The fact that mandibular incisor irregularity

CONTINUING EDUCATION Associations between initial, posttreatment, and postretention alignment of maxillary anterior teeth Burleigh T. Surbeck, BS, a Jon Årtun, DDS, DrOdont, b Natalie R. Hawkins, MS, c and Brian Leroux, PhD d Seattle, Wash. Contradictory findings from studies on pretreatment malalignment as a risk factor for relapse of maxillary incisor alignment may be due to inappropriate sample selection and measurement technique. In an attempt to clarify the issue, 745 sets of study models made before (T1) and after (T2) orthodontic treatment and at long-term out of retention (T3) were screened. On the basis of the configuration of the maxillary anterior teeth on the T3 study models, three groups were established: one with significant spacing (group 1, n 30); one with significant irregularity (group 2, n 49); and one with perfect alignment (group 3, n 28). The occlusal surfaces of the 321 maxillary study models at T1, T2, and T3 were photocopied and the tooth anatomic contact points digitized. An algorithm was used to fit the dental arch to the digitized points. Amount of incisor rotation and anatomic contact point displacement of the maxillary anterior teeth relative to the dental arch were computer generated. Interdental spaces in the maxillary anterior segment, as well as overjet and overbite, were measured manually. Nonstructural data were collected from the charts. Logistic regression analyses revealed that irregularity was associated with greater anatomic contact displacement and with greater incisor rotation both at T1 and T2 (P 0.01). Similar analyses also revealed that spacing was associated with greater interdental spaces at T1 and T2 (P 0.01). Correlation analyses revealed that the pattern of pretreatment rotational displacement has a strong tendency to repeat itself after retention (P 0.001), as opposed to the pattern of contact point displacement and interdental spacing. (Am J Orthod Dentofacial Orthop 1998;113:186-95.) The fact that mandibular incisor irregularity increases after orthodontic treatment and retention, concomitant with a decrease of mandibular dental arch length and width dimensions, is well documented, 1-6 even in cases presenting with generalized spacing. 3 The amount of pretreatment irregularity is not a strong predictor for postretention relapse, 1,5,6 and space opening in the mandibular anterior segment is a very rare finding after retention. 1-6 A likely explanation may be that the amount of postretention malalignment is primarily determined by the multitude of factors responsible for a reduction in mandibular perimeter, and that the expression depends not only on the initial pattern, but also on the restriction frequently provided by the maxillary arch through occlusion. Labial movement of the maxillary incisors is not From the University of Washington. a Dental student. b Professor, Department of Orthodontics. c Research Consultant, Department of Dental Public Health Sciences. d Assistant Professor, Department of Biostatistics and Department of Dental Public Health Sciences. Reprint requests to: Dr. Jon Årtun, Department of Orthodontics, Box 357446, University of Washington, Seattle, WA 98195. Copyright 1998 by the American Association of Orthodontists. 0889-5406/98/$5.00 0 8/1/79617 confined to the hard tissue components of the opposing arch. Accordingly, recurrence of interdental spaces may occur more frequently in the maxillary than the mandibular anterior segment, and movements toward pretreatment tooth positions may not be unusual. Case reports indicate that prevention of space reopening between the maxillary incisors represents a significant retention problem. 7 However, aside from studies on postretention stability after closure of maxillary midline diastema, 8,9 this has not been examined in a representative group of patients. Information is also limited regarding prevalence and severity of maxillary incisor irregularity long-term out of retention. 10-13 There are indications that the amount is always less than that seen before treatment, 10-12 that rotational relapse of individual teeth hardly exceeds 20, 10 and that more than 3 mm crowding in the maxillary anterior segment may be an almost nonexistent observation long-term out of retention. 11 Attempts at establishing predictors of such relapse are very few. One study concludes that the amount of rotational relapse is proportional to the amount of orthodontic correction, 10 whereas a recent Master s thesis concludes that rotation in the opposite direction by no means is uncommon. 13 However, there may be an association between development of 186

