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 (Tes) and skin temperature were measured with thermocouples and EE was measured with a tri-axial accelerometer. To estimate the increase in Tes from EE, we proposed a mathematical model composed of the heat capacity of active muscles (C1, kcal.°C-1), the heat capacity of the sum of resting muscles and skin (C2), the resistance to heat flux from C1 to C2 (R1, °C.min.kcal-1), and the resistance from C2 to the skin surface (R2). We determined the parameters while minimizing the differences between the estimated and measured changes in Tes profiles during graded walking. We found that C1 and C2 in individuals were highly correlated with their body weight (kg) and body surface area (m2), respectively, whereas R1 and R2 were similar across subjects. When the profiles of measured Tes (y) and estimated Tes (x) were pooled in all subjects, they were almost identical and were described by a regression equation without an intercept, y = 0.96x (r = 0.96, P < 0.0001), with a mean difference of - 0.01 ± 0.12 °C (mean ± SD) ranging from - 0.18 to 1.56 °C of the increase in Tes by Bland-Altman analysis. Thus, the model can be used for firefighters to prevent heat illness during firefighting.