Modeling thermoregulatory responses during high-intensity exercise in warm environments

Abstract

The six cylinder thermoregulatory model (SCTM) has been validated thoroughly for resting humans. This type of modeling is helpful to predict and develop guidance for safe performance of work and recreational activities. In the context of a warming global climate, updating the accuracy of the model for intense exercise in warm environments will help a wide range of individuals in athletic, recreational, and military settings. Three sets of previously collected data were used to determine SCTM accuracy. Dataset 1: two groups [large (LG) 91.5 kg and small (SM) 67.7 kg] of individuals performed 60 min of semirecumbent cycling in temperate conditions (25.1°C) at metabolic rates of 570–700 W. Dataset 2: two LG (100 kg) and SM (65.8 kg) groups performed 60 min of semirecumbent cycling in warm/hot environmental conditions (36.2°C) at metabolic rates of 590–680 W. Dataset 3: seven volunteers completed 8-km track trials (∼30 min) in cool (17°C) and warm (30°C) environments. The volunteers’ metabolic rates were estimated to be 1,268 W and 1,166 W, respectively. For all datasets, SCTM-predicted core temperatures were found to be similar to the observed core temperatures. The root mean square deviations (RMSDs) ranged from 0.06 to 0.46°C with an average of 0.2°C deviation, which is less than the acceptance threshold of 0.5°C. Thus, the present validation shows that SCTM predicts core temperatures with acceptable accuracy during intense exercise in warm environments and successfully captures core temperature differences between large and small individuals.

NEW & NOTEWORTHY The SCTM has been validated thoroughly for resting humans in warm and cold environments and during water immersion. The present study further demonstrated that SCTM predicts core temperatures with acceptable accuracy during intense exercise up to 1,300 W in temperate and warm environments and captures core temperature differences between large and small individuals. SCTM is potentially useful to develop guidance for safe operation in athletic, military, and occupational settings during exposure to warm or hot environments.

INTRODUCTION

Heat-related injuries pose a significant threat to the health and safety of civilians, the military, and occupational personnel (1, 2). In occupational settings, most heat injuries and deaths are primarily ascribable to high core temperatures (exertional hyperthermia). Excess environmental heat is the leading cause of death among all weather-related injuries (Occupational Safety and Health Administration, https://www.osha.gov/heat-exposure/rulemaking, accessed on July 26, 2023). Each year in the United States, there are an average of 67,512 emergency department visits due to heat and 700 heat-related deaths (https://ephtracking.cdc.gov/Applications/heatTracker/, accessed on July 3, 2023). In Europe, heat-related deaths are estimated to be ∼25,000 every year (3). Due to global climate change, heat or extreme heat in summer is becoming both more severe and more common, including in many places where it was uncommon until recently (4–7).

Heat stress becomes dangerous when the body is not able to maintain heat balance through thermoregulation. In such conditions, core temperature can rise continuously (called “uncompensable” heat stress), and ultimately, heat-related illnesses occur in the form of heat exhaustion or heat stroke. Human heat balance is defined by the prevailing rates of heat loss from the skin surface to the surrounding environment and rates of internal metabolic heat production. Heat loss is primarily determined by environmental conditions and decreases as environmental temperature and/or humidity increase. Heat production is primarily determined by metabolic rate during exercise or physical activity and ranges from ∼200 W for light manual work to 400 W for moderately strenuous activities to greater than 1,000 W during intense exercise (8, 9). For some activities, ∼80% of metabolic energy expenditure is released as heat that the body has to dissipate to maintain heat balance and thus prevent heat storage (10, 11), and the remaining 20% conducts mechanical work. Thus, exercise can cause or exacerbate heat strain in warm or hot environments that may already be associated with a high risk of heat illness.

