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Predicting the “Wits” appraisal from the ANB angle
Predicting the “Wits” appraiscxl ji-ov~ the ANB angle Saul Rotberg, D.D.S.,* Neil Fried, D.M.D.,** James Kane, D.M.D., M.S.,*** and Everett Shapiro,
Ch Rotberg
D.M.D.****
Boston, Muss. Luterul cephalometric rudiogruphs wew taken of twenty-jitre hogs und r~\‘c’trt~:/7tx~ girls hetrc,een the U~CJSof 10 und 14. Euc,h subject hud either a Clus~ I or C’ltr.\.\ !I mulocclwion. u good gro,cath puttrrn, und un ANB rungr qf I to 8 &~I.cc~.~. TheWits uppruisal for these patients runged from -4 to 9 mm. Ten patients htrd t, nc,qutivc Wits value, runging from -0.5 to -4 mm. und an ANB runge of I to 4 tlcgrec~.\. Fort? putients hud II positive Wits vuiuc, ranging jiwm 0.5 to 9 mm., und (III AN6 ra~r,yc’of I .5 to 8 degrees. TMlelve ($ the putients with a positiw Wits vulue had the .sunw AN6 runge as those \rYth negative Wits vulurs. The Peurson produc,t moment c~orrclution weficient KU.Sperformed on both the neRatiw and positir’r Wits group”. ;lio stutisticully .sign$cant correlation wus jtiund between ANB vulues and the Wits vu1ue.c for the negutive Wits group (r = 0.08. t = 27, df = 8). A .stutisticwll~ ~sign~fic~unt ‘correlation M’USfour~d for the positive Wits group (r = 0.62, t = 3.87, cf = 38. p < 0.001). Using the sunw stutistics. IloM~e~~er,a less stutisticull~~ signjfiwnt correlation MYISdetermined,for thr group with u positiw Wits vulu~ und un ANB value greater than 4 degrees (r = 0.53, t = .Z.l2. cif = 26, p < 0.005). No c~linicull~ .siq$cunt relutionships tt’ere ,ji)und j?w unp of the groups of putier1t.s .studicd.
Key words: Wits appraisal. ANB, cephalometric analyses, malocclusion, orthodontics
H
istorically, orthodontists have related both the maxilla and the mandible to reference points in the cranial base of the skull to determine if there are any disharmonies in growth between them. l6 The measurement most commonly used to detect jaw disharmonies is the ANB angle.” It has long been recognized that nasion is, indeed, not a “fixed” point and, therefore, any changes in its position will, in turn, affect the amount of discrepancy that exists between the jaws as measured by the ANB angle. Any “rotation” of the jaws by either growth or treatment can also change the ANB reading.” In order to obviate these inherent inconsistencies, the “Wits” appraisal,” which relates points A and B to the occlusal plane, was devised. This analysis does not use cranial or extracranial landmarks, and this should, theoretically, give a more accurate picture of any anteroposterior skeletal disharmonies existing between the maxilla and the mandible. I2 From the Department of Orthodontics, Tufts University School of Dental Medicine. *Now in private practice in Mexico City, Mexico. **Graduate Student. ***Orthodontic Consultant, Tufts Dental Facility for the Handicapped; in private practice in Natick, Mass. ****Chairman, Orthodontic Department.
636
0002.9416/80/060636+07$00.70/0
01980
The C. V. Mosby
Co.
Predicting
“Wits”
637
appraisal from ANB angle
Table I. Demographic information ANB (degrees) sex
NO.
Age Mean 2 S.D.
Females Males
25 25
11.7 t 1.2 12.2 2 1.1
OM (degrees)
Mean
S.D.
Mean
S.D.
