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PubMed1999

The relationship between the myocardial kinetics of meperidine and its effect on myocardial contractility: model-independent analysis and optimal regional model.

The myocardial kinetics of meperidine and the relationship between these kinetics and the effect of meperidine on myocardial contractility (maximum positive rate of change of left ventricular pressure) were examined by analysis of previously published data collected in sheep after the i.v. injection of 100 mg of meperidine over 1 s. There was significant hysteresis between reductions in myocardial contractility and the arterial concentrations of meperidine, but not the coronary sinus blood (effluent from the heart) or calculated myocardial concentrations. The peak reduction in contractility occurred after the peak arterial concentration, at the time of the peak myocardial concentration, but before the peak coronary sinus concentration, suggesting that the site of drug action in the heart was not in equilibrium with either arterial blood or effluent blood from the heart. The most appropriate form of a dynamic model (a linear model with a threshold) was determined, without the need to assume a kinetic model, by directly fitting the observed reductions in myocardial contractility to the calculated myocardial concentrations. To determine the optimal kinetic and combined kinetic-dynamic models, a variety of one-, two-, and three-compartment models of the myocardium were fitted to the coronary sinus concentrations by using hybrid modeling. These included "tank in series" models that accounted well for drug dispersion and "peripheral compartment" models that accounted well for deep distribution. The most appropriate model was a "compilation" model, which incorporated features of both these extremes and was a better fit to the observed data than either a traditional single flow-limited compartment or a traditional membrane-limited model.

Algorithms↗

PubMed2001

Application of a sigmapolycyclic aromatic hydrocarbon model and a logistic regression model to sediment toxicity data based on a species-specific, water-only LC50 toxic unit for Hyalella azteca.

Two models, a sigmapolycyclic aromatic hydrocarbon (PAH) model based on equilibrium partitioning theory and a logistic-regression model, were developed and evaluated to predict sediment-associated PAH toxicity to Hyalella azteca. A sigmaPAH model was applied to freshwater sediments. This study is the first attempt to use a sigmaPAH model based on water-only, median lethal concentration (LC50) toxic unit (TU) values for sediment-associated PAH mixtures and its application to freshwater sediments. To predict the toxicity (i.e., mortality) from contaminated sediments to H. azteca, an interstitial water TU, calculated as the ambient interstitial water concentration divided by the water-only LC50 in which the interstitial water concentrations were predicted by equilibrium partitioning theory, was used. Assuming additive toxicity for PAH, the sum of TUs was calculated to predict the total toxicity of PAH mixtures in sediments. The sigmaPAH model was developed from 10- and 14-d H. azteca water-only LC50 values. To obtain estimates of LC50 values for a wide range of PAHs, a quantitative structure-activity relationship (QSAR) model (log LC50 - log Kow) with a constant slope was derived using the time-variable LC50 values for four PAH congeners. The logistic-regression model was derived to assess the concentration-response relationship for field sediments, which showed that 1.3 (0.6-3.9) TU were required for a 50% probability that a sediment was toxic. The logistic-regression model reflects both the effects of co-occurring contaminants (i.e., nonmeasured PAH and unknown pollutants) and the overestimation of exposure to sediment-associated PAH. An apparent site-specific bioavailability limitation of sediment-associated PAH was found for a site contaminated by creosote. At this site, no toxic samples were less than 3.9 TU. Finally, the predictability of the sigmaPAH model can be affected by species-specific responses (Hyalella vs Rhepoxynius); chemical specific (PAH vs DDT in H. azteca) biases, which are not incorporated in the equilibrium partitioning model; and the uncertainty from site-specific effects (creosote vs other sources of PAH contamination) on the bioavailability of sediment-associated PAH mixtures.

Animals↗

PubMed2001

The Rasch model, additive conjoint measurement, and new models of probabilistic measurement theory.

