An Anthropometric Measure Based on an Age-Related Model of Human Growth
7.3 Practical Methods and Techniques
7.3.1 The Mathematical Model of the Human Growth
To establish mathematical models of human growth we identifi ed body height as the primary age- related growth factor. Body height increases monotonically during growth as opposed to body mass, which fl uctuates. To model growth, the best fi t between individual body height ( h ) and body mass ( m ) was calculated separately in boys (B) and girls (G) with the function M p = c H c , where: p =
<B,G>, c , c = sex-specifi c constant, H and M = body height and mass treated as physical variables (Benn 1971 ). The body height is expressed in meters ( m ) and body mass in kilograms (kg). There are several ways to obtain the approximation.
1. The exponent c can be identifi ed by calculation of the best mathematical fi t of the function between body mass, and body height M = c H c .
2. Due to the mathematical properties of the logarithmic function the exponent c can also be calcu- lated as a slope of the linear regression function between the log ( M ) = a + c log ( H ). Any statisti- cal package or Excel or curve fi tting software can be used to calculate one of the above mathematical approximations.
7.3.2 Establishing an Age-Related Growth Model
Sex-specifi c growth models have been developed based on a set of data collected in 847 Polish chil- dren (444 girls and 403 boys, aged 5–18 years) obtained between 1985 and 1990 (Lebiedowska et al.
2008 ) (Table 7.1 ). The sample of Polish children contained a homogeneous sample of children with generally ideal body fat composition, as judged by 95th percentile of BMI (<24.4 in girls and <23.5 in the boys). No obesity/overweight or underweight was reported in the sample.
143 7 The Human Body Shape Index (HBSI): An Anthropometric Measure Based on an Age-Related…
1. The mathematical approximations of the body mass ( m ) against body height ( h ) obtained from individual subjects were calculated separately for boys and girls with the function M p = c H c (Fig. 7.1 ).
2. The same model was calculated using a logarithmic function where the exponent c was equal to the slope of the linear regression function between the log ( M ) = a + c log( H ) (Fig. 7.2 ).
Both mathematical methods generated the following models of growth: M G = 13.1 H 2.84 ( R 2 = 0.9) for girls and M B = 13.1 H 2.84 ( R 2 = 0.91) for boys and M = 13.1 H 2.76 ( R 2 = 0.89) for both sexes.
Table 7.1 Demographics of the sample Polish children 5–18 years old (between 1985
and 1990)
Age (years)
Girls ( N = 444) Boys ( N = 403)
m (kg) h (m) m (kg) h (m) N Mean ± S.D. Mean ± S.D. N Mean ± S.D. Mean ± S.D.
5 26 18.88 ± 2.19 1.12 ± 0.04 29 20.81 ± 2.75 1.14 ± 0.05 6 43 22.57 ± 4.64 1.19 ± 0.06 30 22.37 ± 3.48 1.2 ± 0.06 7 37 24.78 ± 3.55 1.25 ± 0.05 33 25.15 ± 3.6 1.26 ± 0.06 8 23 26.79 ± 5.13 1.28 ± 0.06 34 29.96 ± 6.83 1.33 ± 0.07 9 42 28.68 ± 4.97 1.34 ± 0.06 35 30.23 ± 4.73 1.35 ± 0.05 10 33 34.59 ± 8.3 1.39 ± 0.08 37 34.72 ± 6.83 1.42 ± 0.07 11 30 39.18 ± 8.3 1.49 ± 0.08 31 37.67 ± 6.17 1.46 ± 0.08 12 36 42.25 ± 7.71 1.55 ± 0.08 34 42.71 ± 10.9 1.52 ± 0.1 13 31 48.84 ± 9.14 1.578 ± 0.07 36 48.48 ± 11.3 1.6 ± 0.09 14 38 52.73 ± 6.25 1.63 ± 0.06 38 56.74 ± 9.5 1.68 ± 0.07 15 21 52.97 ± 6.1 1.63 ± 0.04 10 51.61 ± 9.7 1.657 ± 0.07 16 36 56.88 ± 7.26 1.64 ± 0.06 20 65.3 ± 8.47 1.76 ± 0.06 17 37 58.16 ± 8.27 1.63 ± 0.06 29 65.72 ± 7.99 1.78 ± 0.07 18 11 61.35 ± 10.05 1.67 ± 0.08 7 67.97 ± 10.69 1.79 ± 0.08 Reprinted from Lebiedowska et al. (2008). With permission
This table lists the demographics of the children included into the study. N : number of subjects, m : body mass, h : body height, S.D.: standard deviation
Fig. 7.1 Mathematical models of growth based on the exponential fi t between body mass ( M ) and body height ( H ) in 847 (444 girls, and 403 boys) Polish children 5–18 years old. The growth models in girls M G = 13.11 H 2.84 ( R 2 = 0.9) ( left ) and in boys M B = 13.64 H 2.64 ( R 2 = 0.91) ( right ) (Modifi ed from Lebiedowska et al. (2008).
