a new concept of anatomic lingual arch form - luca lombardo forma d'arcata.pdf · a new...

ONLINE ONLY

A new concept of anatomic lingual arch form

Luca Lombardo,a Luca Saba,b Giuseppe Scuzzo,c Kyoto Takemoto,d Lola Oteo,e Juan Carlos Palma,f

and Giuseppe Sicilianig

Ferrera, Italy, Tokyo, Japan, and Madrid, Spain

Introduction: The aim of this study was to describe a natural and anatomic lingual arch form obtained fromsubjects with normal occlusion that could be used, with other criteria, in the construction of personalizedsetups for the lingual straight-wire technique. Methods: The study sample comprised 58 pairs of dental castsof the arches of 58 southern Europeans (37 women, 21 men) with ideal natural occlusions. After the referencepoints of the dental arches were identified and marked, the dental casts were scanned. The exact position ofthe models on the scanner was established by using an acetate sheet with a Cartesian reference system. Foreach image, 14 reference points (x, y) were measured and recorded. The measurements were processed withsoftware to select the polynomial function that best described the shape of the dental arches. The ninth-degree polynomial function was selected to represent the lingual arch form of both arches. Distributionanalysis of the x and y values of each tooth in each arch resulted in the creation of 3 groups (small,medium, and large) to verify the most appropriate measures of the central tendencies of our data. Results:Statistical analysis showed no significant sex difference in the medians of the 6 parameters used to measuredepth and width in both arches. A representation of the variability of the lingual curve of our sample wascreated to document at least 3 sizes of the representative curve of the central tendency for our data. Nostatistically significant differences in shape were found between men and women, considering the mediansas a measure of the central tendencies. Conclusions: Three lingual curves (small, medium, and large) forthe maxillary and mandibular arches, representing the mean values of our sample, were developed and canbe used as guides for the setup in the lingual straight-wire technique. (Am J Orthod Dentofacial Orthop2010;138:260.e1-260.e13)

The form of the dental arch is considered a funda-mental element in orthodontic diagnosis andtreatment planning because of its ability to influ-

ence not only available space and dental and smileesthetics, but also long-term occlusal stability.1-7

Furthermore, respecting this important parameterreduces the possibility of crowding relapse andperiodontal damage.5,8 Moreover, definition of theshape of the arch aids the clinician in achievingresults that agree with the natural laws of biologic

aResearch assistant, Department of Orthodontics, University of Ferrara, Ferrara,

Italy.bResident, Department of Orthodontics, University of Ferrara, Ferrara, Italy.cAdjunct Professor, Department of Orthodontics, University of Ferrara, Ferrara,

Italy.dAdjunct Professor, Department of Orthodontics, University of Ferrara, Ferrara,

Italy.eProfessor, Department of Orthodontics, University Complutense, Madrid,

Spain.fAdjunct Professor, Department of Orthodontics, University Complutense,

Madrid, Spain.gChairman, Department of Orthodontics, University of Ferrara, Ferrara, Italy.

The authors report no commercial, financial, or proprietary interest in the prod-

ucts or companies described in this article.

Reprint requests to: Luca Lombardo, Contrada Nicolizia, 92100 Licata, AG,

Italy; e-mail, [email protected].

Submitted, October 2009; revised and accepted, April 2010.

0889-5406/$36.00

Copyright � 2010 by the American Association of Orthodontists.

doi:10.1016/j.ajodo.2010.04.022

variability.1,5 Andrews,9 father of the labial straight-wire technique, cited the arch form as the seventh ofhis keys to achieving Class I occlusion. Hence, in recentdecades, numerous studies have analyzed the arch formfrom anatomic and anthropologic perspectives10-16 toevaluate its implications in orthodontic therapy17-21 orits modifications after orthodontic treatment.18,22-25

Even though the necessity of individualizing eachpatient’s arch form during treatment is widely recog-nized, after the evolution of labial straight-wire appli-ances and because of the superelastic properties of thelatest generation of archwires, it seems to be clinicallyreasonable to stereotype the constructed arch shapesfrom subjects with normal occlusion into a few sets ofpreformed arches.1,5 The most similar to that of thepatient before treatment could therefore be selected onthe basis of geometric similarity, ethnicity, and type ofmalocclusion.1,3-5 Nevertheless, no objective study hasthus far elucidated the choice of a particular archform,3 although various studies have sought, by usingthe incisal and occlusal margins of the teeth as anatomicreference points, to represent it graphically from thelabial side.1-6,24,25 Numerous authors used geometriccurves to describe the dental arch.24-35 Moreover,various authors have observed that polynomialfunctions can simply and symmetrically describe theshape of the dental arch, and have exploited these

260.e1

mailto:[email protected]

260.e2 Lombardo et al American Journal of Orthodontics and Dentofacial Orthopedics

September 2010

mathematic equations as an accurate method for itsdescription.2,12,24-35

Many articles in the literature have dealt with theshape of the dental arch from the labial perspective,although nothing has yet been published regardingthe lingual side. Many systems for representing thenormal arch form have been proposed, including quali-tative descriptions, geometric constructions, and mathe-matic curves; although there is consensus on theimportance of this factor in orthodontics, a definitivegeometric shape is elusive, as demonstrated recentlyby Trivino et al.2

However, the introduction of the straight-wire to thelingual technique36 and the possibility of replacingFujita’s ‘‘mushroom form’’37 with an arch form withoutinsets has led to the question of which arch form tochoose and which criteria to use in the lingualstraight-wire setup and treatment planning. Becausea ‘‘straight’’ arch form has not previously been de-scribed from a lingual perspective and this is fundamen-tally important in orthodontic treatment planning, in thisstudy it is described with an objective, standardized, andreproducible methodology: a natural and anatomic archform obtained from subjects with normal occlusion.This can be used, with other criteria, in the constructionof personalized setups for the lingual straight-wiretechnique.

