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Clinical Science  |   December 2006
Estimation of Mean Body Temperature from Mean Skin and Core Temperature
Author Affiliations & Notes
  • Rainer Lenhardt, M.D.
    *
  • Daniel I. Sessler, M.D.
  • * Assistant Professor and Vice Chair, Outcomes Research Institute and Department of Anesthesiology & Perioperative Medicine; Director, Neurosciences Intensive Care Unit, University of Louisville. † Chair, Department of Outcomes Research, Cleveland Clinic Foundation; Director, Outcomes Research Institute, and Weakley Professor of Anesthesiology, University of Louisville.
Article Information
Clinical Science / Cardiovascular Anesthesia / Critical Care / Ethics / Medicolegal Issues / Gastrointestinal and Hepatic Systems / Pain Medicine / Respiratory System / Quality Improvement
Clinical Science   |   December 2006
Estimation of Mean Body Temperature from Mean Skin and Core Temperature
Anesthesiology 12 2006, Vol.105, 1117-1121. doi:
Anesthesiology 12 2006, Vol.105, 1117-1121. doi:
BECAUSE the specific heat of human tissue is relatively well established, body heat content can be calculated from mean body temperature (MBT). MBT, defined as the mass-weighted average of tissue temperatures throughout the body, is thus a fundamental characterization of a person’s thermal status. Body heat distribution can be modeled as two thermal compartments, namely the core (trunk and head) and peripheral tissues (the extremities).
Even in a moderate environment, average temperature of the peripheral thermal compartment is 2°–4°C less than core temperature.1 However, this thermal gradient can range from nearly zero to large values depending on the severity of the environment and the consequent vasomotor responses. The perioperative period is dynamic and associated with substantial changes in the core-to-peripheral tissue temperature gradient and internal distribution of body heat. For example, induction of general anesthesia is associated with a substantial flow of heat from the core to peripheral tissues because anesthetics reduce the vasoconstriction threshold (triggering core temperature) by 2°–4°C.2 Vasoconstriction then recurs in patients who become sufficiently hypothermic, usually at a core temperature of approximately 34.5°C; this vasoconstriction constrains metabolic heat to the core thermal compartment and eventually restores the normal core-to-peripheral thermal gradient.3 Because vasomotion has such an important effect on the distribution of body heat in the perioperative period, it would be difficult to predict MBT from core temperature alone.
Core temperature is easy to measure and temperatures are relatively homogeneous throughout the trunk and head; it is thus easy to determine average temperature of the core thermal compartment. Peripheral tissue temperatures, on the other hand, vary widely depending on the region, environmental characteristics, and thermoregulatory vasomotion. Direct measurement of peripheral tissue temperature is difficult, but can be accomplished by insertion of a sufficient number of needle thermocouples, combined with tedious calculations. This procedure is complex, painful, and risky.
In 1935, Burton4 cleverly proposed that MBT could be calculated from a formula: MBT = a · TCore+ (1 − a) · TSkin. The general form of the equation was based on the logic that core tissues are relatively homogeneous whereas tissue temperature in the peripheral decreases parabolically from core temperature to skin temperature. The value of a  , the coefficient describing the contribution of core temperature to MBT, was then estimated by simultaneously measuring the change in body heat content (in a calorimeter), core temperature, and mean skin temperature. The resulting value of the coefficient α was 0.64, thus giving the formula: MBT = 0.64 · TCore+ 0.36 · TSkin.
A similar approach has been used by others, including Hardy and DuBois,5 who proposed a coefficient, a  , of 0.7 for a neutral environment; Stolwijk and Hardy,6 who proposed a coefficient of 0.7 for a hot environment; and Snellen,7 who found the coefficient to be approximately 0.8 during muscular work in a hot environment. Subsequently, Colin et al.  8 showed in an elegant study that Burton’s coefficient was correct for a neutral environment, but that the coefficient increased to 0.79 in an extremely warm environment.
