Introduction to Human Nutrition

Body Composition 17

fat is assumed to be maximal 3% of BF%. This error

is mainly due to violation of the assumption that the

density of the FFM equals 1.100 kg/l in the subject

under study. It can be argued that in certain subjects

or groups of subjects this assumption may be vio-

lated, as for example in young children and in preg-

nant women. Use of Siri’s formula will then lead to

biased conclusions. Some laboratories have attempted

to use water displacement instead of underwater

weighing, but the technique failed, mainly because of

the diffi culty in accurately reading the water level in

the tank.

An air-displacement method has been commer-

cially available since 1995. This method measures

body volume after placing the subject in a small, air-

tight chamber and increasing the pressure by adding

a known amount of air into the chamber. Boyle Gay-

Lussac’s law enables the calculation of body volume.

Corrections are made for temperature and humidity

changes, and lung volume is assessed simultaneously.

Box 2.3

The density of the fat-free mass (FFM) can be calculated if its com-

position is known.

In the calculation example below it is assumed that the FFM

consists of 73.5% water, 19.6% protein, and 6.9% minerals with

densities (at 37°C) of 0.993, 1.340, and 3.038 kg/l, respectively.

In addition, it is assumed that the volumes of the separate com-

partments can be added up to the total volume of the FFM (in fact,

the compartments do not “mix”). Thus, the volume of the FFM

equals the sum of the other compartments:

FFMvolume = Watervolume + Mineralvolume + Proteinvolume

As volume is weight/density, the equation can be written as:

100/DensityFFM = 73.5/0.993 + 6.9/3.038 + 19.6/1.340

From this, the density of the FFM can be calculated as 1.0999 kg/l.

It is obvious that differences in composition of the FFM will

result in a different density.

Box 2.4

Siri’s formula can be derived assuming that the body consists of fat

mass (FM) and fat-free mass (FFM). If body weight is assumed to

be 100% and body fat is x%, then FFM is 100 − x%. It is assumed

that the volumes of these two compartments can be added up to

total body volume. Then:

Bodyvolume = FMvolume + FFMvolume

As volume is weight/density, the equation can be written as:

100/body density = x/0.9 + (100 − x)/1.1

From this, body fat percentage (BF%) can be calculated as:

BF% = 495/density − 450

The general formula to calculate BF% from body density (Db) is:

BF%

b

FFM FM

FFM FM

FM

FFM FM

=×

×

−

⎛

⎝⎜

⎞

⎠⎟− −

⎛

⎝⎜

⎞

⎠⎟

1

D

DD

DD

D

DD

In general, a lower density of the FFM than 1.1 kg/l will result in an

overestimation of BF% if Siri’s formula is used. It is likely that the

density of the FFM is lower in elderly people, owing to bone

mineral loss (osteoporosis).

Densitometry (using Siri’s equation) overestimates body fat

compared with a four-compartment model (see Figure 2.7).

from which, after correction for the water tempera-
ture (density), the displaced water volume (and thus
the body volume) can be calculated. Corrections
must be made for residual lung volume and air in the
gut. Figure 2.1 shows an underwater weighing. The
technique gives very reproducible results within about
1% of BF%. The absolute error in determined body

Figure 2.1 Underwater weighing. The subject is submerged com-

pletely and breathes via a respirometer (1) for simultaneous residual

lung volume measurement. Weight (W) (2) under water (uw) is

recorded and density (D) is calculated as Dbody = Wair/(Wair − Wuw).

Corrections are made for water temperature and lung volume: percent-

age of fat in the body = 495/Dbody − 450.