Mathematical model to estimate the increase in firefighters' core temperature during firefighting activity with a portable calorimeter.

We developed a mathematical model to estimate the increase in firefighters' core body temperature from energy expenditure (EE) measured by accelerometry to prevent heat illness during firefighting. Wearing firefighter personal protective equipment, seven male subjects aged 23-42 years underwent a graded walking test on a treadmill while esophageal temperature (T) and skin temperature were measured with thermocouples and EE was measured with a tri-axial accelerometer. To estimate the increase in T from EE, we proposed a mathematical model composed of the heat capacity of active muscles (C, kcal·°C), the heat capacity of the sum of resting muscles and skin (C), the resistance to heat flux from C to C (R, °C·min·kcal), and the resistance from C to the skin surface (R).