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Modeling individual variations in thermal stress response for humans in transient environments.


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.


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 [+ or -] 5.0

Gender  Surface Area to Mass Ratio  Maximum Aerobic Capacity (VO2
          ([Cm.sup.2][Kg.sup-1])        max)ml(mim-kg)

Female      321.3 [+ or -] 21.4         43.8 [+ or -] 1.3

            307.3 [+ or -] 36.4         49.8 [+ or -] 1.3

            279.3 [+ or -] 11.1         35.8 [+ or -] 1.3

            290.3 [+ or -] 9.4          30.9 [+ or -] 1.3

Male        319.3 [+ or -] 35.9         47.8 [+ or -] 2.4

            270.3 [+ or -] 14.2         47.1 [+ or -] 2.1

            252.3 [+ or -] 11.9         44.4 [+ or -] 2.2

            253.3 [+ or -] 18.6         27.7 [+ or -] 1.5


Three separate models are developed-two gender-based models (male and female using male and female data sets, respectively) and one "general" combined model with gender as an input (using the entire data set). Starting with the basic thermal equations for human modeling, the important "inputs" are identified using a systematic procedure for artificial neural network modeling (Thornton et al. 1997; Mistry and Nair 1993), including their dynamic characteristics, i.e., whether to consider one or two past values of the variable. After such a careful analysis, nine inputs were selected for the general combined model. These were as follows: two environmental parameters (Ta, Pa) and seven individual characteristics (age, gender, VO2max, weight, height, Minitial, and HRinitial; see Table 2 for symbols and description) for the subjects with the only gender variable being omitted in the two gender-based models. The potential user thus has to provide only the environmental conditions and the individual characteristics as inputs. The outputs of the model are Tsk, Tcore, and HR. Esophageal temperature, Tes, and rectal temperature, Trec, were used to represent Tcore in the training process. A feedforward neural network architecture is used for the models with an input layer, two hidden layers, and an output layer, using a back-propagation algorithm for update, with a mean-square error (MSE) performance function. The architecture has feedback of one time-delayed value for each of the three outputs, making it a dynamic model. The structure of the net for the combined model is 12 x 12 x 14 x 3, while for gender-based models it is 11 x 10 x 10 x 3. The data set provided 4759 patterns for training, each separated in time by one minute. An early stopping method (Amari et al. 1997; Pennes 1948) is used to prevent overfitting and ensure generalization, with the data divided into three subsets-50% for training, 25% for validation, and 25% for testing. From the six models, the one with the least MSE for the testing data set is selected. The weights, biases, and number of epochs for the network are then used to train the final model with the entire data set.
Table 2. Description of the Parameters

                 Variables      Description    Unit

Individual       Subject        Identifier

                 Group          1 to 4

                 Age            Age of a       Years

                 [A.sub.d]      Surface area   [m.sup.2]

                 Gender         Male or

                 [VO.sub.2]     Max.aerobic    ml/(
                 Max            capacity

                 Height                        in.

                 Weight                        kg

                 M initial      Initial        W*[m.sup.-2]

                 HR initial     Initial heart  Beat/min

Controlled       Time           A total of     Min
Variables                       140 min

                 Ta             Air            [degrees]C

                 Pa             Ambient vapor  in.-Hg

Measured         Tsk            Skin           [degrees]C
Variables                       temperature

                 Tes            Core           [degrees]C

                 HR             Heart rate     Beat/min

                 Evg            Evaporative    g/min

                 [m.sub.s]      Sweating rate  mg/(min*[cm.sup.2])

                 [K.sub.chest]  Skin           W/([m.sup.2].[degrees]C)
                                in chest

                 [K.sub.arm]    Skin           W/[m.sup.2].[degrees]C

                 M              Metabolic      W*[m.sup.-2]
                                free energy

                 Disc           Discomfort

                 Tsens          Temperature

Calculated       Esk            Heat Transfer  W*[m.sup.-2]
Variables                       via
                                from the skin

                 Tb             Mean body      [degrees]C

                 w              Skin

                 R+C            Dry heat       W*[m.sup.-2]

                 [DELTA]Tb/min  Mean body      W*[m.sup.-2]

                 S              Body heat      W*[m.sup.-2]
                                storage rate

                 Req Esk        Required       W*[m.sup.-2]
                                heat loss

                 ET             Effective      [degrees]C

                 HRR            Heart rate

Sensitivity Analysis

We perform a sensitivity analysis with mean skin temperature (Tsk) and core temperature (Tcore) as outputs, and the individual parameters (age, VO2max, HRinitial, Minitial, HRinitial, height, weight) as inputs. The sensitivity derivative is defined as [delta] (output) / [delta] (parameter), and this derivative is calculated by perturbing each input by one standard deviation of its value within the group, and noting its effect on the steady-state value of the output. Taking the ratio of the change in output to the change in input provides the sensitivity derivative. This analysis is carried out for each input, one at a time, keeping the others constant, in four environmental conditions. An "average" subject from each group is chosen as the representative subject for the sensitivity analyses (Table 3). This value is then scaled by the largest magnitude in the column to provide a ranked estimate of its relative importance. This results in the largest value in each column having a magnitude of 1, and the magnitudes and signs for each parameter provide an indication of its relative importance. Sensitivity analysis provides further insights into system characteristics by permitting us to rank the importance of the "inputs" on influencing the "outputs." Sensitivity analysis also serves as an additional tool to check whether the model has generalized adequately since it can be checked against known trends reported in the literature.
Table 3. Average Subject for Each Group with Mean Individual Parameters

