Modeling of Body Mass Index by Newtons Second Law

arXiv:0808.4149v1 [physics.bio-ph] 29 Aug 2008 Modeling of Body Mass Index by Newton’s Second Law Enrique Canessa∗ The Abdus Salam International Centre for Theoretical Physics, Trieste, Italy 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. ∗E-mail: canessae@ictp.it 1 I. INTRODUCTION The raw (and theoretically smoothed) statistical data of different aspects of human phys- ical growth from birth to adolescence have been collected for decades as a function of gender and nationality. From a practical point of view, these measurements are useful to monitor health care and to highlight secular trends on the fat intake (obesity) by a particular pop- ulation [1, 2]. Child growth records are also of special interest to Governments to enforce national health policies [3]. In particular, there are smoothed growth charts for boys and girls such as those main- tained by the USA National Center of Health Statistics (NCHS) [4] and the unsmoothed data for thousands of Japanese infants, children and adolescents (Hiroshima Growth Study Sample) [5]. Typically, the charts consist of a set of non-linear percentile curves displaying the dependence on age of height h(t), ”weight” w(t) and combinations of them such as the weight-for-height and body mass index (BMI, i.e., ratio B(t) ≡w/h2). According to the CDC growth charts [4], the 85th percentile of BMI for children is considered the overweight threshold, and the 95th percentile is the obesity threshold. In constructing smoothed statistical growth curves a variety of asymptotic mathematical models have been tested to fit results for a population in retrospective [6]. Different trial functions are used because the data for h and w do not increase monotonically with age and because the use of weight-height methods (such as the BMI) affect directly the development of curve smoothing. For example, modeling of human anthropometric data has been done in the contexts of the lambda-mu-sigma (LMS) model [7], the model functions of triple logistic curves [8], Count-Gompertz curves [9, 10] and Jolicoeur et al. curves [11]. Another fine test model used is the infancy-childhood-puberty (ICP) model [12]. This model breaks down growth mathematically into different (exponential, quadratic and logistic) functions using different curve fitting procedures out of the growth data. Predictions of changes in height have also been carried out according to an empirical Bayesian approach [13]. The selection of a definitive parametric approach for the inclusion or exclusion of some empirical data points and to set a criteria of estimation is a topic of active discussions because of its relevance to growth, development and aging in living organisms [6]. For open systems like those in which there are influx of mass, one can apply the con- servation of linear momentum and energy methods of general physics to study their growth 2 dynamics. Examples in which momentum is gained from, or lost to, the surroundings include rockets [14, 15] and the falling of a snow ball [16], respectively. Since the human body is also a system of fluctuating mass (and volume), under the influences of the acceleration of gravity g and food consumption, it is not unreasonable to consider it as a dynamic physics system. One may then in principle make an attempt to derive a relationship based on physics laws and observed ”physical” growth. Since laws of physics exist in nature, their possible relationship to human physical growth is introduced in this work. It is shown how physics seems to influence the physical growth of humans. Using Newton’s second law, analytical relations are deduced for the time de- pendence of h, w, the growth velocity v = dh/dt which depend on common parameters that could relate other aspects of this phenomenon such as environmental conditions and genet- ics and natural processes like metabolism, energy supplied by food, etc. Within a simple physics

…(Full text truncated)…

This content is AI-processed based on ArXiv data.