A comparison of skeletal maturity and growth
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RESEARCH PAPER
A comparison of skeletal maturity and growth
Luciano Molinari1, Theo Gasser2 & Remo Largo1
1Kinderspital Zurich, 8032 Zurich, Switzerland, and 2University of Zurich, Institute of Social and Preventive Medicine,Biostatistics, 8001 Zurich, Switzerland
Background: Somatic and bone development have each been
studied in detail, but rarely in conjunction.
Aim: The aim of this study was to determine what somatic and
bone development have in common and how they differ.
A second aimwas to check for a pubertal spurt in bone age (BA)
and to quantify it in a similar way as has been done for height.
The Preece-Baines model is used to fit longitudinal data for BA.
Subjects andmethods: The data analysed are from the 1st Zurich
Longitudinal Growth Study comprising 120 boys and 112 girls
with almost complete data from birth to adulthood.
Results: Variability of somatic milestones was reduced in terms
of BA and there was an aftergrowth after reaching adult RUS
score 1000. A strong increase in the RUS score was seen at a late
stage of the pubertal spurt (PS). Somatic milestones correlated
with the RUS score attained at these ages and more so at an
early stage of the PS. A PS for BA was clearly identified with a
location at 14.2 years for boys and 12.2 years for girls. Age of
peak bone development correlated highly with age of peak
velocity of somatic variables.
Conclusions: BA can be successfully modelled as a semi-
quantitative entity. Bone development shows marked
associations with somatic development, despite the fact that
the latter reflects changes in size, while the former is essentially
a maturity index and reflects changes in biochemical
composition of tissues.
Keywords: Somatic growth, pubertal spurt, bone age,
longitudinal development
Abbreviations: T6, Age of Minimal Velocity at the onset of the
pubertal spurt (AMV*), T7, Age of Maximal Acceleration before
Age at Peak Velocity, T8, Age at Peak Velocity during the PS
(APV*), T9, Age of Maximal Deceleration after Age at Peak
Velocity, BA, Radius, Ulna and Short Bones Bone Age, ADH, Adult
Height, Biil, Biiliac Width, CA, Chronological Age, LL, Leg Length,
PS, Pubertal Spurt, RUS, Radius, Ulna and Short Bones score, StH,
Standing Height, SitH, Sitting Height. * abbreviations suggested
by J. M. Tanner, supplemented by H in the case of height
(AMHV, APHV)
INTRODUCTION
Chronological age (CA) is the most easily available predictorof somatic growth and can be obtained with minimal error.However, due to the large inter-individual variability intempo and intensity of growth, it is not satisfactory formany questions, such as the prediction of final size or thedescription of growth during periods of rapid development.Generally, bone age (BA) should be a better indicator ofbiological maturity than CA.
In this work we compare somatic and bone developmentand study their relationship. Skeletal maturity is assessedfrom X-rays of the radius, ulna and short bones of the hand(finger bones), leading to a score called RUS, according toTanner et al. (2001) (the TW3 Method). From RUS oneobtains RUS bone age (BA) by a non-linear transformation,in such a way that the median BA at any chronologicalage (CA) equals CA. Somatic growth is described here bythree linear measures, height (Standing Height, StH), leg(Leg Length, LL) and sitting height (SitH) and by biiliacwidth (Biil).
Growth and its milestones are determined by the growthof the bones, while skeletal maturity is expressed by thedegree of calcification of the ossification centres (epiphyses).We expect, however, a rather close relationship betweensomatic growth and skeletal maturity. One importantquestion is whether a pubertal spurt can be found forskeletal maturity; evidence for this is found in the papersby Hewitt and Acheson (1961) and by Prakash andPathmanathan (1991).
We consider BA as a semi-quantitative measure ofskeletal maturity, and will analyse it in much the same way asone analyses height growth. Thus, a Preece-Baines model(Preece and Baines 1978) will be fitted to BA and to RUSdata to determine the individual age of peak bone velocityand related parameters. This allows, for example, correlationof the timing of the pubertal spurt (PS) for growth with thetiming of the PS for BA.
