Frije Universiteit Brussel Laboratorium Anthropogenetica
The growth curve shows various features which can be recognised in each individual but which may considerably vary in timing intensity from the basic pattern of the curve of a single child one and individual to another. The basic pattern of the human growth curve has basicaliy three phases: (1) a period of rapid, but nevertheless decelerating, growth during the first 2 years after birth, often denoted as "early childhood period", (2) a period of more or less constant (or slightly decelerating) growth from about 2 years of age till the onset of adolescence, often denoted as "childhood period", and (3) an adolescent growth spurt. The shape and characteristics of a growth curve can only be studied on the basis of purely longitudinal data, i.e. serial measurements of body size taken at time intervals of the same children. While human growth seems to be a fairly continuous process, we can only, at the best of our abilities, mrasure the phenomenon at discrete time intervals. The data then serve to estimate the suposed smooth growth proess. It is at this level that mathematical modelling is of great use. The main goals of fitting mathematical models to growth data are:
(1) to summarise the often vast amount of longitudinally collected growth data into small number of constants, the function parameters,
(2) to produce a smooth continuous monotonously increasing growth curve based on the the observed measures of growth,
(3) to derive biological parametea characterising the shape of growth curve, such as age, size and velocity at take-off and at peak velocity of adolescent growth spurt,
(4) to generate the typical average growth curve in the sample which does not suffer from smoothing effects such as i cross-sectionally obtained mean growth curves,
(5) to compare shapes of growth curves between individuals and between groups of individuals or to relate particular features of the growth curve to genetic and/or environmental factors.
Several models have been proposed to describe the entire postnatal growth period or to describe parts of the growth (childhood or adolescence). Most curve useful mathematical growth models are non-linear functions. Their characteristics, potential use, and drawbacks are briefly presented and discussed.
Average growth is derived from cross-sectional, mixed-longitudinal or longitudinal growth data. Estimating centile lines is a major technique in describing population growth. Various techniques can be used to estimate centile lines. Among others, the use of Pan-Healy's technique to estimate centile lines will be discussed and illustrated with some examples. Other approaches, based on non-linear regression, polynomial fits and cubic splines, will be illustrated on the basis of centile lines estimated for the growth and growth velocity of patients with Turner syndrome.