A 3-D virtual human thermoregulatory model to predict whole-body and organ-specific heat-stress responses

Heat-related illnesses induced by strenuous physical activity, exposure to adverse environmental conditions, or their combination necessarily involve an increase in core body temperature (Epstein and Roberts 2011; Bouchama and Knochel 2002; Epstein et al. 2012). Heat illness can range from less severe muscle cramps to heat exhaustion and to potentially life-threatening heat stroke (Bouchama and Knochel 2002; Epstein et al. 2012; Varghese et al. 2005), where heat-induced cytotoxicity initiates a systemic inflammatory response that may result in multi-organ failure and death (Varghese et al. 2005). While measurements of core body temperature through a rectal probe can help assess the severity of the body’s heat-stress state in total, they may underestimate localized heat loads and the resulting peak temperatures in vital organs, such as the liver and the brain (Jardine 2007; Wang et al. 2014; Cheshire 2016), masking the actual risk of organ injury. Because it is not feasible to measure organ temperature in humans while performing strenuous physical activity, one way to address this challenge is to use computational models to characterize the spatiotemporal distribution of temperatures throughout the entire body resulting from exertional and environmental heat stressors and use this information to infer potential organ-specific injury.

Numerous computational models of human thermoregulation have been developed over the past 50 years. However, the majority of these models are not anatomically realistic (Gagge 1973; Gagge 1971; Nishi and Gagge 1971; Stolwijk 1971; Fiala et al. 1998, 1999, 2001, 2012) as they represent the entire human body either as a single segment (Gagge 1973, 1971; Nishi and Gagge 1971) or as being composed of multiple segments (Stolwijk 1971; Fiala et al. 1998, 1999, 2001, 2012). For example, Gagge and coworkers modeled the entire human body as a single segment with two concentric cylinders, one to represent the body core and the other the outer layer of the skin (Gagge 1973, 1971; Nishi and Gagge 1971). In contrast, the multiple-segment models represent each part of the body, such as the arms and the legs, as a separate segment, each consisting of one or more concentric cylinders (Stolwijk 1971; Fiala et al. 1998, 1999, 2001, 2012). While the single- and multiple-segment models have been shown to reasonably predict core body temperature as well as skin temperature under different heat-stress conditions (Fiala et al. 1998, 2001), they inherently lack the spatial resolution to predict temperature responses at the organ and tissue levels (Nelson et al. 2009), which limits their applicability.

To overcome these limitations, Nelson et al. and Bernardi et al. separately developed voxel-based, anatomically detailed thermoregulatory models to predict the thermal response in humans exposed to high environmental temperatures (Nelson et al. 2009) and radio frequency radiation (Bernardi et al. 2003), respectively. In this formulation, they first divided the entire human body into equal-sized volume elements, or voxels, and then, using a finite difference-time domain algorithm, applied macroscopic energy balance equations to each voxel to compute the spatiotemporal distribution of temperatures throughout the body. While this voxel-based approach allows for temperature predictions at each internal organ, including the skin, it is unclear the extent to which the relatively large length of the voxel elements (2 mm for (Nelson et al. 2009), and 5 or 6 mm for (Bernardi et al. 2003)) affects the accuracy of the temperature predictions. In addition, neither model has been used to quantify the effects of exertional heat stress, which is known to be the primary driver for increases in core body temperature when compared to environmental stressors (Stolwijk 1971; Sawka et al. 1993; Nielsen and Nielsen 1962).

Previously, we developed a three-dimensional (3-D), anatomically detailed thermoregulatory finite element (FE) model of a rat, where we demonstrated the ability to accurately predict the spatiotemporal temperature distributions throughout the animal for a whole host of environmental as well as exertional stress conditions, including cooling (Rakesh et al. 2013, 2014). Here, we extended this framework and developed a FE model for a human—a 3-D thermoregulatory virtual human model—using an anatomically realistic description of a 50th percentile U.S. male that included 25 major organs, such as the brain, heart, lungs, liver, intestines, as well as the skeletal system, with FE sizes as small as 0.04 µm. The model takes environmental conditions, physical activity, and clothing as inputs and predicts the spatiotemporal distribution of temperatures in the entire virtual human as an output. The model accounts for the transfer of energy within the body through macroscopic energy balance equations, heat transfer from the body to the environment through convection, radiation, respiration, and perspiration, the major thermoregulatory mechanisms of the human body, including shivering, sweating, as well as vasoconstriction and vasodilation, and the day-night cycle of temperature changes due to circadian-rhythm effects. We validated our model by comparing our predictions of organ, muscle, and rectal temperatures [which is often used as a surrogate for core body temperature under heat-stress conditions (Casa et al. 2007, 2015)] with experimental measurements. For brain, liver, stomach, bladder, esophagus, and muscles (vastus medalis and triceps brachii), we compared our model predictions against temperature measurements obtained under normal resting conditions. For rectal temperature validation, we used data from three separate studies encompassing a range of time-varying exertional activity levels, different values of atmospheric temperature, relative humidity, and wind speed, as well as different clothing conditions.

