Three-Dimensional Inclination of the Dental Axes in Healthy Permanent Dentitions A Cross-Sectional Study in a Normal Population

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1 Original Article Three-Dimensional Inclination of the Dental Axes in Healthy Permanent Dentitions A Cross-Sectional Study in a Normal Population Virgilio F. Ferrario, MD a ; Chiarella Sforza, MD a ; Anna Colombo, DDS, PhD b ; Veronica Ciusa, DDS c ; Graziano Serrao, MD, PhD b Abstract: The 3-dimensional (3-D) inclination of the facial axis of the clinical crown (FACC) and the size of the clinical crowns were measured in 100 white northern Italians. The subjects consisted of 22 girls and 21 boys, ages years (adolescents), and 31 women and 26 men, ages years (adults), all with a complete permanent dentition and Class I dental relationships. The 3-D coordinates of dental landmarks were obtained with a computerized electromagnetic digitizer. Clinical crowns heights and FACC inclinations in the anatomical frontal and sagittal planes relative to 2 reference planes, maxillary and mandibular (between the incisive papilla and the intersection of the palatal/lingual sulci of the first permanent molars with the gingival margin), were calculated. Ages and sexes were compared by ANOVA. On average, the frontal plane FACCs of most teeth converged toward the midline plane of symmetry. In contrast, the incisors diverged from the midline plane or were nearly vertical. Within each quadrant, the inclinations of the postincisor teeth progressively increased. In the sagittal plane, most teeth had a nearly vertical FACC. FACC inclinations showed sex- and age-related differences (P.05). In the frontal plane, the canines, premolars, and molars were more inclined in adolescents than in adults. In the sagittal plane, a large within-group variability was observed. Clinical crown height was significantly larger in males than in females in all maxillary and mandibular canines, premolars, second molars, maxillary central incisors, and first molars. With age, some degree of dental eruption was found in maxillary and mandibular canines, maxillary second premolars, and molars. The age-related decrease in FACC inclination may be the effect of a progressive buccal and mesial drift. (Angle Orthod 2001;71: ) Key Words: Facial axis; Facial axis of the clinical crown; Clinical crowns; Growth; Development INTRODUCTION The 3-dimensional arrangement of teeth in a normal, healthy human dentition follows some general rules. For a Professor of Human Anatomy, Laboratorio di Anatomia Funzionale dell Apparato Stomatognatico (LAFAS), Functional Anatomy Research Center (FARC); Dipartimento di Anatomia Umana, Facoltà di Medicina e Chirurgia e Facoltà di Scienze Motorie, Università degli Studi di Milano. b Research Assistant, Laboratorio di Anatomia Funzionale dell Apparato Stomatognatico (LAFAS), Functional Anatomy Research Center (FARC); Dipartimento di Anatomia Umana, Facoltà di Medicina e Chirurgia e Facoltà di Scienze Motorie, Università degli Studi di Milano. c Postgraduate Student, Laboratorio di Anatomia Funzionale dell Apparato Stomatognatico (LAFAS), Functional Anatomy Research Center (FARC); Dipartimento di Anatomia Umana, Facoltà di Medicina e Chirurgia e Facoltà di Scienze Motorie, Università degli Studi di Milano. Corresponding author: Professor Virgilio F. Ferrario, Dipartimento di Anatomia Umana, via Mangiagalli 31, I Milano, Italy. ( farc@unimi.it). Accepted: January Submitted: October by The EH Angle Education and Research Foundation, Inc. 257 instance, the occlusal surfaces of teeth in the mandibular arch have been described as tangent to a 100-mm (or 4- inch) sphere, which was first described by Monson about 80 years ago. 1 This global spatial disposition, which also has recently been measured in different age groups, 2,3 obviously depends on the positions of the single teeth and on their inclinations in the anatomical planes. This last issue is of paramount importance for the orthodontists who treat dentitions where the positions of the teeth differ, more or less, from what is considered the reference standard. Not only should they compare the patient s value to the norm but they should also quantify the amount of 3-dimensional movement to be given to each tooth in order to assess the actual effect of treatment and measure the eventual relapse. Among the several reference systems that have been proposed for the measurement of dental inclination, there is the facial axis of the clinical crown (FACC). 4 Indeed, the clinical crown is the part of the tooth that most obviously influences oral and facial esthetics, and it is the only part that can be easily appreciated by the patient. Angle Orthodontist, Vol. 71, No. 4, 2001

