## Abstract

Changes in mean body temperature (ΔT̄_{b}) estimated by the traditional two-compartment model of “core” and “shell” temperatures and an adjusted two-compartment model incorporating a correction factor were compared with values derived by whole body calorimetry. Sixty participants (31 men, 29 women) cycled at 40% of peak O_{2} consumption for 60 or 90 min in the Snellen calorimeter at 24 or 30°C. The core compartment was represented by esophageal, rectal (T_{re}), and aural canal temperature, and the shell compartment was represented by a 12-point mean skin temperature (T̄_{sk}). Using T_{re} and conventional core-to-shell weightings (*X*) of 0.66, 0.79, and 0.90, mean ΔT̄_{b} estimation error (with 95% confidence interval limits in parentheses) for the traditional model was −95.2% (−83.0, −107.3) to −76.6% (−72.8, −80.5) after 10 min and −47.2% (−40.9, −53.5) to −22.6% (−14.5, −30.7) after 90 min. Using T_{re}, *X* = 0.80, and a correction factor (*X*_{0}) of 0.40, mean ΔT̄_{b} estimation error for the adjusted model was +9.5% (+16.9, +2.1) to −0.3% (+11.9, −12.5) after 10 min and +15.0% (+27.2, +2.8) to −13.7% (−4.2, −23.3) after 90 min. Quadratic analyses of calorimetry ΔT̄_{b} data was subsequently used to derive best-fitting values of *X* for both models and *X*_{0} for the adjusted model for each measure of core temperature. The most accurate model at any time point or condition only accounted for 20% of the variation observed in ΔT̄_{b} for the traditional model and 56% for the adjusted model. In conclusion, throughout exercise the estimation of ΔT̄_{b} using any measure of core temperature together with mean skin temperature irrespective of weighting is inaccurate even with a correction factor customized for the specific conditions.

- body heat storage
- calorimetry
- heat stress
- hyperthermia
- thermoregulation

according to the human heat balance equation, an imbalance between the rates of metabolic heat production and total body heat loss result in a rate of change in body heat storage and subsequently a change in body heat content (ΔH_{b}). Since ΔH_{b} is directly indicative of the thermal status of the individual, the accurate determination of this value is critical when assessing the response of the human body to environments that elicit thermal stress.

It is generally accepted that the concurrent measurements of the total heat generated by the body as a result of anaerobic and/or aerobic metabolic oxidation and ATP hydrolysis, and the total heat dissipated to the ambient environment (whole body calorimetry) are the most accurate means whereby ΔH_{b} can be attained. However, in the absence of calorimetric methods, thermometry is often used to estimate ΔH_{b} by employing the fact that ΔH_{b} is given by the product of the change in the mean temperature of the tissues of the body (ΔT̄_{b}), the total mass of the body (b_{m}), and the average specific heat of all the tissues of the body (C_{p}). For a given body of a known b_{m} and C_{p}, it is therefore assumed that ΔH_{b} can be estimated by thermometrically approximating ΔT̄_{b}. The most commonly used thermometry method is the traditional two-compartment model (3) that estimates ΔT̄_{b} by measuring the change in rectal temperature (ΔT_{re}) that represents a “core” compartment and the change in mean skin temperature (ΔT̄_{sk}) that represents a “shell” compartment. The relative contribution of each compartment to ΔT̄_{b} is given by a sum-to-one ratio of weighting coefficients that are roughly determined by the ambient environmental conditions. Typical core-to-shell ratios range from 9:1 or 4:1 for a hot environment (28, 29) to 2:1 for a moderate or cold environment (4, 9, 15, 19, 35).

On several occasions, the traditional two-compartment thermometry approach has been demonstrated to greatly underestimate ΔT̄_{b} during steady-state exercise, with mean estimation errors ranging from ∼15% (17) to as much as ∼70% (32). The source of error using the two-compartment model of core and shell has been suggested to be the lack of an independent expression representing the heat stored in muscle tissue (17, 21, 30, 33). A three-compartment thermometry model for ΔT̄_{b}, incorporating a “muscle” compartment intermediate to the core and shell, has been subsequently proposed (21, 33) and provides an improved estimation of ΔT̄_{b} and therefore ΔH_{b} (17). However, a three-compartment model requires the invasive measurement of intramuscular temperature, and for the purpose of practicality, an accurate estimation of ΔT̄_{b} using only core and skin temperature measurements is preferred.

