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PubMed1985

Comparison of models describing the sorption of nitroglycerin and diazepam by plastic infusion systems: diffusion and compartment models.

The time course of sorption of diazepam and nitroglycerin from aqueous solutions into plastic materials has been represented by the diffusion and compartmental models for a variety of storage conditions. The diffusion model seemed to be the more satisfactory model in respect to both description and prediction of the drug uptake for all conditions. The compartment model appeared to be useful for describing the drug uptake at earlier times, giving a satisfactory fit to the data and reliable final parameter estimates. However, that model was not able to describe the loss as equilibrium was approached or accurately predict the disappearance profiles for these solutes with alterations in solution volume or infusion bag size. Approximations of the diffusion model gave parameter estimates consistent with those obtained by nonlinear regression using the full equations.

Adsorption↗

PubMed1995

Evaluation of comparative protein modeling by MODELLER.

We evaluate 3D models of human nucleoside diphosphate kinase, mouse cellular retinoic acid binding protein I, and human eosinophil neurotoxin that were calculated by MODELLER, a program for comparative protein modeling by satisfaction of spatial restraints. The models have good stereochemistry and are at least as similar to the crystallographic structures as the closest template structures. The largest errors occur in the regions that were not aligned correctly or where the template structures are not similar to the correct structure. These regions correspond predominantly to exposed loops, insertions of any length, and non-conserved side chains. When a template structure with more than 40% sequence identity to the target protein is available, the model is likely to have about 90% of the mainchain atoms modeled with an rms deviation from the X-ray structure of approximately 1 A, in large part because the templates are likely to be that similar to the X-ray structure of the target. This rms deviation is comparable to the overall differences between refined NMR and X-ray crystallography structures of the same protein.

Amino Acid Sequence↗

PubMed1992

A bootstrap resampling procedure for model building: application to the Cox regression model.

A common problem in the statistical analysis of clinical studies is the selection of those variables in the framework of a regression model which might influence the outcome variable. Stepwise methods have been available for a long time, but as with many other possible strategies, there is a lot of criticism of their use. Investigations of the stability of a selected model are often called for, but usually are not carried out in a systematic way. Since analytical approaches are extremely difficult, data-dependent methods might be an useful alternative. Based on a bootstrap resampling procedure, Chen and George investigated the stability of a stepwise selection procedure in the framework of the Cox proportional hazard regression model. We extend their proposal and develop a bootstrap-model selection procedure, combining the bootstrap method with existing selection techniques such as stepwise methods. We illustrate the proposed strategy in the process of model building by using data from two cancer clinical trials featuring two different situations commonly arising in clinical research. In a brain tumour study the adjustment for covariates in an overall treatment comparison is of primary interest calling for the selection of even 'mild' effects. In a prostate cancer study we concentrate on the analysis of treatment-covariate interactions demanding that only 'strong' effects should be selected. Both variants of the strategy will be demonstrated analysing the clinical trials with a Cox model, but they can be applied in other types of regression with obvious and straightforward modifications.

Brain Neoplasms↗

PubMed1995

Computer modeling of protein folding: conformational and energetic analysis of reduced and detailed protein models.

Recently we developed methods to generate low-resolution protein tertiary structures using a reduced model of the protein where secondary structure is specified and a simple potential based on a statistical analysis of the Protein Data Bank is employed. Here we present the results of an extensive analysis of a large number of detailed, all-atom structures generated from these reduced model structures. Following side-chain addition, minimization and simulated annealing simulations are carried out with a molecular mechanics potential including an approximate continuum solvent treatment. By combining reduced model simulations with molecular modeling calculations we generate energetically competitive, plausible misfolded structures which provide a more significant test of the potential function than current misfolded models based on superimposing the native sequence on the folded structures of completely different proteins. The various contributions to the total energy and their interdependence are analyzed in detail for many conformations of three proteins (myoglobin, the C-terminal fragment of the L7/L12 ribosomal protein, and the N-terminal domain of phage 434 repressor). Our analysis indicates that the all-atom potential performs reasonably well in distinguishing the native structure. It also reveals inadequacies in the reduced model potential, which suggests how this potential can be improved to yield greater accuracy. Preliminary results with an improved potential are presented.

Algorithms↗

PubMed2000

The two-state cross-bridge model of muscle is an asymptotic limit of multi-state models.

