Ethical permission and study population
This study was approved by Filat University Non-Intervention Regional Ethics Committee Decision No. 2025/08-17 (meeting date: May 22, 2025). This retrospective study evaluated computed tomography (CT) images of 90 healthy people (control group: 57 men, 33 women) with no diagnosis of psychiatric or neurological disorders and 90 people diagnosed with schizophrenia (schizophrenia group: 53 men, 37 women) between the ages of 29 and 29 (May 31, 2023 to May 31, 2025). All 64 years were retrieved from the PACS (Picture Communication System) archive. Before being analyzed, all images were fully anonymized and no personally identifying clinical or personal information was processed or accessed. This retrospective study was conducted using previously collected imaging data, so no direct contact with patients occurred. Informed consent was waived by the Non-Interventional Regional Ethics Committee of Firat University. When conducting the study, we followed the Declaration of Helsinki and the organization’s data protection regulations.
CT images were acquired using a 256-slice computed tomography machine (General Electric Health Care-Revolution CT, USA). The imaging parameters used in the examination were as follows: Kv = 120, mA = 200, rotation time = 0.5 seconds. Collimation = 64 × 0.625. Images were transferred to a workstation (DOSEWATCH, General Electric HealthCare, USA) and analyzed. Patients with schizophrenia and healthy individuals with comorbidities, eye disease, trauma, or head surgery were excluded from the study. Furthermore, patients with low-quality CT images, those with detectable pathology, those with orbital growth still in progress (<18 years), and those with significant axial or rotational deviations on the images were excluded.
To reduce geometric variations caused by head rotation and tilt during CT acquisition, all scans were spatially aligned to a common reference frame before morphometry. This registration was performed using 3D Slicer v5.4 (open source software, https://www.slicer.org) through a rigid transformation (6 degrees of freedom) that corrects translational and rotational mismatches without changing anatomical dimensions.
The anterior commissure-posterior commissure (AC-PC) line and the midsagittal plane were used as anatomical reference landmarks. All images were resampled to an isotropic voxel size of 0.5 × 0.5 × 0.5 mm using bilinear interpolation. After registration, the orbital region was extracted within a standardized bounding box to ensure consistent field of view and scaling across all subjects. This preprocessing step ensured that the observed trajectory parameter variations reflected true anatomical differences rather than acquisition-related position artifacts.
Measurement parameters
Keser and colleagues described the following measurement parameters:20. No size reduction was performed during the measurements. Actual images were used directly. The maximum vertical distance between the superior and inferior orbital edges was used to calculate the orbital height (coronal section) (Figure 1A). The maximum horizontal distance between the medial and lateral borders of the orbit at the surface level of the anterior zygomatic suture was used to calculate the width of the orbit (coronal section) (Fig. 1A). At the level where the optic nerve was always tracked, the depth of the orbit (in axial section) was calculated using the shortest vertical distance between the midpoint of the start of the optic canal and the line connecting the lateral and medial edges of the orbit (Fig. 1B). Dimensions of the lateral and medial borders of the orbit (axial section): The length of the medial wall is determined by measuring the distance between the anterior corner of the medial wall and the anteromedial point of the optic canal (Fig. 1C), and the length of the lateral wall is determined by measuring the distance between the anterior corner of the lateral wall and the anterolateral end of the superior orbital fissure (Fig. 1D). The size of the closed bone line drawn after the supraorbital foramen, anterior rim of the lacrimal fossa, anterior zygomatic suture, and infraorbital rim was automatically calculated using software to determine the orbital aperture area (coronal section) (Figure 1E).
Interorbital width (coronal section): Figure 2A shows the measurement of the distance between two dacryon points on the medial border of the orbital opening. Orbital width (coronal section): Figure 2B shows the distance between the most prominent points of the lateral margins of the left and right orbits. The distance between the anterior and most prominent parts of the left and right cheekbones was used to determine the width (coronal section) of both cheeks (intermalar) (Fig. 2C). Transverse diameter of the skull (axial section): The transverse diameter of the skull was measured between the most distal positions after the section with the largest transverse diameter was taken (Fig. 2D). Width of the optic nerve sheath in axial section: The width of the optic nerve and its sheath was measured at its widest point (Figure 2E).
Data analysis using machine learning algorithms and artificial neural networks
Machine learning is an artificial intelligence technique that allows computers to learn from experience without explicit programming. It uses a variety of techniques to identify, classify, and predict patterns in big datasets. Machine learning typically falls into three main categories: supervised learning, unsupervised learning, and reinforcement learning.