An adjusted two-compartment thermometry model has been proposed in previous literature, accounting for the underestimation of the traditional model by employing a mathematical constant or “correction factor.” Snellen (27) directly measured ΔH_{b} using whole body calorimetry on individuals performing muscular work in a hot environment. He subsequently derived a model for ΔT̄_{b} using core and shell coefficients similar to that of the traditional model and a correction factor of ∼0.40. However, only two participants and a single ambient environment were tested (27). An alternative two-compartment approach was proposed by Colin et al. (5), who suggested that a correction factor was not necessary for the improved estimation of ΔT̄_{b} but that the traditional compartmental weighting coefficients varied as a function of body heat storage, and therefore presumably with time, throughout exercise. While the traditional two-compartment thermometry model has been demonstrated to underestimate ΔT̄_{b} after reaching steady-state body temperatures during exercise, it remains unknown if such an error occurs during non-steady-state body temperatures such as those occurring within the initial stages of exercise.

The aim of the present study was to compare the change in mean body temperature, as estimated using a traditional two-compartment thermometry model approach, and an adjusted two-compartment model incorporating a correction factor, with those values directly derived using whole body calorimetry after 10, 30, 60, and 90 min of exercise. It was hypothesized that the difference between the estimates for the change in mean body temperature by an adjusted model relative to calorimetry would be less than by the traditional two-compartment model after 10, 30, 60, and 90 min of exercise.

## METHODS

### Participants

Following approval of the experimental protocol from the University of Ottawa Research Ethics Committee and obtaining written informed consent, 60 healthy, nonsmoking normotensive participants (31 men, 29 women) volunteered for the study. Of the participants, 23 (10 men, 13 women) were exposed to 30°C air temperature (T_{a}) and 30% relative humidity (RH); 13 (8 men, 5 women) to T_{a} = 30°C, 60% RH; 14 (9 men, 5 women) to T_{a} = 24°C, 30% RH; and 10 (4 men, 6 women) to T_{a} = 24°C, 60% RH. Mean characteristics for male and female participants are given in Table 1.

Body composition of each participant was measured using dual-energy x-ray absorptiometry (DEXA) by which the body mass is partitioned into fat tissue mass, lean tissue mass, and bone mass. Lean tissue mass (*m*_{l}) is further subdivided into muscle mass (51.0% of *m*_{l}); skin mass (11.0%); white matter, gray matter, eye, nerve, lens, and cartilage mass (12.9%); blood mass (25.0%); and cerebral spinal fluid mass (0.1%) (11, 25). Using these components, the mean specific heat of the body (C_{P}) was determined (12) and is given in Table 2.

### Instrumentation

#### Thermometry.

Esophageal temperature (T_{es}) was measured by placing a pediatric thermocouple probe of ∼2 mm in diameter (Mon-a-therm Nasopharyngeal Temperature Probe, Mallinckrodt Medical, St. Louis, MO) through the participant's nostril while they were asked to sip water through a straw. The location of the probe tip in the esophagus was estimated to be in the region bounded by the left ventricle and aorta, corresponding to the level of the eighth and ninth thoracic vertebrae (20). Rectal temperature (T_{re}) was measured using a pediatric thermocouple probe (Mon-a-therm General Purpose Temperature Probe, Mallinckrodt Medical) inserted to a minimum of 12 cm past the sphincter. Aural canal temperature (T_{au}) was measured using a tympanic thermocouple probe (Mon-a-therm Tympanic, Mallinckrodt Medical) placed in the aural canal until resting against the tympanic membrane (determined by the participant reporting an audible scratching sound), after which it was withdrawn slightly. The tympanic probe was held in position and isolated from the external environment with cotton and ear protectors. Skin temperature was measured at 12 points over the body surface using 0.3-mm-diameter T-type (copper/constantan) thermocouples integrated into heat-flow sensors (Concept Engineering, Old Saybrook, CT). Thermocouples were attached using porous surgical tape (Blenderm, 3M, St. Paul, MN). Mean skin temperature (T̄_{sk}) was calculated using the 12 skin temperatures weighted to the regional proportions as determined by Hardy and DuBois (13): head 7%, hand 4%, upper back 9.5%, chest 9.5%, lower back 9.5%, abdomen 9.5%, biceps 9%, forearm 7%, quadriceps 9.5%, hamstring 9.5%, front calf 8.5%, and back calf 7.5%.

