## Abstract

The aim of this study was to use whole body calorimetry to directly measure the change in body heat content (ΔH_{b}) during steady-state exercise and compare these values with those estimated using thermometry. The thermometry models tested were the traditional two-compartment model of “core” and “shell” temperatures, and a three-compartment model of “core,” “muscle,” and “shell” temperatures; with individual compartments within each model weighted for their relative influence upon ΔH_{b} by coefficients subject to a nonnegative and a sum-to-one constraint. Fifty-two participants performed 90 min of moderate-intensity exercise (40% of V̇o_{2 peak}) on a cycle ergometer in the Snellen air calorimeter, at regulated air temperatures of 24°C or 30°C and a relative humidity of either 30% or 60%. The “core” compartment was represented by temperatures measured in the esophagus (T_{es}), rectum (T_{re}), and aural canal (T_{au}), while the “muscle” compartment was represented by regional muscle temperature measured in the vastus lateralis (T_{vl}), triceps brachii (T_{tb}), and upper trapezius (T_{ut}). The “shell” compartment was represented by the weighted mean of 12 skin temperatures (T̄_{sk}). The whole body calorimetry data were used to derive optimally fitting two- and three-compartment thermometry models. The traditional two-compartment model was found to be statistically biased, systematically underestimating ΔH_{b} by 15.5% (SD 31.3) at 24°C and by 35.5% (SD 21.9) at 30°C. The three-compartment model showed no such bias, yielding a more precise estimate of ΔH_{b} as evidenced by a mean estimation error of 1.1% (SD 29.5) at 24°C and 5.4% (SD 30.0) at 30°C with an adjusted *R*^{2} of 0.48 and 0.51, respectively. It is concluded that a major source of error in the estimation of ΔH_{b} using the traditional two-compartment thermometry model is the lack of an expression independently representing the heat storage in muscle during exercise.

- body heat storage
- calorimetry
- muscle temperature
- thermoregulation

the derivation of the change in body heat content (ΔH_{b}) is of fundamental importance to the physiologist assessing the exposure of the human body to environmental conditions that result in thermal imbalance. In theory, the measurement of body heat exchange using simultaneous measures of direct and indirect calorimetry is the only method whereby ΔH_{b} can be directly determined. Thus the difference between metabolic heat production using the stoichiometric relationship of the products and reactants of oxidative metabolism (indirect calorimetry) and the total heat lost from the body can be used to estimate ΔH_{b}. By definition, ΔH_{b} is the product of the change of the mean temperature of the tissues of the body (ΔT̄_{b}), the total body mass (b_{m}), and the average specific heat of the tissues of the body (C_{P}). Hence, for a given body mass of a known C_{P}, ΔT̄_{b} is an acceptable surrogate measure of ΔH_{b}. Because of the limited accessibility of direct calorimeters, thermometry is most often used to estimate ΔT̄_{b} and thereby derive ΔH_{b}. The most common thermometry approach is the two-compartment model (4) that estimates ΔT̄_{b} by separating the body into a “core” compartment temperature measured using the change in rectal temperature (ΔT_{re}) and a “shell” compartment temperature measured using the change in mean skin temperature (ΔT̄_{sk}). The relative contribution of each compartment to ΔT̄_{b} is determined by a sum-to-one ratio of weighting coefficients that is dependent upon the external environment. Recommended weighting coefficients are variable, however, and for a hot environment, the suggested “shell” coefficient ranges from as low as 0.05 (40, 41) to as high as 0.2 or 0.3 (5, 11, 20, 26).

Previous research has shown that the two-compartmental thermometry model greatly underestimates ΔT̄_{b} and therefore ΔH_{b} (15, 18, 38, 43). Despite this, the two-compartment model is still extensively used for the estimation of ΔT̄_{b} and ΔH_{b}, both as an analytical tool for assessing individual heat load status for a wide range of subpopulations (1, 7, 36, 49) and extensively as a physiological criterion for maximal heat exposure (2, 16, 17, 19, 22).