American Journal of Orthodontics and Dentofacial Orthopedics Volume 113, No. 2 Surbeck et al. 187 Table I. Sample means of age, overjet, and overbite before treatment (T1), treatment time, and postretention time of patients judged to have significant interproximal spacing (group 1), significant malalignment (group 2), and perfect alignment (group 3) of the maxillary anterior teeth after retention Table II. Distribution of Angle classification, extraction alternative, and gender of patients judged to have significant interproximal spacing (group 1), significant malalignment (group 2), and perfect alignment (group 3) of the maxillary anterior teeth after retention Group 1 (n 30) Group 2 (n 49) Group 3 (n 28) Group 1 (n 30) Group 2 (n 49) Group 3 (n 28) x SD x SD x SD Age T1 (yrs) 13.00 (2.00) 12.76 (2.46) 12.63 (1.51) Treatment time (yrs) 2.98 (1.37) 2.77 (1.18) 2.76 (1.18) Postretention time (yrs) 13.99 (3.52) 14.40 (4.08) 11.89 (3.37) Overjet at T1 (mm) 6.62 (3.61) 6.20 (3.26) 6.84 (3.30) Overbite at T1 (mm) 3.83 (1.78) 3.21 (2.99) 4.07 (1.79) crowding and postretention reduction in arch length and width. 12 In the previously mentioned studies, the amount of maxillary incisor malalignment was measured manually as the difference between available space and the sum of the tooth widths, 11 or as the sum of the distances between adjacent anatomic contact points, 13 rather than as the displacement relative to the dental arch. Such techniques preclude testing of the tendency for labially or lingually displaced teeth to relapse in that same direction. Tooth rotation was measured manually as the angle between the incisal edge and the midpalatal raphe. 13 Accordingly, the measurements for rotational change may have been biased by inconsistencies in locating the raphe on the pretreatment, posttreatment, and postretention study models. Another problem is the influence of any change in arch form, which frequently occurs from one time period to another. 14 If the arch changes to a wider form, the angular measurement will tend to increase, even if no rotational change has occurred relative to the dental arch. Finally, the samples in the previous studies have been selected according to Angle classification or extraction decision, which may not allow sufficient variation of the variable under study to reliably test for associations. The purpose of our study was to use a casecontrol study design to test whether pretreatment malalignment in terms of irregularity and spacing of the maxillary anterior teeth and the quality of the orthodontic alignment are of significance for postretention relapse of alignment, and to perform correlation analyses to test whether the teeth tend to move toward their pretreatment positions relative to the dental arch. MATERIAL AND METHODS Sample Sets of study models made before (T1) and after (T2) orthodontic treatment, and long-term out of retention (T3) of 745 patients who were treated by faculty members or graduate students of the Orthodontic Department at n % n % n % Angle Class I 14 (46.7) 20 (40.8) 5 (17.9) Angle Class II, Division 1 10 (33.3) 19 (38.8) 15 (53.6) Angle Class III 5 (16.7) 3 (6.1) 4 (14.3) Angle Class Other 1 (3.3) 7 (14.3) 4 (14.3) Nonextraction cases 12 (40.0) 12 (24.5) 7 (25.0) Extraction cases 18 (60.0) 37 (75.5) 21 (75.0) Males 22 (73.3) 15 (30.6) 11 (39.3) Females 8 (26.7) 34 (69.4) 17 (60.7) the University of Washington were examined. Sample criteria were limited to patients with presence of all six maxillary anterior teeth and who had not experienced tooth extraction other than third molar removal from T2 to T3. On the basis of the alignment of the maxillary anterior teeth at T3, three groups were established: one with significant spacing, defined as at least one interproximal space of at least 1.0 mm or generalized spacing of at least 0.5 mm in each interproximal site (group 1, n 30); one with significant irregularity, defined as at least 2.0 mm discrepancy in labiolingual direction between anatomic contact points of adjacent teeth in at least one interproximal site (group 2, n 49); and one subjectively determined to have perfect alignment (group 3, n 28). The occlusal relationships at T1 and T2 were not considered in the sample selection. Age at T1, sex, treatment time, and postretention time were collected from the charts (Tables I and II). Measurement on Study Models Manual measurements: The study models at T1, T2, and T3 were measured separately and in random order. In situations with a tooth open contact in the maxillary anterior segment, the distance between anatomic contact points of adjacent teeth was measured along the dental arch, adjusting the labiolingual discrepancies. Overbite was measured as the mean overlap of maxillary to mandibular central incisors, and overjet as the distance parallel to the occlusal plane from the incisal edge of the most labial maxillary to the most labial mandibular central incisor. 15 The measurements were made to the nearest half millimeter with a compass bearing two metal pins at each contact point on arms separated by a spring-loaded dial for fine adjustments, and a clear, plastic millimetric ruler. Angle classification and extraction alternative were also recorded (Table II). Computer-generated measurements: The maxillary study models at T1, T2, and T3 were marked separately and in random order, with an automatic pencil with a 0.5

