Body Composition Models

Compartmentalisation of the body’s components was first described in 1921 by Czech anthropologist J. Matiega; in this model the human body consisted of: the weight of the skeleton, skeletal muscle, skin plus subcutaneous tissue, and a remainder; the sum of which was equal to body mass. Since this time, due to health risks associated with excess body fat and the difficulty of directly measuring body fat, indirect measurement methods have evolved, which divide the body into 2-4 compartments (Ehtisham et al., 2005; Ellis, 2000; Ellis, 2001; Roche et al., 1996; Wang et al., 2005). Due to the lack of a classification system at the organisational level, Wang et al., (1992) developed a five-level model (Figure 2.1), providing a structural basis for body composition research (Ellis, 2000; Lee & Gallagher, 2008): atomic (I); molecular (II); cellular (III); tissue (IV); and whole body (V), where the total number of components within each level equate to body mass. This section will provide a brief summary of the 2-, 3-, and 4-compartment models commonly used in body composition assessment.

Figure 2.1 Basic two-compartment model and five-level multicompartment model of body composition. ECS, extracellular solids; ECF, extracellular fluid Source copied from: Ellis 2000 (p.652).

2.4.3.1 2-Compartment Models

The classic 2-compartment (2-C) model measuring body mass (BM) or mass and body volume (BV), was pioneered by Bhenke et al. in 1942, and was based on Archimedes’ principle that body density (Db) similar to that of an object or substance is a function of the mass and densities of its component parts relative to its volume (Going, 2005), which is defined as its mass per unit volume (i.e. Db = M/V). In this model body BM is divided into FM, and FFM (Ellis, 2000; Ellis, 2001; Heyward & Wagner, 2004; Wells & Fewtrell, 2006), and body volume (BV) is determined by hydrostatic densitometry or underwater weighing (UWW) and more recently by ADP (see section 2.5.3). With assumed constant densities for both FM (0.9g/ml) and FFM (1.1g/ml), led to the development of the reference body, with changes in Db mainly attributed to adiposity (Behnke et al., 1953).

Siri (1956), and Brozek et al (1963) developed prediction equations to determine %FM from Db, which were based on an adult reference body with an assumed Db and %FM, with any difference in the reference Db assumed to be due to %FM (Heyward & Wagner, 2004). This method continues to be used by researchers today, with both equations yielding almost identical results for %FM (Heyward & Wagner, 2004). These equations are presented below, with detailed explanations provided elsewhere of how the densities and proportions of FM and the respective components of FFM are used to derive the constants used in these equations (Heyward & Wagner, 2004; Wang et al., 2005):

%FM = (4.95/Db - 4.50) x 100 (Siri, 1956 equation)

%FM = (4.57/Db - 4.142) x 100 (Brozek et al., 1963 equation)

As explained in section 2.4.2 above, whilst the density of FM is relatively constant, the density of FFM varies with age (particularly during childhood and adolescence), gender, and ethnicity, among other factors, and thus scientists have proposed modifications to these equations based on population-specific conversion formulas, developed from multi-component methods (Going, 2005; Heyward & Wagner, 2004; Lohman, 1989; Wells et al., 2010). Although in the summary of equations provided by Heyward & Wagner (2004), no conversion equation was available specifically for

SA children and adolescents. These conversion equations are considered to provide reasonable estimates of %FM when compared with 4-C model equations (prediction error = 1.9 – 3.4 %FM) at the population level (Heyward & Wagner, 2004). However, greater individual variation has been observed, with 95% limits of agreement (mean ±2SD) ranging from -7.5% to 5% (Roemmich et al., 1997). Other 2-C methods were also emerging at this time, which involved whole body potassium counting (Forbes et al., 1961) and radioactively labelled water (Pace & Rathbun, 1945), which also assumed a constant density for FFM (Ellis, 2000).