A major source of error in the prediction of ΔH_{b} may be accounted for by independently considering the thermal influences of muscle tissue using a three-compartment thermometry model of “core,” “muscle,” and “shell.” Such a model was first described by Nadel et al. (28) using partitional calorimetry and intermittent intramuscular temperature measurements taken in the quadriceps and later by Webb (45) using suit calorimetery but with no concurrent measurements of muscle temperature. Total body mass is composed of ∼40% muscle mass compared with ∼5% skin mass (44), and the specific heat capacity of muscle tissue is very similar to that of skin (13). Despite this, temperature of the skin is independently considered in the two-compartment thermometry model (i.e., “shell”), whereas muscle temperature is not. Furthermore, the traditional two-compartment thermometric approach arbitrarily includes muscle mass as part of the “core.” However, active muscle tissue can be the primary source of thermogenesis during exercise, and inactive muscle may be a major heat sink during exercise. Therefore, overall muscle tissue temperature is typically subject to a greater change relative to measures of core and skin temperature.

The aim of the present study was to compare the change in body heat content, as estimated using a two-compartment thermometry model, and a three-compartment model, incorporating the thermal influences of muscle mass, with those values directly measured using whole body direct calorimetry. It was hypothesized that the difference between the estimates for change in body heat content by a three-compartment thermometry model relative to direct calorimetry, will be less than by the two-compartment approach.

## METHODS

### Participants

After approval of the experimental protocol from the University of Ottawa Research Ethics Committee, 52 healthy, nonsmoking normotensive participants volunteered (26 males, 26 females) for the study. Of the participants, 22 (10 males, 12 females) were exposed to an air temperature of 30°C and relative humidity (RH) of 30%; 6 (3 males, 3 females) to 30°C, 60% RH; 14 (9 males, 5 females) to 24°C, 30% RH; and 10 (4 males, 6 females) to 24°C, 60% RH. The characteristics of the participants are given in Table 1.

The 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 (m_{f}), lean tissue mass (m_{l}), and bone mass (m_{b}). 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%) (12, 37). Using these components (13), we determined the mean average specific heat of the body (C_{P}) (Table 2).

### Instrumentation

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 at the T8/T9 level, in proximity to the left ventricle and aorta. This position is based upon the equation of Mekjavic and Rempel (27). Rectal temperature (T_{re}) was measured using a pediatric thermocouple probe (Mon-a-therm General Purpose Temperature Probe) inserted to a minimum of 12 cm past the sphincter. Aural canal temperature (T_{au}) was measured using a aural canal thermocouple probe (Mon-a-therm Tympanic) placed in the aural canal until resting against the tympanic membrane (determined by the participant reporting an audible scratching sound), following which it was withdrawn slightly. The aural canal 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 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 (14): head 7%, hand 4%, upper back 9.5%, chest 9.5%, lower back 9.5%, abdomen 9.5%, bicep 9%, forearm 7%, quadriceps 9.5%, hamstring 9.5%, front calf 8.5%, and back calf 7.5%.

Regional muscle temperature was measured using a flexible intramuscular temperature probe (Physitemp Instruments, Clifton, NJ, model IT-17:18, type T, time constant of 0.1 s) inserted into the vastus lateralis (T_{vl}), triceps brachii (T_{tb}), and upper trapezius (T_{ut}). Using an aseptic technique, we anesthetized the skin, subcutaneous tissue, and muscle to a maximum depth of 40 mm by infiltrating ∼3 ml of lidocaine with 2% epinephrine. An 18-gauge, 45-mm nonradiopaque FEP polymer catheter (Medex Canada, Toronto, ON, Canada) was then inserted at an angle and parallel to the long axis of the muscle into the anesthetized tract to the required depth (∼3 cm). The catheter stylet was then withdrawn, and the temperature probe was inserted into the catheter shaft. The probe assembly, including the catheter shaft, was secured to the skin with sterile, waterproof dressing (23, 25). The implant site for the vastus lateralis was approximately midway between, and lateral to, a line joining the anterior superior iliac spine and the superior aspect of the centre of the patella (23–25). The triceps brachii muscle temperature probe was inserted approximately midway between, and lateral to, a line joining the greatertubercle of the humerus and the superior aspect of the olecranon of the ulna (23, 25). The upper trapezius muscle temperature probe was inserted 3 cm superior to the center point between the acromion process and superior angle of the scapula.