Correspondence: Luciano Molinari, Kinderspital Zurich, Steinwiesstrasse 75, CH-8032 Zurich, Switzerland. Tel: þ 41 266 79 25. Fax: þ 41 266 71 64.
E-mail: [email protected]
(Received 5 June 2012; revised 29 October 2012; accepted 12 November 2012)
Annals of Human Biology, 2012; Early Online: 1–9Copyright q Informa UK, Ltd.ISSN 0301-4460 print/ISSN 1464-5033 onlineDOI: 10.3109/03014460.2012.756122
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It should be kept in mind that the assessment of skeletal
maturity does not only reflect a substantial biological
variability, but also leads to a non-negligible rating error.
Similarly, determining parameters characterizing growth
entails additional statistical variability—inevitable in view of
the noisy pattern of raw velocities. These factors will increase
variability beyond the biological level and will decrease the
size of correlations (‘attenuated correlations’).Milestones such as age of peak height velocity occur at
widely different ages in healthy children, leading to
substantial variability in many aspects of growth. If bonedevelopment goes hand-in-hand with overall maturity, thevariability in reaching these milestones should be decreasedwhen somatic growth is reported to BA rather than to CA.This was confirmed in the seminal paper byMarshall (1974).Hauspie et al. (1991) reached the same conclusion based ondifferent data.
In a subsequent paper, pubertal parameters (Tannerstages) will be studied in conjunction with somatic growth(Gasser et al. 2012).
SUBJECTS AND METHODS
SubjectsA sample of 232 subjects (120 boys, 112 girls, born between1954–1956), analysed repeatedly by Gasser et al. (1991),was the basis of this study. It can be considered fairlyrepresentative for the Swiss urban population of the time(Prader et al. 1989). Further details on the sample maybe found in Gasser et al. (1990).
Bone ageBone age was assessed by the TW3 method (Tanner et al.2001). For readers not familiar with the assessment ofbone age, a short explanation of the TW3 method follows.
The TW3 method is based on X-rays of the hand andit first assigns numerical weights to precisely definedmaturational stages of the following ossification centres(epiphysis): radius, ulna, metacarpal I, III and V, proximal
1 ChildNr 1 9 bone age
Age (years)
Dis
tanc
e (y
earB
A)
Rus score
Age (years)
Dis
tanc
e (p
oint
s)
200
400
600
800
100015
10
5
Standing height
Age (years)
Dis
tanc
e (c
m)
80
0
2
4
6
8
10
12
100
120
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160
180
Age (years)
Vel
ocity
(ye
arB
A/y
ear)
0.0
0.5
1.0
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2.0
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Age (years)
Vel
ocity
(po
ints
/yea
r)
0
50
100
150
200
250
Age (years)
5 10 15 205 10 15 205 10 15 20
5 10 15 205 10 15 205 10 15 20
Vel
ocity
(cm
/yea
r)
Figure 2. Preece-Baines fits for subject 1 (a boy) for BA, RUS and StH: Distance curves above and velocities below.
Montbeillard’s son
Age (years)
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18
Sta
ndin
g he
ight
(cm
)
0
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100
150
Distance curve
0
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6
8
10
12
Hei
ght v
eloc
ity (
cm/y
ear)
Velocity curve
T6 = AMHV
T8 = APHV
T7T9
Figure 1. Milestones for height data of Montbeillard’s son.T6 ¼ minimal velocity before PS, T8 ¼ maximal velocity, T7 andT9 ¼ inflection points, i.e. points of zero acceleration.
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phalanx I, III and V, middle phalanx III and V, distalphalanx I, III and V, capitate, hamate, triquetral, lunate,scaphoid, trapezium and trapezoid. The weights aredifferent for boys and girls, which makes direct sexcomparisons difficult.
Depending on the ossification centre, eight or ninestages (called A to H or I) are defined. Stage A means thatthe ossification centre has not yet appeared and receiveszero weight. Gender-dependent, age-independent, non-zeroweights, different for different ossification centres, areassigned to stages B to H or I (Tanner et al. 2001). Theweights for the first 13 ossification centres above (radius todistal phalanx V) are then added to form the so-calledRadius Ulna and Short Bones score (RUS). The weights forthe remaining bones are added to form the Carpal Bonesscore. The scores are then transformed by a sex-dependentmonotonic non-linear transformation to RUS bone age(here just BA; carpal bones are not used here) in such a waythat, for all chronological ages, median bone age in thereference sample equals chronological age.