Temperature sensors were previously calibrated using an in-glass thermometer and yielded an accuracy of ±0.01°C. All temperature data were collected using a HP Agilent data-acquisition module (model 3497A) at a sampling rate of 15 s. Data were simultaneously displayed and recorded in spreadsheet format on a personal computer (IBM ThinkCentre M50) with LabVIEW software (version 7.0, National Instruments).

#### Calorimetry.

Change in body heat content (ΔH_{b}) was measured using the temporal summation of metabolic heat production by indirect calorimetry and the net evaporative and dry heat exchange of the body with the environment by direct calorimetry. The measurement technique was identical to that described in a previous publication (17). In summary, indirect calorimetry employed the open-circuit technique using expired gas samples drawn from a 6-liter fluted mixing box yielding a measurement error of ±0.25% for rate of metabolic heat production. Expired gas was analyzed using electrochemical gas analyzers (AMETEK model S-3A/1 and CD 3A, Applied Electrochemistry, Pittsburgh, PA) calibrated before each trial using gas mixtures of 4% CO_{2}, 17% O_{2}, and balance N_{2}. The turbine ventilometer was calibrated using a 3-liter syringe. A modified Snellen whole body air calorimeter was employed for the purpose of measuring whole body changes in evaporative and dry heat loss, yielding an accuracy of ±2.3 W for the measurement of rate of total heat loss. The calorimeter was previously calibrated for rate of dry heat loss using a humanoid manikin heat source made of constant power zone heater cable (5.905 kΩ/m, Easy Heat ZH8-1CBR, New Castle, IN); and for rate of evaporative heat loss using a precision tubing pump (Cole-Palmer, Masterflex 7550-30; Pump head 77200-50) delivering 5 ml/min (±0.01 ml/min) to a heated 1,200-W hotplate. A full technical description of the fundamental principles and performance characteristics of the Snellen calorimeter is available (24).

### Experimental Protocol

All participants volunteered for two separate testing sessions. On the first day, an incremental cycle ergometer peak O_{2} consumption (V̇o_{2peak}) test was performed. On the second day, the calorimetry experimental protocol was performed. Testing days were separated by a minimum of 72 h. All calorimeter trials were performed at the same time of day and between the months of September and April. Participants were asked to arrive at the laboratory after eating a small breakfast (i.e., dry toast and juice) but consuming no tea or coffee that morning and also avoiding any major thermal stimuli on their way to the laboratory. Participants were also asked to not drink alcohol or exercise for 24 h before experimentation.

Following instrumentation, the participant entered the calorimeter regulated to an ambient T_{a} of either 24.0°C or 30.0°C at a RH of 30% or 60%. The participant, seated in the semirecumbent position, rested for a 45-min habituation period until a steady-state baseline resting condition was achieved. Subsequently, the participant cycled at 40% of their predetermined V̇o_{2peak} for a maximum of 60 or 90 min. The exercise duration was such that a steady-state condition defined as a T_{re} stable within 0.1°C (34) was achieved during the final 10 min of exercise.

For all experimentation, clothing insulation was standardized at ∼0.2 to 0.3 clo [i.e., cotton underwear, shorts, socks, sports bra (for women), and athletic shoes].

### Statistical Analyses

For the purpose of comparing thermometry approaches, the data were separated according to ambient T_{a} of the testing condition (i.e., 24 or 30°C). Data were not separated further according to RH due to the confounding effect of a reduced number of data points upon predictive power, and the traditional two-compartment thermometry model employing weighting coefficients based on T_{a} not RH (3). The range of ambient conditions was tested to attain a wide variation in the calorimetric and thermometric measures under compensable heat stress conditions.

#### Change in mean body temperature using calorimetry.

Change in body heat content as measured using calorimetry (ΔH_{b,cal}) was solved for change in mean body temperature (ΔT̄_{b,cal}) after 10, 30, 60, and 90 min of exercise using the following equation (1) where ΔH_{b,cal} is change in body heat content by calorimetry (in kJ), b_{m} is total body mass (in kg), and C_{P} is specific heat of each participant as estimated using DEXA (in kJ·kg^{−1}·°C^{−1}).