Male                    Average Male of  SD     Average Male of   SD
                            group 1                group 2

Age (yrs)                    11          2.58        22           3.69

VO2 Max (W*[m.sup.-2])       48.55       6.29        47.11        5.93

M initial (ml/(min-kg)       54.027      4.42        49.06        5.23

HR initial (bpm)             72          8.64        73.6         5.16

Height (inches)              57.38       6.34        70.9         2.68

Weight (Kg)                  39.1       12.65        70.24        8.04

Female                  Average Female   SD     Average Female     SD
                          of group 1              of group 2

Age (yrs)                    12          1.14        23           2.5

VO2 Max (W*[m.sup.-2])       43.86       3.05        47.35        7.22

M initial (ml/(min-kg)       50.88       6.92        46.32       11.48

HR initial (bpm)             84          3.31        74           8.64

Height (inches)              60.75       7.87        64.37        2.04

Weight (Kg)                  43.25       4.68        51.13        4.17

Male                    Average Male of  SD    Average Male of     SD
                            group 3                group 4

Age (yrs)                    34          6.22       60            5.56

VO2 Max (W*[m.sup.-2])       46.08       7.61       27.6          3.94

M initial (ml/(min-kg)       54.6        6.42       51.05         5.60

HR initial (bpm)             76.5        4.56       83.46         3.82

Height (inches)              73.13       3.32       66.85         2.40

Weight (Kg)                  77.21       4.63       72.61         2.76

Female                  Average Female   SD    Average Female      SD
                           of group 3             of group 4

Age (yrs)                    39          4.94       62            2.82

VO2 Max (W*[m.sup.-2])       37          8.98       30.4         10.60

M initial (ml/(min-kg)       47.66       1.26       41.25         7.99

HR initial (bpm)             74.66       2.82       80            5.65

Height (inches)              64.70       0.61       61.12         0.17

Weight (Kg)                  59.21       8.36       51            3.53

SD: standard deviation of each group


The neural network structures for our models were chosen based on extensive statistical analysis of the data and a review of the literature. These analyses included correlations, ANOVA, and development of linear regression models. Havenith and van Middendorp (1990) have shown that Ta, vapor pressure, and metabolic rate can explain 96% of the variance in mean skin temperature, with Ta being the largest contributor. This finding coincides with our multiple regression analysis of the data set, which gives a value 92% for the same check. Havenith and van Middendorp (1990) show that a multiple regression analysis using Ta, Pa, M, % Fat, and sweating set point can explain 71% of the variance in Tcore. A regression analysis performed with our data set showed that 61% of the variance could be explained when Tsk, HR, Evg, and age group were included along with Ta and Pa. Moran et al. (1995) showed that 77% to 88% of the variance in heart rate can be explained by initial heart rate, metabolic rate, maximum evaporative rate, required evaporative rate, and time of exposure in minutes. Our data analysis showed that Tsk, Tes, Evg, Ta, Pa, and age group could explain 64% of the variance (Table 4). For the variance in heat storage rate, S, 92% could be explained by Ta, Pa, M, %Fat, [A.sup.d], VO2max, and sweating gain (Havenith and van Middendorp 1990).
Table 4. Regression Coefficients for Various Physiological Heat Stress
Reactions with Environmental, Heat Production and Individual's
Parameters from Havenith et al. Study (13)

Dependent Variables                 Ta        [PH.sub.2]O    M    % Fat
                                ([degrees]C)     (kPa)     (kW)

S (J/g)                              x             x         x

S (J/g)                              x             x         x     x

Rectal Temperature ([degree]C)       x             x         x     x

Rectal Temperature ([degree]C)       x             x         x     x

Skin Temperature ([degree]C)         x             x         x     x

HR (bpm)                             x             x         x     x

HR (bpm)                             x             x         x     x


Dependent       Surf:mass     [VO.sub.2max]        %         set
Variables    ([m.sup.2]kg-1)                 [VO.sub.2max]  point

S (J/g)

S (J/g)             x               x


Rectal              x               x                         x


HR (bpm)

HR (bpm)                                             x

Dependent Variables             gain  S  [R.sup.2] (%)  [R'.sup.2] (%)

S (J/g)                                       88

S (J/g)                            x          92              33

Rectal Temperature ([degree]C)                38

Rectal Temperature ([degree]C)                60              37

Skin Temperature ([degree]C)                  96

HR (bpm)                                      75

HR (bpm)                                      88              46

Ta, Ambient temperature; [[PH.sub.2]O], water vapor pressure;
[VO.sub.2] max, maximal oxygen uptake; [r.sup.2], total variance
explained by the equation; [r.sup.'2], the fraction of the residual
variance left after introduction of climatic and work rate parameters
in the prediction equation, which is explained by individual's