All temperature data were collected using a HP Agilent data acquisition module (model 3497A) at 15-s intervals. These data were simultaneously displayed and recorded in spreadsheet format on a personal computer (IBM ThinkCentre M50) with LabVIEW software (Version 7.0, National Instruments, Austin, TX).

#### Direct calorimetry.

The 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 ± 2.3 W for the measurement for total body heat loss. A full technical description of the fundamental principles of the original Snellen calorimeter has been published (39), and a further technical report describing all modifications and performance characteristics is also available (34).

In summary, the calorimeter incorporates a semirecumbent constant load cycle ergometer and is housed within a climatic chamber slightly pressurized (+8.25 mmHg) to nullify potential air leakage through the calorimeter walls. Differential air temperature and humidity are measured over the calorimeter by sampling the influent and effluent air. The water content is measured using precision dew point thermometry (model 373H; RH Systems, Albuquerque, NM), while the air temperature is measured using RTD high-precision thermistors (±0.002°C, Black Stack model 1560, Hart Electronics, American Fork, UT). Air mass flow through the calorimeter is estimated by differential thermometry over a known heat source (2 × 750 W heating elements) placed in the effluent air stream. Differential temperature over the heater is measured using a third aforementioned high-precision thermistor placed downstream from the heater. Air mass flow rate (kg air/min) is continuously measured during each trial. Data from the calorimeter were collected continuously at 8-s intervals throughout the trials. The real-time data were displayed and recorded on a personal computer (Dell OPTIPLEX GX270) with LabVIEW software (Version 7.0, National Instruments).

Evaporative heat loss per minute was calculated using the following equation (1) where (Humidity_{out} − Humidity_{in}) is the difference in absolute humidity across the calorimeter (g water·kg air^{−1}), and 2.427 is the latent heat of vaporization of sweat (kJ·kg sweat^{−1}) (50).

Dry heat loss per minute from radiation, conduction, and convection was calculated using the following equation (2) where (Temperature_{out} − Temperature_{in}) is the difference in air temperature across the calorimeter (°C), and 1.005 is the specific heat of air [kJ·(kg air·°C)^{−1}].

#### Indirect calorimetry.

Oxygen consumption (V̇o_{2}) was measured by the open circuit technique using expired gas samples drawn from a 6-liter fluted mixing box. Expired gas was analyzed using calibrated electrochemical gas analyzers (AMETEK model S-3A/1 and CD 3A, Applied Electrochemistry, Pittsburgh, PA). Expired air was recycled back into the calorimeter chamber to account for respiratory conductive and evaporative heat loss. Before each session, gas mixtures of 4% CO_{2}, 17% O_{2}, balance N_{2} were used to calibrate the gas analyzers and a 3-liter syringe was used to calibrate the turbine ventilometer.

Metabolic energy expenditure (M) was calculated from minute-average values for V̇o_{2} and respiratory exchange ratio using the following equation (3) where e_{c} is the caloric equivalent per liter of oxygen for the oxidation of carbohydrates (21.13 kJ), and e_{f} is the caloric equivalent per liter of oxygen for the oxidation of fat (19.62 kJ).

#### Change in body heat content.

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 cumulative change in heat storage over the exercise period was therefore calculated using the following equation (4) where Ṁ = metabolic rate, (Ṙ + Ċ + K̇) = rate of dry heat loss (radiation, convection, and conduction), Ė = rate evaporative heat loss, and Ẇ = rate of external work being performed.

