A mathematical model for scientifically defining the class characteristics of the human anterior maxilla—Part 1: The dental arch

Bitemark recognition reliability in forensics has been criticized for lacking objectivity and empirical support. Despite doubts about classifying these injuries as bitemarks, pattern injuries must still be legally documented and analyzed. Forensic odontology can benefit from aesthetic dentistry by adopting metric analysis methods to define human dentition and objectively assess whether a pattern resembles a dental arch. In addition, past research on the challenges of individualizing bitemarks has inadvertently also defined these class characteristics. Although objectively quantifying these metrics is critical, prospective research must prove their uniqueness to the human species as well as their dependable transference to substrates such as skin. To explore and qualitatively define the mathematical characteristics of variations in the maxillary dental arch, an under-researched aspect of forensic odontology, two scanners collected digital maxilla scans from 100 participants (50% male, 50% female). The arch shape's intercuspal distance and parabolic curvature (y = ax² + bx + c) were defined, recorded, and analyzed. The mean intercuspal distance of maxillary canines was 33.8 mm (SD: 2.25 mm, 29.0–39.6 mm). The mean fitted curve created by Linear Mixed Model (LMM) for Quadratic Regression Analysis was a mean of y-mean_Total = 0.040x² − 0.0008x − 1.581, an upper limit of y-higher_Total = 0.047x² − 0.00039x + 2.593, and a lower limit of y-lower_Total = 0.032x² − 0.0012x − 5.754. In addition, sexual dimorphism using quadratic analysis was not established. Quadratic regression analysis establishes an objective framework for characterizing the maxillary dental arch. Results indicate that the arches of human dentitions share class characteristics within a narrow range, and can also offer a framework for the assessment of dentitions across species.