2 258 FERRARIO, SFORZA, COLOMBO, CIUSA, SERRAO Andrews 4 measured more than 100 normal dental arches and supplied reference values of size, shape, vestibular prominence, and inclination of the FACCs. In particular, the inclinations were measured as tip and torque with reference to an occlusal plane approximated by a plastic template. 4 All the measurements were performed directly on the casts by using protractors and calipers. This is a time-consuming technique where each measure, comporting a new positioning of the instruments, can be potentially biased. 5 Currently, technology, with 3-dimensional computerized digitizers, 2,3,6,7 allows us to overcome these technical limitations. Dental inclinations can be mathematically calculated from the spatial coordinates of the endpoints of the FACC. Data collection, therefore, comports only with the digitization of single landmarks, thus reducing measurement error. Geometrical and mathematical models then allow us to compute every kind of angular or linear value 2,3,6,7 according to the desired reference system. The use of an approximate occlusal plane as a reference for dental inclinations 4,8 introduces a further bias. If treatment or age modify the occlusal plane, the posttreatment (or longitudinal) measurements will be performed according to a new reference system. To correctly assess dental modifications, the reference plane should be as stable as possible during treatment. 9 At the same time, it must be intrinsic to the cast itself since external planes (eg, cranial planes) will necessitate a further measurement, which should also be transferred to the cast. The aims of the present investigation were to measure the 3-dimensional inclination of the FACCs relative to anatomical planes intrinsic to the dental cast and to assess the size of the clinical crowns in a normal, healthy population. Moreover, the effects of sex and age on the same variables were analyzed in healthy individuals with a sound complete permanent dentition. These data could be used as normal reference values for the assessment of patients seeking orthodontic treatment. MATERIALS AND METHODS Sample Data on a total of 100 white northern Italians collected from 2 different groups were included in this study. The adult group was selected from high school and university students aged 17 years to 26 years and consisted of 26 men (mean age, 20.2 years) and 31 women (mean age, 19.4 years). The adolescent group was selected from junior high school students aged 13 years to 15 years and was composed of 21 boys (mean age, 14.7 years) and 22 girls (mean age, 1 years). All subjects had a sound, full permanent dentition including the second molars, with bilateral Angle Class I molar and canine relationships ( 1 mm), overjet ranging from 2 mm to 4 mm, no cross bite, no cast restorations or cuspal coverage, no previous orthodontic treatments, no history of craniofacial trauma or surgery, and no temporomandibular or cranio-cervical disorders. All subjects and the parents or legal guardians of subjects under 18 years of age gave their informed consent to the experiment. These subjects were analyzed in several longitudinal and cross-sectional growth studies currently being performed in our laboratory, 2,3,6,10 and they entered the present protocol if they met the inclusion criteria. They represented about 13% (adults) and 18% (adolescents) of the original samples. Their data are meant to be reference values collected on normal, untreated individuals. The yellow stone dental casts of all subjects were obtained from alginate impressions. Digitization of landmarks On all casts, a set of standardized dental landmarks was identified as follows: Gingival and occlusal limits of the facial axis of the clinical crown (FACC). 4 In all teeth, the FACC was traced (for incisors, canines, and premolars, it was identified as the most prominent and centermost vertical portion of the labial or buccal surface; for molars, it corresponded to the dominant vertical groove on the buccal surface of the crown) and its limits used as landmarks. Intersections of the palatal/lingual sulci of the first permanent molars with the gingival margin. Maxillary and mandibular incisive papillae. The 3-dimensional (x, y, z) coordinates of the landmarks were obtained with a 3-dimensional electromagnetic digitizer (3Draw, Polhemus Inc, Colchester, VT, USA) interfaced with a computer. A detailed description of the digitizer can be found in Ferrario et al. 2,3,6 Briefly, the system supplies actual metric data independent from external reference systems. The calibration of the instrument can be altered by electromagnetic interferences and metal objects. Its calibration, therefore, was controlled before each data collection session using a 3-dimensional object of known dimensions. Moreover, during data collection, the stylus cable never crossed the tablet and all metal objects and electromagnetic devices (ie, the computer, the video, and the power supply of the digitizer) were positioned a minimum of 3 m from the digitizer. The digitizer resolution was cm/cm of range and its accuracy cm. Digitization of landmarks was performed by a single operator. ASCII files of the 3-dimensional coordinates were obtained and computer programs, devised and written by one of the authors, were used for all the subsequent calculations. Measurements and statistical calculations The 2 maxillary and mandibular reference planes were computed between the incisive papilla and the intersections of the palatal or lingual sulci of the first permanent molars with the gingival margin. These 2 planes were set mathe-

