Multi-response model for rheumatoid arthritis based on delay differential equations in collagen-induced arthritic mice treated with an anti-GM-CSF antibody

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2012
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Wagner, Thomas
Plater-Zyberk, Christine
Lahu, Gezim
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Journal of Pharmacokinetics and Pharmacodynamics ; 39 (2012), 1. - pp. 55-65. - ISSN 1567-567X. - eISSN 1573-8744
Abstract
Collagen-induced arthritis (CIA) in mice is an experimental model for rheumatoid arthritis, a human chronic inflammatory destructive disease. The therapeutic effect of neutralizing the cytokine granulocyte-macrophage colony-stimulating factor (GM-CSF) by an antibody was examined in the mouse disease in a view of deriving a pharmacokinetic/pharmacodynamic (PKPD) model. In CIA mice the development of disease is measured by a total arthritic score (TAS) and an ankylosis score (AKS). We present a multi-response PKPD model which describes the time course of the unperturbed and perturbed TAS and AKS. The antibody acts directly on GM-CSF by binding to it. Therefore, a compartment for the cytokine GM-CSF is an essential component of the mathematical model. This compartment drives the disease development in the PKPD model. Different known properties of arthritis development in the CIA model are included in the PKPD model. Firstly, the inflammation, driven by GM-CSF, dominates at the beginning of the disease and decreases after some time. Secondly, a destructive (ankylosis) part evolves in the TAS that is delayed in time. In order to model these two properties a delay differential equation was used. The PKPD model was applied to different experiments with doses ranging from 0.1 to 100 mg/kg. The influence of the drug was modeled by a non-linear approach. The final mathematical model consists of three differential equations representing the compartments for GM-CSF, inflammation and destruction. Our mathematical model described well all available dosing schedules by a simultaneous fit. We also present an equivalent and easy reformulation as ordinary differential equation which grants the use of standard PKPD software.
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570 Biosciences, Biology
Keywords
Rheumatoid arthritis,Granulocyte-macrophage colony-stimulating factor,Collagen-induced arthritis mice,Delay differential equations,Multi-response pharmacokinetic pharmacodynamic model
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ISO 690KOCH, Gilbert, Thomas WAGNER, Christine PLATER-ZYBERK, Gezim LAHU, Johannes SCHROPP, 2012. Multi-response model for rheumatoid arthritis based on delay differential equations in collagen-induced arthritic mice treated with an anti-GM-CSF antibody. In: Journal of Pharmacokinetics and Pharmacodynamics. 39(1), pp. 55-65. ISSN 1567-567X. eISSN 1573-8744. Available under: doi: 10.1007/s10928-011-9230-4
BibTex
@article{Koch2012-02Multi-17766,
  year={2012},
  doi={10.1007/s10928-011-9230-4},
  title={Multi-response model for rheumatoid arthritis based on delay differential equations in collagen-induced arthritic mice treated with an anti-GM-CSF antibody},
  number={1},
  volume={39},
  issn={1567-567X},
  journal={Journal of Pharmacokinetics and Pharmacodynamics},
  pages={55--65},
  author={Koch, Gilbert and Wagner, Thomas and Plater-Zyberk, Christine and Lahu, Gezim and Schropp, Johannes}
}
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