Predictions of the models developed using a representative "average" for each group (Table 3) compared well with actual data, some of which are shown in Figures 1-3. Actual data for all of the subjects are superimposed in the figures with the prediction for a representative subject in the group with average properties. The correlation coefficients between predicted values and experimental values are shown in Table 5 for each of the subjects, for all the three outputs (Tcore, HR, and Tskin), showing good overall performance using gender-based models. Several other similar investigations were performed that are not described due to space limitations, and the observations from the study are summarized next. The model is found to successfully predict Tcore, HR, and Tskin, given only two environmental variables and seven individual parameters as inputs. Tcore and HR are two of the most important thermal predictors of thermal risk, and they are products of complex internal and external interactions with the surrounding environment and within the body.



Table 5. Coefficients of Correlation (R) of Predicted Values Against
Experimental Values for Each Output for All Groups Using Gender-Based

Group1  Male1   Male2   Male3   Male4   Male5

Tsk     0.985   0.983   0.9728  0.993   0.999
Tcore   0.742   0.853   0.8720  0.778   0.942
HR      0.9207  0.8995  0.8757  0.9019  0.8732

Group2  Male1   Male2   Male3   Male4   Male5

Tsk     0.9850  0.9922  0.9881  0.9930  0.9850
Tcore   0.8705  0.7580  0.9322  0.7390  0.7772
HR      0.9552  0.8983  0.9669  0.8838  0.8428

Group3  Male1   Male2   Male3   Male4   Male5

Tsk     0.9971  0.9963  0.9920  0.9900  0.9912
Tcore   0.9140  0.8381  0.8452  0.8141  0.8274
HR      0.9285  0.8334  0.7425  0.8433  0.8246

Group4  Male1   Male2   Male3   Male4   Male5

Tsk     0.9843  0.9661  0.9783  0.9520  0.9800
Tcore   0.8812  0.8203  0.8672  0.8460  0.8392
HR      0.9470  0.8437  0.8011  0.9054  0.8283

Group1  Female1  Female2  Female3  Female4  Female5

Tsk     0.9262   0.9715   0.9566   0.9825   0.9819
Tcore   0.7843   0.8188   0.9344   0.8504   0.8811
HR      0.9041   0.9225   0.8776   0.8998   0.9086

Group2  Female1  Female2  Female3  Female4  Female5

Tsk     0.9851   0.9843   0.9917   0.9478
Tcore   0.8920   0.8561   0.9193   0.7759
HR      0.9135   0.8886   0.8893   0.7959

Group3  Female1  Female2  Female3  Female4  Female5

Tsk     0.9870   0.9835   0.9748
Tcore   0.7921   0.8912   0.8798
HR      0.9262   0.8925   0.8574

Group4  Female1  Female2  Female3  Female4  Female5

Tsk     0.9761   0.9750
Tcore   0.947    0.9192
HR      0.9318   0.8373

Observations from Sensitivity Analysis

Sensitivity analysis is systematically performed using all three models under four different environmental conditions: normal (Ta = 20, Pa = 24), jungle (Ta = 40, Pa = 30), desert (Ta = 43, Pa = 10), and cold (Ta = 5, Pa = 10). The data set used for the first model has been categorized into four age groups for each gender. From each age group an average subject is generated to test how well the model generalizes. This average subject in each group has a mean value for each input (Table 3). As mentioned earlier, Figures 1-3 show that the model has generalized well without overfitting, since the thermal responses of these average subjects lie within the range of thermal outputs of the group in transient environmental conditions. Results of the sensitivity analyses are provided as ranked values of the scaled sensitivity derivatives ([delta] (output) / [delta] (parameter)) in Tables 6 and 7.

Many interesting observations can be noted, some of which are described next, and they agree with findings reported in the literature. For instance, Havenith et al. (1998) suggested that part of the variance in Tcore could be explained by the [A.sub.d]/mass relationship for the subjects, with "big" subjects who are characterized by large values of [A.sub.d] (body surface area as a function of height and weight) and low [A.sub.d]/mass having a lower Tcore. One physiological explanation is that subjects with high Ad have a larger surface area for heat loss to the environment and have higher heat storage capacity. Small subjects (low mass; high [A.sub.d]/mass) are at a disadvantage when coping with heat stress due to their smaller heat storage capacity, as noted by Havenith et al (1998). Havenith et al. (1998) found a positive correlation between [A.sub.d]/mass ratio and core temperature not only for a warm-humid or jungle, but also for a neutral and a hot-dry (desert) climate. The positive correlation was highest in the warm-humid climate or jungle, however, implying that big subjects have the most marked advantage in the jungle or warm-humid climate. Our sensitivity analysis yielded the same results. As seen in Tables 6 and 7, an increase in weight, implying a smaller [A.sub.d]/mass ratio, causes Tcore to decrease in most of subjects (negative value for the scaled derivative), with the largest effect visible in jungle and desert environments. And the increase in height implying a larger Ad causes an increase in Tcore in most of the male groups, but this was not true for female group 1. With regard to the effect of fitness on thermoregulation, Gonzalez et al. (1997) showed that a higher value of gain in the rate of the total change in evaporative heat loss ([[DELTA]E.sub.SK]) to the change in mean body temperature ([[DELTA].sub.Tb]) indicates a greater ease in handling heat stress by increased evaporation of sweat without incurring excessive excursions of internal body temperature. And there was a significant positive correlation between [[[DELTA]E.sub.SK]/[[DELTA]T.sub.b]] and the maximum aerobic capacity (VO2max). The effect of VO2max on Tcore was confirmed in our sensitivity analysis, where the increase of VO2max leads to a decrease in Tcore in all models in most environmental conditions. There were two cases with a positive increase in Tcore in desert conditions for male groups 1 and 3, using the male model. Age by itself does not seem to be a factor in thermoregulation since the sensitivity analysis shows no major effect on Tcore, Tskin, and HR due to age.