Supervised learning is an approach that builds models by establishing relationships between inputs and outputs in a dataset. Unsupervised learning aims to discover hidden patterns and features in data without using pre-labeled information. Reinforcement learning models are a way to improve the matching of inputs and outputs so that the system reaches the correct output.16.
Several classification algorithms were used in this study. Decision tree (DT) algorithms are a fast, efficient, and commonly used method of recursively partitioning data. Logistic regression (LR) utilizes a sigmoid function to model the probability of class membership. Random Forest (RF) is an ensemble method based on the generation of multiple decision trees. Extra Tree Classifier (ETC), an advanced variant of RF, introduces randomness in node splitting and achieves better performance by utilizing the entire training data. Linear discriminant analysis (LDA) identifies the linear combination of features that best separates multiple classes.16.
Artificial neural networks (ANNs) are mathematical models inspired by the human brain’s learning processes that can analyze complex data patterns through multilayer structures. A typical ANN consists of an input layer, one or more hidden layers, and an output layer. During training, the network learns the mapping between input data and corresponding outputs. After training, its performance is evaluated based on unseen data16.
Machine learning (ML) algorithms and artificial neural networks (ANN) were implemented using a Monster Abra A7 V12.5 model i5 operating system computer. Random forest (RF), decision tree (DT), logistic regression (LR), extra tree classifier (ETC), linear discriminant analysis (LDA), quadratic discriminant analysis (QDA), Gaussian naive Bayes (GaussianNB), k-nearest neighbor (k-NN) algorithms were preferred among ML algorithms, and multilayer perceptron classifier (MLCP) was preferred among ANN algorithms. For the ML and MLCP algorithms, 80% of the data was used as the training set and 20% as the test set. Additionally, we also include a 10x cross-validation value for ML model reliability. For the MLCP model, the input layer consists of 18 neurons, and the output layer consists of 2 neurons and 2 hidden layers: 5 neurons in the first layer and 10 neurons in the second layer. To ensure that the MLCP topology reflects reality, the data was retrained 100, 500, and 1000 times. Accuracy (Acc), specificity (Spe), sensitivity (Sen), and F1 score (F1) were used as the performance criteria of the algorithm.
$$Acc = \frac{TP}{{TP + FN + FP + TN}}$$
$${\text{Sen}} = \frac{TP}{{TP + FN}}$$
$${\text{Spe}} = \frac{TN}{{TN + FP}}$$
$${\text{F}}1 = 2\frac{precision \times recall}{{precision + recall}}$$
Equation 1. (TP; true positive; TN; true negative; FP; false positive; FN; false negative).
ML algorithm analysis was performed using the Python 3.9 programming language and scikit-learn 1.1.1 framework, and ANN algorithm was performed using the Python 3.9 programming language and TensorFlow framework. A dropout method was used to prevent overfitting of the ANN model, and the value was set to 0.05. Among the ML algorithms, for the k-NN algorithm, the maximum depth was set to 5, criterion gini, min-samples-leaf 2, n-estimators 100, min-samples-split 2, criterion entropy 2, and k 5. We also evaluated the influence of the parameters on the overall results using the Shapley Additive Explains (SHAP) solver for the RF algorithm.
In this study, we used the CTGAN technique to evaluate the possible changes in accuracy values resulting from the number of data points. GTGAN is a type of generative adversarial network (GAN), which is a synthetic data generation method used for tabular or numerical data. This newly generated data exhibits similar characteristics to real data. This model is basically built with two main components: a generator and a discriminator. The generator component generates synthetic data, while the discriminator component adjusts how accurately this newly generated data reflects reality. This synthetic data generation method is used in situations where the amount of data is limited.35,36.
In this study, we used the CTGAN model to increase the number of original data points, increasing the number ‘n’ to ‘2n’. This means that 180 additional synthetic data points were created. While training the model, a batch size of 32 was used and epochs were set to 1000. The random noise vector size was 100, the number of hidden layers was 3, and the LeakyRELU function was used to activate the hidden layers.
Basic statistical analysis
The suitability of the parameters to a normal distribution was tested using the Anderson-Darling test. Contains the mean standard deviation value for data that fits a normal distribution and the median (minimum and maximum) values for parameters that do not fit a normal distribution. A two-sample T test was used for normally distributed data, and a Mann-Whitney U test was used for non-normally distributed data. The Minitab 17 package program was used for basic statistical analysis.