This research describes some of the similarities and differences between additive conjoint measurement (a type of fundamental measurement) and the Rasch model. It seems that there are many similarities between the two frameworks, however, their differences are nontrivial. For instance, while conjoint measurement specifies measurement scales using a data-free, non-numerical axiomatic frame of reference, the Rasch model specifies measurement scales using a numerical frame of reference that is, by definition, data dependent. In order to circumvent difficulties that can be realistically imposed by this data dependence, this research formalizes new non-parametric item response models. These models are probabilistic measurement theory models in the sense that they explicitly integrate the axiomatic ideas of measurement theory with the statistical ideas of order-restricted inference and Markov Chain Monte Carlo. The specifications of these models are rather flexible, as they can represent any one of several models used in psychometrics, such as Mokken's (1971) monotone homogeneity model, Scheiblechner's (1995) isotonic ordinal probabilistic model, or the Rasch (1960) model. The proposed non-parametric item response models are applied to analyze both real and simulated data sets.

Humans↗

PubMed2005

Model uncertainty--parameter uncertainty versus conceptual models.

Uncertainties in model structures have been recognised often to be the main source of uncertainty in predictive model simulations. Despite this knowledge, uncertainty studies are traditionally limited to a single deterministic model and the uncertainty addressed by a parameter uncertainty study. The extent to which a parameter uncertainty study may encompass model structure errors in a groundwater model is studied in a case study. Three groundwater models were constructed on the basis of three different hydrogeological interpretations. Each of the models was calibrated inversely against groundwater heads and streamflows. A parameter uncertainty analysis was carried out for each of the three conceptual models by Monte Carlo simulations. A comparison of the predictive uncertainties for the three conceptual models showed large differences between the uncertainty intervals. Most discrepancies were observed for data types not used in the model calibration. Thus uncertainties in the conceptual models become of increasing importance when predictive simulations consider data types that are extrapolates from the data types used for calibration.

Denmark↗

PubMed1983

The analysis of dependence in cross-classifications having ordered categories, using log-linear models for frequencies and log-linear models for odds.

To analyse the dependence of a qualitative (dichotomous or polytomous) response variable upon one or more qualitative explanatory variables, log-linear models for frequencies are compared with log-linear models for odds, when the categories of the response variable are ordered and the categories of each explanatory variable may be either ordered or unordered. The log-linear models for odds express the odds (or log odds) pertaining to adjacent response categories in terms of appropriate multiplicative (or additive) factors. These models include the 'null log-odds model', the 'uniform log-odds model', the 'parallel log-odds model', and other log-linear models for the odds. With these models, the dependence of the response variable (with ordered categories) can be analyzed in a manner analogous to the usual multiple regression analysis and related analysis of variance and analysis of covariance. Application of log-linear models for the odds sheds light on earlier applications of log-linear models for the frequencies in contingency tables with ordered categories.

Biometry↗

PubMed2026

Statistical test to compare the linkage model and the admixture model based on central limit results.

In the Admixture Model, the probability that an individual carries a certain allele at a specific marker depends on the allele frequencies in K ancestral populations and the proportion of the individual's genome originating from these populations. The markers are assumed to be independent. The Linkage Model is a Hidden Markov Model that extends the Admixture Model by incorporating linkage between neighboring loci. We prove consistency and asymptotic normality of maximum likelihood estimators for the ancestry of individuals in the Linkage Model, complementing earlier results by (Pfaff et al., 2004; Pfaffelhuber and Rohde, 2022; Heinzel, 2025) for the Admixture Model. These results are used to prove that a statistical test that allows for model selection between the Admixture Model and the Linkage Model is an asymptotic level-α-test. Finally, we demonstrate the practical relevance of our results by applying the test to real-world data from The 1000 Genomes Project Consortium (2015).

Genetic Linkage↗

PubMed1988

A dynamic model for water flow in a single tree: evidence that models must account for hydraulic architecture.

