Modeling of Body Mass Index by Newton's Second Law

Abstract

Since laws of physics exist in nature, their possible relationship to terrestial growth is introduced. By considering the human body as a dynamic system of variable mass (and volume), growing under a gravity field, it is shown how natural laws may influence the vertical growth of humans. This approach makes sense because the non-linear percentile curves of different aspects of human physical growth from childhood to adolescence can be described in relation to physics laws independently of gender and nationality. Analytical relations for the dependence of stature, measured mass (weight), growth velocity (and their mix as the body mass index) on age are deduced with a set of common statistical parameters which could relate environmental, genetics and metabolism and different aspects of physical growth on earth. A relationship to the monotone smoothing using functional data analysis to estimate growth curves and its derivatives is established. A preliminary discussion is also presented on horizontal growth in an essentially weightless environment (i.e., aquatic) with a connection to the Laird-Gompertz formula for growth.