ANNALSoF HUMANBror-ocy, 1985,vor-. 12,No. 2, 129-148
An analysisof the mid-growth and adolescentspurts of height basedon acceleration
THEO CASSER
Zentralinstitut ftir SeelischeGesundheit, Mannheim
HaNs-Cnonc MUr-len and Walrpn KOslEn
lnstitut ftir Angewandte Mathematik, UniversitAt Heidelberg ANonEa PneoER. REMO Lanco and LucteNo Mor-rNa.nr
Kinderspital, Universitat Zi.irich
Received 28 Februarv 1984: revised 31 Ausust 1984
Summary. Height growth betweenfour weeksand 20 yearsof 45 boys and 45 girls from the Ztirich Longitudinal Growth Study (1955-1976) was analysed using kernel estimates. Timings of the mid-growth spurt (MS) and of the pubertal spurt (PS) were determined in an automatic way from the individual accelerationcurves, together with height, percentageof height, velocity and accelerationat these ages. The small mid-growth spurt is a consistentphenomenon, peaking at 6.4years (M,F) in accelerationand at 7'Tyears (M) and 7'5years (F) in velocity.There are no significantsex differencesin its intensity. In girls, the PS follows in closesuccession to the MS; in boys there is a substantial period in between. ln addition to the age of peak height velocity, ages of onset, maximal accelerationand end of the PS are defined. Sex differencesin timing and size of the pubertal peak previously establishedwere again verified. New results relate to the asymmetry of the PS, which is more pronounced in girls, and to sex differencesin intensity and duration of the first rising phaseof the PS. After this phase, boys and girls do not differ in timing but only in the intensity of deceleration.
1. Introduction The dynamics of human height growth have been investigatedin a considerable number of papers (Tanner, Whitehouse and Takaishi 1966, Marubini, Reseleand Barghini l97l , Tanner,Whitehouse, Marubini and Reselel976,Largo, Gasser,Prader, Stiitzle and Huber 1978, Preece and Baines 1978, Hauspie, Wachholder, Baron, Cantraine, Susanneand Graffar 1980b).These studies have focused on the properties of the pubertal spurt (PS), usually characterizedby ageof onsetand ageof peak height velocity, together with velocity and height at theseages. Recently, the existenceof a small mid-growth spurt (MS) at about ageseven was statisticallyconfirmed by St[tzle, Gasser,Molinari, Prader and Huber (1980)for height, and by Molinari, Largo and Prader (1980)for severalsomatic variables. Based on a measureof convexity, Molinari et al. confirmedthe existenceof a MS in height in both sexes(with statisticalsignificance more pronounced in boys). The cross-sectionallyaveraged velocity curves of height peaked at 7.5years for boys and girls. By a visual judgment, about two thirds of the children of eithersex showed a MS. Using single-yearincrements, Tanner and Cameron (1980)found a MS for measurementsin height for boys, but not for girls. The paper by Tanner and Cameron may also be consulted for a discussionof the older literature which does not offer convincing evidencewith regard to this small phenomenon, leading Tanner et ol. (1966)and Hamill, Drizd, Johnson, Reed and Roche (1977)to excludeit from their height standards.Bock and Thissen(1980) fitted the triple-logistic model to height; the velocity curvesfor the averageparameters showed a MS for both 130 T. Cosser et al. sexes,peaking at approximately six years for girls and sevenyears for boys. Using a variable knot cubic spline method, for yet another longitudinal sample, Berkey, Reed and Valadian (1983)found a MS for about one fourth of the boys and for none of the girls. Summarizing these results, one notes discrepanciesin the proportion of children showing a MS, and in sex differencesin the MS, both as regardsamount and timing. Sincethe statisticalmethods applied differedsubstantially, these discrepancies might be due, at leastpartly, to methodologicaldifferences and not to differencesin samples.A detailed quantification of the MS using a longitudinal type of analysisis still lacking. In a previous paper (Gasser,Kdhler, Miiller, Kneip, Largo, Molinari and Prader 1984a),a method called kernel estimation was presentedfor individually determining distance,velocity and accelerationof height; characteristicages were then definedin the individual acceleration curves, and parameters related to these ages in terms of distance, velocity and acceleration were also extracted. The graphical examples presentedgave rise to the hope that the MS is more easily accessibleto a quantitative analysisvia the individual accelerationcurves than via velocity curves. This may also apply to the PS: the agesof maximal accelerationand maximal decelerationcan be determinedwell from the accelerationcurve, but not reliably in the velocity curve, and they are inaccessiblein the distancecurve. As a consequence,the duration of the PS and its subphasescan be determinedin an intuitively more appropriate way. The following problems will be tackled in this paper:
(l) A statisticaldescription of the PS in termsof someclassical and somenewly intro- duced parameters,extracted from accelerations. (2) A quantification of the mid-growth spurt (MS) with respectto timing, intensity, and duration. (3) An assessmentof sex differencesin parameterscharacterizing the PS and the MS. (4) A quantitative description of the asynchronyin height growth betweenthe sexes, and of the distribution of the difference in adult heieht for consecutive aee intervals.
In order to separatebetter methodological from sample differences,the triple logistic model was also fitted to our samole.
2, Subjectsand methods Forty-five boys and 45 girls wereselected from the Ztirich longitudinal growth study according to criteria set down in Gasser et al. (1984a). The same paper may be consultedregarding details of measurements(Falkner 1960),editing, computation and kernel estimation.
Definition of pqrameters The ageparameters T2-Tswere determinedfrom the individual accelerationcurves (compare figures 2 and 8 of Gasseret al. 1984a, and figures I and2 of this paper). Figure I showsa girl of about averageadult height and experiencingher PS at about averageage. Noteworthy is a very impressiveMS, which is followed immediatelyby the PS, as is often the casein girls (as a consequenceT4-- T). Toi Age of first measurementat four weeks. Ti Age four years. Tz: Age of maximum accelerationduring the mid-growth spurt (MS). Mid-growth and adolescentgrowth spurt of height l3l
T2
t0
B
6
? a
-2
-6 G B l0 l2 lq lD L8 20 8LE ]N ItBF]5
Figure l. Velocity (above) and acceleration (below) in height obtained by kernel estimation for a girl. Timings, T2to l|9, were determinedin the accelerationcurve and are indicated by vertical dashedlines. The small graph givesdistance height measurementsconnected by straight Iines,with cross-sectionalpercentiles (3, 10,25, 50, 75, 90, 97).