In this study, we developed an anatomically detailed 3-D thermoregulatory virtual human model representative of a 50th percentile U.S. male (Fig. 2). This FE model predicts the spatiotemporal temperature distributions throughout the human body, including 25 major organs, such as the brain, heart, lungs, liver, intestines, as well as the skeletal system, as a function of environmental conditions, physical activity, and clothing. It includes a detailed description of the various heat transfer mechanisms occurring within the body and between the body and the environment through convection, radiation, respiration, and perspiration (Fig. 3). It also includes the body’s thermoregulatory mechanisms of shivering, sweating, vasoconstriction, and vasodilation as well as the body’s internal circadian-rhythm response to the day–night cycle of temperature changes. This is in contrast with previous approaches that either represented the human anatomy very simplistically using concentric cylinders (Gagge 1973; Gagge 1971; Nishi and Gagge 1971; Stolwijk 1971; Fiala et al. 1998, 1999, 2001, 2012) or used more realistic anatomical models but did not investigate the effects of exertional heat stress on the human body (Nelson et al. 2009; Bernardi et al. 2003), which is known to be the major contributing factor to heat injuries in young, healthy adults (Stolwijk 1971; Sawka et al. 1993; Nielsen and Nielsen 1962).

We validated the 3-D thermoregulatory virtual human model, first by comparing its temperature predictions in organs and muscles under normal resting conditions and then in the rectum under strenuous heat-stress conditions. It should be noted that rectal temperature is often used as a surrogate for core body temperature under heat-stress conditions (Casa et al. 2007, 2015). Under resting conditions, we observed good agreement between model predictions and experimentally measured values for key organs, such as the brain, liver, stomach, and esophagus, with errors of less than 0.2 °C (Fig. 4). For the case of the liver and the stomach, not all subjects were healthy, as the data represented a heterogeneous mix of subjects from a biopsy diagnostic by Graf (Graf 1959). Due to the lack of other experimental data for these organs, we used the data because Graf reported that most of the subjects had normal or near-normal results, justifying our choice. In spite of such a heterogeneous population, our predicted mean liver and stomach temperatures were within 0.2 °C of the reported mean values. Although the temperature of the liver in this study was measured at only one point for each subject, Graf reported that the temperature measurements at different points within the same liver varied by less than 0.1 °C, indicating a fairly uniform temperature distribution inside the liver under normal resting conditions. We observed a similar response in the predicted spatial temperature distribution within the liver of the virtual human, where ~ 95% of the liver was within 0.1 °C, serving as an additional validation for the temperature distribution within the liver. For the case of the bladder, the prediction error was relatively high (0.4 °C); however, the predicted temperature values were well within the 95% confidence interval of the measured mean value.

It should be noted that very few studies have reported experimental measurements of organ-specific temperature (Fig. 4), owing to the difficulty in accurately measuring organ temperature using existing techniques. Our computational model seeks to address this issue by not only predicting organ temperature during normal resting conditions (for which we observed good agreement between model predictions and experiments) but also under heat-stress conditions involving intense activity, which is not practical to measure experimentally. Although, a few anatomically realistic computational models for human thermoregulation do exist in the literature (Nelson et al. 2009; Bernardi et al. 2003; Moore et al. 2014), none of the previous works have been validated with respect to key organ temperatures (e.g., brain and liver), which is one of the novelties of this work. The need for such an anatomically realistic computational model capable of accurately predicting the temperature distribution throughout the human body can help to fill this gap. In fact, our computational model complements experimental studies, helping characterize the rise in organ temperature due to environmental and exertional conditions and, in the future, helping identify novel cooling strategies to mitigate the adverse effects of heat-related illnesses.