4.5 5.0
1.9 2.0
15.9 15.9
3.2 2.8
The purpose of this article is to correlate the “Wits” appraisal with ANB differences on a group of patients to see how accurately one can predict the “Wits, ” given the latter. Review of the literature Since its introduction into the orthodontic literature by Riedel,i6 who employed point A and point B of Downs,5 the ANB angle has remained the most commonly used cephalometric measurement to describe the variance in apical base relations. This angle is used in most modern cephalometric analyses as a way of differentiating between a skeletal Class I and a Class II malocclusion.* The variability of cranial landmarks, however, has been establishedI since these points are affected by such things as radiographic distortionlo and growth.15 Holdaway” showed that points A and B changed substantially during treatment and that this change was due to both treatment mechanics and growth. Buchin* studied the effect of treatment mechanics on ANB difference and found: “The dentofacial pattern can be greatly improved as a result of orthodontic treatment. Most often this improvement is the result of the distal retraction of the maxillary teeth and the reduction or the holding in place of the anterior limit of maxillary basal bone or point A. If the mandible shows a significant increase in anteroposterior dimensions during this interval, the change in facial profile becomes dramatic.” Freeman8 was one of the first to show that the ANB difference can be very misleading since the relative position of nasion can alter the true value of the angle. Moore,15 Enlow,’ and othersfi have shown that nasion changes during growth, usually in an anterior and slightly superior direction. This is due to resorption and deposition of bone on either side of the frontonasal suture and expansion of the diploe. Point A also varies in a similar manner without treatment. Taylor,*O using 225 patients, showed that the ANB difference was not always a true indication of apical base relationship, since ANB varies with the relative position of nasion and the amount of facial divergence. Baber and Meredith’ demonstrated that between the ages of 5 and 15, point A descends inferiorly from nasion by 11.6 mm, or 27 percent. Thus, the ANB difference is not meant to be used alone to determine whether the maxilla is large or the mandible small. In 1975, Jacobson’* devised the “Wits” appraisal of jaw disharmony which sought to assess apical base disharmonies without the use of cranial landmarks. “In brief, the appraisal entails the dropping of perpendiculars from point A and B onto the occlusal plane. In a Class I malocclusion, points A0 and BO generally coincide; in Class II malocclusions BO point is behind point AO; and in Class III skeletal disharmonies, BO point is ahead of point AO. “14 The normal range of variation is -2 to +6mm. Since points A and B are related to the occlusal plane rather than to a cranial or
im
638 Rother;r: ct rrl
J Orthod. .Ircnr 1980
IANB4'
WITS -&m
Fig. 1. Patient with negative Wits value
extracranial reference point, clockwise or counterclockwise rotation of the jaws does not affect the over-all assessmentof the severity of jaw disharmony. l3 Sperrylg points out that this is important in differentiating between patients who can be treated orthodontically and those patients who are surgical candidates. It is also important to remember, however, that the tilting of the occlusal plane during treatment mechanics or growth can change a Class II to a Class I. Methods and materials Lateral cephalometric radiographs were taken of twenty-five male and twenty-five female subjects who were orthodontically untreated and who exhibited either a Class I or a Class II, Division 1 or Division 2 malocclusion and a good facial growth pattern (OM angle of 8 degrees to 20 degrees with a mean of 15.7 degrees). All subjects were white, of middle socioeconomic status, and were from 10 to 14 years of age, with a mean age of 11.8 years. All of the cephalometric radiographs were taken at the Tufts Orthodontic Clinic with the Margolis cephalostat, a General Electric x-ray head, and Kodak X-Omat film. Each film was traced by the same operator, using the following cephalometric landmarks and planes53s, I23I*, 20,21: N-Nasion, the anteriormost point of the suture between the frontal and nasal bones. A-Subspinale, the deepest point of the curvature of the premaxilla between the anterior nasal spine and the crest of the maxillary alveolar process. B-Supramentale, the most posterior point in the concavity between the crest of the mandibular alveolar process and pogonion.
Volume 71 Number 6
Predicting “Wits” uppraisul from ANB angle
639
WITS+5mm
Fig. 2. Patient with positive Wits value.
