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PubMed1995

General purpose model and a computer program for combined segregation and path analysis (SEGPATH): automatically creating computer programs from symbolic language model specifications.

A general purpose model and a flexible computer program, called SEGPATH, have been developed to assist in the creation and implementation of a variety of genetic epidemiological models. SEGPATH is a computer program which can be used to generate programs to implement linear models for pedigree data, based upon a flexible, model-specification syntax. SEGPATH models can perform segregation analysis, path analysis, or combined segregation and path analysis using any user-specified path model and can be structured to analyze any number of multivariate phenotypes, environmental indices, and/or measured covariate fixed effects (including measured genotypes). Population heterogeneity models, repeated-measures models, longitudinal models, auto-regressive models, developmental models, and gene-by-environment interaction models can all be created under SEGPATH. Pedigree structures can be defined to be arbitrarily complex, and the data analyzed with programs generated by SEGPATH can have any missing value structure, with entire individuals missing, or missing on one or more measurements. Corrections for ascertainment can be done on a vector of phenotypes and/or other measures. Because the model specification syntax is general, SEGPATH can also be used in non-genetic applications where there is a hierarchical structure, such as longitudinal, repeated-measures, time series, or nested models. A variety of applications are demonstrated.

Genetics, Population↗

PubMed1987

Muscle models: what is gained and what is lost by varying model complexity.

Three structurally different types of models have evolved over the years to describe muscle-joint systems. The first, based on an input-output analysis of a given task, results in a simple second-order differential equation description that is adequate over a certain movement operating range. The second, based on the classic structural model of Hill (1938), results in a higher-order nonlinear model described by ordinary differential equations. The third, based on an analysis of the biophysical contractile mechanism, results in a complex partial differential equation description. The advantages and disadvantages of each type of model are considered, based on the criteria of identifying the simplest model that can adequately simulate any fundamental type of human movement without modifying model parameters for different tasks. It is shown that an eighth-order Hill-based antagonistic muscle-joint model is able to satisfy these criteria for a given joint if each of the four basic mechanically-significant non-linearities of the system are included in the model. This same model structure has been used successfully for eight different muscle-joint systems, ranging in size from knee flexion-extension to eye rotation--the only difference between the models is in the parameter values. Second-order models are shown to be task-specific special cases of the input-output behavior of the eighth-order model, while the more complex biophysical models are hypothesized to have insignificant advantages and many disadvantages over the Hill-based model during normal human movement.

Animals↗

PubMed1988

Planning and using PB-PK models: an integrated inhalation and distribution model for nickel.

A general method is presented for the use of mathematical modeling in the design, execution, and interpretation of toxicology experiments. To illustrate the use of mathematical modeling toxicology, a case study is presented of how a dosimetry model for inhaled nickel was developed for use in cancer risk estimation. A physiologically based pharmacokinetic (PB-PK) dosimetry model is used to plan animal experiments and to extrapolate nickel kinetics from animals to humans. These data are then used to estimate human lung cancer risks from human exposure to nickel aerosols. To achieve this goal, a PB-PK dosimetry model for the lung was integrated with a PB-PK dosimetry model for the internal organs. Nickel removal from the lung was found to be saturable and to follow Michaelis-Menten kinetics. The PB-PK lung dosimetry model was used to design both short-term (single exposures) and long-term (multiple intermittent exposures) needed to validate the parameters (Km and Vmax) of the lung dosimetry model. A constant infusion experiment was planned using the PB-PK modeling approach to measure the distribution and elimination of intravenously administered nickel. The two PB-PK models were integrated to estimate the fate of nickel after inhalation and are being used to plan experiments for other routes of exposure such as ingestion of drinking water and dermal contact. The integrated model has been used to calculate a human cancer risk estimate in combination with short-term genotoxic experiments. Using PB-PK models in toxicology, as illustrated here, conserves experimental animals, aids in understanding new physiological phenomena (such as saturable clearance from the lung), incorporates in vitro tests with in vivo experiments, and provides a means of extrapolation to human health risks from multiple routes of exposure. Introducing the concepts of mathematical modeling into toxicity experiments at the beginning of the experiment improves the usefulness of the experiments in risk estimation. PB-PK models are suggested as a new basis for experimental design in toxicology.

