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PubMedDate not supplied

Mathematical modelling and quantitative methods.

The present review reports on the mathematical methods and statistical techniques presently available for hazard characterisation. The state of the art of mathematical modelling and quantitative methods used currently for regulatory decision-making in Europe and additional potential methods for risk assessment of chemicals in food and diet are described. Existing practices of JECFA, FDA, EPA, etc., are examined for their similarities and differences. A framework is established for the development of new and improved quantitative methodologies. Areas for refinement, improvement and increase of efficiency of each method are identified in a gap analysis. Based on this critical evaluation, needs for future research are defined. It is concluded from our work that mathematical modelling of the dose-response relationship would improve the risk assessment process. An adequate characterisation of the dose-response relationship by mathematical modelling clearly requires the use of a sufficient number of dose groups to achieve a range of different response levels. This need not necessarily lead to an increase in the total number of animals in the study if an appropriate design is used. Chemical-specific data relating to the mode or mechanism of action and/or the toxicokinetics of the chemical should be used for dose-response characterisation whenever possible. It is concluded that a single method of hazard characterisation would not be suitable for all kinds of risk assessments, and that a range of different approaches is necessary so that the method used is the most appropriate for the data available and for the risk characterisation issue. Future refinements to dose-response characterisation should incorporate more clearly the extent of uncertainty and variability in the resulting output.

Animals↗
PubMed1987

Cost-effectiveness analysis of patient management alternatives after uncomplicated myocardial infarction: a model.

Quantitative decision analyses provide a means whereby the effectiveness, in terms of patient outcome, and costs of diverse clinical approaches to the care of patients with cardiovascular disease can be made explicit and understandable. Increasingly, the profession is being required to justify the costs of clinical care to society, government and third party payers. Such justifications can be effectively presented when structured in decision analytic format. To demonstrate the utility of decision analysis and its extension--cost-effectiveness analysis--as a technique for presenting the rationale for clinical practices and technology utilization, the Cardiovascular Norms Committee of the American College of Cardiology sponsored a model cost-effectiveness analysis. Alternative management options, 6 month mortality and costs for the post-myocardial infarction patient were compared. The options included exercise electrocardiography, exercise thallium scintigraphy and coronary angiography, followed by coronary artery bypass surgery for patients with left main coronary disease only or patients with left main disease, three vessel disease or single or double vessel disease and a significant amount of myocardium in jeopardy. Within the constraints of the model, proceeding directly to angiography for risk stratification was the most effective approach, lowering expected mortality from 8% to approximately 3%. The marginal costs for this strategy, however, were high. The most cost-effective approach was to screen patients initially with exercise electrocardiography.

Angiography↗
PubMed2001

Practical application of residuals from survival models in quantitative trait linkage analysis.

A number of familial diseases have an age-of-onset component, which can be considered as a censored quantitative trait. However, few software resources are available for the use of time-to-event endpoints in linkage analysis. The purpose of this analysis was to examine the use of martingale residuals from Cox survival models as quantitative traits for familial diseases with variable age at onset. We used these residuals as quantitative traits in variance components linkage scans for the 50 replicates of the general population simulated data for chromosomes 6 and 7. The region on chromosome 6 containing markers D06G034 and D06G035 demonstrated evidence for linkage, consistent with the underlying genetic model. This analysis demonstrates the applicability of using martingale residuals as a quantitative trait in linkage analyses of diseases that depend on age of onset.

Adult↗
PubMed1999

Technical note: a new model for quantitative analysis of brain oedema resolution into the ventricles and the subarachnoid space.

