## 2 Materials and Methods  
The following section outlines the complete digital workflow for measuring models of patients with unilateral cleft lip and palate. It presents an overview of the data collection and model preparation stages before moving on to an examination of the software and analysis protocol with a focus on their practical application. The digital workflow of the Frankfurt approach (Figure 1, Step 1) initiates with an IOS, which serves as the foundation for subsequent digital measurement. IOS of the upper jaw segments is obtained using a 3 Shape intraoral 3D scanner; both the Trios 3 and Trios 4 are in application (3 Shape A/S, Copenhagen, Denmark). To ensure precise image acquisition and optimal texture quality, the intraoral 3D scanner undergoes weekly calibration per the manufacturer's instructions. Before the initial 3D scan, the patient data are entered into the 3D scanner system. For the 3D-scanning procedure, the newborns are positioned supine on a pillow covered with a sterile pad. In order to achieve the best possible 3D scan quality, the patient's jaw area is first cleaned superficially with the aid of a moistened gauze swab, and any adhesive cream residue is removed. Where possible, the jaw segments are then dried with the aid of dry gauze and a saliva ejector. The newborns remain awake and are not sedated during the IOS. A sterilized standard 3D scan tip of the corresponding 3 Shape intraoral 3D scanner is used for the intraoral 3D scan, which typically takes about 3 min (Figures 1 and 2). The IOS must be verified to ensure that all relevant anatomical features have been captured for subsequent measurement. Any missing or poorly captured areas of the alveolar ridge must be re-3D-scanned. Once the intraoral 3D scan is complete, a post-processing step is performed using the IOS software to generate an exportable 3D data set. The model preparation ensures that the data are properly prepared and aligned for accurate measurement. Subsequently, the IOS data obtained are imported into the OnyxCeph3 TM software for processing and preparation for the digital measurement (Figure 1, Step 2). The edges of the IOS are trimmed to eliminate any excess or irrelevant data. Subsequently, a 3D model is generated from the 3D data set using a base (Figure 3, Step 3, and Figure 1). Figure 1: Overview of the steps involved in the digital workflow for computer-aided measurement of unilateral cleft lip and palate according to the Frankfurt approach: intraoral scan of the maxillary segments. The IOS data obtained are imported into the OnxyCeph3 TM software (**A**). In order to ensure the accuracy of the measurement process, it is imperative to meticulously prepare the scan data set. This involves the removal of overlapping structures (**B**), the supplementation of external areas with digital bridges (**C**), and their supplementation (**D**) in the non-relevant areas. The edges of the IOS are trimmed to eliminate any excess or irrelevant data (**E**). Subsequently, a 3D model is generated from the 3D data set using a base (**F**,**G**). The digital cleft palate models can be measured with the module “Evaluation” in OnxyCeph3 TM by setting measuring points (**H**). The software OnyxCeph\({}^{3\text{TM}}\), developed by Image Instruments\({}^{\text{\textregistered}}\) GmbH in Chemnitz, Germany, is implemented for processing the 3D digital dental models of patients with unilateral cleft lip and palate. Developed as a \"native network application for patient- and case-related management of 2D and 3D image data\" [22], this application facilitates advanced 3D data processing and visualization and also enables precise measurements. The digital cleft palate models can be precisely measured with the modules \"Model Alignment\" and \"Evaluation\" in the OnyxCeph\({}^{3\text{TM}}\) software. The system enables the users to define measurement points, which are subsequently saved as X, Y, and Z coordinates (Figure 1, Step 4).