Administration, Inhalation↗

PubMed2004

Stochastic modelling of landfill leachate and biogas production incorporating waste heterogeneity. Model formulation and uncertainty analysis.

A mathematical model simulating the hydrological and biochemical processes occurring in landfilled waste is presented and demonstrated. The model combines biochemical and hydrological models into an integrated representation of the landfill environment. Waste decomposition is modelled using traditional biochemical waste decomposition pathways combined with a simplified methodology for representing the rate of decomposition. Water flow through the waste is represented using a statistical velocity model capable of representing the effects of waste heterogeneity on leachate flow through the waste. Given the limitations in data capture from landfill sites, significant emphasis is placed on improving parameter identification and reducing parameter requirements. A sensitivity analysis is performed, highlighting the model's response to changes in input variables. A model test run is also presented, demonstrating the model capabilities. A parameter perturbation model sensitivity analysis was also performed. This has been able to show that although the model is sensitive to certain key parameters, its overall intuitive response provides a good basis for making reasonable predictions of the future state of the landfill system. Finally, due to the high uncertainty associated with landfill data, a tool for handling input data uncertainty is incorporated in the model's structure. It is concluded that the model can be used as a reasonable tool for modelling landfill processes and that further work should be undertaken to assess the model's performance.

Biodegradation, Environmental↗

PubMedDate not supplied

Predictive models for aquatic toxicity of aldehydes designed for various model chemistries.

Predictive models for the aquatic toxicity of aldehydes were designed for a set of 50 aromatic or aliphatic compounds containing at least one aldehyde group, for which the acute toxicity data for the fathead minnow (Pimephales promelas) are available (96 h test assessing 50% lethal waterborne concentration). The molecular descriptors were based on calculations with various semiempirical or ab initio model chemistries. The resulting four-parameter models were evaluated according to the correlation coefficients R(2). The best predictive model was obtained with the HF/STO-3G model chemistry (R(2) = 0.868), while the models designed for descriptors based on ab initio calculations of higher level showed a slightly worse predictivity (the HF/3-21G(d) based model R(2) = 0.800, the HF/6-31G(d) based model R(2) = 0.808, the B3LYP/6-31G(d,p) based model R(2) = 0.812). With the semiempirical methods a good predictivity was observed with the PM3 based model (R(2) = 0.811) and the AM1 based model (R(2) = 0.791), but the MNDO based model showed the worst predictivity (R(2) = 0.760). In all ab initio models and the PM3 model very similar descriptors were involved. The importance of the descriptor logarithm of the partition coefficient logP for toxicity prediction was confirmed. Additionally, the descriptors encoding the negatively charged molecular surface area, hydrogen bonding molecular surface area, and reactivity of aldehyde group were identified as essential for the toxicity prediction of aldehydes.

Aldehydes↗

PubMed2003

SWISS-MODEL: An automated protein homology-modeling server.

SWISS-MODEL (http://swissmodel.expasy.org) is a server for automated comparative modeling of three-dimensional (3D) protein structures. It pioneered the field of automated modeling starting in 1993 and is the most widely-used free web-based automated modeling facility today. In 2002 the server computed 120 000 user requests for 3D protein models. SWISS-MODEL provides several levels of user interaction through its World Wide Web interface: in the 'first approach mode' only an amino acid sequence of a protein is submitted to build a 3D model. Template selection, alignment and model building are done completely automated by the server. In the 'alignment mode', the modeling process is based on a user-defined target-template alignment. Complex modeling tasks can be handled with the 'project mode' using DeepView (Swiss-PdbViewer), an integrated sequence-to-structure workbench. All models are sent back via email with a detailed modeling report. WhatCheck analyses and ANOLEA evaluations are provided optionally. The reliability of SWISS-MODEL is continuously evaluated in the EVA-CM project. The SWISS-MODEL server is under constant development to improve the successful implementation of expert knowledge into an easy-to-use server.

Computer Graphics↗

PubMed2004

The SWISS-MODEL Repository of annotated three-dimensional protein structure homology models.

