Maxillary and Mandibular Arch Perimeter Prediction Using Ramanujan's Equation for the Ellipse-In vitro Study

Aghera, Rahul; Desai, Hina; Sharma, P.; Dholakiya, Nirav; Agrawal, Nishil

doi:10.9734/bjmmr/2016/28868

Cited by 5 publications

(11 citation statements)

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“…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.…”

Section: Introductionmentioning

confidence: 99%

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

Al-Ansari¹,

Ameer²,

Nahidh³

2019

CCIDE

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Purpose: Dental arch length, width, and perimeter are considered to be important for the diagnosis and treatment of orthodontic cases. This study aimed to utilize dental arch width and length to create an equation for predicting dental arch perimeter. Materials and methods: Sixty-seven pairs of study models for patients with normal occlusion who received dental treatment were included in this study. Dental arch width at the level of the canines, first premolars, and first molars, in addition to dental arch length and perimeter, were measured using a digital vernier with 0.01mm accuracy. Data were subjected to step-wise regression analysis to determine the major predictors of arch perimeters and develop regression equations for both arches. The predicted arch perimeters were compared with the actual measured values using paired sample t-test. Results: For both arches, the perimeter showed a direct, moderate to strong, highly significant correlation with the length and width measurements. Findings from step-wise regression analysis indicated that there was a strong correlation between arch perimeter and the inter-canine width and arch length, which explained 67.7% of the variation in arch perimeter in the maxillary arch. In the mandibular arch, inter-molar width, inter-canine width, and arch length explained 55.1% of the variation in the dental arch perimeter. The arch perimeter values predicted from the developed equations were not significantly different from the actual values that were measured. Conclusion: New regression equations based on dental arch width and length at the level of the premolars, molars, and canines were developed to predict dental arch perimeters for both the mandibular and maxillary arches.

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Section: Introductionmentioning

confidence: 99%

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

Al-Ansari¹,

Ameer²,

Nahidh³

2019

CCIDE

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“…The fixed radius values of the symmetrical axes ( a , b ) were defined by the size of the chamber opening, which was 0.45 cm (CHM2 chamber diameter was 9 mm). Eqn 1 ( Figure 10 B ) is Ramanujan’s second approximation, 40 , 41 and Eqn 2 ( Figure 10 C ) was modified by us from the Knud-Thomsen approximation of ellipsoid surface area. 42 Eqn 2 ( Figure 10 C ) defines the surface area of a half-ellipsoid, SA tissue , which describes the relationships between all 3 axial radii, the ellipsoid equatorial perimeters, and the half-ellipsoid surface area.…”

Section: Methodsmentioning

confidence: 99%

“…( B ) Eqn 1 is Ramanujan’s second approximation. 40 , 41 ( C ) Eqn 2 was modified from the Knud-Thomsen approximation of ellipsoid surface area and defines the surface area of a semi-ellipsoid. 42 SA tissue describes the relationships between all 3 axial radii, the ellipsoid equatorial perimeters, and the half-ellipsoid surface area.…”

Section: Methodsmentioning

confidence: 99%

Claudin-18 Loss Alters Transcellular Chloride Flux but not Tight Junction Ion Selectivity in Gastric Epithelial Cells

