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Human growth has been a subject for scientific investigation for centuries (1), but the fundamental question-How does a child grow?-remains unanswered. Traditionally, human growth is considered to be a relatively smooth process: rapid growth in infancy is followed by steady growth in mid-childhood, and finally, by the pubertal growth spurt in adolescence. However, during short periods, most investigators have found that growth is a nonlinear process, although the exact pattern is not agreed. Butler et al. described growth spurts over 2-year intervals based on growth velocity data from 135 normal prepubertal children (2). Seasonal variation in growth velocity is probably the most well-characterized cyclical pattern of human growth (3–5), with peak velocity in mid-summer. Using knemometry, an accurate and noninvasive technique of lower leg length measurement, Hermanussen et al. showed that lower leg length increased in mini-growth spurts over 30- to 55-d intervals (6). In contrast, Lampl et al. proposed that all gain in length of normal infants occurred in irregular, brief, 1-d growth spurts (saltations), separated by long periods of growth stasis (7). It has also been suggested that the growth process may be governed by the principles of chaos (8). Our own proposal, based on the study of 46 healthy prepubertal children, is that height gain during 1 year is a biphasic process, comprising intense growth spurts lasting an average 8 weeks, separated by periods of very slow growth or stasis over 2 to 3 weeks (9).

Growth rate is determined by a complex interaction of physical, endocrine, and nutritional factors, of which GH and nutrition are the key determinants of mid-childhood growth (10,11). Most of the studies of short-term human growth have been focused solely on stature, without considering changes in weight. The contribution of short-term changes in weight to the growth pattern, therefore, has not been characterized. In addition, there has been no attempt to explore a model that determines the whole growth process. We have now assessed how the pattern of growth in both height and weight may influence both stature and height gained in a large cohort of normal prepubertal children followed during 1 year.

SUBJECTS AND METHODS

Forty-three schoolchildren (17 boys, 26 girls) aged 5.7 to 7.7 years were measured three times per week during 1 academic year, September to July. Children were not measured during holiday periods. The children were volunteers and parental consent was obtained for the study. Ethical approval for the study was granted by the Salford Health Authority ethics committee. Height and weight were measured at the same time of day by two observers using a free-standing Magnimetre (Raven Instruments, England) and electronic weighing scales (Soenhle, Germany) with measuring intervals of 50 g. The SD of the differences between "blind" triplicate measurements of the same 25 children for the two observers was 0.13 and 0.15 cm, with a mean interobserver difference of 0.04 cm.

Height and weight measurements were made on 94 occasions; the median for one subject was 89 (range 60-94). Auxological characteristics of subjects are given in Table 1. Height SDS1 (at the beginning of the study), height SDS2 (at the end of the study), and BMI SDS were calculated from 1990 UK standards (12,13). Growth through the study period was expressed as Δheight (cm) or Δheight SDS (height SDS2-height SDS1).

Table 1 Auxological characteristics of subjects
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Statistical analysis. To assess changes in growth (height and weight) as a function of time and to compare the different patterns of growth within the group, we have used smooth estimates of individual height and weight velocity profiles. These were constructed using locally weighted, least-squares, kernel regression analysis (14), with a bandwidth of 60 d for height velocity and 118 d for weight velocity determined by a predicted squared error criterion (15). A constraint was placed on the height velocity curves that did not allow negative velocities (i.e. loss of stature). Height shrinkage caused by soft tissue or bone compression or both, although recognized during 1 d by conventional height measurements (8), was not considered to be a critical factor over longer measurement intervals. In our previous study (9), we arbitrarily defined a growth stasis as any period in which an increment derived from the smoothed heights was < 0.05 cm during 7 or more d (compared with the mean growth rate of 0.2 cm/week). In keeping with that study, growth stasis was now defined as any period in which the height velocity curve fell below 0.007 cm/d (0.049 cm/week). Growth spurts were identified using local maxima and minima in the velocity curves. Weight gain was defined as any period in which weight velocity was >0 g/d and weight loss as any period with a weight velocity <0 g/d. If there was a major fluctuation in weight velocity during a period of weight gain such that the minima between two maxima fell toward 0 g/d (with the minimum to fulfill the requirement defined arbitrarily as less than half of the smaller maximum), this was classified as two periods of weight gain (Fig. 1). Twelve different characteristics were collated from the height and weight velocity curves of each child (Table 2, Fig. 1). To define the determinants of stature (height SDS1) and growth (Δheight SDS), all 12 characteristics derived for each child were used in stepwise regression analysis. Linear regression and Pearson correlation coefficients were used to define bivariate relationships.