The SWISS-MODEL Repository is a database of annotated three-dimensional comparative protein structure models generated by the fully automated homology-modelling pipeline SWISS-MODEL. The Repository currently contains about 300,000 three-dimensional models for sequences from the Swiss-Prot and TrEMBL databases. The content of the Repository is updated on a regular basis incorporating new sequences, taking advantage of new template structures becoming available and reflecting improvements in the underlying modelling algorithms. Each entry consists of one or more three-dimensional protein models, the superposed template structures, the alignments on which the models are based, a summary of the modelling process and a force field based quality assessment. The SWISS-MODEL Repository can be queried via an interactive website at http://swissmodel.expasy. org/repository/. Annotation and cross-linking of the models with other databases, e.g. Swiss-Prot on the ExPASy server, allow for seamless navigation between protein sequence and structure information. The aim of the SWISS-MODEL Repository is to provide access to an up-to-date collection of annotated three-dimensional protein models generated by automated homology modelling, bridging the gap between sequence and structure databases.

Animals↗

PubMed1989

A comparison of excretion and retention between the current ICRP lung model and a proposed new model.

The current International Commission on Radiation Protection (ICRP) lung model (Health Phys. 12: 173; 1986) was developed from information available in the early 1960s. Since that time considerable new information on lung morphology, deposition, and retention has become available and, where appropriate, has been incorporated into a new model being discussed by a Task Group of the ICRP. This new model is conceptually much simpler in that it contains only three compartments, as opposed to 11 in the current model. The intent of this simpler model is to make it easier to model experimental retention and excretion data, either from in vitro studies, animal or human experiments, or human experience. However, this conceptually simpler model is somewhat more difficult to use than the current model as the new model parameters vary with time after exposure. That is, parameters are time-varying functions rather than constants, as they are in the current model, and retention is not given by the familiar Bateman equations. Default time-varying parameters for the new model have been developed that give results comparable to the current model for Classes D, W, and Y compounds. In addition, parameters have been developed for U ore dust, based on in vitro and in vivo studies, and for UO2 from human experience in U fuel fabrication facilities. The development of these parameters will be described, and the results with the new model compared with those obtained with the current model.

Aerosols↗

PubMed1992

Structure and parameterization of pharmacokinetic models: their impact on model predictions.

There has been an increasing interest in physiologically based pharmacokinetic (PBPK) models in the area of risk assessment. The use of these models raises two important issues: (1) How good are PBPK models for predicting experimental kinetic data? (2) How is the variability in the model output affected by the number of parameters and the structure of the model? To examine these issues, we compared a five-compartment PBPK model, a three-compartment PBPK model, and nonphysiological compartmental models of benzene pharmacokinetics. Monte Carlo simulations were used to take into account the variability of the parameters. The models were fitted to three sets of experimental data and a hypothetical experiment was simulated with each model to provide a uniform basis for comparison. Two main results are presented: (1) the difference is larger between the predictions of the same model fitted to different data sets than between the predictions of different models fitted to the dame data; and (2) the type of data used to fit the model has a larger effect on the variability of the predictions than the type of model and the number of parameters.

Animals↗

PubMed1994

Model-based estimation of vascular parameters: evaluation of robustness and suitability of models.

Left ventricular performance depends not only on myocardial state, but also on the properties of the systemic arterial tree. These properties can be assessed from recordings of aortic root pressure and flow by the use of appropriate vascular models. Noninvasive estimates of aortic root pressure and flow can be obtained by the combined use of calibrated external subclavian artery pulse tracing and Doppler echocardiography. With recent advances in computer technology, estimation of model parameters are thus accessible in the clinical setting. We discuss the suitability of different parametric vascular models together with methods for adapting these models to the measured aortic root pressure. We compared the results obtained with simple vascular models (three-component modified Windkessel models) with those of five-component models. The simpler models gave less accurate approximation of the measured pressure waveform, but for a representative set of aortic root pressure and flow data, the simpler models provided adequate estimates of the peripheral arterial resistance, the total arterial compliance, and the proximal aortic area compliance. Furthermore, the simpler models are robust for measurement noise with simple estimation algorithms. Distal arterial pressure and flow waveforms are more oscillatory, and for these the five-component model has more robust estimation schemes with more accurate estimated parameters. Hence, we conclude that for clinical noninvasive assessment of aortic vascular properties, the simpler three-component models provide adequate information. For assessment of the peripheral arteries with large oscillations in the flow, the three-component models can give more than 10% error in the compliance estimate and more complex models can be appropriate.