MATERIAL AND METHODS

The sample was carefully selected from the recordsof the University of Ferrara Postgraduate School ofOrthodontics in Italy and the Department of Orthodon-tics at the Complutense University of Madrid, Spain. Itincluded southern European white adults with thefollowing characteristics2,26: (1) age not less than 18years (range, 19.08-70.25 years); (2) no previousorthodontic treatment; (3) regular arch form with littleor no crowding; (4) complete dentition up to at leastthe second molars; (5) no extensive restoration andimplants; (6) at least 4 of the 6 Andrews’ keys9 foroptimal occlusion and bilateral Class I molar and caninerelationship; (7) normal (within 2 6 1 mm) overbite andoverjet; (8) no deviations of the interincisal lines; (9) nogingival recession; (10) no muscular or joint patholo-gies; (11) no ectopic teeth, tooth aplasia, or anomaliesin tooth shape; (12) no supernumerary or congenitallymissing teeth; (13) no anterior or posterior crossbite;(14) no visible intraoral or extraoral asymmetry; and(15) minimal diastemas, premolar rotations, and incisorirregularities (present in several subjects). Each subjectparticipating in the study gave informed writtenconsent.

Mandibular and maxillary dental casts of each sub-ject, according to Tweed prescriptions, were obtained,for a total of 75 pairs. The regularity of these modelswas first determined clinically and then quantified byusing Little’s irregularity index38; 9 pairs of modelshad a value greater than 3 and were therefore excluded,as were a further 8 pairs, which, although having a valueless than 3, had spaces greater than 1 mm or a slightlyasymmetrical contraction of the arch in the premolararea. Thus, the definitive sample comprised 58 pairsof dental casts of the arches of 58 white subjects (37women, 21 men) of southern European ancestry (mainlyItalian and Spanish). The mean age of the sample was29.21 years (SD, 8.73 years); the youngest was 19.08,and the oldest was 70.25 years of age.

Reference points for calculation of the shape of thearch were identified and marked on the lingual surfaceof each tooth (from the left second molar to the rightsecond molar) of each dental cast by 1 operator (L.S.)using an indelible marker (.08-mm Pilot drawing pen;Pilot Corp., Tokyo, Japan). In the mandibular arch, thesepoints, which trace the lingual straight plane, were situ-ated at the center of the clinical crown (vertical position)along the central lingual axis and at the most prominentpoint on the lingual surface of each tooth (horizontal po-sition) on the molars and premolars and correspondingto the middle third of the anterior teeth. In the maxillaryarch, the reference points were marked at the mostprominent point on the lingual surface of each tooth(horizontal position) at the intersection between themiddle third and the gingival third of the anterior teeth,along their central axes, and at the center of the clinicalcrown of the posterior teeth. Before permanently mark-ing these points on the lingual surface, the median axisof the clinical crown of each tooth was traced in pencilto determine its horizontal position, and a gauge wasused to measure the height of the clinical crown to de-termine its vertical position. Although the same opera-tor carried out this procedure for each tooth, it was animportant source of error, because the accuracy of iden-tification of the reference points necessarily influencesthe tracing of the curves on which the calculations ofarch shape are based.33

After the reference points had been marked, the den-tal casts were scanned with an Expression 1680 Proscanner (Epson, Cinisello, Balsamo, Italy), and imagesin TIF format at a resolution of 300 dpi were obtained.To avoid distortion of the image, and hence the referencepoints, during the scanning procedure, the models werepositioned so that both the base and the occlusal planewere parallel to the scanner’s surface.39 The exact posi-tion of the models on the scanner was established witha specially created acetate sheet onto which a sheet of

Fig 1. Cartesian system and reference points (black) used to establish lingual dental arch form; eachpoint is described by a copy of x and y coordinates: x measurements, distance between the referencepoint and the y-axis; y measurements, distance between the reference point and the x-axis.

American Journal of Orthodontics and Dentofacial Orthopedics Lombardo et al 260.e3Volume 138, Number 3

millimeter paper had been photocopied. After the photo-copies were made, the prepared acetate and millimeterpapers were superimposed to verify the lack of distortionin the acetate copy. On this acetate sheet, referenceaxes—a horizontal line and a perpendicular verticalline—were drawn with an indelible marker (.05-mm Pi-lot drawing pen). The sheet was subsequently placed onthe glass surface of the scanner under the plaster modelsto align the posterior margin of the second molars withthe abscissa and the median line with the ordinate,thus creating a Cartesian reference system (Fig 1).2

For each image, 14 reference points, correspondingto the distance between each reference point and theabscissa and ordinate were measured and recorded toprovide their Cartesian coordinates (x, y).

Four weeks later, to calculate the method error, 15models were selected at random, and the coordinatesof each reference point on both arches were replottedby the same operator as above. Analysis of the reliabil-ity of measurements was performed by using Dahl-berg’s coefficient,40 Se 5 O

Pd2/2n, where S is the

Dahlberg coefficient, d is the difference between thefirst and second measurements, and n is the number ofrepeated measurements.

The values corresponding to the coordinates of thecentral and lateral incisors and the second premolarswere compared singly with their control measurements.The statistical significance was evaluated by using theStudent t test for paired data. The systematic error ofmeasurement of each value considered was shown tobe not significant at P 5 0.05, thereby confirming thereliability of the results.