Figure 1
figure 1

Schematic explanation of the characteristics of the height (A) and weight (B) velocity curves. Arrowed lines indicate the amplitude of a height velocity peak (a), length of a height velocity peak (b), and length of a stasis (c) in A. Length of weight loss (d), length of weight gain (e), amplitude of weight loss (f), total amplitude of weight velocity (g), and amplitude of weight gain (h) are shown by arrowed lines in B. If the minimum between two peaks (i) was less than half of the amplitude of the smaller peak (h'), then two separate periods of weight gain were identified.

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Table 2 Characteristics of the height and weight velocity curves
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The aim of the next part of the analysis was to investigate the changing relationship between height and weight over time. First, we removed the linear component of the increasing trend for both height and weight from each individual's measurements by substracting estimates calculated from all subjects. These detrended measurements were then standardized for each individual using a pooled estimate of the variation within individuals, which made the transformed height and weight measurements directly comparable. Finally, a profile of height minus weight differences was evaluated for each individual, which was smoothed using a bandwidth of 60 d. This analysis was carried out after an initial log transformation of the height and weight measurements. Thus, if a child had a large derived measurement at a particular time point, this meant that their height relative to weight was high on that day and similarly, that a small derived measurement corresponded to large weight relative to height. The smoothed estimates showed how this relationship changed over time.

To identify groups of children with similar height-to-weight trends over time, we used average linkage cluster analysis (16). We defined the dissimilarity between two individual smooth profiles, as the sum of the squared differences between the two curves, calculated at a set of time points common to all possible pairwise comparisons. Average linkage evaluates the distance between two clusters as the average dissimilarity between all the pairs, where each member of a pair belongs to a separate cluster.

RESULTS

Height and weight velocities. Both height and weight velocities were nonlinear. An example of height and weight velocity curves for one subject is shown in Figure 2. Height velocity curves for the group were characterized by 3 to 6 peaks over a mean 54 d, separated by 0 to 4 growth stases (Table 2). Weight velocity curves were characterized by 2 to 5 periods of weight gain over a mean 66 d, separated by 1 to 4 periods of weight loss (Table 2).

Figure 2
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An example of height (a) and weight (b) velocity curves for a 7-year-old girl.

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Twenty-eight children with 0 to 2 stases grew better during the year than the 15 with 3 to 4 stases (Δheight SDS 0.28 ± 0.14 versus 0.16 ± 0.13; p < 0.001). Twenty-three children who had either 2 or 3 periods of weight gain were significantly taller than the 20 with 4 or 5 periods (height SDS1 0.4 ± 0.8 vs -0.6 ± 0.9; p < 0.001).

Determinants of stature and growth. There was no significant correlation between height SDS1 and Δheight (cm) or Δheight SDS. Height SDS2 was weakly correlated to Δheight (r = 0.38; p < 0.05). Stepwise regression analysis showed that height SDS1 was influenced by 3 characteristics of the velocity curves: negatively by the mean length of height velocity peaks (p = 0.011), positively by the mean total weight velocity amplitude (p = 0.016), and negatively by the number of periods of weight gain (p = 0.019), all accounting for 38% of the variability. These 3 characteristics also accounted for 40% of the variability of height SDS2. Growth through the year, Δheight SDS, was influenced positively by the mean amplitude of the periods of weight gain (p = 0.0001), positively by the mean amplitude of height velocity peaks (p = 0.003), and positively by the number of periods of weight gain (p = 0.005) with r2 = 44%. Tall stature was associated, therefore, with height velocity peaks of short duration and large, infrequent changes in weight velocity. A large increment in height during the year was related to large, frequent gains in weight and large individual spurts in height.