2 a
6 8 io r2 16 r8 20 ECE IN IEFBS
Figure 2. Velocity (above) and acceleration(below) for a late maturing boy, obtained by kernel estimate (solid line) and by firting triple logisticmodel (dashed).Crosses indicate timings with respectto kernel estimaleTt(4yr), f2, Ir, f1(MS), 15(riseof accelerationtoPS),76,f?,78, fe(PS).Thesmallgraphgives heightmeasuremenrs connected by straightlines, with cross-sectionalpercentiles (3, 10,25, 50,75,90,97). t32 T. Gasser et al.
T{ Age where (AT2+ Nl)/2 (as to AT seebelow) is reached(approx. equivalent to age of peak height velocity of the MS). Tqi Age of maximum decelerationat the end of the MS. Ts Age of last minimum in the accelerationcurve before Z6(start of rising of acceler- ation for the PS). Toi Age where accelerationis zero at onset of PS (or: velocity a minimum). Tt: Age of maximal accelerationin PS. Tsi Age of secondzero accelerationin PS (velocity maximal). Tsi Age of maximal decelerationin PS. 4s: Age of 20 years. For one girl and one boy no midspurt (Tz, Tt, 7a) could be quantified. In terms of velocities,parameters T6 (age of minimum height velocity before the PS) and 73 (ageof peak height velocity of PS) have frequently beenused, whereasfor the end of the PS, definedto be Ie, no satisfactorydefinition was possiblefrom the velocity curve (Largo et al. 1978).The parameter ?"7might be useful as a measureof ageof peaking of the PS in addition to Z'. 4 might be an interestingalternative measure of timing of the onset of the PS, but it is not very well defined. Whereasthe definitions of 72 and Ta are unambiguousfor characterizingthe MS, this is not the casefor Z3:since the MS peak is sitting on a falling velocity trend, age of peak height velocity cannot be defined by requiring the accelerationto be zero (Gasseret al. 1984a). In addition, the heightHTt (I: I , . . .9) and the percentageof heightf19o ?|lattained at theseages, and the velocity VT1 and accelerationATlwere determined(I: 1, . . .,9): these 45 parametersare called'standard parameters'.They were determined by computer program from distance, velocity and acceleration curves (Gasser el a/. 1984a). From the standard parameters, the following derived parameters were computed: (l) AT7/s: - ATt/ATs: a measureof asymmetryof the velocitypeak of the PS. (2) Ts-t:Te-Tt: ameasureof durationof thesubphaseoffallingaccelerationof the PS. (3) G o: Ts- T6:a measureof duration of the PS. (4) ATi s: ATt - ATe: a measureof intensityof the PS. (5) HTs-6: HTs- HT6: gain in heightduring PS. (6) HVoTe-6: HVoTs- HVoT6:percentage of heightgained in PS. (7) HT. _6: HT. - HT6: gain in height during phaseof rising, positive accelerationin PS. - (8) HVo T7- 6: HVoTt HVoT6: as HTl - u in percentage. (9) HTs_j:HTg- HTl: gain in heightduring phaseof falling accelerationin PS. - ( l0) .FI9oTe- t : HVoTs HVo f : sameas HTn -, in percentage. (ll) VT8 a: VTa- VT6: height of velocity peak in PS above pre-PS level. (12) VT8 a*Ts-a: a measureof height gain due to velocity peak in PS. (13) AT2 +: ATz- ATq: associatedwith intensityof the MS. (14) T4 z: Tq- ?n2:associated with duration of the MS. - (15) ATj , 4: ATt AT+: increaseof accelerationfrom MS to peaking in PS. Note that HTn-u:97, ' 6* HTs 1 (and HVoTe-a: HVoTt 6l HVoTe-7),due to the differentiationof gain in height in consecutivephases of the adolescentspurt. Allowing for somemethodological differences, Zs - e is equivalentto PB (: peak basis)in Largo et al. (1978),VTs 6to PH (:peak height) and VT8 e*Ts-ato PAR 1: peak area); the age parameterAMHV (age of minimal height velocity = Td and APHV (: Zs) intro- 133 Mid-growth and sdolescent growth spurt of height
respective ducedthere, are part of the presentset of standardparameters, as well as the velocity heights and velocities. The parameter AMHVR (:age of minimal height noteworthy return), characterizingan end to the PS, is relatedto Ze,but there are some differencesas describedin Gasseret al. (1984a)' girls, the For testing for the statisticalsignificance of differencesbetween boys and assumption two-sampleWilcoxon test was used, sincethis test doesnot dependon the : ' significant' of a normal distribution; an error probability of P 0 05 is considered nonlinear Fitting of the triple logisticmodel (Bock and Thissen1980) was basedon a flat least-squaresalgorithm by Deuflhard and Apostolescu (1980). The relatively parameters minima resulting when computing nonlinear least squares of model relatively indicated a tendency for overfitting, which is not surprising in view of the large number of parameters(9) of the triple logistic model'
3. Results latter Table I showsheight at four weeks(7s) and 20 years(?"1s) for our sample;the is in closeagreement with Largo et sl' 1978'
Table l. Means and standard deviation of height and percentage of height at Is (four weeks) and height at 20yr (HT6) for boys (N= 45) and girls (N:45)'
Boys Girls
Parameter SD SD
HTro l7'7. 5 6. I 165.3 5.8 HTo 53.4 53.4 1.8 HVoT6 30.I l'J 32.3 l'l
At four weeks, boys are little different from girls in length, they lag by 2'2Vo regardingpercentage of final height. At 20 they are 12'2cm taller. Dispersionis larger for boys in all three Parameters.
The pubertol spurt (PS) Table 2 gives descriptivestatistics of the standard parametersof the PS, and the girls' resultsof testing for the statisticalsigniflcance of differencesbetween boys and girls' For all timings at adolescence (Ts- i"e),boys show a highly significantlag behind (by and they show consistentlya higher standard deviation and a higher range about year one year;. Peak acceleration (4) is reached approximately one earlier than (boys) velocity (Is) in both sexes.The end ofthe spurt (?'e)is at l5'4years and 13'8years(girls) on average. At all ages,boys are significantlytaller than girls, but the percentageoffinal height (in reached does not differ appreciably: at ?n6only, there is a significant difference for favour of the girls). Heights, but not the percentagesof adult height, show a trend PS higher dispersionin boys. At onset of the PS about 8090 and at the peak of the girls about 919o of adult height are reached.Velocity is significantlyhigher for at onset Ie). The of the PS (i.e. at Ts, To),and significantlylower afterwards(i.e. at Tt, 78, and (l '2) from averagegain in velocity is for boys (girls' resultsin parentheses):2' 3 cm/yr minimal velocity (at76) to maximal acceleration(4) and l'7 (1'0) from ?"7to 4; the - ( - ln decreasefrom maximal velocity (?n) to maximal deceleration(G) is 3'3 2'9)' the velocities,there is a trend for higher variability for girls, and the variability is by far 134 T. Gasser et al.