ANB-The angle formed by the intersection of lines extending from point A and point B of nasion. Occlusal plane-A line joining the distobuccal cusp of the upper first molar (or last molar in occlusion) to a point midway between the incisal tips of the maxillary and mandibular central incisors (same as used in “Wits” appraisal). Gn-Gnathion, midpoint between pogonion and menton at the curvature of the symphysis. Go-Gonion, the most anterior, inferior point in the bony chin. Mandibular plane-A line connecting the points gonion and gnathion. OM angle-The angle formed by the intersection of the occlusal plane and the mandibular plane. “Wits” appraisal-The distance between points A0 and BO which are the points of contact of a perpendicular drawn from points A and B onto the occlusal plane. A second operator traced the cephalometric films, and the landmarks were determined by averaging the distance between his interpretation and that of the first operator where a discrepancy existed. The measurements were compiled. Interrelationships were determined according to the Pearson product moment correlation coefficients and regression analysis. Findings The fifty patients selected for this study had an ANB range of 1 to 8 degrees; an OM r.ange of 8 to 20 degrees, with a mean of 15.7 degrees; and a “Wits” range of -4 to 9
Table II. Statistical summary for negative \amplcs N = 10 ;;i ANB = 2.75 U Wits = 1.35 S- ANB == 1.14 S Wits = 1.02 S; ANB = 0.13 S; Wits = 0. I I r = 0.08; t = 0.23; df = 8 not significant
Table III. Statistical summary for positive samples N = 40 f? ANB = 5.28 Y Wits = 3.73 S+ ANB = 1.77 S’ Wits = 2.32 S; ANB = 0.08 Ss Wits = 0.14 r = 0.62; t = 4.87; df = 38; P < 0.001 significant r2 = 38 I ~ r2 = Error = 62%
Table IV. Statistical summary for positive samples limited to 4.5 degress or more N = 28 ZANB = 6.18 Y Wits = 4.41 S+ ANB = I.19 S+ Wits = 2.37 S; ANB = 0.05 g Wits = 0.19 r = 0.53; t = 3.12; df = 26; P < 0.005 significant rp = 28 I - r* = Error = 72%
mm. (Table I). Ten of these patients had a negative “Wits” value of -0.5 mm. to -4 mm., with an ANB value of 1 to 4 degrees (Fig. 1). Forty patients had positive “Wits” values of 0.5 to 9 mm., with ANB values ranging from 1.5 to 8 degrees (Fig. 2). Both of these groups had similar age and OM angle distributions. The group of forty patients with positive “Wits” values can, in turn, be subdivided into two groups. The first group, consisting of twelve patients, had positive “Wits” values but the same ANB range, namely, 1.5 to 4 degrees, as the group of ten patients with negative “Wits” values. The second group, comprising twenty-eight patients, also had positive “Wits” values but an ANB range of 4.5 to 8 degrees, which was higher than the ANB range of the patients with negative “Wits” values. The Pearson product moment correlation coefficient was performed on negative and positive “Wits” groups separately. No relationship was found for negative “Wits”
Volume 17 Number 6
Predicting “Wits” appraisal from ANB angle
641
measurements (r = 0.08, t = 27, df = 8) (Table II). However, a statistically significant correlation (I’ = 0.62, t = 4.87, df = 38 P < 0.001) was found for the positive “Wits” measurements (Table III). Using the same statistics, however, a statistically significant correlation was determined (r = 0.53, t = 3.12, df = 26) for the group with an ANB value greater than (P < 0.005) 4 degrees (Table IV). Discussion The ANB angle, although a most widely used means of evaluating anteroposterior apical base discrepancies, is subject to great variation, depending on the anteroposterior and vertical position of nasion. If the points A and B remain constant on the same vertical line, there is a 2.5 degree change in the ANB angle for every 5 mm. of displacement of N in an anteroposterior direction. When points A and B remain fixed in the normal positional relationship established by the Bjork analysis, 3 theoretically the ANB angle is decreased by 0.5 degree for each 5 mm. vertical displacement of N in an upward direction. There is a 1 degree increase in the ANB angle for each 5 mm. of vertical displacement of N in a downward direction.2 