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Adolescence: Somatic Growth and Sex Differences

Roland C. Hauspie, Dr.Sc.

Professor, Laboratory of Anthropogenetics, Free University of Brussels, Belgium adolescent growth cycle

Growth at adolescence is characterized by the presence of an adolescent, or pubertal, growth spurt. Figure 3-1 shows a typical example of the growth in height of a girl between 3 and 18 years old (data from the Belgian Growth Study of the Normal Child1-3).

The upper part is a plot of the height-for-age data (distance curve), while the lower part shows the increments in height over 1-year intervals; that is, a proxy for velocity in growth. Actually, the yearly increments reflect average velocity in the considered interval while, strictly speaking, the term velocity refers to instantaneous velocity; that is, the first derivative of a smooth distance curve. Despite this, the terms increments and velocities are often intermixed, such as in this text. The horizontal bars in the graph indicate the length of the intervals over which the increments were calculated. It is common practice to calculate increments from measurements no less than 0.85 years and no more than 1.15 years apart and convert them to whole-year increments by taking the ratio of the difference between the two measurements and the length of the interval. Increments calculated over shorter periods reflect seasonal variation and are relatively more affected by measurement error.4

The growth pattern in height is characterized by a gradually decreasing (sometimes more or less constant) velocity during childhood, which is, in many children, figure 3-1 Growth in height of a girl (no. 29) between 3 and 18 years old. The upper part shows a plot of the height-for-age data (distance curve), while the lower part shows the yearly increments in height (velocity curve). The horizontal bars indicate the length of the intervals. (From the Belgian Growth Study of the Normal Child.)

figure 3-1 Growth in height of a girl (no. 29) between 3 and 18 years old. The upper part shows a plot of the height-for-age data (distance curve), while the lower part shows the yearly increments in height (velocity curve). The horizontal bars indicate the length of the intervals. (From the Belgian Growth Study of the Normal Child.)

interrupted by one or more small prepubertal (or mid-childhood) spurts5,6 (see Chapter 2). The age at minimal velocity before puberty (age at takeoff, TO) is considered as the onset of the pubertal growth spurt. The age at takeoff varies considerably, among populations, individuals (standard deviation = about 1 year), and sexes, boys being in average 2 years later than girls in starting off their adolescent spurt. Maximum velocity in height (or peak height velocity) is reached within 3-3.5 years after the onset of the spurt. The difference in age at takeoff and age at peak velocity (PV) can be used as a measure of the duration of the adolescent spurt. After having reached a peak, the growth velocity rapidly decreases, inducing the end of the growth cycle at full maturity, around 16-17 years for girls and 18-19 years for boys in Western populations. There is a wide variation among populations, individuals and the two sexes as to the attained size at each age, the timing of events such as adolescent growth spurt, and the age at which mature size is reached. The growth curve of height (shown in Figure 3-2) is typical for all post-cranial skeletal dimensions of the body. figure 3-2 Increase in weight of a girl (no. 29) between 3 and 18 years old. The upper part shows a plot of the weight-for-age data (distance curve), while the lower part shows the yearly increments in weight (velocity curve). The horizontal bars indicate the length of the intervals. (From the Belgian Growth Study of the Normal Child.)

figure 3-2 Increase in weight of a girl (no. 29) between 3 and 18 years old. The upper part shows a plot of the weight-for-age data (distance curve), while the lower part shows the yearly increments in weight (velocity curve). The horizontal bars indicate the length of the intervals. (From the Belgian Growth Study of the Normal Child.)