#### Two-compartment thermometry model of change in mean body temperature.

The traditional two-compartment thermometry model (3) was used to estimate change in mean body temperature (ΔT̄_{b,trad}) after 10, 30, 60, and 90 min of exercise using (2) where ΔT_{re} is the change in rectal temperature and ΔT̄_{sk} is the change in mean skin temperature. The value for *X* is the proportion of the body representing the body core and the value for (1 − *X*) is the proportion of the body representing the body shell. Value for *X* may not exceed 1 or be less than 0.

#### Adjusted two-compartment thermometry model of change in mean body temperature.

The adjusted two-compartment thermometry model incorporating a correction factor (5, 27) was used to estimate mean body temperature (ΔT̄_{b,adj}) after 10, 30, 60, and 90 min of exercise using (3) where ΔT_{re} is the change in rectal temperature and ΔT̄_{sk} is the change in mean skin temperature, *X*_{0} is an unconstrained correction factor, and the value for *X* is subject to the same constraints as in *Eq. 2*.

#### Conventional coefficients.

Changes in mean body temperature were calculated using the traditional two-compartment model (ΔT̄_{b,trad}) with the conventional weighting coefficients of *X* = 0.66, 0.79, and 0.90 for 24°C and 30°C (5, 13, 28). Furthermore, changes in mean body temperatures were calculated using the adjusted two-compartment model (ΔT̄_{b,adj}) with the previously recommended weighting coefficient of *X* = 0.80 and correction factor of *X*_{0} = 0.40 (5, 27).

#### Best-fitting coefficients of thermometry models for calorimetry data.

Best-fitting coefficients of the two-compartment thermometry model (ΔT̄_{b,trad}) and the adjusted two-compartment thermometry model (ΔT̄_{b,adj}) were also derived for the ΔT̄_{b,cal} and thermometry (core and skin temperature) measurements in the present study. To study the influence of different measures of core temperature on ΔT̄_{b} prediction, best-fitting coefficients were also derived for ΔT̄_{b,adj} and ΔT̄_{b,cal} using ΔT_{es} and ΔT_{au} instead of ΔT_{re}. The optimization technique of quadratic programming was used to separately fit both models after 10, 30, 60, and 90 min of exercise at 24°C and 30°C. In summary, the quadratic programming problem was to derive coefficient values that minimize a quadratic function while simultaneously satisfying the constraints set for *X* (*X*_{0} in *Eq. 3* was unconstrained) (22). Quadratic programming was performed using the statistical programming language “R” (the open-source software R can be downloaded at http://www.r-project.org/).

#### Adjusted R^{2} statistic.

To compare the predictive power of all thermometry models for ΔT̄_{b,trad} and ΔT̄_{b,adj}, goodness-of-fit was measured for each by adapting the *R*^{2} statistic from linear regression. For *n* observations and *k* parameters in a given model, the quadratic programming problem incorporates *j* equality constraints (in the present case, *j = 1*). Let the *i*th response be denoted by *y*_{i} (for each thermometry model, *y*_{i} = ΔT̄_{b,i}), the *i*th fitted value be denoted by *ŷ*_{i}, and let the mean response be denoted by *ȳ*. Then the variance of the response about the mean is estimated by SSM = [∑(*y*_{i} − *ȳ*)^{2}]/(*n* − 1) and the residual variance, with respect to the quadratic programming model, is estimated by SSE = [∑(*y*_{i}−*ŷ*_{i})^{2}]/(*n* − *k* − *j*).

