J Appl Physiol 103: 443–451, 2007.
First published May 10, 2007; doi:10.1152/japplphysiol.00117.2007.
Estimating changes in mean body temperature for humans during exercise
using core and skin temperatures is inaccurate even with a correction factor
Ollie Jay,1 Francis D. Reardon,1 Paul Webb,2 Michel B. DuCharme,1,3 Tim Ramsay,4 Lindsay Nettlefold,1
and Glen P. Kenny1
1
Laboratory of Human Bioenergetics and Environmental Physiology, School of Human Kinetics, Faculty of Health Sciences,
University of Ottawa, Ottawa, Ontario, Canada; 2Yellow Springs, Ohio; 3Defence Research and Development Canada,
Quebec City, Quebec, Canada; and 4Ottawa Health Research Institute, The Ottawa Hospital, Ottawa, Ontario, Canada
Submitted 25 January 2007; accepted in final form 7 May 2007
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 (⌬Hb). Since ⌬Hb
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 ⌬Hb
can be attained. However, in the absence of calorimetric
methods, thermometry is often used to estimate ⌬Hb by employing the fact that ⌬Hb is given by the product of the change
in the mean temperature of the tissues of the body (⌬T៮ b), the
total mass of the body (bm), and the average specific heat of all
the tissues of the body (Cp). For a given body of a known bm
and Cp, it is therefore assumed that ⌬Hb can be estimated by
thermometrically approximating ⌬T៮ b. The most commonly
used thermometry method is the traditional two-compartment
model (3) that estimates ⌬T៮ b by measuring the change in rectal
temperature (⌬Tre) that represents a “core” compartment
and the change in mean skin temperature (⌬T៮ sk) that represents
a “shell” compartment. The relative contribution of each
compartment to ⌬T៮ 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 ⌬T៮ 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 ⌬T៮ b,
incorporating a “muscle” compartment intermediate to the core
and shell, has been subsequently proposed (21, 33) and provides an improved estimation of ⌬T៮ b and therefore ⌬Hb (17).
However, a three-compartment model requires the invasive
measurement of intramuscular temperature, and for the purpose of practicality, an accurate estimation of ⌬T៮ 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
⌬Hb using whole body calorimetry on individuals performing
muscular work in a hot environment. He subsequently derived
a model for ⌬T៮ b using core and shell coefficients similar to that
of the traditional model and a correction factor of ⬃0.40.
Address for reprint requests and other correspondence: G. P. Kenny, Univ.
of Ottawa, School of Human Kinetics, 125 Univ., Montpetit Hall, Rm. 367,
Ottawa, Ontario, Canada K1N 6N5 (e-mail: [email protected]).
The costs of publication of this article were defrayed in part by the payment
of page charges. The article must therefore be hereby marked “advertisement”
in accordance with 18 U.S.C. Section 1734 solely to indicate this fact.
body heat storage; calorimetry; heat stress; hyperthermia; thermoregulation
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Jay O, Reardon FD, Webb P, DuCharme MB, Ramsay T,
Nettlefold L, Kenny GP. Estimating changes in mean body
temperature for humans during exercise using core and skin temperatures is inaccurate even with a correction factor. J Appl
Physiol 103: 443–451, 2007. First published May 10, 2007;
doi:10.1152/japplphysiol.00117.2007.—Changes in mean body
temperature (⌬T៮ b) estimated by the traditional two-compartment
model of “core” and “shell” temperatures and an adjusted twocompartment 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 O2 consumption for 60 or 90
min in the Snellen calorimeter at 24 or 30°C. The core compartment
was represented by esophageal, rectal (Tre), and aural canal temperature, and the shell compartment was represented by a 12-point mean
skin temperature (T៮ sk). Using Tre and conventional core-to-shell
weightings (X) of 0.66, 0.79, and 0.90, mean ⌬T៮ 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 Tre, X ⫽ 0.80, and a correction factor (X0) of 0.40,
mean ⌬T៮ 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 ⌬T៮ b data was subsequently used to derive
best-fitting values of X for both models and X0 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 ⌬T៮ b for the traditional model and 56% for the adjusted
model. In conclusion, throughout exercise the estimation of ⌬T៮ 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.