Table 2. Mean' standard deviation, and range of standard parametersof the adolescentgrowth spurt for N= 45 boysand N- 45 girls.
Iime TI HTt HVoT, VT, ATt I Boys Girls Girls Boys Girls Boys Girls Girls t g'g** g.g 139.3** l3l.g 78.5 '79.7 4.R+ s.1 -o.72 -0.68 sD 1.3 1.0 t't /') J'Z J'.J 0.61 0.56 0.40 0.3 I ( ^Kange 6.4- 6'4- 123.7- ll4.l_ 70.t- 13.3* 3.6- 4.0- - 1.69- - 1'23_ lrz.+ lr.o 160.5 151.8 84.9 87-2 5.9 6-4 - 0.06 -0.14
t l0.g*+ 9.7 143.6*f136.3 80.9182.4 4.3* 4.8 00 sD t.l 0.96 6.8 7.3 2.4 3'0 0.50 0'58 00 - (8.7- j.4- Kange 131.8- 117.2- 76.2- 74-8, 3.4- 3.9- lt:'+ l2.o 161.9 156.3 87.1 89.8 5.4 6.2
i 12.9x* ll.2 152.9** 143.6 86.1 86.9 6.61 6.0 2'3*+ 1.4 sD 1.0 0.78 7.0 6.2 1.9 2.0 0.59 0.72 0.53 0.s2 - (11.2- 9'4- Kange l4l.l- 131.7_81.6- 82.4- 5.2- 4.5- l.l- 0.5- lts.o l2.g t"/1.9 159.7 90.4 91.8 /'6 /.) 3.8 3.l
, l3.g+* 12.2 161.4*+150.4 90.9 9t.0 8.3* 7.0 00 sD 0.95 0.81 6.6 6.0 l'J l'J 0.82 0.95 00 Rqnoe f12.3- 10.4_ l 50.5- I38.4- 88.2- 88.3- 6.5- 5.2- t t6.2 13.8 t80.7 164.8 93.7 94'3 10.6 9.5
t 15.4** l3.g l'/2.4*+ 160.6 97.1 97.1 5.0+* 4.I -3.6*+ -2.9 sD 0.91 0.84 6.6 6.0 0.8 0.8 0.59 0.62 0.43 0'57 Renoc fl 3'8- l2.o- 161.4- 146.1- 95.l- 95.3- 3.7- 2.8- 4.2- - 4.5- (17.5 15.3 192.1 t76-'7 98.8 98.6 6'7 5.7 2.5 - 1.6 Resultsof testing for significanceof sexdifference by wilcoxon testgiven by symbols: ** p<10_4. * p<10-l; f p<10_z; t p<0.5.10_2.
largestat Is for boys and girls. Decelerationis about the samefor boys and giris before rising to the PS (?'s), but both maximal accelerationand maximal decelerationare significantly larger for boys in adolescence.Maximal deceleration is larger in magnitude than maximal accelerationfor both sexes. By computing skewnessand kurtosis of the above parametersfor the pS, it was checkedwhether rhey follow a Normal distribution. This was in fact true to a good degreeof approximation, exceptfor maximal accelerationduring the pS (,417)for girls which showed a right-skewed long-tailed distribution compared to the Normal one. since this was not the casefor boys, this finding could well be due to chance. There is one derived (secondary)parameter pS for the duration of the (G o) and one for the subinterval, Ts j (table3). Mean total duration(Ts ) is 4.5 yr in boysand yr 'I'he 4' I in girls, and this differenceis significant. phasefrom maximal accelerationto maximal deceleration(Tg -) is, however,almost the samefor boys and girls. The distri- bution of duration is right-skewed long-tailed, particularly for girls. Aspects of the intensity of the spurt can be found in ATt _ s, ATt +, VTa_ e, and,AT7; all are highly significantly larger for boys than for girls. The step from maximal accelerationto . maximal deceleration(ATt ) is 5 9 (M) and 4. 2 (F), the differencebetween minimal pre-PS pS accelerationto maximal acceleration (AT1_ a)is 3 .3 (M) and,2.l (F) and the risingof the velocityabove pre-PS level (vrs_) is 4.0 (M) and 2.2 (F); for girls these parameterstend to be right-skewed and long-tailed. The height gain achieved, in absoluteand percentageterms, is significantlylarger for boys, both for the pS and its subphases.The distribution of the height gain from 16 to T1(HTr-o) deviatesconsider- ably'from a Normal distribution,in particularfor girls. Mid-growth and adolescent growth spurt of height 135
Table 3. Secondary parameters characterizing the adolescent growth spurt for boys (N:45) and girls(N- 45).
Parameter Sex i SD P valucs Range 9r Az 0.33- M 0.65 0.13 0.24 ATt,g <10 4 0.91 o'17- F 0.49 0.13 0.l3 0.81
M 2.6 0.17 0.68* Tst 0'360 J'l F 2.',7 0'33 1.6** 3.9
-J 'O- M 4.5 0.57 0.87** Ts-s 0'003 5.9 J'J_ 4.1 0.54 | .2** F 6.0
1' )- M )'v 0.84 - 0.27 AT <10 4 8.0 z' J- F 1.00 0.90** 7.6
M 28.8 4.0 4 [le.r- 0.30 HTg d <10 (40.0 (t{.1 F 24.3 4.3 tii; -0.r3
M 16.2 2.1 f10.7- -0.10 HVoT" . 0.003 Qt.4 f 8'6- F 14.7 z'o (21.6 0.05 t 4'8- M 9.2 3.4 (20.o l'4++ HT. . 0.001 .4 3'4- F- 7 2.9 (18'5f 2.1** | 2'6- M ).2 1.9 (10.7 l. 444 HVoTI 6 0.018 | 2'o- F 4.5 1.8 (|1.8 2'3**
M 19.6 2.3 lt4-t- 0.31 HT,s ., <10-4 Q4'6 t7.0 t. t\ 1r1.7- - 0.21 F 01-6 7'e- M ll'0 1.3 f(L4.2 0.15 HVoTs 1 0.029 .5 | 6'7- - F 10.3 I (12.8 0.40 2.0- M 4.0 0.86 - 0.32 vra <10 1 f'9 o o.7- F 2.2 0.9r I .3*+ 5.1 e'7- - N{ 17.'7 4'l (23.8f 0.37 vrs e* < l0-4 Tse -- F 8.9 3.9 (20.9I I'l** 2.0- i,1 J'J 0.61 0.2-l AT. ^ <10-4 4'7 I .0- F 2.1 0.63 l.l** 4'0
Bt = skewness,0z - kurtosis; Pvalues obtained by testing for sexdifference with Wilcoxon test. 136 T. Gssser et al.