With permission)
144 M.K. Lebiedowska and S.J. Stanhope
7.3.3 Physical and Physiological Interpretation of Age-Related Growth Models
Assuming that body density does not change, human growth follows the rule of allometry or geo- metrically similar growth, if the proportions between the sizes of body parts are invariant. In prefect geometrical similar growth, an increase in body mass according to the third power of body height would be expected. In other words, if c → 3 the assumption about the geometrically similar growth is more reliable. The difference between the exponent c and number 3 describes the discrepancy between the experimental and geometrically similar model of growth. Growth in Polish children 5–18 years old followed the geometrical model with 10.6% accuracy in boys and 5.3% accuracy in girls (as judged from the differences between the experimentally obtained value of c and number 3).
The larger exponents obtained in girls, in part, refl ects the fact that the fi nal average body height reached by males is larger than in females ( http://www.cdc.gov ). However, gender-specifi c changes in body proportions may play a role. The group of Polish children contained a homogeneous sample of children with generally ideal body fat composition, as judged by 95th percentile of BMI (<24.4 in girls and <23.5 in the boys). Similar exponents reported in a population of English children (Rosenthal et al. 1994 ) suggest similar growth in English and Polish children between years 1985 and 1992. Due to the lack of the generally accepted “golden standards” for human growth at this time, we treat these experimentally established models of growth as a refl ection of ideal age-related growth. It is impor- tant to model age-related growth in order to separate healthy age-related growth from changes in HBS related to changes in percentage body fat.
It should be emphasized that the described growth models may be benefi cial to the description of HBS growth-related changes over a longer period of time, when body height is the most important factor affecting growth. To analyze the shorter periods of growth, or to characterize the diverse popu- lations other models may be more suitable.
7.3.4 General Guidelines for the Establishment of Age-Independent Indices Based on Growth Models
To calculate an individual HBSI, the following procedure should be followed:
1. Body mass data obtained from individual subjects should be divided by the body height to the sex-specifi c exponent c ( c = 2.84 for girls and c = 2.64 for boys).
Fig. 7.2 Mathematical models of growth based on the linear fi t of log( H )-log( M ) function in 847 (444 girls, and 403 boys) Polish children 5–18 years old. The linear regression line in girls ( left ) log( M G ) = 2.57 + 2.84 log ( H G ); r = 0.95) and in boys ( right ) log( M B ) = 2.61 + 2.68 log( H B ); r = 0.95 ( right )
145 7 The Human Body Shape Index (HBSI): An Anthropometric Measure Based on an Age-Related…
2. Correlations between HBSI and body height should be calculated. If there are no statistically signifi cant correlations, the correlation between the index and the calendar age should be calculated. If the correlation with the calendar age is not statistically significant the mean and S.D. of the index may be considered as HBSI of the population from which the sample comes.
3. To determine if it is necessary to introduce age corrections, the data should be divided into age groups and the mean of HBSI of the age groups should be calculated. A one-factor ANOVA test can be used to determine the effect of age on the HBSI. If the groups’ mean is signifi cantly dif- ferent, an age correction for each group should be introduced as the ratio between the mean of each group and the fi rst age group.
7.3.5 Application of Normalization Algorithms in the Establishment of Age-Independent, Sex-Specifi c, Human Body Shape Indices
The sex-specifi c human body shape indices (HBSI p ) were calculated using a sample population of Polish children using body mass and body height of individual subjects as HBSI p = m / h x . Polled HBSI for girls and boys were calculated using the mean power of body height across sexes. Mean and S.D.s, correlations and the slopes of linear regression lines between HBSI and H are displayed in Table 7.2 .