The relationship between the two-state model of muscle contraction and multi-state models is examined from the perspective of matched asymptotic expansions, under the assumption that transition rates between attached states are fast compared to those between detached and attached states. A detailed formal analysis of a three-state model reveals that the classic Huxley (1957. Prog. Biophys. Biophys. Chem.7, 225-318) rate equation, as modified for thermodynamic self-consistency by Hill et al. (1975. Biophys. J.15, 335-372), governs the "outer" solution of the three-state equations. Thus, the two-state model remains a valid description of muscle dynamics on physiologically relevant time scales, which are slow compared to millisecond-scale transitions between attached states. But the asymptotic analysis reveals also that the cross-bridge force must be considered to be a nonlinear function of the cross-bridge strain, in contrast to the usual assumption of two-state models. This apparent, or effective, force is determined by both the intrinsic stiffness of the cross-bridge and the equilibrium distribution of cross-bridges among attached states. Further, the asymptotic analysis yields an expression for the energy liberation rate that implies a reduced rate in stretch vs. shortening. Some behaviors of multi-state models that are suggested by the three-state analysis are discussed in qualitative terms.

Biomechanical Phenomena↗

PubMed2001

A toxicokinetic model for predicting the tissue distribution and elimination of organic and inorganic mercury following exposure to methyl mercury in animals and humans. I. Development and validation of the model using experimental data in rats.

The objective of this study was to develop a biologically based dynamic model for predicting the distribution and elimination of methyl mercury and its metabolite, inorganic mercury, under a variety of exposure scenarios in rats. A model is proposed based on a multicompartment approach; each compartment represents an organ or a group of organs or an excreta. The model translates into a set of coupled differential equations taking into account interorgan rates of exchanges and excretion together with the biotransformation process. The free parameters of the model are determined from statistical fits to the experimental data of the Farris et al. (Toxicol. Appl. Pharmacol. 119, 74-90, 1993) study on the time profiles of blood and tissue concentrations and cumulative excretions. The vast range of time scales that govern tissue absorption, distribution, biotransformation, and excretion served to solve the model step by step. This interplay of time scales in the rates explains the buildups and slow attrition of inorganic mercury in certain key organs such as the brain and the kidney, which are also the sites of the more important toxic effects. The model was validated on additional experimental data provided by Norseth and Clarkson (Arch. Environ. Health 21, 717-727, 1970) and Thomas et al. (Environ. Res. 41, 219-234, 1986; Environ. Res. 43, 203-216, 1987). This approach, when adapted to humans, allows the reconstruction of the time course of blood and tissue concentrations, starting from easily accessible data on hair, urine, and feces.

Animals↗

PubMed1988

Models of hepatic elimination: comparison of stochastic models to describe residence time distributions and to predict the influence of drug distribution, enzyme heterogeneity, and systemic recycling on hepatic elimination.

The residence time distribution of noneliminated solutes in the liver can be represented by a variety of stochastic models. The dispersion model (closed and mixed boundary conditions), gamma distribution, log normal distribution and normal distribution models were used to describe output concentration-time profiles after bolus injections into the liver of labeled erythrocytes and albumin. The dispersion model and log normal distribution model provide the best representation of the data and give similar estimates of relative dispersion and availability for varying hepatocellular enzyme activity. The availability of solutes eliminated from the liver by first-order kinetics is determined by the residence time distribution of the solute in the liver and not on events occurring in the liver when a uniform enzyme distribution is assumed. Both enzyme heterogeneity (axial or transverse) and hepatocyte permeability may affect solute availability. A more complex model accounting for enzyme distribution and the micromixing of solute within the liver is required for solutes undergoing saturable kinetics.

Biological Transport↗

PubMed1985

Theoretical consideration of drug distribution kinetics in a noneliminating organ: comparison between a "homogeneous (well-stirred)" model and "nonhomogeneous (tube)" model.

Drug distribution kinetics in a noneliminating organ or tissue has been mathematically examined. The homogeneous (well-stirred) model regards the noneliminating organ or tissue as a homogeneous compartment in which the drug is equilibrated with that in the blood leaving the organ or tissue. The nonhomogeneous (tube) model views the noneliminating organ or tissue as comprising a number of parallel cylindrical tubes containing binding sites distributed homogeneously along these tubes. These two models are examined, considering the pseudo-distribution equilibrium phase after bolus injection and a linear binding condition. Although both models predict a similar tissue distribution under a variety of conditions, significant differences exist in the predictions of various pharmacokinetic parameters as a function of the drug distribution, such as blood flow, organ volume, slope of the terminal phase, and the tissue-to-blood partition coefficients. The predictability and limitations of these two models are explored. Distribution characteristics of the two models are also examined for adriamycin, actinomycin D, tetrachlorobiphenyl, hexachlorobiphenyl, digoxin, and ethoxybenzamide; no difference is observed. It is concluded that the assumption of a homogeneous (well-stirred) compartment is suitable for describing the drug distribution kinetics of these drugs.