188 Surbeck et al. American Journal of Orthodontics and Dentofacial Orthopedics February 1998 Fig. 1. A, Xerox copy of maxillary study model with pencil marks on occlusal anatomic landmarks. B and C, Computer-generated dental arches fitted to landmarks after photocopying and digitization. Amount of incisor rotation and anatomic contact point displacement relative to dental arch (B) as well as arch length and arch width (C) were computer generated. mm tip. The following anatomic landmarks were marked (Fig. 1, A): mesiobuccal and distobuccal cusp tips of the first permanent molars, buccal cusp tips of the premolars, cusp tips and mesiocuspal point angles of the canines, and mesioincisal and distoincisal point angles and midincisal points of the incisors. In cases of wear, the estimated cusp tips or point angles were used. After this procedure, the occlusal surfaces of the T1, T2, and T3 study models of each patient were photocopied simultaneously with a Xerox 5352C copier (Xerox Corporation). A white cardboard template with three separate square windows was constructed to precisely fit the glass copying surface of the copier. The three models were placed in the windows with the occlusal surface facing the glass. Millimetric plastic rulers were taped at right angles under the cardboard template. A specialized graphic interface Macintosh program was used to digitize each photocopied dental arch on a Scriptel SPA-1212T graphic digitizing tablet. All points were numbered and digitized according to a predetermined sequence. Two points on each of the millimetric rulers, located 5 cm apart, were also digitized as part of the sequence. These were used to assess and correct for any distortion that may have occurred during the photocopying process. A computer-generated arch form was made for each dental arch with an algorithm to fit arcs of conic sections to the digitized data points. 16,17 This algorithm used the sum of squared perpendicular distances from the data points to the fitted conic as the criterion for determining the best fit (Fig. 2, B). Each fitted arch form was evaluated subjectively to ascertain that it accurately represented the arch form by comparing it with the photocopy of the corresponding arch form. In a few T1 arches, outlying data points of ectopically erupted or malposed teeth appeared to exert a large influence on the fit of the conic arc. This resulted in a shape that did not properly represent the arch form. These outlying points were omitted, and the conics were refitted and assessed to ensure that they appropriately described the shape of the dental arches. After this procedure, tooth anatomic contact point displacement and tooth rotation relative to the dental arch (Fig. 1, B), as well as intercanine width, intermolar width, anterior arch length, and total arch length (Fig. 1, C) were computed by using the digitized data points and the fitted arch. Anatomic contact point displacement was computed as the distance from each point representing the mesial point angles of the canines and the mesial and distal point angles of the incisors to the dental arch, and recorded as positive if lingual and negative if labial to the arch, respectively. Rotation of the incisors relative to the dental arch was measured as the angle between the line connecting the points representing the mesial and distal point angles and the line connecting the projections of these points on the arch, recorded as positive if mesially and negative if distally rotated, respectively. Intercanine width (C-C) was computed as the distance between the cusp tip points of the right and left canines, and intermolar (M-M) width as the distance between the mesiobuccal cusp tip points of the right and left first permanent molars. Anterior arch length (ALant) was computed as the distance from the midpoint between the mesial anatomic contact points of the central incisors to the midpoint of the line representing the intercanine width, and total arch length (ALtot) as the distance from the above midpoint to the midpoint of the line representing the intermolar width. Error of the Method The reproducibility of the measurements was assessed by statistically analyzing the difference between double measurements taken at least 1 week apart on 20 sets of study models at T1, T2, and T3, 10 from group 1 and 10 from group 2. On the models from group 1, the manual measurements were repeated. On the models from group 2, the entire procedure for the computer-generated measurements was repeated. The error of the method was calculated from the equation: S x D2 2N where D is the difference between duplicated measurements and N is the number of double measurements. 18 The errors were 0.17 mm for the average interproximal space, 0.04 mm for the average amount of tooth