### Experimental Protocol

All participants volunteered for two separate testing sessions. On the first day, an incremental cycle ergometer V̇o_{2 peak} 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, with each participant entering the calorimeter at 8:45 AM. Participants were asked to arrive at the laboratory in a fasted state, consuming no tea, coffee, or food 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 air temperature of either 24°C or 30°C and either 30% or 60% relative humidity. 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_{2 peak} for a maximum of 90 min. The exercise duration was such that a steady-state condition defined as a rectal temperature stable within 0.1°C, a variation of less than 3% for metabolic heat production (M − W) and constant total heat loss (dry heat loss + evaporative heat loss), would be achieved for at least the final 10 min of exercise (31, 46–48).

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

The data from all participants were pooled and analyzed according to ambient air temperature (24 and 30°C). Data were not separated further according to relative humidity due to the confounding effect of a reduced number of data points upon predictive power, and the traditional two-compartment thermometry approach employing weighting coefficients based upon air temperature not relative humidity (4). This also ensures an optimal statistical validity by attaining a wide variation in the calorimetric and thermometric measures between participants, under each air temperature condition.

Change in body heat content (ΔH_{b}) as measured using calorimetry was solved for mean body temperature (ΔT̄_{b}) using the following equation (5) where ΔH_{b} is the change in body heat content by calorimetry (kJ), b_{m} is total body mass (kg), and C_{P} is specific heat of the human body as estimated using DEXA (in kJ·kg^{−1}·°C^{−1}).

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

The traditional two-compartment thermometry model (4) for mean body temperature (ΔT̄_{b}) is (6) 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.” The value of X may not exceed 1 or be less than 0.

#### Three-compartment thermometry model of mean body temperature.

The three-compartment thermometry model (28, 45) for mean body temperature (ΔT̄_{b}) is (7) where ΔT_{core} is the change in core temperature represented by either rectal (T_{re}), esophageal (T_{es}), aural (T_{au}) temperature or an unweighted mean of the three measurements (T_{c}); ΔT̄_{sk} is the change in mean skin temperature; ΔT_{mus} is the change in muscle temperature represented by either vastus lateralis (T_{vl}), upper trapezius (T_{ut}), triceps brachii (T_{tb}), the unweighted mean of inactive muscle temperature (T_{inact}), or an unweighted mean of all three measurements (T_{m}). Values for coefficients X_{1}, X_{2}, and X_{3} may not exceed 1 or be less than 0, and the sum of all coefficients must equal 1.

#### Derivation of optimal two- and three-compartment models for mean body temperature.

The two- and three-compartment thermometry models were individually fit to the mean body temperature data obtained using calorimetry with the optimization technique of quadratic programming. In summary, the quadratic programming problem is to derive coefficient values that minimize a quadratic function while simultaneously satisfying the set of linear constraints (32). These constraints were that individual coefficients within each model may not exceed 1, be less than 0, and the sum of all coefficients within each model must equal 1. Quadratic programming was performed using the statistical programming language “R” (the open-source software R can be downloaded at http://www.r-project.org/).

#### Goodness-of-fit.

To demonstrate and compare the predictive power of the optimal two- and three-compartment thermometry models for ΔT̄_{b,} the goodness-of-fit was measured for each by simply 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_{bi}), 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* = [∑*i* = 1↕*n* (*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, that is, 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 following 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 *R*^{2} statistic being lower. With this in mind, the adjusted *R*^{2} statistic is reported in the present study.

## RESULTS

### Thermometry Data

Mean values for mean skin temperature and all of the measurements of core and regional muscle temperature at each air temperature condition are given for baseline preexercise rest and across the final 10 min of exercise (Table 3). These data show that during the final 10 min of exercise, rectal temperature (T_{re}) was 0.24°C (SD 0.23) and 0.25°C (0.15) higher than esophageal temperature (T_{es}) and 0.62°C (0.23) and 0.45°C (0.27) higher than aural canal temperature (T_{au}) at 24°C and 30°C, respectively. Active muscle temperature, vastus lateralis (T_{vl}), was higher than the two inactive muscle temperature sites of the triceps brachii (T_{tb}) and the upper trapezius (T_{ut}) by 1.23°C (0.98) and 0.53°C (0.99), respectively, at 24°C, and by 0.63°C (0.74) and 0.62 (0.87), respectively at 30°C. Mean core temperature (T_{c}), T_{es}, and T_{re} was higher than T_{vl} by 0.29°C (0.53), 0.33°C (0.59), and 0.57°C (0.56), respectively, at 24°C, and by 0.08°C (0.37), 0.07°C (0.42), and 0.32°C (0.39), respectively, at 30°C. Whereas T_{au} was 0.03°C (0.23) and 0.14°C (0.36) lower than T_{vl} at 24° and 30°C, respectively.