Kinetics↗

PubMed1976

Comprehensive formal models for pancreatic calcium secretion. With reference to "exchange-diffusion," "two-component," and "unicellular" models of electrolyte secretion.

This is a theoretical paper in which comprehensive formal models are developed for all possible modes of entry of calcium into pancreatic juice. The 15 models include entry via: (1) the chloride-rich secretion, (2) the bicarbonate-rich secretion, (3) protein-bound calcium, and (4) interstitial fluid (ISF), plus the various possible combinations of these. Equations are presented for both calcium-volume and calcium-bicarbonate relationships. Each equation is modified as necessary to conform to the three current models for sodium, chloride, and bicarbonate secretion: (1) "exchange-diffusion," (2) "two-component," and (3) "unicellular" models. We believe the models provide a sound theoretical framework on which to build an understanding of pancreatic calcium secretion. Subsequent papers will be concerned with the physicochemical state of calcium in the juice, the relative contribution of ISF, and the development of an overall model for pancreatic calcium secretion. The long-term objective is to provide a rational approach for the understanding of pancreatic calcification and stone formation.

Bicarbonates↗

PubMed2004

A model to estimate the lifetime health outcomes of patients with type 2 diabetes: the United Kingdom Prospective Diabetes Study (UKPDS) Outcomes Model (UKPDS no. 68).

AIMS/HYPOTHESIS: The aim of this study was to develop a simulation model for type 2 diabetes that can be used to estimate the likely occurrence of major diabetes-related complications over a lifetime, in order to calculate health economic outcomes such as quality-adjusted life expectancy. METHODS: Equations for forecasting the occurrence of seven diabetes-related complications and death were estimated using data on 3642 patients from the United Kingdom Prospective Diabetes Study (UKPDS). After examining the internal validity, the UKPDS Outcomes Model was used to simulate the mean difference in expected quality-adjusted life years between the UKPDS regimens of intensive and conventional blood glucose control. RESULTS: The model's forecasts fell within the 95% confidence interval for the occurrence of observed events during the UKPDS follow-up period. When the model was used to simulate event history over patients' lifetimes, those treated with a regimen of conventional glucose control could expect 16.35 undiscounted quality-adjusted life years, and those receiving treatment with intensive glucose control could expect 16.62 quality-adjusted life years, a difference of 0.27 (95% CI: -0.48 to 1.03). CONCLUSIONS/INTERPRETATIONS: The UKPDS Outcomes Model is able to simulate event histories that closely match observed outcomes in the UKPDS and that can be extrapolated over patients' lifetimes. Its validity in estimating outcomes in other groups of patients, however, remains to be evaluated. The model allows simulation of a range of long-term outcomes, which should assist in informing future economic evaluations of interventions in type 2 diabetes.

Amputation, Surgical↗

PubMed2001

Identifying influences on model uncertainty: an application using a forest carbon budget model.

Uncertainty is an important consideration for both developers and users of environmental simulation models. Establishing quantitative estimates of uncertainty for deterministic models can be difficult when the underlying bases for such information are scarce. We demonstrate an application of probabilistic uncertainty analysis that provides for refinements in quantifying input uncertainty even with little information. Uncertainties in forest carbon budget projections were examined with Monte Carlo analyses of the model FORCARB. We identified model sensitivity to range, shape, and covariability among model probability density functions, even under conditions of limited initial information. Distributional forms of probabilities were not as important as covariability or ranges of values. Covariability among FORCARB model parameters emerged as a very influential component of uncertainty, especially for estimates of average annual carbon flux.

Carbon↗

PubMed2006

Comparison of dose conversion factors for radon progeny from the ICRP 66 regional model and an airway tube model of tracheo-bronchial tree.

Current epidemiological approaches to radon dosimetry yield a dose conversion factor (DCF) of 4 mSv WLM(-1) while the dosimetric approaches give a value closer to 13 mSv WLM(-1). The present study investigated whether the application of compartment models for the bronchial (BB) and bronchiolar (bb) regions, rather than more anatomically realistic airway tube models, has brought the dosimetric DCF to the higher values. The airway tube model of the tracheo-bronchial tree was used to calculate the effective dose per unit radon exposure. All other elements of the human respiratory tract from the reports of the ICRP or NRC were adopted. A dosimetric derivation of the radon DCF using the airway tube model yielded a value of 14.2 mSv WLM(-1). This value is slightly larger than, but not significantly different from, the result obtained through the ICRP 66 approach. It is concluded that utilization of the airway tube model instead of the regional ICRP 66 compartmental model cannot reconcile the gap between dose conversion factors derived from epidemiological and dosimetric approaches.

