General relationship between transit compartments and lifespan models

Koch, Gilbert; Schropp, Johannes

doi:10.1007/s10928-012-9254-4

Cited by 7 publications

(6 citation statements)

References 14 publications

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“…The parameters T RBC , M CFU and M NOR were fixed to 120, 4 and 4 days, respectively RSE relative standard error DDE add-on extensions benefit from increasing their TOL/ ATOL by 1-2 unit (U) to obtain the desired precision in numerical integration of DDEs. The estimate of the lifespan of the apoptotic cells T D was 3.39 days which was consistent with previous publications [1,20]. The results in Table 5 also showed that the parameters were estimated with a very good precision (RSE% \ 30%).…”

Section: Lifespan Based Tumor Growth Inhibition Modelsupporting

confidence: 89%

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Delay differential equations based models in NONMEM

Yan

Bauer

Koch

et al. 2021

J Pharmacokinet Pharmacodyn

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Delay differential equations (DDEs) are commonly used in pharmacometric models to describe delays present in pharmacokinetic and pharmacodynamic data analysis. Several DDE solvers have been implemented in NONMEM 7.5 for the first time. Two of them are based on algorithms already applied elsewhere, while others are extensions of existing ordinary differential equations (ODEs) solvers. The purpose of this tutorial is to introduce basic concepts underlying DDE based models and to show how they can be developed using NONMEM. The examples include previously published DDE models such as logistic growth, tumor growth inhibition, indirect response with precursor pool, rheumatoid arthritis, and erythropoiesis-stimulating agents. We evaluated the accuracy of NONMEM DDE solvers, their ability to handle stiff problems, and their performance in parameter estimation using both first-order conditional estimation (FOCE) and the expectation-maximization (EM) method. NONMEM control streams and excerpts from datasets are provided for all discussed examples. All DDE solvers provide accurate and precise solutions with the number of significant digits controlled by the error tolerance parameters. For estimation of population parameters, the EM method is more stable than FOCE regardless of the DDE solver.

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Section: Lifespan Based Tumor Growth Inhibition Modelsupporting

confidence: 89%

“…Data from both the control and drug treatment groups were used. The lifespan based TGI model has been introduced previously [1,20]. It assumes that the tumor is separated into two populations of cells: a proliferating population P(t) and an apoptotic population A(t).…”

Section: Lifespan Based Tumor Growth Inhibition Modelmentioning

confidence: 99%

Delay differential equations based models in NONMEM

Yan

Bauer

Koch

et al. 2021

J Pharmacokinet Pharmacodyn

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“…Many PKPD models use transit compartments to incorporate delays [9] – [11] , [39] . We used the lifespan model to describe the process of cell division, and since transit compartments are approximations of lifespan models, and are equivalent under certain conditions [40] , [41] , it was natural for us to describe the dying tumor cells using a lifespan model as well.…”

Section: Discussionmentioning

confidence: 99%

Lifespan Based Pharmacokinetic-Pharmacodynamic Model of Tumor Growth Inhibition by Anticancer Therapeutics

Gibbons

Schroeder

et al. 2014

PLoS ONE

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Accurate prediction of tumor growth is critical in modeling the effects of anti-tumor agents. Popular models of tumor growth inhibition (TGI) generally offer empirical description of tumor growth. We propose a lifespan-based tumor growth inhibition (LS TGI) model that describes tumor growth in a xenograft mouse model, on the basis of cellular lifespan T. At the end of the lifespan, cells divide, and to account for tumor burden on growth, we introduce a cell division efficiency function that is negatively affected by tumor size. The LS TGI model capability to describe dynamic growth characteristics is similar to many empirical TGI models. Our model describes anti-cancer drug effect as a dose-dependent shift of proliferating tumor cells into a non-proliferating population that die after an altered lifespan TA. Sensitivity analysis indicated that all model parameters are identifiable. The model was validated through case studies of xenograft mouse tumor growth. Data from paclitaxel mediated tumor inhibition was well described by the LS TGI model, and model parameters were estimated with high precision. A study involving a protein casein kinase 2 inhibitor, AZ968, contained tumor growth data that only exhibited linear growth kinetics. The LS TGI model accurately described the linear growth data and estimated the potency of AZ968 that was very similar to the estimate from an established TGI model. In the case study of AZD1208, a pan-Pim inhibitor, the doubling time was not estimable from the control data. By fixing the parameter to the reported in vitro value of the tumor cell doubling time, the model was still able to fit the data well and estimated the remaining parameters with high precision. We have developed a mechanistic model that describes tumor growth based on cell division and has the flexibility to describe tumor data with diverse growth kinetics.

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“…forcing input (Beq), so that . The exact solution may be written using the matrix exponential [ 9 , 27 ], or by using Laplace Transforms (Appendix 1.4 ). For the transit compartments, we find that where .…”

Section: Analytical Solutions For Equi-dosing Regimensmentioning

confidence: 99%

“…Transit compartment models have been proposed to capture delay effects in PK time courses, through a semi-mechanistic approach of increasing the number of compartments through which the drug is transferred en route to the central compartaament (blood) [ 26 , 27 , 32 , 33 , 44 , 46 , 47 ]. The development of “full” or accurate mechanistic physiologically-based PK models requires much experimental data and knowledge which may be unavailable.…”

Section: Introductionmentioning

confidence: 99%

Exact solutions and equi-dosing regimen regions for multi-dose pharmacokinetics models with transit compartments

Hof

Bridge

2020

J Pharmacokinet Pharmacodyn

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Compartmental models which yield linear ordinary differential equations (ODEs) provide common tools for pharmacokinetics (PK) analysis, with exact solutions for drug levels or concentrations readily obtainable for low-dimensional compartment models. Exact solutions enable valuable insights and further analysis of these systems. Transit compartment models are a popular semi-mechanistic approach for generalising simple PK models to allow for delayed kinetics, but computing exact solutions for multi-dosing inputs to transit compartment systems leading to different final compartments is nontrivial. Here, we find exact solutions for drug levels as functions of time throughout a linear transit compartment cascade followed by an absorption compartment and a central blood compartment, for the general case of n transit compartments and M equi-bolus doses to the first compartment. We further show the utility of exact solutions to PK ODE models in finding constraints on equi-dosing regimen parameters imposed by a prescribed therapeutic range. This leads to the construction of equi-dosing regimen regions (EDRRs), providing new, novel visualisations which summarise the safe and effective dosing parameter space. EDRRs are computed for classical and transit compartment models with two- and three-dimensional parameter spaces, and are proposed as useful graphical tools for informing drug dosing regimen design.

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General relationship between transit compartments and lifespan models

Cited by 7 publications

References 14 publications

Delay differential equations based models in NONMEM

Delay differential equations based models in NONMEM

Lifespan Based Pharmacokinetic-Pharmacodynamic Model of Tumor Growth Inhibition by Anticancer Therapeutics

Exact solutions and equi-dosing regimen regions for multi-dose pharmacokinetics models with transit compartments

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