The mid-growth spurt Judged from a visual inspectionof all velocity and accelerationcurves by one of us (Th. G.), the existenceof a well-definedMS is in doubt for three of 45 boys and for eight of 45 girls. As in the caseof PS, timings of the MS were determined from the accelerationcurve. The mid-growth spurt takes place at about the sametime for both sexes(22 - ?"ain table 4), culminating at about 7.5 yearsin velocity; the end of the MS is slightly later for boys, but the difference is just below significance.Boys become significantlytaller towards the end of the MS. Velocityis almost the sameat all MS ages for boys and girls. The sameapplies to accelerationat agefour and to maximal acceler- ation during the MS (T).A slightly positive averageacceleration appears during the MS (4), whereasbefore and after it (?"1and T) not only the average,but all individual boys and girls showeddeceleration. An equal number of girls and boys show a positive maximal accelerationduring the MS (34 out of 44 for each sex). The decelerationis significantlylarger for boys at the offsetof the MS. Height reachedat T1to ra is mildly right-skewed(more so for girls) and accelerationsat T2 and 13 are right-skewed and long-tailed for boys.
Table4. Mean,standard deviation .":i::JjlTffrd paramerersot rhemidspurt of N- 44 boys "'O
Tt Time HTr HVoTI VTr ATr I Boys Girls Boys Gt.l, Boys Girls Boys Girls Boys Girls i 4.0 4.o t04.4 102.8 58'8*462.2 7.t 7.0 0.99 0.88 SD 4'7 3'9 1.6 1.6 0.64 0.63 0.44 0'42 ( 96'4- 93.3- 55.7- 59.1- 6.1- 6.0- -2.30- - Ranse.-( J - 1.76- lls.0 n2.s 62.9 66.4 8'7 8.6 -0.10 0.06
x 6'4 6.4 119.2 117.9 67'2*471.3 6.t 6.0 o.2t o.2l sD 0.60 0.86 6.1 7.5 2.2 3.6 0.51 0.47 0.30 0.2s ^ ( 4.9- 4.8- I 10.0- 106.1- 63.6- 64-7- 5.t- 5.t- - 0'50- 0.2s- Kange '7 I l.o 8.3 132.9 13'7.9 72'6 79'3 7.4 . l l .30 0.94
x t./ t,) r27.0I 124-3 71.6**75.1 6.1 6.0 -o'361 -0.26 sD 0.82 0.85 6.6 7.0 2'6 3.3 0.50 0.46 0.t7 0.14 116.2-lll.8- 67'l- 68.2- 4.9- 5.1_ -0.72- -0.55- Kanse- l_^ ^ (lu.u 9.9 145'5 146.0 80.6 83.9 7.0 6.9 0.22 0.03
r 8.8 8.5 r33.8i 130'4 75.4*+78.8 5.3 5'4 - 0.93t 0.12 sD 0.84 0.93 6.6 7.O 2.6 3.2 0.46 0.49 0'2'7 '70. 0.26 - \O'/- tIJ- . - Kange 122.2- tt5.5- 4- 7| 4- 4. 1- 4.6- t.64- 1-20- ltt.o ll.o 15l.l 151.8 83.7 8'7.2 6.2 6.6 -0.36 -0.12 Resultsof testing for significanceof sexdifference by Wilcoxon testgiven by symbols: ** p<10 4. * p=.10 3l t p<10 2: i p<0.5.10_2.
The MS lastsfor 2'4yr for boys and for 2. I yr for girls (Tq-), and this differenceis significant (table 5). The intensity of the MS can be measuredby AT2 (table 4) or by AT2 a: the latter is significantlyhigher for boys, but not the former. The fitting of the triple logistic model yielded the following resultswith respectto the MS: maximal acceleration(Z) occurredon averageat 6.4yr (M) and 5.9yr (F); maximal deceleration(T) at 9'7yr (M) and 8.8yr (F). The sexdifferences are starist- ically highly significant.The intensity of the MS was slightly greater for girls, but sex differenceswere small. Figure 2 givesa graphical comparison of kernel estimation and triple logistic modelling with respectto velocity and accelerationin a boy with an adult Mid-growth and adolescent growth spurt of height t37
Table 5. Secondaryparameters characterizing the mid-growth spurt for boys (N=44) and girls(N- 44).
Parameter Sex x SD Pvalues Range A r Az
M l.t4 o.46 (2.2f0'r- 0.21 3.0 AT. ^ 0.039 F 0.93 0.43 (2.0[0'r- 0.25 2.7
M 2'4 0'60 fl'0 0'95* 5. 3* G.4 T,. 0.007 F z'I o.57 (3.4f|'2- 0.s0 2'9
0t - skewness,0z = kurtosis.P valuesobtained by testingfor sexdifference with Wilcoxon test. height slightly below average.This example brings out a problem typically associated with triple logistic fitting. The MS and the PS are forced by the model to follow in immediate succession(compare the accelerationcurve), whereasin many subjects a 'latencyperiod' can be seenin between(more so for boys). For theseindividuals the MS of the triple logistic model becomesthen too long, too late and not intenseenough, and this explainsthe sex differences,mentioned above, in timing and intensity of the MS.
Sexdimorphism qnd asynchrony of development Our results allow the establishmentof a relatively detailed longitudinal timetable for boys and girls (table 6). The sexdifference in timing amounts to I '6 yr at the end of the PS (: Ts), whereasit was only 0' 3 yr at the end of the MS (: Tq).The biggestsex differenceis in the gap which occurs betweenthe MS and the PS (4 to 4), which lasts for I . I yr in boys,but only 0'3 yr in girls.The subphasesduring the PS havean almost identical duration with the exception of the upsurge in accelerationfrom zero to its maximum (T6to T) which lastsI .9yr for boys and I .5 yr for girls.
Table 6. Time of occurrence of characteristicpoints in growth for boys (N-45) and girls (N:45): asynchronyof development.
Duration Duration TO of TO of Boys phases Girls phases Sex Ase (yr) (vr) (vr) (vr) difference
I2 o'4 o'c t'J r'r l1 7.5 3:9 l.l 1.0 T^ 8.8 8.5 ;. l.l u'J T-') 9'9 8.8 r. r 1.0 0.9 :^ t6 r0.9 9'7 1'L 1.9 T. t2'8 ll.2 l.t io 18 13.9 12'2 ,.i 1.5 r'6 r9 l5.4 13.8 i o TO, Time of occurrenceof characteristicpoints in growth.