Air Pollutants, Radioactive↗

PubMed2004

Short-term prediction of Betula airborne pollen concentration in Vigo (NW Spain) using logistic additive models and partially linear models.

Betula pollen is a common cause of pollinosis in localities in NW Spain and between 13% and 60% of individuals who are immunosensitive to pollen grains respond positively to its allergens. It is important in the case of all such people to be able to predict pollen concentrations in advance. We therefore undertook an aerobiological study in the city of Vigo (Pontevedra, Spain) from 1995 to 2001, using a Hirst active-impact pollen trap (VPPS 2000) situated in the city centre. Vigo presents a temperate maritime climate with a mean annual temperature of 14.9 degrees C and 1,412 mm annual total precipitation. This paper analyses two ways of quantifying the prediction of pollen concentration: first by means of a generalized additive regression model with the object of predicting whether the series of interest exceeds a certain threshold; second using a partially linear model to obtain specific prediction values for pollen grains. Both models use a self-explicative part and another formed by exogenous meteorological factors. The models were tested with data from 2001 (year in which the total precipitation registered was almost twice the climatological average overall during the flowering period), which were not used in formulating the models. A highly satisfactory classification and good forecasting results were achieved with the first and second approaches respectively. The estimated line taking into account temperature and a calm S-SW wind, corresponds to the real line recorded during 2001, which gives us an idea of the proposed model's validity.

Allergens↗

PubMed2005

The Fischer 344/NNiaHSd X Brown Norway/BiNia is a better model of sarcopenia than the Fischer 344/NNiaHSd: a comparative analysis of muscle mass and contractile properties in aging male rat models.

Sarcopenia, characterized by profound muscle atrophy and the loss of contractile function, contributes significantly to the development of frailty and functional impairment in older age. Although present in aging humans, rat models have failed to clearly demonstrate a similar degree of this age-associated loss of muscle mass and function. This investigation compared two models of rats raised specifically for aging studies, the Fischer 344/NNiaHSd (F344/N) and the Fischer 344/NNiaHSd X Brown Norway/BiNia (F344/NXBN), and sought to determine which model provides the most accurate representation of human sarcopenia. We found that aging had no effect on F344/N muscle mass or contractile function in the extensor digitorum longus (EDL) and soleus (SOL). Conversely, in the F344/NXBN model, aging was found to decrease EDL and SOL mass and contractile function. These changes were sufficient to satisfy the proposed criteria for the diagnosis of human sarcopenia based upon muscle mass and contractile function. Results indicate that the F344/NXBN provides a better model of the alterations seen in aging human muscle than the F344/N rat model.

Aging↗

PubMed2006

Simple stochastic fingerprints towards mathematical modeling in biology and medicine. 3. Ocular irritability classification model.

MARCH-INSIDE methodology and a statistical classification method--linear discriminant analysis (LDA)--is proposed as an alternative method to the Draize eye irritation test. This methodology has been successfully applied to a set of 46 neutral organic chemicals, which have been defined as ocular irritant or nonirritant. The model allow to categorize correctly 37 out of 46 compounds, showing an accuracy of 80.46%. Specifically, this model demonstrates the existence of a good categorization average of 91.67 and 76.47% for irritant and nonirritant compounds, respectively. Validation of the model was carried out using two cross-validation tools: Leave-one-out (LOO) and leave-group-out (LGO), showing a global predictability of the model of 71.7 and 70%, respectively. The average of coincidence of the predictions between leave-one-out/leave-group-out studies and train set were 91.3% (42 out of 46 cases)/89.1% (41 out of 46 cases) proving the robustness of the model obtained. Ocular irritancy distribution diagram is carried out in order to determine the intervals of the property where the probability of finding an irritant compound is maximal relating to the choice of find a false nonirritant one. It seems that, until today, the present model may be the first predictive linear discriminant equation able to discriminate between eye irritant and nonirritant chemicals.

Algorithms↗

PubMed1985

Genetical ESS-models. I. Concepts and basic model.