Havenith et al. (1998) report that [VO.sub.2max], [A.sub.d], and % body fat were responsible for 62 % of the variance in linear regression model for Tskin. Their data set was obtained from 27 subjects (19 men and 8 women) engaged in ergometer exercise in a warm humid climate (35[degrees]C, 80% humidity) for one hour. The data are different from ours where the subjects are seminude and in a supine resting position in transient environmental conditions. However, our sensitivity study is consistent with this result. Also, there was a gender-based difference in terms of parameter contribution to Tskin. In males, [VO.sub.2max] was a main parameter with a negative impact on Tskin, implying partial acclimation, improved sweating, and skin cooling. However, in females, height and weight were the main parameters representing the heat loss capacity of the female body. But overall contributions of these parameters to Tskin were very small, as Tair and Pa are the main driving factors in our data set.

Heart rate variation accounts for some of the gender-based differences in heat stress responses. Women are reported to have higher heart rates than men (Stephenson and Kolka 1993) since, on average, they have a greater surface area to body mass ratio (Nunneley 1978), lower sweat rates (Frye and Kamon 1981), higher fat percentage, and lower aerobic fitness (Shapiro et al. 1980). In a study presented by Wells and Horvath (1973), the authors noted that independent of other stresses, heat raised HR by 6.5 beats per minute for women. Possibly the higher heart rate, elevated respiration, and metabolic requirements occurring in female subjects implies an inadequacy of circulatory transport of oxygen for women in hot conditions (Havenith and van Middendorp 1990). Havenith and van Middendorp (1990) note that the increase in HR needed is smaller for a higher [A.sub.d], as it provides more heat loss surface, resulting in improved cooling and, thus, efficient heat removal from core to skin (McArdle et al. 1991). Our findings indicate that the group with old women shows a negative effect on HR with increase of [A.sub.d] (by increasing height by one standard deviation) in all four conditions, but the other female groups do not. There are many such trends that can be determined from the sensitivity results in Tables 6 and 7, and we have discussed only some representative ones here. It is important to note that the model reported is a regression model that is valid only for the conditions tested, and not generalizable beyond that range. Also, the model has been developed with a limited data set, both as far as the number of subjects and the different transient conditions, which may influence the trends reported. Furthermore, future studies should consider the effect of different exercise levels, of mechanisms in cold conditions such as non-shivering thermogenesis, of factors such as hydration level, and of non-thermal factors such as smoking, medication, and menstrual cycle, depending on the conditions modeled and the prediction accuracy desired.


A novel transient predictive thermal model is reported for resting semi-nude supine individuals, to reliably predict Tcore, Tskin, and HR in transient environmental conditions for individual subjects. The model was then used to determine the relative importance of individual parameters on thermal stress variables, using a proposed sensitivity method. An important contribution of the reported study is to demonstrate that the predictive thermal model development methodology using neural networks is viable for human thermal response studies and can identify the relative importance of the individual parameters and environmental inputs. The model is validated by demonstrating prediction trends that are consistent with the literature. The ranking of the relative importance of the inputs in Tables 6 and 7 for various conditions provide 'fine-grained' insights into the thermal stress response phenomena. Some such insights are: fitness level is very important for predicting thermal risk but age is not; subjects with large [A.sub.d] will have an advantage in handling heat stress in jungle and desert conditions; the effect of gender on the handling of thermal stress was not obvious from the model, but it seems that women usually have higher core temperature even if their individual physiological characteristics are matched with that of male, and this is something that needs further study. The sensitivity results in Tables 6 and 7 can be used for numerous other comparison studies, depending on the application. For instance, one can compare between environments (jungle, desert, neural, cold), between outputs, and between groups of individuals (Table 3).

The data set we have used was limited to 35 semi-nude subjects resting in a supine position; it will be interesting to determine trends with larger data sets, in varying environmental conditions and exercise levels. Our study does, however, demonstrate that the proposed methodology for modeling and sensitivity analysis using neural networks has the potential to model and also discern the relative importance of the environ mental and individual parameters on thermal stress responses in different conditions.