Table 7 givesthe gains in height (absoluteand percentage)for boys and girls. The largestcontribution to the net differenceof 12'2cm in height at 20yr comes from the latencyperiod Tato T5and the phasesof positiveacceleration in the PS (76 to Zs). The boys gain 7 '3 cm (: 6090)in the pre-PSperiod and 4'9 (:40V0) in the PS period. The sexdifferences during the PS, as compared to the MS, are visualizedby prob- 138 T. Gasser eI al.
Table 7. Increasein height (absoluteand percentages)for longitudinalphases for boys (N- 45) and for girls(N= 45).
Height increase(cm) 9o of adult height Sex Sex Phase Girls difference Cirls difference To-Tr 5l.0 49.4 1.6 28'7 29.9 - 1.2 Tr-Tz l4'8 15.l -0.3 8.4 9.1 0.7 TrTt 7.8 o'4 1.4 q'+ 3.8 0.6 TrTq 6.8 6.1 0'7 3.8 -)'/ 0.1 TrTs )') t.4 4.1 1'l 0.9 2.2 TrTo 4.3 4.5 -0.2 2.4 - 0.3 To-Tt 9.3 2.0 5.2 4.5 0.7 TrTt 8.5 6'8 I't 4.8 4.1 0'7 TrTs I1.0 10.2 0.8 6.2 6.1 0.1 T,;-Tto 5.1 4'l 0'4 2.9 2'9 0.0
ability densitiesin figures3 and 4. The distributionof the ageof peakheight velocity of the PS (: 4) is shiftedtowards an older agefor boys (figurel). At the end of the MS
89 AGEIN YFARS
Figure 3. Timing (7"0)of the end of the MS (left) and timing (?'r) of the peaking of the PS (right): probabilitydensities (kernel estimates) for boys(dotted line) and for girls(solid line).
P
o B D E N S I T
012
CM/YEARMM2
Figure 4. Maximal accelerationAT.intbe MS (left) and in the PS ATl (right): probability densities (kernel estimates)for boys (dotted line) and for girls (solid line). Mid-growth and adolescent growth spurt of height r39
(:Tq), however,the agedistribution is similar, as is the distribution of the maximal accelerationduring the MS. The distribution of the maximal accelerationduring the PS is not only shifted toward higher intensity for boys; the distribution of boys differs also by being sub- stantiallyleft-skewed, whereas girls have a rather symmetric distribution (apart from a small tail consistingof girls with a more intense PS). The graphical representationof estimatedprobability densitieshere replaceshistograms which might be more familiar.
Peuk-centred qverage velocity and acceleration Figure 5 showsthe averagevelocity and the averageacceleration curves for boys and girls, obtained as follows: individual velocity and accelerationcurves were first centred to 4 (MS) and then averagedacross the sample; secondly, they were centred to ?"s @Hm to yield a further averagecurve. In order to obtain one averagecurve over the whole agespan, the first averagewas usedup to the end of the MS (4) and the second one from the start of the PS (7'6)onwards. Between 7a and 76,the curve was definedto be a smooth linear transition from one averageto the next. The averageboy experiences a later and a more intensePS than the averagegirl. The shapeof the PS is, however, similar with one exception:the velocity peak of the averagegirl has a more asymmetric appearance,which in the accelerationcurve is reflectedin maximal accelerationbeing relativelysmall comparedto maximal deceleration.The rising point to the PS is, for the averageboy, at a lower levelin the velocity curve, comparedto the averagegirl, but this is not true in the accelerationcurve. With respectto the MS, the pattern is quite similar for the two sexes.Maximal accelerationis identical regardingtiming and intensity, and
IC
10
,'*"
2 a
0 2 q 6 B l0 12 lq 16 lB 20 RGE I N IEFRS
Figure5. Averagevelocity curves (above) and accelerationcurves (below) for boys (dashedline) and girls (solid line), centredindividually to the MS (f2) and to the PS (Ir) for the respectiveperiods (see text). Crossingsin thecurves are put at I' (age4 yr), at Tt, Tr,4 (MS) and at 76, Ti, Ts, fe (PS). t40 T. Gasser et al. maximal velocity is higher for boys to a small extentonly. A somewhatearlier cessation of the deceleratingtrend for girls is the main sexdifference for the MS period' As far as the small sizeof the MS allows a comparison, no qualitative differencein shapecan be seenbetween MS and PS. The almost identical developmentof the velocity and the accelerationcurve for boys and girls up to the end of the MS (f+) of girls was also confirmed for curvesaveraged cross-sectionally.
4. Discussion The goalsof this paper werea quantification of the MS, and a descriptionof the PS, subdivided into more phasesthan previously considered, and an evaluation of sex differenceswith respectto the MS and the PS.
