Relationships among fat mass, fat-free mass and height in adults: A new method of statistical analysis applied to NHANES data.

OBJECTIVES: The positive influence of fat mass (FM) on fat-free mass (FFM) has been quantified previously by various methods involving regression analysis of population data, but some are fundamentally flawed through neglect of the tendency of taller individuals to carry more fat. Differences in FFM due to differences in FM-and not directly related to differences in height-are expressed as ΔFFM/ΔFM, denoted KF . The main aims were to find a sounder regression-based method of quantifying KF and simultaneously of estimating mean BMI0 , the BMI of hypothetical fat-free individuals. Other, related, objectives were to check the linearity of FFM-FM relationships and to quantify the correlation between FM and height. METHODS: New statistical methods, explored and verified by Monte Carlo simulation, were applied to NHANES data. Regression of height2 on FFM and FM produced estimates of mean KF and indirectly of BMI0 . Both were then adjusted to allow for variability in KF around its mean. Its standard deviation was estimated by a novel method. RESULTS: Relationships between FFM and FM were linear, not semilogarithmic as is sometimes assumed. Mean KF is similar in Mexican American men and women, but higher in men than women in non-Hispanic European Americans and African Americans. Mean BMI0 is higher in men than in women. FM correlates more strongly with height than has been found previously. CONCLUSIONS: A more accurate way of quantifying mean BMI0 and the dependence of FFM on FM is established that may be easily applied to new and existing population data.

Adult fat content: reinterpreting and modelling the Benn Index and related sex differences.

BACKGROUND: In women, the height exponent, p, of the Benn Index, (body mass)/height(p), is typically lower than in men, body masses are more weakly correlated with height and fat masses tend to be higher. In both sexes fat masses correlate only weakly with height. Changes in fat mass are typically accompanied by changes in fat-free mass. AIMS: To integrate these facts, together with other published findings relating to fat content and to explain why p is lower in women. METHODS: Data and statistics are taken from the literature. The differences in p are explored by Monte Carlo and algebraic modelling. Mean transverse areas of the body (MTAs), calculated as (body mass)/height, are related to height. RESULTS AND CONCLUSIONS: The body can be modelled as consisting of a component, M1, varying roughly with the cube of height and another, M2, varying little with height. The low correlation between total body mass and height is due both to M2 and to data scatter. The low p values in women relate especially to M2. Relationships amongst height, fatness, MTAs and girths of body parts generally conform to this interpretation. Questions are raised as to how health risks are best related to fat mass.

Sitting height as a better predictor of body mass than total height and (body mass)/(sitting height)(3) as an index of build.

BACKGROUND: The Rohrer Index and the ratio of sitting height (SH) to height fall similarly with growth in early childhood, then level off and rise slightly towards adulthood. In adults the BMI correlates with SH/height. The mean cross-sectional areas of the legs of adults are correlated positively with upper body masses and negatively with leg lengths. AIM: To find an index of body build that is less dependent on relative leg length and age in children and adults than are the BMI and the Rohrer Index. SUBJECTS AND METHODS: Published data are analysed to establish the relative importance of SH and leg length as predictors of body mass and to investigate the age dependence of the ratio (body mass)/SH(3). RESULTS: SH is a much better predictor of body mass than height, with leg length being barely relevant. Average values of (body mass)/SH(3) vary very little over the age range of 1-25 years, despite small non-random fluctuations. CONCLUSION: The ratio (body mass)/SH(3) is proposed as a useful "sitting-height index of build" that is superior to the Rohrer Index and could prove better than the BMI as a predictor of adiposity. Further studies are needed, notably using individual data and fat-free masses.

Statistical approaches to relationships between sitting height and leg length in adults.

BACKGROUND: Relationships between sitting height (SH) and leg length (LL) in adults are almost always studied in terms of ratios such as the Cormic Index (CI), SH/stature, rather than as primary variables. They are affected by genetics and childhood nutrition. AIM: To characterize these relationships and test whether the CI is ideal as an index of relative LL. SUBJECTS AND METHODS: Regression and reduced major axis (RMA) equations were calculated for 1653 men and women of European descent. For other population groups the RMA parameters were calculated from published means and standard deviations of SH and LL. RESULTS: Linear and 'allometric' (power) equations fit the data equally well. For people of European origin the RMA equations for men and women do not differ significantly. Corresponding equations for other populations differ in line with published CIs. CONCLUSIONS: The linear equations suggest that LL tends to vary in proportion to SH minus a quantity similar to head height. A new index of relative LL may therefore be preferable to the CI for some research purposes to reflect this, but there is otherwise no strong reason to abandon the use of the CI.

A negative relationship between leg length and leg cross-sectional areas in adults.