American Journal of Orthodontics and Dentofacial Orthopedics Volume 113, No. 2 Surbeck et al. 189 Fig. 2. Scattergrams representing highest correlation coefficients of contact point displacement relative to dental arch. A and B, Before treatment (T1) to long-term out of retention (T3) of distal contact points of two central incisors (r 0.33 and 0.29, P 0.05). C and D, After treatment (T2) to T3 of distal and mesial contact points of right lateral incisor (r 0.56 and 0.42, P 0.001 and 0.01). anatomic contact point displacement, and 0.72 for the average amount of incisor rotation. Data Analysis For each study model, the average interproximal space and anatomic contact point displacement in the anterior segment and the average incisor rotation was computed as the average of all available values. Descriptive statistics (means and standard deviations) were computed for all study variables at T1, T2, and T3 for each group. Logistic regression analysis was used to test the effect of interdental spaces at T1 and T2 on the probability of spacing at T3 (group 1 versus group 3), adjusting for intergroup differences in the variables listed in Tables I and II. A similar regression was used to test for the effect of anatomic contact point displacement and rotation on malalignment (group 2 versus group 3). Pearson s product-moment correlation coefficients were calculated to test for associations between amount of anatomic contact point displacement and between amount of interdental space at T3, respectively, and changes in C-C and ALant from T1 to T2 and from T2 to T3, and changes in M-M and ALtot from T2 to T3, respectively. Pearson s productmoment correlation coefficients were also calculated to test for associations between amount and direction of displacement of each anatomic contact point and rotation of each incisor at T1 and T3 and at T2 and T3 for group 2, and to test for associations between the size of each interdental space at T1 and T3 and at T2 and T3 for group 1. RESULTS Association Between Irregularity at T3 and Tooth Anatomic Contact Point Displacement and Tooth Rotation Relative to the Dental Arch at T1 and T2 Irregularity was found to be associated with greater average anatomic contact point displacement relative to the dental arch at T1 (P 0.01) with odds ratio (OR) of 2.3 per 0.2 mm and 95% confidence interval (CI) of 1.4 to 3.9, and at T2 (P 0.01) with OR of 8.0 per 0.2 mm and CI of 1.9 to 34.0. Malalignment was also associated with average incisor rotation relative to the dental arch at T1

190 Surbeck et al. American Journal of Orthodontics and Dentofacial Orthopedics February 1998 Table III. Sample means of average interproximal space (Space), average absolute anatomic contact point displacement relative to the dental arch (Distance), and average absolute incisor rotation relative to the dental arch (Rotation) per patient before treatment (T1), after treatment (T2), and after retention (T3) of patients judged to have significant interproximal spacing (group 1), significant malalignment (group 2), and perfect alignment (group 3) of the maxillary anterior teeth after retention Group 1 (n 30) Group 2 (n 49) Group 3 (n 28) x SD x SD x SD Space T1 (mm) 0.50 (0.34) 0.10 (0.35) 0.19 (0.27) Distance T1 (mm) 0.58 (0.20) 0.83 (0.35) 0.57 (0.21) Rotation T1 (degrees) 9.30 (4.12) 10.85 (5.16) 7.24 (3.35) Space T2 (mm) 0.32 (0.31) 0.07 (0.12) 0.09 (0.13) Distance T2 (mm) 0.28 (0.07) 0.33 (0.11) 0.25 (0.08) Rotation T2 (degrees) 4.31 (1.90) 5.08 (2.37) 3.26 (1.52) Space T3 (mm) 0.57 (0.31) 0.01 (0.06) 0.01 (0.04) Distance T3 (mm) 0.33 (0.11) 0.70 (0.21) 0.27 (0.09) Rotation T3 (degrees) 5.58 (2.31) 8.96 (3.30) 3.50 (1.56) Table IV. Correlation coefficients (r) and statistical significance (P) between changes in intercanine (3-3) and intermolar (6-6) width, anterior arch length (ALant) and total arch length (ALtot) from before to after treatment (T1/T2) and from after treatment to after retention (T2/T3), respectively, and means of absolute distance from tooth anatomic contact point to dental arch (Distance) and interproximal space (Space) per site per patient for the whole sample (n 107) at T3 Distance Space r P r P 3-3 T1/T2 0.26 ( 0.01) 0.25 ( 0.01) 3-3 T2/T3 0.65 ( 0.001) 0.46 ( 0.001) 6-6 T2/T3 0.44 ( 0.001) 0.28 ( 0.01) ALant T1/T2 0.27 ( 0.01) 0.18 ( 0.07) ALant T2/T3 0.15 ( 0.13) 0.36 ( 0.001) ALtot T2/T3 0.11 ( 0.27) 0.41 ( 0.001) (P 0.01) with OR of 2.7 per 4.0 and CI of 1.4 to 5.3, and at T2 (P 0.01) with OR of 6.3 per 4.0 and CI of 1.8 to 22.0. The differences of 0.2 mm and 4.0 were selected because they represent approximately 2 standard deviations (SD) of the values