A model is presented for the dynamics of water flow in a single eastern white cedar tree (Thuja occidentalis L.). The model takes into account the spatial and temporal dependence of the evaporative flux from leaves in the crown. It also accounts for the quantitative hydraulic architecture of the tree, i.e., the model characterizes the tree as a branched catena of > 4000 stem segments in which account is taken of the segment length, diameter, hydraulic resistance, and the total area of leaves attached to the segment. Input values needed to run the model are measurements of evaporative flux, hydraulic conductance of stems versus stem diameter, and leaf and stem water storage capacitances. Output parameters are the spatial and temporal characterization of stem and leaf water potentials, stem and leaf water deficits, sap flow rate, and relative sap velocity. The input and output values of the branched catena model are compared and contrasted to that of an unbranched catena model. It is shown that the branched catena model fits independently measured field parameters better than an unbranched catena model. Close correspondence is found between model predictions and field measurements of shoot water potential, pressure gradients in stems, hysteresis in sap velocity between the lower and upper parts of the tree, and diurnal changes in stem and leaf water deficits. This model is discussed in terms of both the hydraulic architecture of trees and the potential application of the model to questions of tree morphology, ecology, physiology and evolution.

Journal Article↗

PubMed2005

Are syngeneic mouse tumor models still valuable experimental models in the field of anti-cancer drug discovery?

To establish the pharmacological profile of a molecule with anti-cancer potential, it seems essential to add an in vivo approach to the first pharmacological experiments carried out in vitro. The present study aims to characterize the degree of sensitivity of seven syngeneic models (two leukemias and five solid tumors) to eleven molecules which have proven to be clinically reliable. We also used some of these models to investigate whether the molecular effects on the extent of growth in a subcutaneously grafted experimental model correlate with the effects of the same drug on the survival of the animals so grafted. Our data show that all the molecules demonstrated significant anti-tumor activities in two mouse leukemia models (with some discrepancies between the two). Two lymphoma models displayed weaker chemosensitivity profiles than the two leukemia models from which they were developed. Two other models, namely the MXT-HS mammary carcinoma and the B16 melanoma, appeared to be rather chemoresistant. However, a direct relationship was evident between the drug-induced decrease in the tumor growth rate and the increase observed in the survival periods of the MXT tumor-bearing mice. This relationship was also observed in the L1210_LYM lymphoma, though to a lesser extent, and was completely absent from the B16 melanoma model. Finally, our data indicated that we had developed a pair of metastasizing, as opposed to non-metastasizing, lymphoma and mammary carcinoma models. In conclusion, the present study shows that syngeneic mouse tumor models can be used as valuable in vivo experimental models for the screening of potential anti-cancer agents.

Animals↗

PubMed2003

Joint models for efficient estimation in proportional hazards regression models.

In survival studies, information lost through censoring can be partially recaptured through repeated measures data which are predictive of survival. In addition, such data may be useful in removing bias in survival estimates, due to censoring which depends upon the repeated measures. Here we investigate joint models for survival T and repeated measurements Y, given a vector of covariates Z. Mixture models indexed as f (T/Z) f (Y/T,Z) are well suited for assessing covariate effects on survival time. Our objective is efficiency gains, using non-parametric models for Y in order to avoid introducing bias by misspecification of the distribution for Y. We model (T/Z) as a piecewise exponential distribution with proportional hazards covariate effect. The component (Y/T,Z) has a multinomial model. The joint likelihood for survival and longitudinal data is maximized, using the EM algorithm. The estimate of covariate effect is compared to the estimate based on the standard proportional hazards model and an alternative joint model based estimate. We demonstrate modest gains in efficiency when using the joint piecewise exponential joint model. In a simulation, the estimated efficiency gain over the standard proportional hazards model is 6.4 per cent. In clinical trial data, the estimated efficiency gain over the standard proportional hazards model is 10.2 per cent.

Algorithms↗

PubMed2000

Modeling the evolution of genetic architecture: A continuum of alleles model with pairwise AxA epistasis.

