AMERICAN JOURNAL OF HUMAN BIOLOGY 5:615422 (1993)
Children Do Not Grow Continuously But in Spurts MICHAEL HERMANUSSEN’ AX JENS BURMEISTER‘ ’Aschauhof, 24340 Altenhof; Germany; ’Institute /or Information Science and Practical Math’ematics, Uniuer,sity of Kiel, Kiel,Germany
ABSTRACT The description of the human growth pattern is limited largely to the traditional vocabulary of “linear growth rates,” i.e., height or length increments divided by certain time intervals such as months or years. These studies have been performed using conventional techniques of body length or stature measurement with a technical error of approximately 1.5 mm. During the last 10 years, measurements of lower leg length (knemometry)have been performed with a significantly lower technical error (0.09-0.16 mm). Repeated determinations of lower leg length at short intervals are now feasible, and evidence indicates that “short term growth is a phenomenon that includes both length increment and decrement. At measurement intervals of exactly 1 week, growth appears periodic showing marked spurts that alternate with intervals of decreased growth velocity with a peak-to-peak distance of 30-55 days (mini growth spurts). These spurts have significant clinical importance and can be used as predictive criteria for successful growth promotion in growth hormone therapy of short stature. Lower leg length measurements at 24-hour intervals provide evidence for the existence of circaseptan periodicity. c 1993 Wiley-Liss, Inc. The description of the human growth pattern is limited largely to a number of traditional terms such a s “height” and “height increment,” and the term “linear growth rate” is almost ubiquitous in a number of growth studies (Gelato et al., 1985; Karlberg et al., 1987; Wales and Milner, 1987; Hermanussen, 1987). Yet, all of these data on “growth are in fact data on stature, and the information on growth is derived from length measurements taken at different time intervals. Growth itself has never been measured; it has occurred between the measurements. As there seemed to be no practical alternative to measuring growth in any way other than by the determination of length differences, this approach towards a description of growth has generally been accepted and considered adequate. Thus, standards were derived for annual stature differences (annual growth rates) (Tanner et al., 1966), and though these authors specifically warn against it, many investigators use such standards for intervals of less than 1 year for determinations of “growth rates.” However, the use of such standards is erroneous if the time interval between subsequent measurements becomes too short. This was in particular true as most studies
o 1993 Wiley-Liss, Inc.
were based on conventional techniques of stature measurements which have a technical error of approximately 1.5 mm. THE KNEMOMETRIC TECHNIQUE I n 1983, Valk et al. presented a noninvasive technique for accurate lower leg length measurement (knemometry, derived from Greek f j ~ v y ’ p y the : lower leg). It estimates the distance between heel and knee of the sitting child with a technical error (McCammon, 1970) between 0.09 mm (Valk e t al., 1983) and 0.16 mm (Hermanussen et al., 1988a).The child is placed on a chair which can be moved forward and backward with adjustable sitting height and back. The foot is placed on the foot-plate into a small semicircle. It is important that the child feels comfortable during the measurement. The measuring board is then lowered onto the child’s knee which is moved passively under the board. The distance between heel and knee is displayed continuously on a visual electronic display. A counterweight guaran-
Received August 31,1992, accepted January 25,1993. Address reprint rrquesls to M. Hermanussen, Aschauhof, 24340 Altmhof, Germany.
616
M. HERMANUSSEN AND J. BURMEISTER
100
zoo
300
Days
Fig. 1. Lower leg length distance cwves of four children. I. 12:9 year old (years:months) healthy slow-growing boy with a bone age retardation of 1:6 years. The beginning of the pubertal growth spurt is visible at the end of the observation period. 11. 11:6 year old healthy slow-growing boy with a bone agc retardation of 2 : 3 years. The total period of observation is prepubertal. III.7:O year old girl with Turner's syndrome. Spontaneous growth. IV.6:3 year old healthy boy.