at T2 and 1 SD at T1 (Table III). Association Between Spacing at T3 and Interdental Spaces at T1 and T2 Spacing was found to be associated with greater average interdental space at T1 (P 0.01) wit OR of 3.7 per 0.3 mm and CI of 1.5 to 9.0, and at T2 (P 0.01) with OR of 27.3 per 0.3 mm and CI of 2.3 to 330.0. The difference of 0.3 mm was selected because it represents approximately 2 SD of the values at T2 and 1 SD at T1 (Table III). Associations Between Anatomic Contact Point Displacement and Tooth Rotation at T3 and Changes in Arch Length and Width from T1 to T2 and from T2 to T3 Combining the three groups, associations were found between increase in 3-3 and ALant from T1 to T2 and increase in anatomic contact point displacement at T3, and between reduction in 3-3 from T1 to T2 and increase in interdental spaces at T3 (P 0.01, Table IV). Associations were also found between reduction in 3-3 and 6-6 from T2 to T3 and increase in contact point displacement at T3 (P 0.001) and between increase in 3-3, ALant and ALtot from T2 to T3 (P 0.001) and increase in 6-6 from T2 to T3 (P 0.01) and increase in interdental spaces at T3, respectively, (Table IV). Similar trends were detected regarding contact point displacement in group 2 and interdental spaces in group 1. However, few correlation coefficients were significant, probably due to reduced sample size. The patients in group 2 tended to have more increase in 3-3 and less reduction in ALant from T1 to T2 and more reduction in 3-3 and 6-6 from T2 to T3 than those in group 3 (Table V). Associations Between Amount and Direction of Anatomic Contact Point Displacement and Incisor Rotation (Group 2) and Interdental Spaces (Group 1) at T1 and T3 and at T2 and T3 The correlation coefficients between displacement of each of the 10 anatomic contact points

American Journal of Orthodontics and Dentofacial Orthopedics Volume 113, No. 2 Surbeck et al. 191 Table V. Sample means of changes in intercanine (3-3) and intermolar (6-6) width, anterior arch length (ALant), and total arch length (ALtot) from before to after treatment (T1/T2) and from after treatment to after retention (T2/T3) of patients judged to have significant interproximal spacing (group 1), significant malalignment (group 2), and perfect alignment (group 3) of the maxillary anterior teeth after retention, and of the whole sample Group 1 (n 30) Group 2 (n 49) Group 3 (n 28) Total (n 107) x SD x SD x SD x SD 3-3 T1/T2 2.70 (2.22) 4.40 (2.47) 3.32 (2.21) 3.73 (2.43) 3-3 T2/T3 0.28 (1.00) 2.23 (1.60) 0.57 (1.14) 1.09 (1.72) 6-6 T2/T3 0.25 (0.73) 1.66 (1.58) 0.67 (1.30) 1.01 (1.45) ALant T1/T2 1.80 (1.74) 0.55 (1.76) 1.29 (1.67) 1.10 (1.80) ALant T2/T3 0.41 (1.15) 0.30 (1.02) 0.22 (0.59) 0.08 (1.01) ALtot T2/T3 0.37 (1.74) 0.62 (1.32) 0.84 (0.92) 0.40 (1.44) relative to the dental arch at T1 and T3 (group 2) ranged from 0.06 to 0.33. The coefficients were significant only for the distal of the right (r 0.33, P 0.05; Fig. 2, A) and left (r 0.29, P 0.05; Fig. 2, B) central incisors. Similar coefficients at T2 and T3 ranged from 0.07 to 0.56 and were significant for the distal (r 0.56, P 0.001; Fig. 2, C) and mesial (r 0.42, P 0.01; Fig. 2, D) of the right lateral incisor and the distal of the right central incisor (r 0.36, P 0.01). Examination of the scattergrams representing the highest correlation coefficients (Fig. 2) indicates that contact point displacement in opposite directions at the two time periods may not be unusual (Figs. 4 through 7). The correlation coefficients for each of the five interdental distances (group 1) at T1 and T3 were 0.07 (NS) for the distance between the right canine and lateral incisor, 0.06 (NS) for the distance between the right lateral and central incisor, 0.41 (P 0.05) for the distance between the central incisors, 0.03 (NS) for the distance between the left central and lateral incisor, and 0.38 (P 0.05) for the distance between the left lateral incisor and canine. Similar coefficients at T2 and T3 were 0.64 (P 0.001), 0.15 (NS), 0.06 (NS), 0.25 (NS), and 0.51 (P 0.01), respectively. DISCUSSION We could confirm that few patients have severe irregularity of the maxillary anterior teeth long-term out of retention. 