Mathematical Analyses of Dental Arch Curvature in Normal Occlusion

Abstract

Objective: To present a comprehensive mathematical analysis of dental arch curvature in subjects with normal occlusion. Materials and Methods: The materials studied were 40 sets of upper and lower plaster dental casts of subjects presenting with normal occlusion. The sample was equally divided into casts from male and female subjects with an age range from 18 to 25 years. Curve-fitting analyses was carried out and four main categories of functions were considered: the beta function, natural cubic splines, polynomial equations, and Hermite cubic splines. Results:The polynomial function (fourth order) was found to be a reasonable analysis when the objective is to describe the general smooth curvature of the dental arch, while a Hermite cubic spline is more appropriate when it is desired to track arch irregularities, such as evaluating treatment changes. Conclusions: Due to its advantage in providing a more naturally smooth curve, the fourth-order polynomial function may be used as a guide to fabricate customized arch wires, or even an entire fixed orthodontic appliance system.

Mathematical beta function formulation for maxillary arch form prediction in normal occlusion population

“…Unlike conic sections model, it has no inherent limitation of fitting the arch to specific shapes, and unlike other mathematical models, the beta function uses only two parameters and does not utilize the remaining dental landmarks. In fact, decreasing the number of pre-requisite measurements increases the error of curve fitting ability; but on the other hand, this decreases the possible irregularities of achieved curvatures [4]. As it is stated in the literature, the reduction in the amount of error should not be the only factor to be considered for selection of the preferred type of mathematical model.…”

“…The prediction or preservation of the dental arch form is important in orthodontic treatment, as for instance archform should not change greatly during orthodontic treatment, affecting long-term occlusal stability [2,3]. Arch form can be categorized into simple qualitative terms such as elliptic, parabolic, and U-shaped [4], which were inadequate to accurately define the dental arch form [4]. Investigators have, therefore, shifted toward more quantitative approaches including some linear measurements in describing the ideal arch form.…”

“…It has become clear that the models defined by only one parameter cannot describe the dental arch form accurately [4]. It has been shown that the human dental arch form is accurately represented mathematically by the beta function formulation using measures of the same arch, which provides an excellent generalized equation of the maxillary and mandibular arch shapes for each of the Angle classifications of occlusion [9].…”

Dental Arch Form Analysis in Gujarati Males and Females having Normal Occlusion

“…17 Despite their biological significance, conventional anatomic points do not provide clinical evidence of appropriate archwire blank forms. On the contrary, landmarks taken on the vestibular surface of the teeth [facial axis points (FA points)] give direct representation of clinical archwire shape 18 as these correspond fairly well to the position of the brackets for straight wire therapy.…”

Anthropometrical Parameters of the Orthognathic Bite in People of Uzbek Nationality

“…These casts are necessary for making a diagnosis and plan of treatment and also for determining the most appropriate type of orthodontic appliance [1]. When losing teeth, the re-creation of bite becomes problematic because parameters of the rows of teeth in correlation with proportions of the head, face and jaws in different ethnic groups are not determined in contemporary anthropomorphology and dentistry.…”