Scores range from 0–1000: a score of 1000 is equivalentto the complete closure of all epiphyses; it implies, at leasttheoretically, that no growth occurs after this age. However,some subjects may show a small growth after reachingscore 1000.
X-rays had been taken at ages 3, 6, 9, 12 and 18 monthsand then yearly from age 2 onwards until the subjects weredismissed from the study or age 20, depending on whichoccurred first. At this age all subjects, with the exception ofone boy with RUS score 991, had reached the final stage forall ossification centres.
Six children (four boys and two girls) who had missingX-rays over several years and for whom milestones T6–T9with respect to BA could not be reliably calculated, wereomitted in all calculations: this left samples of 116 boys and110 girls for the analysis.
Somatic growthThe measurements have been described previously (Gasseret al. 1991). Milestones characterizing growth were: T6, theage of minimal velocity at the onset of the pubertal spurt
(AMV), T7, the age of maximal acceleration, T8, age at peakvelocity (APV) and T9, the age of maximal deceleration asan operational end of the pubertal spurt (Gasser et al. 1984).Our focus will be on milestones T6 and T8. As described inGasser et al. (1984), these milestones were determined forCA by estimating the first and second derivative of theoriginal data and then determining the zeroes of these twoderivatives. The developmental course is qualitatively thesame for all body measurements considered here, i.e.milestones T6–T9 can be meaningfully defined for standingheight, sitting height, leg length and biiliac width. The T’swith respect to BA are defined, by interpolation, as thebone ages corresponding to the CA of the same T’s.
Figure 1 illustrates these milestones for height data ofMontbeillard’s son (Sandland and McGilchrist 1979).
Velocity and AMV/APV for bone ageIn their seminal 1978 paper, Preece and Baines (1978)introduced a family of sigmoid-shaped curves to describehuman growth from childhood to adulthood.
Of the four models presented, Model 1 was consideredmost satisfactory because of its simplicity (it has fiveparameters, one being adult measurement) and also becausethe quality of the fit was only slightly worse than for models2 and 3 (with six parameters). Model 1 has since beenapplied in a variety of situations.
The course of BA as well as of RUS as a function ofchronological age parallels in most children the growth instature and suggests the occurrence of a pubertal spurt.Therefore, we applied Preece-Baines Model 1 to the data ofBA and to those of RUS. In this case the number ofparameters is reduced to four, because final BA and finalRUS are pre-determined (BA, 16.5 for boys and 15 for girls,for RUS the final score is 1000 for both genders).
For BA and RUS data the minimization algorithm (of theGauss-Newton type, S-Plus function nls) converged to asatisfactory fit in most cases (107 out of 112 boys and 84 outof 110 girls).
Table I. Reduction in variability of T6–T9, with respect to BAcompared to CA. Tabulated are means and SDs for height, sitting andleg height and biiliac width.