Mathematical modeling of thermoregulatory responses is a useful tool to estimate performance limitations in individuals exposed to environmental extremes. Numerous mathematical models of human thermoregulation have been developed to predict human thermal responses to heat, cold, and water immersion over the past 50 years (12–14). Most of these models are rational models and are based on the first principles of physiology and the physical laws of heat transfer. Generally, these models are mathematical constructs that solve the heat balance equation within the body and between it and the environment. Their outputs are numerical solutions, representing the body’s thermal responses to the environment given a metabolic rate and various physiological systems responsible for thermoregulation and metabolism.

The human thermoregulation system is modeled as a combination of a passive system and an active system (12, 15, 16). The passive system describes anatomical characteristics of the modeled individual, body tissue thermal properties, heat transfer mechanisms within the body (e.g., adjacent tissue types), and heat transfer mechanisms between the skin, clothing, and environment. The active system refers to thermoregulatory mechanisms that either alter skin surface heat transfer (i.e., vasodilation, vasoconstriction, sweating) or internal heat production (i.e., shivering). Differences among thermoregulatory models stem from the descriptions of the passive and active systems and how they interact. Thermoregulatory models have been widely used for various applications, e.g., the development of operational doctrine for heat and cold injury management (17–19), and analyzing heat transfer mechanisms of rapid brain cooling (20, 21). One such thermoregulatory model is the six cylinder thermoregulatory model (SCTM) developed at the US Army Research Institute of Environmental Medicine (22, 23). The SCTM has been validated for a broad range of conditions, including resting exposure to extreme cold and hot air (22, 24), moderate exercise (22, 25), and rest and exercise during cold water immersion (23, 26). The SCTM has been actively used to develop guidance for military and civilian activities in the cold, evaluate performance of personal protective equipment (PPE), and has been integrated into digital decision aids for operational use (24, 27, 28).

However, the accuracy of the SCTM during intense exercise in warm environments remains uncertain. Three datasets from published literature and studies of human thermal responses to intense exercise in warm and cool environments (29–31) are available for SCTM validation. The goals of the present analysis were to use these datasets to validate and/or update SCTM accuracy for the prediction of thermal responses during intense exercises and to determine if SCTM can acceptably discriminate individual differences due to body size in humans working at the same absolute rates of metabolic heat production.

MATERIALS AND METHODS

Dataset 1: Exercise in Neutral Environments

Cramer and Jay (30) conducted an experiment that examined thermal responses between two groups of individuals (men) with distinctly different body sizes. Following 30 min of baseline data collection while seated on a cycle ergometer, 16 participants of either small mass (n = 8) or large mass (n = 8) performed 60 min of semirecumbent cycling in temperate ambient conditions (25.1 ± 0.5°C, 36.8 ± 12% relative humidity (RH), and 1.2 ± 0.1 m·s⁻¹ air velocity) at metabolic rates of ∼570 ± 34 W or 672 ± 60 W for small group (SM) and 575 ± 94 W or 706 ± 68 W for large group (LG). The mean physical attributes of the small group (SM) were: 67.6 ± 5.6 kg, 1.73 ± 0.06 m, and 12.5 ± 2.6% body fat. The mean physical attributes of the large group (LG) were: 91.5 ± 6.8 kg, 1.81 ± 0.05 m, and 22.0 ± 5.2% body fat. Rectal temperatures were measured using thermocouple probes (Mon-a-therm, Mallinckrodt Medical, St. Louis, MO). Skin temperatures were measured with thermistors integrated into heat flux sensors (Concept Engineering, Old Saybrook, CT) at eight locations.

Dataset 2: Exercise in Warm Environments

Similar to dataset 1, Ravanelli et al. (31) also examined the thermoregulatory responses of two groups of individuals (men), but in this case, exercising in hot and humid conditions. Beginning after 30 min of rest, 16 participants of either small or large mass cycled on an ergometer at metabolic rates of ∼593 ± 44 W and 677 ± 71 W for 60 min in a 36.2 ± 0.2°C, 70 ± 1% relative humidity, and 1.2 m·s⁻¹ air velocity environment on four occasions. These trials will herein be referred to as “sustained work,” as no rest was taken for the duration of the cycling. Physical attributes of the SM participants were: 65.8 ± 6.2 kg, 1.72 ± 0.03 m, and 12.3 ± 3.5% body fat. Physical attributes of the LG participants were: 25 ± 3 yr, 100.0 ± 13.1 kg, 1.87 ± 0.05 m, and 24.9 ± 8.2% body fat. As with dataset 1, rectal temperatures were measured using thermocouple probes, and the probe was inserted to a depth of 20 cm past the anal sphincter.

