Body temperature effects on basal energy expenditure (BEE): proposed protocols for experiments and application of "average" equations for prediction of BEE for individuals.

Body Temperature Effects on Basal Energy Expenditure (BEE): Proposed Protocols for Experiments and Application of “Average” Equations for Prediction of BEE for Individuals To the Editor: Typical experimental efforts to measure basal energy expenditure (BEE) in large numbers of people show a substantial “apparent” random scatter in BEE. We find that a major portion of this scatter is not random but is related to variations in body temperature between the study participants. This finding has a major impact on the design of future experiments and on the use of standard BEE equations when applied to an individual. Daily energy needs are normally estimated from an equation based on regressions to data for BEE. Typical regression variables are height, weight, and age, or fat-free mass (FFM). The most commonly used equation is that of Harris and Benedict, which requires height, weight, and age as input variables. Also frequently used is an equation of the form BEE a FFM b, where a and b are constants found from regression analyses. These equations are averages over a large number of people and can have substantial errors when applied to a specific individual. The apparent data scatter above and below the regression curve can span a range from 30% to as much as 55%. In both popular and scientific publications, it is noted that BEE varies with body temperature and that the variation is on the order of 14% per 1°C. A variation of 1°C is slightly more than 3 SD about the average human body temperature. This variation is not included in the standard “average” equations noted above nor in any other analyses of which we are aware except those of Faisy et al. (where it is noted that a variation of 13% per 1°C occurs at temperatures of 37°C) and White et al. We have shown that the 14% variation can be reproduced theoretically by calculations with the Boltzmann equation—which is often termed the Arrhenius equation in medical literature. Specifically, we created a multiplicative factor, ST, which accounts for the difference in body temperature between individuals and the average human temperature. It is, ST e . Here, Ee is an effective energy constant. We have determined the value of Ee, which corresponds to a 14% per degree change in BEE at 37°C, to be 112.3 kJ/mol (1.17 eV). T is the body temperature of an individual, Tc is the average human oral temperature–-98.2°F or 36.8°C, and k is the Boltzmann constant. A similar multiplicative scaling factor, ST, was used by Gillooly et al. to compare BEE between different species, where the range of Ee was from 0.2 eV to 1.2 eV. We have also verified that a 3-SD envelope utilizing this variation encloses approximately 90% of the apparent data “scatter” in published BEE measurements such as those of McCrory et al. (We note there is a scale error in both plots shown in Figure 1 of McCrory et al., which has been resolved in private communication [M. W. Munn and M. McCrory, private communication, March 25, 2005]. If the scale values are multiplied by [4.186], then the resulting scales are in kJ/day.) We propose that daily energy needs can be particularized to individuals by use of one of the “average” equations multiplied by the scaling factor, ST, which requires only a measurement of that person’s oral body temperature as an additional input variable. The precise scaling factor requires calculations with the Boltzmann equation. However, over the relatively narrow range of human body temperatures, this scaling law can be well approximated for clinical use by a simple relationship obtained from a linear regression to the exact Boltzmann results. We find this linearized equation to be, ST (0.0899 x T[°F] – 7.8219) or ST (0.1618 T[°C] 4.9448). These equations are valid over the range 35.3 T(°C) 40.1 or 95.6 T(°F) 104.3. To accommodate special classes of patients, such as those with polio, we have derived a quadratic form of ST that extends this range down to 92°F. It is ST (0.003 x T[°F] 0.5 x T[°F] 21.626). For an otherwise healthy patient, their BEE is given, for example, simply by BEE ST BEE(HB), where BEE(HB) is the Harris–Benedict equation. We further propose that future experimental efforts to measure BEE utilize this temperature-based scaling methodology to reduce all measurements to a common baseline temperature, namely, the average human body temperature. This reduction would be made before regression to any remaining variables such as height, weight, age, or fat-free mass. In this case, reduction of individual BEE measurements to a common temperature is made by dividing by the factor, ST. The regressions of Faisy et al. and White et al. include temperature as a linear, additive variable in a multivariate regression and do not correct for it a priori as a multiplicative and predictable factor as we propose.