StHCA StHBA SitHCA SitHBA LLCA LLBA BiilCA BiilBA
BoysT6 Mean 11.2 10.4 11.2 10.5 11.0 10.3 10.8 10.2T6 SD 1.1 1.0 1.2 1.0 1.2 1.2 1.4 1.2T7 Mean 13.0 12.2 13.1 12.3 12.6 11.7 12.9 12.0T7 SD 0.9 0.8 1.0 0.9 1.0 1.0 1.1 1.0T8 Mean 14.0 13.3 14.2 13.6 13.7 12.9 14.1 13.4T8 SD 0.9 0.6 0.9 0.7 0.9 0.7 1.0 0.7T9 Mean 15.2 14.8 15.5 15.1 15.0 14.6 15.4 15.0T9 SD 0.9 0.5 1.0 0.6 0.9 0.6 1.0 0.7GirlsT6 Mean 9.8 9.1 9.8 9.0 9.4 8.7 9.4 8.7T6 SD 1.0 1.1 1.0 1.0 1.2 1.3 0.8 1.0T7 Mean 11.2 10.5 11.3 10.6 10.6 9.8 11.1 10.4T7 SD 1.0 0.9 1.2 1.0 1.2 1.2 0.9 1.0T8 Mean 12.2 11.6 12.4 11.8 11.6 10.9 12.4 11.9T8 SD 1.0 0.7 1.1 0.8 1.1 0.9 1.0 0.8T9 Mean 13.5 13.1 13.9 13.5 13.3 12.9 14.0 13.6T9 SD 1.0 0.6 1.1 0.8 1.0 0.6 1.1 0.8
Age (years)
Hei
ght (
cm)
80
100
120
140
160
180
109876543 11 12 13 14 15 16 17 18 19 20
Subject 131Subject 251
Figure 3. Early developing boy (131, blue) and late developing boy(251, red) with respect to chronological (thin) and bone age (thick).
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Figure 2 presents, for distance and velocity, the fits forBone Age, RUS and Standing Height for the first subject inthe study. From the four model parameters in the Preece-Baines model ‘biological’, descriptive parameters, AMV andAPV, as well as T7 and T9, were calculated.
Such figures were inspected for plausibility for allsubjects. The agreement between the course of skeletalmaturity and of somatic growth was usually good-to-verygood, judged visually, as in the above example. Theagreement was better for APV than for AMVand the resultstended to be slightly more plausible for BA compared toRUS for AMV. Thus, we mostly relied on milestones forskeletal maturity obtained for BA.
For 35 subjects the fit for BAwas poor and no reasonableAMV and/or APV could be derived (this is to be expectedsince subjects close to the average development show adistance curve close to a straight line by construction). Forthese subjects the milestones AMV and APV (BA) were firstset to missing. Following a standard statistical strategy wethen computed estimates for these missing values byimputation techniques (Package MICE in R: Van Buurenand Groothuis-Oudshoorn 2011). In all but two cases, animputation of APV by the respective value obtained for RUSwas successful; for AMV the imputation (which usedadditional information from RUS and Standing Height) wasnot convincing in 10 cases (including the two with missingAPV), where AMV was eventually set to missing.
Statistical methodsData are summarized as means and standard deviations. Inaddition, correlations and regression analyses are computed,as appropriate. The software S-PLUSw 8.0 for WindowsENTERPRISE DEVELOPER, 2007 Insightful Corp. is usedthroughout.
RESULTS
Variability for CA and BATo illustrate the potential shortcomings of chronological agefor assessing the development of different subjects, wepresent the case of two boys (Figure 3).
Subject 131 was developing very early withAPHV ¼ 11.85 years (the minimum among all boys),ADH ¼ 171.3 cm, below average (P16). Subject 251 was a
late developer, APHV ¼ 16.15 years (above P97),ADH ¼ 180.2 cm, above average (P67).
From age 5–16 years subject 131 was taller than subject251. Both subjects reached PHV at BA 13.3 years. Withrespect to BA subject 251 was taller than 131 by , 10 cmfrom childhood to adult age. Both subjects grew by , 1 cmafter reaching final BA.
Table I illustrates the reduction in variability ofmilestones for a BA scale compared to a CA scale. Overall,the reduction in the size of standard deviations in terms ofBA was modest.
Growth after reaching adult BAIt is noteworthy to which extent sitting height showed a lategrowth compared to leg height (Table II).
Growth in standing height after reaching adult BAdepended significantly on final height, age of reaching adultBA and gender. Not surprisingly, tall subjects as well as earlymaturers tended to grow more after reaching final BA, asdid boys compared to girls. This is demonstrated by thefollowing regression of growth after reaching RUS 1000(i.e. ADH-sth1000) as dependent variable and adult height(adh), age at which RUS 1000 was achieved (age1000) andsex as predictors (Table III).
After reaching adult BA, boys grew on average 6mmmorethan girls, after adjusting for adult height and age of reachingadult RUS. Similarly, tall children grew 0.2mmmore per cmof final stature, after adjusting for the other variables. Also,subjects grew 2mm less per 1 year delay in reaching adult BA,after adjusting for gender and adult height.