This research was supported in part by grant # DAAD16-03-P-0119, from US Army Research Institute of Environmental Medicine, Natick, MA. The authors also gratefully acknowledge the numerous insights provided by Richard Gonzalez of USARIEM.
Table 6a. Ranked and Scaled Sensitivity Derivatives in Jungle and
Desert Conditions for "Average" Male from Each Group


               Male Group 1                    Male Group 2

        'Height'    -1.0000 (0.0307)    'VO2max'    -1.0000 (0.0499)
        'VO2max'        -0.8168         'Height'         -0.6403
Skin    'Weight'        -0.5168           'HR'           0.5607
          'HR'           0.4580          'age'          -0.3570
          'M'            0.1808           'M'            0.2425
         'age'          -0.0729         'Weight'        -0.1791

        'Height'    -1.0000 (0.0208)    'VO2max'    -1.0000 (0.0456)
        'VO2max'         0.6244           'M'            0.6592
Core    'Weight'        -0.5352         'Height'         0.5426
          'HR'          -0.5329         'Weight'        -0.4719
          'M'            0.3199           'HR'           0.3152
         'age '         -0.0128          'age'           0.0543

        'Height'    1.0000 (0.6435)     'VO2max'    -1.0000 (1.6084)
        'VO2max'         0.6887           'M'            0.6686
HR      'Weight'        -0.6825         'Weight'        -0.5244
          'HR'          -0.5687         'Height'         0.4324
          'M'            0.2964           'HR'           0.3781
         'age '          0.0407          'age'           0.0388


               Male Group 3                    Male Group 4

        'VO2max'    -1.0000 (0.0402)    'Height'    -1.0000 (0.0358)
        'Height'        -0.9099           'HR'           0.4420
Skin      'HR'           0.5445          'age'          -0.3815
         'age'          -0.3629         'VO2max'        -0.3348
        'Weight'        -0.3210           'M'           -0.1268
          'M'            0.1272         'Weight'         0.1177

        'VO2max'    -1.0000 (0.0345)    'Height'    1.0000 (0.0186)
          'M'            0.6557           'M'            0.4067
Core    'Height'         0.6164          'age'           0.3757
        'Weight'        -0.4187         'Weight'        -0.3748
          'HR'           0.3391           'HR'          -0.1680
         'age'           0.1024         'VO2max'        -0.0047

        'VO2max'    -1.0000 (1.1731)    'Height'    1.0000 (0.4831)
          'M'            0.7125         'Weight'        -0.6204
HR      'Weight'        -0.5661           'M'            0.5774
          'HR'           0.4910          'age'           0.4706
        'Height'         0.4096         'VO2max'         0.0639
         'age'           0.1027           'HR'          -0.0028


               Male Group 1                    Male Group 2

        'Height'    -1.0000 (0.1226)    'Weight'    -1.0000 (0.0384)
        VO2max'         -0.6771         'Height'        -0.9929
Skin     'age'          -0.1032         VO2max'         -0.7021
          'M'           -0.0824          'age'          -0.1229
        'Weight'        -0.0797           'M'           -0.0891
          'HR '          0.0289           'HR'          -0.0148

        'Height'    1.0000 (0.0667)     'Height'    1.0000 (0.0192)
        'VO2max'        -0.6832         'VO2max'         0.7685
Core      'HR'           0.0712         'Weight'         0.6059
          'M'            0.0539           'HR'          -0.1172
        'Weight'         0.0512           'age'          0.0431
         'age'          -0.0173            'M'           0.0119

        'VO2max'    -1.0000 (0.8082)    'Weight'    -1.0000 (0.8205)
        'Height'        -0.9513          'age'           0.6184
HR       'age'           0.8146         VO2max'          0.5288
        'Weight'        -0.5613           'HR'          -0.2391
          'HR'          -0.2875           'M'            0.0714
          'M '           0.0845         'Height'         0.0368


              Male Group 3                    Male Group 4

        'Weight'    -1.0000 (0.1588)    'Height'    1.0000 (0.1146)
          'HR'          -0.8961         'VO2max'         0.7765
Skin    'VO2max'        -0.4687          'age'          -0.5112
          'M'           -0.3690           'M'           -0.1242
         'age'           0.1485           'HR'          -0.0624
        'Height'        -0.0679         'Weight'         0.0616

        'Weight'    1.0000 (0.0536)     'VO2max'    -1.0000 (0.0127)
          'HR'           0.8775         'Height'        -0.9101
Core    'VO2max'         0.6373           'HR'           0.3905
          'M'            0.3704           'M'            0.3741
        'Height'         0.2671         'Weight'         0.3580
         'age'          -0.1984          'age'           0.1439

        'Weight'    -1.0000 (1.2349)    'Height'    1.0000 (0.7449)
         'age'           0.6460         'VO2max'         0.8327
HR      'Height'        -0.2815         'Weight'        -0.3591
        VO2max'          0.1717           'M'            0.2020
         'HR'           -0.1112          'age'          -0.1281
         'M'             0.0678           'HR'           0.0783

