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Article Excerpt
INTRODUCTION
Researchers have developed thermal computational models using different approaches, such as analytical, statistical, empirical, and physiological, to forecast and to better understand human thermal responses under different environ mental conditions (Bue 1971; Campbell et al. 1994; French et al. 1997; Fu 1995; Gonzalez et al. 1997; Gonzalez 2001; Guan et al. 2003; Hsu et al. 1971; Pennes 1948; Stolwijk 1971; Tanabe et al. 2002; Wissler 1971; Hwang and Konz 1977). However, due to the complexity of human thermoregulation, including interactions with the environment, the suitability of such models to real-world applications has been limited. Better characterization of the uncertainties involved, including physiological mechanisms and parameter variations will be important as we seek improved understanding of human thermophysiology related to heat stress.
One of the earliest human thermal efforts was the development of a steady-state model to analyze heat transfer in a resting human forearm by Pennes (1948). This cylindrical model served as the basis for a more advanced model by Wissler (1971) and is still being used for the prediction of temperature elevation during hyperthermia (Frank et al. 1999). Subsequent advances in computing technology and increased experimental data on human physiology helped researchers in developing more sophisticated human thermal models. In the 1960s, early versions of the well-known Wissler (1964) and Stolwijk (1971) models were being developed. Later human thermal models derive their ideas largely from these three mathematical models.
Various research teams (Fu 1995; Huizenga et al. 2001; Iyoho 2002) have developed models in the past decade to be used in environments that range from steady-state to transient and non-uniform cases. Examples of models that are being improved include the Wissler (1964) model, a detailed finite element model (Fu 1995), a model by Huizenga et al. (2001), and one by the authors' group. All of these models include heat transfer within the body and between the body and its environment, as well as sweating, shivering, and vasomotor functions. The authors' group has also been investigating human thermal dynamic modeling issues (Campbell et al. 1994; Iyoho 2002; Thornton et al. 2002; Thornton and Nair 2000) and are developing an advanced two-dimensional human thermal model as part of a larger goal to design an automatic thermal controller for astronauts during extra vehicular activities (Iyoho 2002; Thornton et al. 2002).
Quantitative comparisons among human thermoregulation models have been difficult due to the individual characteristics of each model-in particular, environmental conditions (Campbell et al. 1994; Gonzalez 2001; Guan et al. 2003). From a user's point of view, it has not been clear which of the models would be best suited for a particular environment and application. From a physiology point of view, many aspects of the human active (thermoregulatory/control) thermal system are still not well understood. The passive thermal system (conduction through body regions, etc.) has been modeled with more success, but the effect of uncertainties, such as intra-subject and inter-subject variations in thermal parameters, continue to be poorly understood. Hence, although human thermal models predict core and mean skin temperature fairly accurately, they fail to predict other thermal responses, such as sweat production and metabolic heat production, particularly in extreme conditions. Important indicators for thermal risk, such as heart rate and dehydration level due to the excess sweating, are not typically considered explicitly in the models. Perturbations, such as fast transient and widely disparate environmental conditions, individual physiological differences, altitude, clothing, and terrain level, also cause problems for such models. As an example, causes for large variations in thermal responses and tolerance time limits among individuals continue to be poorly understood.
A neural network model has been developed by our team to predict heat stress using transient experimental thermal data from a group of subjects, details of which are provided in the next section. The inputs to the model are prior values of core temperature (Tcore), heart rate (HR), skin temperature (Tsk), and seven "individual" parameters, and the model outputs are future predictions of Tcore, HR, and Tsk. The seven parameters considered to characterize individual differences are gender, age, height, weight, maximal oxygen consumption (VO2max), basal metabolic rate (Minitial), and initial heart rate (HRinitial). A methodology is then proposed to identify the relative importance of "individual" parameters on heat stress variables, such as core temperature and heart rate, using a sensitivity analysis. A method to calculate the relative importance of environmental conditions on those variables is also reported.
MODEL DEVELOPMENT
The data set used to develop the neural network was provided by Dr. Richard Gonzalez of the US Army Research Institute of Environmental Medicine (USARIEM), Natick, Massachusetts, and contains thermal observations for 35 healthy male and female subjects, ranging in age from 8 to 67 years. The data were collected in compliance with appropriate guidelines. For each subject, in a resting supine position through the experiment, 10 variables were measured for 140 min, in still air, with transient environmental conditions (from 9[degrees]C to 50[degrees]C, and from dry to humid environments). After an initial period of 30 min at Ta 30[degrees]C, the chamber temperature was increased at a rate of 1.5[degrees]C [min.sup.-1], rising rapidly for the first 20 min, and leveling off at 50[degrees]C. Following a 30 min hot-dry exposure, the dew-point temperature was raised to 32[degrees]C, and responses were observed for another 25 min, after which the chamber temperature was lowered, falling rapidly and leveling off at 10[degrees]C . For more details, refer to Gonzalez et al. (1981). The data set is divided into eight groups by age and gender, as shown in Table 1. Since the subjects are resting, the metabolic rate is considered constant for each subject, with a term added separately if shivering occurs.
Table 1. Details of the Experimental Data Set Gender Group N[degrees] of Subjects Age (years) Female F1 5 11.7 [+ or -] 1.6 F2 5 22.5 [+ or -] 2.3 F3 3 40.0 [+ or -] 6.0 F4 2 61.8 [+ or -] 2.0 Male M1 5 11.8 [+ or -] 2.8 M2 5 22.3 [+ or -] 2.9 M3 5 34.0 [+ or -] 5.6 M4 5 60.2 [+...
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