# Subject-specific modeling of response to physical stress via hypothalamic-pituitary-adrenal and sympathoadrenal axes

## TL;DR

This paper introduces a new model combining two stress response systems to better understand how the body reacts to physical stress.

## Contribution

A novel mathematical model integrating both HPA and SA axes for stress response analysis.

## Key findings

- The extended model shows qualitative agreement with cortisol and catecholamine data under stress.
- Sensitivity analysis and parameter estimation were successfully applied to the combined model.

## Abstract

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.