tees a constant pressure of the measuring board of approximately 200 g. The minimum distance which can be discriminated by the device is 0.1 mm. THE MEASUREMENT OF GROWTH Valk originally investigated 21 Dutch children who were measured at weekly intervals for up to 4 months by knemometry (Valk et al., 1983). There were significant increments of lower leg length in 41 of 49 one week intervals, in 36 of 38 two week intervals, and in 34 of 35 three week intervals. Valk, therefore, concluded that growth
was detectable after a three week interval. There was confidence that significant increment of lower leg length (i.e., an increment that significantly exceeded the error of the measurement) was synonymous with growth. This confidence was based on the historic approach of detecting growth by the evaluation of differences in length, and thus, was of great importance for the dilemma of other investigators of short-term growth who persisted in the synonymous use of length increment and growth (rate). With few exceptions k e . , in anorexia nervosa [Hermanussen et al., 1987b11, there is evi-
CHILDREN DO NOT GROW CONTINUOUSLY
617
b
‘ii 2-
-
-
I
c ul E
W
E, c
U
.-c
c
0
ZE
Ti me 1.2. Four Tour-week-growth-rates” of child I (Fig. he first pattern was derived from lower leg length iurements at exact 4 week intervals startingat Feby 2, 1985, March 2,1985, March 30, 1985, etc. The id pattern was derived from measurements a t 4
week intervals starting at February 9, 1985, the third pattern started a t February 16, and the fourth pattern started at February 23, 1985. There i s suggestive evidence for seasonal variation in some of these patterns, though all of the patterns differ markedly.
1
r
Time Fig. 3. Four “four-week-growth-rates”of child I1 (Fig. 1 ). The figure is an analogue to Figure 2.
M. HERMANUSSEN AND J. BURMEISTER
618 L o w e r Leg growth r a t e (rnrnld 1
d
0 20-
0 100 05-
- 0 101
‘50 ]Jan1 Feb
Days 1’00
I Mar
I Apr
1‘50
I May
]
2’0 0 Jun
I Jul
2’50
I Aug
I Sep
3 00
I Oct
]
33 0 Nov
I Oec
4‘ 00 851 Jan
Fig. 4. Calculated mean daily lower leg growth velocities of child I (Fig. I ) . There is evidence for periodic changes of growth velocity throughout the total period of observation. The peak-to-peak distance between subsequent mini growth spurts varies between 30 and 55 days.
dence that length increments persist during long-term growth. However, there is increasing evidence that differences of stature are inadequate to provide statements on growth if these differences are obtained within short intervals. In other words, the terms stature differences and growth do not substitute for each other if used in the description of short-term growth. This is not due to the error of measurement. This is difficult to understand, and selected examples are provided subsequently (Hermanussen, 1989). Figure 1shows incremental growth (length) curves of four individuals measured a t weekly intervals or partially twice weekly (child 11)throughout a 1 year period with few missing values due to holidays, personal reasons, or illness. Let us suppose that the children were measured only once a month. In spite of 44-74 measurements, only 13 determinations of lower leg length would be available. Figures 2 and 3 demonstrate “growth patterns” derived from successive 4 week intervals of children I and 11. Since measurements were taken at weekly intervals, four “growth patterns” were derived starting a t the first, second, third, and fourth weeks of the observation period, and using only those
measurements that followed the initial measurements a t exact 4 week intervals. It is evident that all four “growth patterns” differ markedly although they are derived from the same individuals during the same annual intervals. This example shows unambiguously that 4 week intervals are inadequate for the description of short-term growth. Several alternatives have been explored. Wales and Milner (1987) used weekly lower leg length measurements from which linear regression lines were derived. Wit et al. (1987) have applied orthogonal polynomials and concluded that a significant number of lower leg growth curves are nonlinear. Similar results were observed in 73 healthy children, of whom 70% showed nonlinear length increments if measured more than 35 times within observation periods of up t o almost 1 year (Hermanussen et al., 1988b). At the moment, an ultimate solution for the description of weekly series of lower leg length measurements has not yet been found. A simple approach similar to the calculation of the moving average has been used (Hermanussen et al., 1988b). The individual growth curves were cut into intervals of 31 days. Since all children were measured
CHILDREN DO NOT GROW CONTINUOUSLY
619
Lower leg growth rate (mrnld 1
d
0 201
-0 05-
- 0.10-
I
2’00 Dec
I Jon
2’5 0
85 I F e b
I Mar
3’00
1 Apr
350 I May I Jun
Goo I Jul
I Aug
4 SO I Sep
5 00
I Oct
I Nov
Days 550 IOec
Fig. 5. Calculated mean daily lower leg growth velocities of child I1 (Fig. 1).
