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Modelling individual longitudinal human growth from fetal to adult life - QEPS I

Journal article
Authors Andreas FM Nierop
Aimon Niklasson
Anton Holmgren
Lars Gelander
Sten Rosberg
Kerstin Albertsson-Wikland
Published in Journal of Theoretical Biology
Volume 406
Pages 143-165
ISSN 0022-5193
Publication year 2016
Published at Institute of Neuroscience and Physiology
Institute of Clinical Sciences, Department of Pediatrics
Pages 143-165
Language en
Keywords Growth model, Height, Individual, Infancy, Childhood, Puberty, Adult height, Shape-invariant model, mathematical-models, height velocity, hormone treatment, healthy boys, evo-devo, children, curve, age, birth, profiles, Life Sciences & Biomedicine - Other Topics, Mathematical & Computational, Biology
Subject categories Pediatrics


Background: Only one mathematical model to date describes human growth and its different phases from fetal life until adult height. Aim: To develop a model describing growth from fetal life to adult height taking maturation/biological tempo into consideration. Methods: Subjects: The model was developed based on longitudinal mean height values obtained from published growth references for a cohort of 3650 healthy Swedish children followed from birth circa 1974 until adult height combined with birth-length for circa 400 000 healthy infants born 1990-1995. Results: The QEPS-model for individual growth was constructed with a combination of four basic shape invariant growth functions: a quadratic Q-function and a negative exponential E-function, both started during fetal life, 8 months before birth; the E-function levelled off after birth, whereas the Q-function continued until end of growth. A specific nonlinear pubertal P-function started at onset of puberty, and a stop S-function ended growth according to both the Q-function continuing during puberty and the specific P-function. For each function, an individual height-scale parameter was defined, and for the E and P-functions, a time-scale parameter; giving six modifying parameters in total. In addition standardized proportional scores were used for biological interpretations. The QEPS-model was used to fit and generate mathematical functions suitable to describe the growth of the healthy population of Swedish children; thereafter, the model was modified using four height scale parameters to model individual height in cm, and two time-scale parameters to adjust for the individual tempo of growth. Individual confidence intervals were calculated for all parameters. Conclusions: A new shape-invariant growth model, QEPS, was developed, that requires only four basic growth functions to describe the total pattern of growth in height from fetal life to adult height, with addition of height- and time-scale parameters describing individual growth. The model can describe a wide variety of growth curves. Moreover, it is the first model to provide confidence intervals which enable us to describe the precision/quality of individual parameters.

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