OBJECTIVES: These were to examine the relationship between leg cross-sectional areas (CSAs) and leg length while making allowance for other factors, such as fatness and the load on the legs. METHODS: Body mass, stature, and sitting height were directly measured and volumes and leg CSAs were obtained by 3D scanning for 155 men and 162 women. Leg CSAs were regressed simultaneously on upper body mass and leg length. RESULTS: With allowance made for positive correlations with upper body mass, leg CSAs showed a negative correlation with leg length (P = 0.00006-0.027). CONCLUSION: There is a negative correlation between leg lengths and CSAs that is largely obscured by other influences.

Human allometry: adult bodies are more nearly geometrically similar than regression analysis has suggested.

It is almost a matter of dogma that human body mass in adults tends to vary roughly in proportion to the square of height (stature), as Quetelet stated in 1835. As he realised, perfect isometry or geometric similarity requires that body mass varies with height cubed, so there seems to be a trend for tall adults to be relatively much lighter than short ones. Much evidence regarding component tissues and organs seems to accord with this idea. However, the hypothesis is presented that the proportions of the body are actually very much less size-dependent. Past evidence has mostly been obtained by least-squares regression analysis, but this cannot generally give a true picture of the allometric relationships. This is because there is considerable scatter in the data (leading to a low correlation between mass and height) and because neither variable causally determines the other. The relevant regression equations, though often formulated in logarithmic terms, effectively treat the masses as proportional to (body height)(b). Values of b estimated by regression must usually underestimate the true functional values, doing so especially when mass and height are poorly correlated. It is therefore telling support for the hypothesis that published estimates of b both for the whole body (which range between 1.0 and 2.5) and for its component tissues and organs (which vary even more) correlate with the corresponding correlation coefficients for mass and height. There is no simple statistical technique for establishing the true functional relationships, but Monte Carlo modelling has shown that the results obtained for total body mass are compatible with a true height exponent of three. Other data, on relationships between body mass and the girths of various body parts such as the thigh and chest, are also more consistent with isometry than regression analysis has suggested. This too is demonstrated by modelling. It thus seems that much of anthropometry needs to be re-evaluated. It is not suggested that all organs and tissues scale equally with whole body size.

Body fat and skinfold thicknesses: a dimensional analytic approach.

BACKGROUND: Body fat may be estimated from skinfold thickness measurements (Skfs), but current prediction equations are dimensionally inconsistent and do not properly allow for the influence of body size on fat mass. AIM: To find a dimensionally correct formula relating fat content to Skfs and body size. SUBJECTS AND METHODS: 285 African children aged 9-11 years, with fat content measured by dual-energy X-ray absorptiometry, were studied. Because least-squares regression parameters can be a misleading guide to true functional relationships, the real data were compared with simulated data sets conforming to a dimensionally correct statistical model. RESULTS: The data are consistent with functional relationships such that fat mass is proportional to Skfxheight(2). The mean ratio (fat mass)/(Skfxheight(2)) is 6% higher in the girls than in the boys. DISCUSSION: Appropriately, Skfxheight(2) has the dimensions of fat mass/density. Height(2) has no obvious physical significance and a more meaningful expression might be 'heightxX', where X corresponds to some measure of body width or girth. CONCLUSION: In formulae for predicting fat mass, multiplying Skfs by height(2) gives better estimates, especially for the tallest and shortest individuals. Fat mass, rather than percentage body fat (%BF), is best taken as the variable initially predicted.

The scaling of eye size in adult birds: relationship to brain, head and body sizes.

Birds' eyes seem often to be about as large as head size allows and brain size is taken here as a measure of the ill-defined space that is available to accommodate them. In four data sets for non-passerines eye size relates more strongly to brain size than to body mass and most non-passerine data are consistent with eye:brain (or eye:head-space) isometry. Eye:body allometry thus seems to follow from a negative head-space:body allometry. In passerines the eye:brain size correlations seem to be secondary to strong eye:body, brain:body, and perhaps therefore head-space:body correlations, a difference attributed to the passerines' greater anatomical uniformity.

Estimating body surface area from mass and height: theory and the formula of Du Bois and Du Bois.

BACKGROUND: Body surface areas are usually estimated by means of a formula due in its general form to Du Bois and Du Bois (1916), i.e. area = C x mass(a) x height(b), where C, a and b are empirical constants. Its physical basis is unknown. AIM: The present study aimed to explain this formula, correct some errors in the associated literature and provide a clear basis for future developments. SUBJECTS AND METHODS: Use is made of published data, but arguments are largely based on mathematics and modelling. RESULTS: A more fundamental formula is as follows: area = alpha(mass x height)(1/2) + beta(mass/height), where alpha and beta are constants. For realistic values of mass and height the two equations are numerically equivalent. For individuals, beta cannot be negative and b cannot exceed a, but, as regression parameters, these conditions may not be satisfied. This could be due to systematic or statistical relationships between individual values of alpha or beta and the ratio height(3)/mass. Values of alpha, beta, C, a and b are calculated for some published data. CONCLUSIONS: The original type of formula suffices for practical purposes, but the new one is better in analytical contexts when other terms, e.g. for body shape, are to be incorporated.