approximately once a week, each of these intervals contained four to five measurements. The slope of the linear regression line was calculated within each interval and was plotted as mean daily lower leg growth velocity of the central day (day 16) of the interval. I n analogy to the calculation of the moving average, the intervals of calculation were moved along the growth curves, i.e., the first interval ranged from day 1 to day 31 (central day 16),the second interval from day 2 to day 32 (central day 17), etc. Thus, mean daily lower leg growth velocities could be calculated for each day of a n individual period of observation, with the exception of the first and the last 15 days. Using this approach on the lower leg length data of Figure 1, the irregular pattern of “4-week growth rates” disappears, and periodicity is visible throughout the total period of observation (Figs. 4,5 ) . MINI GROWTH SPURTS The following pattern is found in approximately 70% of healthy children: Marked growth spurts alternate with intervals of decreased growth velocity with a peak-to-peak distance of 30-55 days as long as the children are measured a t exact weekly intervals. This pattern is labeled mini growth
spurts. Mini growth spurts are neither sexnor age-dependent. Mini growth spurts have significant clinical importance. They appear immediately after the onset of successful growth hormone supplementation (Hermanussen et al., 1987a) with a characteristic broad initial growth spurt followed by a series of additional minor spurts. According to our experience, any kind of successful growth promotion after a period of growth failure seems to initiate this characteristic pattern regardless of the origin of the growth failure. It was also observed after tonsillectomy which has also been shown by others to improve poor growth (Wales and Milner, 1987; Bate et al., 1984). The onset of mini growth spurts can be used a s a predictive criterion for successful growth promotion in growth hormone therapy of short stature (Hermanussen et al., 1989). The presence of mini growth spurts is a n obvious reason why single differences of lower leg length obtained at short intervals do not provide reasonable information on growth. Whenever a 4 week difference of length covers a period of growth arrest between two mini growth spurts, overall growth will be underestimated, whereas growth will be overestimated when a 4 week
M. HERMANUSSEN AND J. BURMEISTER
620
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.-
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c
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0.2
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Fig. 6. The behavior of coefficients of correlation (r)in two children calculated for i = 5 to i = 100 days. The coefficients were computed at 0.2 day steps for i = 5 to i = 20 and at 1.0 day steps for i = 21 to i = 100 days. The horizontal lines give the common levels of significance w i t h P = 0.01 and P = 0.001.
interval just covers a period of one spurt. We conclude that short-term growth is a nonlinear process. The detection of periodic elements is strongly dependent on the time intervals between subsequent measurements of length. CIRCASEPTAN PERIODICITY IN THE GROWTH PROCESS In order to further illustrate the kinetic behavior of the growth process, 23 healthy children, 10 girls and 13 boys, 9-15 years of age were investigated by almost daily (24 hour) measurements of lower leg length during a 3 month period (Burmeister and Hermanussen, 1989). In order to illustrate the periodic behavior of growth velocity, the measurements were treated as follows. The individual series of N measurements (t,, y,);
i = 1 . . . N were investigated for the existence of a linear trend by calculating the linear regression defined by y(t) = at + b with a slope (a) and an intercept (b). This trend was eliminated by a linear transformation according to dt,) = y, - y(tJ = y, - (at, + b)
f o r i = 1 . . . N.
The aim of further investigation was a mathematical description of the observed periodic structure of the individual series of measurements by a sine curve. For this purpose, a second set of N hypothetical measurements was defined by (tl, s[t,l). The theoretical variance of s(t) is given by 1/2 for any period. The variances of the individual series of measurements were thus equili-
CHILDREN DO NOT GROW CONTINUOUSLY
n
Q I
5
15
10
20
Days Fig. 7. The distribution of 73 significantly correlating sine pcriods. Each bar represents the number of correlations (P< 0.01 black area, P < 0.001 white area) at a given day. As the sine periods were comput.ed at 0.2 day steps, each bar summarizes a group of five calculations within a n interval of L 0.4 days. Control analysis of simulated random series revealed no periodicity that significantly surpassed the level of expectatiun.
621
exist in Man. This has in particular been investigated during physical therapy and cure treatment and in the course of infectious illness, wound healing, and other reparation functions (Agishi and Hildebrandt, 1989). Yet, circaseptan periodicity is found almost ubiquitously and has recently even been shown in algae, such as acetabularia and Gonyaulax polyedru (Halberg et al., 1985). However, the control mechanism of this periodicity remains unclear. Thus, the significant correlation between lower leg measurements and sine periods of an approximate length of 7 days corresponds well to circaseptan periodicity already found in nature. However, the biological phenomena that cause such periodicity and ultimately provide periodic growth remain speculative. Yet, the presence of these short periods of growth velocity explains why measurements at exactly weekly intervals might seriously reinforce and cause interferences at intervals of 30-55 days hitherto known as mini growth spurts. LITERATURE CITED
brated and a correlation analysis was performed. Coefficients of correlation were plotted for i = 5 to i = 100 days. Figure 6 shows the coefficients of correlation in two children as an example of the behavior of the coefficients. Several sine periods show significant correlation with the individual series of measurements. The significantly correlating sine periods are situated approximately around days 6, 7, and 8. Harmonic multiples of these correlations are visible around the corresponding days 12-16,2632, etc. These characteristics were apparent in all 23 children investigated by this technique. Figure 7 summarizes the significantly correlating sine periods from i = 5 to i = 20 days in all children. The majority of correlations is situated around days 7 , 8 , and 9. In boys, a harmonic multitude of this period is visible between days 13 and 16. Because there was little interindividual agreement between significant sine periods beyond 20 days, the total number of 23 children was regarded insufficient for further analysis of the period behavior of growth at intervals of more than 20 days.
