ei He ane y . vy SUT AY X won S&h es FG6> HAHOLIO UAGAALdAS 6 ONG TOA NOLLALLIN bie? The reliance that can be placed in an estimate of fat by this method is affected by the one empirical constant, a, in addition to the errors in measuring density and water. The magnitude of the uncertainty this produces can be estimated by applying the Law of Propagation of Eqs. (19) and (20) to determine the over-all standard deviation a, The variance in d, and in f takes the forms given in Appendix 3. Inserting the numerical values for d,, d,, and d., the variance in the estimate of fat reduces to (22) 2 4.22 z 04. + 0.00804* + (1.126 — 1.015 — 0.108) +2 apa a ad The effect of biologica) variability introduced through a depends somewhat on the fatness of the individual; it ia greatest for very lean individuals and becomes amaller with obesity. Although there are no direct data other than that referred to above, it is reasonable on the basis of this and indirect data to assume that the standard deviation in the ratio of mineral to protein for humans is not greater than +0.1, i.e, about £30%. of the assumed mean value of «. The uncertainty to be expected in a determination of fat by the density-total body water method may be illustrated for a subject with d == 1,050 gm/ce and w= 0.55. Substituting o = + 0.1 and the experimental errors of o, == + 0.0026 pm/cc and o, == + 0.02 into Eq. (22) yields a standard deviation in fat estimate of a, = + 2.0% body weight. From the preceding analysis several conclusions may be drawn regarding the applicability and validity of the method. First, the d-w method is valid for all states of hydration. Moreover, since the isotopes of hydrogen can be used as solutes in measuring body water, the method is for practical reasona the only one that appears to be generally valid in estimating fat when extensive edema, pleural effusion, or ascitic fluid is present. In some circumstances the test solutes for extracellular water, which in principle is the only alternative measure of excess hydration, cannot be expected to give a correct fluid volume because of their rapid disappearance and slow diffusion. Second, the estimate of fat and of p + mis relatively little affected by biological variability. Third, it is evident from Eq. (22) that little is to be gained in measuring body density more accurately than 0.0025 gm ‘ce. In fact, an error as great as 0.004 gm/ce does not greatly affect the over-all accuracy of the fat estimate. This conclusion applies even if the error in water measurement were reduced to +1%%of body weight. Fourth, the error in measuring total body water, set here at 2, introduces the largest single source of error. In the example given above, a reduction in the water error from 2% to 41% of body weight would reduce o; to +1.5% of body 237 weight. Fifth, if the experimental) errors were altogether negligible, the uncertainty in fat estimate would still remain about +1.2% body weight unless o, were substantially less than +0.1. On the other hand, even if o. were as great as +0.2, the resulting uncertainty in fat would be only -£1.7%. Sixth, an estimate of total protein plus mineral is just as valid as that for fat, although the relative error is slightly greater. Density—Extracellular Fluid Method Intuitively, it would seem advantageous to combine extracellular fluid apace and corporeal density in u method similar to that of total body water and density for eatimating fat. However, the reliability that might be anticipated is offset by the increased complexities of the assumptions that are inherent in such a method and by the sub- stuntial uncertainties that extracellular fluid space introduces both on theoretical and practical grounds (Siri, 1956). With the introduction of extracellular fluid, the body must be rewarded as a system of five componenta instead of four, i.e, 1 == f +1 +¢+p-+ m, where t and ¢ are the intra- and extracellular water proportions of the body reapectively. The additional compartment necessarily increases the number of assumptions needed to relate f, i, e, p, and m. It is also necessary, as in other methods to introduce w reference body and a prescribed form of adipose tissue. A considerable array of possible relationships among the five constituents are available for a formulation of this method in addition to the basic equation above and the corresponding yeneral equation for density: 1 (23) f t+e p m a7 Gta tera To include the possibility of abnormal hydration, it is necessary to regard e as the sum of a component g associated with the normally hydrated person and a component hk representing the excess as in edema, or deficit as in dehydration. Whatever approach ia then taken, the following relations ure inherent in a formulation of the method: m= apor m= Bp (1 — f — h) toon (1—f—h) (24) - 7= vi where a and @ are empirical constants relating mineral to protein, p is a constant relating intracellular water to the fat-free body, and vy is a constant relating extracellular to intracellular water. In particular it is necessary to the validity of the method to assume that intracellular water is in no way affected by abnormal hydration. 238 OISSW1D WSTTOUVLAR NOLLRLL IN Fae cementpene Oe eS en