Aorta↗

PubMed1997

Modeling neural mechanisms for genesis of respiratory rhythm and pattern. II. Network models of the central respiratory pattern generator.

The present paper describes several models of the central respiratory pattern generator (CRPG) developed employing experimental data and current hypotheses for respiratory rhythmogenesis. Each CRPG model includes a network of respiratory neuron types (e.g., early inspiratory; ramp inspiratory; late inspiratory; decrementing expiratory; postinspiratory; stage II expiratory; stage II constant firing expiratory; preinspiratory) and simplified models of lung and pulmonary stretch receptors (PSR), which provide feedback to the respiratory network. The used models of single respiratory neurons were developed in the Hodgkin-Huxley style as described in the previous paper. The mechanism for termination of inspiration (the inspiratory off-switch) in all models operates via late-I neuron, which is considered to be the inspiratory off-switching neuron. Several two- and three-phase CRPG models have been developed using different accepted hypotheses of the mechanism for termination of expiration. The key elements in the two-phase models are the early-I and dec-E neurons. The expiratory off-switch mechanism in these models is based on the mutual inhibitory connections between early-I and dec-E and adaptive properties of the dec-E neuron. The difference between the two-phase models concerns the mechanism for ramp firing patterns of E2 neurons resulting either from the intrinsic neuronal properties of the E2 neuron or from disinhibition from the adapting dec-E neuron. The key element of the three-phase models is the pre-I neuron, which acts as the expiratory off-switching neuron. The three-phase models differ by the mechanisms used for termination of expiration and for the ramp firing patterns of E2 neurons. Additional CRPG models were developed employing a dual switching neuron that generates two bursts per respiratory cycle to terminate both inspiration and expiration. Although distinctly different each model generates a stable respiratory rhythm and shows physiologically plausible firing patterns of respiratory neurons with and without PSR feedback. Using our models, we analyze the roles of different respiratory neuron types and their interconnections for the respiratory rhythm and pattern generation. We also investigate the possible roles of intrinsic biophysical properties of different respiratory neurons in controlling the duration of respiratory phases and timing of switching between them. We show that intrinsic membrane properties of respiratory neurons are integrated with network properties of the CRPG at three hierarchical levels: at the cellular level to provide the specific firing patterns of respiratory neurons (e.g., ramp firing patterns); at the network level to provide switching between the respiratory phases; and at the systems level to control the duration of inspiration and expiration under different conditions (e.g., lack of PSR feedback).

Adaptation, Physiological↗

PubMed2004

A comparative study of an accelerated life-test model and a toxicokinetics-based model for the analysis of Porcellio scaber survival data.

Statistical models have long been used for reliability analysis and risk assessment. In the present study, an accelerated life-test model was used to analyze a set of dose-time-response data obtained with the terrestrial isopod Porcellio scaber. Survival data were experimentally obtained by exposing P. scaber to diazinon (a nonpersistent insecticide) at six concentrations between 2 and 11.31 microg/g (toxicant/soil). Survival data are presented on a weekly basis. The accelerated life-test model assumed a log-normal distribution and constant variance across all diazinon concentrations. Model parameters were obtained by maximum likelihood estimation. The accelerated life-test model was compared to a toxicokinetics-based model reported in the literature. Survival predictions made by both models were compared with the observed data. Both the accelerated life-test model and the toxicokinetics-based model underestimated toxicity at a diazinon concentration of 8 microg/g. Overall, however, the accelerated life-test model outperformed the toxicokinetics-based model, with survival predictions closer to the observed data in most cases and a stronger correlation between predicted and observed survivals. However, as a statistical model, the accelerated life-test model did not reveal mechanistic information, and only statistical and distributional interpretations of its model parameters could be made.

Animals↗

PubMed2002

Modeling sorption isotherms of volatile organic chemical mixtures in model and natural solids.

