The use of regularity as estimated by approximate entropy to distinguish saltatory growth

A time-varying biased random walk approach to human growth

Growth and development are dominated by gene-environment interactions. Many approaches have been proposed to model growth, but most are either descriptive or describe population level phenomena. We present a random walk-based growth model capable of predicting individual height, in which the growth increments are taken from time varying distributions mimicking the bursting behaviour of observed saltatory growth. We derive analytic equations and also develop a computational model of such growth that takes into account gene-environment interactions. Using an independent prospective birth cohort study of 190 infants, we predict height at 6 years of age. In a subset of 27 subjects, we adaptively train the model to account for growth between birth and 1 year of age using a Bayesian approach. The 5-year predicted heights compare well with actual data (measured height = 0.838*predicted height + 18.3; R² = 0.51) with an average error of 3.3%. In one patient, we also exemplify how our growth prediction model can be used for the early detection of growth deficiency and the evaluation of the effectiveness of growth hormone therapy.

Infant head circumference growth is saltatory and coupled to length growth

BACKGROUND

Rapid growth rates of head circumference and body size during infancy have been reported to predict developmental pathologies that emerge during childhood.

AIMS

This study investigated whether growth in head circumference was concordant with growth in body length.

SUBJECTS

Forty infants (16 males) were followed between the ages of 2 days and 21 months for durations ranging from 4 to 21 months (2616 measurements).

STUDY DESIGN

Longitudinal anthropometric measurements were assessed weekly (n=12), semi-weekly (n=24) and daily (n=4) during home visits. Individual head circumference growth was investigated for the presence of saltatory patterns. Coincident analysis tested the null hypothesis that head growth was randomly coupled to length growth.

RESULTS

Head circumference growth during infancy is saltatory (p<0.05), characterized by median increments of 0.20 cm (95% confidence interval, 0.10-0.30 cm) in 24-h, separated by intervals of no growth ranging from 1 to 21 days. Daily assessments identified that head growth saltations were coupled to length growth saltations within a median time frame of 2 days (interquartile 0-4, range 1-8 days). Assessed at semi-weekly and weekly intervals, an average 82% (SD 0.13) of head growth saltations was non-randomly concordant with length growth (p≤0.006).

CONCLUSIONS

Normal infant head circumference grows by intermittent, episodic saltations that are temporally coupled to growth in total body length by a process of integrated physiology that remains to be described.