Reference values for percentages of attained adult heightPercentages of adult height reached at different bone agesare of some clinical interest and useful for the prediction ofadult height (Table IV).
At the onset of the pubertal spurt (T6), the medianpercentage of adult size reached was 81% for boys and 83%for girls. At the operational end of the spurt (T9) thesepercentages were 96% and 97%, for boys and girls,respectively, with narrow limits. At a bone age of 16.5 yearsfor boys and 15 years for girls, growth had practically stopped(sees Table II and IV for details). The difference between the90th and the 10th percentiles is a measure of variability: thiswas large around age of school entrance—from 7–8% forboth sexes. In subsequent years, variability dropped to 5–6%for boys and 4–5% for girls. In pubertal years, variabilitydropped further to 3–4% and later to 1–2%.
ChronologyGirls started their pubertal spurt (T6) around 9.5 yearsand had reached then a RUS of slightly less than 450
Table II. Growth after reaching adult BA (16.5 for boys and 15 for girls).Mean1 and SD1 refer to those subjects for whom growth wascontinuing after reaching adult BA.
Mean SD Max% with growth
stopped Mean1 SD1
AdHB 1.18 0.78 3.0 10.0 1.32 0.69AdHG 0.96 0.66 3.1 4.5 1.00 0.64ShB 1.16 0.74 2.6 7.7 1.26 0.67ShG 0.91 0.68 3.4 9.8 1.00 0.65LLB 0.06 0.22 1.2 65.0 0.21 0.30LLG 0.05 0.25 1.1 54.5 0.21 0.24BiilB 0.34 0.24 1.2 8.5 0.37 0.22BiilG 0.40 0.33 1.2 14.7 0.48 0.28
Table III. Regression coefficients.
Value Std. Error t-value Pr (. jtj)
(Intercept) 20.948 0.873 21.086 0.279adh 0.018 0.007 2.598 0.010age1000 20.207 0.038 25.474 0.000sex 0.279 0.135 2.072 0.039
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points (Figure 4). The peak of the spurt T8 occurred
around 12.2 years, except for leg height where it occurred
already at 11.4 years. A RUS of , 650 was attained at
APHV. The operational end of the pubertal spurt (T9)
took place around 13.5 years with a RUS slightly below
800 points. Thus, despite the fact that at this age 97% of
adult height had been reached (Table V), the RUS had
still 200 points to go. For boys the onset of the pubertal
spurt (T6) was around 11 years with a RUS of 350
points. The peak of the spurt (T8) took place around 14
years, again earlier for leg height. At that milestone, a
RUS of , 530 was attained. The end of the spurt T9 was
found between 15–15.5 years, with a RUS slightly above
700. Again, somatic growth was advanced at that age,
Table IV. Distribution of the percentage of final stature attained as a function of BA, including milestones T6–T9. Tabulated are medians (50), 10thand 90th percentiles.
BA Boys BA Girls
n 10 50 90 n 10 50 90
3.0 82 49.8 54.0 58.5 64 52.3 56.0 59.24.0 111 54.4 57.5 60.9 99 58.0 61.2 64.35.0 118 58.1 61.2 64.6 106 62.5 66.5 70.96.0 120 61.7 65.6 70.5 111 66.4 70.7 74.77.0 120 65.2 69.2 73.0 112 71.6 75.6 78.98.0 120 68.2 72.4 75.6 112 77.9 80.1 82.69.0 120 72.5 76.0 79.2 112 80.6 83.1 85.4
T6 110 80.0 83.1 87.310.0 120 76.9 80.4 83.2 112 84.0 86.5 89.0T6 116 78.3 81.5 84.7 T7 110 84.8 87.9 91.011.0 120 80.5 83.3 86.6 112 87.0 89.8 91.8
T8 110 89.7 91.5 93.812.0 120 84.0 87.1 89.7 112 90.4 93.0 95.0T7 116 85.1 87.7 89.513.0 120 86.4 90.1 92.2 112 94.4 96.5 97.6T8 116 89.5 91.5 92.9 T9 110 95.3 96.7 97.514.0 120 91.1 93.9 95.7 112 96.9 98.0 98.8T9 116 94.7 95.9 97.215.0 120 94.8 96.5 98.1 112 98.9 99.4 99.916.0 120 97.5 98.3 99.116.5 119 98.7 99.3 100.0
Chronological age (years)
1098 11 12 13 14 15 16
StH
SitH
Leg length
Biiliac W.
