A new approach to modelling human height growth is presented which is also suitable for other variables. In a mathematical algorithm, some guess about the functional form of this growth process is improved consistently using the data; the resulting shape-invariant model (SIM) allows an approximately bias-free fitting for longitudinal data from 1 to 20 years with six parameters assigned to each individual. The SIM approach and the use of velocities rather than distances proved to be suitable for biomathematical modelling in order to answer questions qualitative in nature. In comparison of an additive two-component SIM and one where the appearance of puberty inhibits further growth of the non-pubertal component ('switch-off model'), the latter proved to be superior in various aspects. Among the qualitative features found are notable: a pronounced midspurt, and a dip before the onset of puberty, as well as the asymmetry of the pubertal peak. A preliminary analysis of individual parameters confirmed some results found previously by other methods regarding sex differences and relations between parameters and with adult height.

Adolescent↗

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Velocity and acceleration of height growth using kernel estimation.

A method is introduced for estimating acceleration, velocity and distance of longitudinal growth curves and it is illustrated by analysing human height growth. This approach, called kernel estimation, belongs to the class of smoothing methods and does not assume an a priori fixed functional model, and not even that one and the same model is applicable for all children. The examples presented show that acceleration curves might allow a better quantification of the mid-growth spurt (MS) and a more differentiated analysis of the pubertal spurt (PS). Accelerations are prone to follow random variations present in the data, and parameters defined in terms of acceleration are, therefore, validated by a comparison with parameters defined in terms of velocity. Our non-parametric-curve-fitting approach is also compared with parametric fitting via a model suggested by Preece and Baines (1978).

Body Height↗

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Menstrual patterns in adolescent Swiss girls: a longitudinal study.

Menstrual patterns were studied longitudinally in 140 adolescent Swiss girls. The mean cycle length was 32.2 (S.D. 11.24) d in the first year after menarche, and 29.9 (S.D. 7.12) d in the sixth year after menarche. The values of the mean cycle length became essentially constant from the sixth post-menarcheal year, the chronological age of 20 y and the 36th post-menarcheal cycle. No association was found between cycle length and age at menarche. The menarcheal age of mothers and that of their daughters were significantly correlated with each other (r = 0.29, P less than 0.001). The most frequent cycles of 21-27 and 28-34 days constituted 64-81% of all cycles depending on post-menarcheal age. Short cycles (14-20 d), representing 2-6% of all cycles, were present in 14-31% of the girls; long cycles (35-41 d), constituting 10-16% of all cycles, occurred in 46-68% of the girls. The frequency of the long cycles tended to decrease at higher post-menarcheal ages. There were minimal changes in the duration of menstrual flow throughout the first six years after menarche. The mean duration was 5.4 (S.D. 1.72) d for the first year, and 5.1 (S.D. 1.33) d for the sixth year. The most frequent flow duration was 3-7 d, present in 88-94% of cycles. Prolonged bleeding tended to decrease with rising post-menarcheal and chronological age. The intensity of menstrual flow was mild in 11-16%, moderate in 62-78% and severe in 11-25% of the girls. The frequency of these three categories remained essentially unchanged during the first five post-menarcheal years.

Adolescent↗

PubMedDate not supplied

An analysis of the mid-growth and adolescent spurts of height based on acceleration.

Height growth between four weeks and 20 years of 45 boys and 45 girls from the Zürich 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 acceleration curves, together with height, percentage of height, velocity and acceleration at these ages. The small mid-growth spurt is a consistent phenomenon, peaking at 6.4 years (M,F) in acceleration and at 7.7 years (M) and 7.5 years (F) in velocity. There are no significant sex differences in its intensity. In girls, the PS follows in close succession to the MS; in boys there is a substantial period in between. In addition to the age of peak height velocity, ages of onset, maximal acceleration and end of the PS are defined. Sex differences in timing and size of the pubertal peak previously established were again verified. New results relate to the asymmetry of the PS, which is more pronounced in girls, and to sex differences in intensity and duration of the first rising phase of the PS. After this phase, boys and girls do not differ in timing but only in the intensity of deceleration.

Adolescent↗

PubMedDate not supplied

Symptoms related to menstruation in adolescent Swiss girls: a longitudinal study.

Symptoms related to menstruation are reported in 140 Swiss girls according to postmenarcheal and chronological age. Premenstrual abdominal pains were present in 9-28% of the girls, depending on postmenarcheal age (i.e. years after menarche) (2-30% depending on chronological age). Dysmenorrhoea occurred in 44-64% of the girls according to postmenarcheal age (51-67% according to chronological age). Occasional severe dysmenorrhoea was the type most often reported, by 20-35% of the girls. Large intra-individual and inter-individual variabilities in the occurrence and severity of dysmenorrhoea were observed. The frequency of dysmenorrhoea increased in the first three postmenarcheal years and decreased thereafter. The prevalence of premenstrual headache was low, 0-5%. The frequency of headache during menstruation was 2-11% according to postmenarcheal age (2-19% by chronological age) which was low in comparison with other studies. Severe menstrual headache was more often reported than mild headache. Frequency of severe headache decreased in higher age groups. Other reported symptoms related to menstruation were general discomfort in 1-10% of the girls and premenstrual vaginal discharge in 10-22% according to postmenarcheal age (3-17% according to chronological age). Severe vaginal discharge was more frequent than mild discharge, 8-20% versus 0-3%. The frequency of vaginal discharge increased from the first to the fourth year after menarche.

Abdomen↗

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Human height growth: correlational and multivariate structure of velocity and acceleration.

In this paper the correlations between parameters quantifying the mid-growth spurt (MS) and the pubertal spurt (PS) of height are explored. These parameters are defined in individual acceleration, velocity, and distance curves, which are obtained via kernel estimates as previously introduced. The MS proves to be a phenomenon largely independent of the PS. Intensity, timing, and duration of the PS are also independent mechanisms of growth and neither of them influences adult height in an appreciable way. Adult height depends mostly on pre-adolescent velocity. Short-, medium- and long-term regulatory mechanisms for explaining height growth are considered. For short-term mechanisms, acceleration plays a crucial role.

Adolescent↗

PubMedDate not supplied

A method for determining the dynamics and intensity of average growth.

A new statistical method is presented for determining an average growth curve which is valid in the sense of representing both the average dynamic, or tempo, and the average intensity of the growth process studied. In this context, growth curve means either distance, velocity or acceleration curve. The principal idea is to shift individual curves continuously (and non-linearly) in age to an average developmental age scale. Since the resulting curves represent the typical shape rather than individual variations of it, they are of interest for comparisons of different variables of boys and girls and of subgroups. The method is illustrated with longitudinal growth data from the first Zurich longitudinal study.

Body Height↗