There are, on the other hand, no comparable experimental data to
support a similar conclusion for the constancy of the human body.
On the contrary, there ia some direct (Forbes et al., 1953; Mitchell
et al, 1945; Widdowson ef al., 1951) as well as indirect (Siri et al,
to be published) evidence to demonstate that such a pattern is not
foliowed quantitatively. Adipose tissue is thought by some investiga-
tors to consist in part of water and protein so that these constituents
should increase in absolute amount with obesity (Behnke, 1954;
Keys and Brozek, 1953). A yreater variability in the ratio of mineral
to protein among humans, compared to small mammals, would also
affect independently the constancy of the total body water fraction,
as would also transient and pathological! alterations in hydration.
There is no way in which either altered hydration or deviations in the
ratio of mineral to protein can be taken into account in estimating
fat solely from total body water. However, if water is associated
with adipose tissue, this can be expressed in the formula relating fat
to total body water, assuming the water fraction of adipose tissue is
constant. In principle, a somewhat more general equation than that
above should be obtained.
As we have seen, a reference body and a generalized form of adipose
tissue are inherent in a formulation of the densitometric method. They
are equally necessary in deriving the body water formula for estimating fat. Not only are the same assumptions required, but the
reference body must be identically the sume in the densitometric
and total body water methods if they are to be mutually consistent.
A subject who then differs in composition from that of the reference
body is presumedto differ only in posseasing a proportion A of adipose
tissue that is wreater or amaller than that of the reference body. The
total water and fat in the normally hydrated person are then the aums
of these constituents associated with the difference A in adipose tissue,
plus that associated with the proportion 1-- A of the body that
corresponds to the reference body:
(14)
ws Aw, + (1---A) uw,
(15)
= Af, == (1 -- Af) f.
Combining equations, the general
water is
(16)
relation between
The choice of reference man, insofar as it is an accurate average in a
given obesity range, is otherwise arbitrary.
The numerical form of the fat estimating equation based upon the
Minnesota standard man
(Keys and Brotzek, 1953)
(See the Section on General Principles) becomes
(17)
as a reference
f == 1.016 -~ 1.600 w
If, however, the fat-free body ia the appropriate reference, the equa
tion is then
(18)
f = 1.000 ~~ 1.390 w
The validity of the total body water method for estimating fat rests
upon the same assumptions that are inherent in the densitometric
method. The uncertainty associated with fat eatimated by this method
will consequently reflect the error in measuring total body water together with the actual and irreducible variability in body composition
for the population, and of course, any uncertuinty in reference body
composition.
The variance in the estimate of fat, taking these factors into
account, may be derived from Eq. (16), and is given in explicit form
in Appendix 3.
The numerical magnitude of the uncertainty in the estimated fat
may be illustrated with a subject for whom water constitutes 55%
of body weight, and using Minnesota standard man as a reference
(See Section on General Principles). The numerical values of the
standard deviations in w., w,, f,, and f, were discussed in the Section
on Technica) Errors and Riological Uncertainty and the Section on
Total Body Water Method. The estimate of fat and the attendant
standard deviation calculated with Eq. (18) above and the formula
for o, in Appendix 3 are
{== 23.6 + 4.8%body weight
Af == 12.4 + 5.5%body weight
Similarly, an estimate of fat in the same subject may be calculated
from Eq. (18) based on the fat-free body as a reference:
total
fat and
fam We (font +f
Wy — Ww
Af =A = f = 23.6 + 3.5% body weight
Although in the example given here, in which w = 0.55, the caleulated value of fat is the same by both formulas, in very lean and very
obese persons the two formulas differ by about 3% of body weight.
== Af, Eq. (16) is the most general relation between fat and water
This, however, is still within the estimated uncertainty of the method.
It is seen at once, in view of technical difficulties involved, that
reducing the error in total] body water measurement below + 2% of
that is consistent with what is presently known of body composition.
body weight is of doubtful value. More precise water measurement
233
234
The difference in adipose tissue between reference and subject is
then: A --(w,—.w)/(w,— w,), while the difference in fat is Af
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