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Comparison of some secondary body composition algorithms.

Body composition measurements vary greatly in degree of measurement difficulty and accuracy. Hydrostatic weighing, chemical dilution or their equivalents were the accepted "gold" standards for assessing fat mass. Dual Energy X-ray Absorptiometry (DEXA) is fast replacing these techniques as the preferred standard. However, these direct measurement techniques require expensive and precise equipment and must be operated by highly trained personnel. For this reason the "Body Mass Index" or "BMI" is being widely used to indicate body composition. The BMI is thought to be reasonably accurate and simply requires body weight and height measurements. Between these two extremes lie the many other approaches and their corresponding algorithms. The discrepancies inherent in these algorithms are discussed. The prediction accuracy of the more popular empirical algorithms is evaluated. These evaluations indicate that a promising approach to body composition measurements is a combination of both BMI and bioelectric impedance measurements.


Body composition such as the ratio of fat mass to total body mass cannot be measured. However, parameters used to predict body composition can be measured. These parameters are classed as either primary or secondary. Primary parameters are used in analytical algorithms to represent body composition. Secondary parameters are used in empirical algorithms to predict primary parameters. Secondary parameters are needed since primary parameters are difficult to measure. However, prediction errors are inherent in the use of these secondary parameters. This paper evaluates the accuracy of skin fold, body mass index and three bioelectrical secondary algorithms. The bioelectrical algorithms (presented by Kushner, 1992, and Thomas, Cornis and Ward, 1992) are implemented by the Tanita Corporation. The accuracy of these algorithms is indirectly compared to the well accepted hydrostatic weighing technique (as first described by Garrow, Stalley, Diethelm et al, 1979).


In order to establish a common basis of understanding, a model of body composition measurement techniques and terminology is first presented. With this background, the measurement techniques to be evaluated are selected and described. Also, a suitable data base for testing these measurement techniques is developed. Finally, performance criteria and procedures for testing this performance are established.

A Body Composition Model

Figure 1 shows a model of the components of body composition technology. Body composition can be represented in either the volumetric (plethysmography) or hydrometric domain. The two domains are equivalent. Equivalency is insured by domain transforms. In both domains there are primary algorithms that operate on primary measurements to represent body composition and there are secondary algorithms that operate on secondary measurements to predict primary measurements. The primary algorithms are well accepted by the industry since they are analytical and use well accepted assumptions for the domain constants. The secondary algorithms are not yet well accepted by the industry. One reason for this lack of acceptance is that the techniques have either been demonstrated to be inaccurate or have not yet been fully evaluated for accuracy. The latter is the case for the body mass index and bioelectric techniques. Inaccuracy is inherent in the secondary algorithms since they must be empirically derived by statistically fitting the secondary parameters to a finite set of measured primary parameters.


Primary Algorithms

In the volumetric domain the de facto standard primary algorithm for representing body composition is:

f(D) = [DfDo / (Df - [D.sub.o])] (D-1 - Do-1) (1)

where: [D.sub.f] = Density of body fat,

[D.sub.o] = Density of other lean body tissue,

D = Composite body density and

f(D) = Ratio (as a function of D) of body fat mass to total body mass.

This algorithm was first reported by (Sift, 1961).

The composite body density, D, is total body weight normalized by body volume. Body volume is usually measured by body displacement techniques using either hydrostatic weighing or, more recently, the "Bod Pod" described by (Fields, Goran and McCrory, 2002) and (Yee, Fuerst, Salamone et al, 2001). The hydrostatic weighing technique measures water displacement and is based on an application of Archimedes' principle whereas the Bod Pod measures air displacement and is based on an application of Boyles' law. More recently, Dual Energy X-ray Adsorptiometry or DEXA (as evaluated by Kohrt, 1998) is being used to directly measure body density.

In the hydrometric domain, the de facto standard primary algorithm for representing body composition is:

f(w) = 1 - w/[K.sub.o] (2)


[K.sub.o] = Ratio of body water mass to total mass of lean body tissue,

w = Ratio of body water mass to total body mass and

f(w) = Ratio (as a function w) of body fat mass to total body mass.