Agishi Y, Hildebrandt G (1989) Chronobiological Aspects of Physical Therapy and Cure Treatment. Sapporo: Kokoku. Bate TWP,Priece DA, Holme CA, McGucken RB (1984) Short stature caused by obstructive apnoea during sleep. Arch. Dis. Child. 59:78-80. Burmeister J, Hermanussen M (1989) The measurement of short-term growth. Addendum. In JM Tanner (ed.): Auxology 88: Perspectives in the Science of Growth and Development. London: Smith-Gordon, pp. 60-61. Gelato MC, Ross JL, Malozowski S , Pescovitz OH, Skcrda M, Cassorla F, Loriaux L, Merriam GR (1985) Effects of pulsatile administration of growth hormone (GH)-releasing hormone on short term linear growth in children with GH deficiency. J. Clin. Endocrinol. Metab. 61:444450. Halberg F, Hastings W, Cornelissen G, Broda H (1985) Go:or~yu~~lm polyedru ‘talks’ both ‘circadian’ and ‘circaseptan’. Chronobiologia 12:185. Hermanussen M ( 3 987)How linear is growth? Arch. Dis. Child. 62:763. Hermanussen M, Geiger-Benoit K, Rurmeister J, Sippell WG (1987a) Can the knemometer shorten the time for growth rate assessment? Acta Paediatr. Scand., Suppl. 337:30-36. Hermanussen M, Geiger-Benoit K, Sippell WG (1987133 “Negative growth in anorexia nervosa assessed by knemometry. Eur. J . Pediatr. 146,561-564. Hermanussen M, Geiger-Benoit K, Burmeister J, Sippell WG (1988a) Knemometry in childhood: Accuracy and standardization of a new technique of lower leg length measurement. Ann. Hum. Biol. 15:l-16. DISCUSSION Hermanussen M, Geiger-Benoit K, Burmeister J, Sippel1 WG (1988b) Periodical changes of short term There is a large body of evidence that circagrowth velocity (“mini growth spurts”) in human septan, o r approximately-7-day-rhythmns, growth. Ann. Hum. Biol. 15:103-109.
622
M. HERMANUSSEN AND J. BURMEISTER
Hermanussen M, Geiger-Renoit K, Partsch C-J, Burmeister J (1989) Predictive criteria for successful growth promotion in growth hormone therapy of short stature: A comparison between common endocrine parameters and knemometry. Acta Paediatr. Scand. 78555-562,
Hermanussen M 11989) The measurement of short-term growth. In JM Tanner (ed.): Auxology 88: Perspectives in the Science of Growth and Development. London: Smith-Gordon, pp. 4%60. Karlberg J, Engstrom 1; Karlberg P, Fryer J G (1987) Analysis of linear growth using a mathematical model. Acta Paediatr. Scand. 76t478-488. McCammon RW (1970) Human Growth and Development. Springfield, IL: CC Thomas.
Tanner JM, Whitehouse RH, Takaishi M (1966) Standards from birth to maturity for height, weight, height velocity, and weight velocity: British children, 1965. I and 11. Arch. Dis. Child. 41:454-471, 613625. Valk IM, Langhout Chabloe AME, Smals AGH, Kloppenborg PWC, Cassorla FG, Schutte EAST (19831Accurate measurement of the lower leg length and the ulnar length and its application in short term growth measurements. Growth 47t5366. Wales JKH, Milner RDG (1987) Knemometry in assessment of linear growth. Arch. Dis. Child. 62:16&171. Wit JM, van Kalsbeek EJ, von Wijk-Hoek JM, Leppink GJ (1987) Assessment of the usefulness of weekly knemometric measurements in growth studies. Acta Paediatr. Scdnd. 76tY74980.