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Table 1. Mean descriptive characteristics for male and female participants
24°C
30°C
24°C
30°C
Sex
n
Age, yr
Weight, kg
Height, cm
BSA, m2
BMI, kg/m2
V̇O2peak, ml 䡠 kg⫺1 䡠 min⫺1
M
M
F
F
13
18
11
18
25 (8)
24 (6)
24 (6)
23 (3)
78.1 (12.9)
77.5 (13.2)
63.4 (5.4)
61.0 (7.7)
178.5 (6.4)
178.6 (5.7)
167.4 (6.2)
166.9 (6.8)
1.96 (0.17)
1.95 (0.18)
1.71 (0.09)
1.68 (0.13)
24.5 (3.4)
24.2 (3.2)
22.6 (1.8)
21.8 (2.1)
52.1 (7.2)
48.3 (7.2)
41.5 (9.1)
41.1 (6.7)
Values are means (SD). Body surface area (BSA) was estimated using the equation of DuBois and DuBois (7), body mass index (BMI), and peak O2
consumption (V̇O2peak). M, male participant; F, female participant.
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 (Ta) and
30% relative humidity (RH); 13 (8 men, 5 women) to Ta ⫽ 30°C, 60%
RH; 14 (9 men, 5 women) to Ta ⫽ 24°C, 30% RH; and 10 (4 men, 6
women) to Ta ⫽ 24°C, 60% RH. Mean characteristics for male and
female participants are given in Table 1.
Body composition of each participant was measured using dualenergy x-ray absorptiometry (DEXA) by which the body mass is
partitioned into fat tissue mass, lean tissue mass, and bone mass. Lean
tissue mass (ml) is further subdivided into muscle mass (51.0% of ml);
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 (CP) was determined (12) and is given in Table 2.
Instrumentation
Thermometry. Esophageal temperature (Tes) 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 (Tre) 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 (Tau) 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-mmdiameter 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 (T៮ 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
Table 2. Mean dual-energy X-ray absorptiometry results for male and female participants
Sex
n
Lean Mass, kg
Fat Mass, kg
Bone Mass, kg
CP, kJ 䡠 kg⫺1 䡠 K⫺1
24°C
M
13
30°C
M
18
24°C
F
11
30°C
F
18
60.44 (6.43)
71.59–50.48
61.92 (6.39)
74.01–51.89
44.85 (3.85)
51.08–38.76
43.41 (6.56)
58.81–33.40
14.46 (8.16)
28.43–3.24
14.17 (8.68)
31.72–5.66
15.99 (4.92)
21.18–4.73
14.36 (3.50)
20.20–6.15
3.23 (0.48)
4.01–2.38
3.25 (0.46)
4.02–2.38
2.57 (0.19)
2.85–2.32
2.58 (0.38)
3.18–1.91
3.48 (0.05)
3.56–3.42
3.49 (0.05)
3.55–3.39
3.43 (0.05)
3.53–3.36
3.43 (0.04)
3.49–3.38
Values are means (SD) and range (maximum–minimum). Specific heat of the human body (CP) was calculated from partitioning total body mass into lean,
fat, and bone, with lean mass subdivided into muscle mass (51.0%), skin mass (11.0%), combined white matter, gray matter, eye, nerve, lens, and cartilage mass
(12.9%), blood mass (25.0%) and cerebral spinal fluid mass (0.1%); and assigning a specific heat for each component (11, 12, 25).
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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 ⌬T៮ 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 ⌬T៮ 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 twocompartment 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.
