‘ 1 d (25) 1—A—h A h d+ a tear but on the other hand, it is not alwaya likely to do so in practice. It w where the subscripts o and 1 signify reference body and adipose tissue respectively. When combined with the expression for total extracellular fluid, ¢=-(1— A —A)e, -+- Ae, -}- #, and that for total fat, f=(1—A—h)f., the estimating equation for total fat has the form (26) fon WOO NO) fi (1 — €.) — fe (1 — #,) bg 1— ¢€ 1—e, The constants in the equation may now be evaluated for the two reference bodies. With the values proposed by Keys and Brozek, the equation becomes (27) can only be interpreted as altered hydration, whereas it may be a normal] variation in the extra- to intracellular water ratio, and a systematic error in fat is then introduced. The method in principle takes into account abnormal hydration, is questionable whether any of the solutes that are employed in measuring extracellular fluid can be expected to yield valid results in the presence of a substantial volume of transudate (Siri, 1956). Additional uncertainties are introduced, ag in the other methods, by the normal variability in total body water and the mineral to protein ratio amony individuals in a population. These factors alone lead to an uncertainty in the fat estimate of about +4%body weight. In view of the great number of assumptions that are necesaary and the possibility of large systematic error, it seems unlikely that the combination of density and extracellular fluid will yield an estimate of fat as reliable as that derived from density alone. f= POS. _ 0.573 « — 4.612 Extracellular—Total Body Water Method For a subject with d= 1.050 gm/ce and e = 0.14, as an example, f= 21.0%. body weight. ° If, however, the fat-free body were the more nearly correct reference, then f, = 1, f, =e, =—0, ¢, is about 0.18, and the general fat formula reduces to ost €66 YAHO.LIO-4SEWALdaS “¢ ON 6 TOA NOLLTLLOIN (28) 4.476 fxAz- a — 0,535 e — 3.972 An analysis of methods for estimating body composition would not be complete without examining the use of combined measurements of the extracellular fluid space and total body water. The general assumptions described in the last section governing the reference body and adipose tisaue are again necessary in easentially the same form for this method. Assuming as before that an excess or deficit in total Whenapplied to the subject above, a value of f = 21.5% body weight is calculated. In the middle range of fatness, i.e, 15 to 30%, the difference between the two estimating formulas is negligible, while in the extremes of leanness and obesity, the difference is never greater than 3% of body weight. Even under the extreme conditions, the difference in the fat estimates derived on the basis of two references is far less than the uncertainty associated with either formula. So far as the method [s concerned, it seems immaterial whether one chooses to think of adipose tissue as pure fat or some combination of fat, water, and protein. For the same reason it makea relatively little difference whether the fat-free body or some other reference is used. A serious limitation in the reliability of this method stems from the large uncertainty in measuring extracellular fluid and the ambiguity in precisely what it means. Related to this is the difficulty in ascertaining the normal variability in extracellular water. By the method in this and the following section any deviation in the volume of extracellular fluid from that of the reference plus adipose tissue fluids, expressed as a fraction h of the body weight, is associated 239 240 only with extracellular fluid space, the actual proportions of total water and extracellular water are then (29) w= (1— A—A) w+ Au, +h (30) e=(1— A—Ah) eo, 4+ Ae, th where the subscripta o and 1 designate quantities associated respectively with the reference body and adipose tissue. Combining these two equations to eliminate A, and then with f=-(1-—A--h) f, to eliminate A, the fat estimating equation becomes (31) f—ek | ftw.) fw) | _ wh [ a—er— pen |+ | f1(00,— 0.) fol0o — 4) ] where k=1 /\ea—w) — e,(1 — wv) + w,—w; | VSN TO INSTIORTW LAIN, SOLD TE LIN oy 2 ‘hae Cbd: LOS A person who differa from the reference by a proportion of adipose tissue A and possibly an abnormal proportion of extracellular water h must then have a density given by