Oxygen resaturation rate as a measure of fitness: A simple mathematical model with Excel template

This model presents a simple mathematical model describing the dynamics of oxygen resaturation during recovery after physical exertion. The model assumes constant energy consumption and oxygen uptake proportional to the remaining saturation capacity, resulting in a differential equation for oxygen saturation over time. The simple mathematical model shows that saturation approaches a steady-state value at a rate determined by a key parameter, the oxygen resaturation rate (λ). This rate is proposed as a potential indicator of physical fitness.
The simple mathematical model was applied to muscle near-infrared spectroscopy (mNIRS) data to gain deeper insights into local muscle oxygenation and fatigue during the assessment. Example data were recorded using a continuous-wave mNIRS device (Moxy Monitor; Fortiori Designs LLC, US), sampling at 0.5 Hz. The sensors were affixed with medical adhesive tape to the point of greatest circumference of the medial gastrocnemius muscle on both legs. Participants performed a standardized Single Leg Heel Raise Test. For further methodological details, see:
Schrefl, A., Kolokythas, N., Stamm, M., Erlacher, D., & Schärli, A. (2024). Reliability of a standardized protocol of the Single Leg Heel Rise Test. Current Issues in Sport Science (CISS), 9(1), 009. https://doi.org/10.36950/2024.9ciss009