The HBSI were compared for 4 age categories (5–9, 9–12, 12–15 and 15–18 years old). To determine the degree to which the mean indices were affected by age, indices for each age were compared using ANOVA test with Bonferroni adjustment. The HBSI were statistically different in girls (Table 7.3 ) but not in boys (Table 7.4 ).
The largest difference occurred between age groups 9–12 and 15–18 years (1.28 or 0.75 S.D.s, p = 0.003). Based on the analysis, appropriate age corrections had been introduced in girls (Table 7.4 ).
7.3.6 The Physical and Physiological Interpretation of the HBSI
HBSI exhibited very low and statistically not signifi cant correlations between indices and body height and next calendar age with the slopes of the regression lines approaching 0. The fact that HBSI could be considered independent of body height sanctions the characterization of a population of children 5–18 years old with one mean and one S.D. The Polish data model is designed to refl ect the normal age-related changes in HBS. It seems that at least in some applications, BMI in children 5–18 years old may be replaced as a HBS measure with the HBSI which is coherent with the biome- chanics of human growth. The HBSI may also replace multiple indices with two sex-specifi c, age- invariant indices.
HBSI may be very useful in some applications requiring comparison of HBS changes over time, coming from different populations. In the case of one sex or single subject analysis the application of gender-specifi c HBSI should be considered. In the case of a single population of children of both genders, the pooled HBSI could be benefi cial to healthcare professionals.
PI based on the ideally geometrically similar growth ( c = 3) decreases slightly with the body height and age, introducing more variability over the age groups (Lebiedowska et al. 2008 ) . Due to larger variability of PI over HBSI, PI may introduce a slightly larger error over HBSI in the classifi cation of
146 M.K. Lebiedowska and S.J. Stanhope
Table 7.2 PI, HBSI of Polish children (5–18 years old; between years 1985 and 1990) as a function of body height (horizontal line)
Girls N = 444 Boys N = 403
Regression equation Mean ± S.D. Regression equation Mean ± S.D.
PI = m / h 3 (kg/m 3 )
15.81– 2.28 H r = –0.15, p = 0.002
12.47 ± 1.64 17.32– 3.46 H r = 0–0.34, p < 0.001
12.21 ± 1.62
HBSI G (kg/
m 2.84 )
12.93 + 0.19 H r = 0.02, p = 0.66
13.21 ± 1.73 –
HBSI B (kg/
m 2.68 )
– 13.51 + 0.15 H
r = 0.02, p = 0.7
13.74 ± 1.72
HBSI (kg/
m 2.76 )
12.18 + 0.98 H r = 0.1, p = 0.03
13.6 ± 1.79 14.2– 0.59 H r = 0–0.08, p = 0.13
13.34 ± 1.67
Modifi ed from Lebiedowska et al. (2008). With permission
This table illustrates that HBSI : Human Body shape Index, but not PI : Ponderal Index can be considered as independent on the body height ( H ) (horizontal line in all graphs)
abnormal HBS. PI may still be useful, especially in the analysis of different populations, irrespective of location and time (Seltzer 1966 ; Nahum 1966 ; Huber 1969 ; Hattori and Hirohara 2002 ; Rolland- Cachera et al. 1982 ; Ricardo and Araujo 2002 ) .
As the HBSI described above were based on growth models treated as the “gold standard” of human growth, they carry over the advantages and the limitations already mentioned. HBSI may be useful to describe HBS growth-related changes over a larger period of time, when increase in body height is the most important factor affecting growth. To analyze shorter periods of growth (for example during puberty) other indices, may be more suitable.
