Maxillary arch perimeter prediction using Ramanujan's equation for the ellipse

<p>A New Method for Prediction of Dental Arch Perimeter</p>

“…Ricketts et al 25 found that the arch length increased by 1 and 0.25 mm for each 1 mm increase in the inter-canine and inter-molar distances, respectively, but their method of assessment was not published. Alternatively, a parabolic curve equation 26,27 and Ramanujan's equation for measurement of the ellipse 28,29 have also been proposed.…”

Correlation Between Maxillary Arch Perimeter of Pre and Post Orthodontic Study Models Using Ramanujan’s Equation for Perimeter of Ellipse.

“…Chung and Wolfgramm [6] stated that a 2mm expansion in inter-molar width resulted in 1.64mm expansion of intercanine width. They predicted 1.47mm increase of arch perimeter for every 2mm expansion of molar-width, this result is similar to results in this study of 0.684mm increase in arch perimeter.…”

“…Ricketts et al suggested guidelines state that each millimeter of canine expansion provides for a 1mm increase in arch perimeter, and that 1 mm of molar expansion increased the perimeter by 0.25 mm. [6] In a study performed by Adkins et al, it was concluded that changes in premolar arch-width were approximately 0.7 times the premolar expansion. [10] When the canine width and incisor positions were held constant, an initial 1mm increase in molar width produced approximately 0.27 mm increase in perimeter, the second millimeter produced an increase of 0.31 mm, and the fifth millimeter of molar width increase was related to a perimeter increase of 0.41 mm.…”

“…However, without accurate prediction of the arch perimeter to be gained 392 when proclining or expanding the arch in a borderline extraction patient, the orthodontist may underestimate the space gained and erroneously prescribe extractions that will then require excess space closure or, conversely, expect to gain more space and be unable to resolve the ALD. [6] Dental arch-form is an important element in orthodontic treatment and retention. During orthodontic treatment, excessive tooth movement over the basal bone may lead to periodontal complications and an unstable treatment effect.…”

To Measure the Perimeter of an Ellipse Using Image Processing and Mathematical Reasoning

“…Furthermore, the existing perimeter equations are too complex. Accordingly, various perimeter equations have been presented by researchers already [8][9][10][11][12]. The proposed approach attempts to find a predictive perimeter of an ellipse based on image processing via a pattern-based mathematical reasoning.…”