Surely the most severe thermal stress humans endure is hypothermic cardiopulmonary bypass. Bypass machines, through which the entire circulation flows, contains powerful heat exchangers that can essentially set blood temperature to any desired value. Consequently, it is quite possible—and hardly unusual—to change core temperature at rates approaching a degree centigrade per minute. The changes are especially notable when patients are cooled to core temperatures near 18°C for circulatory arrest during repairs of complex cardiac, aortic arch, and brain abnormalities.9 In these patients especially, it would be virtually impossible to predict MBT from core temperature alone, especially during periods of rapid thermal perturbation.
It is similarly by no means obvious that a simple combination of mean skin and core temperatures will accurately reflect average temperature of human tissues under such dynamic perioperative conditions. Certainly Burton’s formula4 and its successor8 were not designed for, nor validated under, such circumstances. Therefore, we tested Burton’s approach in the perioperative period because a formula that remains valid in the face of such large tissue-temperature inhomogeneities and rapid flows of heat from the core to the periphery is likely to be generally applicable.
Materials and Methods
We evaluated four previously published heat balance studies; in each, patients underwent substantial thermal perturbations. Each individual study was approved by the respective local institutional review boards and informed consent obtained from all patients. Two studies evaluated core and peripheral temperatures in patients undergoing cardiac surgery during extracorporeal circulation,9,10 one evaluated heat balance during anesthesia and induced fever,11 and the fourth tested the efficacy of an endovascular heat-exchanging catheter in healthy human volunteers.12 In each case, MBT was calculated and estimated at 15-min intervals.
Arm and leg tissue temperatures were determined as previously described.13 In each subject, the leg was divided into five segments: upper thigh, lower thigh, upper calf, lower calf, and foot. Each thigh and calf segment was further divided into an anterior and posterior section, with one third of the estimated mass considered to be posterior. At each circumference, leg muscle temperatures were recorded using 8-, 18-, and 38-mm-long, 21-g needle thermocouples (Tyco-Mallinckrodt Anesthesiology Products, Inc., St. Louis, MO) inserted perpendicular to the skin surface. Skin-surface temperatures were recorded immediately adjacent to each set of needles and directly posterior to each set. Subcutaneous temperature was measured on the ball of the foot and palm using deep-tissue thermometers (Terumo Medical Corp., Tokyo, Japan).14,15 These devices estimate tissue temperature approximately 1 cm below the skin surface.
Anterior segment tissue temperatures, as a function of radial distance from the center of the leg segment, were calculated using skin-surface and muscle temperatures and fourth-order regressions. Temperature at the center of the thigh was assumed to equal core temperature. In contrast, temperature at the center of the lower leg segments was estimated from the regression equation with no similar assumption. Average anterior limb temperature was estimated from these individual temperatures using the fourth-order version of a previously described formula13 :
where TAveis average temperature of the leg segment from the center to radius r  and a  2(°C/cm2) and a  4(°C/cm4) are the fourth-order regression constants.
Rather than assume full radial symmetry, we assumed only that radial temperature distribution in the posterior leg segments would also be parabolic. Accordingly, we calculated the regression constant a  2in the posterior leg segments from a  0determined from the adjacent anterior segment and the posterior segment skin temperature. Average posterior segment tissue temperatures were then determined from the second-order version of equation 1. We have previously described the derivation of these equations and their limitations.13 
“Deep temperature,” measured on the ball of the foot, was assumed to represent the entire foot. Average temperatures of the thigh and lower leg (calf and foot) were calculated by weighting values from each of the nine segments in proportion to their estimated masses. The right and left legs were treated comparably throughout this study, so we assumed that average tissue temperatures in the two limbs were similar.
The lengths of the right arm (axilla to elbow) and forearm (elbow to wrist) were measured in centimeters. The circumference was measured at the midpoint of each segment. As in the right leg, 8-, 18-, and 38-mm-long needle thermocouples were inserted into each segment. Skin-surface temperatures were recorded immediately adjacent to each set of needles.
