Model parameters and sources.

In acute stroke, dysregulated cytokine interactions drive secondary injury, yet bidirectional feedback mechanisms between pro-inflammatory mediators (TNF-α, IL-6) and the anti-inflammatory mediator IL-10 remain poorly quantified. We developed a systems biology model using nonlinear ordinary differential equations (ODEs) to resolve these dynamics, incorporating Nuclear Factor kappa-light-chain-enhancer of activated B cells (NF-κB)-mediated cross-activation, delayed IL-10 induction via a Hill function, and empirical parameterization from stroke data. Mathematical analysis revealed bistable inflammatory states via bifurcation theory, mechanistically explaining divergent inflammatory trajectory. Steady-state and stability analyses identified a critical IL-10 suppression threshold ( hr ⁻ ¹·nM ⁻ ¹) governing transitions between pro-inflammatory dominance and resolution phases. The model replicated experimentally observed cytokine dynamics, including TNF-α/IL-6 peaks (6–24 hours) and delayed IL-10 elevation (48 hours). Global sensitivity analysis highlighted IL-10 production () and TNF-α suppression () as key control parameters. Simulations predicted that IL-10 augmentation accelerates resolution, while TNF-α inhibition attenuates IL-10 induction, potentially compromising long-term recovery. By integrating dynamical systems theory with translational immunology, this model provides a mechanistic basis for optimizing immunomodulatory therapies in stroke and related inflammatory pathologies.在急性脑卒中中，细胞因子相互作用失调可诱发继发性脑损伤，但促炎介质（肿瘤坏死因子-α(TNF-α)、白细胞介素-6(IL-6)）与抗炎介质白细胞介素-10(IL-10)之间的双向反馈机制，尚未得到精准量化。本研究构建了基于非线性常微分方程（ODEs）的系统生物学模型，以解析该炎症动态过程；模型纳入了活化B细胞κ轻链增强子结合因子(NF-κB)介导的交叉激活通路、通过希尔函数（Hill function）实现的IL-10延迟诱导过程，以及基于脑卒中临床数据的经验参数化设置。数学分析借助分岔理论揭示了双稳态炎症状态，从机制层面阐释了炎症轨迹的差异性走向。稳态与稳定性分析确定了一个关键的IL-10抑制阈值（小时⁻¹·纳摩尔⁻¹），该阈值调控着促炎优势期与炎症消退期之间的状态转换。该模型复现了实验观测到的细胞因子动态变化特征，包括TNF-α/IL-6的峰值表达（6~24小时）以及IL-10的延迟升高（48小时）。全局敏感性分析显示，IL-10生成（）与TNF-α抑制（）为关键调控参数。模拟实验预测，IL-10的上调可加速炎症消退，而TNF-α的抑制会削弱IL-10的诱导过程，或对长期康复产生不利影响。本研究将动力学系统理论与转化免疫学相结合，该模型为优化脑卒中及相关炎症性疾病的免疫调节治疗方案提供了机制层面的理论依据。