Similarly, any tipping of the jaws from treatment will also affect the ANB reading. A counterclockwise rotation, as evidenced by an upward tipping of ANS and a low mandibular plane angle, will lessen the ANB value. Conversely, a clockwise rotation of the jaws, resulting in a downward tipping of ANS and a high mandibular plane angle, will increase the ANB angle.r3 The “Wits” appraisal also measures apical base discrepancies, but it does so by relating points A and B to the occlusal plane, thus eliminating cranial landmarks and some geometric inconsistencies just described. There are, however, certain shortcomings to the “Wits” analysis. Changes in the occlusal plane during treatment, such as intrusion of incisors or extrusion of molars, will alter the “Wits” value and perhaps change a Class II malocclusion into a Class I. Since both the ANB angle and the “Wits” appraisal are used to evaluate the same parameters, there should theoretically be a strong correlation between the two. In our study, we found that with a positive ANB angle of 4 degrees or less, the “Wits” value could be either positive or negative and that there is no correlation between the ANB and “Wits” measurements if the latter is negative. Therefore, in order to use a regression equation to predict the value of the “Wits” appraisal when the ANB is between 1 and 4 degrees, we must first know whether the “Wits” value is positive or negative. Furthermore. when both the ANB and “Wits” values are positive, we can predict the “Wits” measurement, given the ANB angle, with only a 38 percent accuracy. The ‘clinical uselessnessof these relationships should be obvious. It is interesting to note that, in our sample, when the ANB angle was greater than 4 degrees, the “Wits” values were all positive. The accuracy of predicting the “Wits” -from the ANB angle was 28 percent, however, which was less than in the sample as a ,whole (ANB, 1 to 8 degrees). Further studies are indicated, perhaps with larger sample sizes, to determine if the lack of a clinically significant correlation between ANB and “Wits” values is indeed due to the variability of the ANB measurement as a parameter of apical base discrepancy or the “Wits” analysis. The effect of the cant of the occlusal plane on the “Wits” appraisal should also be studied.‘*
642
Rothcq et id.
Summary
and conclusions
The ANB and “Wits” values of fifty patients were correlated to see how accurately one can predict the “Wits” value, given the ANB measurement. There is no correlation between these two values when the “Wits” measurement is negative. In our study. when the positive ANB measurement was less than 4 degrees, the “Wits” values could be either positive or negative. When the ANB angle was between 4 and 8 degrees, all “Wits” values were positive. When both the “Wits” values were positive and the ANB values ranged between 1 and 8 degrees, we could predict the “Wits” measurement with a 38 percent accuracy. If the ANB range was narrowed to 4 to 8 degrees, all “Wits” values were positive and we could predict them 28 percent of the time. Both these figures are statistically significant but clinically irrelevant. Further studies are needed to determine the exact nature of these interrelationships. We thank Dr. Russi K. Gheewalla for his guidance during the study and in the preparation of the cephalometric tracings. We also thank R. Ernest Clark, Ph.D., for his help in the statistical analysis of our data. Finally, we would like to thank Ms. Linda S. Johnson for her typing of the manuscript. REFERENCES I. Baber. W. E., and Meredith, H. V.: Childhood change in depth and height of the face, with special reference to Downs’ A point, AM. J. ORTHOD. 51: 913, 1965. 2. Binder, R. C.: The geometry of cephalometrics, J. Clin. Orthod. 13: 258, 1979. 3. Bjork, A.: The face in profile, Sven. Tandlak. Tidskr. 40: 5 B, 1947. 4. Buchnin, Irving D.: An appraisal of the effect of the edgewise arch appliance in modifying the dentofacial profile, AM. J. ORTHOD. 43: 801-818, 1957. 5. Downs, W. B.: Variations in facial relationship: Their significanoe in treatment and prognosis, AM. J. ORTHOD. 34: 812-840,
1948.
