A mathematical model of heat flow in a thermopile for measuring muscle heat production: implications for design and signal analysis

Contracting muscles produce heat which largely arises from the biochemical reactions that provide the energy for contraction. Measurements of muscle heat production have made, and continue to make, important contributions to our understanding of the bases of contraction. Most measurements of muscle heat production are made using a thermopile, consisting of a series of thermocouples arranged so that alternate thermocouples are in thermal contact with the muscle and with an isothermal reference. In this study, a mathematical model was constructed of a muscle lying on a thermopile consisting of antimony-bismuth thermocouples sandwiched between polymer sheets. The validity of the model was demonstrated by its ability to accurately predict thermopile outputs in response to applying heat to the thermopile surface, to generating heat in the thermocouples using the Peltier effect and to adding heat capacity on the thermopile surface. The model was then used to show how practical changes to thermopile construction could minimise response time and thermopile heat capacity and allow measurement of very low rates of heat production. The impulse response of a muscle-thermopile system was generated using the model and used to illustrate how a measured signal can be deconvolved with the impulse response to correct for lag introduced by the thermopile.