10,11 Only 49 of the 745 cases examined, or less than 7%, fit our criteria for significant irregularity. The average case in this subgroup had a total of 7.0 mm displacement of the 10 anatomic contact points relative to the dental arch (Table III). Such displacement does not necessarily reflect lack of space. Our results may therefore not be interpreted to contradict a previous finding 11 that none in a group of 96 orthodontic cases had more than 3 mm crowding of the maxillary anterior teeth long-term out of retention. Our data also confirm that the majority of rotational relapse of the maxillary incisors is within a range of approximately 10, and that more than 20 relapse is very rare 10 (Table III). Our data confirm the assumption that pretreatment irregularity of the maxillary anterior teeth is a significant risk factor for postretention relapse of irregularity. The odds of experiencing severe irregularity of the maxillary anterior teeth rather than perfect alignment long-term out of retention, defined according to our inclusion criteria, may be 2.3 times higher for every 0.2 mm of average anatomic contact point displacement relative to the dental arch, and 2.7 times higher for every 4.0 of average incisor rotation relative to the dental arch, before treatment. These results suggest that retention strategies may be modified according to pretreatment alignment, and that patients presenting with severe malalignment should be informed about the likelihood of postretention relapse. We also found that incomplete alignment during active treatment is a significant risk factor for relapse. The odds for severe postretention irregularity rather than perfect alignment may be 8.0 times higher for every 0.2 mm of average contact point displacement and 6.3 times higher for every 4.0 of average incisor rotation relative to the dental arch at time of appliance removal. These results underscore the importance of treatment quality to improve the chance for postretention alignment of the maxillary anterior teeth. Our results indicate that expansion of the maxillary anterior arch segment during active treatment is a risk factor for anatomic contact point discrepancy and tooth rotation relative to the dental arch long-term out of retention, and that such malalignment is associated with compression of the anterior segment after retention (Table IV). These findings

192 Surbeck et al. American Journal of Orthodontics and Dentofacial Orthopedics February 1998 Fig. 3. Scattergrams representing lowest correlation coefficients of tooth rotation relative to dental arch. A and B, Before treatment (T1) to long-term out of retention (T3) of two central incisors (r 0.62 and 0.71, P 0.001). C and D, After treatment (T2) to T3 of two central incisors (r 0.47 and 0.49, P 0.001). Fig. 4. Maxillary study models made before (A) and after (B) treatment and approximately 12 years after retention (C) of patient treated with extraction of four first premolars. Note labiolingual relapse in opposite direction of left central and lateral incisors. Also note no labial relapse of right central incisor, despite slight undercorrection during appliance therapy. may suggest that part of the initial and postretention irregularity of the maxillary anterior teeth in our sample was due to crowding, and therefore indirectly support that relapse of such crowding is associated with reduction in arch length. 11 However, the correlation coefficients were small, suggesting that arch length changes only partly may explain the variation in postretention irregularity of the maxillary anterior teeth. Another relapse factor may be the tendency for individual teeth to return to their initial positions, due to periodontal fiber pull. 19-21 However, the pattern of anatomic contact point displacement relative to the dental arch had a small tendency to

American Journal of Orthodontics and Dentofacial Orthopedics Volume 113, No. 2 Surbeck et al. 193 Fig. 5. Maxillary study models made before (A) and after (B) treatment and approximately 14 years after retention (C) of patient treated with extraction of four first premolars. Note rotational relapse in same direction of right central incisor, and slight undercorrection during appliance therapy. Also note relapse in opposite direction of contact point relationship between central incisors, despite slight overcorrection, and no relapse of contact point relationship between right lateral and central incisors, despite slight undercorrection during appliance therapy. Fig. 6. Maxillary study models made before (A) and after (B) treatment and approximately 23 years after retention (C) of patient treated with extraction of four first premolars. Note rotational relapse in same direction of lateral incisors and left central incisor and in opposite direction of right central incisor, despite perfect alignment during appliance therapy. Also note development of labiolingual contact point discrepancy between central incisors after retention, despite no such discrepancy before treatment. Fig. 7. Maxillary study models made before (A) and after (B) treatment and approximately 15 years after retention (C) of patient treated nonextraction. Note relapse of median diastema and incomplete closure during appliance therapy. Also note minimal relapse of left central and lateral incisors, despite slight undercorrection during appliance therapy, and relapse in same direction of contact point relationship between right central and lateral incisors. repeat itself in our sample of cases with severe postretention