Average arm tissue temperatures were calculated from parabolic tissue temperature regressions and the equation above. In the arms, we assumed full radial symmetry and thus did not separately calculate posterior segment values. Adductor pollicis temperature was assumed to represent that of the entire hand. As in the leg, average temperatures of the arm and forearm (forearm and hand) were calculated by weighting values from each of the three segments in proportion to their estimated masses.
Trunk and head weight was estimated by subtracting the calculated weight of the extremities (from the radial integration) from the total weight of each subject. Measured MBT was determined from the mass-weighted average of core and peripheral tissue temperatures.
Area-weighted, mean skin-surface temperature was computed from measurements at 15 sites by assigning the following regional percentages to each area: head, 6%; upper arms, 9%; forearms, 6%; hands, 2.5%; fingers, 2%; back, 19%; chest, 9.5%; abdomen, 9.5%; medial thigh, 6%; lateral thigh, 6%; posterior thigh, 7%; anterior calves, 7.5%; posterior calves, 4%; feet, 4%; and toes, 2%.16 MBT was estimated from mean skin and core temperatures using the formula of Burton4 : MBT = 0.64 · TCore+ 0.36 · TSkin. Measured and estimated MBTs were compared using linear regression and Bland-Altman analysis.17 Results are presented as mean ± SD (95% confidence interval).
Results
We included 913 data pairs from four studies in the analysis (44 study subjects).11,14–16 Morphometric and demographic characteristics and study details are presented in table 1. Core temperature ranged from 18.5° to 37.1°C, and measured MBT ranged from 18° to 36.5°C. There was a remarkably good relation between measured and estimated MBT: MBTmeasured= 0.94 MBTestimated+ 2.15, r  2= 0.98 (fig. 1).
Table 1. Morphometric and Demographic Characteristics and Study Details 
Image not available
Table 1. Morphometric and Demographic Characteristics and Study Details 
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Fig. 1. Linear regression including all 913 data pairs from 44 subjects.  9–12 Mean body temperature (MBT) was estimated from core and mean skin temperatures and compared with directly measured values. There was a remarkably good relation between measured and estimated mean body temperatures: MBTestimated= 0.94 · MBTMeasured+ 2.15  , r  2= 0.98. 
Fig. 1. Linear regression including all 913 data pairs from 44 subjects.  9–12Mean body temperature (MBT) was estimated from core and mean skin temperatures and compared with directly measured values. There was a remarkably good relation between measured and estimated mean body temperatures: MBTestimated= 0.94 · MBTMeasured+ 2.15 
	, r  2= 0.98. 
Fig. 1. Linear regression including all 913 data pairs from 44 subjects.  9–12 Mean body temperature (MBT) was estimated from core and mean skin temperatures and compared with directly measured values. There was a remarkably good relation between measured and estimated mean body temperatures: MBTestimated= 0.94 · MBTMeasured+ 2.15  , r  2= 0.98. 
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The bias (average difference between estimated and measured MBTs) was −0.09°± 0.42°C, solid line in figure 2(95% confidence interval, −0.12° to −0.06°C). The precision (average of the absolute value of the difference between estimated and measured MBTs) was 0.31°± 0.29°C (95% confidence interval, −0.29° to 0.33°C). Over the entire data set, 87% of the MBT estimates were within 0.5°C of the measured values, and 92% were within 0.7°C.
Fig. 2. Bland-Altman plot for all 913 data pairs from all four studies.  9–12 The bias (average difference between estimated and measured mean body temperatures) is −0.09°± 0.42°C  , solid line  (95% confidence interval, −0.12° to −0.06°C). The precision (average of the absolute value of the difference between estimated and measured mean body temperatures) is 0.31°± 0.29°C (95% confidence interval, −0.29° to 0.33°C). Over the entire data set, 87% of the mean body temperature estimates were within 0.5°C of the measured values. 