Dataset 3: High-Intensity Exercise in Cool and Warm Environments

Ely et al. (29) investigated whether running performance is impaired when rectal temperature is 40°C and skin temperature remains modest. Seven volunteers (3 men and 4 women) completed 8-km track time trials in cool air temperatures (T_a ∼17°C, 45% RH) and warm conditions (T_a ∼30°C, 61% RH). The mean radiant temperature was estimated to be 45°C. Finishing times were 27.9 ± 2.3 min and 29.8 ± 3.1 min for the cool and warm conditions, respectively. The trials were run on measured tracks: 400 m (outdoors, for warm conditions) or 200 m (indoor, for cool conditions). Physical attributes of the volunteers were 62.9 ± 9.3 kg and 1.71 ± 0.09 m. Before the time trial, volunteers were instrumented with a heart rate monitor (Acti-heart; Mini Mitter, Bend, OR). Once instrumented, volunteers completed a 15–30-min self-paced warm-up jog. After the warm-up period, volunteers inserted a telemetry pill (Jonah core body temperature capsule, Mini Mitter) as a suppository 8–10 cm beyond the anal sphincter. The rectal temperature and chest skin temperature were logged continuously. The metabolic rates were not measured, thus, the following equation was used to estimate the metabolic rate during the time trials for each volunteer (9):

$$M=0.5926\hspace{0.17em}·v^2+0.1186\hspace{0.17em}·v+5.6986\hspace{0.17em}[W\hspace{0.17em}·\hspace{0.17em}k{g}^{-1}]$$ (1)

where M is the metabolic rate in W·kg⁻¹ and v is the running speed m·s⁻¹. In SCTM, the default mechanical efficiency is 20% and thus 80% of the calculated metabolic rate become metabolic heat production.

All previous research for the datasets used in the present analysis was approved by the human use committee and relevant ethical committees of the institutions at which the research was conducted (29–31).

Application 1: Effects of Body Mass on Thermal Responses

To demonstrate that SCTM is able to differentiate thermal responses of individuals with different body masses, SCTM was used to simulate thermal responses of 10 individuals during exercise at fixed metabolic rate per mass of 6 W·kg⁻¹ and a fixed metabolic rate of 600 W at 40°C, 40% RH, and 1.5 m·s⁻¹. The characteristics of the volunteers were taken from a previous study (32), height 1.76 ± 0.1 m, weight 73.5 ± 17.8 kg, and fat 24.8 ± 6.2%.

Application 2: Safe Environment Limits during Light and Moderate Exercise

To demonstrate the use of SCTM for evaluation of heat stress, we used SCTM to predict thermal responses of an individual during light work of 250 W and moderate work of 350 W at various environmental conditions. Predicted thermal responses were used to identify environments where the predicted core temperature rises above 38°C within 6 h, indicating risk of hyperthermia and heat illness. This individual is 1.7 m and 78 kg and wears summer clothing.