3 THREE-DIMEIONAL INCLINATION OF THE DENTAL AXES 259 FIGURE 1. Mandibular cast with the horizontal reference plane and the X, Y, Z axes. The FACCs are also indicated. FIGURE 3. Mandibular cast, lateral view. The FACCs are indicated as well as the inclination of the left second premolar on the sagittal plane. The height of the clinical crown (linear distance between the gingival and occlusal limits of the FACC, mm) was also computed for each tooth. and standard deviation were computed within each sex and age group (boys, girls, men, women) using bivariate (angles) or univariate (distances) statistics. Comparisons between ages and sexes were performed by 2-way factorial analyses of variance, with a level of significance set at 5% (P.05). Method error FIGURE 2. Mandibular cast, frontal view. The FACCs are indicated as well as the inclination of the left central incisor on the frontal plane. matically horizontal with the x axis corresponded to the line connecting the 2 molar landmarks (right-left), the z axis vertical (inferior-superior), and the y axis antero-posterior (Figure 1). For each plane, the origin of axes (0, 0, 0) was set at the incisive papilla. All coordinates were rotated and translated according to the new reference system and were used to calculate the inclination of the FACCs in the frontal (x, z) (Figure 2) and sagittal (y, z) (Figure 3) planes for each tooth (degrees) relative to the z, axis. These 2 planes are relative to the new anatomical reference system (maxillary-palatal and mandibular-lingual) and therefore do not depend on the occlusal plane. For each quadrant in the frontal plane, positive angles were those with a cervical-to-occlusal FACC directed toward the same side of the mouth (ie, for the posterior teeth, in the buccal-vestibular direction; for the anterior teeth, in a direction diverging from the midline plane of symmetry). In the sagittal plane, positive angles were those with a cervical-occlusal FACC directed from posterior to anterior. Intraoperator repeatability was assessed by repeated tracings (landmark positions) and digitization (landmark coordinates) of the same casts. Ten casts were randomly selected from the entire sample, and all procedures for data acquisition were repeated twice with a 1-month interval. Data were analyzed as described for all 28 teeth of each cast, and the differences between the inclinations (frontal and sagittal plane) and the crown dimensions computed on the 2 separate occasions were obtained and averaged. No systematic errors were found. Overall, the mean and standard deviation of the random error for the inclinations measured in the sagittal plane angles was In the frontal plane, the error was Crown height had a mean random error of mm. RESULTS On average, in all 4 age and sex groups, the dental inclinations in the frontal plane were negative, ie, the cervicoto-occlusal facial axis of the clinical crown converged toward the midline plane of symmetry. In other words, the cervico-to-occlusal facial axis was directed toward the opposite side of the mouth (Table 1). Exceptions were found for the incisors, which, in about half the cases, showed positive axes (diverged from the midline plane) or nearly vertical axes (inclinations next to 0). The largest positive

4 260 FERRARIO, SFORZA, COLOMBO, CIUSA, SERRAO TABLE 1. Degrees) a Tooth Descriptive Statistics (s and Standard Deviation) and Statistical Comparisons of FACC Inclinations in the Frontal Plane (in Girls Women s Boys Men s Comparison Sex Age X b a Positive angles: cervical-to-occlusal FACC directed toward the same side of the mouth (ie, for the posterior teeth, in the buccal-vestibular direction; for the anterior teeth, in a direction diverging from the midline plane of symmetry). b Two-way factorial analysis of variance: factor 1, sex; factor 2, age; X sex age interaction (1,106 degrees of freedom for all sources)., not significant (P.05). P.05. P.01. value ( ) was found for the left mandibular central incisor in the adult men. Indeed, when the dental inclinations of the single subjects were observed, about 40 50% of the mandibular incisors had positive inclinations. Similar inclinations were found in about 20 30% of the maxillary incisors. Within each quadrant, the inclinations of the postincisor teeth progressively became more negative toward the first (maxillary) or the second (mandibular) molar. Overall, inclinations in the frontal plane were more negative in the mandibular than in the maxillary arch, with differences up to (first molars). The inclinations of the FACCs in the frontal plane showed several significant sex- and age-related differences as well as sex age interactions (Table 1). In particular, the canines, premolars, and molars of all 4 quadrants were more inclined in adolescents than in adults, with differences up to 12 and 14 (mandibular second molars in males). The age-related behavior of the incisor teeth was variable, with no significant differences (upper right incisors), larger inclinations in the adults than in the adolescents (upper left central, lower right lateral, and both lower left incisors), or larger inclinations in the adolescents (upper left lateral, lower right central incisors). The effect of sex was not consistent, with several (in 19 teeth out of 28) significant sex age interactions. In the sagittal plane, the inclinations of the FACCs showed a large within-group variability (high standard deviations) together with several significant sex- and age-related differences as well as sex age interactions (Table 2). Indeed, the observed differences cannot be easily classified. Overall, most maxillary teeth were, on average, nearly upright, with cervico-to-occlusal inclinations of the FACCs within 5. Noticeable exceptions were found for both the second molars in the adolescent group. Interestingly, in both sexes, the right-side tooth was more inclined in the posterior direction (negative inclination) than its leftside homologue (about twice). In women, all 4 maxillary