OBJECTIVE: The aim of the current study was to develop an experimental animal model for quantitative analysis of oedema resolution via the subarachnoid space and the ventricular system using fluorescent oedema markers. METHODS: Artificial cerebrospinal fluid (CSF) containing TRITC-albumin (MW 67.000D) and Na(+)-fluorescein (MW 376D) was continuously infused into the white matter of the left frontal lobe of New Zealand white rabbits (n = 6) at a rate of 100 microliters/h for 3 hrs. A closed cranial window for superfusion of the brain surface with artificial CSF fluid (3 ml/h) was implanted above the left parietal cortex for measurement of the fluorescence markers in the subarachnoid space. Uptake of the fluorescence indicators into the ventricles was quantified by ventriculo-cisternal perfusion (3 ml/h). The effluates were collected at 30 min intervals for 3 hrs after the start of infusion. Clearance of the oedema fluid into the perfusates was measured by fluorescence spectrophotometry. RESULTS: At an intracranial pressure of 15.0 +/- 1.7 mm Hg (mean +/- SEM) both indicators started to accumulate in the subarachnoid and ventricular perfusates at 90 min following onset of oedema fluid infusion. The concentrations of the indicators in the ventricular system increased to 7.7 +/- 5.1% of Na(+)-fluorescein and 16.1 +/- 13.0% of TRITC-albumin of the total amount infused were recovered in the ventricular system at 3 hours after start of the oedema infusion, while 3.4 +/- 3.2% of Na(+)-fluorescein and 3.7% +/- 3.2 of TRITC-albumin, respectively, were found in the effluates of the subarachnoid space. CONCLUSION: The present study demonstrates that resolution of vasogenic brain oedema into the cerebral ventricular system and the subarachnoid space following its entry into cerebral white matter can be quantitatively analysed using fluorescence markers, which serve as oedema fluid indicators. The results indicate that the oedema fluid is cleared not only into the ventricular system but also via the subarachnoid space.

Animals↗
PubMed2005

[Bayesian regularized BP neural network model for quantitative relationship between the electrochemical reduction potential and molecular structures of chlorinated aromatic compounds].

Bayesian regularized BP neural network (BRBPNN) technique was applied in QSPR model in environmental field. The BRBPNN model for quantitative relationship between the electrochemical reduction potential (ERP) and chemical structures of 87 chlorinated aromatic compounds was established. The structure descriptor pool is consisted of Cl number (Cl), molecular weight (MW) and 6 quantum chemistry parameters which are calculated by MOPAC2000 built in ChemOffice2004, including energy of the highest occupied molecular orbital (E(HOMO)), energy of the lowest occupied molecular orbital (E(LUMO)), heat of formation(HF), dipole(DIP), electronic energy(EE), core-core repulsion(CCR). The achieved optimal network structure was 6-20-1, which possessed stronger fitting and prediction capacity than that of the stepwise linear regression and with the correlation coefficients square and the mean square error for the training set and the test set as 0.999 and 0.000105, 0.965 and 0.00159 respectively. The sum of square weights between each input neuron and the hidden layer of BRBPNN(6-20-1) indicate the effect of descriptor on the electric potential declining in the order of ELUMO > EHOMO > HF> CCR > EE > DIP. The scatter diagrams show that the EE descriptors had positive effect on ERP, and ELUMO, HF, DIP had negative effects, and EHOMO and CCR showed ambiguous effects. Results show that Bayesian regularized BP neural network is of automated regularization parameter selection capability and thus may ensure the excellent generation ability and robustness. This study threw more light on the applicability of electrochemical treatment for the chlorinated aromatic compounds and the analysis on electrochemical reduction mechanism.

Bayes Theorem↗
PubMed1998

Molecular modelling and quantitative structure-activity relationship studies on the interaction of omeprazole with cytochrome P450 isozymes.

Molecular modelling of the anti-ulcerative agent, omeprazole, with the putative active sites of cytochromes P4503A4 and P4502C19, enzymes which are the major catalysts of omeprazole metabolism in man, are reported. Interactive docking of omeprazole in both CYP3A4 and CYP2C19 gives rise to binding orientations which are consistent with both the known sites of metabolism reported for these isoforms and with evidence from site-directed mutagenesis experiments on CYP2C19, a P450 associated with genetic polymorphism in human drug metabolism. The potential P450 enzymic interactions, inhibition and induction of omeprazole are discussed in the light of molecular modelling and QSAR (quantitative structure-activity relationship) studies on related compounds.

Anti-Ulcer Agents↗
PubMed2002

Combination of linear solvent strength model and quantitative structure-retention relationships as a comprehensive procedure of approximate prediction of retention in gradient liquid chromatography.