Fig. 2. Bland-Altman plot for all 913 data pairs from all four studies.  9–12The bias (average difference between estimated and measured mean body temperatures) is −0.09°± 0.42°C 
	, solid line  (95% confidence interval, −0.12° to −0.06°C). The precision (average of the absolute value of the difference between estimated and measured mean body temperatures) is 0.31°± 0.29°C (95% confidence interval, −0.29° to 0.33°C). Over the entire data set, 87% of the mean body temperature estimates were within 0.5°C of the measured values. 
Fig. 2. Bland-Altman plot for all 913 data pairs from all four studies.  9–12 The bias (average difference between estimated and measured mean body temperatures) is −0.09°± 0.42°C  , solid line  (95% confidence interval, −0.12° to −0.06°C). The precision (average of the absolute value of the difference between estimated and measured mean body temperatures) is 0.31°± 0.29°C (95% confidence interval, −0.29° to 0.33°C). Over the entire data set, 87% of the mean body temperature estimates were within 0.5°C of the measured values. 
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Differences between estimated and measured values were greatest during deep hypothermia (MBT < 31°C for cardiopulmonary bypass)9 and during pyrogen-induced fever.11 When the analysis was restricted to the remaining two studies,10,12 the bias (average difference between estimated and measured MBTs) was −0.15°± 0.33°C, solid line in figure 3(95% confidence interval, −0.18° to −0.12°C). The precision (average of the absolute value of the difference between estimated and measured MBTs) was 0.28°± 0.23°C (95% confidence interval, −0.26° to 0.30°C). Over the entire data set, 91% of the MBT estimates were within 0.5°C of the measured values.
Fig. 3. Bland-Altman plot of 535 data pairs  10,12 when the studies of deep hypothermia for circulatory arrest  9 and fever  11 were excluded. The bias (average difference between estimated and measured mean body temperatures) is −0.15°± 0.33°C  , solid line  (95% confidence interval, −0.18° to −0.12°C). The precision (average of the absolute value of the difference between estimated and measured mean body temperatures) is 0.28°± 0.23°C (95% confidence interval, −0.26° to 0.30°C). Over the entire data set, 91% of the mean body temperature estimates were within 0.5°C of the measured values. 
Fig. 3. Bland-Altman plot of 535 data pairs  10,12when the studies of deep hypothermia for circulatory arrest  9and fever  11were excluded. The bias (average difference between estimated and measured mean body temperatures) is −0.15°± 0.33°C 
	, solid line  (95% confidence interval, −0.18° to −0.12°C). The precision (average of the absolute value of the difference between estimated and measured mean body temperatures) is 0.28°± 0.23°C (95% confidence interval, −0.26° to 0.30°C). Over the entire data set, 91% of the mean body temperature estimates were within 0.5°C of the measured values. 
Fig. 3. Bland-Altman plot of 535 data pairs  10,12 when the studies of deep hypothermia for circulatory arrest  9 and fever  11 were excluded. The bias (average difference between estimated and measured mean body temperatures) is −0.15°± 0.33°C  , solid line  (95% confidence interval, −0.18° to −0.12°C). The precision (average of the absolute value of the difference between estimated and measured mean body temperatures) is 0.28°± 0.23°C (95% confidence interval, −0.26° to 0.30°C). Over the entire data set, 91% of the mean body temperature estimates were within 0.5°C of the measured values. 
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Discussion
To our surprise, Burton’s formula worked remarkably well over the entire tested range of MBTs from 31° to 36.5°C. Even over this enormous range, the average difference between estimated and measured MBTs was −0.09°± 0.42°C. As might be expected, the formula was somewhat less accurate at the coldest temperatures and especially poor during the rapid cooling phase. This is because only a relatively small volume of the core was initially cooled, but Burton’s formula assumes that 64% of the body mass is represented by core temperature—a fraction that is obviously not the case during rapid cooling. For less obvious reasons, the formula was also less accurate during fever in several volunteers, but not in all of them.