First, the dimensions of both dental arches wereevaluated via 3 transversal and 3 sagittal measurements:the transverse diameters and arch depths at the canines,first molars, and second molars, as described by Raberinet al.6 The lingual reference points considered were (1)the interincisor point; (2) the most prominent point onthe central axis of the lingual surface of the canine

crown; (3) the most prominent point on the lingual sur-face of the first molar at the center of its clinical crown;and (4) the most prominent point on the lingual surfaceof the second molar at the center of its clinical crown.

Thus, 6 measurements of distance were taken foreach arch to analyze their width and depth. To measurearch width, the following were considered: intercaninediameter (D3), intermolar diameter at the first molars(D6), and intermolar diameter at the second molars (D7).

To measure the arch length, the following were con-sidered: (1) canine depth, the distance between the inter-incisor point and the line connecting the caninereference points (L3); (2) molar depth at the first molars,the distance between the interincisor point and the lineconnecting the reference points on the first molars(L6); and (3) molar depth at the second molars, thedistance between the interincisor point and the line con-necting the reference points on the second molars (L7).

Subsequently, the shape of the dental arch was eval-uated from the lingual side. The measurements (x and ycoordinates) of each reference point were all obtainedand processed by using Curve Expert software (version1.3, http://curveexpert.webhop.biz) by the same opera-tor. This software was used to select the polynomial func-tion that best described the shape of the dental arches.

After the dental arches were viewed and thepresence of slight asymmetry was established, eventhough patients with normal occlusion had been usedas models, the reference point coordinates of the 58dental casts were divided into the left and right sides.

Each arch half, described by 7 reference points (7 xand y coordinates), was then ‘‘mirrored’’ to obtain 116whole maxillary and 116 whole mandibular archeswith symmetrical curves.2

Based on the number of reference points (7 for eachsemiarch mirrored) and after the graphs obtained of thevarious mathematical functions were viewed, the ninth-degree polynomial function was selected to representthe lingual surfaces of both arches.

http://curveexpert.webhop.biz

Table I. Descriptive statistics of the 6 parameters used to measure dental arch depth and width by arch and sex

Mean Median Minimum MaximumPercentile

25Percentile

75 SD

Mandibles in men

D3-3 21.2 21 18 26 20 22 1.928

D6-6 32.7 32 28 42 30 34 3.034

D7-7 38.5 38 30 48 36 40 3.783

L3 4.1 4 2 6 4 5 0.899

L6 25.2 25 22 30 24 26 1.914

L7 35.3 355 31 42 34 37 2.472

Mandibles in women

D3-3 21.0 20 18 26 20 22 1.826

D6-6 33.4 34 30 40 32 36 2.399

D7-7 39.6 40 34 48 38 42 3.153

L3 4.1 4 2.5 8 4 5 0.871

L6 25.2 25 21 31 24 26 1.960

L7 35.1 35 30 43 33 36 2.647

Maxillae in men

D3-3 27.1 26 24 34 26 28 2.510

D6-6 36.7 36 30 50 34 38 3.502

D7-7 42.2 42 34 52 40 44 3.769

L3 6.9 7 4 9 6 8 1.173

L6 29.3 30 22.5 41 28 30.5 2.870

L7 38.5 39 32 48 37 40 2.987

Maxillae in women

D3-3 26.6 26 22 34 24 28 2.447

D6-6 36.9 36 29 46 34 38 3.367

D7-7 42.4 42 34 50 40 46 4.028

L3 6.6 7 5 9 6 7 1.035

L6 28.9 29 25 34 27 30 2.193

L7 42.1 39 33 41 36 40 3.328

D3-3, Intercanine diameter; D6-6, intermolar diameter at the first molars; D7-7, intermolar diameter at the second molars; L3, canine depth;

L6, depth at the first molars; L7, depth at the second molars.


September 2010

This polynomial function yielded the curve mostrepresentative of the shape of the lingual dental arch.It was first selected according to visual inspection crite-ria, and then, to confirm this choice objectively, wedetermined which marker could be considered to estab-lish the suitability of the model.2,6 With the residualanalysis, we ascertained whether the observed valuesfell outside the trend of the expected curve.

The residual plot graphically depicts the differencebetween the data points and the model evaluated atthe data points. The residual at point i is defined byresidual 5 yi – f(xi), where yi is the measured value atxi, and f(xi) is the predicted value at xi. These distancesare shown as bars or points on the residual plot; the mag-nitudes of the data points are simply replaced by theresidual defined above. If the residual is positive, thenthe data point is above the model’s prediction; if theresidual is negative, then the data point is below themodel’s prediction. The residuals can provide an indica-tion of a particular model’s performance. If there areruns of like-signed residuals, then a better model forthe data is likely to exist.

Optimally, the residuals should show a randomscatter around zero, which indicates that the data pointsare randomly distributed around the curve. A ‘‘run’’ isa sequence of like-signed residuals, which stand outon the residual plot. A large number of runs indicatesthat the data systematically deviate from the curve.

The critical reference measurement for a residualvalue is usually 1.96. If this value is exceeded at 1 pointor more, the fit is unacceptable, and adaptations must bemade. The measurement error was compared with thestandard error values of various models to ascertainwhich model better interpolated the data—ie, that char-acterized by the lowest standard error was consideredthe best; in our case, it was the ninth-degree polynomial.

The standard error was calculated with minimiza-tion of the so-called merit function (http://mathworld.wolfram.com/MeritFunction.html).