### Comparison of Thermometry with Calorimetry

An example of the minute-by-minute calorimetry data with concurrent thermometry data is given in Fig. 1. The mean differences between calorimetry and the two thermometric models for the change in mean body temperature (ΔT̄_{b}) and change in body heat content (ΔH_{b}) at 24 and 30°C are detailed in Table 4.

The optimal coefficients for the estimation of ΔT̄_{b} using the traditional two-compartment thermometry model of “core” represented by T_{re} and “shell” represented by T̄_{sk} for the direct, whole body calorimetry data measured in the present study were The resultant estimation of ΔH_{b} using the two-compartment model for ΔT̄_{b} shows a very poor predictive capability at 24°C and a systematic shortfall compared with calorimetry (as indicated by the negative adjusted *R*^{2} value) at 30°C. Change in body heat content (ΔH_{b}) is below the line of identity between thermometry and calorimetry in 43 of the 52 total participants, and in 26 of the 28 participants at 30°C (Fig. 2*A*).

Results for the quadratic programming analyses of the three-compartment model of core, muscle, and skin for the estimation of ΔT̄_{b} are detailed for 24°C (Table 5) and 30°C (Table 6). At 24°C, it is evident that in all of the models T̄_{sk} has a consistent influence with a weighting coefficient between ∼0.20 and 0.30. Models employing T_{re} as a representation of the “core” yield the higher adjusted *R*-squared statistics, with “muscle” effectively represented by T_{vl}, T_{tb}, and T_{inact}. In contrast, the three-compartment models at 30°C are minimally influenced by T̄_{sk}; however, T_{re} again provides the best representation of the “core” relative to T_{es}, T_{au}, and T_{c}. By incorporating T_{re} as “core”, T_{vl}, T_{tb}, and T_{inact} again provide effective representations of the “muscle” compartment. At both 24 and 30°C, all models using T_{ut} as “muscle” yielded the lowest adjusted *R*-squared statistics. The optimal three-compartment models for the data in the present study were The resultant estimation of ΔH_{b} using the optimal three-compartment thermometry model for ΔT̄_{b} shows an unbiased relationship with calorimetry at both 24 and 30°C (Fig. 2*B*).

## DISCUSSION

The main findings from this study show that the traditional two-compartment thermometry model of “core” and “shell” underestimates changes in body heat content (ΔH_{b}) during moderate-intensity, steady-state exercise by between 15 and 35%. Upon investigating change in mean body temperature (ΔT̄_{b}) within the two-compartment thermometry model, there was a systematic underestimation of ΔT̄_{b} relative to calorimetry. At 30°C, the adjusted *R*-squared statistic for the two-compartment model was negative (−0.37), indicating a bias, that is, simply using the group mean value for ΔT̄_{b} of 1.11°C measured using calorimetry provides a better estimation than the two-compartment model. The three-compartment thermometry model of core, muscle, and skin at both 24 and 30°C was unbiased and was found to consistently yield a more precise estimate of ΔT̄_{b} and therefore ΔH_{b} than the two-compartment model.

The notion of a three-compartment thermometry model for the improved estimation of ΔH_{b} has been supported for some time. However, the present study, with the exception of Snellen (38), is the first to use whole body direct air calorimetry to assess such a concept. Nadel et al. (28) developed the following theoretical three-compartment model for the calculation of absolute mean body temperature (T̄_{b}) during positive and negative work on a semirecumbent bicycle ergometer, by estimating the mass of working muscles from the data of Stolwijk and Hardy (42) where T_{es} is esophageal temperature; T_{m} is quadriceps temperature, and T̄_{sk} is mean skin temperature.