Apart from organ-temperature validation, we also compared the predicted arm- and leg-muscle temperature response at various depths with experimental data under normal resting conditions. As would be expected, the temperature was high near the bone, and gradually dropped as we moved outwards to the skin, where body heat is lost to the atmosphere via external convection, radiation, and evaporation. We observed a good match for the temperature variation within the vastus medialis muscle (Fig. 5a, RMSE = 0.2 °C). For the triceps brachii, the temperature predictions at 10 and 25 mm from the humerus bone were within the 95% confidence interval of the measured mean values, except for a discrepancy observed at the 40-mm location (Fig. 5b, RMSE = 0.5 °C). Such a discrepancy could be due to localized differences in fat-layer thickness in the experimental subjects when compared to the virtual human, as well as the variability in the sensor location below the skin surface. A thicker fat layer is expected to provide more insulation and would result in a higher temperature. As for the sensor location, we tried to accurately match the position of the sensor in the virtual human with the one described in the experiment, however, there may be a mismatch. Because of the high spatial dependency of muscle temperature near the skin surface, any discrepancy in the location of the sensor is likely to result in distinct temperature values. Nonetheless, we observed good agreement between model predictions and experimental values at other muscle sites in the leg and the arm.

For comparing the predicted values in the rectum with experimental measurements, we used three separate studies, including a range of time-varying exertional activity levels, different environmental humidity, temperature, and wind-speed values, and different clothing. For each of the three studies, we observed a very good agreement between the model predictions and the experimental measurements (the RMSE values ranged from 0.1 to 0.3 °C, Figs. 1 and 6), indicating that our model can accurately infer core body temperature across a range of conditions. In addition to using existing literature data to validate our models, as in Study 2b (walking on a treadmill, Fig. 6a) (Kazman et al. 2015) and Study 2c (pedaling on a bicycle ergometer, Fig. 6b) (Stolwijk 1971), we performed a new study (Study 2a, strenuous physical activity on a treadmill) to ensure that we tested our model in scenarios that led to a substantial and nonmonotonic increase in core body temperature for a prolonged period of time (Fig. 1). In Study 2a, subjects performed three 80-min exercise bouts with a rest period of 50 min between each bout, under four different conditions: two environmental (30 °C and 60% RH, 36 °C and 30% RH) and two clothing (T-shirt/shorts and ACU). For each condition, we observed considerable variation in temperature distribution with time throughout the body, which is the result of internal heat generation from metabolic activity, transfer of heat within the body, and transfer of heat between the body and the environment. During physical activity, exertional heat is mostly generated in the muscles of the torso and the upper leg, which is then transported to the surface of the body through conduction and convection (i.e., through blood perfusion). This high metabolic activity in the torso along with the torso’s low surface-to-volume ratio caused a rise in its temperature (Fig. 8). In contrast, the temperature in the peripheral regions was cooler, because of their low-heat generation capacity as well as their large surface-to-volume ratio, which enabled greater heat loss to the environment.

For each of the four conditions in Study 2a, as expected, the predicted and measured rectal temperature increased during the exercise bouts and decreased during the rest periods between bouts (Fig. 1). While the predicted rectal temperature increased slightly with each successive bout and rose by as much as 0.3 °C between bouts, both the predicted and measured rectal temperature values were not affected by changes in environmental or clothing conditions. We believe that the presence of high-speed wind (2.5 m/s) generated by the fan diminished the barrier to sweat evaporation from the clothing’s evaporative resistance, leading to similar rise in core-body temperature for the various conditions in Study 2a. However, we expect a different outcome in the absence of forced winds, with the clothing exhibiting a stronger influence on the core-body temperature for the same study conditions.

To tease out the contribution of physical activity in the increase of core body temperature, we carried out a simulation for the conditions corresponding to those in Fig. 1a but without any physical activity (i.e., we set MET = 1 as an input to the model). After 6 h, starting from a pre-activity state, the maximum increase in core body temperature was 0.7 °C, instead of the 2.4 °C increase predicted under the combined exertional and environmental heat-stress conditions in Fig. 1a. After discounting for the 6-h effect of circadian rhythm on the predictions, we found that, consistent with prior observations (Stolwijk 1971; Sawka et al. 1993; Nielsen and Nielsen 1962), physical activity alone contributed to 94% of the temperature rise in the rectum, with the remaining 6% coming from the elevated temperature and moderately high relative humidity.

