Department of Mathematics and Statistics, University of Konstanz, P.O. Box 195, 78457, Konstanz, Germany.
J Pharmacokinet Pharmacodyn. 2012 Feb;39(1):55-65. doi: 10.1007/s10928-011-9230-4. Epub 2011 Dec 23.
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.
胶原诱导性关节炎（CIA）在小鼠中是类风湿关节炎的实验模型，类风湿关节炎是一种人类慢性炎症性破坏性疾病。通过抗体中和细胞因子粒细胞-巨噬细胞集落刺激因子（GM-CSF）在小鼠疾病中的治疗效果进行了检查，目的是建立药代动力学/药效学（PKPD）模型。在 CIA 小鼠中，疾病的发展通过总关节炎评分（TAS）和关节强直评分（AKS）来衡量。我们提出了一个多反应 PKPD 模型，描述了未受干扰和受干扰的 TAS 和 AKS 的时间过程。抗体通过与 GM-CSF 结合直接作用于 GM-CSF。因此，GM-CSF 细胞因子的一个隔室是数学模型的一个基本组成部分。该隔室在 PKPD 模型中驱动疾病的发展。CIA 模型中关节炎发展的不同已知特性包含在 PKPD 模型中。首先，由 GM-CSF 驱动的炎症在疾病开始时占主导地位，一段时间后会减少。其次，在 TAS 中会出现一种延迟的破坏性（强直）部分。为了对这两个特性进行建模，我们使用了延迟微分方程。PKPD 模型应用于不同的实验，剂量范围为 0.1 至 100mg/kg。药物的影响通过非线性方法进行建模。最终的数学模型由三个微分方程组成，代表 GM-CSF、炎症和破坏的隔室。我们的数学模型通过同时拟合很好地描述了所有可用的给药方案。我们还提出了一个等效且易于转化为常微分方程的公式，允许使用标准的 PKPD 软件。