Comparison with previous results for the PS Table 8 contains a comparison of some traditional parameterscharacterizing the PS, basedon different samplesof subjectsand on different statisticalmethods (Tanner et al. l966.Marubini et al. 1977,Tanner et ol. l976,Largo et sl. 1978,Preece and Baines 1978(model 3), Hauspie et sl. 1980b, Zachartasand Rand 1983,the latter three using model I of Preeceand Baines 1978).It is, of course,not alwayspossible to assigndiffer- encesunambiguously to either the method or the sample. The fact that the present samplehas also beenanalysed by parametric fitting (Gasseret al. 1984a)using model 3 of Preeceand Baines(1978) and also the triple logistic model (Bock and Thissen 1980)' and the fact that smoothing methodslead to a small bias with respectto timing and to a downward bias with respectto peaks, might be helpful for this differentiation. Preece and Baines(1978), Largo et al. (1978)and the presentstudy closelyagree regarding the onset of the spurt (26) for boys, whereasTanner et al. (1976)deviate by about a year. The latter differencecan probably be attributed to a methodologicalbias when fitting the logistic function to the PS (seebelow the discussionon the asymmetry of the PS). For girls, the picture is more disparate:the onset is again very late inTanner et al. (1976)and closelyagrees with Largo et ol. (1978)and the presentstudy. Compared to thesetwo studies,the averageage of onset was earlier by about half a year in Preece and Baines(1978) and by about one year in Hauspieet al. (1980a)andinZacharias and Rand (1983).The above three studiesrelied on parametric fitting according to Preece and Baines(1978). This was also true for the analysisof an Indian sampleby Hauspie, Das, Preeceand Tanner (1980a)which yielded an averageage somewhat later than the one found by Preeceand Baines (1973).These differences are primarily of methodo- logical origin, sinceparametric fitting to our samplealso yielded an earlier averageage of onset(9.0 insteadof 9'7 yr, Gasseret s\.1984a) and sinceHauspie et al. (1980b) obtained9. 5 yr (insteadof 8'5 yr) by graphicalmethods. The reasonfor the compara- tively early onsetof the PS for parametricfitting following Preeceand Baines(1978) lies in an inadequatefitting of the prepubertal period. It was shown in Gasser, Mtiller, Kohler, Molinari and Prader (1984b) that the lack of a MS in the parametricmodel may also lead to an unsatisfactoryquantification of the onset of the PS, and this holds in particular for girls, where MS and PS usually follow in immediate succession(figures 3 and 6 in Gasseret al. 1984aillustrate this point). For age of peak height velocity (Za), there is close agreementamong the studies compiled in table 8 (this is also true for the resultsof Taranger,Engstrom, Lichtenstein and Svennberg-Redegren(1976) and of Ljung, Fischbeinand Lindgren(1977))' except for rhoseof Marubini et al. (1971)andZacharias and Rand (1983).The sameapplies to height and percentageof height HVoTs (exceptfor the Indian sampleof Hauspie et al. Mid-growth ond odolescent growth spurt of heiShl t4l
66r_6-r ra b\s . hrnhnet I I x;(d66;d6;t <; --SNhN- 3e rrrr€ s^ ^r € hN ! :^ :: lt ? :Y !.t - 6 VS 9Z @ I I' lo 63 i rr 9r ^E -ii o 9 ?T ! ;.b h 99 F\ e E !^ r.=+ rr h €h 3 ilz d t^ 60 -.: @- ils E OO -i":€ ? ?: 6 0- ,6.yz 6 o @^ 3aa \ 6O 66 d$ N6 k>; :?? - -6 : dd dd o&v ^^^^N ^ ^^6 O ^^h ^^ =^S h: O:6 6 oNrrod6rN .'-:rjX: o F\ i---oF --oo--o-- o6.: : -@roffr o*-h--Q€d o@€o€6 6€6rr@rrr &re .-:E N^ - ,o d .l .l 5 do o | 2a N-O 66 6 zsi 6 dr-o@o :6;i a ;.bG; h hht996 + h6iSrN o ts @6d9 lF&z - OOOOr€ 13 .-,_- t vhnhvi 99Ah l:o- 6*6^h^ l.- ll 6 o 66666O €r6€o6@NO t:23 b\ -6tO6o -€6ON6d€3 t; 6 d s6d--v do-dN*d-d lt{1 | .- X €^ON A^^€€W tN : h€h€ 6rrhr9 ts oooo Iti e rdo6 6@9€69 t..z: +++; h9$*9* l^-- lrrrN nd al lz-@ € --6 dv s lq: o ss s l6E- ls ^ 6hr@- or--6hi ls d 9€-9.; r9rdro9 tzi :?T9f 66@ro-o ': 9:moO rOh6eO- l'- ss$$d 6666n6N t= p tvr- 6 ^^^^ hN^^€^^ l3 .- €id l1s I: ioihrO 1980a). The deviation of Zachariasand Rand ( 1983)is probably due to a variability that is consistentlylarger compared to other studiesand not to the sample(age of menarche '0 13 yr is in line with other studies),nor to the fitting method (which leads to an only marginally earlier age compared to our method, see Gasser et al. l9g4d. The dis- crepant result of Marubini et ql. can be explainedonly partly by the fitting of a sym- metric velocity peak to a peak which is highly asymmetric for girls (seebelow). Regarding peak height velocity (PHn, there is a wide variation in the averages obtainedin the various studies.These differences are probably mostly due to differences in methods rather than in samples.For boys, Tanner et al. (1966)obtained l0.3cm/yr by graphical methods and similar valueswere found by Tarangeret at. (1976)and by Ljung el ol' (1977),when adjusting from whole year to instantaneousvelocity. The parametric and non-parametric fitting methods yielded much lower averages,ranging from 8'3-9'0cm/yr (Tanneret ql. lgj6,Largo et al. 197g,preece and Baines 197g, Hauspie et ol. 1980a,b, present investigation). A method for obtaining an approx- imatelyunbiased value for the averagepHV (Gasseret al.l9g4b) gave9.g cm/yr for our sample(this method is not applicableto individual curves).This is distinctly higher compared to the fitting methods and slightly lower than the graphical methods which may overestimalePHV to some extent. PHV showeda similar trend for girls when comparing different studies: it was highest (around 9.0cm/yr) when determined graphically (Thnner et al. 1966,Taranger et sl. 1916,Ljunget ot. 1977)and lower for logisticfitting (8'l in Tanner et ol. (1976)and g.4 in Marubini et at. (1971)).when performing non-parametricfitting (Largo et al. and,presentstudy) or parametric fitting accordingto Preeceand Baines(1978) (see also Hauspie et ol. (1980a,b)and Zacharias andRand(1983),PHVvariedfromT.0toT.8cm,/yr.Anaveragewhichisexpectedto have a small downward bias only was for our sample 7.9cm/yr (Gasseret ot. l9g4b). Sinceour sample of girls consistentlyshowed values smaller by about 0.5 cm,/yr than other studies when using the same method (Gasser et ol. l9g4a), a more typical, approximatelyunbiased average @Hn might lie around g.4cm/yr. This is about 0'5 cm/yt lessthan for the graphicalmethods, a differencewhich might be partly due to someupward bias of the latter approach and furthermore to six-monthly measurement intervalsused in our study insteadof three-monthly intervals (London and Stockholm studies).The parameter VTg e:VTs- VT6meastres the height of the velocity peak above pre-PS level. The differencebetween boys and girls is very accentuatedfor this parameter(almost doubled for boys). Our values for VTs 6 agreeclosely with those of Preeceand Baines(1978) and are somewhat smaller than those of Largo et at. (197g). Further results related to the PS Velocity is different for boys and girls before rising to the PS, but accelerationis almost