Case Study on Skin Calorimetry: Modeling Localized Muscle Heat Transfer During Exercise

Direct measurement of heat loss in a moving limb requires attached heat-flux sensors, which are strongly affected by convection and radiation. Skin calorimetry minimizes these effects, enabling an accurate measurement. A skin calorimeter was used to measure the heat flux in the rectus femoris (thigh) of a subject exercising for 30 min at a mechanical power of 80 W. In this work, we have developed an analytical model able to describe the thermal evolution of the rectus femoris during exercise and subsequent recovery. This model consists of a sum of two exponentials <i>f</i>(<i>t</i>) = <i>A₁</i>(1 - <i>e</i>^{-<i>t</i>/<i>τ</i>}) + <i>A₂</i>·<i>t</i>·<i>e</i>^{-<i>t</i>/<i>τ</i>}, with the novelty that the second term is a linear-exponential, which opposes the first term, and that allows the initial thermal transient characterization. The time constants are the most relevant parameters, with mean values of 5 min during exercise and 10 min during recovery (for the 4 cm² sensing area). The mean exercise amplitude (<i>A₁</i>) is 1.1 mW/W, while in post-exercise it is -0.8 mW/W. In addition, the measurement of the thermal resistance of the skin before and after exercise allowed for the estimation and analysis of the evolution of the subcutaneous internal temperature, which follows the same exponential function. The developed mathematical model defines a Transfer Function (TF)-a potential invariant that can predict the thigh's heat flux response to any exercise protocol (for the subject analyzed). This mathematical approach may be useful for sports and clinical applications.