Parameters from single-component isotherm models were used in multicomponent isotherm models to predict the aqueous phase sorption of trichloroethylene (TCE) in the presence of tetrachloroethylene (PCE) in four zeolites, Tenax, and three natural solids. The Langmuir, the Polanyi-Dubinin, and the Freundlich or the Langmuir-Freundlich isotherm models were used to simulate single-component sorption in zeolites. The Langmuir two-site, the Polanyi-Dubinin two-site, and the Freundlich or the Langmuir-Freundlich isotherm models were used to simulate single-component sorption in Tenax and natural solids. Two-site models have been used previously to model sorption in soils and sediments, and they combine an adsorption component (e.g., Langmuir) with a linear partitioning component. By using parameters from the different single-component isotherm models, the multicomponent Langmuir, the ideal adsorbed solution theory, and the Polanyi theory were each used to predict multicomponent sorption. In general, the ability to predict TCE sorption in the presence of PCE depended more on the choice of the single-component model than the multicomponent model, and better results were obtained when the Freundlich or the Langmuir-Freundlich isotherm was used for single-component sorption. This suggests that the more mechanistically based Langmuir and Polanyi-type models may not adequately describe the distribution of adsorption sites in some model and natural solids. The Freundlich or the Langmuir-Freundlich model, although empirical, has greater flexibility in characterizing sorbent heterogeneity and results in better multicomponent model predictions. However, this last statement is tenuous, because more solids must be tested against various model combinations.

Adsorption↗

PubMed2001

Exploring among-site rate variation models in a maximum likelihood framework using empirical data: effects of model assumptions on estimates of topology, branch lengths, and bootstrap support.

We have investigated the effects of different among-site rate variation models on the estimation of substitution model parameters, branch lengths, topology, and bootstrap proportions under minimum evolution (ME) and maximum likelihood (ML). Specifically, we examined equal rates, invariable sites, gamma-distributed rates, and site-specific rates (SSR) models, using mitochondrial DNA sequence data from three protein-coding genes and one tRNA gene from species of the New Zealand cicada genus Maoricicada. Estimates of topology were relatively insensitive to the substitution model used; however, estimates of bootstrap support, branch lengths, and R-matrices (underlying relative substitution rate matrix) were strongly influenced by the assumptions of the substitution model. We identified one situation where ME and ML tree building became inaccurate when implemented with an inappropriate among-site rate variation model. Despite the fact the SSR models often have a better fit to the data than do invariable sites and gamma rates models, SSR models have some serious weaknesses. First, SSR rate parameters are not comparable across data sets, unlike the proportion of invariable sites or the alpha shape parameter of the gamma distribution. Second, the extreme among-site rate variation within codon positions is problematic for SSR models, which explicitly assume rate homogeneity within each rate class. Third, the SSR models appear to give severe underestimates of R-matrices and branch lengths relative to invariable sites and gamma rates models in this example. We recommend performing phylogenetic analyses under a range of substitution models to test the effects of model assumptions not only on estimates of topology but also on estimates of branch length and nodal support.

Animals↗

PubMed2005

Reassembly and interfacing neural models registered on biological model databases.

The importance of modeling and simulation of biological process is growing for further understanding of living systems at all scales from molecular to cellular, organic, and individuals. In the field of neuroscience, there are so called platform simulators, the de-facto standard neural simulators. More than a hundred neural models are registered on the model database. These models are executable in corresponding simulation environments. But usability of the registered models is not sufficient. In order to make use of the model, the users have to identify the input, output and internal state variables and parameters of the models. The roles and units of each variable and parameter are not explicitly defined in the model files. These are suggested implicitly in the papers where the simulation results are demonstrated. In this study, we propose a novel method of reassembly and interfacing models registered on biological model database. The method was applied to the neural models registered on one of the typical biological model database, ModelDB. The results are described in detail with the hippocampal pyramidal neuron model. The model is executable in NEURON simulator environment, which demonstrates that somatic EPSP amplitude is independent of synapse location. Input and output parameters and variables were identified successfully, and the results of the simulation were recorded in the organized form with annotations.

Computational Biology↗

PubMed2006

Analysis of a Schnute postulate-based unified growth model for model selection in evolutionary computations.