equal (,47r). Maximal accelerationduring the pS (AT), agood measureof the intensity of the rising phaseof the PS is much larger for boys, the sex differencebeing highly significant. (Previously, the height of the velocity above pre-pS level, vrs_6, was used to quantify the intensity of the spurt (Largo et al. 1978,Preece and Baines 'maximal 1978.)When postulating the criterion accelerationhas to be positive' for the existenceof the PS, none of our children is lacking a PS (in contrast to the resultsof Zachariasand Rand (1983)).Maximal decelerationin the PS is also significantlylarger for boys than for girls, but the relative sex difference is smaller than for maximal acceleration(to be explainedby the fact that pre-PS velocity, which is higher for girls, has also to be stopped). The higher maximal decelerationthan accelerationfor boys and girls is closely Mid-growth snd adolescent growth spurt of height 143 linked to the asymmetry of the velocity peak. eualitatively, the asymmetry of the pubertal peak had been noted with a varying degreeof confidenceby Tanner et al. (1966)' (1978) Largo et al. and Stiitzleet al. (1980).For furrher investigarion,a measure of asymmetry was introduced as the ratio betweenmaximal decelerationand maximal (- acceleration ATtD).There is no singlechild with a completelysymmetric peak (i.e. -ATID The mid-growth spurt some older studiesreported on the MS (Backman 1934,count 1943,Grubb 1942; namedas mid-growth spurt by Tanner (1947)),but it was not quantified and statistically analysed. As illustrated in Gasseret al. (1984a),acceleration allows an easieraccess to timing and intensity of the MS. There is one free parameter in our method. the band_ width b, and our choice leadsto a conservativeestimate of acceleration:this does not introduce many artefactual peaks, but will, inevitably, tend to reducethe size of true t44 T. Gasser et al. peaks.By a visual judgment, most boys and girls have a discernibleMS, with, it seems, slightly more boys than girls doing so. This differencemight be simply a failure of visual discrimination, due to the close successionof MS and ps in girls: a more objective criterion, positivemaximal acceleration,led to exactlythe samerates for the two sexes. The methodologicalproblems describedabove, which are more accentuatedfor girls, might also explain why Tanner and cameron (1980)and Berkey et ul. (1983)confirmed a MS of height for boys but not for girls. A variable knot cubic spline algorithm, as used by Berkey et al., might for example respond not sensitivelyenough to the close successionof MS and PS of girls when placing knots. We decidedagainst introducing some cut-off with respectto intensity of the MS, and then analysingthe subgroup of children above that cut-off, which would lead to bias problems. Reliable identification was difficult due to the small size of the MS and also our yearly intervals betweenmeasurements from 2 to 9 or l0 years.In order to investigate whether missing observationsmay have inflated the number of children with a small MS, a separateanalysis was made for children with complete (N:75) and incomplete (N= 15)data from 4-9 years. Resultsproved, however, to be much alike. The averageage of peak height velocity of the MS is 7.5 yr for girls and,7.7 yr for boys (the differenceis not significant),and both are 6.4yr old at the time of maximal acceleration.The timing of the MS is, to our surprise,approximately equal for the two sexes,whereas a developmentallag (in terms of bone age)already exists in that period. Given the similarity in timing, it is not surprisingto find almost equalvelocities for boys and girls, keepingin mind the similarity or pre-adolescentgrowth. The lack of any sex difference in the intensity of the MS (as given by AT2, maximal acceleration) is, however, remarkable. The trend of a falling accelerationin the MS stops earlier for girls, associatedwith a lower maximal decelerationfor boys and a later end of the MS. Thesedifferences are attributable to this one factor-'earlier stopping of the deceler- ating trend' (seefigure 5)-and it is plausible that this is due to the advent of the PS. This finding of an almost identicaltiming of the MS for the two sexesis certainly not an artefact of the kernel method used, sincesimple cross-sectionalanalysis-which is unbiasedwith respectto timing-led to the same conclusions(Molinari et al. 1980, Gasseret al. 1984a;figures 7 and 8). when fitting the triple logistic model, Bock and Thissen(1980) found the MS to occur earlier for girls than for boys in their sample(see their figure 7.2). This differencebetween their resultsand ours is not due to differences in subjectsbut due to deficienciesof the triple logistic model, for our girls also had a significantlyearlier MS than boys when fitted with this model. One deficiencyof the triple logisticmodel is that MS and PS haveto follow in immediatesuccession, whereas 'latency in reality a period' betweenMS and PS often takes place,this is more accent- uated for boys than for girls (table 6, period T4to Ts;see also figure 2). This immediate successionleads to an artificial stretchingof the MS for boys, which makes it longer, later and lessintense than would be expectedfrom the data. It has beenspeculated that adrenal androgensare responsiblefor the MS (Molinari et al. 1980).Our findingswith respectto the timing of the MS, and the lack of sexdiffer- encesin timing and intensity, as well as the dissociationof MS and PS. are not in dis- agreementwith the presentliterature concerningthe adrenarche(de Peretti and Forest 1976,Reiter, Fuldauer and Root 1977,Sizonenko 1978,Sklar, Kaplan and Grumbach 1980). Sexdifferences in timing and height gains With respectto the sexasynchrony of development,that is the developmentallag of Mid-growth and adolescent growth spurt of height t45 boys, a surprisinglyclear picture emerged:at the end of the PS, the lag is I '6 yr, but is zero ar 72, the ageof maximal accelerationin the MS, and only 0'3 yr at the end of the MS (table 6). Sinceat the time of the MS mean bone age is already different for boys and girls, this is somewhat surprising. The largestcontribution to the lag comes from the latencyperiod betweenthe end of the MS and the onset of the PS, followed by the interval of rising accelerationat the start of the PS (T6ro T) which again lasts longer for boys. From maximal acceleration (T) onwards, the two sexes are in time synchrony. We can, therefore, say that the developmental lag is a phenomenon evolvingbetween the end of the MS and maximal accelerationin the PS (4 to 4). The 'regulation time from maximal accelerationto maximal velocity-something like a delay'-is about one year for girls and boys. The duration from the onset to peak height velocity is two thirds of the total duration of the PS for boys, for girls it is less. The higher standarddeviation of the timing of the PS for boys may be associatedwith the longer latency period which leads to a higher