Height Exponent Research Articles

Cardiac magnetic resonance (CMR) height-based allometric scaling in Southeast Asians; implications in the diagnosis and prognosis of left ventricular hypertrophy (LVH): the REMODEL study

Abstract Background Left ventricular hypertrophy (LVH) is a strong predictor of adverse cardiovascular outcomes (1). Although normalizing LV mass (LVM) to height exponents has been shown to reduce variability from body size, specific recommendations for height exponents are lacking due to the scarcity of normal cohorts to define appropriate height exponents (2). Cardiac magnetic resonance (CMR) is increasingly used in assessing LVM, and the existing body of research is based primarily on the MESA cohort (3). While the MESA cohort is ethnically diverse, the intrinsic effects of ethnicity may not fully be discerned if certain ethnic groups are under-represented. Purpose We aimed to demonstrate the diagnostic and prognostic implications of establishing height exponents specific to sex in a Southeast Asian cohort. Methods Non-overweight/obese Southeast Asian healthy volunteers (n=416) were used to establish appropriate height exponents and normal reference ranges of LVM. The impact of these height exponents was examined in a separate cohort of Southeast Asians with hypertension (n=878). All individuals underwent standardized cardiovascular magnetic resonance imaging (CMR). Primary outcome was a composite of acute coronary syndrome, heart failure hospitalization, stroke, and cardiovascular mortality. Cox regression analysis of various LVH measures were adjusted for 24-hour systolic blood pressure, diabetes, and hyperlipidemia. Results The height exponents for healthy females and males were 1.57 and 2.33, respectively. In patients with hypertension, sex-specific height exponents significantly increased the detection of LVH compared with body surface area (BSA) indexing (47% [n=409/878] versus 27% [n= 236/878], p<0.001). Most individuals re-classified to LVH with sex-specific height exponents were overweight (33.1%, n=58/175) or obese (64.6%, n=113/175). There were 37 primary events over 60 [37-73] months of follow-up. Regardless of indexing method, LVH was independently associated with increased adverse events (sex-specific height exponent hazard ratio (HR): 2.8 [1.25-6.29], P=0.013). The prediction ability of LVH diagnosis by sex-specific height exponents was similar to BSA indexing (HR: 5.43 [2.49-11.8], P<0.001). Conclusions Reference ranges specific to the ethnicity, sex and imaging modality are necessary to establish appropriate height exponents. Although utilizing sex-specific height exponents to index LVM resulted in significantly more LVH reclassification when compared with BSA indexing, this did not translate to a notable improvement in event prediction. Further research into alternative methods of LVM indexing is warranted.Abstract SummaryPredictive Ability of LVH Measures

Variations in indexation of left atrial volume across different races

BackgroundLeft atrial volume (LAV) has prognostic value. Guidelines propose indexation to body surface area (BSA), however studies demonstrate this can overcorrect for body size. Limited studies investigate indexation across different ethnicities. We sought to evaluate the effect of ethnicity on indexation. MethodsUsing data from the World Alliance of Societies of Echocardiography (WASE) cohort, healthy subjects were classified by race as White, Black, Asian, or Other. Biplane LAV was indexed to traditional isometric measurements (BSA, height, weight, ideal body weight (IBW) and IBW derived BSA (IBSA)), as well as previously-derived allometric height exponents (2.7 and 1.72). Additionally, an allometric height exponent for our cohort was derived (linear regression of the logarithmic transformation of LAV = a(height)b) as 1.87. All indices were then assessed using Spearman correlation, with a good index retaining correlation of LAV/index to raw LAV (r∼1), while avoiding overcorrection by the index (r∼0). ResultsThere were 1366 subjects (White: 524, Black: 149, Asian: 523, Other: 170; median age 44 years, 653 females (47.8%)). In the entire group, BSA, IBSA, height1.87 and height1.72 performed well with retaining correlation to raw LAV (r > 0.9 for all), and minimising overcorrection to body size (r < 0.1 for all). On race-specific analysis, BSA overcorrected for body size in the White population (r = 0.128). Height1.72 minimised overcorrection for body size in all populations (r ≤ 0.1 for all races). ConclusionDespite a cohort with normal BMI, there was still disparity in LAV indexation with BSA across races. Allometric height indexation, particularly using height1.72, is a possible solution, although further validation studies in BMI extremes are required.