Children Do Not Grow Continuously But in Spurts MICHAEL HERMANUSSEN’ AX JENS BURMEISTER‘ ’Aschauhof, 24340 Altenhof; Germany; ’Institute /or Information Science and Practical Math’ematics, Uniuer,sity of Kiel, Kiel,Germany
ABSTRACT The description of the human growth pattern is limited largely to the traditional vocabulary of “linear growth rates,” i.e., height or length increments divided by certain time intervals such as months or years. These studies have been performed using conventional techniques of body length or stature measurement with a technical error of approximately 1.5 mm. During the last 10 years, measurements of lower leg length (knemometry)have been performed with a significantly lower technical error (0.09-0.16 mm). Repeated determinations of lower leg length at short intervals are now feasible, and evidence indicates that “short term growth is a phenomenon that includes both length increment and decrement. At measurement intervals of exactly 1 week, growth appears periodic showing marked spurts that alternate with intervals of decreased growth velocity with a peak-to-peak distance of 30-55 days (mini growth spurts). These spurts have significant clinical importance and can be used as predictive criteria for successful growth promotion in growth hormone therapy of short stature. Lower leg length measurements at 24-hour intervals provide evidence for the existence of circaseptan periodicity. c 1993 Wiley-Liss, Inc. The description of the human growth pattern is limited largely to a number of traditional terms such a s “height” and “height increment,” and the term “linear growth rate” is almost ubiquitous in a number of growth studies (Gelato et al., 1985; Karlberg et al., 1987; Wales and Milner, 1987; Hermanussen, 1987). Yet, all of these data on “growth are in fact data on stature, and the information on growth is derived from length measurements taken at different time intervals. Growth itself has never been measured; it has occurred between the measurements. As there seemed to be no practical alternative to measuring growth in any way other than by the determination of length differences, this approach towards a description of growth has generally been accepted and considered adequate. Thus, standards were derived for annual stature differences (annual growth rates) (Tanner et al., 1966), and though these authors specifically warn against it, many investigators use such standards for intervals of less than 1 year for determinations of “growth rates.” However, the use of such standards is erroneous if the time interval between subsequent measurements becomes too short. This was in particular true as most studies
o 1993 Wiley-Liss, Inc.
were based on conventional techniques of stature measurements which have a technical error of approximately 1.5 mm. THE KNEMOMETRIC TECHNIQUE I n 1983, Valk et al. presented a noninvasive technique for accurate lower leg length measurement (knemometry, derived from Greek f j ~ v y ’ p y the : lower leg). It estimates the distance between heel and knee of the sitting child with a technical error (McCammon, 1970) between 0.09 mm (Valk e t al., 1983) and 0.16 mm (Hermanussen et al., 1988a).The child is placed on a chair which can be moved forward and backward with adjustable sitting height and back. The foot is placed on the foot-plate into a small semicircle. It is important that the child feels comfortable during the measurement. The measuring board is then lowered onto the child’s knee which is moved passively under the board. The distance between heel and knee is displayed continuously on a visual electronic display. A counterweight guaran-
Received August 31,1992, accepted January 25,1993. Address reprint rrquesls to M. Hermanussen, Aschauhof, 24340 Altmhof, Germany.
616
M. HERMANUSSEN AND J. BURMEISTER
100
zoo
300
Days
Fig. 1. Lower leg length distance cwves of four children. I. 12:9 year old (years:months) healthy slow-growing boy with a bone age retardation of 1:6 years. The beginning of the pubertal growth spurt is visible at the end of the observation period. 11. 11:6 year old healthy slow-growing boy with a bone agc retardation of 2 : 3 years. The total period of observation is prepubertal. III.7:O year old girl with Turner's syndrome. Spontaneous growth. IV.6:3 year old healthy boy.