Statistical analysis

The sample was initially subjected to descriptivestatistical analysis including mean, standard deviation,variance, minimum, and maximum values.

http://mathworld.wolfram.com/MeritFunction.html

http://mathworld.wolfram.com/MeritFunction.html

Table II. Results of the Mann-Whitney nonparametric U test used to evaluate the sex differences of the 6 parametersused to measure dental arch depth and width

VariableRank sum for

womenRank sum for

men U P valueN validwomen

N validmen

Mandible

D3-3 4273.5 2512.5 1498.5 0.752040 74 42

D6-6 4584 2202 1299 0.143744 74 42

D7-7 4598 2188 1285 0.122974 74 42

L3 4156 2630 1381 0.321717 74 42

L6 4272 2514 1497 0.745508 74 42

L7 4163 2623 1388 0.341744 74 42

Maxilla

D3-3 4158.5 2627.5 1383.5 0.328780 74 42

D6-6 4387 2399 1496 0.741164 74 42

D7-7 4401.5 2384.5 1481.5 0.679161 74 42

L3 4083 2703 1308 0.158455 74 42

L6 4132.5 2653.5 1357.5 0.260194 74 42

L7 4146 2640 1371 0.294463 74 42

D3-3, Intercanine diameter; D6-6, intermolar diameter at the first molars; D7-7, intermolar diameter at the second molars; L3, canine depth;

L6, depth at the first molars; L7, depth at the second molars.

Significance level, P \0.05.


The analysis of sexual dimorphism was carried outwith a comparative analysis of the lingual distancesD3-3, D6-6, D7-7, L3, L6, and L7 to verify whetherthere were statistically significant differences betweenthe measures of the central trend in the men and women.Due to the abnormal distribution of data, the nonpara-metric Mann-Whitney U test was applied to comparethe 2 independent groups.41

To provide a visible representation of a hypotheticalideal arch form curve, first the means and standarddeviations of the 14 coordinates of the abscissa andordinate were calculated for all curves relative to the lin-gual sides of both arches. Three groups—small,medium, and large—were created by a distributionanalysis of the x and y values of each tooth in eacharch to verify the most appropriate measure of the cen-tral tendencies for our data. It was verified that all x andy values were characterized by strongly nonnormal,asymmetrical, and unimodal distributions. This led usto choose the median value as the reference measureof the central tendency, and then the values of the25th (first quartile) and 75th (third quartile) percentilesas measures of variability. Assuming that the medianwas an adequate representation of the measure of thecentral tendencies for the medium group, the measuresof the central tendency for the small and large groupswere identified. The objective was to identify 3 curves,corresponding to the 3 groups, that interpolated themeasures of central tendency in a parallel fashion. Be-cause of the many anomalous values and the variabilitythat characterized each tooth, it was not possible to

consider the first and third quartiles as measures of thecentral tendency for each tooth in the small and largegroups. Hence, the coordinates characterized by theminimum variability (x7, y1) were considered, anda maximum deviation around the median equal to 1mm in both arches was identified. Thus the followingmeasures were obtained.

Central tendency for x7 small 5 median (x7) – 1.Central tendency for x7 large 5 median (x7) – 1.Central tendency for y1 small 5 median (y1) – 1.Central tendency for y1 large 5 median (y1) – 1.

Thus, the central tendency of the small and largegroups for the other coordinates were obtained, apply-ing the 1-mm displacement to the median of all x andy values. In this way, constant ‘‘distances’’ along allpoints of the mouth between the central tendency mea-sures of the medium group and those of the small andlarge groups were created.

RESULTS

The descriptive statistics of each of the 6 parametersused to measure depth and width, subdivided by archand sex, are reported in Table I. The values for mean,median, minimum, maximum, 25th percentile, 75th per-centile, and standard deviation are also reported.

The results of the Mann-Whitney nonparametric Utest are reported in Table II. The P values show nosignificant statistical sex difference for the mediansmeasured in both arches.

Table III. Descriptive statistics of the values of the coordinates of the reference points for the 2 arches

MinimumPercentile

25 MedianPercentile

75 Maximum Mean

Mandible

1X �24 �20.5 �19 �19 �15 �19.67

2X �21 �17 �16 �16 �14 �16.58

3X �18 �15 �14.25 �14 �12 �14.62

4X �16 �13 �13 �12 �11 �12.78

5X �13 �11 �10 �10 �9 �10.53

6X �8 �7 �7 �6 �5.5 �6.84

7X* �4 �3 �2 �2 �2 �2.45

1Y* �7 �5 �4.5 �4 �3 �4.40

2Y �17 �15 �14 �13.5 �11 �14.31

3Y �28 �24 �23 �22 �19 �23.01

4Y �36 �30 �29 �28 �24.5 �29.19

5Y �44 �37 �35 �34 �30 �35.42

6Y �46 �40 �38 �36 �33 �38.15

7Y �47 �41 �39 �37.5 �34 �39.56

Maxilla

1X �26 �22.75 �21 �20 �17 �21.12

2X �25 �19 �18 �17 �14.5 �18.46

3X �22 �17.25 �16 �15.75 �13.5 �16.55

4X �20 �15 �14 �13.5 �12 �14.33

5X �17 �14 �13 �13 �11 �13.4

6X �12 �10 �10 �9 �7 �9.65

7X* �5 �4 �4 �3.5 �2 �3.85

1Y* 3 4 4 3.5 2 4.09

2Y 10 13 13 14 17 13.21

3Y 18 21 22 23 29 22.25

4Y 24 27 29 30 35 28.79

5Y 27 34 35.5 37 44 34.89

6Y 35 38 40 42 50 40.25

7Y 37 40 42 44 52 42.32

*These coordinates varied the least.


September 2010

Initially, a simple graphic representation of the lin-gual side of the arch form was obtained by using themeans and standard deviations of the coordinates forthe maxillary and mandibular arches, respectively.Subsequently, a representation of the variability of thelingual curve of our sample was created to documentat least 3 sizes of the representative curve.