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Experimental Protocol
All participants volunteered for two separate testing sessions. On
the first day, an incremental cycle ergometer peak O2 consumption
(V̇O2peak) 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 Ta 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 V̇O2peak for a maximum of 60 or 90 min. The
exercise duration was such that a steady-state condition defined as a
Tre 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 Ta 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 Ta 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 (⌬Hb,cal) was solved
for change in mean body temperature (⌬T៮ b,cal) after 10, 30, 60, and 90
min of exercise using the following equation
(1)
⌬T៮ b,cal ⫽ ⌬Hb,cal/(bm 䡠 Cp)
where ⌬Hb,cal is change in body heat content by calorimetry (in kJ),
bm is total body mass (in kg), and CP is specific heat of each
participant as estimated using DEXA (in kJ 䡠 kg⫺1 䡠 °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
(⌬T៮ b,trad) after 10, 30, 60, and 90 min of exercise using
(2)
⌬T៮ b,trad ⫽ (X 䡠 ⌬Tre) ⫹ [(1 ⫺ X) 䡠 ⌬T៮ sk]
where ⌬Tre is the change in rectal temperature and ⌬T៮ 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 (⌬T៮ b,adj) after 10, 30, 60, and 90 min of
exercise using
(3)
⌬T៮ b,adj ⫽ X0 ⫹ (X 䡠 ⌬Tre) ⫹ [(1 ⫺ X) 䡠 ⌬T៮ sk]
where ⌬Tre is the change in rectal temperature and ⌬T៮ sk is the change
Table 3. Mean core temperature and mean skin temperature, and whole body calorimetry measurements of change in mean
body temperature and body heat content at 24°C and 30°C after 0, 10, 30, 60, and 90 min of exercise
Core Temperatures, °C
24°C
30°C
0 min
10 min
30 min
60 min
90 min
0 min
10 min
30 min
60 min
90 min
Shell Temperature, °C
Tes
Tre
Tau
T៮ sk
36.64 (0.30)
36.91 (0.27)
37.15 (0.24)
37.23 (0.22)
37.27 (0.25)
36.84 (0.23)
37.13 (0.30)
37.33 (0.35)
37.41 (0.39)
37.44 (0.27)
36.82 (0.27)
36.90 (0.28)
37.25 (0.24)
37.44 (0.24)
37.51 (0.23)
37.01 (0.23)
37.09 (0.25)
37.42 (0.29)
37.64 (0.36)
37.71 (0.26)
36.48 (0.29)
36.62 (0.28)
36.93 (0.28)
36.95 (0.29)
36.90 (0.32)
36.83 (0.28)
36.93 (0.31)
37.23 (0.29)
37.27 (0.37)
37.33 (0.29)
31.39 (0.52)
31.34 (0.19)
32.47 (0.73)
32.63 (0.72)
32.52 (0.74)
33.27 (0.71)
33.44 (0.72)
33.92 (0.73)
33.93 (0.83)
33.88 (0.93)
⌬T៮ b,cal, °C
⌬Hb,cal, kJ
0.47 (0.10)
0.93 (0.22)
1.08 (0.31)
1.06 (0.36)
116.8 (32.9)
226.3 (56.9)
263.0 (77.8)
260.7 (94.1)
0.48 (0.14)
0.91 (0.30)
1.17 (0.47)
1.43 (0.51)
112.9 (29.9)
211.6 (62.6)
272.6 (100.0)
332.7 (125.6)
Values are means (SD) for n ⫽ 24 at 24°C after 10, 30, 60, and 90 min; n ⫽ 36 at 30°C after 10, 30, and 60 min; and n ⫽ 26 at 30°C after 90 min. Core
temperature was measured in the esophagus (Tes), rectum (Tre), and aural canal (Tau). Mean skin temperature (T៮ sk) was measured as a weighted mean of 12 sites
(13). All thermometry measurements are in °C. Changes in mean body temperature (⌬T៮ b,cal) and changes in body heat content (⌬Hb,cal) were concurrently
measured using the Snellen calorimeter.
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(IBM ThinkCentre M50) with LabVIEW software (version 7.0,
National Instruments).
Calorimetry. Change in body heat content (⌬Hb) 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% CO2, 17% O2, and balance N2. 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 k⍀/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 7720050) 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).
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CHANGE IN MEAN BODY TEMPERATURE USING THERMOMETRY
programming language “R” (the open-source software R can be
downloaded at http://www.r-project.org/).
Adjusted R2 statistic. To compare the predictive power of all
thermometry models for ⌬T៮ b,trad and ⌬T៮ b,adj, goodness-of-fit was
measured for each by adapting the R2 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 ith response be denoted by yi (for each
thermometry model, yi ⫽ ⌬T៮ b,i), the ith fitted value be denoted by ŷi,
and let the mean response be denoted by y៮ . Then the variance of the
n
response about the mean is estimated by SSM ⫽ [¥i⫽1
(yi ⫺ y៮ )2]/
(n ⫺ 1) and the residual variance, with respect to the quadratic
programming model, is estimated by SSE ⫽ [¥(yi⫺ŷi)2]/(n ⫺ k ⫺ j).
