Stochastic modeling in toxicokinetics. Application to the in vivo micronucleus assay

Hyrien, Ollivier; Kles, V.; Concordet, Didier; Bonneu, Michel; Laurentie, Michel; Sandérs, Pascal

doi:10.1016/s0025-5564(00)00052-3

Cited by 2 publications

(7 citation statements)

References 23 publications

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“…administration of a single dose of 6-MP to mice. However, the model (Hyrien et al, 2001) is general enough to be applied to any other compound, whatever its mechanisms of action and pharmacokinetics. For other compounds, slight modifications of the equations would be required to adapt the model to the new set of biological hypotheses (metabolism, duration of action, cell toxicity, etc.…”

Section: Discussionmentioning

confidence: 99%

“…The stochastic model used in this paper to describe the kinetics rate of micronucleated PCEs was a slight extension of a general model presented in detail in Hyrien et al (2001). It is based on three distinct models that, respectively, described the population of cells targeted by the administered compound, i.e.…”

Section: Discussionmentioning

confidence: 99%

“…The above-mentioned hypotheses were included in the model that was developed and detailed in Hyrien et al (2001). A description of the specific model used to analyse the rate of micronucleated PCEs induced by 6-MP is reported in the Appendix.…”

Section: The Stochastic Modelmentioning

confidence: 99%

“…It was assumed in this model that dividing cells gave birth to two new offspring after a random time supposed to be drawn from a gamma distribution with two parameters, and that maturating cells expelled their main nucleus after an exponentially distributed time. In Hyrien et al (2001), the time to division of any dividing cell was assumed to be distributed exponentially. In the present article, we used a gamma distribution instead because it provided a more realistic and more flexible description of the variability of the mitotic cycle duration.…”

Section: Mathematical Description Of the Kinetics Of The Population Omentioning

confidence: 99%

“…The second model was developed from a mechanistic approach and uses stochastic processes. It was a slight extension of a general model developed by Hyrien et al (2001). Both models were tested for their pertinence through computer simulations.…”

Section: Introductionmentioning

confidence: 99%

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Application of pharmacokinetic/pharmacodynamic and stochastic modelling to 6‐mercaptopurine micronucleus induction in mouse bone marrow erythrocytes

Kles

Hyrien

Poul

et al. 2003

J of Applied Toxicology

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This study investigates the kinetics of bone marrow micronucleated polychromatic erythrocytes and some mechanistic aspects of micronuclei induction using mathematical models. Female mice were administered a single intraperitoneal injection of the purine antagonist 6-mercaptopurine at 50 mg kg(-1). The time course evolution of the drug concentrations in the plasma and the micronucleated polychromatic erythrocyte kinetic rate in bone marrow were observed. Two mathematical models were developed for this study. The first model was built from a simultaneous pharmacokinetic/pharmacodynamic approach, but was invalidated after comparing its predictions to experimental data. The second model was a stochastic model based on some biological hypotheses involved in micronuclei induction. This model predicted a wavy kinetic rate of micronucleated polychromatic erythrocytes that was confirmed by a second data set obtained from a specifically built experimental design. The biological hypotheses were then discussed. It turned out from this work that mathematical modelling could be used as a tool to explore the cellular mechanisms of toxicity of the compound: for instance, the assumptions that 6-mercaptopurine induced micronuclei mainly in cells entering the S phase, and not only during the last cell cycle but during one of the earlier cycles preceding the extrusion of the main nucleus, were confirmed. Moreover, the use of the stochastic model would help to schedule more accurately the bone marrow or blood harvesting times in the in vivo rodent micronucleus test.

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Section: Discussionmentioning

confidence: 99%

Section: Discussionmentioning

confidence: 99%

Section: The Stochastic Modelmentioning

confidence: 99%

Section: Mathematical Description Of the Kinetics Of The Population Omentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Application of pharmacokinetic/pharmacodynamic and stochastic modelling to 6‐mercaptopurine micronucleus induction in mouse bone marrow erythrocytes

Kles

Hyrien

Poul

et al. 2003

J of Applied Toxicology

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A Stochastic Model to Analyze Clonal Data on Multi‐Type Cell Populations

et al. 2005

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This article presents a stochastic model designed to analyze experimental data on the development of cell clones composed of two (or more) distinct types of cells. The proposed model is an extension of the traditional multi-type Bellman-Harris branching stochastic process allowing for nonidentical time-to-transformation distributions defined for different cell types. A simulated pseudo likelihood method has been developed for the parametric statistical inference from experimental data on cell clones under the proposed model. The method uses simulation-based approximations of the means and the variance-covariance matrices of cell counts. The proposed estimator for the vector of unknown parameters is strongly consistent and asymptotically normal under mild regularity conditions, while its variance-covariance matrix is estimated by the parametric bootstrap. A Monte Carlo Wald test is proposed for the test of hypotheses. Finite sample properties of the estimator have been studied by computer simulations. The model and associated methods of parametric inference have been applied to the analysis of proliferation and differentiation of cultured O-2A progenitor cells that play a key role in the development of the central nervous system. It follows from this analysis that the time to division of the progenitor cell and the time to its differentiation (into an oligodendrocyte) are not identically distributed. This biological finding suggests that a molecular event determining the type of cell transformation is more likely to occur at the start rather than at the end of the mitotic cycle.

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Stochastic modeling in toxicokinetics. Application to the in vivo micronucleus assay

Cited by 2 publications

References 23 publications

Application of pharmacokinetic/pharmacodynamic and stochastic modelling to 6‐mercaptopurine micronucleus induction in mouse bone marrow erythrocytes

Application of pharmacokinetic/pharmacodynamic and stochastic modelling to 6‐mercaptopurine micronucleus induction in mouse bone marrow erythrocytes

A Stochastic Model to Analyze Clonal Data on Multi‐Type Cell Populations

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