Modeling Montbeillards height data of a human male

Abstract

Growth is a dynamic activity of simultaneous biological processes happening at multiple time-scales varying from orders of fractions of a second to several years. Rather than modeling growth with differential equations, this multiple time-scale dynamics is modeled using a simpler algebraic approach that involves continued fraction of the linear time scale. This algebraic approach offers models that are infinitely differentiable like an exponential function but also robust and superposable like linear equations. Thus, unique insights into growth dynamics can be obtained without much need of a calculus background. Growth of bacterial colonies, yeast cultures, Drosophila population, mean individual attributes of Helianthus and rats have already been modeled using this approach. In this work, we extend the modeling procedure to individual human growth using Montbeillards height measurements of his son starting from birth upto almost 18 years of age. Good fits are obtained on the data and growth rates are estimated directly from the model. Thus, this methodology provides generic, flexible, simpler and more interpretable growth models.