5 THREE-DIMEIONAL INCLINATION OF THE DENTAL AXES 261 TABLE 2. Degrees) a Tooth Descriptive Statistics (s and Standard Deviation) and Statistical Comparisons of FACC Inclinations in the Sagittal Plane (in Girls Women s Boys Men s Comparison Sex Age X b a Positive angles: cervical-occlusal FACC directed from posterior to anterior. b Two-way factorial analysis of variance: factor 1, sex; factor 2, age; X sex age interaction (1,106 degrees of freedom for all sources)., not significant (P.05). P.05. P incisors had their FACC directed in the anterior direction (positive angles). A similar side-related variation also was found for the upper second molars, with the right-side tooth being about twice as inclined as the left-side one. Also in the mandibular arch, most teeth had a nearly vertical FACC, apart from the left-side quadrant of the adolescent females. Within each sex and age group, in all 4 quadrants, the second molars had the smallest clinical crown heights (Table 3). Within each maxillary quadrant, the largest clinical crown height was found for the central incisor, with the canine being the second longest, tooth. The only exception was found in the maxillary left quadrant of the adult men, where the clinical crowns of the canine and central incisor were practically identical. Within each mandibular quadrant, the canine had the largest clinical crown height. Within each age and sex group, crown dimensions were on average, symmetric. Clinical crown height was significantly influenced by sex (males larger than females) in all maxillary and mandibular canines, premolars, second molars, maxillary central incisors, and first molars, with differences up to mm (maxillary left canine in the adult group). With age, some degree of dental eruption was found (larger clinical crown height in the adult group), with statistically significant differences for maxillary and mandibular canines, maxillary first premolars, and molars, with differences up to 1 mm (maxillary canines in the male group). No significant sex age interactions were found. DISCUSSION The present cross-sectional study analyzed the 3-dimensional inclination of FACCs and the size of the clinical crowns in normal healthy permanent dentition modified as a function of age and sex. The 2 analyzed groups should correspond to the beginning of a complete permanent dentition (4 second molars erupted and in occlusion) and to a (possible) steady-stage of dentition before substantial tooth wear takes place. 3 It has to be mentioned that the present investigation did

6 262 FERRARIO, SFORZA, COLOMBO, CIUSA, SERRAO TABLE 3. Tooth Descriptive Statistics (s and Standard Deviation) and Statistical Comparisons of Clinical Crown Heights (mm) Girls Women s Boys Men s Comparison Sex Age X a a Two-way factorial analysis of variance: factor 1, sex; factor 2, age; X sex age interaction (1,106 degrees of freedom for all sources)., not significant (P.05). P.05. P not assess growth changes because a cross-sectional model was adopted. Therefore, all the age-related modifications may also be explained by secular trends, a limitation intrinsic to all cross-sectional studies. Indeed, this shortcoming is probably of limited importance when the age difference is less than 10 years and the subjects are living in the same environment. 3,10 A further limitation pertains to the sample itself. Due to the well-known effects that race and ethnicity have on the general arrangement of dental arches, 11 the following considerations obviously should be limited to untreated subjects of the same race and ethnic origin as those analyzed in the current study (white northern Italians). All the measurements were performed using a 3-dimensional electromagnetic digitizer 2,3,6 and geometrical-mathematical models, thus reducing the measurement error and the time necessary for the analysis of each cast. 5 All linear and angular measurements were performed starting from selected landmarks. These landmarks were first identified on each cast and subsequently digitized once only, independent from the number of measurements. 7 All the angles and distances were then automatically computed off line. This process appears easier, less time-consuming, and with reduced measurement error compared with conventional procedures employing calipers and goniometers, especially when large numbers of individuals are to be analyzed. 5,12,13 Obviously, the resolution and accuracy of the instrument, as well as the dimensions of the stylus used to collect the data, impose a physical limit to the reduction of the measurement error. For instance, some of the greater variability observed for the FACC angles measured in the sagittal plane may be due to this limit; however, in this case, the angles are small and little variations have a larger impact on the relevant standard deviations (Table 2). In the current study, all angles were measured relative to anatomical planes (sagittal and frontal) and to 2 reference planes (maxillary and mandibular) and were computed between the incisive papilla and the intersections of the palatal/lingual sulci of the first permanent molars with the gingival margin. These 2 planes, which are not actually horizontal if observed in the mouth of a subject in natural head position, 6 were mathematically set horizontal to obtain a common reference for the comparison of different individuals. The choice of the reference plane is obviously fun-

