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A revision of body surface area estimations

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Eur J Appl Physiol (1985) 53:376--379
European Journal of
pplied Physiology
and Occupational Physiology 9 Springer-Verlag 1985
A revision of body surface area estimations
Peter R. M. Jones, Sue Wilkinson, and Peter S. W. Davies
Human Biology Laboratory, Department of Human Sciences, University of Technology, Loughborough, Leics. LEll 3TU, Great Britain
Summary.
The results from the present study inidi- cate that the equation of Dubois and Dubois (1916), now in common use for estimating body surface area, is not the most accurate of those available. Our new equation is based on the measurement of body weight and upper calf circumference only. It accounts for a large percentage of the toal variance (88.9 ), and has a low standard error of estimate (0.05 m2), which suggests that this equation may be more useful in the estimation of human body surface area than many of the equations previously produced. Direct compari- sons of the accuracy of other workers' equations is difficult to assess due to the different methods by which the equations have been produced and expressed. We do not advocate the use of different equations for males and females because the data indicate that the present equation probably applies equally well to both sexes.
Key words:
Body surface area - Anthropometry
Introduction
The importance of knowing body surface area has been well established in a number of areas, such as body composition, physiological and clinical studies. Its significance has been particularly well established in consideration of metabolism, or more specifically in its relationship with resting metabolic rate. In clinical studies body surface area is used for determining optimal drug dosage (Siber et al. 1979; Battler et al. 1980) in particular for spinal anesthetics
* Present address:
Department of Growth and Development, Institute of Child Health, 30 Guilford Street, London, WC1N 1EH
Offprint requests to.
P. R. M. Jones at the above address
(Feingold 1979) and has also been used in studies on gastric emptying rates (Lavigns et al. 1978). The armed services in the UK and USA have also made considerable use of body surface area in their work on ergonomics (Dempster 1955; Clauser et al. 1969). Surface area of regular geometric shapes is easy to calculate from sound mathematical principles. The surface area of the human body, however, poses much more of a problem. Although the human body can be roughly described in terms of regular shapes, such as the head as a sphere, the arms as cylinders and the upper legs as truncated cones, calculations of total body surface area using formulae for each shape would be time-consuming and probably inaccurate. If the surface area of the body needs to be known, then the ideal situation would be to have a means of obtaining an accurate answer from manipulation of measurements which are readily available. One of the earliest attempts at creating a formula for estimating body surface area was by a German scientist (Meeh 1879) who made use of the law relating area to volume. Later, two scientists (Dubois and Dubois 1916), became interested in surface area studies as they were dissatisfied with the equations avialable to them and needed a more accurate method for their studies on metabolism. Their work was to make considerable impact on surface area calculations for the next 60 years. From measure- ments made directly when making a paper mould of the body, they produced a linear formula by which areas of the body segments were calculated and then summed to arrive at the total. However, for their formula they only measured one leg and one arm, assuming the body to be symmetrical. Since then, however, this assumption has been found to be invalid (Banerjee and Sen 1954). Because their linear formula was complex and time consuming Dubois and Dubois (1916) sought a simpler method. As height and weight data were readily available from
P. R. M. Jones et al.: Body surface area
their metabolic study, these variables were used in their next formula which took the form: SA = (a) weight x (b) height x (c) constant. The values for a and b were found using trial numbers and then interpolating graphically. The final equation arrived at has been used since its first publication: SA (cm 2) = wt ~ x Ht ~ x 71.84 (Dubois and Dubois 1916). This formula, now almost universally used for calculating surface area, was based on measurements taken from 12 subjects who were, by any standards, unrepresentative of the general population (Table 1). Many other investigators have since questioned the accuracy of the formula (Breitman 1932; Boyd et al. 1930; Banerjee and Sen 1954; Gehan and George 1970; Haycock et al. 1978). In particular, it has been shown to grossly over-estimate the surface area of obese people, and further it does not take into account the distortion obse~wed in the thigh and trunk. However, despite this, the formula of Dubois and Dubois (1916) continues to be used, probably in regard more to tradition than to accuracy (Passmore and Robson 1976). This paper aims at establishing the best predictors of body surface area from simple anthropometric variables, to compare the accuracy of an equation using the predictors obtained, with the accuracy using height and weight, and to test the accuracy of this equation on other available data. The aim is not to exclude height and weight from any formula to calculate body surface area, but to determine whether
377
or not these two variables are, in fact, the best predictors available at the present time, something which seems to have been rather surprisingly over- looked in previous studies.