Six Cylinder Thermoregulatory Model

The SCTM is a rational model and is based on the first principles of physiology and the physical laws of heat transfer (22, 23). As shown in Fig. 1, the human body is represented as six cylinders each with six concentric layers. The six cylinders represent the head, torso, arm, hand, leg, and foot; four layers represent the body tissue types (i.e., core, muscle, fat, and skin) and two represent an air space and clothing layer. SCTM relies on simplified mechanisms of thermoregulation (e.g., vasomotor changes, metabolism, and sweat), which collectively function to maintain homeostasis or minimize changes in the internal body temperature. Blood flow in SCTM is an independent compartment represented as a one-loop circulatory system. Human temperature regulation is controlled by central (mostly hypothalamic) sites, which integrate thermal inputs from both central and peripheral thermoreceptors to elicit appropriate efferent thermoregulatory responses (33). When the afferent information indicates increases in body temperature, reflex heat dissipation effectors (sweating, cutaneous vasodilation) are elicited to counteract these increases in a negative feedback loop (34, 35). When the afferent information indicates decreases in body temperature, reflex heat conservation and/or generation effectors (cutaneous vasoconstriction, shivering, nonshivering thermogenesis) are elicited to counteract these decreases.

Figure 1.

Schematic of six cylinder model of human thermoregulation system (24).

The energy balance equation for each cylinder in one-dimensional cylindrical coordinates is:

$${\rho }_i{c}_i\frac{\partial T_i}{\partial t}={\dot{M}}_i+{\lambda }_i\{\frac{{\partial }^2{T}_i}{\partial r^2}+\frac{1}{r}·\frac{\partial T_i}{\partial r}\}+{\beta }_i{Q}_i{\rho }_b{c}_b\left(T_b-T_i\right)$$ (2)

where ρ_i is the density (kg·m⁻³), c_i is the specific heat (J·kg⁻¹°C⁻¹), i is the cylinder number, T_i is the temperature (°C) of the tissue, t is the time (s), ${\dot{M}}_i$ is the total metabolic rate (W·m⁻³), λ is the thermal conductivity (W·m⁻¹·°C⁻¹) of the tissue, r is the cylinder radius (m), β is the countercurrent factor by which the heat exchange between arterial blood and venous blood is approximated (dimensionless), Q_i(r,t) is the blood flow rate per volumetric unit of the tissue (m³·s⁻¹·m⁻³), ρ_b is the density of the blood (kg·m⁻³), c_b is the specific heat of the blood (J·kg⁻¹°C⁻¹), and T_b(t) is the temperature of the blood pool (°C).

The skin surface is the SCTM boundary. Convection, radiation, and evaporation all contribute to the heat exchange at the boundary and the boundary condition is described as:

$$-\lambda \frac{\partial T}{\partial r}=R+C+E$$ (3)

where λ is the thermal conductivity of the tissue (W·m⁻¹·°C⁻¹), T is the tissue temperature (°C), r is the radius (m), R is the radiative heat exchange (W·m⁻²), C is the convective heat exchange (W·m⁻²), and E is the evaporative heat exchange (W·m⁻²).

Assuming the mean radiant temperature is equal to the ambient temperature (T_a), the dry and evaporative heat losses from the body surface to the environment are described by

$$R+C=\frac{T_s-T_a}{R_{cl}+\frac{1}{f_{cl}\hspace{0.17em}·\hspace{0.17em}(h_c+h_r)}}\hspace{0.17em}[\text{W}·{\text{m}}^{-2}]$$ (4)

$$E=w\hspace{0.17em}·\hspace{0.17em}\frac{P_{sk}-P_a}{R_{cl,e}+\frac{1}{f_{cl}\hspace{0.17em}·\hspace{0.17em}{h}_c\hspace{0.17em}·\hspace{0.17em}LR}}\hspace{0.17em}[\text{W}·{\text{m}}^{-2}]$$ (5)

where T_s is the skin temperature (°C); R_cl is clothing intrinsic resistance (m²·°C·W⁻¹); f_cl is clothing area factor, the ratio of the clothing surface to body surface area (dimensionless); h_c is convective heat transfer coefficient (W·°C⁻¹·m⁻²); h_r is radiative heat transfer coefficient; w is skin wettedness (dimensionless), 0 for dry skin and 1 for completely wet skin; P_sk is water vapor pressure at the skin (kPa); Pa is water vapor pressure of the ambient environment (kPa; R_cl,e is clothing intrinsic evaporative resistance (m²·kPa·W⁻¹); and LR is the Lewis ratio, 0.0165°C·Pa⁻¹. Evaporative heat loss is regulated by the thermoregulation system and restricted by skin and environmental conditions. E_max is the maximal evaporative heat loss (W·m⁻²) when the skin is saturated (w = 1.0) as described by:

$$E_{max}=\frac{P_{sk,s}-P_a}{R_{cl,e}+\frac{1}{f_{cl}\hspace{0.17em}·\hspace{0.17em}{h}_c·LR}}\hspace{0.17em}[\text{W\hspace{0.17em}}·\hspace{0.17em}{\text{m}}^{-2}]$$ (6)

where P_sk,s is the saturated water vapor pressure at skin (kPa). E_max reduces as the vapor pressure P_a of the environment increases and reduces to zero when the saturated vapor pressure at skin is equal to the vapor pressure of the environment.

SCTM inputs include individual characteristics (i.e., height, weight, body fat percentage), environmental (i.e., air/water temperature, humidity, and wind velocity), and clothing (clothing insulation, moisture permeability index) parameters for each of the six cylinders. Outputs from the model include predicted physiological responses in each of the six body regions: including core temperature (the center of the torso cylinder), skin temperatures, and sweat rates.

The mean values mentioned in datasets 1, 2, and 3 were used as inputs, including height, weight, body fat percentage, metabolic rate, air temperature, relative humidity, wind speed, etc. SCTM was run to simulate the mean thermal responses. In this study, the SCTM predicts group mean responses and not individual responses.

RESULTS

As shown in Figs. 2 and 3, SCTM predicted thermal responses during exercise at 570 W or 672 W from SM and 575 W or 706 W for LG in 25°C environments (dataset 1). Predicted core temperatures were compared with measured core temperatures for SM and LG individuals. Figure 2 shows the predicted and measured core temperatures during exercise at 672 W for SM and 706 W for LG. Figure 3 shows the predicted and measured core temperatures during exercise at 570 W for SM and 575 W for LG. The predicted core temperatures were within 1 standard deviation (or closer) to the actual measured temperatures except for SM in dataset 1. The root mean square deviation (RMSD) was used for goodness of fit comparison of model output predictions (36). The RMSD was calculated between time courses of the predicted and measured values at each time point (with an interval of 5 min). The RMSD values are shown in Table 1.

Figure 2.

Comparison of predicted and measured core temperatures (means ± SD) during exercise at metabolic rates of 706 W for LG (A) and 672 W for SM (B) in 25°C environments. LG, large; SM, small.

Figure 3.

Comparison of predicted (mean) and measured core temperatures (means ± SD) during exercise at metabolic rates of 575 for LG (A) and 570 W for SM (B) in 25°C environments. LG, large; SM, small.

Table 1.

Root mean square deviations (°C)

	LG	SM
Dataset 1 Fig. 2	0.06	0.19
Dataset 1 Fig. 3	0.08	0.24
Dataset 2 Fig. 4	0.31	0.36

	Cool	Warm
Dataset 3 Fig. 5	0.21	0.13

Figure 4 shows SCTM predictions of core temperature during exercise at 590 W for SM and 677 W for LG in 35°C environments along with directly measured values (dataset 2). The predicted core temperatures are close to the measured values or within the SD. As noted above, RMSD values are shown in Table 1.

Figure 4.

Comparison of predicted (mean) and measured core temperatures (means ± SD) during exercise at metabolic rates of 677 W for LG (A) and 593 W for SM (B) in 35°C environments. LG, large; SM, small.

For the third dataset, SCTM predicted thermal responses during high-intensity exercise in warm and cool environments. For this analysis, metabolic rates were estimated to be 1,166 W for the warm condition and 1,268 W for the cool condition (using Eq. 1). In this study, the volunteers had a warm-up period to prepare for the run, thus their body temperature was elevated, even though they started the run in thermoneutral conditions. The default initial conditions for SCTM are the following thermal neutral conditions: core temperature (T_c) = 36.79°C and T_s = 33.13°C at T_a = 29°C, 40% RH, and 0.1 m·s⁻¹. Thus, to make the simulation more realistic, the SCTM was run with a warm-up period. SCTM was run to generate initial conditions that matched the observed core temperatures before the time trial started. Figure 5 shows the predicted and measured core temperature in warm and cool conditions. The running speed varied by individual. In warm conditions, four volunteers remained for 30 min. In cool conditions, only two volunteers remained for 30 min. The predicted core temperatures are close to the measured values or within the SD. The RMSD values for cool and warm conditions are shown in Table 1.