In order to evaluate the feasibility of a combined evolutionary algorithm-information theoretic approach to select the best model from a set of candidate invasive species models in ecology, and/or to evolve the most parsimonious model from a suite of competing models by comparing their relative performance, it is prudent to use a unified model that covers a myriad of situations. Using Schnute's postulates as a starting point [Schnute, J., 1981. A versatile growth model with statistically stable parameters, Can. J. Fish Aquat. Sci. 38, 1128-1140], we present a single, unified model for growth that can be successfully utilized for model selection in evolutionary computations. Depending on the parameter settings, the unified equation can describe several growth mechanisms. Such a generalized model mechanism, which encompasses a suite of competing models, can be successfully implemented in evolutionary computational algorithms to evolve the most parsimonious model that best fits ground truth data. We have done exactly this by testing the effectiveness of our reaction-diffusion-advection (RDA) model in an evolutionary computation model selection algorithm. The algorithm was validated (with success) against field data sets of the Zebra mussel invasion of Lake Champlain in the United States.

Algorithms↗

PubMed2000

Comparison of simple neural networks and nonlinear regression models for descriptive modeling of Lactobacillus helveticus growth in pH-controlled batch cultures.

A set of 20 Lactobacillus helveticus growth curves was obtained from pH-controlled batch cultures with different pH setpoints, whey permeate and yeast extract concentrations. To find the best descriptive model of the biomass concentration versus time (y = X(t)) growth curve, fitting results of a large number of models were compared with statistical and approximate methods. Models studied included simple neural networks, reparameterized Logistic, Gompertz, Richards, Schnute, Weibull, and Morgan-Mercier-Flodin models, Amrane-Prigent model, and four new models based on autonomous growth functions. Simple neural networks with only four weights were good descriptive models of the growth curves and fitting qualities were similar to those of the best existing four-parameter models, such as the Logistic model. However, meaningful parameters had to be calculated numerically and use of simple neural networks yielded no distinctive advantages over other models. A new five-parameter model, based on an autonomous growth function, yielded the best fitting results, even when the number of model parameters was accounted for in the comparisons. However, the maximum specific growth rate was not always well estimated. Therefore the five-parameter Richards model was chosen as the best descriptive model of the growth curve.

Journal Article↗

PubMed1996

Factors affecting the performance of the models in the Mortality Probability Model II system and strategies of customization: a simulation study.

OBJECTIVES: To examine the impact of hospital mortality and intensive care unit (ICU) size on the performance of the Mortality Probability Model II system for use in quality assessment, and to examine the ability of model customization to produce accurate estimates of hospital mortality to characterize patients by severity of illness for clinical trials. DESIGN: Prospective evaluation of model performance, using retrospective data. SETTING: Data for the simulation were assembled from six adult medical and surgical ICUs in Massachusetts and New York. PATIENTS: Consecutive admissions (n = 4,224) to the Massachusetts and New York ICUs were studied. The mortality rate in the database was 18.7%. INTERVENTIONS: A computer simulation of several different hospital mortality rates and ICU sample sizes, using a multicenter database of consecutive ICU admissions, was utilized. We simulated 20 different mortality rates by randomly changing the outcomes at hospital discharge from "survived" to "deceased" and from "deceased" to "survived". Four sample size simulations used 75%, 50%, 25%, and 10% of the database. Ten replications of each mortality rate and samples size were constructed, and model calibration and discrimination were assessed for each replication. Model coefficients were customized, using logistic regression. MEASUREMENTS AND MAIN RESULTS: Vital status at hospital discharge was the outcome measure among the ICU patient population. Model performance was assessed using the Hosmer-Lemeshow C statistic for calibration, and the area under the receiver operating characteristic curve for discrimination. Goodness-of-fit tests and receiver operating characteristic curve areas demonstrated that the models were sensitive to differences in hospital mortality, indicating that they are useful quality assurance tools. Goodness-of-fit tests were more sensitive than the receiver operating characteristic curve areas. The further the hospital mortality rate diverged from the original rate, the worse the performance of the model. Sample size had an impact on these results. The smaller the sample size, the less likely the model was to perform poorly. Model coefficients were successfully customized to demonstrate that improved model performance can be achieved when necessary for clinical trial stratification. CONCLUSION: Mortality Probability Model II models can be used to assess quality of care in ICUs, but the size of the sample should be considered when assessing calibration and discrimination.

Adult↗