Mathematical Models of Physiological Responses to Exercise

This paper develops empirical mathematical models for physiological responses to exercise. We first find single-input single-output models describing heart rate variability, ventilation, oxygen consumption and carbon dioxide production in response to workload changes and then identify a single-input multi-output model from workload to these physiological variabilities. We also investigate the possibility of the existence of a universal model for physiological variability in different individuals during treadmill running. Simulations based on real data substantiate that the obtained models accurately capture the physiological responses to workload variations. In particular, it is observed that (i) different physiological responses to exercise can be captured by low-order linear or mildly nonlinear models; and (ii) there may exist a universal model for oxygen consumption that works for different individuals.