Table III documents the descriptive statistics of the 14coordinates corresponding to the reference points used todescribe the curves that best represent the shapes of thearches, respectively. Figure 2 depicts the data in TableIII; it is possible to observe the difference in variation ofthe coordinates. Thus, the x and y coordinates that variedthe least were considered, as shown in Table III. Afteridentifying 1 mm as the constant measure to be subtractedand added to the median measures, the central tendenciesrelative to the small and largegroups were obtained, as de-scribed in Table IV. Figure 3 shows the 3 curves, large,medium, and small, superimposed onto the scatter plot.

Figure 4 displays the values of all coordinates relativeto both arches for each group (large, medium, and small)and the corresponding curves. The values reported in

Table IV were determined by the Curve Expert softwareto visualize the ninth-degree polynomial curve that inter-polates the points relative to the large, medium, and smallgroups, respectively. Figure 5 illustrates the 3 representa-tive curves describing the arch forms from the lingualside in the mandibles and the maxillae of our sample.At this point, the presence or absence of differences inshape between the arches and between the sexes wasverified, considering the medians as a measure of centraltendencies. The Mann-Whitney U test was used to com-pare the central tendencies (medians) of the 2 arches(Table V) and the 2 sexes (Table VI). Table V showsthe significant differences between the medians of the 2arches. For instance, the median of x1 in the maxillaryarch (21) was significantly greater (P \0.000) than thecorresponding measurement in the mandibular arch(19). Likewise, the median of y1 in the maxillary arch(4) was significantly lower (P 5 0.002) than that mea-sured in the mandibular arch (4.5), and so on.

No statistically significant differences were foundbetween the central tendencies of the sexes as shownin Table VI.

Line Plot of multiple variableDescriptive.sta 6v*14c

X1 X2 X3 X4 X5 X6 X7 Y1 Y2 Y3 Y4 Y5 Y6 Y7-50

-40

-30

-20

-10

0

Minimum Percentile 25% Median Percentile 75% Maximum Mean

1X 2X 3X 4X 5X 6X 7X 1Y 2Y 3Y 4Y 5Y 6Y 7Y-30

-20

-10

0

10

20

30

40

50

60

Minimum Percentile 25% Median Percentile 75% Maximum Mean

Fig 2. Difference in variation of the measures of central tendency of the coordinates of the referencepoints: A, mandibular arch; B, maxillary arch. In the x-axis are reported the coordinates (7X and 7Y),and in the y-axis is reported the range of variation in values of the coordinates for the maxillary andmandibular arches (Table I).


DISCUSSION

Many studies in the literature document analyses ofthe shape of the dental arches, with different methodol-ogies, of similar samples of healthy subjects withnormal occlusion to obtain clinical data pertinent tothe labial edgewise technique.1-6,10-16 All of these

authors concluded that it was impossible to represent1 ideal arch form.

However, in the literature, no study has reported ref-erence points to describe the dental arch from the lin-gual perspective. The introduction of straight-wireconcepts to the lingual technique has led clinicians to

Table IV. Median central tendencies of the 3 groups

Large Medium Small Side

Mandible

1X �20 �19 �18 L

2X �17 �16 �15 L

3X �15.25 �14.25 �13.25 L

4X �14 �13 �12 L

5X �11 �10 �9 L

6X �8 �7 �6 L

7X �3 �2 �1 L

1Y �5.5 �4.5 �3.5 L

2Y �15 �14 �13 L

3Y �24 �23 �22 L

4Y �30 �29 �28 L

5Y �36 �35 �34 L

6Y �39 �38 �37 L

7Y �40 �39 �38 L

1X 20 19 18 R

2X 17 16 15 R

3X 15.25 14.25 13.25 R

4X 14 13 12 R

5X 11 10 9 R

6X 8 7 6 R

7X 3 2 1 R

1Y �5.5 �4.5 �3.5 R

2Y �15 �14 �13 R

3Y �24 �23 �22 R

4Y �30 �29 �28 R

5Y �36 �35 �34 R

6Y �39 �38 �37 R

7Y �40 �39 �38 R

Maxilla

1X �22 �21 �20 L

2X �19 �18 �17 L

3X �17 �16 �15 L

4X �15 �14 �13 L

5X �14 �13 �12 L

6X �11 �10 �9 L

7X �5 �4 �3 L

1Y 5 4 3 L

2Y 14 13 12 L

3Y 23 22 21 L

4Y 30 29 28 L

5Y 36.5 35.5 34.5 L

6Y 41 40 39 L

7Y 43 42 41 L

1X 22 21 20 R

2X 19 18 17 R

3X 17 16 15 R

4X 15 14 13 R

5X 14 13 12 R

6X 11 10 9 R

7X 5 4 3 R

1Y 5 4 3 R

2Y 14 13 12 R

3Y 23 22 21 R

4Y 30 29 28 R

5Y 36.5 35.5 34.5 R

6Y 41 40 39 R

7Y 43 42 41 R

L, Left; R, right.


