类风湿关节炎的数学建模

中文摘要 AI 辅助

我们开发了一个数学模型来描述关节炎发展和消退过程中的炎症动力学，重点关注关节组织内三种关键免疫细胞群体之间的相互作用，即中性粒细胞（N）、衬里下层滑膜组织驻留巨噬细胞（SL-TRM，T）以及被招募到发炎关节并分化为单核细胞衍生巨噬细胞（MoMac，M）的循环单核细胞。炎症信号（S）代表对外部致关节炎刺激的反应，驱动中性粒细胞和MoMac的招募和激活，而SL-TRM发挥调节和保护作用。我们提出了一个进入关节的急性炎症反应的最小常微分方程模型，该模型将炎症信号S与三个细胞群体（N、T、M）耦合，并纳入招募、刺激、非线性自我限制和相互调节。我们表明平衡结构取决于三个无量纲参数A、B、C，并推导出一个表征非平凡稳态的三次方程。我们对平衡点及其稳定性进行了分析研究，并确定了在A=1处的一个分岔，将无病状态与持续炎症状态分开。数值模拟说明了各种情景下典型的瞬态动力学，并展示了模型捕捉从急性炎症向慢性炎症转变以及在某些条件下炎症消退的能力。总之，我们的模型提供了一个框架来探索急性与持续性关节炎症背后的机制，并为从实验数据估计参数以及未来扩展到评估治疗策略提供了基础。

英文摘要

We developed a mathematical model to describe the inflammatory dynamics during arthritis development and resolution, focusing on the interaction between three key immune cell populations within the joint tissue, namely neutrophils (N), sublining synovial tissue-resident macrophages (SL-TRM, T), and circulating monocytes that are recruited into the inflamed joint and differentiate into monocyte-derived macrophages (MoMac, M). An inflammatory signal (S), representing the response to an external arthritogenic stimulus, drives the recruitment and activation of neutrophils and MoMac, while SL-TRM exert a regulatory and protective role. We propose a minimal ordinary differential equation model of acute inflammatory response into a joint that couples an inflammatory signal S to the three cell populations (N, T, M) and incorporates recruitment, stimulation, nonlinear self-limitation and mutual regulation. We show that the equilibrium structure depends on three adimensional parameters A, B, C and derive a cubic equation characterizing nontrivial steady states. We perform an analytical study of equilibria and their stability, and identify a bifurcation at A = 1 separating a disease-free regime from a sustained inflammatory state. Numerical simulations illustrate typical transient dynamics under various scenarios and show the ability of the model to capture the transition from acute to chronic inflammation, as well as the resolution of inflammation under certain conditions. In conclusion, our model provides a framework to explore mechanisms underlying acute versus sustained joint inflammation and offers a basis for parameter estimation from experimental data, as well as future extensions toward evaluation of therapeutic strategies.

发表机构

• Université de Montpellier（蒙彼利埃大学）
• INSERM（法国国家健康与医学研究院）
• Montpellier University Hospital Lapeyronie（拉佩龙尼蒙彼利埃大学医院）

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