Subjects, materials and methods
Fifteen female subjects were chosen to represent a variety of body sizes and shapes. Of these 13 were from the University student population. Anthroposcopic somatotype estimates were made from photographs taken with the subjects standing in a posed position (Tanner 1954). The age range of the sample population was from 17 to 39 years. All anthropometric measurements were taken on the left side of the body, with the subject standing in the true anatomical position in accordance with the recommendations of the Interna- tional Biological Programme (Weiner and Lourie 1981). The varia- bles are listed below: General Circum- Heights Skinfolds ferences (cm) (cm) (mm) Stature (m) Wrist Knee Subcapsular joint space Weight (kg) Upper arm Upper Biceps calf Bideltoid Mid calf Triceps (max) Gluteal Ankle Supra- furrow (min) iliac Knee joint space Upper calf (minimum below knee) Mid calf (maximum) Ankle (minimum above bi- malleolar)
Table
1. Subjects and data for the dubois surface area formula (1916) Case Age Sex Weight Height Comment no. (years) (kg) (cm) 1 36 M 24.2 110.5 2 21 M 64.0 164.3 3 22 M 64.0 178.0 4 32 M 74.49 179.2 5 ? F 93.0 149.7 6 18 M 45.25 171.8 7 1.75 F 6.27 73.2 8 12.45 M 32.74 141.5 9 26 F 57.62 164.8 10 21.5 M 63.0 184.2 11 43 M 12 34 M Cretin, physical development of 8 year old child Measured 31/2 months after severe typhoid infection Tall, thin, little subcutaneous fat Tall, average build Very short and fat (age unknown) Tall, thin, emaciated from diabetes. Went 11 days practically without food, had only whisky Had "invisible" oedema Measured 2 h after death. Had rachitis, large epiphyses at wrists, pigeon-breasted, chest narrow, and deep anteroposteriorily Well-formed, no signs of puberty Sculptor's model; well-proportioned Unusually tall, thin. On reduction diet just prior to measure- ment Both legs amputated in accident 5 years previously; stumps atrophied. Face, arms, and trunk were fat Legs amputated when 6 years old, developed crab-like form with powerful arms. Had stroke with spastic paralysis of right side 6 years before measured
378 P.R.M. Jones et al.: Body surface area
Table
2. The raw data means and standard deviations of the variables used in the prediction and calculation of body surface area, for 15 female subjects Subject Age Height Weight Upper calf Body surface area (m e (dec. years) (m) (kg) circumf. (cm) Measured Predicted Calculated (from Dubois) 1 21.3 1.636 63.1 31.6 1.70 1.70 1.68 2 17.3 1.719 76.2 35.8 1.95 1.91 1.89 3 21.4 1.672 64.0 33.7 1.79 1.77 1.72 4 20.8 1.689 59.8 35.1 1.75 1.78 1.73 5 21.8 1.701 58.4 34.2 1.77 1.74 1.68 6 20.6 1.583 61.9 36.6 1.76 1.84 1.62 7 21.8 1.626 56.2 32.1 1.68 1.66 1.60 8 19.5 1.678 70.2 35.4 1.91 1.86 1.80 9 23.0 1.622 80.8 38.7 2.06 2.03 1.86 10 30.0 1.660 54.3 31.1 1.55 1.62 1.60 11 39.2 1.547 52.2 30.3 1.63 1.58 1.49 12 21.4 1.642 79.0 36.2 1.85 1.95 1.86 13 21.5 1.749 53.7 31.5 1.65 1.63 1.65 14 21.0 1.577 59.3 33.0 1.65 1.71 1.60 15 21.0 1.704 47.0 31.0 1.55 