September 2010

pose the important questions of which form should beused in setting up indirect bonding and according towhich criteria.36 Thus, from our sample of 58 subjectswith normal occlusion, we described, with an objective,standardized, and reproducible method, a natural archform for the lingual straight wire that can be used asa guide, along with other criteria, for the personalizedsetup; this is fundamentally important in the lingualtechnique.42-44 Adults were therefore selected so thatthe influence of growth on the arch form wasminimized, although not entirely excluded, since theliterature suggests that alterations can also occur inadulthood.15

In the literature, there is great diversity in the refer-ence points that authors used to evaluate and describe thesize and shape of the arches; most previous studies usedconventional anatomic reference points such as the inci-sal margin for the anterior teeth and the cusps of the ca-nines, molars, and premolars,6,12,34,45,46 whereas otherschose the contact points,47 the edge of the alveolarbone,1 the mesiodistal diameters of the teeth,1,2 andcranial structures.2 Despite their anatomic significance,however, these points cannot provide a clinical represen-tation that could feasibly be used as an arch form guide.In contrast, reference points on the surface of the teeth(FA points) are a direct representation of the clinicalarch form that can serve as a template for the manufac-ture of archwires for orthodontic treatment.1-3,9,26,30,31

As in studies analyzing arch forms from a labialperspective, the reference points in this study wereselected according to Takemoto and Scuzzo,36 so thatthe FA points could provide a direct clinical representa-tion of the shape of the lingual side of the arch.3,9,26

After the reference points were identified, we eval-uated the forms and dimensions of the lingual side ofthe arch according to a method previously describedby Trivino et al2; likewise, an article by Raberin et al6

was used as a reference for the dimensional evaluation.Not surprisingly, the results of descriptive analysis ofthe mean values relative to the width and depth of thearches were lower that those regarding the labial sidereported by Raberin et al6 and other authors13,19

because the reference points considered were on thelingual surfaces of the arches, which necessarily havea smaller circumference. Thus, a direct comparisonwith other studies could not be made.

The results of this study of possible sexual dimor-phism in the diameters between the intercanine, inter-first molar, and inter-second molar diameters, and thedepth of the arch on the lingual side showed no statisti-cal differences between the medians in men and womenin either arch. These results contrast with previous re-ports that document evident sex dimorphism in

Fig 3. Three curves (not mirrored): A, mandibular arch; B, maxillary arch. Large, medium, and smallare superimposed on the scatter plot. In the x-axis is reported the range of variation of values of the xcoordinates, and in the y-axis is reported the range of variation of values of the y coordinates.


dimension (men have wider arches than women, withmore marked differences generally seen in the inter-first molar than the intercanine and inter-second molardiameters).6,12,26,31 This difference is probably due tothe choice of reference points on the lingual sides ofthe teeth, which excluded the dimensional differencesin the buccolingual diameter of the molars thatpresumably exist between the sexes, and have been

documented in anthropologic studies on the shape ofthe arch by Ferrario et al.11,12

To obtain an accurate graphic representation of theshape of the lingual arch, in this study, the curves thatinterpolated the measure of the central tendency asprecisely as possible were used. By using Curve Expertsoftware, the median values of the x and y coordinatesof our sample were interpolated with various

X

Y

-25 -20 -15 -10 -5 0 5 10 15 20 25-45

-40

-35

-30

-25

-20

-15

-10

-5

0

LARGEMEDIUMSMALL

X

Y

-20 -10 0 10 200

10

20

30

40

50

LARGEMEDIUMSMALL

Fig 4. Central tendencies relative to the values (mirrored): A, mandibular arch; B, maxillary arch.In the x-axis is reported the range of variations of values of the x coordinates, and in the y-axis isreported the range of variations of values of the y coordinates.


September 2010

polynomial curves, from the fourth to sixth degrees,as described in the literature.2,12,30-35 The mostappropriate curve was first determined by visualmeans, taking into account the regularity of the shapeof the curve and its proximity to the values of themedian of the coordinates.2 Subsequently, to confirmthis visual assessment objectively, it was determinedwhich markers to consider to establish the goodness-of-fit of our curve. Residual analysis permitted us toverify whether the observed values fell outside theexpected curve. The measurement error was calculated

by using the standard error method in the Curve Expertsoftware manual.

The polynomial function characterized by the low-est standard error was that of the ninth degree, and,even though it had not previously been described inthe literature, it was adopted to represent the shape ofthe arches from the lingual side. The anterior portionof this curve is considerably flattened in correspondenceto the frontal group and fairly straight toward the poste-rior; it is reminiscent of the ‘‘flat form’’ of Raberin et al6

and the ‘‘Form B’’ of Trivino et al2 to describe the labial

Fig 5. Mandibular and maxillary lingual dental arch forms for natural, normal occlusion in small,medium, and large sizes.

Table V. Mann-Whitney nonparametric U test used to evaluate differences in shape between the arches

Median forthe mandible

Median forthe maxilla U P value

N validlower

N validupper

1X 19* 21* 3817* 0 116* 116*

1Y 4.5* 4* 5183* 0.0025 116* 116*

2X 16* 18* 2463.5* 0 116* 116*

2Y 14* 13* 3552.5* 0 116* 116*

3X 14.25* 16* 2136.5* 0 116* 116*

3Y 23* 22* 4968* 0.0006 116* 116*

4X 13* 14* 2358* 0 116* 116*

4Y 29 29 6061 0.1923 116 116

5X 10* 13* 420* 0 116* 116*

5Y 35 36 6553 0.7328 116 116

6X 7* 10* 108.5* 0 116* 116*

6Y 38* 40* 3853.5* 0 116* 116*

7X 2* 4* 750.5* 0 116* 116*

7Y 39* 42* 3165.5* 0 116* 116*

*Significant at P \0.05.


side of the arch. This shape is probably attributable tothe choice of reference points on the lingual surfaces,which annul the difference in buccolingual diameter be-tween the teeth in the anterior and posterior sections.Three groups, small, medium, and large, were created;the 3 sizes allowed more accurate individualization offorms and dimensions, since our objective was to de-scribe a natural and anatomic arch form from subjectswith normal occlusion that, we hope, can be used,

with other criteria, in the construction of personalizedsetups for the lingual straight-wire technique, thus re-ducing errors in the selection of the best initial dentalarch form for a patient. To this end, a distributive anal-ysis of the x and y values for each tooth was performedto determine the measure of the central tendency mostappropriate for our data. The aim of our research wasto identify 3 curves, corresponding to the 3 groups(small, medium, and large) that could interpolate the