‘At risk’ waist-to-height ratio cut-off points recently adopted by NICE and US Department of Defense will unfairly penalize shorter adults. What is the solution?

ObjectivesTo a) demonstrate that adopting ‘at risk’ waist-to-height ratio (WHTR) cut-off points, recently approved by National Institute for Health and Care Excellence (NICE) and the United States Department of Defense (USDoD), will unfairly penalize shorter individuals and will be too lenient for taller individuals, b) to confirm that waist circumference (WC) of a sample of US service personnel, scales to approximately height0.5, supporting the notion that WC, to be independent of height (HT), should be normalized using WC.HT−0.5 (WHT•5R), and c) to identify the WHT•5R cut-off points that will reduce or eliminate this unwanted bias. Subjects/methodsWe employed a three independent cross-sectional sample design. All n = 58,742 participants underwent anthropometric assessment of body mass, stature and waist circumference. ResultsThe allometric power-law model WC=a.HT^b for US service personnel identified the height exponent to be b= 0.418 (95 % CI 0.251–0.585), confirming that the simple body-shape index for WC to be independent of HT, should be WC.HT−0.5. Chi-square tests of independence and for linear trend confirmed that by adopting WHTR cut-off point, shorter individuals (both service personnel and non-service participants) will be over penalized (classified as being ‘at risk’). New WC independent-of-height ratio cut-off points were found to resolve this problem. ConclusionsAdopting WHTR cut-off thresholds (either 0.5 or 0.55) will lead to shorter adults being unfairly classified as being ‘at risk’ in terms of their central adiposity and general health status. Adopting new WHT•5R cut-off point thresholds were found to greatly reduce or eliminate this bias.

Variations in LA Volume Indexation Across Different Ethnicities in Healthy Subjects With Normal Body Mass Index (BMI)

Left atrial volume (LAV) is central to diastolic function evaluation and has demonstrated prognostic value. Guidelines recommend LAV indexation to BSA; however recent studies demonstrate allometric height is superior. Our aim was examine indexation by allometric height and BSA for different ethnicities. Using the World Alliance of Societies of Echocardiography (WASE) normal cohort, subjects with “normal” BMI (18.5-27.5kg/m2 [Asian], 18.5-30kg/m2 [other populations]) were classified by race: White, Black, Asian, or Other. Biplane LAV was indexed to BSA and allometric height; exponents of height for each ethnicity was derived (linear regression of logarithmic transformation of LAV=a(height)b). Indices (heightb) were assessed using Spearman’s correlation of LAV/heightb to raw LAV and body size (heightb). 1,366 subjects, (653 female (47.8%), mean age 47±17years; White:524, Black:149, Asian:523 and Other:170) were evaluated. LAV measurements were lowest in the Asian group (mean 41.5±13.4mL vs 49.1±17.0mL White, 50.6±14.3mL Black, 46.7±13.2mL Other; p<0.001). The calculated allometric height exponent for all subjects was 1.87, but varied across ethnicities (2.21 for White, 1.19 Black, 1.14 Asian, and 1.43 Other). The height exponents for each race were good indexation markers; indexed LAV correlated well with raw LAV (r∼1), without overcorrection by the index (r∼0) and was similar to BSA indexation (Figure). Despite normal BMI, there was disparity in LAV indexation across races. With respect to allometric height indexation, different exponents need to be derived based on race. Future validation studies are required in subjects with a wide BMI range.