Webb (45) proposed an alternative three-compartment thermometry model for the estimation of change in mean body temperature (ΔT̄_{b}) during level and uphill walking with a suit calorimeter. While muscle temperature was not measured, the estimated weighting coefficients for muscle suggested substantial heat storage during exercise where ΔT_{re} is the change in rectal temperature, ΔT_{m} is the change in mean muscle temperature; and ΔT̄_{sk} is change in mean skin temperature.

The three-compartment models derived in the present study suggest that the role of skin temperature in the estimation of ΔT̄_{b} becomes progressively less with increasing ambient air temperature as is the case with the traditional two-compartment approach (4). As such, the model derived at 30°C is similar to that proposed by both Webb (45) and Nadel et al. (28). Furthermore, the “core” weighting coefficient derived by Webb (45) is almost identical to the 30°C model in our study, while the weighting coefficient derived by Nadel et al. (28) is closer to that of the 24°C model; however, T_{re} provided the best representation of the “core” compartment at both 24 and 30°C. The “muscle” compartment weighting coefficient of 0.46 at 30°C is very similar to that proposed previously by Webb (45), but the coefficient of 0.13 at 24°C is lower than previously suggested with the body “shell” (i.e., ΔT̄_{sk}) having a more prominent effect.

Whole body, direct air calorimetry was used by Snellen (38) to develop an improved estimation of ΔH_{b} and therefore ΔT̄_{b}. This was a unique study that incorporated multiple tissue measurements, including the estimation of subcutaneous temperature, for individuals exposed to ambient conditions from 12.3 to 35.0°C. However, there were considerable limitations of the methodology, in that only seven young male subjects were tested and subcutaneous temperatures were not directly measured, but estimated, using zero-flux heat devices, which have been since demonstrated not to give a reliable estimate of muscle temperature (3). Furthermore, the multiple linear regression method used for deriving the improved estimating equation for ΔT̄_{b} appears statistically unstable due to the number of variables introduced for such a small sample size, potential collinearity between variables, and the use of a nonintercept design, giving disproportionate *R*-squared statistics. In the case of the present study, a large subject group of 52 was used, ranging in age and physical characteristics; active and inactive muscle temperatures were directly measured using intramuscular probes; and the analytical techniques for deriving an improved estimation of ΔT̄_{b} were meticulously considered, so that collinearity between variables was avoided and fallacious *R*-squared statistics were not attained.

Mean body temperature is defined as the average temperature of the tissues of the body (4). In the two-compartment thermometry model, change in mean skin temperature is independently included in the estimation of the change mean body temperature. However, in a typical person, ∼40% of total body mass is muscle mass, where as only ∼5% is skin mass (44). The specific heat of muscle (3.639 kJ·kg^{−1}·°C^{−1}) is very similar to that of skin (3.662 kJ·kg^{−1}·°C^{−1}), and in the present study, change in mean muscle temperature was 2.08 and 3.35 times greater than the change in mean skin temperature at 24°C and 30°C, respectively. It therefore seems logical to consider changes in muscle temperature when estimating changes in mean body temperature. It has previously been viewed in the two-compartment thermometry model that the “muscle” compartment is enclosed in the “core” compartment once muscle becomes well perfused with blood during exercise. However, the data from the present study show that the change in both active and inactive muscle temperature is poorly represented by any measure of core temperature. After 90-min of exercise, change in T_{vl}, T_{tb}, and T_{ut} were 4.0, 4.3, and 1.8 times greater that of T_{re} at 24°C; and 3.4, 3.1, and 1.4 times greater than T_{re} at 30°C.

The findings of the present study suggest that the source of error observed with the two-compartment thermometry model for the estimation of ΔT̄_{b} and therefore ΔH_{b} is an underestimation of the tissue temperature transients of the body during exercise. The three-compartment model by no means reflects the level of complexity of the thermal interactions between various tissues of the body; however, the inclusion of a “muscle” compartment does give a degree of representation to the considerable influences of muscle heat load upon body heat content. Indeed, regional muscle temperature at any point in time is the result of regional differences in metabolic rate, conductive heat loss to adjacent tissue, and deep and peripheral convective blood flow (9). Furthermore, the convective transfer of muscle heat load to cooler tissues in the body has been demonstrated to significantly prolong the elevation of core temperature and presumably body heat content after exercise, with hyperemic previously active musculature considered to have the most profound influence (23, 25).