Nonetheless, our results suggest that Burton’s formula is generally accurate over a wide range of circumstances and can be substituted for direct measurements that are invasive and painful. It is important to recognize, however, that an error of 0.5°C in MBT corresponds to 29 kcal in a 70-kg person. Hence, Burton’s formula should be used cautiously in applications where accurate detection of small changes in body heat content is required. Fortunately, previous work4,8 indicates that the formula is highly accurate in near–steady state neutral conditions.
A limitation of our study is that our determination of average peripheral tissue temperature is imperfect because it is based on a limited number of measurements and a number of approximations. For example, our calculation of leg heat content assumes radial symmetry. To minimize risk to our volunteers, we did not verify this assumption by inserting more than three needles in each leg segment. It remains likely that tissue heat content in the posterior third of the leg decreased somewhat less than estimated because heat loss from this region was minimized by the foam insulation covering the operating table. Nonetheless, given the cylindrical shape of the leg and the central position of its major blood vessels, tissue temperatures are likely to be roughly symmetrical. An assumption of angular symmetry is used in nearly all models of heat balance, including some that have been extensively validated.18 
Our calculations make the further assumption that each leg segment is cylindrical. Although not strictly accurate, a cylinder is a reasonable approximation of leg shape and simplifies analysis. Once again, most heat balance models make this assumption and still produce experimentally verifiable results.18 Finally, hand and foot temperature was estimated from “deep temperatures.” Deep temperatures are at best an approximation of average tissue temperature in these inhomogeneous structures; fortunately, both the hands and feet are small and thus contribute relatively little to MBT. Despite the limitations of our tissue temperature measurements, changes in body heat content determined from these measurements are similar to those determined from metabolic rate and cutaneous heat loss.19 These data suggest that the tissue measurements are not far wrong.
Rectal temperature often differs substantially from true core body temperature, especially during rapid thermal transients.20–22 Given this limitation, rectal temperature seems to be suboptimal even for routine clinical use, to say nothing of thermoregulatory research. Therefore, we measured core body temperature at the tympanic membrane,11 nasopharynx,9,10 or distal esophagus12 in our studies. Each was appropriate for the circumstances of the studies. For example, distal esophageal temperature is usually the best minimally invasive core temperature measurement site but is subject to artifact during cardiopulmonary bypass and is accordingly less reliable than the nasopharynx in these patients. Tympanic membrane temperatures are accurate so long as the thermocouple is properly position, the ear canal is occluded, and the face is protected from direct thermal manipulation—as was the case here.
In summary, direct measurement of peripheral tissue temperature can be accomplished by insertion of sufficient needle thermocouples, combined with relatively complex calculations; the procedure is complex, painful, and risky. An alternative is a simple formula, based on core and mean skin temperatures, proposed by Burton. However, this formula has not been well validated. We thus compared the two methods and found, perhaps surprisingly, that Burton’s formula worked well—even during severe thermal perturbations—over the range of core temperatures from 18.5° to 37.1°C. The formula was especially accurate when core temperatures were between 31° and 36.5°C, with the estimated temperatures differing from measured values by only −0.09°± 0.42°C. We conclude that Burton’s 1935 formula is remarkably accurate and precise.
The authors thank Gilbert Haugh, M.S., for the statistical analysis and Nancy Alsip, Ph.D., for editorial assistance (both from the Outcomes Research Institute at the University of Louisville, Louisville, Kentucky).
References
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Fig. 1. Linear regression including all 913 data pairs from 44 subjects.  9–12 Mean body temperature (MBT) was estimated from core and mean skin temperatures and compared with directly measured values. There was a remarkably good relation between measured and estimated mean body temperatures: MBTestimated= 0.94 · MBTMeasured+ 2.15  , r  2= 0.98. 
Fig. 1. Linear regression including all 913 data pairs from 44 subjects.  9–12Mean body temperature (MBT) was estimated from core and mean skin temperatures and compared with directly measured values. There was a remarkably good relation between measured and estimated mean body temperatures: MBTestimated= 0.94 · MBTMeasured+ 2.15 
	, r  2= 0.98. 
