# Growth pattern prediction of maxillary segments in infants with unilateral cleft lip and palate: a prospective in vivo study

## TL;DR

This study finds that linear regression models best predict the growth of maxillary segments in infants with unilateral cleft lip and palate before surgery.

## Contribution

The study introduces a linear regression model as the most accurate method for predicting maxillary growth in infants with cleft lip and palate.

## Key findings

- Linear regression with mixed effects showed the best fit for predicting maxillary segment growth.
- Surface area increased significantly with age at rates of 2.88 mm²/day for total area and 1.62 mm²/day for the large segment.
- Linear models outperformed intercept-only models for all measured areas (p < 0.01).

## Abstract

The aim of the study was to identify the best prediction model for the growth pattern of the maxillary segments of infants with unilateral cleft lip and palate post birth and prior to the primary surgical cleft closure.

195 digital maxillary models of 50 infants with unilateral cleft lip and palate were collected during their preoperative alveolar molding therapy period. Intraoral scans were taken shortly after birth, at the monthly checkups and just before the surgical cleft closure at approximately 6 months of age. Surface measurements of maxillary segments were conducted using the diagnostic program OnyxCeph³™. For identifying the best fit for the growth pattern, mixed-effects regression models (fractional polynomials and B-splines) with the surface measurement as dependent variable, patient age (days) as predictor and the patient as random effect were fitted to the data. The best fit was selected according to the Akaike Information Criterium. A likelihood ratio test was performed for comparing the selected model with the intercept-only model.

The linear regression with mixed effects model showed the best fit for the total area, the area of the large segment and the area of the small segment. A highly significant association between the surface area and patient age was observed (p < 0.001). An increase of the area with time was estimated at 2.88 mm2 per day for the total area, 1.62 mm2 per day for the area of the large segment and 1.25 mm2 per day for the area of the small segment. The likelihood ratio tests indicated that the linear regression models were significantly better than the intercept-only models for all the measured areas (p < 0.01).

The growth pattern for the maxillary segments of patients with unilateral cleft lip and palate in the preoperative period can be best predicted by using a linear regression model. The growth curve model developed by the present study can be used in future treatment planning of patients with unilateral cleft lip and palate.

The online version contains supplementary material available at 10.1007/s00784-025-06378-2.