Results of the study of selected head measurements of Jena children]

Secular changes of head measurements (frontal breadth, bizygomatic breadth, bigonial breadth, auricular height, morphological facial height, lower face height) are analysed. The data are based on the Jena anthropological investigations of school children from 1975 and 1985. The inclusion of the data of the Jena longitudinal study carried out since 1985 allows an analysis of the further secular trend. Noticeable changes are proved in most of the analysed traits (frontal breadth, bigonial breadth, auricular height, morphological facial height, lower face height) between 1975 and 1985. The vertical measurements show greater percentage differences than the horizontal measurements, which, among other things, results in a relative narrowing of the face. In some head measurements (frontal breadth, bigonial breadth, auricular height) the trends continue after 1985. The secular trends show no obvious connection with the temporal acceleration of the dentition in the probands of the longitudinal study. However, a connection seems to be possible between the accelerated puberal growth spurt of the body height and the puberal growth spurt in some head dimensions.     

Kunze-Murken growth-specific approximations of somatograms

Tables for human height at age values by Kunze and Murken are submitted to mathematical approximations applying the 2-step-model introduced by Sager (1981). The basic term reflects growth as expected when a growth spurt is lacking which may be the case for children with chromosomal aberrations. The 2nd term comprises an expression for the growth spurt proper thus allowing an evaluation for the intensity of the spurt. The approximations as gained with nonlinear regressions show very close agreement with the measurements. Besides the growth curve its first derivative--the growth velocity or increase--is calculated and represented graphically. Moreover the results and their relative amounts against the final values at adulthood are compared for nine height at age tables treated hitherto with the same growth model.     

Phenomenologic-mathematical modeling of the human-body-length growth through the analysis of growth periods and their quantitative-analytical registration

The body height growth (of masculine beings) was modelled in a phenomenologic-mathematical manner by partitioning the time course of measured growth curve in parts every of which corresponds to a separated growth period. This partitioning was reached in a natural way so that a superposition of the single spurts yields the whole measured course. Every growth batch will be described in its time course by one term of inverse tangent function. The biological meaning and an explanation of the succession of the growth spurt as an effect of control circuits need further exploratory work. For detailed statements on acceleration phenomena concerning the body height growth this analysis gives possibilities for comparing the single growth spurts of the mean growth process of two populations in question. For measured values given by BROCK (1954) and SALZLER (1967) there are five growth periods in the time intervall reaching from time of conception until the end of the first year. Comparing the mathematical functions of the corresponding growth spurts for these two groups one can conclude that the second spurt (fetal spurt) is responsible for an increase of birth body height and the fourth for an increase of body height in the suckling age of the latter group against the former one.     

A survey on growth and sexual development of adolescent students in Changhua City: growth of body height and weight

In order to understand the physical growth and sexual development of contemporary adolescents, a cross-sectional survey was conducted during the period September 1983 to May 1984. The population came from all the pupils from 4th grade up, and all the junior and senior high students of Changhua City. By using stratified cluster sampling, 1419 boys and 1599 girls participated, ranging in age from 8 to 19 years. Body weight and height were measured. Growth spurt is a unique event during adolescence. It is well shown in the distance curves and pseudo-velocity curves of body height and weight. In boys, the growth spurt of height spanned from 12.0 to 14.8 years, with peak height velocity (PHV) at 13.5 years. In girls it was from 10.0 to 12.6 years and peaked at 11.5 years. The growth spurt of weight occurred from 12.0 to 15.9 years in boys with peak weight velocity (PWV) at 14.5 years, while girls had a growth spurt at 10.0-12.7 years with PWV at 11.5 years. Girls entered into the growth spurt about 2 years earlier, and also entered into PHV, PWV, two and three years earlier respectively than boys, while boys had a more intense and longer growth during the growth spurt than girls. Between 10.0-13.0 years girls were taller than boys, and between 12.0-13.0 years they were heavier than boys. However, from 13.5 years onward girls were soon surpassed by boys both in height and weight. Growth in height after 16.5 years in boys and after 15.5 in girls was minimal. Growth in weight in boys also became minimal after 16.5 years while girls weight even dropped a little bit after 16.5 years. At the mean age of 17.5 years, boys were 168.1 cm, girls were 156.2 cm in average, boys being 12 cm taller than girls after reaching their final height.     