RUS1y
1y
T6 T7 T8 T9
T6 T7 T8 T9
T6 T7 T8 T9
T6 T7 T8 T9
400 500 600 700 800 900
APV
T6 T7 T8 T9
T6 T7 T8 T9
T6 T7 T8 T9
T6 T7 T8 T9
400 500 600 700 8009 00
APV
Figure 4. Chronology of the somatic milestones T6 to T9: the vertical bars are placed at the average age at which the milestones are reached. Depictedare also ages where pre-defined RUS-scores and APV for BA are reached. The length of the bar (one standard deviation of the correspondingmilestone) should be compared with the black bar at the left. Girls red, boys blue.
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since 96% of adult height had been reached, whereas theRUS score still had 250–300 points to go. The somaticmilestones used had been extracted from the samesample and published in the Annals of Human Biology(Gasser et al. 1991).
Bone age velocity and Preece-Baines fitsFigure 5 shows bone age velocity curves for a randomsample of subjects.
Timing of PSIn Table V, means and SDs of AMV and APV for BA arecompared with the corresponding parameters for standingand sitting height, leg length and biiliac width.
APV for BA was in the mean close to the valuesobtained for somatic variables. Variability was somewhathigher for BA. AMV for BA was for boys earlier by severalmonths and by almost 2 years for girls compared tosomatic milestones.
Duration and intensity of the PSIn Table VI the duration and intensity of the PS areexpressed as APV-AMVand peak velocity–minimal velocity,respectively (for BA only for non-imputed subjects).
The duration of the PS for BA was longer than for bodymeasurements. While for the latter the PS was longer forboys than for girls, for BA the opposite was true. With theexception of biiliac width, the intensity was clearly strongerfor boys than for girls and this was true also for BA.
Table V. Timing (CA) of the PS for BA and somatic variables. Means and SDs tabulated.
BA StH SitH LL Biil
AMV APV T6 T8 T6 T8 T6 T8 T6 T8
Boysn 112 114 120 120 120 120 120 120 120 120Mean 10.4 14.2 11.2 14.0 11.2 14.2 11.0 13.7 10.8 14.1SD 1.4 1.2 1.1 0.9 1.2 0.9 1.2 0.9 1.4 1.0Girlsn 104 110 112 112 112 112 112 112 112 112Mean 8.0 12.2 9.8 12.2 9.8 12.4 9.4 11.6 9.4 12.4SD 1.2 1.1 1.0 1.0 1.0 1.1 1.2 1.1 0.8 1.0
27 8
Age (years)
5 10 15 20
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5 10 15 20
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Vel
ocity
(ye
arB
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ear)
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ocity
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Figure 5. Bone Age (BA) velocity as derived from the Preece-Baines fits to BA for a random sample of subjects. The child number and gender (8 forgirls, 9 for boys) is indicated.
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Correlations between milestones for somatic variablesand BAThe correlation of APV for BAwith the somatic T8 was highfor boys, nearly 0.8, and smaller for girls, , 0.6 (Table VII).This indicates a partial common origin of the correspondingdevelopmental processes.
Correlations between milestones for somatic variablesCorrelations were very high between different pubertalmilestones for one somatic variable and somewhat lower formilestones for different somatic variables (Table VIII). Outof 120 correlations, 114 were slightly higher for boys thanfor girls.
Correlating somatic milestones and BAThe correlations between the age of reaching the milestonesT6–T9 in terms of CA and in terms of BA are presented inFigure 6 for standing height and biiliac width for boys andgirls. The abscissa of the points in the curves is the mean ageat which the corresponding milestone is reached.