Table 6b. Ranked and Scaled Sensitivity Derivatives in Jungle and
Desert Conditions for "Average" Female from Each Group


           Female Group 1               Female Group 2

      'Height'  1.0000 (0.2052)     'HR '     1.0000 (0.0839)
      'VO2max'      -0.0792       'Height'       0.2866
Skin  'Weight'      -0.0422       VO2max'       -0.2551
        'HR'        -0.0383       'Weight'      -0.0998
        'M'          0.0152         'M'          0.0254
       'age'         0.0070        'age'         0.0046

      'Height'  -1.0000 (0.0074)  'VO2max'  -1.0000 (0.0767)
      'VO2max'      -0.7913       'Height'       0.7765
Core  'Weight'      -0.4197       'Weight'      -0.3896
        'HR'        -0.3538         'HR'         0.0527
        'M'          0.1738        'age'         0.0461
       'age'         0.0582         'M'          0.0047

      'Height'  1.0000 (4.0794)     'HR '     1.0000 (2.9869)
      'VO2max'      -0.0464       'VO2max'       0.8947
HR    'Weight'      -0.0257       'Height'      -0.6043
        'HR'        -0.0183       'Weight'       0.3455
        'M'          0.0110        'age'        -0.0492
       'age'         0.0034         'M'          0.0217


           Female Group 3                Female Group 4

      'Height'  1.0000 (0.2052)     'HR'      1.0000 (0.0839)
      'VO2max'      -0.0792       'Height'       0.2866
Skin  'Weight'      -0.0422       VO2max'       -0.2551
        'HR'        -0.0383       'Weight'      -0.0998
        'M'          0.0152         'M'          0.0254
       'age'         0.0070        'age'         0.0046

      'Height'  -1.0000 (0.0074)  'VO2max'  -1.0000 (0.0767)
      'VO2max'      -0.7913       'Height'       0.7765
Core  'Weight'      -0.4197       'Weight'      -0.3896
        'HR'        -0.3538         'HR'        0.0527
        'M'          0.1738        'age'         0.0461
       'age'         0.0582         'M'          0.0047

      'Height'  1.0000 (4.0794)     'HR'     1.0000 (2.9869)
      'VO2max'      -0.0464       'VO2max'       0.8947
HR    'Weight'      -0.0257       'Height'      -0.6043
        'HR'        -0.0183       'Weight'       0.3455
        'M'          0.0110        'age'        -0.0492
       'age'         0.0034         'M'          0.0217


           Female Group 1                Female Group 2

      'Height'  -1.0000 (0.1737)    'HR'     -1.0000 (0.0969)
      'Weight'      -0.5117       'Height'      -0.6465
Skin    'M'          0.4560       'Weight'      -0.4915
        'HR'         0.4544         'M'         -0.3519
      'VO2max'      -0.3486        'age'         0.1297
       'age'         0.0033       'VO2max'      -0.0638

      'Height'  -1.0000 (0.2101)  'Height'  1.0000 (0.0888)
      'VO2max'      -0.3828         'HR'        -0.6387
Core    'M'          0.3810       'VO2max'      -0.5965
      'Weight'      -0.2437       'Weight'      -0.4501
        'HR'         0.2225         'M'          0.0513
       'age'        -0.0396        'age'         0.0464

        'M'     1.0000 (0.9551)   'Height'  -1.0000 (3.7397)
        'HR'         0.7674         'HR'         0.5831
HR    'VO2max'      -0.5548       VO2max'        0.4943
      'Height'      -0.3551       'Weight'       0.2906
      'Weight'      -0.3133         'M'         -0.0351
       'age'        -0.0079        'age'        -0.0186


           Female Group 3               Female Group 4

      'Weight'  -1.0000 (0.2013)    'HR'     -1.0000 (0.1002)
        'M'         -0.1653       'VO2max'       -0.6901
Skin    'HR'         0.1031         'M'          -0.3525
      'Height'       0.0783       'Weight'       -0.0950
      VO2max'        0.0686        'age'          0.0926
       'age'         0.0681       'Height'        0.0846

      'Weight'  -1.0000 (0.0507)  'Height'   1.0000 (0.2851)
      'Height'       0.8240         'HR '        -0.1692
Core  'VO2max'      -0.5391       'Weight'       -0.1195
        'HR '       -0.2055       'VO2max'       -0.1001
        'M '         0.0592        'age '         0.0207
       'age '        0.0520         'M '          0.0202

      'Height'  -1.0000 (1.2761)  'Height'  -1.0000 (10.9790)
      'VO2max'       0.8468         'HR'          0.1449
HR      'HR'         0.7491       'Weight'        0.1163
      'Weight'      -0.1037        'age'         -0.0186
        'M'         -0.0921       VO2max'         0.0183
       'age'         0.0340         'M'          -0.0015

Table 7a. Ranked and Scaled Sensitivity Derivatives in Neutral and Cold
Conditions for an "Average" Male from Each Group