Figure 5.

Comparison of predicted and measured core temperatures (means ± SD) while running at ∼1,268 W in cool (17°C, B) and ∼1,166 W in warm (30°C, A) environments, with initial conditions modified to account for warm-up period before time trials.

Figure 6 shows the effects of body mass on the thermal responses during exercise in W·kg⁻¹ and exercise in W (application 1). This result demonstrates that thermal responses vary with body mass.

Figure 6.

Predicted core temperatures of 10 volunteers with different body masses (52 kg open circle to 102 kg black circle) during exercise at 6 W·kg-1 (A) and 600 W metabolic rates (B) in 30°C, 40% RH, and 1.5 m·s⁻¹ environments.

Figure 7 shows curves that separate environmental conditions (application 2). The environmental conditions above the curve are conditions that in the predicted core rise above 38°C, indicating a risk of hyperthermia and heat illness. The curves shift downward significantly when exercise intensities increase, e.g., 350 W versus 250 W.

Figure 7.

Environmental conditions above the curves indicate that the predicted core temperature reaches 38°C for light exercise (250 W) and for moderate exercise (350 W) while wearing summer clothing.

DISCUSSION

Thermoregulatory models have been widely used in a variety of applications, including prevention of heat and cold injury (24, 37), as well as mission planning tools, e.g., probability of survival decision aid (PSDA), and the cold weather ensemble decision aid (CoWEDA) (24, 27). Continuous validation remains critical to ensuring models predict accurately under various conditions and for individual differences (e.g., SM, LG). Therefore, herein we validated the SCTM under high-intensity exercise conditions, using measured core temperature data from three previously published human studies.

The major new findings of the present study were 1) that SCTM accurately predicted group mean core temperatures during exercise at high intensity up to 1,268 W metabolic rates (within 1 SD) and 2) that the accuracy of the SCTM in predicting core temperature during exercise in the heat was not different between groups of subjects with larger versus smaller body size (dataset 2, RMSD 0.31 and 0.36°C, respectively). These results are summarized in Figs. 2, 3, 4, and 5. For model evaluation, a core temperature RMSD < 0.5°C indicated the model’s predicted values were in good agreement with the measured outcomes (38, 39). All RMSDs in Table 1 are less than this threshold. These are important updates to the accuracy of the SCTM and indicate a wider range of applicability and utility for this model, which has already been used in a range of mission plannings, e.g., PSDA and CoWEDA (24, 27, 28), as well as design and evaluation of personal protective equipment (25, 40, 41).

As indicated in Eq. 2 and Eq. 3, core temperature is primarily determined by a combination of metabolic heat production and environmental conditions. The magnitude of thermal strain imposed by exercise in warm environments depends on the metabolic rate, capacity for heat exchange with the environment, and body mass. Resting metabolic rates are approximately ∼100 W and may increase by up to an order of magnitude during exercise, e.g., 500–700 W during exercise on ergometers, and 1,268 W during running. Approximately 80% of heat production becomes a source of heat gain (temperature increase) in the body (10, 11). The percentage is highly situation dependent and likely even higher (42, 43). In the absence of appropriate heat dissipation responses, this will result in high core temperature and can induce or exacerbate thermal strain. We have previously demonstrated that the SCTM was valid compared with directly measured body temperatures during exercise at ∼440 W in warm and humid environments (22, 25, 44). This study demonstrates that SCTM predicts core body temperature with acceptable accuracy during exercise at high intensities of exercise (up to 1300 W). Thus, SCTM is applicable to a wide range of exercise conditions.