As shown in Figure 6, correlations between pubertalmilestones and RUS scores reached at these milestonesstarted high (, 0.7) at the onset of the pubertal spurt T6 forboth sexes. When passing through the spurt, they declinedto reach , 0.4 at the end of the spurt.
DISCUSSION
While there is general agreement that both for clinical andscientific work a better descriptor of the maturational stagethan chronological age is mandatory, and that, as far assomatic growth is concerned, this descriptor should bebased on X-ray of some bones, there is much less agreementon the relative merits of the numerous procedures which
have been proposed over the years (besides the TW3method; Greulich and Pyle 1959; Roche et al. 1975).
Variability of somatic milestones for CA and BAIdeally, with a good assessment of the maturational stage,the variability in reaching the milestones T6–T8 should besubstantially reduced. With regard to T6 we found only amodest reduction in variability, when representing somaticmilestones in terms of BA instead of CA. For T8 thereduction in variability was of the order of 20–30%, both forboys and girls, and also for SitH and Biil. This is in line withprevious work (Marshall 1974; Hauspie et al. 1991). Hauspieet al. give an interpretation of these differences between T6and T8 in terms of the hormonal processes underlying pre-pubertal and pubertal growth and maturation. We think,however, that the statistically more critical estimation of T6compared to T8 should also be considered, since this canreduce the size of the effect.
There is a non-negligible growth after reaching adult BA,in particular for sitting height. Roche and Davila (1972)previously studied late growth for stature. That sittingheight, and not leg height, contributes mostly to late growthhas been shown earlier (Gasser et al. 1991). It makes sensebiologically that late growth after reaching adult BA is largerin tall subjects and in early maturers.
Somatic milestones and increase in RUS score gonaturally hand-in-hand. It is, however, noteworthy howmuch the RUS score increases at a late stage of the pubertalspurt (after T9). Somatic milestones are reached some 1.5years later in boys than in girls for CA, and the same appliesto BA; they are reached, however, at a much lower RUS scorein boys (by , 100 points).
It has been previously speculated that BA shows also aPS and this has also been partly verified by relatively simple
Table VII. Correlations between milestones for growth variables and BA (girls above the diagonal, boys below).
BA StH SitH LL Biil
AMV APV T6 T8 T6 T8 T6 T8 T6 T8
BA AMV 0.85 0.36 0.46 0.35 0.40 0.21 0.29 0.45 0.43APV 0.89 0.47 0.65 0.45 0.62 0.29 0.50 0.41 0.62
StH T6 0.56 0.69 0.82 0.81 0.78 0.48 0.52 0.50 0.60T8 0.61 0.81 0.84 0.76 0.96 0.44 0.61 0.42 0.78
SitH T6 0.47 0.62 0.84 0.80 0.73 0.32 0.46 0.36 0.58T8 0.61 0.78 0.82 0.96 0.79 0.40 0.60 0.39 0.76
LL T6 0.52 0.62 0.65 0.71 0.51 0.67 0.78 0.25 0.46T8 0.61 0.80 0.79 0.96 0.72 0.91 0.72 0.21 0.62
Biil T6 0.42 0.61 0.73 0.75 0.64 0.73 0.58 0.70 0.41T8 0.62 0.80 0.83 0.96 0.78 0.93 0.68 0.93 0.74
Table VI. Duration and intensity of the PS for BA and growth variables.
Duration: APV-AMV Intensity: Velocity APV-AMV
BA StH SitH LL Biil BA StH SitH LL Biil
BoysMean 3.9 2.8 3.0 2.7 3.2 1.0 4.2 2.9 1.5 0.8SD 0.6 0.6 0.7 0.8 0.9 0.5 0.9 0.7 0.6 0.2GirlsMean 4.3 2.4 2.7 2.2 3.0 0.8 2.3 1.9 0.8 0.8SD 0.6 0.6 0.8 0.8 1.0 0.4 0.8 0.7 0.6 0.3
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statistical tools (Hewitt and Acheson 1961; Prakash andPathmanathan 1991).
