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 FEVl/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 FEVl 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. (Pediatr Res 25:316-321, 1989) Abbreviations FVC, forced vital capacity FEVI, forced expired volume in one second SG, somatic growth M, maturation GVP, growth velocity peakThe relationships between lung function and anthropometric growth in adolescents have been studied by several investigators (1-9). Although some reports have focused on the reproducibility of lung function and anthropometric variables (6) thoracic growth and stature (2,3,5,6). The latter studies have all reported an apparent lag time between growth in stature and subsequent growth in lung function. That is to say, increases in lung function continue to occur for at least 1 y after cessation of increase in stature. These results were also suggested by Simon et al. (8), who showed that the growth spurt for lung length (determined from chest radiographs) occurred 6 mo after that for standing height, for males and females ages 6-15 y. The two major contributing factors of functional lung development are: I ) SG assessed by a power function of height, which as mentioned above, leads functional growth; and 2) M, which we propose lags behind the functional growth component. For our purposes, lung M is defined as that portion of functional lung development which is not directly related to changes in SG. An estimate of M is then determined as that portion of the observed FEVl not predicted, using a power function of simple allometry. This approach assumes that FEV1 growth can be described by a simple allometry model and that any deviations f...