biological (rather than methodo- logical) variability in the onset and in the transition through the PS. The higher gain in height for boys, as compared to girls, for various stagesof developmentcan be compared witir the resultsof Largo et al. (1978)and with Hauspie et ql. (1980a)(table 7), keepingin mind methodologicaldifferences. The sexdifference in adult heightfor the sampleof Largo et al. was 12'6cm and ours is l2'2cm. They found + I .6 cm causedby more extensiveprepubertal growth of boys, attributed to a higher velocity of boys before the sixth month of life by Prader (1984).This interpret- ation is also plausible for our differenceof + l'6cm at four years. Largo et al. (1978) had a differenceof + 6'4cmdue to the boys' delayin spurt, and this is by and largecon- sistentwith our findingof + l'8cm achievedduring the MS and of + 3'9cm between the end of the MS and the onset of the PS ('latency period'). The following discrep- anciesarise after the onsetof the PS: they found + 6 ' 0 cm from onsetto end attributed to the greatermale spurt, and - 1'4cm due to the more extensivepost-Ps growth of girls; our valuesfor thesetime periods were + 4'5 cm and + 0'4 cm. Thesedifferences are entirelydue to a different definition of the end of PS (cf . Gasseret al . 1984a): When using the definition of Largo et al., we obtained for our sample a sex differenceof +6'5cm during the PS and of - l'6cm post-PS.When acceptingthe new definition (G) in terms of acceleration,the post-PSgain of girls disappears,and the contribution of the time span Z6 to 7e to the adult sex differenceis reduced from about 5090 to slightly below 40V0.Let us also note that the latter differenceis due to a combined effect of a more impressivemale spurt and a higher pre-pubertalfemale baselineof velocity, somewhatcompensating for the first factor. The + 2'5 cm found by Tanneret al. (1976) from onsetof PS to adulthood are inferior to our + 4'9 cm and the 4' 6 cm of Largo et ol. (1978). When using Preece-Bainesmodel I instead of the logistic function for fitting, Hauspie et al. (1980a) also obtained 2'5cm for the London data. For parametricfitting, our sampleled to a differenceof 2'4cm (Gasseret al. 1984a), so that the discrepancyfor London and Swissdata is of methodologicalorigin (due to an early onsetof the PS for Preece-Bainesmodels, proportionally more so for girls). Again the latency period and the period T6 to Tj contribute most to sex differences,probably primarily due to a longer duration. The gain after onset is 33' 9 cm for boys (29'0 f or girls),ascomparedto33'6cm(29'0cm)byLargoetal.(1978),to35'7cm(33'6cm)by PreeceandBaines(1978),andto2T'6cm(25'3cm)byTanneretal.(1976).Theonsetof the PS is somewhatearly-in particular for girls-for methodologicalreasons in Preece and Baines (1978) (as outlined in Gasser et ol. 1984a) and this accounts for their relatively large height gain (for parametric fitting according to Preeceand Baines, we 146 T. Gasser et al. obtained35'4 and 33'0cm, Gasseret al. 1984a).The small valuesof Tanner et sl. (1976)might be due to their unusual late timing of the onset of the PS (seeabove). As regardsthe percentagegain, the age 4 (: maximal accelerationin the MS) is a turning point for sexdifferences: before that age,girls alwaysgain more than boys, afterwards boys gain more (with the small exceptionof the period Ts to T6).The period in the PS beforethe ageof peak height velocitv (?"a)adds substantially to the relativegain of boys but not the period from Zs to Ze. Acknowledgements We aregrateful to Miss Willeseggerwho actedas the unfailing secretaryand anthro- pometrist of the Ziirich Longitudinal Growth Study. The suggestionsof Professor Tanner for improving the presentationand for making the paper more conciseare also gratefully acknowledged. This work was supported by the DeutscheForschungsgemeinschaft as part of the researchprogram ofthe Sonderforschungsbereich123 (project B1) at the University of Heidelberg,it was also partly supportedby the Fritz Hoffmann-La Roche Foundation. 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Addresscorrespondence to: Dr Th. Gasser,Zentralinstitut fiir SeelischeGesundheit, P.O.8.5970, D-6800Mannheim, FR Germany. Zusammenfassung. Das KOrperhdhenwachstumzwischen 4 Wochenund 20 Jahrenbei 45 Knabenund 45 Miidchen der Ztiricher Ldngsschnittuntersuchung(1955-1976) wurde mithilie von Kernel-Schatzungen analysiert.Der Zeitpunkt desmittleren Wachstumsschubes (MS) und despuberalen Schubes (PS) wurde ausden individuellen Zuwachskurven automatisch bestimmt, zusammen mit Korperhcihe,Prozentzahl der Korperhcihe,Geschwindigkeit und Beschleunigungin diesenAltern. Der kleine mittlere Wachstumsschubist ein durchgehendesPhdnomen, mit einem Gipfel bei 6,4 Jahren (m,f) fur die Beschleunigungund bei 7,7 Jahren(m) und 7,5 Jahren(f) fiir Geschwindigkeit.Es fandensich keine signifikanten Geschlechtsunterschiedein seiner Intensitat. Bei Miidchen folgt der PS dicht auf den MS; bei Knaben gab es eine nennenswerteZeitspanne dazwischen.Zusiitzlich zum Alter bei der grciBten Kcirperhdhengeschwindigkeitwird das Alter beim Beginn, die maximale Beschleunigungund das Ende des PS definiert. Geschlechtsunterschiedeim Zeitpunkt und AusmaB des puberalen Gipfels, die bereits friiher festgestelltworden waren, wurden erneut bestatigt. Neue Ergebnissebetreffen die Asymmetrie des PS, die bei Mlidchen starkerausgepragt ist, und die Geschlechtsunterschiedein Intensitat und Dauer der ersten Anstiegsphasedes PS. Nach dieserPhase unterscheiden sich Knaben und Miidchen nicht im Zeitpunkt, sondernnur in der Intensitatder Dezeleration. R6sumd. La croissancede la taille entre 4 semaineset 20 ans de 45 gargonset 45 filles de I'Etude Longi- tudinalede Croissancede Ztirich (1955-1976)a 6tdanalys€e d I'aided'estimations de grain. La chronologie de la pouss6ed la mi-croissance(MS) et celle de la pouss6epubertaire (PS) ont 6t6 d6termin6esde fagon auromatique?r partir descourbes individuelles d'acc6l6ration, conjointement d la taille, le pourcentagede taille, la vitesseet I'acc6l6rationd cesAges. La petite pouss6ed la mi-croissanceest un phdnomener6gulier, atteignant son pic d'acc6l6ration d 6,4 ans (garqons,filles) et son pic de vitessea 7,7 ans (gargons)et 7,5 ans (filles).Il n'y a pas de diff6rence sexuellesignilicative dans son intensit6. Chez les filles, le PS survientpeu aprdsle MS; chezles garqons une p6riodeconsid6rable les s6pare. En plus de I'Ageau pic de vitessede la taille,les Ages de d6but, d'acc6l6r- ation maximum et de fin de la PS sont definis. Les diffdrencessexuelles de chronologie et de hauteur du pic 148 T. Gasser et"al. pubertaire 6tablies ant6rieurement ont 6t6 v€rifi€esune fois de plus. Les nouveaux r€sultats concernent l'asym6triedu PS, qui estplus prononc€echez les filles, et lesdiff6rences sexuelles d'intensir6 et de dur6ede la premidre phase montante de la PS. Aprds cette phase, garqons et filles ne diffdrent pas en chronologie mais seulementen intensit6de la d6c€l€ration.