Growth specific analysis of Schmid's (1983) data on Down syndrome carriers

After a short introduction to the phenomena of children with Down's syndrome, values describing body status as gained by Schmid at the Aschaffenburg hospital for child disease (F.R.G.) are recalled. In a cross-sectional study values for body height, head circumference and body weight for 393 girls and 436 boys were gathered in 1983 reflecting the status for medically treated patients of the present. After insuring that the scattering of the data keeps within tolerable limits growth specific analysis became a challenge. Body length is approximated with the 2 step model by Sager (1981) comprising a basic function without a growth spurt superimposed by a spurt term. As a result, an usual but somewhat reduced growth spurt can be secured for the girls whilst the boys show no intermediate maximum in growth velocity. Nevertheless velocity keeps well above that for the basic function thus indicating a silent spurt after the definition of Pelez and Sager (1984). Head circumference too is treated with the same model after tests with Czech values for common and gypsy children. As a result, a reduced but acute growth spurt with a growth hump for the increase function has been found for both sexes. In contrast to height, however, a short term formula for values from birth to near pubescence cannot be applied due to the vivid head growth in the postnatal phase. Values for body weight W allow first conclusions after plotting log W against the body length L. In the case of the Down patients, 2 different forms of fundamental relations emerge, one of them related to normal growth, the other to impeded or less differentiated development as found in the rhesus for example. For both cases, mathematical expressions as proposed and used by Sager are applied. Results show near to normal behaviour for the girls and a less intricate course in weight growth for the boys. Results are given in graphs and tables allowing detailed calculations if desired. Quotients of momentary to finally attained values for body height and weight as well as head circumference are added.     

Adolescent growth in main somatometric traits of Japanese boys: Ogi Longitudinal Growth Study.

Considerable information is available on peak growth velocity characteristics of various body dimensions but the age at minimal velocity (AMV) and the duration of the spurt are not that well documented. Authors applied the mathematical growth model of Preece and Baines (PBGM1) to six longitudinally followed somatometric traits [height, sitting height, iliospinal height (B-ic), upper limb length (a-da), biacromial diameter (a-a), and biiliocristal diameter (ic-ic)] of Japanese boys of Ogi Growth Study. Biological variables derived from the estimated parameters were studied with emphasis on duration and velocity characteristics of the adolescent spurt. Ages for measurements at peak velocities tend to be younger than previously reported non-Japanese ones. Spurt duration in limb measurements was significantly the shortest. Earlier AMV and later age at peak velocity (APV), thus the longest spurt duration, are the characteristic for transverse measurements (a-a, ic-ic). B-ic and a-da had the largest, while a-a and ic-ic had the smallest relative velocity at AMV. Another result for the transverse measurements is that the magnitudes of differences between relative minimal and peak velocities (RMV, RPV) are the largest. It is suggested that a high level of RMV results from early maturation of bones, thus leading to the shortest spurt duration in limb dimensions, while a low level of RMV results from late maturation of the bones, consequently leading to the longest spurt duration in transverse measurements. This tendency of reverse relation was present in the rest of the measurements as well. Transformation of velocity variables (minimal velocity -- MV, peak velocity -- PV) to relative ones, proved to be useful in observing the relation of spurts in measurements.     

Quantitative mathematical evaluation of growth studies from the viewpoint of exogenously or genetically influenced variability

Firstly, the ideas are sketched which serve as the basis for the phenomenologic-mathematical kind of modeling of the body length growth process of man. For proving the biological relevance of the spurts analyzed by numerical procedures one has to consider the social and the biological circumstances in which the growth process takes place. An analysis of longitudinal data series of the body length of (monozygotic) twins will give further hints to the possible meaning of the growth spurts by way of separation of exogenous and of genetic determined endogenous agents on the growth process. The data available for our examinations cover the time interval of the praepubertal and the postpuberal development as well as the time interval in which the puberal growth spurt takes place. The way to proceed in evaluation these time series will be presented.     

