# Applicability of Human Thermophysiological Model for Prediction of Thermal Strain in PPE
## 2 Materials and Methods
### Verification of Usability of the Thermophysiological PHS and FMTK Models  
Two thermophysiological mathematical models, the PHS and FMTK, were tested to verify their applicability for estimating the permissible work time limit in a protective ensemble in terms of the thermal strain caused by the heat accumulation in the body and the associated increase in body core temperature. The purpose of the comparison between the two models is important to determine whether the PHS, FMTK, or both result in different and/or reasonable predictions also for protective clothing with properties outside the validity range of the models:  
* The predicted heat strain (PHS) model is described in the ISO standard 7933 [19] and is intended for the prediction of body core temperature, mean skin temperature, and intensity of sweating. The PHS is a simpler and less time-consuming model in comparison with the FMTK model below. The validity range of the PHS model is shown in Table 1[19; 30].
* The FIALA-based model of thermal comfort (FMTK) [15; 20] is based on the calculation of heat exchange in the body with respect to the individual anthropometric data of the user, external climatic conditions, thermal insulating properties of the protective ensemble, and expected intensity of physical activity. The FMTK model works as a dynamic model, i.e., it consists of a system of partial differential equations of heat transfer in human tissues. The FMTK model is based on the numerical solution of heat transfer in the human body with a resolution of 19 human body segments and provides a prediction of the mean skin temperature, rectal temperature, and local skin temperatures. The validity range of the model is shown in Table 1[15; 20].  
Both models, the PHS and FMTK, were implemented in the MATLAB software (version 2020b) based on the publications [15; 19].  
Firstly, a preliminary usability study [24] was conducted for both models. The resulting predictions were compared with the actual values of the body core temperature obtained from the real test with one proband in a climatic chamber for three types of ensembles: Klimatex underwent, air-permeable military filtration NBC suit M2000, and impermeable chemical protective clothing Tychem(r) F (DuPont de Nemours, Luxembourg). For more details, see the study [24].  
In this research, further experiments with more probands wearing various protective suits under various conditions were carried out to verify the results of the study [24] on a larger set of measured data. In accordance with the preliminary study [24], the FMTK model was determined to be more suitable for the PPE application; see the Section 3 for more details.  
For the comparison of the simulated data with the real experiments, the mean absolute error (MAE) was used. It was calculated according to Equation (5):  
\[\text{MAE}=\frac{1}{n}\sum_{i=1}^{n}\left|x_{i}-y_{i}\right| \tag{5}\]  
MAE--Mean absolute error;  
\(n\)--Number of measurements;  
\(x_{i}\)--Measured values;  
\(y_{i}\)--Simulated values.  
Moreover, for the later validation of the PTS tool and the comparison of the simulated data with the real experiments, the mean absolute percentage error (MAPE) generally used for the regression models was calculated according to Equation (6):  
\[\text{MAPE}=\frac{100}{n}\sum_{i=1}^{n}\left|\frac{x_{i}-y_{i}}{x_{i}}\right| \tag{6}\]  
MAPE--Mean absolute percentage error;  
\(n\)--Number of measurements;  
\(x_{i}\)--Measured values;  
\(y_{i}\)--Predicted values.