Quantitative structure-retention relationships (QSRR) combined with the linear solvent strength (LSS) model are demonstrated to provide approximate predictions of gradient reversed-phase high-performance liquid chromatography (HPLC) retention time for any structurally defined analyte on a once characterized column. The approach requires at first the determination of retention times for a predesigned model series of 15 analytes in two gradient runs. Then by employing the LSS theory a given HPLC system of interest is quantitatively characterized. Structure of the model analytes is next described quantitatively by means of three structural descriptors from standard molecular modeling: total dipole moment, electron excess charge of the most negatively charged atom and water-accessible molecular surface area. With those data the general QSRR equations are derived which describe gradient retention times of the model analytes in the specific column/eluent system. Having now the structural descriptors for any analyte to be chromatographed in such a characterized HPLC system, one employs respective general QSRR equations to calculate its expected gradient retention time at given gradient conditions by means of appropriate LSS equations. Additionally, the chromatographic parameters log kw and S can be calculated and retention coefficients corresponding to chosen isocratic conditions evaluated. The approach provides retention predictions which can be treated as a first approximation of actual data. Predictions are not yet precise enough for practical separation purposes but can be of use in rational modification of analytical conditions aimed at optimization of separations.

Chromatography, High Pressure Liquid↗
PubMed1998

Apoptosis- and necrosis-inducing potential of cladribine, cytarabine, cisplatin, and 5-fluorouracil in vitro: a quantitative pharmacodynamic model.

PURPOSE: The purpose of this study was to characterize the concentration-dependent induction of apoptosis by anticancer drugs in vitro. METHODS: The apoptosis- and necrosis-inducing potential of the anticancer drugs cladribine (CDA), cytarabine (ARA-C), cisplatin (CDDP), and 5-fluorouracil (5FU) were studied in vitro in the human leukemia cell lines HSB2 and Jurkat using a flow-cytometry assay that permits the simultaneous quantification of vital, apoptotic, and necrotic cells by double-staining with fluorescein isothiocyanate (FITC)-labeled Annexin-V and propidium iodide. The results were fit to different multicompartmental models and the sensitivity of the cell lines to apoptosis and necrosis was estimated. RESULTS: A time- and dose-dependent decrease in vital cells as well as an increase in apoptotic and necrotic cells was observed in HSB2 cells upon continuous incubation with 10(-5)-10(-7) MCDA, 10(-5)-10(-8) MARA-C, 5 x10(-5)-5 x 10(-6) M CDDP, and 10(-4)-10(-5) M 5FU, whereas no effect was observed relative to controls upon incubation with 10(-8)-10(-9) M CDA, 10(-9) M ARA-C, 10(-7)-10(-8) M CDDP, or 10(-6)-10(-9) M 5FU. In Jurkat cells, apoptosis- and necrosis-inducing effects were observed at 10(-4)-5 x 10(-6) M CDA, 10(-5)-10(-7) M ARA-C, 5 x 10(-5)-5 x 10(-6) M CDDP, and 10(-4)-10(-5) M 5FU. In all experiments, apoptotic cells reached a peak after 6-48 h of drug exposure. These data were best fit by a model in which vital cells became irreversibly apoptotic by a direct pathway and necrotic by an irreversible indirect pathway following the apoptotic state (mean R = 0.9876; range 0.9510-0.9993; mean modified Akaike's information criterion 3.88; range 1.86-5.82) and the rate constants of either pathway (Kva and Kan, respectively) were assessed. The sensitivity of both cell lines to apoptosis and necrosis (expressed as EC50 and Emax values) induced by the anticancer drugs could be calculated from the sigmoidal concentration-effect curves. Furthermore, it was shown that drug treatment (10(-6) M CDA or 10(-6) M ARA-C) potentiated the apoptosis-inducing effects of irradiation (6 Gy) but not its necrosis-inducing potential. CONCLUSION: This study demonstrates that CDA, ARA-C, CDDP, and 5FU possess concentration-dependent apoptosis-inducing potential in the cell lines studied. The cytotoxic mechanism and cell-killing potential of these drugs is different, which is reflected by different EC50 and Emax values. Furthermore, a method for pharmacodynamic modeling is introduced that permits a quantitative approach for the assessment of the sensitivity of tumor cells to anticancer drugs and combined treatments.