Whilst the Siri equation requires a measure of body density, %FM and FFM can also be determined directly from hydrometry (see sections 2.4.3b & 2.6) using the 2-C model formulas (Pace & Rathbun, 1945), based on the age- and gender-specific constant values for TBW as follows:

FFM (kg) = TBW/C

%FM = {[BM – (TBW/C)]/BM} x 100

where BM = body mass; TBW = total body water; and C is the age- and gender- specific constant value for TBW = 73.2% for adults.

2.4.3.2 3-Compartment Models

To account for population variability in the hydration of FFM (see section 2.4.2), Siri (1961) developed a 3-C model equation sub-dividing FFM into water and solid (i.e. protein and mineral) fractions, and thus compartmentalising the body into fat, water, and fat-free dry mass (Ellis, 2000; Going, 2005; Heyward & Wagner, 2004; Wells et al., 1999; Wells & Fewtrell, 2006):

%FM = (2.118/Db – 0.78TBW – 1.354) 100 where Db = body density; and TBW = total body water

This model assumes a constant density for the protein and mineral fractions, and in addition to measuring BM, and BV to determine Db using densitometry; total body water (TBW) is also measured by hydrometry, usually by the isotope (2_H2O

deuterium) dilution method (Ellis, 2000; Heyward & Wagner, 2004; Schoeller, 2005; Wells & Fewtrell, 2006; see section 2.6). Lohman (1986), also developed a 3-C model

using DXA (see section 2.5.2), which divided the body into fat, mineral, and water + protein, to account for variability in the mineral content of FFM. Comparisons between the 4-C model, and the 3-C water and 3-C mineral model revealed much greater errors in the mineral model, which was not recommended for use in children and adolescent populations (Roemmich et al., 1997).

2.4.3.3 4-Compartment Models

The 4-C model further sub-divides body mass into water, bone mineral, fat, and residual mass (including protein, soft tissue minerals and glycogen), with constant densities assumed for the four components (Ellis, 2000; Wang et al., 2005; Wells et al., 1998; Wells & Fewtrell, 2006). In this model bone mineral content (BMC) measured by DXA (Ellis, 2000; Heyward & Wagner, 2004; Wells et al., 1999; Wells & Fewtrell, 2006; see section 2.5.2) is added to the measures in Siri’s 3-C model (i.e. BM, BV, and TBW). Although several 4-C equations have been developed (Friedl et al., 1992; Fuller et al., 1992), the resulting estimates of %FM are similar (Wang et al., 2005). The simultaneous equations used to develop 4-C equations are based on the body mass or body mass and body volume models are:

BM = FM + TBW + BMC + RM

Where BM = body mass; FM = fat mass; TBW = total body water; BMC = bone mineral content; RM = residual mass and units are in kg.

BV = FM/0.9007 + TBW/0.99371 + BMC/2.982 + RM/1.404

Where BV = body volume; and each component is divided by its assumed constant density in g/ml (Wang et al., 2005).

In the development of paediatric references for the hydration of FFM (see section 2.4.2), Wells et al. (2010) used the following 4-C equation to determine FM in children and adolescents aged 5-20y:

FM = (2.747 x BV) – (0.710 x TBW) + (1.460 x BMC) – (2.050 x BM),

(Where FM = fat mass (kg); BV = body volume (l); TBW = total body water (kg); BMC = bone mineral content (kg); and BM = body mass (kg)).

In that study as the majority of the cohort was white, it was recommended that variations in lean tissue composition between ethnic groups be further investigated, although the researchers considered any ethnic differences to be relatively small. The validity and accuracy of any of the equations is dependent on the assumed constants of the densities and proportions of the component fractions to the individual or population to which they are applied (Going, 2005). The 4-C model is considered the most accurate and valid model for estimating body fat for in vivo body composition measurement, as it requires the least assumptions (Going, 2005; Wells & Fewtrell, 2006). However, this model also has an increased risk of measurement error by virtue of the number of different methods involved in determining the body’s component parts (Going, 2005; Heyward & Wagner, 2004).