A continuum of alleles model with pair-wise AxA epistasis is proposed and its transmission genetic, and variational properties are analysed. The basic idea is that genes control the values of underlying variables, which affect the genotypic value of phenotypic characters proportional to a "scaling factor". Epistasis is the influence of one gene on the average effect of another gene. In this model, epistasis is introduced as a mutational effect of one gene on the scaling factors of another gene. In accordance with empirical results, the model assumes that the average direct effect of mutations is zero, as is the average epistatic effect. The model predicts that, on average, a mutation at one locus increases the expected mutational variance of mutations at another interacting locus. The increase in mutational variance is predicted to be equal to the variance of the pair-wise epistatic effects. This result is consistent with the observation that mutant phenotypes tend to be more variable than the wildtype phenotype. Another generic result of this model is that the frequency of canalizing mutations can at most be equal to the frequency of de-canalizing mutations. Furthermore, it is predicted that the mutational variance of a character increases at least linearly with the size of the character; hence this model is scale variant. In the case of two characters it is shown that the dimensionality of the locus-specific mutational effect distribution is invariant, i.e. the rank of the mutational covariance matrix M is invariant. While in additive models the mutational covariance matrix is always and entirely invariant, the invariance in the case of epistatic models is unexpected. Epistatic interactions can change the magnitude of the mutational (co)variances at a locus and can thus influence the structure of the mutational covariance matrix. However, in the present model the dimensionality of the mutational effect distribution remains the same. A consequence of this result is that, in this model, the genetic architecture of a set of characters is always evolvable i.e. no hard constraints can evolve.

Alleles↗

PubMed2000

Tendency modeling: a new approach to obtain simplified kinetic models of metabolism applied to Saccharomyces cerevisiae.

A novel approach to construct kinetic models of metabolic pathways, to be used in metabolic engineering, is presented: the tendency modeling approach. This approach greatly facilitates the construction of these models and can easily be applied to complex metabolic networks. The resulting models contain a minimal number of parameters; identification of their values is straightforward. Use of in vitro obtained information in the identification of the kinetic equations is minimized. The tendency modeling approach has been used to derive a dynamic model of primary metabolism for aerobic growth of Saccharomyces cerevisiae on glucose, in which compartmentation is included. Simulation results obtained with the derived model are satisfying for most of the carbon metabolites that have been measured. Compared to a more detailed model, the simulations of our model are less accurate, but taking into account the much smaller number of kinetic parameters (35 instead of 84), the tendency the modeling approach is considered promising.

Biomedical Engineering↗

PubMed2004

Development of a novel approach for secondary modelling in predictive microbiology: incorporation of microbiological knowledge in black box polynomial modelling.

This research deals with the development of a novel secondary modelling procedure within the framework of predictive microbiology. The procedure consists of three steps: (i) careful formulation of the available microbiological information, both from literature and from the experimental case study at hand, (ii) translation of these requirements in mathematical terms under the form of partial derivatives throughout the complete interpolation region of the experimental design, and (iii) determination of parameter values with suitable optimisation techniques for a flexible black box modelling approach, e.g., a polynomial model or an artificial neural network model. As a vehicle for this procedure, the description of the maximum specific growth rate of Lactobacillus sakei in modified BHI-broth as influenced by suboptimal temperature, water activity, sodium lactate and dissolved carbon dioxide concentration is under study. The procedure results in a constrained polynomial model with excellent descriptive and interpolating features in comparison with an extended Ratkowsky-type model and classical polynomial model, by combining specific properties of both model types. The developed procedure is illustrated on the description of the lag phase as well. It is stressed how the confrontation with experimental data is very important to appreciate the descriptive and interpolating capacities of new or existing models, which is nowadays not always carefully performed. Alternatively, the first two steps of the novel procedure can be used as a tool to demonstrate clearly (possible) interpolative shortcomings of an existing model with straightforward spreadsheet calculations.

Carbon Dioxide↗

PubMed2006

QSAR modeling of human serum protein binding with several modeling techniques utilizing structure-information representation.

