Unified Mathematical Framework for Biological Stress: The Intersection of System Dynamics and Clinical Physiology

This paper proposes a revised, quantitative definition of biological stress, shift- ing the scientific focus from the external stressor itself to the dynamic rate of sys- temic transition. Stress (S) is defined as the required rate of adaptation, expressed mathematically as the quotient of the magnitude of change (∆C) to the product of the system’s internal resilience (R) and the available time (∆t) for the transition (S= ∆C R·∆t ). By quantifying resilience as a composite of available energy, structural health, and cognitive or biological complexity, the model successfully bridges cel- lular responses, psychological strain, and multiorgan clinical failure under a single, unified framework. The temporal integral of this instantaneous pressure accurately calculates allostatic load, successfully predicting the system’s structural yield point, termed the “Georgiadis Limit.” Furthermore, this framework finds critical and di- rect applications in Intensive Care Unit (ICU) environments. It provides a robust physiological basis for understanding the Rapid Shallow Breathing Index (RSBI) during ventilator weaning, decrypts the lethal dynamics of septic shock, and estab- lishes a clear predictive mathematical model for preoperative surgical risk assess- ment (GSS). Ultimately, the Georgiadis Model provides a quantifiable methodology for the early identification, measurement, and prevention of biological collapse.