Defined as the proportion of the variance in the response explained by the model, the *R*^{2} statistic is given by the expression [1 − (SSE/SSM)]. As with linear regression, the *R*^{2} statistic in a quadratic programming model has a maximum value of 1. However, as SSE may be greater than SSM, *R*^{2} may be less than 0. It is possible for SSE to be greater than SSM as the model does not contain a constant intercept. In the event of this, the model is considered biased, i.e., a systematic under- or overestimation of the response. For a biased model, the average observed response will actually perform better as a predictor than the model itself. In other words, the variance about the mean (SSM) will be less than the variance about the fitted values (SSE), and *R*^{2} will be negative. As is the case with linear regression, if there are many parameters in the model, it is possible for the *R*^{2} statistic to be biased by overfitting. The adjusted *R*^{2} statistic, which takes into account the possibility of overfitting, is given by the expression {1 − [(*n* − 1)SSE/(*n − k* −*j*)SSM]}. When *k* is large relative to *n*, the adjusted and unadjusted *R*^{2} statistics will be somewhat different, with the adjusted being lower. With this in mind, the adjusted *R*^{2} statistic is reported in the present study.

#### Error analysis.

The error observed with each thermometry model relative to calorimetry was also analyzed further. Mean percentage error for each thermometry model was calculated with 95% confidence intervals. Percentage error of each thermometric estimate of ΔT̄_{b} is defined as 100 times the difference between ΔT̄_{b} estimated using the given thermometry model (*ŷ*) and ΔT̄_{b} measured with calorimetry (*y*), divided by ΔT̄_{b} measured with calorimetry (*y*): 100 × (*ŷ* − *y*)/*y*. Since mean percentage error equates to percentage bias (23), employing 95% confidence intervals and observing if these intervals include zero is equivalent to testing to the null hypothesis that the model is unbiased at the 0.05 significance level.

## RESULTS

The mean changes in mean body temperature and body heat content as measured using calorimetry, and mean skin temperature and all measures of core temperature after 10, 30, 60, and 90 min of constant exercise at 24°C and 30°C are given in Table 3.

### Traditional Two-Compartment Model

In comparison to the change in mean body temperature derived using calorimetry (ΔT̄_{b,cal}), the traditional two-compartment thermometry model for ΔT̄_{b} using the conventional coefficients of *X* = 0.66, 0.79, and 0.90 were statistically biased (*P* ≤ 0.05) after 10, 30, 60, and 90 min of exercise at both 24°C and 30°C (Fig. 1, *A–C*). After 10 min of exercise, mean percentage error (shown with lower and upper limits of confidence interval in parentheses) for ΔT̄_{b} was between −95.2% (−83.0, −107.3) and −86.7% (−75.9, −97.5) at 24°C and between −81.7% (−76.8, −86.5) and −76.6% (−72.8, −80.5) at 30°C. After 90 min of exercise, mean percentage error for ΔT̄_{b} was between −30.3% (−21.4, −39.2) and −22.6% (−14.5, −30.7) at 24°C, and between −47.2% (−40.9, −53.5) and −46.1% (−39.4, −52.8) at 30°C.

The quadratic programming analyses results for the best-fitting coefficients for ΔT̄_{b,trad} after 10, 30, 60, and 90 min of exercise using three separate indexes of core temperature (i.e., T_{re}, T_{es}, and T_{au}) are detailed for 24°C and 30°C (Table 4). The best-fitting models for ΔT̄_{b,trad} at 24°C were statistically biased (*P* ≤ 0.05) after 10 and 30 min of exercise and gave an unbiased but low predictive power after 60 min (adjusted *R*^{2} = 0.07) and 90 min of exercise (adjusted *R*^{2} = 0.20). At 30°C, the best-fitting models for ΔT̄_{b,trad} were statistically biased (*P* ≤ 0.05) at all the time points analyzed throughout exercise (Fig. 1*D*). Individual values for ΔT̄_{b,trad} relative to ΔT̄_{b,cal} at each time point for both 24°C and 30°C are given in Fig. 2.

### Adjusted Two-Compartment Model

Compared with ΔT̄_{b,cal} at 24°C, the adjusted two-compartment thermometry model for ΔT̄_{b} using the previously suggested core-to-shell weighting coefficient of *X* = 0.80 and the correction factor of *X*_{0} = 0.40 yielded an adjusted *R*^{2} statistic of 0.05 after 10 min, 0.46 after 30 min, and 0.39 after 60 min of exercise; however, a systematic overestimation was evident after 90 min of exercise (Fig. 3*A*). At 30°C, a statistical bias (*P* ≤ 0.05) was apparent after 10 and 90 min of exercise, but an unbiased model with adjusted *R*^{2} statistics of 0.49 and 0.36 was evident after 30 and 60 min, respectively (Fig. 3*A*).