Four modeling techniques, using topological descriptors to represent molecular structure, were employed to produce models of human serum protein binding (% bound) on a data set of 1008 experimental values, carefully screened from publicly available sources. To our knowledge, this data is the largest set on human serum protein binding reported for QSAR modeling. The data was partitioned into a training set of 808 compounds and an external validation test set of 200 compounds. Partitioning was accomplished by clustering the compounds in a structure descriptor space so that random sampling of 20% of the whole data set produced an external test set that is a good representative of the training set with respect to both structure and protein binding values. The four modeling techniques include multiple linear regression (MLR), artificial neural networks (ANN), k-nearest neighbors (kNN), and support vector machines (SVM). With the exception of the MLR model, the ANN, kNN, and SVM QSARs were ensemble models. Training set correlation coefficients and mean absolute error ranged from r2=0.90 and MAE=7.6 for ANN to r2=0.61 and MAE=16.2 for MLR. Prediction results from the validation set yielded correlation coefficients and mean absolute errors which ranged from r2=0.70 and MAE=14.1 for ANN to a low of r2=0.59 and MAE=18.3 for the SVM model. Structure descriptors that contribute significantly to the models are discussed and compared with those found in other published models. For the ANN model, structure descriptor trends with respect to their affects on predicted protein binding can assist the chemist in structure modification during the drug design process.

Blood Proteins↗

PubMed2004

Model-free analysis of protein dynamics: assessment of accuracy and model selection protocols based on molecular dynamics simulation.

The popular model-free approach to analyze NMR relaxation measurements has been examined using artificial amide (15)N relaxation data sets generated from a 10 nanosecond molecular dynamics trajectory of a dihydrofolate reductase ternary complex in explicit water. With access to a detailed picture of the underlying internal motions, the efficacy of model-free analysis and impact of model selection protocols on the interpretation of NMR data can be studied. In the limit of uncorrelated global tumbling and internal motions, fitting the relaxation data to the model-free models can recover a significant amount of quantitative information on the internal dynamics. Despite a slight overestimation, the generalized order parameter is quite accurately determined. However, the model-free analysis appears to be insensitive to the presence of nanosecond time scale motions with relatively small magnitude. For such cases, the effective correlation time can be significantly underestimated. As a result, proteins appear to be more rigid than they really are. The model selection protocols have a major impact on the information one can reliably obtain. The commonly employed protocol based on step-up hypothesis testing has severe drawbacks of oversimplification and underfitting. The consequences are that the order parameter is more severely overestimated and the correlation time more severely underestimated. Instead, model selection based on Bayesian Information Criteria (BIC), recently introduced to the model-free analysis by d'Auvergne and Gooley (2003), provides a better balance between bias and variance. More appropriate models can be selected, leading to improved estimate of both the order parameter and correlation time. In addition, the computational cost is significantly reduced and subjective parameters such as the significance level are unnecessary.

Anisotropy↗

PubMed1998

Equivalence of a sprouting-and-retraction model and correlation-based plasticity models of neural development.

A simple model of correlation-based synaptic plasticity via axonal sprouting and retraction (Elliott, Howarth, & Shadbolt, 1996a) is shown to be equivalent to the class of correlation-based models (Miller, Keller, & Stryker, 1989), although these were formulated in terms of weight modification of anatomically fixed synapses. Both models maximize the same measure of synaptic correlation, subject to certain constraints on connectivity. Thus, the analyses of the correlation-based models suffice to characterize the behavior of the sprouting-and-retraction model. More detailed models are needed for theoretical distinctions to be drawn between plasticity via sprouting and retraction, weight modification, or a combination. The model of Elliott et al. involves stochastic search through allowed weight patterns for those that improve correlations. That of Miller et al. instead follows dynamical equations that determine continuous changes of the weights that improve correlations. The identity of these two approaches is shown to depend on the use of subtractive constraint enforcement in the models of Miller et al. More generally, to model the idea that neural development acts to maximize some measure of correlation subject to a constraint on the summed synaptic weight, the constraint must be enforced subtractively in a dynamical model.

Animals↗

PubMedDate not supplied

Temperature-dependent versus constant-rate blood perfusion modelling in ferromagnetic thermoseed hyperthermia: results with a model of the human prostate.