6. Dreyer, C. J., and Joffe, B. M.: A concept of cephalometric interpretation, Angle Orthod. 33: 123, 1963. 7. Enlow, Donald H.: A morphogenetic analysis of facial growth, AM. J. ORTHOD. 52: 283, 1966. 8. Freeman, R. S.: A radiographic method of analysis of the relation of the structures of the lower face to each other and to the occlusal plane of the teeth, M. S. D. thesis, Northwestern University Dental School, 1950. 9. Graber, T. M.: Roentgenographic cephalometric workshop, AM. J. ORTHOD. 44: 928, 1958. 10. Hatton, M. E., and Grainger, R. M.: Reliability of measurements from cephalograms at the Burlington Orthodontic Research Center, J. Dent. Res. 37: 853.859, 1958. 11. Holdaway, Reed A.: Changes in relationship of points A and B during orthodontic treatment. AM. I. ORTHOD. 42: 176, 1956.
12. 13. 14. 15. 16. 17. 18. 19. 20.
Jacobson, A.: The “Wits” appraisal of jaw disharmony, AM. J. ORTHOD. 67: 125-138. 1975. Jacobson, A.: Application of the “Wits” appraisal, AM. J. ORTHOD. 70: 179-189, 1976. Jacobson, A.: The proportionate template as a diagnostic aid, AM. J. ORTHOD. 75: 156. 1979. Moore, Alton W.: Observations on facial growth and itsclinical significance, AM. J. ORTHOD. 45: 399-423, 1959. Riedel, Richard A.: The relation of maxillary structures to cranium in malocclusion and in normal occlusion, Angle Orthod. 22: 140-145, 1952. Salzmann, J. A.: The Research Workshop on Cephalometrics, AM. J. ORTHOD. 46: 834, 1960. Schudy, F. F.: Cant of the occlusal plane and axial inclination of teeth, Angle Orthod. 33: 69, 1963. Sperry, T. P.: Differential treatment planning for mandibular prognathism, AM. J. ORTHOD. 71: 531, 1977. Taylor, C. M.: Changes in the relationship of nasion, point A, and point B and the effect upon ANB, AM. J. ORTHOD. 56: 143, 1969.
21. Sassouni, V., and Sotereanos, G. C.: Diagnosis and treatment of dentofacial abnormalities, Springfield, Ill., 1974, Charles C Thomas Publisher. 83 speen St
Ch Rotberg
D.M.D.****
Boston, Muss. Luterul cephalometric rudiogruphs wew taken of twenty-jitre hogs und r~\‘c’trt~:/7tx~ girls hetrc,een the U~CJSof 10 und 14. Euc,h subject hud either a Clus~ I or C’ltr.\.\ !I mulocclwion. u good gro,cath puttrrn, und un ANB rungr qf I to 8 &~I.cc~.~. TheWits uppruisal for these patients runged from -4 to 9 mm. Ten patients htrd t, nc,qutivc Wits value, runging from -0.5 to -4 mm. und an ANB runge of I to 4 tlcgrec~.\. Fort? putients hud II positive Wits vuiuc, ranging jiwm 0.5 to 9 mm., und (III AN6 ra~r,yc’of I .5 to 8 degrees. TMlelve ($ the putients with a positiw Wits vulue had the .sunw AN6 runge as those \rYth negative Wits vulurs. The Peurson produc,t moment c~orrclution weficient KU.Sperformed on both the neRatiw and positir’r Wits group”. ;lio stutisticully .sign$cant correlation wus jtiund between ANB vulues and the Wits vu1ue.c for the negutive Wits group (r = 0.08. t = 27, df = 8). A .stutisticwll~ ~sign~fic~unt ‘correlation M’USfour~d for the positive Wits group (r = 0.62, t = 3.87, cf = 38. p < 0.001). Using the sunw stutistics. IloM~e~~er,a less stutisticull~~ signjfiwnt correlation MYISdetermined,for thr group with u positiw Wits vulu~ und un ANB value greater than 4 degrees (r = 0.53, t = .Z.l2. cif = 26, p < 0.005). No c~linicull~ .siq$cunt relutionships tt’ere ,ji)und j?w unp of the groups of putier1t.s .studicd.