Fig. 1. Linear regression including all 913 data pairs from 44 subjects.  9–12 Mean body temperature (MBT) was estimated from core and mean skin temperatures and compared with directly measured values. There was a remarkably good relation between measured and estimated mean body temperatures: MBTestimated= 0.94 · MBTMeasured+ 2.15  , r  2= 0.98. 
×
Fig. 2. Bland-Altman plot for all 913 data pairs from all four studies.  9–12 The bias (average difference between estimated and measured mean body temperatures) is −0.09°± 0.42°C  , solid line  (95% confidence interval, −0.12° to −0.06°C). The precision (average of the absolute value of the difference between estimated and measured mean body temperatures) is 0.31°± 0.29°C (95% confidence interval, −0.29° to 0.33°C). Over the entire data set, 87% of the mean body temperature estimates were within 0.5°C of the measured values. 
Fig. 2. Bland-Altman plot for all 913 data pairs from all four studies.  9–12The bias (average difference between estimated and measured mean body temperatures) is −0.09°± 0.42°C 
	, solid line  (95% confidence interval, −0.12° to −0.06°C). The precision (average of the absolute value of the difference between estimated and measured mean body temperatures) is 0.31°± 0.29°C (95% confidence interval, −0.29° to 0.33°C). Over the entire data set, 87% of the mean body temperature estimates were within 0.5°C of the measured values. 
Fig. 2. Bland-Altman plot for all 913 data pairs from all four studies.  9–12 The bias (average difference between estimated and measured mean body temperatures) is −0.09°± 0.42°C  , solid line  (95% confidence interval, −0.12° to −0.06°C). The precision (average of the absolute value of the difference between estimated and measured mean body temperatures) is 0.31°± 0.29°C (95% confidence interval, −0.29° to 0.33°C). Over the entire data set, 87% of the mean body temperature estimates were within 0.5°C of the measured values. 
×
Fig. 3. Bland-Altman plot of 535 data pairs  10,12 when the studies of deep hypothermia for circulatory arrest  9 and fever  11 were excluded. The bias (average difference between estimated and measured mean body temperatures) is −0.15°± 0.33°C  , solid line  (95% confidence interval, −0.18° to −0.12°C). The precision (average of the absolute value of the difference between estimated and measured mean body temperatures) is 0.28°± 0.23°C (95% confidence interval, −0.26° to 0.30°C). Over the entire data set, 91% of the mean body temperature estimates were within 0.5°C of the measured values. 
Fig. 3. Bland-Altman plot of 535 data pairs  10,12when the studies of deep hypothermia for circulatory arrest  9and fever  11were excluded. The bias (average difference between estimated and measured mean body temperatures) is −0.15°± 0.33°C 
	, solid line  (95% confidence interval, −0.18° to −0.12°C). The precision (average of the absolute value of the difference between estimated and measured mean body temperatures) is 0.28°± 0.23°C (95% confidence interval, −0.26° to 0.30°C). Over the entire data set, 91% of the mean body temperature estimates were within 0.5°C of the measured values. 
Fig. 3. Bland-Altman plot of 535 data pairs  10,12 when the studies of deep hypothermia for circulatory arrest  9 and fever  11 were excluded. The bias (average difference between estimated and measured mean body temperatures) is −0.15°± 0.33°C  , solid line  (95% confidence interval, −0.18° to −0.12°C). The precision (average of the absolute value of the difference between estimated and measured mean body temperatures) is 0.28°± 0.23°C (95% confidence interval, −0.26° to 0.30°C). Over the entire data set, 91% of the mean body temperature estimates were within 0.5°C of the measured values. 
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Table 1. Morphometric and Demographic Characteristics and Study Details 
Image not available
Table 1. Morphometric and Demographic Characteristics and Study Details 
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