Evaluation of adolescent statural growth in health and disease: reliability of assessment from height measurement series and development of an automated algorithm

OBJECTIVES: The precise evaluation of adolescent growth spurt is necessary for numerous clinical research studies of growth disorders and treatments. The objectives of our study were: (1) to evaluate the reliability of clinicians' 'manual' evaluation of the adolescent growth spurt from a collected series of height data, and (2) to construct an automated algorithm to determine the duration of the two phases of growth in health and disease (spurt and final slow growth) independent of clinical pubertal stages. METHODS: One hundred and seventy-four growth curves of normally growing, GH-deficient and Turner's syndrome subjects were presented twice to 2 experienced clinicians. Disagreement between evaluations and clinicians were settled to obtain a 'consensual gold standard' evaluation versus which the algorithm was assessed. Kappa statistics and Bland-Altman analyses were used to evaluate the reliability and agreement of the evaluations. RESULTS: The reliability of 'manual' evaluation of adolescent growth spurt from collected series of height data appeared to be poor. Conversely, the developed algorithm is perfectly reliable and satisfactorily valid. Discrepancies with the clinical consensual gold standard were always fewer than the discrepancies between the expert clinicians, and were observed in similarly difficult curves. CONCLUSION: The developed algorithm may be useful for diverse clinical and biological research applications in children with growth disorders. This study also confirms the value of a comprehensive investigation of growth during adolescence independent of clinical staging.     

Growth patterns and final height in congenital adrenal hyperplasia due to classical 21-hydroxylase deficiency. Results of a multicenter study

BACKGROUND: Longitudinal growth and bone age (BA) development are the most important clinical parameters for monitoring adequate glucocorticoid replacement in children with congenital adrenal hyperplasia (CAH). AIM OF THE STUDY: To analyze the growth pattern of patients treated for CAH of the salt wasting (SW) and simple virilizing (SV) clinical forms; to evaluate final height as compared to reference data and individual target height; to evaluate the course of BA development. PATIENTS AND METHODS: A large database of 598 patients with CAH was created in 5 Central European countries and growth data of 341 treated patients with 21-hydroxylase deficiency were analyzed retrospectively. The patients were of Caucasian origin. Centiles were constructed in a cross-sectional manner and an additional longitudinal analysis was performed in order to evaluate the pubertal growth spurt by applying particular statistical methods (Preece-Baines model). RESULTS: The growth of SW CAH patients was impaired in infancy and early childhood (0-3 years of age), but followed normal patterns in childhood until puberty. In contrast, children with SV CAH had normal patterns of growth in infancy and early childhood and were considerably taller than healthy references during childhood. In the longitudinal study, peak height velocity in both boys and girls was normal, but it occurred at an earlier age than in the standard population. The final height of patients with CAH was reduced in comparison to both the reference and the individual target height. No correlations were found between final height and age at the start of the therapy in SV patients or between final height and year of birth. BA was advanced in both types of CAH, but more accelerated in SV patients. CONCLUSION: Characteristic growth patterns for treated SV and SW CAH children were identified, with a normal pubertal growth spurt and reduced final height being observed.     

Normal growth spurt and final height despite low levels of all forms of circulating insulin-like growth factor-I in a patient with acid-labile subunit deficiency

BACKGROUND: In a recently described patient with acid-labile subunit (ALS) deficiency, the inability to form ternary complexes resulted in a marked reduction in circulating total insulin-like growth factor (IGF)-I, whereas skeletal growth was only marginally affected. To further study the role of circulating versus locally produced IGF-I in skeletal growth in this patient, we now describe in detail growth changes and their relationship with several components of the circulating IGF system. DESIGN AND METHODS: We followed growth and development up to the final height in a patient with complete ALS deficiency and determined both spontaneous and growth hormone (GH)-stimulated changes in the IGF system, including measurements of total, free and bioactive IGF-I, total IGF-II and insulin-like growth factor binding protein (IGFBP)-1, IGFBP-2 and IGFBP-3. RESULTS: The patient had a delayed growth and pubertal onset. Six months of GH treatment had no effect on growth. At the age of 19.3 years, he spontaneously completed puberty and had a normal growth spurt for a late adolescent (peak height velocity of 8.4 cm/year). A normal final height was attained at 21.3 years (167.5 cm; -0.78 SDS). During as well as after puberty, basal levels of total, free and bioactive IGF-I were low, as were total IGF-II, IGFBP-1, IGFBP-2 and IGFBP-3. GH treatment for 6 months normalized free IGF-I and increased bioactive IGF-I, but had no effect on growth velocity. CONCLUSIONS: This case story shows that in the presence of complete ALS deficiency, a height within normal limits can be obtained despite low levels of all forms of circulating IGF-I. Furthermore, the patient presented a delayed but normal growth spurt without any marked increment of circulating IGF-I.     