Defined as the proportion of the variance in the response explained
by the model, the R2 statistic is given by the expression [1 ⫺ (SSE/
SSM)]. As with linear regression, the R2 statistic in a quadratic
programming model has a maximum value of 1. However, as SSE
may be greater than SSM, R2 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
Fig. 1. A–D: percentage error for best-fitting traditional 2-compartment thermometry model for change in mean body temperature (⌬T៮ b) relative to calorimetry
after 10, 30, 60, and 90 min of exercise at 24°C (open circles) and 30°C (shaded circles) using the conventional core-to-shell coefficient of X ⫽ 0.66 (A), 0.79
(B), and 0.90 (C); and for the best-fitting X at each time point for the present data set (D). Error bars indicate 95% confidence intervals.
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in mean skin temperature, X0 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 (⌬T៮ 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 (⌬T៮ b,adj) with the previously recommended weighting
coefficient of X ⫽ 0.80 and correction factor of X0 ⫽ 0.40 (5, 27).
Best-fitting coefficients of thermometry models for calorimetry data. Best-fitting coefficients of the two-compartment thermometry model (⌬T៮ b,trad) and the adjusted two-compartment thermometry
model (⌬T៮ b,adj) were also derived for the ⌬T៮ b,cal and thermometry
(core and skin temperature) measurements in the present study. To
study the influence of different measures of core temperature on ⌬T៮ b
prediction, best-fitting coefficients were also derived for ⌬T៮ b,adj and
⌬T៮ b,cal using ⌬Tes and ⌬Tau instead of ⌬Tre. 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 (X0 in Eq. 3 was unconstrained)
(22). Quadratic programming was performed using the statistical
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CHANGE IN MEAN BODY TEMPERATURE USING THERMOMETRY
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. 3A). At 30°C, a statistical bias
(P ⱕ 0.05) was apparent after 10 and 90 min of exercise, but
an unbiased model with adjusted R2 statistics of 0.49 and 0.36
was evident after 30 and 60 min, respectively (Fig. 3A).
The quadratic programming analyses results for the bestfitting coefficients of the adjusted two-compartment model
for mean body temperature (⌬T៮ b,adj) after 10, 30, 60, and 90
min of exercise using three separate indexes of core temperature (i.e., Tre, Tes, and Tau) are detailed for 24°C and
30°C (Table 5). Unbiased models were evident for ⌬T៮ b,adj at
all time points at 24°C and 30°C (Fig. 3B). 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 R2
statistics. Individual values for ⌬T៮ b,adj relative to ⌬T៮ b,cal at
each time for both 24°C and 30°C are given in Fig. 4.
RESULTS
DISCUSSION
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 (⌬T៮ b,cal), the traditional twocompartment thermometry model for ⌬T៮ b using the conventional coefficients of X ⫽ 0.66, 0.79, and 0.90 were statistically biased (P ⱕ 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 ⌬T៮ 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 ⌬T៮ 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 bestfitting coefficients for ⌬T៮ b,trad after 10, 30, 60, and 90 min of
exercise using three separate indexes of core temperature (i.e.,
Tre, Tes, and Tau) are detailed for 24°C and 30°C (Table 4). The
best-fitting models for ⌬T៮ b,trad at 24°C were statistically biased
(P ⱕ 0.05) after 10 and 30 min of exercise and gave an
unbiased but low predictive power after 60 min (adjusted R2 ⫽
0.07) and 90 min of exercise (adjusted R2 ⫽ 0.20). At 30°C, the
best-fitting models for ⌬T៮ b,trad were statistically biased (P ⱕ
0.05) at all the time points analyzed throughout exercise (Fig.
1D). Individual values for ⌬T៮ b,trad relative to ⌬T៮ b,cal at each
time point for both 24°C and 30°C are given in Fig. 2.
