A mathematical model for predicting post-exercise heart rate recovery

The Heart-Rate recovery following maximal exercise is controlled mainly by interplay of central input, mechanoreceptors, metaboreceptors and baroreflex system. This study presents a mathematical model to explain the recovery pattern following maximal exercise. The equation explains the role and extent of different regulator in heart rate control during the whole recovery period. Our mathematical model of heart rate recovery has a decaying exponential component and a sinusoidal component which is also undergoing exponential decay. Our model shows high degree of reliability and agreement as well as correlation with the real-time decay pattern. The constant ‘α’ represents the resting heart rate and is outcome of interaction between central input, mechanoreceptors and metaboreceptors. The ‘ βe -δt ’ component of our equation quantifies the role of metaboreceptor during heart rate recovery. Also, it seems to approximate the sympathetic decay during recovery period. The ‘ e -φt γ cos ( ωt )’ component of our equation quantifies the role of baroreflex system during the recovery period and it appears to approximate the parasympathetic reactivation during recovery. The constant ‘T’ (or ‘ ω ’) is time period of sinusoidal oscillation happening during the recovery. It quantifies the elasticity of baroreflex system against any deviation from heart rate set-point and it falls in the Ultra-Low Frequency range of Heart Rate Variability.