Antineoplastic Agents↗
PubMed1993

Mutation models and quantitative genetic variation.

Analyses of evolution and maintenance of quantitative genetic variation depend on the mutation models assumed. Currently two polygenic mutation models have been used in theoretical analyses. One is the random walk mutation model and the other is the house-of-cards mutation model. Although in the short term the two models give similar results for the evolution of neutral genetic variation within and between populations, the predictions of the changes of the variation are qualitatively different in the long term. In this paper a more general mutation model, called the regression mutation model, is proposed to bridge the gap of the two models. The model regards the regression coefficient, gamma, of the effect of an allele after mutation on the effect of the allele before mutation as a parameter. When gamma = 1 or 0, the model becomes the random walk model or the house-of-cards model, respectively. The additive genetic variances within and between populations are formulated for this mutation model, and some insights are gained by looking at the changes of the genetic variances as gamma changes. The effects of gamma on the statistical test of selection for quantitative characters during macroevolution are also discussed. The results suggest that the random walk mutation model should not be interpreted as a null hypothesis of neutrality for testing against alternative hypotheses of selection during macroevolution because it can potentially allocate too much variation for the change of population means under neutrality.

Biological Evolution↗
PubMed2006

Model storage, exchange and integration.

The field of Computational Systems Neurobiology is maturing quickly. If one wants it to fulfil its central role in the new Integrative Neurobiology, the reuse of quantitative models needs to be facilitated. The community has to develop standards and guidelines in order to maximise the diffusion of its scientific production, but also to render it more trustworthy. In the recent years, various projects tackled the problems of the syntax and semantics of quantitative models. More recently the international initiative BioModels.net launched three projects: (1) MIRIAM is a standard to curate and annotate models, in order to facilitate their reuse. (2) The Systems Biology Ontology is a set of controlled vocabularies aimed to be used in conjunction with models, in order to characterise their components. (3) BioModels Database is a resource that allows biologists to store, search and retrieve published mathematical models of biological interests. We expect that those resources, together with the use of formal languages such as SBML, will support the fruitful exchange and reuse of quantitative models.

Animals↗
PubMed1998

Canalization, genetic assimilation and preadaptation. A quantitative genetic model.

We propose a mathematical model to analyze the evolution of canalization for a trait under stabilizing selection, where each individual in the population is randomly exposed to different environmental conditions, independently of its genotype. Without canalization, our trait (primary phenotype) is affected by both genetic variation and environmental perturbations (morphogenic environment). Selection of the trait depends on individually varying environmental conditions (selecting environment). Assuming no plasticity initially, morphogenic effects are not correlated with the direction of selection in individual environments. Under quite plausible assumptions we show that natural selection favors a system of canalization that tends to repress deviations from the phenotype that is optimal in the most common selecting environment. However, many experimental results, dating back to Waddington and others, indicate that natural canalization systems may fail under extreme environments. While this can be explained as an impossibility of the system to cope with extreme morphogenic pressure, we show that a canalization system that tends to be inactivated in extreme environments is even more advantageous than rigid canalization. Moreover, once this adaptive canalization is established, the resulting evolution of primary phenotype enables substantial preadaptation to permanent environmental changes resembling extreme niches of the previous environment.

Adaptation, Physiological↗
PubMed2004

Refining the Amsterdam Criteria and Bethesda Guidelines: testing algorithms for the prediction of mismatch repair mutation status in the familial cancer clinic.