Adjusted Two-Compartment Model
Compared with ⌬T៮ b,cal at 24°C, the adjusted two-compartment thermometry model for ⌬T៮ b using the previously suggested core-to-shell weighting coefficient of X ⫽ 0.80 and the
correction factor of X0 ⫽ 0.40 yielded an adjusted R2 statistic
J Appl Physiol • VOL
The change in mean body temperature (⌬T៮ 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 ⌬T៮ b to derive the best-fitting
Table 4. Results for quadratic fitting of traditional
two-compartment model of “core” (⌬ Tcore) and “shell”
(⌬T៮ sk) at 24°C and 30°C
Best-Fit Coefficients
24°C
30°C
24°C
30°C
24°C
30°C
10
30
60
90
10
30
60
90
10
30
60
90
10
30
60
90
10
30
60
90
10
30
60
90
Measures
X (⌬Tcore)
1 ⫺ X (T៮ sk)
Adjusted R2
Tes
1.00
0.40
0.37
0.35
1.00
0.10
0.12
0.12
1.00
0.37
0.41
0.42
0.00
0.00
0.35
0.70
1.00
0.36
0.30
0.24
1.00
0.00
0.00
0.00
0.00
0.60
0.63
0.65
0.00
0.90
0.88
0.88
0.00
0.63
0.59
0.58
1.00
1.00
0.65
0.30
0.00
0.64
0.70
0.76
0.00
1.00
1.00
1.00
⫺6.93
⫺0.51
⫺0.01
0.09
⫺2.05
⫺0.37
⫺0.72
⫺0.71
⫺17.41
⫺0.62
0.07
0.20
⫺5.58
⫺0.39
⫺0.57
⫺0.63
⫺15.58
⫺0.61
⫺0.22
⫺0.12
⫺5.60
⫺0.39
⫺0.73
⫺0.71
min
min
min
min
min
min
min
min
min
min
min
min
min
min
min
min
min
min
min
min
min
min
min
min
Tre
Tau
Data obtained for the model of ⌬T៮ b,trad ⫽ X 䡠 ⌬Tcore ⫹ (1 ⫺ X) 䡠 ⌬T៮ sk. The
term ⌬Tcore is represented by esophageal (Tes), rectal (Tre), or aural canal (Tau)
temperature. The term ⌬T៮ sk is represented by mean skin temperature. Value for
X may not exceed 1 or be ⬍0 and was derived using the optimization technique
of quadratic programming.
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the mean (SSM) will be less than the variance about the fitted values
(SSE), and R2 will be negative. As is the case with linear regression,
if there are many parameters in the model, it is possible for the R2
statistic to be biased by overfitting. The adjusted R2 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 R2 statistics will be somewhat
different, with the adjusted being lower. With this in mind, the
adjusted R2 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
⌬T៮ b is defined as 100 times the difference between ⌬T៮ b estimated
using the given thermometry model (ŷ) and ⌬T៮ b measured with
calorimetry (y), divided by ⌬T៮ 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.
448
CHANGE IN MEAN BODY TEMPERATURE USING THERMOMETRY
than half of the variation in ⌬T៮ b remained unexplained by
thermometry.
The traditional thermometry model has been previously
shown to underestimate ⌬T៮ 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
⌬T៮ 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 ⌬T៮ 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 ⌬T៮ 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 Tes). Therefore, the concept that ⌬T៮ 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 Tre, because of the well-documented time lag
of this indicator of core temperature (6).
The addition of a correction factor (X0) within the bestfitting adjusted two-compartment thermometry models re-
Fig. 2. A comparison between change in mean
body temperature derived by whole body calorimetry and estimated by thermometry after 10, 30, 60,
and 90 min using the best-fitting traditional 2-compartment model at 24°C (open squares) and 30°C
(shaded circles). Dashed line indicates the line of
identity (y ⫽ x).
J Appl Physiol • VOL
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core-to-shell weighting coefficients for the specific range of
individuals and experimental conditions in the present study,
an accurate estimation of ⌬T៮ 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 ⌬T៮ 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 ⌬T៮ b was statistically
biased, that is, employing the mean group ⌬T៮ b response derived using calorimetry provided a better individual estimation
of ⌬T៮ b than any combination of their thermometry responses.
The adjusted two-compartment thermometry model provided a more accurate estimation of ⌬T៮ 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 ⌬T៮ 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-toshell weighting coefficients and correction factors for the
present data set, an unbiased estimate of ⌬T៮ 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 ⌬T៮ 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
CHANGE IN MEAN BODY TEMPERATURE USING THERMOMETRY
moved the systematic underestimation of ⌬T៮ 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 X0 are only appropriate for the specific
experimental conditions and range of individuals in the present
study. Best-fitting values for X and X0 varied greatly with
exercise duration (and therefore ⌬T៮ b) as well as between 24°C
and 30°C. It is therefore probable that different values for X
and X0 would be necessary for the thermometric estimation of
⌬T៮ 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 ⌬T៮ b across a range of
J Appl Physiol • VOL
“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
⌬T៮ 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 ⌬T៮ b
occurred after 90 min of exercise at 30°C. Under this condition,
the absolute error of the estimation of ⌬T៮ b using thermometry
relative to calorimetry appeared to increase multiplicatively
with increasing heat stress using both the traditional (Fig. 2D)
and adjusted two-compartment best-fitting models (Fig. 4D).