Effect of larval density and algal concentration on growth, survival and feeding rates of the scallop Nodipecten subnodosus (Sowerby, 1835)

The scallop Nodipecten subnodosus is the largest pectinid species targeted in Mexico for hatchery seed production. Thus, effects of larval density (LD = 5, 10 and 15 ml−1) and food concentration (FC = 15,000; 30,000; 45,000 and 60 cells ml−1) were assessed on survival (S) and growth. Clearance (CR) and ingestion rates (IR) were also studied. Lowest S was observed at 15,000 cells ml−1 (19%–22%), while S > 50% prevailed at ≥30,000 cells ml−1. Both LD and FC significantly affected gross growth rate (GGR), with maximal values (7.3 µm d−1) observed at 5 larvae ml−1. Mean GGR of 6.1 to 6.9 µm d−1 was recorded at 10–15 larvae ml−1 and 45,000 to 60,000 cells ml−1. Maximal CR (13.8–23 ml larva−1 h−1) was recorded at 15 cells ml−1. Ingestion rates increased as FC increased, reaching asymptotic values (9.7–11.5 cells larva−1 min−1) at 45,000 and 60,000 cells ml−1. Allometric IR—Shell height exponents increased (b = 1.1 to 1.9) as FC increased. The combined results suggest that N. subnodosus larvae may be reared at stocking densities from 5 to 15 larva ml−1 and reach maximal GGR if fed 45,000 to 60,000 cells ml−1.

Body size and shape characteristics for Cooper's 12 minutes run test in 11-13 years old Caucasian children: an allometric approach.

The Cooper Test, is a field test, simple and useful in the school context. The aim of this research was the definition of the trend in Cooper endurance test along with the growth. In particular, through the scaling method (allometric). A total of 556 of European sedentary children aged 11-13 years (282 boys; 274 girls) were involved. All subjects were evaluated through the Endurance Cooper test (12 min run test). To identify the most appropriate body size and shape characteristics as well as any categorical differences (sex, age) associated with the measure of the Cooper test, a multiplicative model with allometric body-size components was applied. The multiplicative model relating to the Cooper test and the body-size components was: Cooper test = a · mass-0.325 · height0.878 with the mass and height exponents being k1=-0.325 (SEE=0.40) and k2= 0.878 (SEE=0.141), respectively. The adjusted coefficient of determination (adj R2) was 32.3%, with a log-transformed error ratio of 0.136 or 14.5% having taken antilogs. Significant differences in the constant 'a' parameter were identified by sex (P<0.001) and age (P<0.001) while the interaction of sex per age was not significant (P=0.761). The results suggested that the scaling method identified the optimal height-to-body mass ratios associated with Cooper endurance test corresponding to ectomorph body shape. Furthermore, growth fluctuations become important to avoid alarming judgment in case children will be poorly evaluated.

Can waist circumference provide a new "third" dimension to BMI when predicting percentage body fat in children? Insights using allometric modelling.

Body mass index (BMI) is often criticized for not being able to distinguish between lean and fat tissue. Waist circumference (WC), adjusted for stature, is proposed as an alternative weight status index, as it is more sensitive to changes in central adiposity. The purpose of the study is to combine the three dimensions of height, mass, and WC to provide a simple, meaningful, and more accurate index associated with percentage body fat (BF%). We employed a four independent sample design. Sample 1 consisted of 551 children (320 boys) (mean±SD of age=7.2±2.0years), recruited from London, UK. Samples 2, 3, and 4 consisted of 5387 children (2649 boys) aged 7 to 17years recruited from schools in Portugal. Allometric modelling was used to identify the most effective anthropometric index associated with BF%. The data from samples 2, 3, and 4 were used to confirm and cross-validate the model derived in sample 1. The allometric models from all four samples identified a positive mass exponent and a negative height exponent that was approximately twice that of the mass exponent and a waist circumference exponent that was approximately half the mass exponent. Consequently, the body shape index most strongly associated with BF% was . The component of the new index can simply be interpreted as a WC "weighting" of the traditional BMI. Compared with using BMI and WC in isolation, could provide a more effective and equally noninvasive proxy for BF% in children that can be used in public and community health settings.