As shown in Figs. 2, 3, and 4, SCTM is capable of predicting differences in thermal responses of SM and LG volunteers, which is increasingly important due to the range of body sizes and increasing rates of overweight and obesity in Western civilization (45). For this purpose, we used the inputs of height, weight, and fat% within the SCTM to define SM and LG groups. Figure 6 shows further that SCTM-predicted thermal responses vary with body mass during exercise in W·kg⁻¹ and exercise in W. The tendencies of SCTM predictions are consistent with physiological results observed during exercise at metabolic rates in W·kg⁻¹ and in W (30, 31). Exercise in W·kg⁻¹ minimizes the systematic impact of body size on thermal responses compared with exercise in W, but individual differences still exist and increase as exposure times increase. The predicted results in Fig. 6 show, for example, that the core temperature varied from 38.4 to 39.0°C after exercise in 6 W·kg⁻¹ for 60 min. The observed core temperatures of 24 volunteers ranged from 37.8 to 38.9°C after exercise at 6 W·kg⁻¹ in 40°C environments for 40 min (46). In addition to body size, individual differences are also likely related to surface/mass ratio, maximum skin wettedness, acclimatization, and training status (47). Figure 8 is the predicted core temperatures at the end of 60 min of exercise (all time series results are in Fig. 6). Core temperatures at the absolute metabolic rate of 600 W decrease as the body mass increases. This is consistent with previous observations that the body mass is negatively correlated to the core temperatures during exercise or activity at a fixed metabolic rate in W (8). Thus, SCTM is able to simulate the effects of differences in size (body mass and surface area) on human thermoregulation.

Figure 8.

Volunteer body masses and predicted core temperatures at the end of 1 h exercise at 6 W·kg⁻¹ and 600 W metabolic rates in 30°C, 40% RH, and 1.5 m·s⁻¹ environments.

Another novel aspect of the present analysis was that we were able to alter the initial core temperature using the SCTM to match the fact that, in dataset 3, the participants had warmed up before the time trials. We were able to use the model to reproduce the slightly elevated core temperatures before starting exercise and thereby improve prediction accuracy. In most previous uses of the SCTM model, the simulations have assumed that a human body was at thermal neutral conditions before any exposure. The thermal neutral condition refers to conditions that a person rests in an environment of 29°C, 40% RH, and wind speed of 0.1 m·s⁻¹. Corresponding core and mean skin temperatures are 36.8°C and 33.1°C, respectively. For the running study shown in Fig. 5, all volunteers engaged in warm-up exercises before the time trials, and their core temperatures were between 37.3 to 38.4°C and 37.9 to 38.7°C for cool and warm conditions. Our ability to include modeling of the warm-up period therefore avoided the potential for inaccurate results if that aspect had been ignored.

In contrast, for the studies in Figs. 2, 3, and 4, the volunteers rested before trials, and thus, their core temperatures were close to the thermal neutral conditions and no adjustment was necessary. This is especially salient given that previous studies have demonstrated that time to heat exhaustion can be increased by lowering body temperature before exercise, i.e., initial conditions (48). Thus, when the initial core temperature deviates a certain amount from the thermal neutral core temperature, adjustment is necessary to improve the prediction accuracy. Further research is needed to determine the specific factors that contribute to whether adjustment of the initial condition is necessary.

Figure 7 shows that safe exposure limits are significantly influenced by metabolic rates. The curves are also influenced by clothing properties, as shown in Eqs. 3–6. Furthermore, the curves indicate that, besides metabolic rate, it is the combination of temperature and humidity that determines the limit. In a recent study, young volunteers conducted light work with a metabolic rate of 250 W and were exposed to progressive heat stress to find the environmental conditions above which heat balance cannot be maintained (49–51). Those observed limits, e.g., 36°C/56% RH and 38°C/46% RH, are similar to the predicted limits in Fig. 7. Thus, SCTM can be used to develop individualized guidance for safe operation during exercise in warm or hot environments.