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 ⌬T៮ 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 ⌬T៮ b after 90 min of steady-state exercise
relative to the traditional two-compartment model. However, the proportion of variance in ⌬T៮ 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 ⌬T៮ 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 ⌬T៮ b, particularly at greater levels of exerciseinduced hyperthermia. This may require temperature measurements at several depths intermediate to the core and shell,
possibly with a differing Cp value designated to each compartment.
In conclusion, ⌬T៮ 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 ⌬T៮ b at
only one particular time point. The adjusted two-compartment
thermometry model incorporating a correction factor provided
a more accurate estimation of ⌬T៮ 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 ⌬T៮ b. These results
suggest that at steady-state and non-steady-state body temperatures, the estimation of ⌬T៮ b using any of the three common
measures of core temperature together with mean skin temper-
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Fig. 3. A and B: percentage error for best-fitting adjusted 2-compartment
thermometry model for change in mean body temperature relative to calorimetry after 10, 30, 60, and 90-min of exercise at 24°C (open circles) and 30°C
(shaded circles) using previously suggested core-to-shell coefficient of X ⫽
0.80 and correction factor of X0 0 .40 (A); and best-fitting X and X0 at each time
point for the present data set (B). Error bars indicate 95% confidence intervals.
449
450
CHANGE IN MEAN BODY TEMPERATURE USING THERMOMETRY
Table 5. Results for quadratic fitting of adjusted 2-compartment model of “core” (⌬Tcore), “shell” (⌬T៮ sk) and adjustment
factor (X0) at 24°C and 30°C
Best-Fit Coefficients
24°C
30°C
24°C
30°C
30°C
min
min
min
min
min
min
min
min
min
min
min
min
min
min
min
min
min
min
min
min
min
min
min
min
X0
X (⌬Tcore)
1 ⫺ X (⌬T៮ sk)
Adjusted R2
Tes
0.39
0.29
0.31
0.28
0.24
0.33
0.54
0.70
0.45
0.36
0.28
0.26
0.38
0.38
0.51
0.65
0.45
0.31
0.37
0.45
0.38
0.40
0.61
0.78
0.45
0.70
0.67
0.61
0.62
0.54
0.46
0.48
0.56
0.77
0.69
0.64
0.85
0.60
0.50
0.60
0.45
0.68
0.65
0.67
0.69
0.53
0.45
0.50
0.55
0.30
0.33
0.39
0.38
0.46
0.54
0.52
0.44
0.23
0.31
0.36
0.15
0.40
0.50
0.40
0.55
0.32
0.35
0.33
0.31
0.47
0.55
0.50
0.24
0.30
0.40
0.45
0.40
0.54
0.47
0.30
0.15
0.48
0.46
0.53
0.11
0.56
0.51
0.43
0.13
0.26
0.25
0.46
0.22
0.56
0.50
0.34
Tre
Tau
Data obtained for the model of ⌬T៮ b,adj ⫽ X0 ⫹ X 䡠 ⌬Tcore ⫹ (1 ⫺ X) 䡠 ⌬T៮ sk. The term ⌬Tcore is represented by Tes, Tre, and Tau. The term ⌬T៮ sk is represented
by mean skin temperature. Value for X may not exceed 1 or be ⬍0, and the correction factor (X0) was not subject to any constraint. Values for X and X0 were
derived using the optimization technique of quadratic programming.
Fig. 4. A comparison between change in mean
body temperature derived by whole body calorimetry and estimated by thermometry after 10, 30, 60
and 90 min using the best-fitting adjusted 2-compartment model at 24°C (open squares) and 30°C
(shaded circles). Dashed line indicates the line of
identity (y ⫽ x).
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24°C
10
30
60
90
10
30
60
90
10
30
60
90
10
30
60
90
10
30
60
90
10
30
60
90
Measures
CHANGE IN MEAN BODY TEMPERATURE USING THERMOMETRY
ature 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 ⌬T៮ 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]).
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