When using a “muscle” compartment for the estimation of ΔT̄_{b}, the present findings suggest a minimal predictive role of the “shell” compartment at warmer ambient temperatures. In addition to the fact that total body mass is composed of a relatively small proportion of skin mass, the contribution of mean skin temperature to the estimation of ΔT̄_{b} is further confounded by several factors. Skin temperature is strongly influenced by skin blood flow, which itself can be significantly modified independently of whole body thermal state. For example, varying levels of exercise intensity result in different skin-to-muscle perfusion ratios, with increasing blood flow shunted away from skin to working muscle groups with greater levels of exercise (23). Furthermore, factors such as hydration status (29), training status (30), level of acclimatization (10), and the administration of topically applied medications, such as corticosteroids and nicotinates (21), have been demonstrated to alter skin blood flow during exercise. The use of mean skin temperature as an estimate of the thermal status of the skin is itself also subject to potential error. Measurement methods range from as few as four sites (33) to as many as 12 sites (14), and as mean skin temperature is in reality an interface temperature between the body surface with the external environment, factors such as clothing and environmental conditions will also have an influence.

Similarly, as with the two-compartment thermometry model, the data from the present study indicated that T_{re} was the “core” measurement that best associated with ΔT̄_{b} within the three-compartment thermometry model. Models using T_{es} as an indicator of “core” temperature provided the worst association with ΔT̄_{b}. This is thought to be a consequence of T_{es} generally representing the central arterial blood temperature (6). Although a response lag is inevitable with T_{re}, it is suggested that during steady-state exercise T_{re} provides a better representation of equilibrated tissue temperatures of the deep visceral/splanchnic region. The use of T_{au} also provided an acceptable means by which changes in core temperature could be represented in the three-compartment thermometry model; however, T_{au} was consistently lower than both T_{re} and T_{es}, possibly due to insufficient insulation of the probe in the aural canal from the air within the calorimeter and are therefore thought to be less reliable.

The present study does have limitations in terms of the range of ambient conditions tested and the employment of only one workload. Indeed core and active muscle temperature has been demonstrated to be dependent upon relative workload (35); therefore, thermometry models for ΔH_{b} may also differ across the range of workloads that steady-state exercise is possible. Furthermore, the employment of the three-compartment thermometry model does require the direct measurement of intramuscular temperature; however, in many cases, such an invasive technique may not be possible. The development of an accurate noninvasive method of estimating muscle temperature using novel zero-heat-flux methods is ongoing (3, 51).

Despite the inclusion of a “muscle” compartment yielding an improved estimation of ΔT̄_{b} relative to the traditional two-compartment thermometry model, the optimal models only explained 48% and 51% of the variation found in ΔT̄_{b} at 24°C and 30°C, respectively. Increasing the number of tissue temperature measurements intermediate to the “core” and “shell” may further improve the estimation of ΔT̄_{b} somewhat; however, the determination of the primary sources of individual variability in body heat content is of paramount importance for its more precise estimation. Further research must therefore be conducted to elucidate the relative effects of factors such as adiposity, age, gender, physical fitness, and acclimation upon ΔH_{b}.

In conclusion, whole body direct air calorimetry shows that a two-compartment thermometry model of “core” and “shell” for the derivation of ΔT̄_{b} underestimates ΔH_{b} by between 15 and 35% under the conditions tested in this study. A three-compartment thermometry model independently removed the statistical bias seen with the two-compartment model, including the thermal influences of “muscle,” and consistently yielded a more precise estimate of ΔT̄_{b} and therefore ΔH_{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 Natural Sciences and Engineering Research Council (to Dr. G. Kenny).

## Footnotes

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- Copyright © 2007 the American Physiological Society