tees a constant pressure of the measuring board of approximately 200 g. The minimum distance which can be discriminated by the device is 0.1 mm. THE MEASUREMENT OF GROWTH Valk originally investigated 21 Dutch children who were measured at weekly intervals for up to 4 months by knemometry (Valk et al., 1983). There were significant increments of lower leg length in 41 of 49 one week intervals, in 36 of 38 two week intervals, and in 34 of 35 three week intervals. Valk, therefore, concluded that growth
was detectable after a three week interval. There was confidence that significant increment of lower leg length (i.e., an increment that significantly exceeded the error of the measurement) was synonymous with growth. This confidence was based on the historic approach of detecting growth by the evaluation of differences in length, and thus, was of great importance for the dilemma of other investigators of short-term growth who persisted in the synonymous use of length increment and growth (rate). With few exceptions k e . , in anorexia nervosa [Hermanussen et al., 1987b11, there is evi-
CHILDREN DO NOT GROW CONTINUOUSLY
617
b
‘ii 2-
-
-
I
c ul E
W
E, c
U
.-c
c
0
ZE
Ti me 1.2. Four Tour-week-growth-rates” of child I (Fig. he first pattern was derived from lower leg length iurements at exact 4 week intervals startingat Feby 2, 1985, March 2,1985, March 30, 1985, etc. The id pattern was derived from measurements a t 4
week intervals starting at February 9, 1985, the third pattern started a t February 16, and the fourth pattern started at February 23, 1985. There i s suggestive evidence for seasonal variation in some of these patterns, though all of the patterns differ markedly.
1
r
Time Fig. 3. Four “four-week-growth-rates”of child I1 (Fig. 1 ). The figure is an analogue to Figure 2.
M. HERMANUSSEN AND J. BURMEISTER
618 L o w e r Leg growth r a t e (rnrnld 1
d
0 20-
0 100 05-
- 0 101
‘50 ]Jan1 Feb
Days 1’00
I Mar
I Apr
1‘50
I May
]
2’0 0 Jun
I Jul
2’50
I Aug
I Sep
3 00
I Oct
]
33 0 Nov
I Oec
4‘ 00 851 Jan
Fig. 4. Calculated mean daily lower leg growth velocities of child I (Fig. I ) . There is evidence for periodic changes of growth velocity throughout the total period of observation. The peak-to-peak distance between subsequent mini growth spurts varies between 30 and 55 days.
dence that length increments persist during long-term growth. However, there is increasing evidence that differences of stature are inadequate to provide statements on growth if these differences are obtained within short intervals. In other words, the terms stature differences and growth do not substitute for each other if used in the description of short-term growth. This is not due to the error of measurement. This is difficult to understand, and selected examples are provided subsequently (Hermanussen, 1989). Figure 1shows incremental growth (length) curves of four individuals measured a t weekly intervals or partially twice weekly (child 11)throughout a 1 year period with few missing values due to holidays, personal reasons, or illness. Let us suppose that the children were measured only once a month. In spite of 44-74 measurements, only 13 determinations of lower leg length would be available. Figures 2 and 3 demonstrate “growth patterns” derived from successive 4 week intervals of children I and 11. Since measurements were taken at weekly intervals, four “growth patterns” were derived starting a t the first, second, third, and fourth weeks of the observation period, and using only those
measurements that followed the initial measurements a t exact 4 week intervals. It is evident that all four “growth patterns” differ markedly although they are derived from the same individuals during the same annual intervals. This example shows unambiguously that 4 week intervals are inadequate for the description of short-term growth. Several alternatives have been explored. Wales and Milner (1987) used weekly lower leg length measurements from which linear regression lines were derived. Wit et al. (1987) have applied orthogonal polynomials and concluded that a significant number of lower leg growth curves are nonlinear. Similar results were observed in 73 healthy children, of whom 70% showed nonlinear length increments if measured more than 35 times within observation periods of up t o almost 1 year (Hermanussen et al., 1988b). At the moment, an ultimate solution for the description of weekly series of lower leg length measurements has not yet been found. A simple approach similar to the calculation of the moving average has been used (Hermanussen et al., 1988b). The individual growth curves were cut into intervals of 31 days. Since all children were measured
CHILDREN DO NOT GROW CONTINUOUSLY
619
Lower leg growth rate (mrnld 1
d
0 201
-0 05-
- 0.10-
I
2’00 Dec
I Jon
2’5 0
85 I F e b
I Mar
3’00
1 Apr
350 I May I Jun
Goo I Jul
I Aug
4 SO I Sep
5 00
I Oct
I Nov
Days 550 IOec
Fig. 5. Calculated mean daily lower leg growth velocities of child I1 (Fig. 1).