Caron

Scott

Sinha

et al. 2021

Cellular and Molecular Gastroenterology and Hepatology

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Claudin-18 loss during Helicobacter pylori infection promotes neoplastic progression. This phenotype was not due to barrier dysfunction, because paracellular permeability was not affected by claudin-18 deletion but may be secondary to transcellular anion transporter expression/function in the absence of claudin-18. BACKGROUND & AIMS: Tight junctions form a barrier to the paracellular passage of luminal antigens. Although most tight junction proteins reside within the apical tight junction complex, claudin-18 localizes mainly to the basolateral membrane where its contribution to paracellular ion transport is undefined. Claudin-18 loss in mice results in gastric neoplasia development and tumorigenesis that may or may not be due to tight junction dysfunction. The aim here was to investigate paracellular permeability defects in stomach mucosa from claudin-18 knockout (Cldn18-KO) mice. METHODS: Stomach tissue from wild-type, heterozygous, or Cldn18-KO mice were stripped of the external muscle layer and mounted in Ussing chambers. Transepithelial resistance, dextran 4 kDa flux, and potential difference (PD) were calculated from the chambered tissues after identifying differences in tissue histopathology that were used to normalize these measurements. Marker expression for claudins and ion transporters were investigated by transcriptomic and immunostaining analysis. RESULTS: No paracellular permeability defects were evident in stomach mucosa from Cldn18-KO mice. RNAseq identified changes in 4 claudins from Cldn18-KO mice, particularly the upregulation of claudin-2. Although claudin-2 localized to tight junctions in cells at the base of gastric glands, its presence did not contribute overall to mucosal permeability. Stomach tissue from Cldn18-KO mice also had no PD versus a lumen-negative PD in tissues from wild-type mice. This difference resulted from changes in transcellular Clpermeability with the downregulation of Clloading and Clsecreting anion transporters. CONCLUSIONS: Our findings suggest that Cldn18-KO has no effect on tight junction permeability in the stomach from adult mice but rather affects anion permeability. The phenotype in these mice may thus be secondary to transcellular anion transporter expression/function in the absence of claudin-18.

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“…Aghera et al 4 conducted a study in which they compared the measured value of maxillary and mandibular arch perimeter with the calculated value using Ramanujan’s formula. They found Ramanujan’s equation used to calculate the arch perimeter with a 1.5% chance of error in the maxillary dental arch and a 1.7% chance of error in the mandibular dental arch.…”

Section: Introductionmentioning

confidence: 99%

“…It can also be used to predict change in the arch perimeter by molar expansion and incisor proclination. 4…”

Section: Introductionmentioning

confidence: 99%

Ramanujan’s Equation as an Aid to Predict Arch Perimeter Changes with Precision: A Retrospective Study

Antala

Iyengar

Desai

et al. 2022

J Indian Orthod Soc

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Introduction The aim of this study was to evaluate the validity of Ramanujan’s equation in measuring arch perimeter on untreated natural dentition models and their orthodontically corrected posttreatment models. The secondary objective was to apply the equation to predict the arch perimeter gained by the expansion of the molar teeth or proclination of the incisor teeth and compare it with the actual posttreatment arch perimeter changes. Methods 32 maxillary and mandibular (16 pretreatment and 16 posttreatment each) fairly aligned diagnostic casts of orthodontically treated nonextraction patients with class I molar relationships were used. The arch perimeter was measured using 0.012 mm stainless steel wire and was compared with the calculated arch perimeter obtained using Ramanujan’s equation. Pearson correlations were used to determine the correlation between the measured and predicted values. Paired t-tests were used to assess changes in different variables in the pre- and posttreatment study casts of maxilla and mandible. Results Positive correlation of 0.06 (90% CI) between predicted and measured values was found. In maxillary ( P = .04) study models, predicted arch perimeter by use of Ramanujan’s equation was more reliable than mandibular ( P = .74) study models. Conclusion Ramanujan’s equation can be an important aid to calculate the arch perimeter change by the expansion of molar teeth and proclination of incisor teeth 0.06 (90% CI). It is helpful for more accurate nonextraction treatment planning before the start of orthodontic treatment. In maxillary ( P = .04) study models, calculated arch perimeter using Ramanujan’s equation is even more reliable than mandibular study models ( P = .74).

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Maxillary and Mandibular Arch Perimeter Prediction Using Ramanujan's Equation for the Ellipse-In vitro Study

Cited by 5 publications

References 0 publications

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

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

Claudin-18 Loss Alters Transcellular Chloride Flux but not Tight Junction Ion Selectivity in Gastric Epithelial Cells

Ramanujan’s Equation as an Aid to Predict Arch Perimeter Changes with Precision: A Retrospective Study

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