Increase in weight has a different pattern, in the sense that the start of the adolescent growth spurt in weight does not correspond with the age of minimal increment in weight before puberty. Most children show the lowest annual increase in weight in late infancy or early childhood, around 2-3 years old.7 Thereafter, increase in weight slowly but steadily accelerates until the onset of puberty, when there is a sudden rapid increase in weight velocity. The pattern of increase in weight and weight velocity shown by the data of the girl in Figure 3-2 illustrates these typical features very well. In this example, the sudden change in velocity of weight between childhood and puberty can be identified at 11.5 years old. The precise location of the onset of the adolescent growth spurt is generally more problematic and subjective for weight than it is for height.

growth modeling and biological parameters

Most of our knowledge on the shape of the human growth curve comes from longitudinal growth data, i.e., sequential measurements of size taken at regular intervals on the same subject, such as shown in Figures 3-1 to 3-3. Serial measurements of height, for instance, form a basis for estimating the supposed underlying continuous growth curve of stature. However, recent studies have shown that frequent measurements of size (at daily or weekly intervals) with high precision techniques (such as knemometry with a measurement error of about 0.1 mm) recently showed that the underlying growth process is, at the micro-level, not as smooth as we usually assumed9,10 (see Chapter 12). Nevertheless, for the description of the general shape of the growth curve in height, based on body measurements taken with classical techniques at intervals varying between several months and 1 year, we can readily assume that the growth process is continuous.

Various mathematical models have been proposed to estimate a smooth growth curve on the basis of a set of discrete measurements of growth of the same subject over time.11-13 An interesting review of various approaches in modeling human growth has been given by Bogin.14 More than 200 models have been proposed figure 3-3 Growth in head circumference of a girl (no. 29) between 3 and 18 years old. The upper part shows a plot of the head circumference-for-age data (distance curve), while the lower part shows the yearly increments in head circumference (velocity curve). The horizontal bars indicate the length of the intervals. (From the Belgian Growth Study of the Normal Child.)

figure 3-3 Growth in head circumference of a girl (no. 29) between 3 and 18 years old. The upper part shows a plot of the head circumference-for-age data (distance curve), while the lower part shows the yearly increments in head circumference (velocity curve). The horizontal bars indicate the length of the intervals. (From the Belgian Growth Study of the Normal Child.)

to describe part or all of the human growth process, only a small number of which are of practical use. The possibilities and limitations to commonly used mathematical functions for analyzing human growth have recently been discussed.15,16 Here, we concentrate on the Preece-Baines model 1 (PB1), which has been proven to be a very robust model in describing the adolescent growth cycle on the basis of growth data covering the period from 2-5 years of age up to full maturity.17 Whenever longitudinal data from birth to adulthood is at hand, one can better estimate the whole growth curve by means of the triple logistic function18 or the JPA-2 function,19 for instance.

The mathematical expression of Preece-Baines model 1 is

0 (t-e)+ e si (t-v with y = height in centimeters; t = age in years; and h1, h6 s0, s1, and 6 are the five function parameters. Parameters of nonlinear growth models usually allow some functional interpretation of the growth curve. In the case of PB1, parameter h1 is the upper asymptote of the function and thus corresponds to an estimate of mature size. Parameter 6 is very highly correlated with age at peak velocity. Parameter h6 is the size at age 6. Parameters s0 and s1 are rate constants controlling, respectively, prepubertal and pubertal growth velocity.

The parameter estimation of nonlinear growth functions like the PB1 curve are usually obtained by nonlinear least-squares techniques based on numerical minimization algorithms, such as the simplex,20 Marquardt,21 and Gauss22 methods. Most statistical and several graphical software programs now offer the possibility of nonlinear regression analysis of user-entered functions.

The outcome of modeling an individual's serial growth data is a set of values for the function parameters (five in the case of PB1). Hence, growth modeling (or curve fitting) is a technique by which longitudinal growth data can be summarized in a limited number of constants, which have the same meaning for all subjects, thus allowing easy comparison among individuals. By entering the values of the function parameters into the model, one can graph the individual's smooth growth curve. Likewise, when entering the parameter values into the first derivative of the growth model, one obtains an estimation of the instantaneous growth velocity. The growth velocity function for PB1 follows:

Figure 3-4 shows a plot of the PB1 function fitted to the distance data for height of the same girl as in previous figures. The lower part of Figure 3-4 shows a plot of the yearly increments together with the instantaneous velocity curve obtained as the mathematical first derivative of the fitted distance curve. The values of the function parameters for this example are given in Table 3-1.

The standard error of estimate (= square root of the residual variance) is often used as a measure of the goodness of the fit: 