The quadratic programming analyses results for the best-fitting coefficients of the adjusted two-compartment model for mean body temperature (ΔT̄_{b,adj}) after 10, 30, 60, and 90 min of exercise using three separate indexes of core temperature (i.e., T_{re}, T_{es}, and T_{au}) are detailed for 24°C and 30°C (Table 5). Unbiased models were evident for ΔT̄_{b,adj} at all time points at 24°C and 30°C (Fig. 3*B*). However, the greatest proportion of variance explained by the best-fitting adjusted two-compartment models at any time point was 53% at 24°C and 56% at 30°C, as evidenced by the adjusted *R*^{2} statistics. Individual values for ΔT̄_{b,adj} relative to ΔT̄_{b,cal} at each time for both 24°C and 30°C are given in Fig. 4.

## DISCUSSION

The change in mean body temperature (ΔT̄_{b}) is systematically underestimated during steady- and non-steady-state body temperatures using any of the conventional core-to-shell weighting coefficients within the traditional two-compartment thermometry model of core and shell. Furthermore, even when employing three different measurements of core temperature and calibrating the traditional two-compartment model against the calorimetrically measured ΔT̄_{b} to derive the best-fitting core-to-shell weighting coefficients for the specific range of individuals and experimental conditions in the present study, an accurate estimation of ΔT̄_{b} was still not obtained at any time point for 24°C or 30°C. The most accurate best-fitting traditional two-compartment model was derived after 90 min of exercise at 24°C with only 20% of the variation in ΔT̄_{b} accounted for by thermometry. After 10 and 30 min of exercise at 24°C and at all time points analyzed at 30°C, the traditional two-compartment thermometry model for ΔT̄_{b} was statistically biased, that is, employing the mean group ΔT̄_{b} response derived using calorimetry provided a better individual estimation of ΔT̄_{b} than any combination of their thermometry responses.

The adjusted two-compartment thermometry model provided a more accurate estimation of ΔT̄_{b} than the traditional two-compartment thermometry model during steady-state and non-steady-state body temperatures. The previously suggested adjusted model with a core-to-shell weighting coefficient of 0.80 and a correction factor of 0.40 (5, 27) gave an unbiased estimate of ΔT̄_{b} after 30 and 60 min of exercise but not after 10 and 90 min. When calibrating the adjusted two-compartment model against calorimetry to derive the best-fitting core-to-shell weighting coefficients and correction factors for the present data set, an unbiased estimate of ΔT̄_{b} was obtained at all time points at both 24°C and 30°C for all three separate measurements of core temperature. However, the greatest amount of variation in ΔT̄_{b} accounted for by thermometry using the adjusted two-compartment model at any time point under any condition was only 56%, and in most cases more than half of the variation in ΔT̄_{b} remained unexplained by thermometry.

The traditional thermometry model has been previously shown to underestimate ΔT̄_{b} during steady-state body temperatures (14, 16, 26). Several other authors (5, 10, 18) have suggested that the source of estimation error in the traditional thermometry model is the relative weightings of the core and shell compartments (*X*) changing as a function of thermal state because of non-steady-state body temperatures as exercise progresses. While the best-fitting value for *X* varied at each time point throughout exercise, the present study shows that the traditional model continues to systematically underestimate ΔT̄_{b} irrespective of whether body temperatures are steady state or not. However, relative to steady-state body temperatures at the end of exercise, the magnitude of percentage error in the estimation of ΔT̄_{b} using the traditional thermometry model was even greater during the early stages of exercise (10 min). This error is due to a large rate of change of ΔT̄_{b} [0.47°C (SD 0.10) at 24°C and 0.48°C (SD 0.14) at 30°C over 10 min] occurring with minimal concurrent changes in thermometry measurements (except T_{es}). Therefore, the concept that ΔT̄_{b} may be estimated using the minute-by-minute integration of changes in core and shell temperature with fixed core-to-shell ratios during thermal transients (8, 31) appears fallacious, particularly when employing T_{re}, because of the well-documented time lag of this indicator of core temperature (6).