PURPOSE: Hereditary nonpolyposis colon cancer (HNPCC) is a Mendelian dominant syndrome of bowel, endometrial, and other cancers and results from germline mutations in mismatch repair (MMR) genes. HNPCC is now best diagnosed on molecular grounds using MMR mutation screening, aided by microsatellite instability (MSI) and immunohistochemistry in tumors. Selection of families for molecular investigation of HNPCC is usually based on suboptimal methods (Amsterdam Criteria or Bethesda Guidelines), but these can be improved using additional clinical data (mean ages of affected persons and presence of endometrial cancer) in a quantitative model. METHODS: We have verified the performance of the Wijnen model and have shown that it remains valid when HNPCC is diagnosed using mutation screening, MSI, and immunohistochemistry. We have also set up and verified our own models (Amsterdam-plus and Alternative), which perform at least as well as the Wijnen model. RESULTS: The Amsterdam-plus model improves on the Amsterdam Criteria by using five extra variables (numbers of colorectal and endometrial cancers in the family, number of patients with five or more adenomas, number with more than one primary cancer of the colorectum or endometrium, and mean age of presentation) and performs better than the Wijnen model. The Alternative model avoids the need to evaluate the Amsterdam Criteria and performs nearly as well as the other models. CONCLUSION: We believe that a quantitative model, such as the Amsterdam-plus model, should be the first choice for selecting families or patients for evaluation of HNPCC using molecular tests. We present an algorithm for this process.

Adult↗
PubMed1992

A model for quantitative follow-up studies of cervical lesions.

A model for follow-up studies of cervical lesions is described in which the specimen were taken in a noninvasive way using Cytobrushes and in which automatic measurement of the abnormal nuclei in the sampled epithelial fragments was possible because 2-microns thin Feulgen-stained plastic sections were prepared. The planimetric parameters AREA, PERIMETER, FORM PE, and FORM ELL, and the densitometric parameters optical density (OD) and integrated optical density (IOD) were assessed. The mean total volume and the mean total DNA were calculated using stereological methods. The moderate dysplasias differed from the carcinoma in situs for all the densitometric parameters except for OD, and from the invasive carcinomas for IOD and 5cER. In the moderate-dysplasia group, there were three types of DNA histograms: a highly abnormal type resembling the histograms of the carcinoma group, a normal type, and an intermediate type. Changes in DNA histograms can be established during follow-up studies of dysplasias without having disturbed the lesion due to the efficient and elegant noninvasive sampling method that was not used in earlier quantitative studies.

Carcinoma in Situ↗
PubMed2001

Toward a biologically based dose-response model for developmental toxicity of 5-fluorouracil in the rat: acquisition of experimental data.

Biologically based dose-response (BBDR) models represent an emerging approach to improving the current practice of human health-risk assessment. The concept of BBDR modeling is to incorporate mechanistic information about a chemical that is relevant to the expression of its toxicity into descriptive mathematical terms, thereby providing a quantitative model that will enhance the ability for low-dose and cross-species extrapolation. Construction of a BBDR model for developmental toxicity is particularly complicated by the multitude of possible mechanisms. Thus, a few model assumptions were made. The current study illustrates the processes involved in selecting the relevant information for BBDR modeling, using an established developmental toxicant, 5-fluorouracil (5-FU), as a prototypic example. The primary BBDR model for 5-FU is based on inhibition of thymidylate synthetase (TS) and resultant changes in nucleotide pools, DNA synthesis, cell-cycle progression, and somatic growth. A single subcutaneous injection of 5-FU at doses ranging from 1 to 40 mg/kg was given to pregnant Sprague-Dawley rats at gestational day 14; controls received saline. 5-FU was absorbed rapidly into the maternal circulation, and AUC estimates were linear with administered doses. We found metabolites of 5-FU directly incorporated into embryonic nucleic acids, although the levels of incorporation were low and lacked correlation with administered doses. On the other hand, 5-FU produced dose-dependent inhibition of thymidylate synthetase in the whole embryo, and recovery from enzyme inhibition was also related to the administered dose. As a consequence of TS inhibition, embryonic dTTP and dGTP were markedly reduced, while dCTP was profoundly elevated, perhaps due to feedback regulation of intracellular nucleotide pools. The total contents of embryonic macromolecules (DNA and protein) were also reduced, most notably at the high doses. Correspondingly, dose-related reductions of fetal weight were seen as early as GD 15, and these deficits persisted for the remainder of gestation. These detailed dose-response parameters involved in the expression of 5-FU developmental toxicity were incorporated into mathematical terms for BBDR modeling. Such quantitative models should be instrumental to the improvement of high-to-low dose and cross-species extrapolation in health-risk assessment.

