A multi-response model for rheumatoid arthritis based on delay differential equations in collagen induced arthritic mice treated with an anti-GM-CSF antibody
G. Koch(1), T. Wagner(2), C. Plater-Zyberk(3), G. Lahu(2), J. Schropp(1)
(1) Department of Mathematics and Statistics, University of Konstanz, Germany; (2) Department of PKPD and Biomarker Sciences, Nycomed GmbH, Germany; (3) Non-Clinical Development, Micromet AG, Munich, Germany;
Objectives: 22E9 is a monoclonal antibody that binds to the pro-inflammatory cytokine granulocyte macrophage colony-stimulating factor (GM-CSF), thereby neutralizing its biological activity. This cytokine is thought to play a key pathogenic role in rheumatoid arthritis. Our goal was to describe the time course of the unperturbed arthritis development and the effect of the anti-GM-CSF antibody 22E9 in the collagen induced arthritis (CIA) mouse model . The pharmacodynamic readouts consist of the total arthritic score (TAS), an overall estimation of disease severity, and the ankylosis score (AKS), a measure for bone destruction.
Methods: Three doses (0.1, 1 and 10 mg/kg) of 22E9 were administered intravenously (i.v.) once a week starting from the day of first signs of arthritis in the mice. PK samples and PD readouts were collected throughout the observation period of 24 days. The PD readouts, TAS (scored by integer values ranging from 0 to 16) and AKS (integer values from 0 to 8) where assessed every second day. Start of visible ankylosis was delayed by about 10 days in comparison to the TAS. The PK as well as PD data of the different dosing groups were modelled simultaneously using MATLAB and ADAPT.
Results: We used a semi-mechanistic PKPD model consisting of three meaningful compartments: a hypothetical cytokine compartment at which the drug operates, an inflammation I(t) compartment, and a bone destruction D(t) compartment. Primary assumption in the model was that the cytokine drives the inflammation and causes ankylosis, delayed in time. The sum I(t)+D(t) corresponds to the measured TAS and D(t) stands for AKS. To account for the large time shift observed in AKS, we used delay differential equations. The nonlinear dose-response of the drug is incorporated into the model by an effect term of exponential type. The concentration data of 22E9 were fitted very well by a 2-cmp i.v. PK model. The final PKPD model describes both PD readouts simultaneously over all available doses. This model was equivalently rewritten into ordinary differential equations (ODE) which grants the use of standard solvers.
Conclusions: We developed a PKPD model, based on delay differential equations, describing the development of arthritis in the CIA mouse model and its attenuation by a monoclonal antibody. Our mechanistic model fitted adequately the data. Further development into a population PKPD model is planned for the future.
 RO Williams. Collagen-induced arthritis as a model for rheumatoid arthritis. Methods Mol Med 2004; 98:207-16.