Key words: Wits appraisal. ANB, cephalometric analyses, malocclusion, orthodontics
H
istorically, orthodontists have related both the maxilla and the mandible to reference points in the cranial base of the skull to determine if there are any disharmonies in growth between them. l6 The measurement most commonly used to detect jaw disharmonies is the ANB angle.” It has long been recognized that nasion is, indeed, not a “fixed” point and, therefore, any changes in its position will, in turn, affect the amount of discrepancy that exists between the jaws as measured by the ANB angle. Any “rotation” of the jaws by either growth or treatment can also change the ANB reading.” In order to obviate these inherent inconsistencies, the “Wits” appraisal,” which relates points A and B to the occlusal plane, was devised. This analysis does not use cranial or extracranial landmarks, and this should, theoretically, give a more accurate picture of any anteroposterior skeletal disharmonies existing between the maxilla and the mandible. I2 From the Department of Orthodontics, Tufts University School of Dental Medicine. *Now in private practice in Mexico City, Mexico. **Graduate Student. ***Orthodontic Consultant, Tufts Dental Facility for the Handicapped; in private practice in Natick, Mass. ****Chairman, Orthodontic Department.
636
0002.9416/80/060636+07$00.70/0
01980
The C. V. Mosby
Co.
Predicting
“Wits”
637
appraisal from ANB angle
Table I. Demographic information ANB (degrees) sex
NO.
Age Mean 2 S.D.
Females Males
25 25
11.7 t 1.2 12.2 2 1.1
OM (degrees)
Mean
S.D.
Mean
S.D.
4.5 5.0
1.9 2.0
15.9 15.9
3.2 2.8
The purpose of this article is to correlate the “Wits” appraisal with ANB differences on a group of patients to see how accurately one can predict the “Wits, ” given the latter. Review of the literature Since its introduction into the orthodontic literature by Riedel,i6 who employed point A and point B of Downs,5 the ANB angle has remained the most commonly used cephalometric measurement to describe the variance in apical base relations. This angle is used in most modern cephalometric analyses as a way of differentiating between a skeletal Class I and a Class II malocclusion.* The variability of cranial landmarks, however, has been establishedI since these points are affected by such things as radiographic distortionlo and growth.15 Holdaway” showed that points A and B changed substantially during treatment and that this change was due to both treatment mechanics and growth. Buchin* studied the effect of treatment mechanics on ANB difference and found: “The dentofacial pattern can be greatly improved as a result of orthodontic treatment. Most often this improvement is the result of the distal retraction of the maxillary teeth and the reduction or the holding in place of the anterior limit of maxillary basal bone or point A. If the mandible shows a significant increase in anteroposterior dimensions during this interval, the change in facial profile becomes dramatic.” Freeman8 was one of the first to show that the ANB difference can be very misleading since the relative position of nasion can alter the true value of the angle. Moore,15 Enlow,’ and othersfi have shown that nasion changes during growth, usually in an anterior and slightly superior direction. This is due to resorption and deposition of bone on either side of the frontonasal suture and expansion of the diploe. Point A also varies in a similar manner without treatment. Taylor,*O using 225 patients, showed that the ANB difference was not always a true indication of apical base relationship, since ANB varies with the relative position of nasion and the amount of facial divergence. Baber and Meredith’ demonstrated that between the ages of 5 and 15, point A descends inferiorly from nasion by 11.6 mm, or 27 percent. Thus, the ANB difference is not meant to be used alone to determine whether the maxilla is large or the mandible small. In 1975, Jacobson’* devised the “Wits” appraisal of jaw disharmony which sought to assess apical base disharmonies without the use of cranial landmarks. “In brief, the appraisal entails the dropping of perpendiculars from point A and B onto the occlusal plane. In a Class I malocclusion, points A0 and BO generally coincide; in Class II malocclusions BO point is behind point AO; and in Class III skeletal disharmonies, BO point is ahead of point AO. “14 The normal range of variation is -2 to +6mm. Since points A and B are related to the occlusal plane rather than to a cranial or
im
638 Rother;r: ct rrl
J Orthod. .Ircnr 1980
IANB4'
WITS -&m
Fig. 1. Patient with negative Wits value
extracranial reference point, clockwise or counterclockwise rotation of the jaws does not affect the over-all assessmentof the severity of jaw disharmony. l3 Sperrylg points out that this is important in differentiating between patients who can be treated orthodontically and those patients who are surgical candidates. It is also important to remember, however, that the tilting of the occlusal plane during treatment mechanics or growth can change a Class II to a Class I. Methods and materials Lateral cephalometric radiographs were taken of twenty-five male and twenty-five female subjects who were orthodontically untreated and who exhibited either a Class I or a Class II, Division 1 or Division 2 malocclusion and a good facial growth pattern (OM angle of 8 degrees to 20 degrees with a mean of 15.7 degrees). All subjects were white, of middle socioeconomic status, and were from 10 to 14 years of age, with a mean age of 11.8 years. All of the cephalometric radiographs were taken at the Tufts Orthodontic Clinic with the Margolis cephalostat, a General Electric x-ray head, and Kodak X-Omat film. Each film was traced by the same operator, using the following cephalometric landmarks and planes53s, I23I*, 20,21: N-Nasion, the anteriormost point of the suture between the frontal and nasal bones. A-Subspinale, the deepest point of the curvature of the premaxilla between the anterior nasal spine and the crest of the maxillary alveolar process. B-Supramentale, the most posterior point in the concavity between the crest of the mandibular alveolar process and pogonion.