Table VI. Mann-Whitney nonparametric U test used to evaluate differences in shape between the arches of the sexes

Median forthe mandible

Median forthe maxilla U P value

N validwomen

N validmen

1X 20 20 5840 0.6220 152 80

1Y 4 4 5893.5 0.7019 152 80

2X 17 17 5753 0.5016 152 80

2Y 14 14 5661.5 0.3896 152 80

3X 15.75 15 5770 0.5241 152 80

3Y 22 23 5617.5 0.3417 152 80

4X 13 13 5913.5 0.7326 152 80

4Y 29 29 5419.5 0.1744 152 80

5X 12 12 5907.5 0.7233 152 80

5Y 35 36 5561.5 0.2864 152 80

6X 8 8 5885 0.6889 152 80

6Y 39 39.5 5584 0.3078 152 80

7X 3 3 6026.5 0.9131 152 80

7Y 40.5 42 5584.5 0.3083 152 80


September 2010

measures of the central tendencies to represent our sam-ple. Because of many anomalous values and the vari-ability that characterized each tooth, it was decidedarbitrarily to consider the coordinates characterized byminimum variability (x7, y1); we identified a maximumdeviation around the median equal to 1 mm in botharches.

When we analyzed the differences in shape, weconsidered the values of the medians of our coordinates,and no significant differences between the arches ineither sex were found. This finding agrees with thoseof Ferrario et al,11 who found no sexual dimorphism be-tween the arches when evaluated via Euclidean distancematrix analysis, and Camporesi et al,26 who reached thesame conclusions using thin-plate spline analysis, a mor-phometric system. The samples examined in these 2studies, like ours, included subjects with natural idealocclusion from southern Europe, and thus the studiesare comparable. Other investigators found significantmorphologic differences in the shape of the labial archamong different ethnic groups; this is a possible topicfor future research into the shape of the dental archfrom the lingual side.4,48 Our results should beconsidered specific only for European populations inthe Mediterranean area.

CONCLUSIONS

We analyzed the shape of the lingual sides of themaxillary and mandibular dental arches in a sample ofadults from southern Europe with natural ideal occlu-sions. Analysis of the shape of the arches calculatedfrom the lingual side indicated the following.

1. There is no sexual dimorphism for the dimensionsof the lingual diameter in the intercanine, inter-first molar, and inter-second molar measurements.

2. There are no significant differences in shapebetween the arches or between the sexes.

3. Three lingual curves, small, medium, and large, forthe 2 arches, representing the mean values of oursample, were developed.

4. The maxillary curves coordinate with the mandibu-lar ones and can be used as a guide for the setup inthe lingual straight-wire technique.

REFERENCES

1. Ronay V, Miner MR, Will LA, Arai K. Mandibular arch form: the

relationship between dental and basal anatomy. Am J Orthod Den-

tofacial Orthop 2008;134:430-8.

2. Trivino T, Siqueira DF, Scanavini MA. A new concept of mandib-

ular dental arch forms with normal occlusion. Am J Orthod

Dentofacial Orthop 2008;133:10.e15-22.

3. Fujita K, Takada K, QianRong G, Shibata T. Patterning of human

dental arch wire blanks using a vector quantization algorithm.

Angle Orthod 2002;72:285-94.

4. Nojima K, McLaughlin RP, Isshiki Y, Sinclair PM. A comparative

study of Caucasian and Japanese mandibular clinical arch forms.

Angle Orthod 2001;71:195-200.

5. Lee RT. Arch width and form: a review. Am J Orthod Dentofacial

Orthop 1999;115:305-13.

6. Raberin M, Laumon B, Martin JL, Brunner F. Dimensions and

form of dental arches in subjects with normal occlusions. Am J

Orthod Dentofacial Orthop 1993;104:67-72.

7. de Rysky S, Collesano V, Avril C, Slavicek R. Clinical functional

analysis. Riv Ital Stomatol 1983;52(2):111-24.

8. De La Cruz AR, Sampson P, Little RM, Artun J, Shapiro PA.

Long-term change in arch form after orthodontic treatment

and retention. Am J Orthod Dentofacial Orthop 1995;107:

518-30.

9. Andrews LF. Composites. I: straight-wire, the concept and appli-

ance. San Diego, Calif: L.A. Wells; 1989.

10. Brader AC. Dental arch form related with intraoral forces: PR 5

C. Am J Orthod 1972;61:541-61.

11. Ferrario VF, Sforza C, Miani A Jr, Tartaglia G. Human dental arch

shape evaluated by Euclidean-distance matrix analysis. Am J

Phys Anthropol 1993;90:445-53.


12. Ferrario VF, Sforza C, Miani A Jr, Tartaglia G. Mathematical def-

inition of the shape of dental arches in human permanent healthy

dentitions. Eur J Orthod 1994;16:287-94.

13. Ferrario VF, Sforza C, Poggio CE, Serrao G, Colombo A. Three-

dimensional dental arch curvature in human adolescents and

adults. Am J Orthod Dentofacial Orthop 1999;115:401-5.

14. Ferrario VF, Sforza C, Colombo A, Ciusa V, Serrao G. Three-

dimensional inclination of the dental axes in healthy permanent

dentitions—a cross-sectional study in a normal population. Angle

Orthod 2000;71:257-64.

15. Harris EF. A longitudinal study of arch size and form in untreated


16. Carter GA, McNamara JA Jr. Longitudinal dental arch changes in


17. Ricketts RM. Research in factors of appliance design and arch

form. Foundation for Orthodontic Research 1979;9:45-57.

