Pediat.Res. 1: 185-195 (1967) Metabolism basal metabolic rate growth REVIEW kidney glomerular filtration rate body surface area body weight oxygen consumption organ growth The Relation of Metabolic Rate to Body Weight and Organ Size A Review M.A. HOLLIDAY[54J, D. POTTER, A.JARRAH and S.BEARG Department of Pediatrics, University of California, San Francisco Medical Center, San Francisco, California, and the Children's Hospital Medical Center, Oakland, California, USA Introduction Historical Background The relation of metabolic rate to body size has been a The measurement of metabolic rate was first achieved subject of continuing interest to physicians, especially by LAVOISIER in 1780. By 1839 enough measurements pediatricians. It has been learned that many quanti- had been accumulated among subjects of different tative functions vary during growth in relation to sizes that it was suggested in a paper read before the metabolic rate, rather than body size. Examples of Royal Academy of France (co-authored by a professor these are cardiac output, glomerular filtration rate, of mathematics and a professor of medicine and oxygen consumption and drug dose. This phenomenon science) that BMR did not increase as body weight may reflect a direct cause and effect relation or may be increased but, rather, as surface area increased [42]. a fortuitous parallel between the relatively slower in- In 1889, RICHET [38] observed that BMR/kg in rab- crease in metabolic rate compared to body size and the bits of varying size decreased as body weight increased; function in question. RUBNER [41] made a similar observation in dogs. Both The fact that a decrease in metabolism and many noted that relating BMR to surface area provided re- other measures of physiological function in relation to a sults that did not vary significantly with size. These unit of body size is observed in most biological systems. intraspecies observations were then extended to inter- This phenomenon can be demonstrated by inter- species observations. In 1901, VOIT [48] observed that species comparisons of mammals and birds, as well as the BMR of 7 species of varying size ranged from 776 within a species during growth or among matured to 1089 calories/m2 (cal/m2) while the BMR/kg varied members of a species that vary in size. Mice, for example, from 11.3 to 75.1 calories/kg (cal/kg). He concluded have a basal metabolic rate per kg (BMR/kg) approxi- that BMR varied as surface area varied. This relation mately thirteen times that of elephants. In the case of came to be known as the 'surface area law'. To some, humans during growth, the infant has a BMR/kg more the 'surface area law' acquired the status of a funda- than twice that of the normal adult. A normal adult mental biological principle [29]. Nonetheless, as tech- may have a BMR/kg one and one-half times that of an nics improved, data were accumulated which ultimate- obese adult. ly challenged the 'surface area law'. The purpose of this paper is to review this subject and propose reasons why there is a lower BMR/kg as body size increases. When applied to growing humans, the Mathematical Models Relating BMR to Body Size information developed should allow a greater precision In studying the differences among species, the BMR in estimating BMR from body weight during growth. predicted for small animals from their surface area and It will be seen that the factors responsible for the de- the BMR/m2 of larger animals was not as high as the cline in BMR/kg during growth differ from the factors observed rate. In 1932, KLEIBER [23] compared BMR operative among different species. The equation de- to body weight of animals of 10 species which ranged scribing the relation of BMR to body weight during from mouse to steer. He plotted the log of BMR as a growth also differs from the equation describing this function of the log of body weight. The relationship was relation among different species. expressed by the equation: C = 71 ±1.8 W-75 where 186 HOLLIDAY, POTTER, JARRAH, BEARG C = BMR in calories/day (cal/day) and W = weight body in kg. A similar relationship was described by BRODY and PROCTER [7] in the same year. In 1945, BRODY [8] developed this relationship in great detail and sum- marized the data which related endogenous nitrogen and sulfur metabolism as well as BMR to the W-73. KLEIBER1 [24,25] confirmed his previous equation, using new data from animals of 16 species; his newly derived equation was C = 69 ± 1.5 W-'5, which he sim- plified to 70 x W-75. The fit was close for all the species studied, except for elephants and whales, where meas- urements were few and were difficult to obtain (fig. 1). 