1.57 1.53 Mean 22.8 1.654 62.4 33.8 1.75 1.76 1.69 SD 5.3 0.056 10.1 2.5 0.15 0.14 0.12 The body surface area was determined using aluminium baking foil. The foil was placed on the body, covering one segment at a time. The body segments used were i) head and neck, ii) trunk, iii) right arm and hand, iv) left arm and hand, v) right leg and foot, vi) left leg and foot. The body was carefully skin-marked to ensure complete coverage was obtained without any overlap. Various methods for measuring the area of the aluminium foil were considered. These were 1) direct geometry, 2) planimetry, and 3)direct digitising. We rejected the first method of direct geometry on account of the irregularity of the pieces of aluminium foil which posed considerable mathematical difficulties. Planimetry was also rejected as it was difficult to master the technique to any repeatable degree of accuracy. We therefore elected to use the electronic digitiser which recorded coordinates accurate to _ 0.1 ram. From these the area was calculated and the results automatically printed. To test the accuracy of this method we made several measurements on regular geometric objects whose area could be calculated accurately using mathematical formulae. We used the standard error of measurement (S meas =SD) to ~/2 cal- culate the accuracy obtained from 12 repeated measurements on three geometric shapes viz. triangle, circle, and a square, this gave a value of S meas=0.24 cm 2. The within observer reliability of measuring the body surface area of four randomly selected sub- jects, using the aluminium foil method, was calculated as S meas = 0.05 m 2.
Statistical analysis.
All data were stored on file in order to be manipulated using the statistical computer package "MINITAB" (Ryan et al. 1976).
Results
Table 2 gives the raw values and the means and standard deviations of the anthropometric character- istics of the subjects. It also shows the body surface area measured directly, predicted by anthropometry and calculated, using the Dubois formula. Table 3 Table 3. Correlations of anthropometric measurements with body surface area for 15 female subjects aged 17-39 years Measurement Correlation coefficients Present Dubois' study data Height (m) Weight (kg) Wrist (circumference) Upper arm (circumference) Deltoid (circumference) Gluteal furrow (circumference) Mid calf (circumference) Upper calf (circumference Ankle (circumference) 0.08 0.91 0.92 0.90 0.82 0.75 0.78 0.84 0.85 0.91 0.79 Table 4. Stepwise regression of body surface area on the anthropometric predictor variables for 15 female subjects Constant 0.327 Weight (Xi) 0.0071 t-ratio 2.41 Upper calf circumference (X2) 0.0292 t-ratio 2.34 s 0.0524 Explained variation 88.9% (df 1, 12) Regression equation 0.327 + 0.0071 X~ + 0.0292 X 2 shows the correlation coeffients of the anthropom- etric variables with the total body surface area. The results of the stepwise regression analysis for body surface area related to the anthropometric variables are given in Table 4.