147 7 The Human Body Shape Index (HBSI): An Anthropometric Measure Based on an Age-Related…
Table 7.3 HBSI B in age groups in boys
Age group (years old) N Mean ± STD
5–9 124 13.80 ± 1.55
9–12 103 13.51 ± 1.65
12–15 107 13.69 ± 1.93
15–8 69 14.03 ± 1.75
Reprinted from Lebiedowska et al. (2008). With permission
This table shows the lack of statistically signifi cant differences ( p = 0.253) between mean HBSI G in age groups
Table 7.4 HBSI G in age groups in girls
Age group (years old) N Mean ± STD HBSI G age correction
5–9 129 13.42 ± 1.37 a,b 0.98
9–12 105 12.65 ± 1.76 c 0.96
12–15 105 12.69 ± 1.83 d 0.96
15–18 105 13.93 ± 1.67 1.05
Reprinted from Lebiedowska et al. (2008). With permission
This table shows the differences between the mean HBSI G in age groups a 5–9 and 9–12 years old, p = 0.003
b 5–9 and 15–18 years old, p = 0.006 c 9–12 and 15–18 years old, p = 0.001 d 12–15 and 15–18 years old, p = 0.001
The appropriate age corrections for girls have been calculated (last column)
7.3.7 Application of HBSI for the Establishment of Standard Thresholds for Detection of Overweight and Obesity in Children
Out of the full spectrum of the HBS two extremes are especially important from the humanitarian, social and economic point of view. Malnutrition causes 53% of all deaths in children younger than 5 years (Bryce et al. 2005 ) , whereas obesity has been announced as a major public health crisis in the USA (Cole et al. 2000 ; Wang et al. 2008). The limitation of BMI to detect obesity in children based on the growth charts was reported by Piers et al. 2000 and de Onis, 2004 . The differences in the estimates of the prevalence of obesity in children and adolescents vary from 11–24%, despite using the same set of the data (Troiano and Flegal 1999 ) . The lack of uniform, absolute thresholds for obesity classifi cation in children must play a role in the diffusion of the estimates. Future studies should compare the sensitivity and specifi city of HBSI versus other indices in the classifi cation of the obesity/malnutrition in children (Field et al. 2003 ) . The model of growth which was used to establish the HBSI was based on the sample of population of Polish children (5–18 years old; between years 1985 and 1990), characterized by ideal fat composition as judged by 95th percentile of BMI values. In addition, a similar model of growth (during a comparable period of time) was reported in English children (Rosenthal et al. 1994 ) . The lack of any other “golden standard” suggests that the model based on the population of Polish children may serve as a model of natural growth. The abso- lute thresholds for HBS based on the model are displayed in Table 7.5 .
The thresholds are based on the sex- and age-specifi c percentiles values: “underweight” (<5th percentiles), “normal” (5th–85th percentiles), “at risk of overweight” (85th–95th percentiles) and
“overweight” ( ³ 95th percentiles). Since these thresholds for overweight and obesity were established
148 M.K. Lebiedowska and S.J. Stanhope
Table 7.5 Thresholds for overweight and obesity based on a model of growth of Polish children (5–18 years old) between years 1985 and 1990.
Ranges of indices in Polish children population
Sex Girls ( N = 444) Boys ( N = 403)
HBSI G (kg/m 2.84 ) Underweight <10.67 –
Normal 10.67–14.97
At risk of overweight 14.97–16.4
Overweight ³ 16.4
HBSI B (kg/m 2.68 ) Underweight – >11.27
Normal 11.27–15.36
At risk of overweight 15.36–17.19
Overweight ³ 17.19
HBSI (kg/m 2.76 ) Underweight >10.96 >10.97
Normal 10.96–15.39 10.97–14.93
At risk of overweight 15.39 – 16.85 14.93–16.57
Overweight ³ 16.85 ³ 16.57
Modifi ed from Lebiedowska et al. (2008). With permission
This table displays the ranges of sex-independent (HBSI) and sex-specifi c (HBSI B , HBSI G ) body shape indices for: underweight (<5th percentiles), normal (5th percentiles–85th percentiles), at risk of overweight ( ³ 85th percentiles and ³ 95th percentiles) and overweight ( ³ 95th percentiles) conditions
N : number of children, B , G : boys and girls respectively
using sample distributions, the development of physiologically based thresholds for overweight and obesity should be explored. There exists a discrepancy between the defi nitions for abnormal HBS in children and adults. It is well established that increased BMIs in adults (for overweight BMI ³ 25 and for obesity BMI ³ 30) are associated with the changes in other anthropometric, biochemical and instrumental measure of obesity (Dahlström et al. 1985 ; Wang et al. 2004). The projection of well established adult thresholds into the pediatric population may lead to the development of physiologically based thresholds. It seems however, that the thresholds may be sex specifi c.