Volume 71 Number 6
Predicting “Wits” uppraisul from ANB angle
639
WITS+5mm
Fig. 2. Patient with positive Wits value.
ANB-The angle formed by the intersection of lines extending from point A and point B of nasion. Occlusal plane-A line joining the distobuccal cusp of the upper first molar (or last molar in occlusion) to a point midway between the incisal tips of the maxillary and mandibular central incisors (same as used in “Wits” appraisal). Gn-Gnathion, midpoint between pogonion and menton at the curvature of the symphysis. Go-Gonion, the most anterior, inferior point in the bony chin. Mandibular plane-A line connecting the points gonion and gnathion. OM angle-The angle formed by the intersection of the occlusal plane and the mandibular plane. “Wits” appraisal-The distance between points A0 and BO which are the points of contact of a perpendicular drawn from points A and B onto the occlusal plane. A second operator traced the cephalometric films, and the landmarks were determined by averaging the distance between his interpretation and that of the first operator where a discrepancy existed. The measurements were compiled. Interrelationships were determined according to the Pearson product moment correlation coefficients and regression analysis. Findings The fifty patients selected for this study had an ANB range of 1 to 8 degrees; an OM r.ange of 8 to 20 degrees, with a mean of 15.7 degrees; and a “Wits” range of -4 to 9
Table II. Statistical summary for negative \amplcs N = 10 ;;i ANB = 2.75 U Wits = 1.35 S- ANB == 1.14 S Wits = 1.02 S; ANB = 0.13 S; Wits = 0. I I r = 0.08; t = 0.23; df = 8 not significant
Table III. Statistical summary for positive samples N = 40 f? ANB = 5.28 Y Wits = 3.73 S+ ANB = 1.77 S’ Wits = 2.32 S; ANB = 0.08 Ss Wits = 0.14 r = 0.62; t = 4.87; df = 38; P < 0.001 significant r2 = 38 I ~ r2 = Error = 62%
Table IV. Statistical summary for positive samples limited to 4.5 degress or more N = 28 ZANB = 6.18 Y Wits = 4.41 S+ ANB = I.19 S+ Wits = 2.37 S; ANB = 0.05 g Wits = 0.19 r = 0.53; t = 3.12; df = 26; P < 0.005 significant rp = 28 I - r* = Error = 72%
mm. (Table I). Ten of these patients had a negative “Wits” value of -0.5 mm. to -4 mm., with an ANB value of 1 to 4 degrees (Fig. 1). Forty patients had positive “Wits” values of 0.5 to 9 mm., with ANB values ranging from 1.5 to 8 degrees (Fig. 2). Both of these groups had similar age and OM angle distributions. The group of forty patients with positive “Wits” values can, in turn, be subdivided into two groups. The first group, consisting of twelve patients, had positive “Wits” values but the same ANB range, namely, 1.5 to 4 degrees, as the group of ten patients with negative “Wits” values. The second group, comprising twenty-eight patients, also had positive “Wits” values but an ANB range of 4.5 to 8 degrees, which was higher than the ANB range of the patients with negative “Wits” values. The Pearson product moment correlation coefficient was performed on negative and positive “Wits” groups separately. No relationship was found for negative “Wits”
Volume 17 Number 6
Predicting “Wits” appraisal from ANB angle
641