Long-term follow-up of spontaneous development in a boy with familial male precocious puberty

BACKGROUND/AIMS: Limited data are available about spontaneous growth, pubertal growth spurt and the long-term outcome of patients suffering from familial male precocious puberty (FMPP). We report on a boy with FMPP whose growth pattern and pubertal development was studied longitudinally without treatment. METHODS: Long-term prospective follow-up without treatment of a 6.2-year-old boy with FMPP having inherited a mutation of the LH receptor gene (A568V) from his father. RESULTS: The pubertal growth spurt was of unusual maximal amplitude (growth rate 12.4 cm/year at the age of 5-6 years) and of extraordinary duration lasting for 5.2 years from age 3.8 to 9.0 years. No deterioration of height potential was observed. Height (174 cm) was within target height range (171.5-188.5 cm) at age 13 years. No central precocious puberty occurred. CONCLUSION: FMPP is an experiment of nature demonstrating that the amplitude and duration of the pubertal growth spurt are much more variable than previously described. Furthermore, this case emphasizes that the indication for treatment is highly dependent on intrafamilial and individual factors.     

达斡尔族中小学生体质发育现状及20多年来的变化

本文报道了6~18岁1993名达斡尔族学生8项体质指标(身高、坐高、体重、肩宽、骨盆宽、胸围、腰围和臀围)的测量结果,并计算了10项体质指数。结果发现,达斡尔族在我国属体质发育较高的民族,并表现为一定的城乡差异;20多年来达斡尔族学生身高、体重、胸围全面增长,男女生身高最大增长年龄均提前约1岁左右,男生高年龄组身高和身体充实度增幅较大,但女生变化不大且肩宽和骨盆宽呈下降趋势。提示达斡尔族青少年体质发育表现为以生长突增提前为主的生长长期趋势,但女生高年龄组身高增长不明显、身体充实度有待提高,应采取营养和锻炼等措施促进其生长发育水平全面提高。     

Pubertal growth of the short normal girl

OBJECTIVES: To determine the timing, magnitude and duration of the pubertal spurt for short normal and average height girls, to compare these with Tanner's standard and to investigate predictors of pubertal growth. METHODS: The growth of 46 short normal and 55 control girls, identified at school entry, was monitored throughout puberty. Height and weight were measured at 6-month intervals from which body mass index (BMI) was derived. Annual velocities were calculated and used to estimate the age and magnitude of peak height velocity (PHV). Age of menarche was recorded to the nearest month. Parents provided information on the child's medical and social history. RESULTS: The mean age at PHV, the magnitude of PHV and age at menarche were similar for both groups and close to Tanner's 50th centile values. Pre-pubertal BMI predicted age at menarche for short and control girls, accounting for 17% of the variance. There was a tendency for early maturing girls of average stature to have greater PHV. However, this relationship was not observed in short girls, nor did any other variable, genetic or environmental, predict the timing or magnitude of their pubertal spurt. CONCLUSIONS: Delayed puberty in short normal girls is unlikely and their growth during puberty is comparable to girls of average height. The pubertal variables measured remain close to Tanner's original standards for both groups, suggesting the lack of a secular trend towards earlier puberty in girls. The onset of menstruation is influenced by pre-pubertal BMI. However, the clinician should be aware that short normal girls have normal pubertal growth and that no genetic or environmental variable can predict the timing or magnitude of their growth spurt.     

Growth and timing of puberty: reciprocal effects.