Seasonal trend. The mean height and weight velocity curves showed a strong seasonal trend, with a declining height velocity during the autumn months reaching a nadir in midwinter followed by an increment in spring, whereas weight gain was initiated in winter, peaked in spring, and declined during summer and autumn (Fig. 3).

Figure 3
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Mean height (black) and weight (gray) velocity curve for the whole group (n = 43) during the year.

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Short-term changes in height relative to weight. The short-term change in height relative to weight (mean smoothed "height relative to weight" curve) for the whole group during the year is shown in Figure 4, a. Height relative to weight increased in autumn and spring, whereas the reverse occurred during the winter months. Using average linkage cluster analysis of individual smoothed "height relative to weight" curves, three groups of children with similar patterns were identified (Fig. 4, b-d). The "height relative to weight" curve of one other child (height -2.9 SDS) was identified separately from the others. The "height relative to weight" curve during the year in group 3 differed from those in groups 1 and 2 because the increase in height relative to weight during the autumn and spring/summer was modest. Further analysis showed that children in group 3 (n = 5) were significantly shorter (mean height SDS1 -0.9 ± 1.2) than those in group 1 (n = 13; height SDS1 + 0.9 ± 0.6; p < 0.001), but the difference compared with group 2 (n = 24; height SDS1 -0.2 ± 0.9) was not significant.

Figure 4
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Mean smoothed "height relative to weight" curves for: (a) the whole group (n = 43), (b) group 1 (n = 13), (c) group 2 (n = 24), and (d) group 3 (n = 5). The groups (b-d) were identified using average linkage cluster analysis. The group with the lowest height SDS (d) had the smallest change in height relative to weight in spring and autumn.

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DISCUSSION

This study is an evaluation of the pattern of short-term growth in height and weight in 43 normal prepubertal children. We used a nonparametric technique to generate velocity curves to avoid imposing a particular form to the growth process, which would result from the use of a linear, polynomial, or step function. We have previously described height regression curves in these children (9). However such curves do not adequately define the dynamic growth process; the smoothing component tends to mask abrupt changes in height. For this reason, we have used velocity curves to describe the characteristics (e.g. length, amplitude) of the growth process both in height and weight. Both height and weight velocities showed a biphasic pattern, characterized by periods of height and weight gain, separated by periods of height stasis or weight loss. A pulsatile growth pattern has been found in many growth studies (2,6,7,9,17). Lampl et al., using a saltation and stasis analysis method (7), proposed that all growth in infancy (length) and adolescence (height) occurs by brief 1-d saltatory spurts separated by periods of no growth. Inspection of our raw height data also suggested that there are significant increments in height between adjacent measurements in many children, but such a saltatory mechanism accounted for only a small amount of the total growth in mid-childhood (9). In a knemometry study of 73 children measured once or twice weekly during 6 to 10 months, where daily lower leg growth rate was extrapolated from data collected over intervals of 31 d, "mini growth spurts" occurring at 30- to 55-d intervals were found (6). We now report a mean interpeak interval for total height of 69 d; this is similar to the 61-d interval found in children with celiac disease during catch-up growth (18).

The pattern of weight gain in mid-childhood has received less attention. A pulsatile weight velocity pattern has been found in very low birth weight babies appropriate for gestational age with 9- to 11-d cycles (19) and in children with celiac disease during catch-up growth with a mean interpeak interval of 57 d (18). In both studies there were no data about the periods of weight loss (weight velocity < 0 g/d). However, these subjects experienced intense periods of weight gain during the study; this probably explains the shorter interval between weight peaks than was found in our study (92 d).