Abnormalities, Drug-Induced↗
PubMed1992

Extended pedigree patterned covariance matrix mixed models for quantitative phenotype analysis.

Overt computational constraints in the formation of mixed models for the analysis of large extended-pedigree quantitative trait data which allow one to reliably characterize and partition sources of variation resulting from a variety sources have proven difficult to overcome. The present paper suggests that by combining a restricted patterned covariance matrix approach to modeling and partitioning the variation arising from polygenic and environmental forces with an Elston-Stewart like algorithmic approach to modeling variation resulting from a single genetic locus with large phenotypic effects one can produce a model that is at once intuitively appealing, efficient computationally, and reliable numerically. Extensions and variations of this approach are also discussed, as are some simulation and timing studies carried out in an effort to validate the accuracy and computational efficiency of the proposed methodology.

Humans↗
PubMed2003

Microarray as a model for quantitative visualization chemistry.

For visualization of proteins or nucleic acids, direct and indirect in situ fluorescence and absorption methods (immunohistochemistry and cytochemistry) have existed for many years. The authors describe a new experimental approach using microarray as a model to quantitatively compare both visualization methods. The spots obtained with the microarray robot had a progressive twofold decrease in concentrations and are used as objects with known amounts of DNA. Subsequent hybridization resulted in a direct fluorescence (DF) label or in hapten for indirect fluorescence (IF) and absorption. The results show that the image of the object in the IF method is larger than that in the DF method because of an edge effect, with stronger staining at the circumference. This leads to a higher plateau level and an 8- to 10-fold reduction in the detection threshold for IF compared with DF. These features are especially useful for one-color DNA-related microarray analysis, such as single nucleotide polymorphism, loss of heterozygosity, and mutation analysis, provided that the spots are not designed directly adjacent to each other, so that the edge effect is taken into account. The slope of the linear range for the IF method is much steeper than for the DF method, pointing to a narrow dynamic range in immunohistochemistry. It is noteworthy that the detection limit for absorption images after indirect immunoenzyme visualization is lower than for the DF images. The indirect immunohistochemistry semiquantitative absorption signal was at least similar compared with the DF fluorescence. In conclusion, an explanation for the difficulties experienced in quantitative immunohistochemistry is provided, and the data emphasize that in general, for daily pathology, semiquantitative patterns should suffice. Indirect labeling of DNA has useful characteristics for application in microarray analyses because of the large signal enhancement.

Carbocyanines↗
PubMed2004

Quantitative genetic models of sexual selection.

Modeling of R.A. Fisher's ideas about the evolution of male ornamentation using quantitative genetics began in the 1980s. Following an initial period of enthusiasm, interest in these models began to wane when theoretical studies seemed to show that the rapid evolution of ornaments would not occur if there were costs associated with female mate choice. Recent theoretical work has shown, however, that runaway evolution and other kinds of extensive diversification of ornaments and preferences can occur, even when female choice is costly. These new models highlight crucial parameters that profoundly influence evolutionary trajectories, but these parameters have been neglected in empirical studies. Here, we review quantitative genetic models of sexual selection with the aim of fostering communication and synergism between theoretical and empirical enterprises. We also point out several areas in which additional empirical work could distinguish between alternative models of evolution.

Journal Article↗
PubMed2004

[Biomass structure and quantitative relationship models of modules in clonal population of Puccinillia chinampoensis in Songnen plain].

In this paper, quantitative analysis was conducted at module level on the biomass structure of modules in clonal population of Puccinillia chinampoensis, the relationship between modules' biomass and turf sizes, and the relationship between one module's biomass and another one's. Based on these, the corresponding models of these relationships were established. The results showed that the regularities on the biomass of all functional modules and their ratio were the same at earing stage and at vegetative stage after fruiting. There existed linear correlation between functional modules and turf sizes at earing stage, and exponential correlation at vegetative stage after fruiting. Among all quantitative relationship models, only the one between photosynthesis modules and supporting modules was linear function at earing stage and exponential correlation at vegetative stage after fruiting. The relationship models between any other two functional models were all exponential correlation at two stages.

Biomass↗