approximately once a week, each of these intervals contained four to five measurements. The slope of the linear regression line was calculated within each interval and was plotted as mean daily lower leg growth velocity of the central day (day 16) of the interval. I n analogy to the calculation of the moving average, the intervals of calculation were moved along the growth curves, i.e., the first interval ranged from day 1 to day 31 (central day 16),the second interval from day 2 to day 32 (central day 17), etc. Thus, mean daily lower leg growth velocities could be calculated for each day of a n individual period of observation, with the exception of the first and the last 15 days. Using this approach on the lower leg length data of Figure 1, the irregular pattern of “4-week growth rates” disappears, and periodicity is visible throughout the total period of observation (Figs. 4,5 ) . MINI GROWTH SPURTS The following pattern is found in approximately 70% of healthy children: Marked growth spurts alternate with intervals of decreased growth velocity with a peak-to-peak distance of 30-55 days as long as the children are measured a t exact weekly intervals. This pattern is labeled mini growth
spurts. Mini growth spurts are neither sexnor age-dependent. Mini growth spurts have significant clinical importance. They appear immediately after the onset of successful growth hormone supplementation (Hermanussen et al., 1987a) with a characteristic broad initial growth spurt followed by a series of additional minor spurts. According to our experience, any kind of successful growth promotion after a period of growth failure seems to initiate this characteristic pattern regardless of the origin of the growth failure. It was also observed after tonsillectomy which has also been shown by others to improve poor growth (Wales and Milner, 1987; Bate et al., 1984). The onset of mini growth spurts can be used a s a predictive criterion for successful growth promotion in growth hormone therapy of short stature (Hermanussen et al., 1989). The presence of mini growth spurts is a n obvious reason why single differences of lower leg length obtained at short intervals do not provide reasonable information on growth. Whenever a 4 week difference of length covers a period of growth arrest between two mini growth spurts, overall growth will be underestimated, whereas growth will be overestimated when a 4 week
M. HERMANUSSEN AND J. BURMEISTER
620
I
D 1
r0 6 c
.-
2
d
0.5
n
\c
0 +
c
aJ 'J .-
0.2
01
' -4c
g
U
b
I0
2-0
so
IOOOaysI
Fig. 6. The behavior of coefficients of correlation (r)in two children calculated for i = 5 to i = 100 days. The coefficients were computed at 0.2 day steps for i = 5 to i = 20 and at 1.0 day steps for i = 21 to i = 100 days. The horizontal lines give the common levels of significance w i t h P = 0.01 and P = 0.001.
interval just covers a period of one spurt. We conclude that short-term growth is a nonlinear process. The detection of periodic elements is strongly dependent on the time intervals between subsequent measurements of length. CIRCASEPTAN PERIODICITY IN THE GROWTH PROCESS In order to further illustrate the kinetic behavior of the growth process, 23 healthy children, 10 girls and 13 boys, 9-15 years of age were investigated by almost daily (24 hour) measurements of lower leg length during a 3 month period (Burmeister and Hermanussen, 1989). In order to illustrate the periodic behavior of growth velocity, the measurements were treated as follows. The individual series of N measurements (t,, y,);
i = 1 . . . N were investigated for the existence of a linear trend by calculating the linear regression defined by y(t) = at + b with a slope (a) and an intercept (b). This trend was eliminated by a linear transformation according to dt,) = y, - y(tJ = y, - (at, + b)
f o r i = 1 . . . N.
The aim of further investigation was a mathematical description of the observed periodic structure of the individual series of measurements by a sine curve. For this purpose, a second set of N hypothetical measurements was defined by (tl, s[t,l). The theoretical variance of s(t) is given by 1/2 for any period. The variances of the individual series of measurements were thus equili-
CHILDREN DO NOT GROW CONTINUOUSLY
n
Q I
5
15
10
20
Days Fig. 7. The distribution of 73 significantly correlating sine pcriods. Each bar represents the number of correlations (P< 0.01 black area, P < 0.001 white area) at a given day. As the sine periods were comput.ed at 0.2 day steps, each bar summarizes a group of five calculations within a n interval of L 0.4 days. Control analysis of simulated random series revealed no periodicity that significantly surpassed the level of expectatiun.