1000 10,000 100,000 The observed BMR/kg in 5 examples selected from Body weight (kg) KLEIBER varied from 181 to 14.1 cal/kg/day but in each Fig. 1. Solid line ( ) calculated regression equation instance the observed value agreed with that predicted of observed BMR and body weight. Hashed line ( ) from his equation (table I). BRODY [8] published studies theoretical line should BMR increase as a linear func- in birds in which the relation between body size and tion of body weight, i.e. BMR/kg = constant. Dashed BMR was almost the same as that noted for mammals 75 line ( ) theoretical line should BMR increase as a (cal = 70X [kg]- ). The consistency of this relation function of surface area or W-67 (KLEIBER [24]). over so wide a range of sizes and species suggests some unique biological advantage inherent within this rela- tion. As size increases BMR increases less than weight to surface area than in the detailed formula of HARRIS but more than surface area. and BENEDICT. More recently, MILLER and BLYTH [33] In the meantime, an intensive search was being measured oxygen consumption in male college stu- made for the best reference standard for BMR in adult dents (weight range 54 to 136 kg) and found least varia- humans, whose range in size was 5 to 10-fold. GEPHART bility when they related it to lean body mass, as opposed and DuBois [14] published standards for males from to surface area or weight. A still more recent study [50] 20 to 50 years of age, of 'normal' stature, in which 90% observed the BMR to show the best degree of correla- fell within i 15 % of a standard value. HARRIS and tion with extracellular fluid volume. The difficulty in BENEDICT [16] published an analysis of their data and determining which function of size correlates with derived a separate equation for men and women which BMR among adult humans arises from the narrow took into account their height, weight and age. BOOTH- range of size and BMR differences within this group, BY and SANDIFORD [4] compared their results calculat- and the interdependence of the various functions of ed from the empirical formulae of HARRIS and BENE- size to each other within the range. DICT and from the surface area formula of DuBois [13] The relation of BMR to body size during growth and found no greater variability in the data referred covers a wider range, so that correlations between BMR and different variables of body size can be tested. Both GEPHART and DuBois [14] and BENEDICT and Table I. BMR in adult mammals of various sizes (ob- 2 served cal/kg/day compared to predictions from Klei- TALBOT [2] noted that BMR/m during growth differ- ber's formula: cal = 70 xW-75) ed significantly from that predicted from average adult values/m2 (fig. 2). In newborn humans, the observed Species Body BMR Cal/kg/day figures are lower; in the age group from 6 months to weight Observed Predicted 3 to4 years they are higher than those predicted; there- 2 (kg) (cal/day) after, they tend to approach the adult figure for cal/na / day. A similar pattern of difference is noted in rats and Mouse 0.021 3.8 181 171 in cattle during growth [8]. Rat 0.282 27 96 100 The standard values of BMR found by BENEDICT Dog 6.6 288 44 44 and TALBOT [2] and more recently by LEWIS et al. [32] Man 55 1400 25 22 define an empiric and varying relation between BMR Cow 600 8460 15 13 and body weight. An arithmetic plot of this relation- ship in boys, using the data of BENEDICT and TALBOT, 1 The equation derived by BRODY was C = 70.5 W-734, is illustrated in figure 3. The data for girls and the which he rounded off to C = 70.5 W'7, while KLEIBER independent data of LEWIS et al. [32] are not different preferred using W-75. in any important respects. The relation of metabolic rate to body weight and organ size 187 to 80 kg the increase in BMR is 15 cal/kg. For com- * 2 1200 * . parison, the predicted BMR from the adult rate/m • 1100 v '•s surface area, using standard surface area figures for •." • weight, and the BMR predicted from KLEIBER'S for- 1000 75 • /• •—* mula: C = 70 xW- are plotted. The predictions, 900 * * using either theoretical relation, come close to the ob- / served figures at points in infancy and again at matur- 700 ity, but with considerable differences at other points. 600 .2 .3 .4 .5 .6 .7 .8 .9 1.0 1.1 1.2 1.3 \A 1.5 m2 The highest BMR/kg in humans during growth is 56 calories at 6 kg; the lowest is 25.5 calories at 70 kg Fig.