Our model can also be used to answer “what-if” research questions that cannot be addressed through experiments alone. For example, what are the specific contributions of the different heat-transfer mechanisms on the body’s thermal response to the conditions in Fig. 1a discussed above? Based on our simulations (Fig. 10), we determined that the metabolic heat generated by the body ranged from 115 to 970 W. In contrast, sweating caused a heat loss of 780 W during peak activity while, during the same period, convection and radiation caused a heat gain of 50 W due to the elevated environmental conditions. Interestingly, sweating, which is modulated by temperature changes in the hypothalamus and the skin from their baseline values, closely followed the temporal profile of the metabolic heat source and was ten times larger than the combined heat gain by convection and radiation. The relatively minor contributions of the convection and radiation heat-transfer mechanisms to the total heat balance within the body explain why the core temperature was largely independent of the environmental heat stress.

Rectal-temperature measurements are considered to be accurate and less prone to measurement errors than alternative means of estimating core body temperature (Casa et al. 2007; Moran and Mendal 2002). However, it is also known that there is considerable temperature variation in the rectal cavity (Miller et al. 2017; Lee et al. 2010; Buono et al. 2014). For instance, Lee et al. reported that the rectal temperature at a 4-cm depth from the anal sphincter is lower than the temperature at a 13-cm depth by at least 0.3 °C (Lee et al. 2010). Similarly, Buono et al. showed that the rectal temperature measured at a depth of 4 cm from the anal sphincter is lower than the temperature measured at depths of 7, 13, and 15 cm (Buono et al. 2014). In agreement with these studies, our model predictions showed that rectal-cavity temperature varied with cavity depth (Fig. 7a). They also showed that, at depths of 6 and 13 cm, the temperature response time was faster than that at depths of 8 and 10 cm. Moreover, in addition to the depth, we observed that temperature in the rectum also depends on the distance from the wall of the cavity. The peak rectal temperature at the wall was higher than the peak temperature at any location within the rectal wall by as much as 0.3 °C and increased at a faster rate than the temperature inside the lumen (Fig. 7b). This behavior is due to the presence of metabolic activity and perfusion of blood in the rectal wall, in contrast to the lumen. Furthermore, as heat conduction is the only mode of heat transfer within the lumen, the temperature differences decreased and eventually became negligible as we moved away from the wall. These results, which show that the temperature response can vary by as much as 0.5 °C even for adjacent regions of the body, further highlight the importance of accurately representing the human anatomy in thermoregulatory models.

In addition to the core body temperature, our 3-D FE model provides spatiotemporal temperature distribution information in the major organs of the human body, which cannot be experimentally measured or attained by thermoregulatory models with a simplistic anatomical representation (Gagge 1973; Gagge 1971; Nishi and Gagge 1971; Stolwijk 1971; Fiala et al. 1998, 1999, 2001, 2012). This gives us the unique ability to assess the thermal load at the organ level, and at the different parts of an organ, for any heat-stress condition. For example, in the simulations corresponding to Fig. 1a in Study 2a, the temperature at the muscular regions of the heart was higher than the temperature at the heart cavity, which was assumed to be filled with blood in our model. In addition, the temperature of the muscles at the left ventricle were as much as 0.2 °C higher than the temperature at the right ventricle during physical activity, because the thicker left ventricular wall leads to greater net heat generation when compared to the right ventricle. We also observed that the maximum volume-averaged temperature in the major organs was consistently higher than the predicted maximum rectum temperature (Table 4), in agreement with previous studies (Jardine 2007; Cheshire 2016). Moreover, the peak temperature in each organ was higher than the predicted peak temperature in the rectum. For example, the maximum temperature in the heart and the liver exceeded that of the rectum by 0.6 °C, and at 5.8 h into the heat-stress challenge, when these organs reached their peak-temperature values (Fig. 9), 100% of the volumes of the heart and the liver were above 38.5 °C, the lower-limit temperature for the onset of heat injury (Laxminarayan et al. 2018).