18. Felton MJ, Sinclair PM, Jones DL, Alexander RG. A computer-

ized analysis of the shape and stability of mandibular arch form.

Am J Orthod Dentofacial Orthop 1987;92:478-83.

19. Braun S, Hnat WP, Fender DE, Legan HL. The form of the dental

arch. Angle Orthod 1998;68:29-36.

20. Noroozi H, Nik TH, Saeeda R. The dental arch form revisited.

Angle Orthod 2001;71:386-9.

21. McLaughlin RP, Bennett JC. Considerazioni sulla forma d’arcata

per ottenere stabilita ed estetica. Ortognatodonzia Italiana 2001;

10:217-35.

22. BeGole EA, Fox DL, Sadowsky C. Analysis of change in arch

form with premolar expansion. J Dent Res 1998;113:307-15.

23. Poggio CE, Mancini E, Salvato A. Valutazione degli effetti

sulla forma d’arcata della terapia fissa e della recidiva me-

diante thin-plate spline analysis. Ortognatodonzia Italiana

2000;9:345-50.

24. Mutinelli S, Manfredi M, Cozzani M. A mathematic-geometric

model to calculate variation in mandibular arch form. Eur J

Orthod 2000;22:113-25.

25. Mutinelli S, Cozzani M, Manfredi M, Siciliani G. Dental arch

analysis system. Prog Orthod 2004;5:200-8.

26. Camporesi M, Franchi L, Baccetti T, Antonini A. Thin-plate

spline analysis of arch form in a southern European population

with an ideal natural occlusion. Eur J Orthod 2006;28:135-40.

27. Lele S, Richtsmeier JT. Euclidean distance matrix analysis:

a coordinate-free approach for comparing biological shapes using

landmark data. Am J Phys Anthropol 1991;86:415-27.

28. McAlarnay ME, Chiu WH. Comparison of numeric techniques in

the analysis of cleft palatal dental arch form change. Cleft Palate

Craniofac J 1997;34:281-91.

29. McIntyre GT, Mossey PA. Size and shape measurement in

contemporary cephalometrics. Eur J Orthod 2003;25:231-42.

30. Trivino T, Vilella OV. Form and dimensions of the lower dental

arch. Rev Soc Bras Orthod 2005;5:19-28.

31. Kageyama T, Domınguez-Rodrıguez GC, Vigorito JW,

Deguchi T. A morphological study of the relationship between

arch dimensions and craniofacial structures in adolescents with

Class II Division 1 malocclusions and various facial types. Am

J Orthod Dentofacial Orthop 2006;129:368-75.

32. Lu KH. An orthogonal analysis of the form, symmetry and asym-

metry of the dental arch. Arch Oral Biol 1966;11:1057-69.

33. Pepe SH. Polynomial and catenary curve fits to human dental

arches. J Dent Res 1975;54:1124-33.

34. Wakabayashi K, Sohmura T, Takahashi J, Kojima T, Akao T,

Nakamura T. Development of the computerized dental cast form

analyzing system—three dimensional diagnosis of dental arch

form and the investigation of measuring condition. Dent Mater J

1997;16:180-90.

35. Ferrario VF, Sforza C, Dellavia C, Colombo A, Ferrari RP. Three-

dimensional hard tissue palatal size and shape: a 10-year longitu-

dinal evaluation in healthy adults. Int J Adult Orthod Orthognath

Surg 2002;17:51-8.

36. Takemoto K, Scuzzo G. The straight-wire concept in lingual

orthodontics. J Clin Orthod 2001;35:46-52.

37. Fujita K. New orthodontic treatment with lingual bracket and

mushroom archwire appliance. Am J Orthod 1979;76:657-75.

38. Little RM. The irregularity index: a quantitative score of mandib-

ular anterior alignment. Am J Orthod 1975;68:554-63.

39. Robinson DL, Blackwell PG, Stillman EC, Brook AH. Impact of

landmark reliability on the planar Procustes analysis of tooth

shape. Arch Oral Biol 2002;47:545-54.

40. Dahlberg G. Statistical methods for medical and biological

students. London: George Allen and Unwin; 1940.p.12-22.

41. Flowler J, Jarvis P, Chevannes M. Statistica per le professioni san-

itarie. 2006, EdiSES S.r.l.-Napoli.

42. Siciliani G, Terranova S. Chapter 8. In: Masson, editor. Ortodon-

zia linguale. Milan, Italy: Vivendi Universal Publishing; 2001.

43. Scuzzo G, Takemoto K. Invisible orthodontics: current concepts

and solutions in lingual orthodontics. Berlin, Germany: Quintes-

senz Verlags; 2003.

44. Fillion D, Buso-Frost L. An overall view of the different labora-

tory procedures used in conjunction with lingual orthodontics.

Semin Orthod 2006;12:203-10.

45. Taner T, Ciger S, El H, Germec D, Es A. Evaluation of dental arch

width and form changes after orthodontic treatment and retention

with a new computerized method. Am J Orthod Dentofacial

Orthop 2004;126:464-76.

46. Nie Q, Lin J. A comparison of dental arch forms between Class II

Division 1 and normal occlusion assessed by Euclidean distance

matrix analysis. Am J Orthod Dentofacial Orthop 2006;129:528-35.

47. Savostin-Asling I. The geometric analysis of mandibular dental

arch form. Ann Dent 1980;39:3-11.

48. Burris BG, Harris FH. Maxillary arch size and shape in American

blacks and whites. Angle Orthod 2000;70:297-302.

a new concept of anatomic lingual arch form - luca lombardo forma d'arcata.pdf · a new...

Documents