The addition of a correction factor (*X*_{0}) within the best-fitting adjusted two-compartment thermometry models removed the systematic underestimation of ΔT̄_{b} at all time points. However, the predictive power of these models was at best modest for all conditions irrespective of the method of core temperature measurement, and it is likely that the derived values for *X* and *X*_{0} are only appropriate for the specific experimental conditions and range of individuals in the present study. Best-fitting values for *X* and *X*_{0} varied greatly with exercise duration (and therefore ΔT̄_{b}) as well as between 24°C and 30°C. It is therefore probable that different values for *X* and *X*_{0} would be necessary for the thermometric estimation of ΔT̄_{b} for colder or warmer environmental temperatures, with different levels of clothing insulation (1, 2), and for various exercise intensities or modes. As such, the notion that an accurate thermometric estimation of ΔT̄_{b} across a range of “hot,” “moderate,” or “cold” conditions may be attained using a generic core-to-shell coefficient as per usual practice (4, 19, 28, 29), even with a correction factor, appears highly questionable. In fact the present study suggests that the estimation of ΔT̄_{b} using any of the three common measures of core temperature together with mean skin temperature irrespective of their relative weighting is inaccurate even with a correction factor customized for the specific conditions.

The greatest increase in body heat content and therefore ΔT̄_{b} occurred after 90 min of exercise at 30°C. Under this condition, the absolute error of the estimation of ΔT̄_{b} using thermometry relative to calorimetry appeared to increase multiplicatively with increasing heat stress using both the traditional (Fig. 2*D*) and adjusted two-compartment best-fitting models (Fig. 4*D*). At greater levels of exercise-induced hyperthermia, core and skin temperature measurements therefore appear to provide an increasingly erroneous indication of whole body thermal state. The underestimation of the traditional two-compartment thermometry model has been previously ascribed to a substantial heat storage in active and inactive muscle mass that is not accurately represented by changes in core or skin temperature (21, 30, 33). Particularly during exercise, individuals with large proportions of muscle mass therefore have a greater potential for body heat storage and may subsequently be at a greater risk of heat-related illnesses. Under circumstances where core temperature alone is employed as an indicator of thermal stress, the absolute estimation error of ΔT̄_{b} will be likely even greater.

A study by Jay et al. (17) showed that the inclusion of a “muscle” compartment yielded an improved thermometric estimation of ΔT̄_{b} after 90 min of steady-state exercise relative to the traditional two-compartment model. However, the proportion of variance in ΔT̄_{b} described by the three-compartment thermometry model (∼50%) was similar to that found presently with an adjusted 2-compartment model. Calorimetry therefore appears to be the optimal method for precisely determining ΔT̄_{b}. Since most researchers have limited access to whole body calorimeters, further work must be conducted to derive a more accurate thermometric technique for estimating ΔT̄_{b}, particularly at greater levels of exercise-induced hyperthermia. This may require temperature measurements at several depths intermediate to the core and shell, possibly with a differing C_{p} value designated to each compartment.

In conclusion, ΔT̄_{b} is systematically underestimated during steady-state and non-steady-state body temperatures using the traditional two-compartment thermometry model with all conventional coefficients at both 24°C and 30°C. When employing three separate measurements of core temperature and calibrating the model against calorimetry to derive the best-fitting core-to-shell weighting coefficients for the specific conditions of the present study at each time point, the most accurate model only accounted for 20% of the variation observed in ΔT̄_{b} at only one particular time point. The adjusted two-compartment thermometry model incorporating a correction factor provided a more accurate estimation of ΔT̄_{b} during steady-state and non-steady-state body temperatures at both 24°C and 30°C. However, the best-fitting models only accounted for between ∼45% and 55% of the variation observed in ΔT̄_{b}. These results suggest that at steady-state and non-steady-state body temperatures, the estimation of ΔT̄_{b} using any of the three common measures of core temperature together with mean skin temperature irrespective of their relative weighting is inaccurate even with a correction factor customized for the specific conditions. Further research must be conducted to provide an improved thermometric method for estimating ΔT̄_{b}.

## GRANTS

This research was supported by the U.S. Army Medical Research and Material Command's Office of the Congressionally Directed Medical Research Programs and by a Discovery Grant from the Natural Sciences and Engineering Research Council (grants held by G. P. Kenny; [email protected]).

## Footnotes

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- Copyright © 2007 the American Physiological Society