Finite-element solutions to the Pennes bioheat equation are obtained with a model of a tumour-containing, human prostate and surrounding normal tissues. Simulations of ferromagnetic hyperthermia treatments are conducted on the tissue model in which the prostate is implanted with an irregularly spaced array of thermoseeds. Several combinations of thermoseed temperatures with different Curie points are investigated. Non-uniform, constant-rate blood perfusion models are studied and compared with temperature-dependent descriptions of blood perfusion. Blood perfusions in the temperature-dependent models initially increase with tissue temperature and then decrease at higher temperatures. Simulations with temperature-dependent versus constant-rate blood perfusion models reveal significant differences in temperature distributions in and surrounding the tumour-containing prostate. Results from the simulations include differences (between temperature-dependent and constant-rate models) in (1) the percentage of normal tissue volume and tumour volume at temperatures > 42 degrees C, and (2) temperature descriptors in the tumour (subscript t) and normal (subscript n) tissues including Tmax.t, Tmin.t and Tmax.n. Isotherms and grey-scale contours in the tumour and surrounding normal tissues are presented for four simulations that model a combination of high-temperature thermoseeds. Several simulations show that Tmin.t is between 1.7 and 2.6 degrees C higher and Tmax.n is between 2.1 and 3.3 degrees C higher with a temperature-dependent versus a comparable constant-rate blood perfusion model. The same simulations reveal that the percentages of tumour volume at temperatures > 42 degrees C are between 0 and 68% higher with the temperature-dependent versus the constant-rate perfusion model over all seed combinations studied. In summary, a numerical method is presented which makes it possible to investigate temperature-dependent, continuous functions of blood perfusion in simulations of hyperthermia treatments. Simulations with this numerical method reveal that the use of constant-rate instead of temperature-dependent blood perfusion models can be a conservative approach in treatment planning of ferromagnetic hyperthermia.

Body Temperature Regulation↗

PubMed1997

Predictive model selection for repeated measures random effects models using Bayes factors.

The random effects model fit to repeated measures data is an extremely common model and data structure in current biostatistical practice. Modern data analysis often involves the selection of models within broad classes of prespecified models, but for models beyond the generalized linear model, few model-selection tools have been actively studied. In a Bayesian analysis, Bayes factors are the natural tool to use to explore these classes of models. In this paper, we develop a predictive approach for specifying the priors of a repeated measures random effects model with emphasis on selecting the fixed effects. The advantage of the predictive approach is that a single predictive specification is used to specify priors for all models considered. The methodology is applied to a pediatric pain data analysis.

Bayes Theorem↗

PubMed1997

Homology modeling with internal coordinate mechanics: deformation zone mapping and improvements of models via conformational search.

Five models by homology containing insertions and deletions and ranging from 33% to 48% sequence identity to the known homologue, and one high sequence identity (85%) model were built for the CASP2 meeting. For all five low identity targets: (i) our starting models were improved by the Internal Coordinate Mechanics (ICM) energy optimization, (ii) the refined models were consistently better than those built with the automatic SWISS-MODEL program, and (iii) the refined models differed by less than 2% from the best model submitted, as judged by the residue contact area difference (CAD) measure [Abagyan, R.A., Totrov, M.J. Mol. Biol. 268:678-685, 1997]. The CAD measure is proposed for ranking models built by homology instead of global root-mean-square deviation, which is frequently dominated by insignificant yet large contributions from incorrectly predicted fragments or side chains. We demonstrate that the precise identification of regions of local backbone deviation is an independent and crucial step in the homology modeling procedure after alignment, since aligned fragments can strongly deviate from the template at various distances from the alignment gap or even in the ungapped parts of the alignment. We show that a local alignment score can be used as an indicator of such local deviation. While four short loops of the meeting targets were predicted by database search, the best loop 1 target T0028, for which the correct database fragment was not found, was predicted by Internal Coordinate Mechanics global energy optimization at 1.2 A accuracy. A classification scheme for errors in homology modeling is proposed.

Models, Molecular↗