This technology was first developed by (Pace and Rathburn, 1945). Pace and Rathburn used the value of [K.sub.o]=73% however, more recent studies (by Garrow, 1982) indicates that 72% might be more accurate. Body water is usually measured by chemical dilution techniques as described by (Schoeller, Santen, Peterson et al, 1980, and Schoeller, Kushner, Taylor et al, 1985). These techniques measure the dilution of heavy water as it passes through the body.

In order to insure equivalency between domains the measured value of w must be such that equation 1 equals equation 2 so that for measured values of D the transform of equation 3 applies, i.e.

w = [[D.sub.o] / ([D.sub.o]-[D.sub.f])](1- [D.sub.f][D.sup.-1])[K.sub.o] (3)

In like manner the measured value of D must be such that for measured values of w the inverse transform of equation 4 applies, i.e.

D = [D.sub.o][D.sub.f][K.sub.o] / [[K.sub.o][D.sub.o] - ([D.sub.o] - [D.sub.f]) w] (4)

It should be noted that the choice of domain parameters [D.sub.o],[D.sub.f] & [K.sub.o] must be chosen so that consistency between domains is accomplished (i.e. equations 3 & 4 are satisfied). From the transform of equations 3 and 4 we see that only one set of domain measurements is needed in order to work in either domain.

Secondary Algorithms

Secondary algorithms operate on secondary measurements to predict primary parameters. In the volumetric domain these algorithms predict body density. In the hydrometric domain these algorithms predict body water. The number of secondary algorithms is limited only by the many ways the effects of body composition can be detected. These algorithms are usually statistically developed by empirically fitting mathematical functions to measured data points of independent, primary and their dependent, secondary parameters. Since the primary parameters are not solely dependent on the measured secondary parameters, other personal data parameters are needed to increase the accuracy of the algorithm. This data is typically age and sex and, in the case of the Tanita algorithms, physical condition. Only the most popular algorithms will be studied.

The Skin Fold Algorithms

The skin fold algorithms (such as developed by Jackson and Pollock, 1978) are based on the measurement of skin fold as its secondary parameter. For this algorithm skin fold is measured in three locations on the body. These locations are sex dependent as is the algorithm. Also the algorithm is age dependent. Of all the body density algorithms, skin fold is chosen here because of the simplicity of equipment (calipers) needed. The Jackson-Pollock algorithm is chosen because it appears to be the most accurate of the skin fold algorithms (when evaluated by Scherf, Franklin, Lucas et al, 1986)

The Body Mass Index

The "Body Mass Index" or "BMI" has been widely accepted as the standard measure for indicating body composition. It is most conveniently calculated as the ratio of body mass to the square of body height. As such the BMI is a secondary volumetric parameter and not a secondary algorithm. Since body composition parameters have no basis for comparison, the accuracy of the BMI, as such, cannot be tested. However, the BMI can be incorporated into a secondary algorithm by performing a least square linear regression of BMI onto the inverse of body density measurements. The representation evaluated in this paper is:

[D.sup.-1] = 0.864 + 0.00255 BMI for males (5)

[D.sup.-1] = 0.899 + 0.00243 BMI for females (6)

where: BMI is the body mass index in grams per square centimeter.

The Tanita Algorithms

Tanita has implemented four body composition algorithms into the model TBF 300A Body Composition Analyzer. This analyzer is a bioelectric device in that it measures the body impedance between two electrodes applied to the bottom of each foot. Two of the four Tanita algorithms are volumetric and the other two are hydrometric. All four algorithms are functions of body impedance as well as BMI. Both volumetric and hydrometric algorithm pairs consist of 1) a "standard" algorithm and 2) an "athletic" algorithm. The "standard" algorithm is intended for subjects who, among other things, exercise less than 10 hours a week and have a resting pulse rate of greater than 60 beats/min. The standard algorithm is also a function of age.