A new waist-to-height ratio predicts abdominal adiposity in adults

ABSTRACTOur aim was to identify the best anthropometric index associated with waist adiposity. The six weight-status indices included body mass index (BMI), waist-to-hip ratio (WHR), waist-to-height ratio (WHTR), and a new waist-by-height0.5 ratio (WHT.5R). The association between three waist skinfolds and the six anthropometric indices was conducted using ANCOVA, MANCOVA, allometric modelling and non-linear regression. The strongest predictors of waist adiposity were (1st) WHT.5R, (2nd) WHTR, (3rd) waist circumference (WC), (4th) BMI, (5th) WHR, and lastly (6th) a body shape index ABSI = WC/(BMI2/3 * height1/2). The allometric and non-linear regression analyses identified the optimal waist-to-height ratio associated with waist adiposity to be (waist * height −0.6). The 95% confidence intervals of the height exponents encompassed −0.5 but excluded −1.0 assumed by WHTR. Assuming that excess waist adiposity is an important cardiovascular risk factor, we recommend that the new WHT.5R be used to advise people how to maintain a “healthy” weight.

Scaling children's waist circumference for differences in body size

Both waist circumference (WC) and body size (height) increase with age throughout childhood. Hence, there is a need to scale WC in children to detect differences in adiposity status (eg, between populations and different age groups), independent of body size/height. Using two culturally different samples, 1 English (10-15.9 years n = 9471) and 2 Colombian (14-15 years, n = 37,948), for WC to be independent of height (HT), a body shape index was obtained using the allometric power law WC = a.HTb . The model was linearized using log-transformation, and multiple regression/ANCOVA to estimate the height exponents for WC controlling for age, sex, and any other categorical/population differences. In both samples, the power-law height exponent varied systematically with age. In younger children (age 10-11 years), the exponent was approximately unity, suggesting that pre-pubertal children might be geometrically similar. In older children, the height exponent declined monotonically to 0.5 (ie, HT0.5 ) in 15+ year-olds, similar to the exponent observed in adults. UK children's height-adjusted WC revealed a "u" shaped curve with age that appeared to reach a minimum at peak-height velocity, different for boys and girls. Comparing the WC of two populations (UK versus Colombian 14-15-year-old children) identified that the gap in WC between the countries narrowed considerably after scaling for height. Scaling children's WC for differences in height using allometric modeling reveals new insights into the growth and development of children's WC, findings that might well have been be overlooked if body size/height had been ignored.

Relations between body mass, height, fat mass, and waist circumference in American and Korean men and women

Relations between body mass, height, fat mass, and waist circumference in American and Korean men and women

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)/heightp, 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.

The fat mass index: why its height exponent should be 3 and not 2

The fat mass index: why its height exponent should be 3 and not 2

Measures of adiposity: the inappropriate use of the fat mass index

The fat content of the body is sometimes expressed as the fat mass index (FMI), calculated as fat mass/height2.1 This is advocated because, unlike percentage body fat (%BF), the FMI is independent of fat-free mass.2, 3 However, for most purposes as explained below, the height exponent should be three, not two.

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.

Predicting backscatter-biomass and height-biomass trends using a macroecology model

This study describes the use of a plant structure model from the field of macroecology to make generalized predictions about backscatter-biomass and height-biomass trends from synthetic aperture radar data over forests. A theoretical relationship between canopy height and biomass density is derived. The predicted values of the height exponent are comparable with those from the remote sensing literature. A radiative transfer model parameterized by the macroecology model is also used to predict trends in P-band backscatter. The results imply that backscatter can saturate even for low-opacity canopies and decreasing basal area results in backscatter saturating at lower biomass levels. The theoretical analysis is supported by reference to a range of published results.