irregularity. The correlation coefficients were significant only for 3 of the 10 sites that were measured. Moreover, despite the fact that 9 of the 10 correlation coefficients were positive, evaluation of the scattergrams representing the sites with the highest associations indicates that relapse opposite to the direction of treatment by no means may be unusual (Figs. 2, 4 through 7). The situation was similar regarding associations between anatomic contact point displacement relative to the dental arch after treatment and retention. The latter correlation coefficients were all positive and generally higher than the previous ones. However, evaluation of individual scattergrams indicates that anatomic contact points that are displaced relative to the

194 Surbeck et al. American Journal of Orthodontics and Dentofacial Orthopedics February 1998 Fig. 8. Maxillary study models made before (A) and after (B) treatment and approximately 18 years after retention (C) of patient treated nonextraction. Note space reopening between central incisors and between right lateral and central incisors. dental arch after treatment occasionally may relapse in the opposite direction after retention (Figs. 2, 4 through 7). On the other hand, we cannot rule out that some of the teeth may have been placed in overcorrected positions during treatment in our sample. In keeping with a previous study, 10 we found that the pattern of rotational displacement relative to the dental arch has a high tendency to repeat itself. The correlation coefficients for all four incisors were statistically significant, and high enough to be considered clinically significant, both between before treatment and after retention, as well as between after treatment and after retention. Moreover, evaluation of the scattergrams representing the teeth with the lowest association between before treatment and after retention indicate that rotational relapse opposite to the direction of treatment may be very unusual (Figs. 3 through 7). The reason why a few teeth showed rotational relapse opposite to the direction of posttreatment rotational position relative to the dental arch may be due to overcorrection of teeth that were severely rotated before treatment. Taken together, our data regarding anatomic contact point discrepancy and incisor rotation may be interpreted to indicate that postretention displacement of anatomic contact points relative to the dental arch that is due to labial or lingual displacement of the teeth is random relative to the pattern of pretreatment tooth positions and most likely the result of arch length reduction, whereas contact point displacement that is due to tooth rotation has a strong tendency to mimic the pretreatment pattern. If so, a slight overcorrection of severely rotated teeth during active treatment may be considered justified. Our results confirm the assumption that pretreatment spacing in the maxillary anterior segment is a significant risk factor for interdental spacing after retention (Figs. 7 and 8). The odds of experiencing severe spacing rather than perfect alignment of the maxillary anterior teeth, defined according to our inclusion criteria, may be 3.7 times higher for every 0.3 mm of average interdental spacing before treatment. This result suggests that the retention strategy may be modified according to pretreatment spacing, and that patients presenting with severe spacing should be informed about the likelihood of postretention relapse. We also found that incomplete space closure is a risk factor for relapse (Fig. 7). The odds for severe postretention spacing rather than perfect alignment may be 27.3 times higher for every 0.3 mm of average interdental space at time of appliance removal. These results underscore the importance of treatment quality to improve the chance for postretention alignment of the maxillary anterior teeth. Our results indicate that constriction of the maxillary anterior arch segment during active treatment is a risk factor for interdental spacing longterm out of retention, and that such spacing is associated with expansion of the anterior segment after retention (Table IV). However, the correlation coefficients were small, suggesting that arch length changes only partly may explain the variation in postretention spacing of the maxillary anterior teeth. Another relapse factor may be the tendency for individual teeth to return to their initial positions, due to fiber pull, 19-21 insufficient root parallelism during space closure, piling up interdental tissue, or presence of abnormal frenum attachments. 8 Such variables were not controlled for in our study. However, the pattern of interdental spaces had a small tendency to repeat itself in our sample of cases with severe postretention spacing. The fact that the data indicate anatomic contact point discrepancy and incisor rotation relative to the dental arch after retention also in the group selected for perfect alignment (Table III) suggests that the computer-generated arch forms may not consistently represent the actual dental arch. One reason

