A Mathematical Procedure for Estimating the Spatial Relationships between Lung Function, Somatic Growth, and Maturation

Abstract

A mathematical procedure is described for examining growth velocity rates of lung function (FEVi) in relationship to somatic growth and maturation. This procedure uses a polynomial smoothing spline model to yield a fitted curve through the data and to estimate the process first derivatives (i.e. growth velocity curves). We demonstrate this technique using data from children and adolescents enrolled in the Tucson Epidemiological Study of Airway Obstructive Diseases. The study group consisted of 772 healthy normal subjects, aged 3 to 25 y. The results for the normal subjects (male and female) indicate that the growth velocity peak (GVP) of somatic growth leads the GVP of functional growth (FEVi) by approximately 7 and 11 mo for females and male subjects, respectively, and that the GVP of maturation lags behind that of functional growth (FEVi) by approximately 1 y (male and female subjects). In addition, the normal subjects' growth velocity curves for FVC and FEVi/FVC were examined. The FEVi/ FVC ratio was consistently high, and its growth velocity was not significantly different than 0 over the age range studied. This suggests that in normal children, the GVP seen in FEVi is primarily due to a GVP in vital capacity or lung vol, rather than to a direct effect on expiratory flow rates alone. From this study we concluded that the polynomial smoothing spline procedure can adequately model the inherently noisy pulmonary function data and additionally yield an accurate estimate of the process first derivative.