weight because of irreducible variabilities in the other factors,
A particularly significant result is the fact that the standard deviation associated with the differential fat estimate is, if anything,
greater than that for the estimate of total fat. The reason for this is
explicit in the formulas for ¢, and o,, , both of which contain the same
factors affected by biological variability and error of measurement.
No attempt was made to evaluate systematic errors inasmuch as
they may vary widely with techniques used. Such errors include
hydrogen exchange in measuring body water with hydrogen isotopes,
errors in the estimate of the compositions of the reference body and
adipose tissue, and possibly the use of a reference body of one composition for the whole of the emaciation-obesity range. Altered hydration
will, of course, render the method invalid,
one is best suited to the present method. It assumes that the ratio of
minera] to protein is constant, i.e., ni == ap, or itr equivalent, that
mineral forms a constant percentage of the mineral-protein fraction
of the body. This ratio is not altered by abnormal hydration, and the
effect that adiposity may have upon it is relatively small, but more
important, the estimate of fat is not strongly affected by fluctuation
or uncertainty in the mineral to protein ratio.
The formula for fat, as well as that for estimating the standard
deviation, is greatly simplified by introducing the aubstitution s — p
+ m=p (1+a) and the combined density, d., of protein and
mineral given by
a) dd,
d, == {1+
duet
(19)
errors in measurement, both methods must in the atrictest sense yield
Combining these equations with the fundamental! equations in the
in whatever formulation one chooses to accept.
If, on the average,
the two methods, when used separately, lead to different values for
fat, it can only mean that inadvertently two different reference bodies
were implicitly involved and consequently the constants in the density
£661 HAHOLDO-AMAUWALdES 6 ON 6 IOA NOLLIBLAIN
may be any assumption one chooses that relates two of the constituents by means of a conatant. However, among the numerous retationships between constituents that can, and have been postulated, only
Finally, it may be noted that the densitometric and total body water
methods are not independent means for eatimating fat. Aside from
identical values, for they are derived on precisely the same premises
eke
mental equations (1) and (2) which, it may be recalled, apply to a
body of any description.
One additional relationship is needed to complete the system, but it
or in the total body water equation, or in both, must be readjusted.
Density—Total Body Water Method
Combined measurements of density and total body water yield a
method for estimating body composition that does not require a reference body nor an explicit description of the composition of adipose
tissue. The method is based, not on separate estimates of fat by the
two measurements, but rather on a single formulation in which density and water occupy the roles of independent variables (Keys and
BroZek, 1953; Siri, 1956). Although it is the method that appears
to be the least affected by biological variability, because it requires
the fewest assumptions concerning interrelations between constituents, it is not, nevertheless, wholly free of such uncertainties. On the
other hand, since only one assumption need be made, it is possible to
choose an empirical relationship for which the associated biological
variability has relatively little eect on the reliability of the fat eatimating equation.
A formulation of the method is derived directly from the funda-
235
Section on General Principles, the general formula for fat becomes
(20)
f==
Pu d, [ ‘.
-- w ( oof )-- 1 |
The value of a, upon which an estimate of d, depends, resta on
admittedly meager data for humans, Although it is relatively consistent in laboratory animals, with a value of about 0.25 (Pacé and
Rathbun, 1945; Spray and Widdowson, 1950), the ratio appears to be
substantially greater and more variable in humans. The direct analyses of five cadavers by Mitchell et al. (1945), Forbes ef al. (1953),
and Widdowson ef al. (1951), whose resulis are summarized by Keys
and Brozek (1953), yielded values ranging from 0.292 to 0.404. For
the present purpose in illustrating a numerical form of the fatestimating equation, a value of a —0.35 is adopted, which corresponds to total mineral of about 7%of the fat-free body. The exact
value of a, either for the individual or for the average, is not needed
however, for as shown below a considerable variation in a dues not
greatly affect the estimate of fat and of p 4m.
The combined density of protein and minera! for « --= 0.35 ig then
d,== 1.665 gm/ce. Substituting this and the numerical values for d,
and d,. into Eg. (20), the fat estimating equation becomes:
(21)
2.118
foo",
0.7R0w —- 1.354
236
DcSPe LTA NCALLEN EOIN
yields little improvement in the reliability of the fat estimate. If
Oo. = 1 11, the uncertainty in fat would be reduced only to + 3.9%,
Indeed, if there were no error whatever in total body water measurement the uncertainty o, in total fat would still be -+3.6%of body