Error measures.

The two main pathways for hormonal stress response are the hypothalamic-pituitary- adrenal (HPA) axis and the sympathoadrenal (SA) axis. The HPA axis produces and secretes cortisol, while the SA axis produces and secretes the fast-acting catecholamines, epinephrine and norepinephrine, which in turn stimulate cortisol. Since it is difficult to consistently measure or monitor their concentrations in plasma, mathematical modeling of the catecholamines and their connection to cortisol can provide more information about the acute stress response. Previous mathematical models have simulated the dynamics of the HPA axis, but a model of the SA axis has not been created nor one with the combined effects of the HPA and SA axes. We propose an extension of Bangsgaard and Ottesen’s differential equation-based HPA axis model that includes the SA axis [1]. We performed sensitivity analysis using Morris screening and estimated model parameters using constrained optimization with respect to time series data of cortisol and catecholamine dynamics under acute physical stress. After subject-specific parameter estimation, the proposed model that includes both the HPA and SA axes shows qualitative agreement with the collected data.激素应激反应的两条主要通路为下丘脑-垂体-肾上腺轴（hypothalamic-pituitary-adrenal, HPA）与交感肾上腺轴（sympathoadrenal, SA）。HPA轴可合成并分泌皮质醇，而SA轴则合成并分泌起效迅速的儿茶酚胺类物质——肾上腺素与去甲肾上腺素，后者可进一步刺激皮质醇的产生。由于难以在血浆中持续检测或监测这些物质的浓度，针对儿茶酚胺类及其与皮质醇的关联构建数学模型，可为急性应激反应的研究提供更多信息。既往已有数学模型对HPA轴的动态变化进行了模拟，但尚未有针对SA轴的建模研究，也未出现同时涵盖HPA与SA轴协同效应的模型。本研究基于Bangsgaard与Ottesen提出的基于微分方程的HPA轴模型，提出了纳入SA轴的扩展模型[1]。本研究采用Morris筛选法进行敏感性分析，并基于急性物理应激下皮质醇与儿茶酚胺动态变化的时间序列数据，通过约束优化方法估计模型参数。在针对个体进行参数估计后，本研究提出的同时涵盖HPA与SA轴的模型，与所收集的实验数据在定性层面具有良好一致性。