Because stature and growth in this study were not closely related, with the exception of a weak correlation between height SDS2 and Δheight (cm), we investigated further how the pattern of height and weight gain could determine both stature and growth. A knemometry study of 73 healthy children had shown a positive correlation between height SDS and the frequency of "mini growth spurts" (r = 0.54; p < 0.001) i.e. the taller the subject, the more frequently mini-spurts appeared (6). We found that variability in height was related to features of both the height and weight velocity curves: short stature was associated with height velocity peaks of long duration, but also low amplitude and frequent changes in weight. Growth during the study (Δheight SDS) was influenced by the amplitudes of weight gain and of height velocity and the number of periods of weight gain. Poor growth, therefore, was associated with a small number of periods of weight gain of low amplitude and small individual growth spurts within the year.

This is the first study in which detailed characteristics for both height and weight velocity curves have been used to describe the variation in height and short-term growth in normal prepubertal children. These data indicate that the pattern of short-term change in both height and weight gain determines stature and height gain, implying that factors, that control the conversion of nutrients into fat stores, or energy expenditure, are key determinants of the growth process.

Seasonal variation in growth is well recognized in humans (3–5,20,21) as well as in animals (22,23). In this study, the peak height velocity occurred in early summer, similar to previous findings (4,17,24). Seasonality in weight velocity in humans has been less vigorously investigated (17,24). Five siblings, aged 3 to 9 years, measured monthly during 9 years, showed two weight peaks, one in late winter and early spring, and the other in autumn, whereas the nadir was always in midsummer (17), a pattern very similar to that found in the children in the present study. Seasonality in growth may be influenced by external factors such as nutrition (24), physical activity, the light and dark cycle, and possibly by hormonal factors such as GH and IGF-I (25,26). Nevertheless, the seasonal variation in growth in the whole population only approximately reflects the individual seasonal variability, as demonstrated in Figure 2 versus Figure 3.

Not surprisingly, in view of the seasonal data, in the majority of subjects the height velocity peaks were not coincident with weight velocity peaks, similar to an observation found in the study of Togo and Togo (17), where trends in the monthly height and weight velocities were compared in 5 siblings. To investigate the relationship between height and weight velocities during the year, we used a method to describe the short-term changes in height relative to weight after removal of the overall mean linear trend for the whole group. The mean "height relative to weight" curve showed a strong seasonal trend, i.e. height relative to weight increased in autumn and spring, whereas during the winter months it decreased (Fig. 4, a). Because the profile of individual "height relative to weight" curves varied widely, we used average linkage cluster analysis (16) to identify children with a similar pattern. The shape of the "height relative to weight" curve was similar in groups 1 and 2, but in group 3 the increase in height relative to weight during the autumn and spring was modest. Further analysis showed that children in this group were significantly shorter than those in group 1. This suggests that the pattern of height and weight gain within the seasons may differ in tall and short children.

In conclusion, these data indicate that 1) prepubertal stature and growth through the year are related to short-term changes in height and weight, and 2) short-term change in height relative to weight, which is in part governed by the season, appears to differ between tall and short children. When trying to answer the question-How does a child grow?-we must consider, therefore, the whole growth process. The relationship between short-term changes in height and weight, which we have described, implies that similar short-term changes in hormone secretion may occur within the GH-IGF-I axis. We have documented marked individual day-to-day and month-to-month variation in both urinary GH (27) and urinary IGF-I excretion (unpublished observations) in normal children. The negative relationship between fat mass and GH secretion is a consistent feature in normal children and those with growth disorders. Brief periods dominated by weight gain therefore could be associated with a short-lived decrease in GH secretion providing a mechanism for dynamically altering GH output during a period of weeks or months. The inability of a constant daily dose of exogenous GH treatment to influence final stature markedly in short but non-GH-deficient children (28) may reflect the fact that this pattern of GH administration is not consistent with the endogenous dynamic changes in height, weight, and GH output. Treatment regimens may be more successful if tailored to the underlying growth process. This could be particularly relevant in an era in which orally active growth-promoting agents may become widely available.