American Journal of Orthodontics and Dentofacial Orthopedics Volume 113, No. 2 Surbeck et al. 195 may be that despite perfect tooth alignment, some point angles may have been marked slightly off center on the study models, making it impossible to fit a curve to intersect all the digitized points. However, such biases are likely to be randomly distributed in the sample, and small compared with those associated with manual measurements. It was considered meaningless to include the cases selected for perfect postretention alignment when testing for associations between individual tooth positions at the different time periods. Likewise, it was considered meaningless to include the cases selected for irregularity when testing for associations between individual interdental spaces, and the cases selected for spacing when testing for associations between anatomic contact point displacement and rotation. The whole sample was used when testing for associations between changes in arch dimensions and malalignment to ensure the largest variation possible of the outcome variable. CONCLUSIONS Our results suggest that anatomic contact point displacement of the maxillary anterior teeth and maxillary incisor rotation relative to the dental arch, as well as interdental spacing before treatment, are significant risk factors for postretention relapse of alignment. The pattern of postretention contact point displacement and interdental spacing may be random relative to the pattern of initial tooth positions, whereas the pattern of rotational displacement relative to the dental arch has a strong tendency to repeat itself. We thank Dr. Paul Sampson for sharing his computer programs for fitting conic sections. REFERENCES 1. Little RM, Wallen TR, Riedel RA. Stability and relapse of mandibular anterior alignment first premolar extraction cases treated by traditional edgewise orthodontics. Am J Orthod 1981;80:349-64. 2. Edwards JG. A long-term prospective evaluation of the circumferential supracrestal fiberotomy in alleviating orthodontic relapse. Am J Orthod Dentofac Orthop 1988;93:380-7. 3. Little RM, Riedel RA. Postretention evaluation of stability and relapse mandibular arches with generalized spacing. Am J Orthod Dentofac Orthop 1989;95:37-41. 4. McReynolds DC, Little RM. Mandibular second premolar extraction postretention evaluation of stability and relapse. Angle Orthod 1991;61:133-44. 5. Paquette ED, Beattie JR, Johnston LE. A long-term comparison of nonextraction and premolar extraction edgewise therapy in borderline Class II patients. Am J Orthod Dentofac Orthop 1992;102:1-14. 6. Årtun J, Garol JD, Little RM. Long-term stability of mandibular incisors following successful treatment of Angle Class II, Division 1 malocclusions. Angle Orthod 1996;66:229-38. 7. Zachrisson BU. The bonded lingual retainer and multiple spacing of anterior teeth. Swed Dent J 1982;15(Suppl):247-55. 8. Edwards JG. the diastema, the frenum, the frenectomy: a clinical study. Am J Orthod 1977;71:489-508. 9. Sullivan TC, Turpin DL, Årtun J. A postretention study of patients presenting with maxillary midline diastema. Angle Orthod 1996;66:131-8. 10. Swanson WD, Riedel RA, D Anna JA. Postretention study: incidence and stability of rotated teeth in humans. Angle Orthod 1975;45:198-203. 11. Sadowsky C, Sakols E. Long term assessment of orthodontic relapse. Am J Orthod 1982;82:456-63. 12. Uhde MD, Sadowsky C, BeGole EA. Long-term stability of dental relationships after orthodontic treatment. Angle Orthod 1983;53:240-52. 13. Johnson-Egger N. Long-term stability of maxillary anterior alignment following orthodontic treatment and retention. [MSD thesis.] Seattle: University of Washington; 1992. 14. de la Cruz A, Sampson P, Little RM, Årtun J, Shapiro PA. Long-term changes in arch form after orthodontic treatment and retention. Am J Orthod Dentofac Orthop 1995;107:518-30. 15. Lundstrom A. Tooth size and occlusion in twins. New York: S Karger; 1948. 16. Sampson PD. Dental arch shape: a statistical analysis using conic sections. Am J Orthod 1981;79:535-47. 17. Sampson PD. Fitting conic sections to very scattered data: an iterative refinement of the Bookstein algorithm. Comput Graph Image Proc 1982;18:97-108. 18. Dahlberg G. Statistical methods for medical and biological students. London: George Allen and Unwin Ltd.; 1940. p. 122-32. 19. Reitan K. Tissue rearrangement during rotation of orthodontically rotated teeth. Angle Orthod 1959;29:105-13. 20. Edwards JG. A study of the periodontium during orthodontic rotation of teeth. Am J Orthod 1968;54:441-6. 21. Edwards JG. A surgical procedure to eliminate rotational relapse. Am J Orthod 1970;57:35-46.