A new family of mathematical models describing the human growth curve

Abstract

A new family of mathematical functions to fit longitudinal growth data is described. All members derive from the differential equation dh/dt = s(t). (h1-h) where h1 is adult size and s(t) is a function of time. The form of s(t) is given by one of many functions, all solutions of differential equations, thus generating a family of different models. Three versions were compared. All were superior to previously described models. Model 1, in which s(t) was defined by ds/dt = (s1 - s)(s - s0) was especially accurate and robust, containing only five parameters to describe growth in stature from age two to maturity. Derived "biological" parameters such as Peak Height Velocity were very consistent between these three members of the family but, in some cases, differed signficantly from previous estimates.