Based on the analysis of the pubertal growth spurt and final height in different pathological conditions, this paper provides evidence that variations in age at onset of puberty have a major influence on the subsequent acceleration of the growth rate but a minor impact on final height. A reciprocal effect of the growth rate on the timing of onset of puberty is also suggested by a number of clinical observations.     

Growth rates and phylogeny in primates

There is sufficient evidence to indicate that man grows for a longer period of time than chimpanzee who in turn has a greater duration of growth than rhesus monkey. The problem of this paper was to determine if there was a concomitant decrease in a rate of growth. Using the relative growth rate of Fisher ('21), it appears that for most of their period of growth, the rate of change is the same. Immediately after birth, when we have no data for children, rhesus monkey grows significantly faster than chimpanzee. By a year and a half their rates are the same, and neither species shows a sex difference. From seven years (age of youngest children) until children start through puberty, there is no sex difference in Homo sapiens, and the human rate does not differ from the chimpanzee rate. Because of the resemblance between the primate curve for rate and that for dairy cattle, it is postulated that this curve is more mammalian than primate and that during phylogeny the primates have merely increased the duration of time when growth is possible. Man does show one new feature, the puberal growth spurt, which is not found in the non-human data considered. The implications of these conclusions for primate phylogeny and for growth are discussed.     

An integral dynamic model for the UASB reactor

In this article a dynamic model of a continuous working UASB reactor is described. It results from the integration of the fluid flow pattern in the reactor, the kinetic behavior of the bacteria (where inhibition and limitation were taken into account), and the mass transport phenomena between different compartments and different phases. The mathematical equations underlying the model and describing the important mechanisms were programmed and prepared for computations and simulations by computer. The settler efficiency has to be over 99% to prevent the reactor from wash-out. When the settler efficiency is over 99%, the total sludge content of the reactor increases steadily, so the reactor is hardly ever in a steady state. This implies dynamic modeling. The model is able to predict the various observable and nonobservable or difficult to observe state variables, e.g., the sludge bed height, the sludge blanket concentration, the short-circuiting flows over bed and blanket, and the effluent COD concentration as a function of the hydrodynamic load, COD load, pH, and settler efficiency. The optimal pH value is between 6.0 and 8.0; fatty acid shock loadings are difficult to handle outside this optimal pH range.     

Longitudinal analysis of adolescent growth in height,fatness, and fat patterning in rural South African black children

Adolescent growth in height, fatness, and fat patterning was investigated in a sample of 79 rural South African black children studied longitudinally from 6–18 years. Data were analyzed relative to peak height velocity (PHV) to identify the phenomenon of “compensatory” growth in height during adolescence and to describe changes in fatness and fat patterning. Compensatory growth following PHV was clearly observed relative to NHANES data for African-Americans in that Z-scores for height at the start of the adolescent growth spurt were greater than those at the end of the spurt. Statistically significant differences in fatness and centralization between males and females did not occur until about 2 years after PHV was attained. Centralization of fat occurred in both sexes but moreso in males. The lack of centralization in females was due to relatively greater triceps skinfold velocities. The rapid gain in post-PHV fatness in females may represent a physiological adaptation to an energetically sub-optimal environment, buffering the energetic costs of reproduction. © 1994 Wiley-Liss, Inc.     

A mathematical approach to defining clade names, with potential applications to computer storage and processing

Clade names may be objectively defined based on conditions of phylogeny. Definitions usually take one of three forms — node-, branch- or apomorphy-based — but other forms and complex permutations of these forms are also possible. Some database projects have attempted to store definitions of clade names in a manner accessible to computer applications, but, so far, they have only provided ways of storing the most common types of definition. To create a more extensible system, I have taken a mathematical approach to defining clade names. To render definitions accessible to computer storage and analysis, I propose using Mathematical Markup Language (M ath ML) with extensions. Since the mathematical approach is granular to the level of the organism, not to fuzzy higher levels such as population or species, it sheds light on some theoretical difficulties with defining clade names. For example, some definitions do not resolve to a single organism as the ancestor, but to sets of organisms which are not ancestral to each other and share common descendants. I term such sets 'cladogenetic sets'.