# Cephalometric Evaluation of Facial Height Ratios and Growth Patterns: A Retrospective Cohort Study
## 1 Introduction  
Cephalometry, an essential diagnostic tool in orthodontics, allows for the evaluation of the relationship between skeletal, dental, and soft tissue components of the face. It is important to look at both the anteroposterior (AP) and vertical dimensions when determining the severity of a malocclusion, especially in the AP direction, which can affect changes in the vertical direction [1]. Facial growth, relative to the cranial base line, comprises horizontal forward development and vertical downward growth. Mandibular growth significantly influences facial development, with hypodivergent patterns observed in short faces and hyperdivergent patterns in long faces [2,3]. Various factors influence cranial development, leading to diversefacial morphologies. This variability in growth patterns underscores the multifactorial nature of cranial development, giving rise to diverse facial morphologies [4]. Orthodontic diagnosis emphasizes the anteroposterior connection between maxillary and mandibular apical bases. Vertical disharmonies are often accompanied by sagittal discrepancies in the jaw relationship. These can be found by carefully analyzing the linear and angular measurements of the skull [5]. Achieving appropriate vertical proportions during orthodontic treatment involves categorizing vertical facial forms into distinct categories, such as long, average, and short faces. [PERSON] observed clear associations between facial patterns and anterior vertical facial proportions, measured by parameters like anterior facial height (AFH) and posterior face height (PFH) [6]. The accurate diagnosis and evaluation of developing patients are imperative in orthodontics for effective therapy planning and prognostic assessments [7]. However, predicting individual facial growth remains a formidable challenge due to the inherent variability in growth direction and magnitude [8; 9]. Genetic and environmental influences on the craniofacial system further compound this challenge, necessitating the development of predictive models to infer dentoalveolar imbalance progression in line with growth principles [10; 11]. Genetic and environmental influences on the craniofacial system determine the complexity of growth pattern prediction [11]. Predictive models use relevant parameters to predict how the dentoalveolar imbalance will worsen over time based on growth principles [12]. Facial structure development involves variable growth vectors along the horizontal and vertical axes. Balanced growth along these axes is essential to prevent facial imbalances. Extreme facial forms result from disproportionate vertical development, such as in the long face syndrome [13]. A precise diagnosis considers the sagittal jaw-base relationship, as highlighted by [PERSON]'s classification of malocclusion in the late 19 th century. This classification system, still in use, categorizes occlusion based on the relationship between the first permanent molars. Linear measurements of the sagittal jaw-base relationship offer a more accurate diagnosis of anteroposterior discrepancies than angular measurements. Cephalometric assessments integrate both linear and angular measurements to determine treatment strategies [14]. The soft tissue paradigm, introduced in the 21 st century, emphasizes the role of soft tissue in orthodontic and orthognathic treatment planning. [PERSON]'s findings on vertical inter-maximillary correlations in the Caucasian population underscore the importance of cephalometric tests in understanding facial growth patterns. Thus, examining facial height ratios and growth patterns, as well as the relationship between the facial height ratio (FHR) and certain cephalometric angles, can help with diagnosis and treatment planning for a wide range of malocclusions [15]. Nowadays, cephalometric analysis typically uses computer-assisted analysis software to perform manual tracing. In cephalometric analysis, precise definitions of landmarks, operator calibration, and trace replication are all crucial.