7 THREE-DIMEIONAL INCLINATION OF THE DENTAL AXES 263 damental for the quantitative analysis of dental inclination. The plane should be easy to detect, intrinsic to the cast itself, and not be significantly modified if dental inclinations change. Easy detection allows reduction in measurement error, and intrinsic planes abolish the need for adjunctive data collection procedures. For instance, cranial planes may provide useful reference planes for dental inclination (the palatal plane for the upper dentition, the mandibular plane for the lower dentition), but they have to be measured on a radiograph. 9 The measurement must then be transferred to the dental cast, thus introducing possible error. To correctly assess dental modifications, the reference plane should be as stable as possible during treatment. 9 From this point of view, the occlusal plane 4,8 is not adequate because it is often modified by orthodontic treatment. In contrast, the 2 reference planes used in the present study should be stable after the eruption of a complete permanent dentition. 6 Obviously, major maxillofacial surgical intervention may change even this plane and, in this case, pre/ posttreatment comparisons should be analyzed with caution. The use of different reference planes can partly explain the diverse findings reported in the literature. 4,8 Furthermore, while Andrews 4 assessed dental tip and torque, the current inclinations are relative to the anatomical planes and perpendicular to the horizontal reference planes. Therefore, the present data cannot be compared with classic findings. Overall, while dental inclinations in the frontal plane (excluding the incisors) had limited variability (low standard deviations in Table 1), larger variations were found in the sagittal plane in all 4 samples analyzed. Indeed, when the dental inclinations of the single subjects were observed in several teeth, positive and negative inclinations were found in about the same percentage. For instance, in men, the first premolar of the right maxillary hemiarch had a positive inclination in 50% of subjects (mean inclination, ) and a negative inclination in the other 50% (mean inclination, 3.6 ). The overall mean, as reported in Table 2, was. On average, the facial axis of the clinical crown of this tooth seemed nearly vertical, with a standard deviation larger than the mean. When the calculation of mean values eliminated the positive and negative findings, a large standard deviation resulted and the overall pattern of sex and age differences was difficult to describe. Indeed, Andrews 4 reported large standard deviations, sometimes even larger than the present ones. The well-known sexual dimorphism in dental size, with the male crowns being larger than the female ones, was confirmed also for clinical crown height. 14 Furthermore, in most instances, the age-related modifications in the clinical crown height of postincisor teeth were larger in males than in females (Table 3). A sex-related pattern in the quantitative modifications of dental arches with age has already been reported, with larger variations in men than in women. 15 Indeed, no significant sex age interactions were found for clinical crown height (Table 3). This means that, overall, the same pattern of age-related modifications (some degree of dental eruption) was observed in both sexes (even if of different magnitude) and males had a larger crown than females. The sex-related differences, found for the inclination of FACCs in both the frontal and sagittal planes, were not consistent, and several interactions with age were observed (Tables 1 and 2). It is therefore difficult to interpret the present findings. The effect of age on the inclinations of postincisor teeth in the sagittal plane was similar in both sexes, adolescent teeth being more inclined than adult teeth. While no modifications in incisor relationships had already been described in adult dentitions, 15 Carter and McNamara 16 found a significant decrement in overjet in healthy male subjects from adolescence (mean age, 13.8 years) to young adulthood (17.2 years) but no modifications in females. The present age-related decrements in the inclinations of canines, premolars, and molars may be the effect of the progressive buccal and mesial drift already found between the beginning of a complete permanent dentition (4 second molars erupted and in occlusion) and a (possible) steady stage of permanent dentition at the onset of adulthood. 3 An extensive discussion can be found in Ferrario et al. 3 Similar findings were also reported by Harris, 15 who measured a mesial and buccal drift for postcanine teeth in adult dentitions between 20 years and 55 years of age. In that investigation, the effect was tentatively explained by the presence of an occlusal force with an anterior component. Carter and Mc- Namara 16 ascribed adolescent and adult modifications in dental arch size to muscular forces also. Presently, we cannot propose other explanations for this result. CONCLUSIO The samples studied in the present investigation were highly selected as far as the dental and occlusal characteristics were concerned, and the collected data could be used for the quantitative description of normal dental inclinations and size. Moreover, the applied method allowed the direct measurement of the age-related spatial arrangement of the clinical crowns relative to anatomical planes in adolescent and young adult untreated subjects. The same measurements could be performed before, during, and after orthodontic treatment. In particular, within the limits of the present cross-sectional design, it should be remembered that The 3-dimensional inclination of the facial axis of the clinical crowns modifies from adolescence to young adulthood, with an age-related decrease in dental inclination. This process may be the effect of a buccal and mesial dental drift.

