In the following sections each of the methods for estimating body composition from the fluid apaces, density, or their combination is examined in reference to its basic premises, inherent uncertainties, and general conclusiona. The primary formulation is expressed in as general a form as the underlying assumptions in a method permit. WILLiaM E. Sret - Although this has been done, it must be emphasized that such formulas are provisional The procedures for estimating body composition, and more particularly fat, from the volume of the fluid spaces and corporeal density are well established in principle. Quantitatively they have been open to a variety of interpretations ever since the early use by Behnkeef al, however, the inherent limitations in the accuracy of any of the andthe first uses of solutes for measuring extracellular and total body water. For the moat part, these methods when applied to laboratory animals give results in close agreement with direct chemical analyses. €661 WAPOLDO/AFIAWALATS “S (ON 6 TOA NOLLALLIN numerical values are assigned to the constants. Introduction (1942) of the underwater weighing technique for determining density, [eh Differentiation into specific working formulas occurs only when Whether or not they can be applied to humans with expectation of equally reliable quantitative results is stil] open to conjecture, because the human population at large tends toward greater variability in some aspects of body compornition than do laboratory animals. Because of this variability, estimates of fat derived from fluid spaces and density have in some instances been treated with considerably more confidence than the underlying premises of these methods would appear to grant. Moreover, estimates by one indirect method have been used to corroborate estimates by another, whereas, for example, total body water and body density must necessarily give identica} fat values because the constants in the fat-estimated formulas are derived from lhe sume basic assumptions. Keys and Brozek (1953) reviewed critically the methods and concepts that had evolved in the inveatigation of body composition up to 1953. More recently Morales and Williams (1958) undertook an analysis of the densitometric method but failed to take into account some of the basic premises of this and the total-body-water methods for estimating fat. The specific methods for estimating body composition from density and fluid spaces still warrant closer analysis for the purpose of answering the fundamental questions: (1) How are fat, and protein plus mineral best estimated from total body water, extracellular fluid space, and body density, or a combination of such measurements? (2) What are the underlying assumptions in these methods and their range of validity? (3) What uncertainty does biological variability as well as error of measurement introduce into the final estimate? (4) For practical purposes, what accuracy is desirable in each of these measurements? 223 until the numerical values rest on more definitive data. Even then, tormulas should be recognized. General Principles The sole constituents of the body considered in the following analyais are lipida, water, protein, and mineral. The addition of carbohydrates, and a separation of lipids into “essential” and ‘“nonessential” is not warranted, because none of the indirect methods for determining body composition is capable of differentiating such divisions. Water alone can for this purpose be regarded as two compart- ments, namely, the intra- and extracellular fluid spaces, For con- venience in formulating the alyebraic expressions relating to body composition, the constituents nre expressed as decimal proportions of body weight, or of adipose tissue where this is indicnted, Hence, fat is designated by f (kg fat/ke body weight, or if specified, kg fat/kg adipose tissue), with w, 7, ¢, p, and om, similarly defined for total water, intra- and extracellular water, protein, and mineral. All methods for deriving body composition have in common the two fundamental relations that the sums of the proportions of the constituents by weight and by volume must equal unit weight and volume: (1) f 40 4 p-+- m= 1 (unit wt.) (2) F4t+Ww+P+4M—t1 (unit vol.) A third expression may be derived that is more useful than Eq. (2) when densitometry is employed: (3) 1 f ‘dd, + w dy. + d dy + m da, in which d is the combined density, the density of the whole body, and d,, d., d,, and d,, are the separate densities of the constituents expressed in gm/cc. The definitions of f, w, p, and mt must be explicit if an interpretation of fat estimating equations is to be unambiguous. Jn any method 224 MASWL ASTIOHY LEI NOLLTLAN BODY COMPOSITION FROM FLUID SPACES ANJ) DENSITY: ANALYSIS OF METHODS