University of Montevallo Data Base

Sixty-one University of Montevallo students were measured using the Jackson-Pollock skin fold technique and three of the four bioelectrical algorithms implemented by Tanita. This population consisted of 16 adult education students (six male and 10 female) and 25 male and 20 female kinesiology department students. This data base is shown in Table 1. The body water, body impedance and body fat measurements were made by the Tanita Body Composition Analyzer model TBF 300A. The skin fold measurements were made by Lange skin fold calipers and applied to the Jackson-Pollock skin fold algorithms. The three Tanita algorithms used were the "standard" and "athletic" body fat and the athletic body water algorithms that reside in the model TBF 300A Analyzer. The "std./athl." column of table 1 is a combination of the "standard" and "athletic" algorithms. The "standard" algorithm was used for those subjects who do not qualify as "athletic" and the "athletic" algorithm was used for those subjects who do qualify as athletic. All University of Montevallo students listed in table 1 were approved for testing as required by the University of Montevallo.

Performance Criteria For Testing Procedures

Discrepancies in representing body composition may result from 1) measurement inaccuracies, 2) inaccurate assumptions or 3) prediction errors. Inaccurate assumptions are most often made in using the analytically derived primary algorithms whereas prediction errors will always exist to some degree when using the empirically derived secondary algorithms. In deriving the primary algorithms it has been implicitly assumed that the density and percent water content of lean body tissue is the same from subject to subject. However, these constants will vary somewhat depending on the proportion of muscle mass in lean body tissue (see Womersley, Durnin, Boddy et al, 1976). These variations have been observed to cause as much as four to five percent variation in percent body fat. Also variation may be caused by aging, racial or ethnic differences. This paper does not evaluate measurement inaccuracies or inaccurate assumptions. It does, however, evaluate prediction errors made by secondary algorithms.

Prediction Errors

The value of secondary algorithms is judged by the ease of secondary parameter measurement and the prediction accuracy of the algorithm. In this paper prediction accuracy is defined by the accuracy with which the algorithm under test can correctly categorize a subjects' body composition condition as either excellent, good, fair, poor or very poor. Table 2 shows the "Phoenix Fitness & Racquet Club" category norms used for this evaluation. An evaluation of this type requires knowledge of the correct categorization. Normally we would use hydrostatic measurements to acquire this knowledge. However, accurate hydrostatic measurements could not be obtained. Therefore, an equivalent replacement was needed. This replacement resulted from correction of the athletic mode of the volumetric, Tanita measurements. Figure 2 shows a statistical comparison of the body fat measurement error for hydrostatic as reported by (Scherf Franklin, Lucas et as, 1986) vs. the Tanita measurements of Table 1. These errors are referenced to the Jackson-Pollock skin fold measurements. When the Tanita measurements are corrected by consistently subtracting 1.8%, the mean and root mean square (rms) error of the corrected Tanita measurements are made equal to the hydrostatic measurements. Thus the corrected Tanita measurements are a likely replacement for hydrostatic weighing.



Figure 3 shows the errors made in categorizing fat mass condition as either excellent, good, fair, poor or very poor. These errors were counted for the subjects of Table 1 using the norms specified by Table 2. They were counted for the secondary body composition algorithms shown in the Figure 3, abscissa. The corrected athletic mode was used as a replacement for hydrostatic weighing for determining the correct categorization. All of the algorithms evaluated, except body water are volumetric algorithms in that they predict body density. The hydrometric body water algorithm evaluated was the Tanita athletic mode algorithm.



Use of fat mass measurements as an indicator of fat mass condition has not been widely accepted. The parameters necessary to represent body fat have either been too difficult to measure or their results cannot be trusted. Instead the "body mass index (BMI)" has become the standard. Based on the Figure 3 results, it does appear that the skin fold and Tanita standard/athletic techniques are quite inaccurate. The BMI did not fair as well as expected in that only three out of four subjects were categorized correctly. A more accurate approach is to combine BMI with the bioelectric impedance measurements as is done in the Tanita athletic and body water algorithms. More precisely, the Tanita athletic mode algorithm can be corrected as a practical replacement for hydrostatic weighing.