         Male Group 1        Male Group 2

Skin  'VO2max'  -1.0000   'VO2max'  -1.0000
                (0.0596)            (0.0943)
      'M'        0.7546   'M'        0.5339
      'HR'       0.6593   'HR'       0.4549
      'age'      0.3512   'Weight'  -0.3209
      'Weight'  -0.2115   'age'     -0.1890
      'Height'  -0.0608   'Height'  -0.0288

Core  'VO2max'  -1.0000   'M'        1.0000
                (0.0494)            (0.0346)
      'M'        0.9818   'HR'       0.7116
      'HR'       0.7320   'VO2max'  -0.5670
      'Weight'  -0.2322   'Height'   0.2015
      'age'     -0.1995   'Weight'  -0.1186
      'Height'   0.0992   'age'     -0.1130

HR    'VO2max'  -1.0000   'M'        1.0000
                (1.7602)            (1.1042)
      'M'        0.9260   'VO2max'  -0.8093
      'HR'       0.6919   'HR '      0.7340
      'Weight'  -0.2702   'Weight'  -0.2925
      'age'     -0.2027   'Height'   0.1750
      'Height'   0.1044   'age '    -0.1177


         Male Group 1        Male Group 2

Skin  'VO2max'  -1.0000   'VO2max'  -1.0000
                (0.1254)            (0.0916)
      'M'        0.6508   'M'        0.9661
      'HR'       0.4718   'HR'       0.7239
      'Weight'  -0.3122   'Weight'  -0.3813
      'age '    -0.2065   'age'     -0.2169
      'Height'   0.1588   'Height'   0.1440

Core  'M'        1.0000   'M'        1.0000
                (0.0108)  'VO2max'  (0.0044)
      'HR'       0.8668   'HR'      -0.8247
      VO2max'   -0.8210   'Height'   0.6706
      'Weight'  -0.2639   'Weight'   0.4811
      'Height'   0.1094   'age'      0.0732
      'age'     -0.0298             -0.0485

HR    'VO2max'  -1.0000   'VO2max'  -1.0000
                (0.9350)            (0.6525)
      'M'        0.6692   'M'        0.9854
      'HR'       0.5025   'HR'       0.7294
      'Weight'  -0.3224   'Weight'  -0.3266
      'Height'   0.1524   'Height'   0.2299
      'age'     -0.1220   'age'     -0.1688


         Male Group 3        Male Group 4

Skin  'VO2max'  -1.0000   'VO2max'  -1.0000
                (0.0915)            (0.0761)
      'Weight'  -0.5862   'HR'       0.7357
      'M'        0.4256   'M'        0.6903
      'age '    -0.1335   'Height'  -0.2913
      'HR'       0.1155   'Weight'  -0.2654
      'Height'   0.0658   'age'     -0.1324

Core  'M'        1.0000   'Height'   1.0000
                (0.0535)            (0.0619)
      'HR'       0.8582   'age'     -0.3773
      'VO2max'  -0.5472   'M'        0.2728
      'age'     -0.1770   'VO2max'   0.2440
      'Height'   0.1097   'Weight'   0.1029
      'Weight'   0.0093   'HR'       0.0431

HR    'M'        1.0000   'VO2max'  -1.0000
                (1.6003)            (1.6833)
      'HR'       0.8076   'M'        0.6670
      'VO2max'  -0.6502   'HR'       0.6355
      'Weight'  -0.2326   'Weight'  -0.2567
      'age'     -0.1512   'Height'  -0.2002
      'Height'   0.0669   'age'     -0.0601


         Male Group 3        Male Group 4

Skin  'VO2max'  -1.0000   'Height'   1.0000
                (0.1099)            (0.0864)
      'M'        0.8237   'M'        0.7971
      'Weight'  -0.5119   'VO2max'  -0.5506
      'HR'       0.4979   'HR'       0.5298
      'Height'   0.2050   'age'     -0.4803
      'age'     -0.1843   'Weight'  -0.3115

Core  'HR'       1.0000   'VO2max'  -1.0000
                (0.0093)            (0.0260)
      'M'        0.8360   'M'        0.7896
      'Weight'   0.5040   'HR'       0.5192
      'VO2max'  -0.3730   'Height'  -0.2338
      'age'     -0.1399   'Weight'  -0.1972
      'Height'   0.0718   'age'      0.0144

HR    'M'        1.0000   'VO2max'  -1.0000
                (0.7283)            (0.9646)
      'VO2max'  -0.9832   'M'        0.8780
      'HR'       0.8712   'HR'       0.6396
      'Weight'  -0.2380   'Weight'  -0.3306
      'age'     -0.1957   'Height'  -0.0959
      'Height'   0.1582   'age'     -0.0489

Table 7b. Ranked and Scaled Sensitivity Derivatives in Neutral and Cold
Conditions for an "Average" Female from Each Group


        Female Group 1      Female Group 2

Skin  'Height'  -1.0000   'HR'        1.0000
                (0.4401)             (0.0379)
      'HR'       0.1941   'Height'    0.4880
      'M'        0.1908   'M'        -0.4250
      'VO2max'  -0.0468   'VO2max'   -0.3696
      'age'      0.0060    'Weight'   0.1242
      'Weight'  -0.0024   'age'       0.0596