Visually, our rather complete data for RUS-scores and,thus, for BA give the impression of a quite clear pubertalspurt for BA (or RUS score). Straightforward fitting of aPreece-Baines model (Preece and Baines 1978) wassuccessful in most cases. The fit was in general better forBA than for RUS, with some exceptions, as was to beexpected: the RUS score is converted to BA such that theaverage BA corresponds to chronological age. Inevitably, forsome average subjects, development of BA then moves alonga linear line—the diagonal—and this pattern does per se notallow a meaningful fit via the Preece-Baines model. Thesecases were treated as missing information and for these caseswe applied an imputation procedure for the missinginformation. Imputation was done using the RUS fit andother information. Visually, the agreement of somaticvelocities and BA velocities was surprisingly good in a largemajority of cases. The agreement was better for age of peakvelocity (T8) compared to the onset of the spurt (T6).
The correlation of APV for BA with the somatic T8’s washigh for boys (nearly 0.8) and smaller for girls (, 0.6).
This is surprisingly high, since the methodologicalvariability introduced by determining somatic milestonesand by rating RUS scores and fitting BA data decreases theinherently true biological correlations (so-called ‘attenu-ated correlations’). Similar correlations were lower for girlsand for the onset of the spurt (T6) compared to T8: thesedifferences can be attributed to ‘attenuated correlations’,since determining growth milestones is more difficult andthus more variable in girls and T6 is more difficult toextract than T8. The size of these correlations indicates apartial common origin for the developmental processesacting for linear growth and for bone development: this isnot at all obvious a priori, since somatic development isone of size, while bone age is essentially a maturity indexand rather reflects changes in biochemical composition oftissues.
That correlations are high between different somaticmilestones within one somatic variable is in linewith expectations. This holds also for the fact that theyare lower—but still high—when correlating the samemilestones for different somatic variables. That thesecorrelations are in general somewhat higher for boys thanfor girls is attributed to the fact that the less pronounced PSfor girls leads to more variability in determining pubertalmilestones and this in turn lowers correlations. The timingof somatic milestones correlates quite highly with the RUSscore attained at these ages. However, these correlationsdrop to lower values as one moves through the pubertalspurt. This drop might be due to the fact that variability ofthe RUS score becomes more and more restrained towardsthe end of the PS.
In conclusion, BA is in many ways a better indicator ofbiological maturity than CA. Growth, a change in size, andbone maturation, a change in composition of cartilagetissue, are a priori quite different and distinct processes.However, our analysis shows that somatic development andbone maturation are closely linked processes. The derivationof a pubertal spurt for BA proves to be helpful in provingthe case, but is itself of interest for the field.
Table VIII. Correlations of milestones T6–T9 for standing, sitting and leg height and biiliac width (girls above the diagonal, boys below).
T6 T7 T8 T9 T6sh T7sh T8sh T9sh T6ll T7ll T8ll T9ll T6bi T7bi T8bi T9bi
T6 0.84 0.82 0.75T7 0.83 0.90 0.82T8 0.84 0.98 0.92T9 0.78 0.93 0.96T6sh 0.80 0.74 0.57T7sh 0.78 0.88 0.72T8sh 0.79 0.90 0.81T9sh 0.70 0.79 0.89T6ll 0.90 0.77 0.48T7ll 0.79 0.88 0.52T8ll 0.71 0.88 0.63T9ll 0.60 0.81 0.93T6bi 0.45 0.44 0.30T7bi 0.72 0.75 0.58T8bi 0.73 0.83 0.81T9bi 0.65 0.71 0.88
Age (years)
Cor
rela
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10 12 14 16
0.2
0.4
0.6
0.8
1.0
T6
T7
T8
T9
99%
T6
T7
T8T9
T6
T7
T8
T9
99%
T6
T7T8 T9
Standing height - BoysStanding height - GirlsBiiliac width - BoysBiiliac width - Girls
Figure 6. Correlations between milestones for somatic growth of StHand Biil with BA for boys (blue lines) and girls (red lines)
8 L. MOLINARI ET AL.
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Declaration of interest: The authors report no conflicts ofinterest. The authors alone are responsible for the contentand writing of the paper.
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