“Real World” Considerations

From a physiological perspective, the interpretation of the present results should include a few caveats. First, the exercise intensities studied here were (by design) very high—these intensities are not achievable at all by the majority of the population, and very unlikely to be achieved by people who are sedentary or otherwise have low fitness levels. Therefore, the prediction and validation are limited to individuals with relatively high fitness levels. Second, for those who can achieve the intensities discussed here, such as certain types of military operations or training, the exercise would often be conducted discontinuously, such as using prescribed work-rest cycles, to minimize the risk of reaching dangerous levels of hyperthermia. The SCTM can potentially be very useful in optimizing the design of such intermittent exercise. In particular, the thermal inertia associated with larger individuals would need to be taken into consideration since core temperature would likely decrease less in those individuals during the rest breaks compared with smaller individuals.

Although the present validation demonstrates that the SCTM predicts group mean core temperatures within an acceptable range, SCTM should be used with caution. The magnitude of differences between the predicted and measured values varies over the simulation period. This may affect the decision point based on predicted values. One approach to address this issue is that the SCTM is run iteratively with both the input values and a set of possible input values (e.g., one variable change by ±SD), and the distribution of predicted outcomes is then used to determine the decision point.

Limitations

The validation in this paper is limited to the group responses instead of individual responses. Individual differences in thermoregulation have been comprehensively studied, but more data are still required to establish algorithms that describe the effects of biophysical and physiological factors on individual responses to heat stress (8, 52). Thus, SCTM’s predictions of individual thermal responses are limited to weight, height, and fat%, and do not incorporate additional individual factors like V̇o_2max and acclimatization. The predicted SM results in Figs. 2, 3, and 4 appeared to be consistently higher than the measured values after 20–30 min. Reasons behind this are likely related to individual factors such as V̇o_2max (SM had high V̇o_2max ∼55 mL·kg⁻¹·min⁻¹), but currently SCTM predictions cannot confirm if this is the reason. In addition, the durations of datasets in this study are all less than 1 h, thus, the accuracy of SCTM prediction for high intense exercise beyond 1 h needs to be validated further.

Conclusions

Our present results indicate that the SCTM acceptably estimates core temperature responses during exercise at metabolic intensities of up to 1,300 W in temperate and warm weather. Similarly, it accurately captures core temperature differences between large and small individuals during exercise working at the same absolute heat production rates. This study also shows that appropriate adjustment of the initial core temperatures improves the accuracy of SCTM predictions when the initial core temperature deviates a certain amount from thermal neutral values. Further research is required to determine conditions where such adjustment is necessary. We, therefore, conclude that the SCTM can be used to develop individualized guidance for safe operation during intense exercise in warm environments.

DATA AVAILABILITY

Physiological data for this study were obtained from the following previously published articles: Refs. 29, 30, and 31. Additional simulation data will be made available upon reasonable request.

DISCLAIMERS

Approved for public release; distribution is unlimited. The opinions or assertions contained herein are the private views of the authors and are not to be construed as official or as reflecting the views of the Army, or the Department of Defense. Any citations of commercial organizations and trade names in this report do not constitute an official Department of the Army endorsement or approval of the products or services of these organizations.

DISCLOSURES

O. Jay is an editor of Journal of Applied Physiology and was not involved and did not have access to information regarding the peer-review process or final disposition of this article. An alternate editor oversaw the peer-review and decision-making process for this article. None of the other authors has any conflicts of interest, financial or otherwise, to disclose.

AUTHOR CONTRIBUTIONS

X.X., A.P.W., and N.C. conceived and designed research; X.X., O.J., and B.R.E. performed experiments; X.X., T.P.R., and A.P.W. analyzed data; X.X. interpreted results of experiments; X.X. prepared figures; X.X. drafted manuscript; X.X., T.P.R., A.P.W., O.J., B.R.E., and N.C. edited and revised manuscript; X.X., T.P.R., and N.C. approved final version of manuscript.