Practical Applications

Inexpensive bioelectric devices using appropriate volumetric or hydrometric algorithms based on BMI and body impedance measurements can be deployed and easily used to accurately monitor body fat conditions. The techniques employed in this paper can be used to test the prediction accuracy of various body composition algorithms. The error performance definitions along with appropriately simulated data could be used as a basis for design of uniform industry standards.


* Kushner RE Bioelectrical impedance analysis: A review of principles and applications. J. Am. Coll. Nutr: 1992; 11:199.

* Thomas BJ, Cornish BH & Ward LC. Bioelectrical impedance analysis for measurement of body fluid volumes. A review: 1992; 17:505.

* Jackson AS, Pollock ML. Generalized equations for predicting body density of men. British Journal of Nutrition 40: 1978; 497-504.

* Jackson AS, Pollock ML, Ward A. Generalized equations for predicting body density of women. Medicine and Science in Sports and Exercise 12: 1980; 175-182.

* Garrow JS, Stalley S, Diethelm R et al. A new method for measuring the body density of obese adults. British Journal of Nutrition 42: 1979; 173-183.

* Siri WE. Body composition from fluid spaces and density. Analysis of methods. Techniques for Measuring Body Composition. National Academy of Sciences, National Research Council, Washington D.C: 1961; 223-244.

* Fields DA, Goran MI, Mccrory MA. Body composition assessment via air displacement plethysmography in adults and children: a review. American Journal of Clinical Nutrition 75: 2002; 453-467.

* Yee AJ, Fuerst T, Salamone Let al. Calibration and validation of an air displacement plethysmography method for estimating percentage body fat in an elderly population: a comparison among compartmental models. American Journal of Clinical Nutrition 74: 2001; 637642.

* Pace N, Rathburn EN. Studies on body composition. III. The body water and chemically combined nitrogen content in relation to fat content. Journal of Biological Chemistry 158: 1945; 685-691.

* Garrow JS. Indices of adiposity. Nutrition Abstracts and Reviews 53: 1982; 697-708.

* Schoeller DA, Santen E van, Peterson DW et al. Total body water measurement in humans with [sup.18]O and [sup.2]H labeled water. American Journal of Clinical Nutrition 33: 1980; 2686-2693.

* Schoeller DA, Kushner RF, Taylor Pet al. Measurement of total body water: isotope dilution technique: Roche AF (ed) Body Composition Assessments in Youth and Adults. Report of the Sixth Ross Conference on Medical Research, Ross Laboratories, Columbus, Ohio: 1985; 24-28.

* Womersley J, Durnin JVGA, Boddy K et al. Influence of muscular development, obesity and age on the fat free mass of adults. Journal of Applied Physiology 41: 1976; 223-229.

* Scherf J, Franklin BA, Lucas CP et al. Validity of skin fold thickness measures of formerly obese adults. American Journal of Clinical Nutrition 43: 1986; 128-135.

* Kohrt WM. Preliminary evidence that DEXA provides an accurate assessment of body composition. Journal of Applied Physiology 84: 1998; 372-377.


Department of Kinesiology

University of Montevallo
Table 1
University of Montevallo Data Base

                 body         body       body      body
stud.   sex   height (a)   weight (b)   age (c)   imp (d)

  1      F       65.0         265         35        363
  2      F       61.0         292         45        323
  3      F       63.0         152         36        392
  4      F       66.0         193         20        495
  5      F       66.0         258         21        420
  6      F       69.0         216         22        458
  7      F       64.5         294         22        348
  8      F       63.0         222         20        433
  9      F       66.0         147         60        592
 10      F       63.0         132         48        574
 11      F       64.0         132         21        556
 12      F       62.0         117         20        594
 13      F       66.0         139         18        521
 14      F       64.0          97         21        675
 15      F       65.0         116         19        582
 16      F       65.5         142         58        605
 17      F       62.0         135         51        587
 18      F       64.5         115         52        647
 19      F       71.0         134         46        511
 20      F       63.0         143         62        626
 21      F       69.0         140         17        567
 22      F       70.5         155         21        511
 23      F       69.0         156         22        577
 24      F       72.0         156         20        629
 25      F       70.0         156         18        554
 26      F       64.0         135         21        573
 27      F       69.0         148         20        571
 28      F       67.5         129         22        583
 29      F       70.0         146         20        542
 30      F       64.0         116         19        564

