological multiproduct batch plant. A first level of detail posynomial model is constructed for each unit, as well as decisions regarding the structural optimization of the plant. A particular feature of this model is that it contains composite units in which semicontinuous items operate on the material contained by batch items. This occurs in the purification steps, in particular with the microfilters operating between retentate and permeate vessels, and with the homogenizer and ultrafilters operating on the material contained in a batch holding vessel. Also, the unit models rely on batch operating time expressions that depend on both the batch size and the size of semicontinuous items. The model takes into account all of the available options to increase the efficiency of the batch plant design: unit duplication in-phase and out-of-phase and intermediate storage tanks. The resulting mathematical model for the minimization of the plant capital cost is a mixed integer non-linear program (MINLP), which is solved to global optimality with an implementation of the outer approximation/ equality relaxation/ augmented penalty (OA/ER/AP) method. A plant that produces four recombinant proteins in eight processing stages is used to illustrate the proposed approach. An interesting feature of this example is that it represents an attempt to standardize a plant for the production of both therapeutic and nontherapeutic proteins; the model applied is generic and can thus be applied to any such modular plant. Results indicate that the best solution in terms of minimal capital cost contains no units in parallel and with intermediate storage tank allocation.

Algorithms↗
PubMed2006

Contribution of water-leaving radiances to multiangle, multispectral polarimetric observations over the open ocean: bio-optical model results for case 1 waters.

Multiangle, multispectral photopolarimetry of atmosphere-ocean systems provides the fullest set of remote sensing information possible on the scattering properties of aerosols and on the color of the ocean. Recent studies have shown that inverting such data allows for the potential of separating the retrieval of aerosol properties from ocean color monitoring in the visible part of the spectrum. However, the data in these studies were limited to those principal plane observations where the polarization of water-leaving radiances could be ignored. Examining similar potentials for off-principal plane observations requires the ability to assess realistic variations in both the reflectance for and bidirectionality of polarized water-leaving radiances for such viewing geometries. We provide hydrosol models for use in underwater light scattering computations to study such variations. The model consists of two components whose refractive indices resemble those of detritus-minerallike and planktonlike particles, whose size distributions are constrained by underwater light linear polarization signatures, and whose mixing ratios change as a function of particulate backscattering efficiency. Multiple scattering computations show that these models are capable of reproducing realistic underwater light albedos for wavelengths ranging from 400 to 600 nm, and for chlorophyll a concentrations ranging from 0.03 to 3.0 mg/m(3). Numerical results for spaceborne observations of the reflectance for total and polarized water-leaving radiances are provided as a function of polar angles, and the change in these reflectances with wavelength, chlorophyll a concentration, and hydrosol model are discussed in detail for case 1 (open ocean) waters.

Journal Article↗
PubMed1991

Effect of the curvature of the O2 equilibrium curve on alveolar O2 uptake: theory.

The effect of the curvature of the O2 equilibrium curve (OEC), in the range between mixed venous and alveolar PO2, on alveolar O2 uptake was quantitatively investigated in a simple homogeneous lung model. The O2 uptake achieved with a linear OEC (Mlin) was subtracted from the O2 uptake (M) attained with the physiologically curved, sigmoid OEC, and the relative difference was considered as the 'curvature effect', CE [= (M - Mlin)/M], indicating, if positive, the enhancement of O2 uptake by the non-linearity of the OEC. Calculations show CE to be close to nil (less than 1%) in normal lungs during rest both in normoxia and in hypoxia. CE is more important in heavy exercise both in normoxia (CE less than 19%) or slight hypoxia (CE less than 15%). In deep hypoxia, CE is negligible again even during exercise. Thus, the simplified approach to the analysis of alveolar O2 uptake using a linear OEC, in the mixed venous-to-alveolar PO2 range, constitutes in most cases a valid approximation.

Models, Biological↗
PubMed1997

Dose proportionality of cisatracurium.

The dose proportionality of cisatracurium pharmacokinetics was assessed using a population approach by incorporating the collection of sparse blood samples from patients in clinical trials. Plasma concentration-time data from 131 patients with limited concentration-time data and 38 patients with full sampling were pooled and analyzed using nonlinear mixed-effects modeling (NONMEM). Dose proportionality was assessed using dichotomous parameterization and a linear model. The population pharmacokinetic approach revealed that the pharmacokinetics of cisatracurium are independent of dose between 0.1 mg/kg and 0.4 mg/kg, as was expected based on the importance of Hofmann elimination, a chemical process dependent on pH and temperature.

Adult↗
PubMed2004

Willingness-to-pay for reducing fatal accident risk in urban areas: an Internet-based Web page stated preference survey.