8 264 FERRARIO, SFORZA, COLOMBO, CIUSA, SERRAO An age-related increment in clinical crown height was observed for almost all posterior teeth. These dental movements could be of importance in explaining some of the relapses of orthodontic treatments. 16 ACKNOWLEDGMENT This research was partially supported by the Società Italiana di Biodinamica Cervico-Dento-Facciale (Italy) and by grants from the University of Milan and MURST (Italy, ex-60%). REFERENCES 1. Ash MM. Wheeler s Dental Anatomy, Physiology and Occlusion. 7th ed. Philadelphia, Pa: WB Saunders; 1993:88 89, Ferrario VF, Sforza C, Miani A Jr. Statistical evaluation of Monson s sphere in permanent healthy dentitions in man. Arch Oral Biol. 1997;42: Ferrario VF, Sforza C, Poggio CE, Serrao G, Colombo A. Threedimensional dental arch curvature in human adolescents and adults. Am J Orthod Dentofacial Orthop. 1999;115: Andrews LF. Straight Wire. Basi Teoriche e Applicazioni. Masson: Milano; Morris KM, Seow WK, Burns YR. Palatal measurements of prematurely born, very low birth weight infants: comparison of three methods. Am J Orthod Dentofacial Orthop. 1993;103: Ferrario VF, Sforza C, Schmitz JH, Colombo A. Quantitative description of the morphology of the human palate by a mathematical equation. Cleft Palate-Craniofac J. 1998;35: Kulmer S, Ruzicka B, Niederwanger A, Moschen I. Incline and length of guiding elements in untreated naturally grown dentition. J Oral Rehabil. 1999;26: Ugur T, Yukay F. Normal faciolingual inclinations of tooth crowns compared with treatment groups of standard and pretorqued brackets. Am J Orthod Dentofacial Orthop. 1997;112: Watanabe E, Demirjian A, Buschang P. Longitudinal post-eruptive mandibular tooth movements of males and females. Eur J Orthod. 1999;21: Ferrario VF, Sforza C, Poggio CE, Schmitz JH. Soft tissue facial morphometry from 6 years to adulthood: a three-dimensional growth study using a new modeling. Plast Reconstr Surg. 1999; 103: Ferrario VF, Sforza C, Colombo A, Duncan V, Carvajal R, Palomino H. Dental arch size in human permanent healthy dentitions: ethnic differences as assessed by discriminant analysis. Int J Adult Orthod Orthognath Surg. 1999;14: Ladner PT, Muhl ZF. Changes concurrent with orthodontic treatment when maxillary expansion is a primary goal. Am J Orthod Dentofacial Orthop. 1995;108: Hsu BS. The nature of arch width difference and palatal depth of the anterior open bite. Am J Orthod Dentofacial Orthop. 1998; 113: Ferrario VF, Sforza C, Tartaglia GM, Colombo A, Serrao G. Size and shape of the human first permanent molar: a Fourier analysis of the occlusal and equatorial outlines. Am J Phys Anthropol. 1999;108: Harris EF. A longitudinal study of arch size and form in untreated arches. Am J Orthod Dentofacial Orthop. 1997;111: Carter GA, McNamara JA Jr. Longitudinal dental arch changes in adults. Am J Orthod Dentofacial Orthop. 1998;114:88 99.