INVITED REVIEW: Kinetic models for normal and impaired growth

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Abstract
Although microkinetic models are expected to play in the future the same role that macrokinetic models have played in the past, classic mechanistic growth functions are still worthy of study and may still provide insight into auxological problems. The rather rigid shape of macrokinetic models may ignore many interesting fluctuations of growth velocity, but a strong structure allows a robust estimate of growth kinetics even in the case of growth profiles which are largely incomplete, as those derived from current clinical records. In any case, the too simplified shape of these models may be adjusted, to some extent, by adding some unstructured smooth function of residuals which takes into account minor aspects of growth (such as slight spurts during childhood), which cannot be detected in an individual profile because of random errors and inadequate number of observations. This paper recalls the reasons why growth models are useful, analyses briefly the structure and the characteristics of the two fundamental human growth functions, i.e. triple-logistic and PB1, and shows how the use of PB1 model may be extended also to impaired growth, e.g. in girls with Turner syndrome. In this regard, the use of the same model for normal and pathological growth offers the important advantage that differences between growth patterns are not confounded with differences between models.