Core  'Height'  -1.0000   'Height'   -1.0000
                (0.2805)             (0.0919)
      'HR'       0.1273   'VO2max'    0.6874
      'M'        0.1246   'HR'       -0.3885
      'VO2max'  -0.0501   'Weight'    0.3716
      'Weight'  -0.0267   'age'      -0.0661
      'age'     -0.0001   'M'         0.0546

HR    'HR'       1.0000   'Height'    1.0000
                (0.5884)             (3.4201)
      'Height'  -0.9977   'HR'        0.8945
      'M'        0.9580   'VO2max'   -0.7080
      'VO2max'  -0.2107   'Weight'    0.4223
      'Weight'  -0.1902   'M'        -0.0703
      'age'      0.1173   'age'       0.0537


        Female Group 1      Female Group 2

Skin  'Height'  -1.0000   'Height'   -1.0000
                (0.5384)             (0.3751)
      'Weight'   0.1941   'HR'       -0.5662
      'M'        0.1908   'VO2max'   -0.2842
      'HR'       0.0468   'Weight'   -0.1759
      'age'     -0.0060   'M'         0.0929
                 0.0024   'age'      -0.0589

Core  'Height'  -1.0000   'VO2max'   -1.0000
                (0.2581)             (0.0906)
      'HR'       0.1273   'HR'       -0.9480
      'M'        0.1246   'Height'    0.4039
      'Weight'   0.0501   'Weight'   -0.3758
      'age'     -0.0267   'M'         0.0584
                -0.0001   'age'       0.0445

HR    'HR'       1.0000   'Height'   -1.0000
                (0.7461)             (3.5811)
      'M'        0.9977   'VO2max'    0.6936
      'Height'   0.9580   'HR'        0.6396
      'Weight'   0.2107   'Weight'    0.4979
                -0.1902   'M'         0.1032
      'VO2max'  -0.1173   'age'      -0.0772


        Female Group 3      Female Group 4

Skin  'M'        1.0000   'Height'   1.0000
                (0.0145)            (0.0691)
      'Height'  -0.9927   'VO2max'  -0.7113
      'HR'       0.9741   'HR'       0.4191
      'Weight'   0.3912   'M'        0.2255
      'age'      0.1264   'Weight'  -0.1747
      'VO2max'   0.1055   'age'      0.0765

Core  'Height'   1.0000   'Height'   1.0000
                (0.0331)            (0.3721)
      'VO2max'  -0.6904   'Weight'  -0.1253
      'HR'      -0.5064   'VO2max'  -0.0920
      'Weight'  -0.2698   'HR'      -0.0688
      'M'        0.1636   'age '     0.0284
      'age'      0.0627   'M'        0.0103

HR    'HR'       1.0000   'Height'  -1.0000
                (1.1482)            (14.1845)
      'Height'  -0.9973   'HR'       0.1828
      'VO2max'   0.8577   'Weight'   0.1232
      'Weight'   0.3942   'VO2max'   0.0477
      'M'        0.1622   'M'        0.0248
      'age'     -0.0050   'age'     -0.0240


         Female Group 3       Female Group 4

Skin  'Height'  -1.0000   'HR'       -1.0000
                (0.3742)             (0.2593)
      'Weight'   0.9927   'VO2max'   -0.9295
      'M'        0.9741   'Height'    0.1834
      'age'     -0.3912   'M'         0.1763
      'VO2max'  -0.1264   'Weight'    0.1172
      'HR'      -0.1055   'age'      -0.0612

Core  'VO2max'  -1.0000   'Height'    1.0000
                (0.0249)             (0.4716)
      'HR'      -0.6904   'HR'       -0.1713
      'Height'  -0.5064   'VO2max'   -0.1411
      'M'        0.2698   'Weight'   -0.1178
      'Weight'  -0.1636   'age'       0.0245
      'age'     -0.0627   'M'         0.0117

HR    'Height'  -1.0000   'Height'   -1.0000
                (1.7732)            (17.0163)
      'HR'       0.9973   'Weight'    0.1329
      'VO2max'   0.8577   'HR'        0.0898
      'Weight'   0.3942   'M'         0.0310
      'M'        0.1622   'age'      -0.0309
      'age'     -0.0050   'VO2max'   -0.0064


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Tai S. Jang

Anthony E. Iyoho

Larry G. Berglund, PhD, PE


Satish S. Nair, PhD, PE


Tai S. Jang and Anthony E. Iyoho are PhD students and Satish S. Nair is a professor in Electrical and Computer Engineering at the University of Missouri, Columbia, MO. Larry G. Berglund works in the Biophysics and Biomodeling Division, U.S. Army Research Institute of Environmental Medicine, Natick, MA.
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Author:Jang, Tai S; Berglund, Larry G; Iyoho, Anthony E; Nair, Satish S
Publication:ASHRAE Transactions
Article Type:Report
Geographic Code:1USA
Date:Jan 1, 2009
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