Evolutionarily Stable Strategies (ESS) in phenotypic models are used to explain the evolution of animal interactive behaviour. As the behavioural features under consideration are assumed to be genetically determined, the question arises how underlying a genetical system might affect the results of phenotypic ESS-models. This question can be fully treated in terms of ESS-theory. A method of designing Genetical ESS-Models is proposed, which transfers the question of evolutionary stability to a "lower" level, the genetical basis. Genetical ESS-models - although nonlinear even in the simplest cases - can be analysed in a way that is familiar to ESS-theorists and yield immediate results on gene pool ESSs, which then may or may not maintain ESSs on the phenotypic level. Moreover, general results can be obtained to characterize evolutionarily stable gene pool states and their interrelation with commonsense, phenotypic ESSs. This part of the article presents the basic concepts and an outline of the method of genetical ESS-models. It gives, as a demonstration, a complete analysis for phenotypic two-strategy models (linear or nonlinear) based on a diploid, diallelic single-locus system under random mating. The results in this case suggest that a phenotypic ESS should indeed be expected to evolve but, maybe, only after passing through a succession of temporarily stable states.

Animals↗

PubMed1989

Physiologically based pharmacokinetic modeling of the pregnant rat: a multiroute exposure model for trichloroethylene and its metabolite, trichloroacetic acid.

A physiologically based pharmacokinetic (PB-PK) model was developed to describe trichloroethylene (TCE) kinetics in the pregnant rat exposed to TCE by inhalation, by bolus gavage, or by oral ingestion in drinking water. The kinetics of trichloroacetic acid (TCA), an oxidative metabolite of TCE, were described by a classical one-compartment pharmacokinetic model. Among the required model parameters for TCE, partition coefficients (PCs) and kinetic constants for oxidation were determined by vial equilibration and gas uptake methods, respectively. The fat:blood PC was 33.9; the blood:air PC was 13.2; and the fetal tissue:fetal blood PC was 0.51. TCE was readily metabolized with high substrate affinity. In naive and pregnant female rats the maximum velocities of oxidative metabolism were 10.98 +/- 0.155 and 9.18 +/- 0.078 mg/kg/hr, while the estimated Michaelis constant for the two groups of rats was very low, 0.25 mg/liter. The first-order rate constant for oral absorption of TCE from water was 5.4 +/- 0.42/hr-1 in naive rats. With TCA, the volume of distribution (0.618 liter/kg) and the plasma elimination rate constant (0.045 +/- 0.0024/hour) were estimated both from intravenous dosing studies with TCA and from an inhalation study with TCE. By comparison of the two routes of administration, the stoichiometric yield of TCA from TCE was estimated to be 0.12 in pregnant rats. To develop a data base for testing the fidelity of the PB-PK model, inhalation and bolus gavage exposures were conducted from Day 3 to Day 21 of pregnancy and a drinking water exposure from Day 3 to Day 22 of pregnancy. Inhalation exposures with TCE vapor were 4 hr/day at 618 ppm. The TCE concentration in drinking water was 350 micrograms/ml and the gavaged rats received single daily doses of 2.3 mg TCE/kg. Time varying physiological parameters for compartment volumes and blood flows during pregnancy were obtained from the published literature. Using the kinetic parameters determined by experimentation, TCE concentrations in maternal and fetal blood and TCA concentrations in maternal and fetal plasma were predicted from the PB-PK model by computer simulation and compared favorably with limited data obtained at restricted time points during pregnancy for all three routes of exposure. On the basis of the PB-PK model, fetal exposure to TCE, as area-under-the-curve, ranged from 67 to 76% of maternal exposure. For TCA the fetal exposure was 63 to 64% of the maternal exposure. The fetus is clearly at risk both to parent TCE and its TCA metabolite.(ABSTRACT TRUNCATED AT 400 WORDS)

Administration, Inhalation↗

PubMed1995

Comparison of multi-media transport and transformation models: regional fugacity model vs. CalTOX.

Two multimedia environmental transport and transformation computer models are summarized and compared. The regional fugacity model published by Mackay and Paterson (1991), termed Fug3ONT, is a four compartment steady-state model designed to simulate the relative distribution of nonionic organic chemicals in a multimedia system. CalTOX is a seven compartment multimedia total exposure model for hazardous waste sites. Both models are based on the principles of fugacity. CalTOX, however, separates the soil into three layers (surface, root, and vadose) and uses a different approach to estimate the diffusive mass transfer rate in soil. These differences result in lower estimates of the steady-state contaminant concentrations of six environmentally relevant chemicals in the root soil of CalTOX as compared to the bulk soil of Fug3ONT. The difference is greatest for compounds with low mobility in soil such as 2,3,7,8-Tetrachlorodibenzo-p-dioxin and Benzo(a)pyrene where estimates from CalTOX and Fug3ONT differ by more than 3 orders of magnitude. Otherwise, the models provide similar estimates for the distribution of the six chemicals among the air, water, sediment and surface soil.

Air Pollutants↗