P. R. M. Jones et al.: Body surface area 379
Discussion
The purpose of this paper is to establish the best predictor variables for use in an equation to estimate body surface area. A number of anthropometric measurements were taken and, with the aid of computer analysis, the multiple regression equation which accounted for the greatest amount of variance is shown in Table 4. It is interesting to compare the correlations, shown in Table 3, for height and weight using the Dubois data with those obtained in this study. Weight shows a high correlation throughout, though the high correlation of height is only shown in the Dubois sample due to the inclusion of subjects numbers i and 7 of the sample (Table 1). Removal of these two very extreme results reduce this correlation coefficient of 0.91 to 0.11 which is then more consistent with the findings of this study (r = 0.08). Meeh's equation (1879) consistently over-esti- mates the surface area measured, while those pro- duced by Dubois and Dubois (1916); Lariez (1930); Breitmann (1932); Boyd et al. (1930); Gehan and George (1970); Haycock et al. (1978) and the present study all show bias toward under-estimating the true value, on account of the large number of negative errors obtained. Breitmann's (1932) and this study have errors more evenly distributed around zero. Inter- estingly, it is the Dubois equation which gives the largest errors in this group, ranging from -0.199 m 2 to +0.056 m 2 (~2 = -0.058 m2); whereas the present study has the smallest range from -0.10m 2 to +0.026 m 2 (J~ = 0.031 m2). Another important point is that the equation produced in the present study is far simpler to use, by virtue of its linear form, than many of the other equations available. Application of this equation to males has not, as yet, been fully explored and we recognise tl)at further studies are desirable for both sexes covering a wider range of ages and physiques. However, data were available for four young males and the predictions of body surface area were encouraging with a mean error of only -0.004 m 2. The significance and the importance of knowing human body surface area has been reported by many workers who have been concerned with the difficul- ties and errors in its determination. The method described here for its prediction from two easily obtained anthropometric measurements seems to hold a good deal of promise.
References
Banerjee S, Sen R (1955) Determination of the surface area of the body of indians. J App Physiol 7:585--588 Battler A, Foelicher VF, Gallagher KP, Kumada T, McKnown D, Kemper WS, Ross J (1980) Effects of the changes in ventricu- far size on regional and surface QRS amplitudes in the con- scious dog. Circulation 62:174--180 Boyd E, Scammon RE, Lawrence D (1930) The determination of surface area of living children. Proc Soc Exp Biol Med 27 : 445- 449 Breitman M (1932) Eine vereinfachte Methodik der K6rperober- flfichenbestimmung. Scitti Biologi 7:395-399 Clauser CE, McConville JT, Young JW (1969) Weight, volume and centre of mass of segments of the human body. AMRL-TR-69-70 Wright-Patterson Airforce Base, Ohio Dempster WT (1955) Space requirements of the seated operator. Wright-Patterson Airforce Base, Ohio. Wright Air Dev Centre TA 55-159 AD87892 Dubois D, Dubois EF (1916) Clinical calorimetry. A formula to estimate the approximate surface area if height and weight be known. Arch Int Med 17:863-871 Feingold A (1979) Body weight vs surface area for calculating dose of spinal anesthetic. Anesthesiology 51:568-569 Gehan EA, George SL (1970) Estimation of human body surface area from height and weight. Cancer Chemother Rpts 54 : 225- 235 Haycock GB, Schwartz GJ, Witosky DH (1978) Geometric method for measuring body surface area: A height-weight formula validated in infants, children and adults. J Paediatr 93 : 62-66 Lariez G (1931) D'etermination de la surface corporelle en fonction du poids de la taille et de l'indice d'obesite. Comptes Rend Soc Biol 105:951-952 Lavigns ME, Wiley ZD, Meyer JH, Martin P, MacGregor IL (1978) Gastric emptying rates of solid food in relation to body size. Gastroenterology 74 : 1258-1260 Meeh K (1879) Oberflfichenmessungen des menschlichen K6rpers und seine einzelnen Teile in den verschiedenen Altersstufen. Z F Biol 15:425-458 Passmore R, Robson JS (1976) A Companion to medical studies, vol 1. 2nd Edit Blackwell Sci Publ Oxford, chpts 4.7-4.10 Ryan TA, Joiner BL, Ryan BF (1976) Minitab student handbook. Duxbury Press, Belmont. California Siber GR, Smith AL, Levin MJ (1979) Predictability of peak serum Gentamicin concentration with dosage based on body surface area. J Pediatr 94:135--138 Tanner JM (1954) Reliability of anthroposcopic somatotyping. Am J Phys Anthrop 12:257--266 Weiner JS, Lourie JA (1981) Practical human biology. Academic Press, London, pp3-499 Accepted November 11, 1984

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