Sediment-Wave Development in Subcritical Water Flow

A power law relating bed-form magnitudes (lengths or heights) to time, with all parameters normalized by equilibrium values, is promoted to describe ripple or dune growth with time from plane-bed to equilibrium conditions. In order to use this relation for prediction purposes, new expressions are presented herein for both the times required for ripples and dunes to achieve equilibrium magnitudes, and also the respective growth exponents for the development of bed-form heights and lengths. These new relations have been determined based on 15 new and 76 previously published laboratory experiments covering ranges of sands and flow strengths, although additional work is warranted to confirm these expressions for field scales. The power-law relation for bed-form growth from a plane bed is also extended in concept herein to describe changes in bed-form size from nonzero initial magnitudes. In preliminary tests, this modified power-law expression was found to provide reasonable descriptions of trends in increasing and decreasing bed-form heights and lengths with changes in flow strength. At this stage, application of this modified expression is principally conceptual in nature, with further work required to facilitate prediction for changes in flow of both times to achieve equilibrium magnitudes and also height and length growth exponents.

Predicting Body Fat Using Data on the BMI

A data set contained in the Journal of Statistical Education's data archive provides a way of exploring regression analysis at a variety of teaching levels. An appropriate functional form for the relationship between percentage body fat and the BMI is shown to be the semi-logarithmic, with variation in the BMI accounting for a little over half of the variation in body fat. The fairly modest strength of the relationship implies that confidence intervals for body fat, and tolerance intervals for BMI, can be quite wide, so that strict reliance on the BMI as a measure of body fat, and hence obesity, is unwarranted. Nevertheless, when fitting percentage body fat as a function of the class of “power weight for height indices”, i.e., indices of the form weight/heightp, the BMI, with a height exponent of p = 2, is an appropriate choice to make.

Structural Reliability of Monopods Under Storm Overload

The structural reliability of a generic caisson under storm overload is investigated using typical Australian North West Shelf (NWS) environmental data. The bending moment due to the hydrodynamic loading is shown to increase in proportion to the fourth power of the wave height in certain critical cases, rather than the more usual exponent of α≈2. Combined with the steep wave height return period curve on the NWS, this may lead to low structural reliability, as much as two orders of magnitude smaller than more typical structures in other locations. The wave height exponent α varies with water depth and environmental force type (e.g. shear or bending moment) and increases rapidly near water line. This nonproportional nature of the loading is not addressed in design codes of practice or in traditional pushover analysis.

Influence of Non-Proportional Environmental Loading on the Reliability of Production Jack-ups

Inherent features of jack-up units, including their mobility and their integrated and standardized form, make them well suited for certain field developments. An overview of the configurations and attributes of production jack-ups is presented, including a database of applications to date. The relationship between jack-up configuration and structural reliability under storm overload is then explored. Critical values of the wave height exponent α are presented for a wide range of water depths and jack-up geometries, along with selected pushover analysis results. There is a strong tendency for the structural reliability to decrease in shallower water depths and when the jack-up is elevated in the water column by a storage tank or braced base. The latter is due essentially to the non-proportional increase in environmental loading down the structure with increasing return period.

Environmental load distributions: influence of platform configuration

Long term distributions of environmental loading are determined for generic jacket, jack-up and monopod “minimum facilities” platforms. Australian North West Shelf met-ocean data are used, with both shallow (40 m) and moderate (90 m) water depths. Global (system) loads are related to the critical local (component) forces that trigger structural collapse. The various distributions are quantified and compared in terms of the wave height exponent α . It is demonstrated why base shear is a good measure of the critical environmental load for typical jackets. However, this is not the case for other structural configurations due to non-proportionality of the loading, which is accentuated in shallow water. As a result, monopods in particular may be expected to have considerably lower structural reliability than jackets when designed to the same Code.