621
exist in Man. This has in particular been investigated during physical therapy and cure treatment and in the course of infectious illness, wound healing, and other reparation functions (Agishi and Hildebrandt, 1989). Yet, circaseptan periodicity is found almost ubiquitously and has recently even been shown in algae, such as acetabularia and Gonyaulax polyedru (Halberg et al., 1985). However, the control mechanism of this periodicity remains unclear. Thus, the significant correlation between lower leg measurements and sine periods of an approximate length of 7 days corresponds well to circaseptan periodicity already found in nature. However, the biological phenomena that cause such periodicity and ultimately provide periodic growth remain speculative. Yet, the presence of these short periods of growth velocity explains why measurements at exactly weekly intervals might seriously reinforce and cause interferences at intervals of 30-55 days hitherto known as mini growth spurts. LITERATURE CITED
brated and a correlation analysis was performed. Coefficients of correlation were plotted for i = 5 to i = 100 days. Figure 6 shows the coefficients of correlation in two children as an example of the behavior of the coefficients. Several sine periods show significant correlation with the individual series of measurements. The significantly correlating sine periods are situated approximately around days 6, 7, and 8. Harmonic multiples of these correlations are visible around the corresponding days 12-16,2632, etc. These characteristics were apparent in all 23 children investigated by this technique. Figure 7 summarizes the significantly correlating sine periods from i = 5 to i = 20 days in all children. The majority of correlations is situated around days 7 , 8 , and 9. In boys, a harmonic multitude of this period is visible between days 13 and 16. Because there was little interindividual agreement between significant sine periods beyond 20 days, the total number of 23 children was regarded insufficient for further analysis of the period behavior of growth at intervals of more than 20 days.
Agishi Y, Hildebrandt G (1989) Chronobiological Aspects of Physical Therapy and Cure Treatment. Sapporo: Kokoku. Bate TWP,Priece DA, Holme CA, McGucken RB (1984) Short stature caused by obstructive apnoea during sleep. Arch. Dis. Child. 59:78-80. Burmeister J, Hermanussen M (1989) The measurement of short-term growth. Addendum. In JM Tanner (ed.): Auxology 88: Perspectives in the Science of Growth and Development. London: Smith-Gordon, pp. 60-61. Gelato MC, Ross JL, Malozowski S , Pescovitz OH, Skcrda M, Cassorla F, Loriaux L, Merriam GR (1985) Effects of pulsatile administration of growth hormone (GH)-releasing hormone on short term linear growth in children with GH deficiency. J. Clin. Endocrinol. Metab. 61:444450. Halberg F, Hastings W, Cornelissen G, Broda H (1985) Go:or~yu~~lm polyedru ‘talks’ both ‘circadian’ and ‘circaseptan’. Chronobiologia 12:185. Hermanussen M ( 3 987)How linear is growth? Arch. Dis. Child. 62:763. Hermanussen M, Geiger-Benoit K, Rurmeister J, Sippell WG (1987a) Can the knemometer shorten the time for growth rate assessment? Acta Paediatr. Scand., Suppl. 337:30-36. Hermanussen M, Geiger-Benoit K, Sippell WG (1987133 “Negative growth in anorexia nervosa assessed by knemometry. Eur. J . Pediatr. 146,561-564. Hermanussen M, Geiger-Benoit K, Burmeister J, Sippell WG (1988a) Knemometry in childhood: Accuracy and standardization of a new technique of lower leg length measurement. Ann. Hum. Biol. 15:l-16. DISCUSSION Hermanussen M, Geiger-Benoit K, Burmeister J, Sippel1 WG (1988b) Periodical changes of short term There is a large body of evidence that circagrowth velocity (“mini growth spurts”) in human septan, o r approximately-7-day-rhythmns, growth. Ann. Hum. Biol. 15:103-109.
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Hermanussen M, Geiger-Renoit K, Partsch C-J, Burmeister J (1989) Predictive criteria for successful growth promotion in growth hormone therapy of short stature: A comparison between common endocrine parameters and knemometry. Acta Paediatr. Scand. 78555-562,
Hermanussen M 11989) The measurement of short-term growth. In JM Tanner (ed.): Auxology 88: Perspectives in the Science of Growth and Development. London: Smith-Gordon, pp. 4%60. Karlberg J, Engstrom 1; Karlberg P, Fryer J G (1987) Analysis of linear growth using a mathematical model. Acta Paediatr. Scand. 76t478-488. McCammon RW (1970) Human Growth and Development. Springfield, IL: CC Thomas.
Tanner JM, Whitehouse RH, Takaishi M (1966) Standards from birth to maturity for height, weight, height velocity, and weight velocity: British children, 1965. I and 11. Arch. Dis. Child. 41:454-471, 613625. Valk IM, Langhout Chabloe AME, Smals AGH, Kloppenborg PWC, Cassorla FG, Schutte EAST (19831Accurate measurement of the lower leg length and the ulnar length and its application in short term growth measurements. Growth 47t5366. Wales JKH, Milner RDG (1987) Knemometry in assessment of linear growth. Arch. Dis. Child. 62:16&171. Wit JM, van Kalsbeek EJ, von Wijk-Hoek JM, Leppink GJ (1987) Assessment of the usefulness of weekly knemometric measurements in growth studies. Acta Paediatr. Scdnd. 76tY74980.