Contemporary transport project evaluation requires the ability to value reductions in the number of estimated fatal and non-fatal accidents after project implementation. In this quest, we designed a stated preference (SP) experiment to estimate willingness-to-pay (WTP) for reducing fatal accident risk in urban areas. The survey was implemented in a Web page allowing rapid turnover and a complete customisation of the interview. The sample was presented with a series of route choice situations based on travel time, cost and number of car fatal accidents per year. With this data we estimated Multinomial Logit (MNL) and Mixed Logit (ML) models based on a consistent microeconomic framework; the former with linear and non-linear utility specifications and allowing for various stratifications of the data. The more flexible ML models also allow to treat the repeated observations problem common to SP data and, as expected, gave a better fit to the data in all cases. Based on these models, we estimated subjective values of time, that were consistent with previous values obtained in the country, and also sensible values for the WTP for reductions in fatal accident risk. Thus, the Internet appears as a potentially very interesting medium to carry out complex stated choice surveys.

Accidents, Traffic↗
PubMed2002

The influence of baseline characteristics on viral dynamic parameters in chronic hepatitis B patients treated with lamivudine.

BACKGROUND/AIMS: Viral decline during lamivudine therapy in chronic hepatitis B patients is bi-phasic. We studied the influence of lamivudine dose and baseline characteristics on parameters obtained from a mathematical model. METHODS: Chronic hepatitis B patients were randomized to receive 150 mg (group 1; n=11) or 600 mg (group 2; n=10) lamivudine daily for 4 weeks. Hepatitis B virus DNA was measured frequently with the Digene Hybrid Capture II test and the Roche PCR assay. RESULTS: The description of viral decline in our closely monitored patients by means of the mixed-effects approach with both the bi-phasic model and a piecewise linear regression model resulted in a good fit. Baseline alanine aminotransferase (ALT) was significantly related to the slope of the second phase of viral decline. Previous lamivudine-treated patients showed a significant slower first phase than patients naive to lamivudine treatment. CONCLUSIONS: The initial observed difference in viral decline between 150 and 600 mg of lamivudine disappeared when baseline ALT was taken into account. This strengthens the hypothesis that the level of intrinsic activity is related to the turnover of infected hepatocytes. Moreover, reintroduction of lamivudine in previously lamivudine-treated patients should be considered carefully.

Adolescent↗
PubMed1998

Mixed dentition analysis for Asian-Americans.

One of the important aspects of diagnosis in the mixed dentition is the determination of the tooth size-arch length relationship. Such a determination is often made before eruption of the permanent canines and first and second premolars. The most commonly used prediction method of Tanaka and Johnston is based on data from a sample of children of Northern European descent. The accuracy of this method when applied to a different ethnic population is questionable. In this study, 201 dental plaster casts of Asia-Pacific-American subjects, all of whom were under the age of 21 years, were used. The actual measurements were compared with the predicted values derived from the Tanaka and Johnston equations and significant differences were found. The data illustrate the limitations of the Tanaka and Johnston method when applied to a sample population of other than European descent. From this data, two linear regression equations were developed for tooth size prediction in Asian-American children.

Adult↗
PubMed2000

Mixed dentition space analysis in a Thai population.

This study produced simple linear regression equations to be used for mixed dentition space analysis for males and females, and sexes pooled in a population living in northeastern Thailand. Measurements of teeth were made to within 0.01 mm on the dental casts of 215 boys and 215 girls (mean age 15.7 years). All dentitions were required to be free of any signs of dental pathology or anomalies. It was found that males had significantly larger teeth than females as represented by summations of mandibular incisor, canine, and premolar widths. ANOVA of regression indicated a close relationship between mandibular incisor summation and corresponding summations of canine and premolars. The low coefficients of determination (r2) of the regressions ranged between 0.29 and 0.42, and were higher for females than males, which might be attributable to the ethnic diversity of the sampled population. The regression equations produced predictions of mesio-distal width summations for maxillary and mandibular canine, and premolar arch segments that were slightly different from other reported Asian studies. Moyers' prediction tables at the 50th percentile were found to under-estimate tooth size summation compared with the present investigation. The predictions from simplified regression equations matched well with those of this study for sexes pooled, and for males and females separately.

Adolescent↗
PubMed2006

Image denoising using total least squares.

In this paper, we present a method for removing noise from digital images corrupted with additive, multiplicative, and mixed noise. An image patch from an ideal image is modeled as a linear combination of image patches from the noisy image. We propose to fit this model to the real-world image data in the total least square (TLS) sense, because the TLS formulation allows us to take into account the uncertainties in the measured data. We develop a method to reduce the contribution from the irrelevant image patches, which will sharpen the edges and reduce edge artifacts at the same time. Although the proposed algorithm is computationally demanding, the image quality of the output image demonstrates the effectiveness of the TLS algorithms.

Algorithms↗