Predicting the peak growth velocity in the individual child: validation of a new growth model

Abstract

Predicting the peak growth velocity in an individual patient with adolescent idiopathic scoliosis is essential or determining the prognosis of the disorder and timing of the (surgical) treatment. Until the present time, no accurate method has been found to predict the timing and magnitude of the pubertal growth spurt in the individual child. A mathematical model was developed in which the partial individual growth velocity curve was linked to the generic growth velocity curve. The generic curve was shifted and stretched or shrunk, both along the age axis and the height velocity axis. The individual age and magnitude of the PGV were obtained from the new predicted complete growth velocity curve. Predictions were made using 2, 1.5, 1 and 0.5 years of the available longitudinal data of the individual child, starting at different ages. The predicted values of 210 boys and 162 girls were compared to the child's own original values of the PGV. The individual differences were compared to differences obtained when using the generic growth velocity curve as a standard. Using 2 years of data as input for the model, all predictions of the age of the PGV in boys and girls were significantly better in comparison to using the generic values. Using only 0.5 years of data as input, the predictions with a starting age from 13 to 15.5 years in boys and from 9.5 to 14.5 years in girls were significantly better. Similar results were found for the predictions of the magnitude of the PGV. This model showed highly accurate results in predicting the individual age and magnitude of the PGV, which can be used in the treatment of patients with adolescent idiopathic scoliosis.

Fig. 1

Graphical representation of the predictive model. The original individual partial growth velocity curve (cyan line), the generic growth velocity curve (dashed black line), and the new individual predicted growth velocity curve (red line) are shown. A _i, scaling of the vertical amplitude of the growth velocity curve, T _i, scaling of the width of the velocity curve, c _i, shift of the growth velocity along the age axis, k _i, shift of the growth velocity curve along the growth velocity axis

Fig. 2

Example of the prediction of a new individual growth velocity curve. The black curve represents the smooth fit of the original individual growth curve of total body height. The dashed cyan growth velocity curve of this individual contains a continuous part, which was used as input for the model. The gray dashed line represents the generic growth velocity curve from which the new, predicted individual growth velocity curve was constructed (red velocity curve). The vertical dashed lines represent the original (cyan) and new predicted (red) age of the PGV of this individual

Fig. 3

Results of the average absolute differences between the original and predicted age of the PGV (upper graph) or magnitude of the PGV (lower graph) in boys. The thick black bar represents the average absolute difference between the values of the generic growth velocity curve and the original ages or magnitudes of the PGV of the individual children. The vertical bars represent the SD. Asterisks indicate significantly smaller difference between the prediction and the original age or magnitude of the PGV in comparison to the difference between the values of the generic growth velocity curve and the original age or magnitude of the PGV

Fig. 4

Results of the average absolute differences between the original and predicted age of the PGV (upper graph) or magnitude of the PGV (lower graph) in girls. The thick black bar represents the average absolute difference between the values of the generic growth velocity curve and the original ages or magnitudes of the PGV of the individual children. The vertical bars represent the SD. Asterisks indicate significantly smaller difference between the prediction and the original age or magnitude of the PGV in comparison to the difference between the values of the generic growth velocity curve and the original age or magnitude of the PGV