                            body fat measurements

          body      Jacks-Poll.     Tanita      Tanita
stud.   water (e)    skin fold    std./athl.   athletic

  1        107         48.1%        46.6%       44.2%
  2         97         67.9%        56.2%       54.8%
  3         88         18.6%        19.7%       20.7%
  4         89         35.2%        43.3%       37.2%
  5         96         44.0%        54.5%       49.4%
  6        102         32.4%        39.6%       35.4%
  7        105         42.9%        52.8%       51.2%
  8         87         46.0%        46.7%       46.7%
  9         77         24.1%        34.8%       27.9%
 10         71         22.7%        28.8%       26.2%
 11         74         27.7%        23.5%       23.5%
 12         66         28.8%        22.9%       22.9%
 13         80         21.8%        21.3%       21.3%
 14         61         17.3%        13.8%       13.8%
 15         70         20.0%        17.1%       17.1%
 16         74         19.2%        35.5%       28.7%
 17         68         23.4%        34.1%       31.5%
 18         66         19.8%        26.1%       19.8%
 19         86         18.4%        12.1%       12.1%
 20         67         29.0%        38.7%       36.1%
 21         82         21.7%        19.8%       19.8%
 22         92         20.6%        19.3%       19.3%
 23         84         19.5%        26.3%       26.3%
 24         86         19.5%        24.7%       24.7%
 25         88         21.7%        23.0%       23.0%
 26         73         21.7%        26.4%       26.4%
 27         84         14.8%        22.7%       22.7%
 28         77         18.3%        18.7%       18.7%
 29         87         16.0%        18.9%       18.9%
 30         70         12.3%        17.7%       17.7%

(a) body height in inches

(b) body mass in pounds

(c) body age in years

(d) body impedance in ohms

(e) body water in pounds

Table 2
Categories for Body Fat Measurements


NORM (a)               BODY AGE (b)

               < 30        30-39        40-49

Excellent   3.6-19.8%    9.5-20.7%    14.2-22.8%
  Good      19.9-24.8%   20.8-24.5%   22.9-26.8%
  Fair      24.9-27.3%   24.6-27.2%   26.9-29.5%
  Poor      27.4-28.3%   27.3-33.1%   29.6-35.8%
Very Poor   28.4-42.1%   33.2-42.3%   35.9-43.5%

NORM (a)         BODY AGE (b)

              50-59         60+

Excellent   18.3-24.9%   14.5-24.6%
  Good      25.1-28.5%   24.7-27.2%
  Fair      28.6-31.9%   27.3-31.5%
  Poor      32.0-36.6%
Very Poor   36.7-44.0%   37.4-42.6%


NORM (a)                BODY AGE (b)

               < 30        30-39        40-49

Excellent   5.4-13.7%    7.8-16.7%    9.9-18.1%
  Good      13.8-17.3%   16.8-21.1%   18.2-22.7%
  Fair      17.4-22.1%   21.2-24.5%   22.8-25.7%
  Poor      22.2-27.9%   24.6-29.4%   25.8-30.3%
Very Poor   28.0-40.7%   29.5-41.6%   30.4-41.4%

NORM (a)         BODY AGE (b)

              50-59         60+

Excellent   12.3-19.3%   11.4-18.1%
  Good      19.4-23.2%   18.2-22.1%
  Fair      23.3-26.4%   22.2-26.2%
  Poor      26.5-31.1%   26.3-30.2%
Very Poor   31.2-41.5%   30.3-43.5%

(a) ranges of body fat mass as a percent of total
body mass

(b) body age in years
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Author:Sutton, Robert A.; Miller, Carolyn
Publication:College Student Journal
Geographic Code:1USA
Date:Dec 1, 2006
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