To demonstrate the benefit of the increased spatial resolution of the 3-D virtual human model, we repeated the simulations for Study 2a and predicted the core-body temperature using a cylinder model (Fiala et al. 1998). We constructed the cylinder model geometry and implemented the model equations using the commercial FE software COMSOL v5.4. To this end, we compared and contrasted the results from the cylinder model with the measured data and the 3-D model predictions. Figure S1 in the online Supplementary Material shows the core-body temperature predictions from the cylinder model and the 3-D model, along with the experimental measurements. First, we observed that our 3-D model consistently provided lower RMSEs (0.2–0.3 °C) against the experimental data when compared to the results from the cylinder model, which yielded errors two- to threefold larger (0.5–0.6 °C). Second, when we compared the maximum temperature difference (ΔT_max) between the experimental data and model predictions (Table S2, in the online Supplementary Material), we consistently observed that the ΔT_max for the cylinder model was as much as two to three times higher than its 3-D counterpart (0.4 vs. 1.1 °C), indicating that the worst 3-D model predictions were considerably closer to the measured data. These differences in prediction accuracy are substantial (16 vs. 44%), when we consider that the range of the changes in the measured core-body temperature during the entire study was ~ 2.5 °C. Third, when we qualitatively compared the trends in core temperature predictions between the two models, the 3-D model more closely followed the experimental trends. Finally, when we performed an in-between comparison of the simulation results from the two models, we observed a sizeable difference between the two predictions (RMSE: 0.6 °C, ΔT_max: 1.2 °C). The observed improvement in the 3-D model over the cylinder model arises mainly from the differences in the geometrical details, the larger heat capacity in our model (257 vs. 237 kJ/K), and the associated material properties considered in the two models.

Our study has limitations. First, we did not explicitly represent the vasculature of the human body in our model and did not consider the spatial variation in the blood temperature as well as the countercurrent heat exchange between arteries and veins. Instead, we considered heat transfer between the tissue and the blood via the Pennes bioheat transfer equation. While such an assumption might not influence the blood temperature within the torso, it might affect the temperature of the blood in the peripheral regions of the body, in particular during rapid cooling. However, the contribution from the countercurrent heat exchange is expected to be minimal during a heat-stress condition (Nelson et al. 2009; Brinck and Werner 1994). The results from our simulation show that the impact of these assumptions on the core body temperature during heat stress is negligible, as demonstrated by the good agreement with experimental data in each of the three validation studies. Second, we validated our predictions of organ temperature only for normal resting conditions and not for heat-stress conditions, owing to the unavailability of such experimental data in the literature as measuring organ-specific temperature in vivo under strenuous human activity is challenging. Third, our model did not consider acclimatization effects of the human body and the associated changes in the thermoregulatory responses. Finally, our model is based on a 50th percentile U.S. male and, therefore, does not account for variations in body size or body-fat percentage. In spite of these limitations, the model results are still valid and can help us better understand the potential risk of heat injury to humans due to exertional and environmental heat stressors.

We developed an anatomically accurate 3-D thermoregulatory computational model to predict the spatiotemporal distribution of temperatures in the human body during exertional and environmental heat-stress conditions. We validated the model by comparing experimentally measured temperature with the predicted temperature in the major organs (brain, liver, stomach, bladder, and esophagus), within intramuscular regions, and in the rectum. While we performed the organ- and muscle-temperature validation using experimental measurements under normal resting conditions, we performed validation of rectal temperature using experimental measurements from three diverse heat-stress conditions, covering a range of physical activities, environmental conditions, and clothing. We showed that for the heat-stress conditions, the predicted peak temperature in key organs, such as the heart, brain, liver, and kidney, exceed the peak temperature in the core, and that in large fractions of these organs their temperature is higher than that of the core for prolonged periods of time. Hence, this new capability can help stratify the risk of organ injury for any combination of exertional and environmental heat-stress conditions. We envision that this new modeling framework can be extended, by incorporating countercurrent heat exchange between arteries and veins, an improved form of the bioheat equation, and modified thermoregulation distributions and convective heat transfer coefficients, to compare and contrast the efficacy of different whole-body or localized cooling strategies in reducing the heat load to major organs and maintaining organ integrity.