Perspectives on modelling human growth: Mathematical models and growth biology

Preece-Baines 1 model validation for cross-sectional data in male soccer players according to maturity status

AIM

The aim of the present study was to compare the Preece-Baines 1 (PB1) model fit between longitudinal and cross-sectional data in male soccer players and to adjust the height growth curve by maturity status.

METHODS

A final sample of 57 male Portuguese soccer players from professional soccer academies was included. Longitudinal height records were measured between 8 and 17 times in each subject from 2-8 years to 14-17 years. Additionally, longitudinal height records were used as cross-sectional data along with 1087 cross-sectional height records taken from 602 Portuguese soccer players. Skeletal age was estimated by Tanner-Whitehouse III method from a left hand-wrist radiograph. Age at peak height velocity (PHV) was estimated by PB1 model for longitudinal and cross-sectional data and by maturity status.

RESULTS

No significant differences were found between all the longitudinal estimates of 57 players and the random cross-sectional samples for, S1 parameter and for growth velocity at PHV, at TO, and for age at PHV. The age at PHV in early, on-time, and late maturers were 12.26, 12.9, and 13.58 years, respectively.

CONCLUSION

PB1 adjusted the height growth of Portuguese male soccer players from cross-sectional data, obtaining an estimate PHV very similar to that found from longitudinal data. A maturity time difference of ≈0.6 years was found between the age at PHV of on-time, early, and on-time and late maturity state.

Physical Growth, Body Scale, and Perceptual-Motor Development

In this chapter we consider from the theoretical framework of the ecological approach to perception and action, the relations between physical growth and body scale in the context of children's perceptual-motor development. Body scale and the timescale of its change through growth are shown to relate to the emergence and dissolution of the fundamental skills in infancy, the perception of what an environment affords functionally for action, together with the emergent pattern of movement coordination. A central issue in typical and atypical motor development is the mapping of the timescale of adaptive change in the acquisition of perceptual-motor skill to the accompanying timescale of change in physical 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.

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

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.

Growth characteristics in cerebral palsy subtypes: a comparative assessment

AIM

Children with quadriplegic cerebral palsy (CP) have been found to have growth rates that differ from those of children with typical development. Little research has been performed to distinguish whether growth patterns in hemiplegic, diplegic, and quadriplegic CP differ from one another. The purpose of this study was to compare growth of children with quadriplegic, hemiplegic, and diplegic CP.

METHOD

Retrospective data were collected from the electronic medical record of patients with CP at an outpatient center. Linear mixed models were used to examine growth by diagnosis, using International Classification of Diseases, Ninth Revision (ICD-9) diagnosis codes 343.0 (diplegia), 343.1 (hemiplegia), and 343.2 (quadriplegia).

RESULTS

Heights and weights of children with quadriplegic CP were consistently lower than those with hemiplegic or diplegic CP. Children with hemiplegic CP had greater heights and weights than other CP subtypes. There were statistically significant differences in weight gain curves among the three diagnoses for males (p<0.05).

INTERPRETATION

Our study reveals differences in growth rates between hemiplegic, diplegic, and quadriplegic CP subtypes.

How domain growth is implemented determines the long-term behavior of a cell population through its effect on spatial correlations

Domain growth plays an important role in many biological systems, and so the inclusion of domain growth in models of these biological systems is important to understanding how these systems function. In this work we present methods to include the effects of domain growth on the evolution of spatial correlations in a continuum approximation of a lattice-based model of cell motility and proliferation. We show that, depending on the way in which domain growth is implemented, different steady-state densities are predicted for an agent population. Furthermore, we demonstrate that the way in which domain growth is implemented can result in the evolution of the agent density depending on the size of the domain. Continuum approximations that ignore spatial correlations cannot capture these behaviors, while those that account for spatial correlations do. These results will be of interest to researchers in developmental biology, as they suggest that the nature of domain growth can determine the characteristics of cell populations.

Auxological perspectives on 'growth' in DOHaD

David Barker established growth as a seminal link between early development and later health attainment and disease risk. This was nothing less than a paradigm shift in health and medicine, turning the focus of disease causality away from contemporary environmental influences to earliest growth as a time when functional anatomy and physiology sets in place critical structures and function for a lifetime. Barker's prodigious work investigated time- and place-specific interactions between maternal condition and exogenous environmental influences, focusing on how growth unfolds across development to function as a mechanistic link to ensuing health. Subsequent applications do not always attend to the specificity and sensitivity issues included in his original work, and commonly overlook the long-standing methods and knowledge base of auxology. Methodological areas in need of refinement include enhanced precision in how growth is represented and assessed. For example, multiple variables have been used as a referent for 'growth,' which is problematic because different body dimensions grow by different biological clocks with unique functional physiologies. In addition, categorical clinical variables obscure the spectrum of variability in growth experienced at the individual level. Finally, size alone is a limited measure as it does not capture how individuals change across age, or actually grow. The ground-breaking notion that prenatal influences are important for future health gave rise to robust interest in studying the fetus. Identifying the many pathways by which size is realized permits targeted interventions addressing meaningful mechanistic links between growth and disease risk to promote health across the lifespan.

Bridging paradigms: hybrid mechanistic-discriminative predictive models

Many disease processes are extremely complex and characterized by multiple stochastic processes interacting simultaneously. Current analytical approaches have included mechanistic models and machine learning (ML), which are often treated as orthogonal viewpoints. However, to facilitate truly personalized medicine, new perspectives may be required. This paper reviews the use of both mechanistic models and ML in healthcare as well as emerging hybrid methods, which are an exciting and promising approach for biologically based, yet data-driven advanced intelligent systems.