measurements (r = 0.08, t = 27, df = 8) (Table II). However, a statistically significant correlation (I’ = 0.62, t = 4.87, df = 38 P < 0.001) was found for the positive “Wits” measurements (Table III). Using the same statistics, however, a statistically significant correlation was determined (r = 0.53, t = 3.12, df = 26) for the group with an ANB value greater than (P < 0.005) 4 degrees (Table IV). Discussion The ANB angle, although a most widely used means of evaluating anteroposterior apical base discrepancies, is subject to great variation, depending on the anteroposterior and vertical position of nasion. If the points A and B remain constant on the same vertical line, there is a 2.5 degree change in the ANB angle for every 5 mm. of displacement of N in an anteroposterior direction. When points A and B remain fixed in the normal positional relationship established by the Bjork analysis, 3 theoretically the ANB angle is decreased by 0.5 degree for each 5 mm. vertical displacement of N in an upward direction. There is a 1 degree increase in the ANB angle for each 5 mm. of vertical displacement of N in a downward direction.2 Similarly, any tipping of the jaws from treatment will also affect the ANB reading. A counterclockwise rotation, as evidenced by an upward tipping of ANS and a low mandibular plane angle, will lessen the ANB value. Conversely, a clockwise rotation of the jaws, resulting in a downward tipping of ANS and a high mandibular plane angle, will increase the ANB angle.r3 The “Wits” appraisal also measures apical base discrepancies, but it does so by relating points A and B to the occlusal plane, thus eliminating cranial landmarks and some geometric inconsistencies just described. There are, however, certain shortcomings to the “Wits” analysis. Changes in the occlusal plane during treatment, such as intrusion of incisors or extrusion of molars, will alter the “Wits” value and perhaps change a Class II malocclusion into a Class I. Since both the ANB angle and the “Wits” appraisal are used to evaluate the same parameters, there should theoretically be a strong correlation between the two. In our study, we found that with a positive ANB angle of 4 degrees or less, the “Wits” value could be either positive or negative and that there is no correlation between the ANB and “Wits” measurements if the latter is negative. Therefore, in order to use a regression equation to predict the value of the “Wits” appraisal when the ANB is between 1 and 4 degrees, we must first know whether the “Wits” value is positive or negative. Furthermore. when both the ANB and “Wits” values are positive, we can predict the “Wits” measurement, given the ANB angle, with only a 38 percent accuracy. The ‘clinical uselessnessof these relationships should be obvious. It is interesting to note that, in our sample, when the ANB angle was greater than 4 degrees, the “Wits” values were all positive. The accuracy of predicting the “Wits” -from the ANB angle was 28 percent, however, which was less than in the sample as a ,whole (ANB, 1 to 8 degrees). Further studies are indicated, perhaps with larger sample sizes, to determine if the lack of a clinically significant correlation between ANB and “Wits” values is indeed due to the variability of the ANB measurement as a parameter of apical base discrepancy or the “Wits” analysis. The effect of the cant of the occlusal plane on the “Wits” appraisal should also be studied.‘*
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Rothcq et id.
Summary
and conclusions
The ANB and “Wits” values of fifty patients were correlated to see how accurately one can predict the “Wits” value, given the ANB measurement. There is no correlation between these two values when the “Wits” measurement is negative. In our study. when the positive ANB measurement was less than 4 degrees, the “Wits” values could be either positive or negative. When the ANB angle was between 4 and 8 degrees, all “Wits” values were positive. When both the “Wits” values were positive and the ANB values ranged between 1 and 8 degrees, we could predict the “Wits” measurement with a 38 percent accuracy. If the ANB range was narrowed to 4 to 8 degrees, all “Wits” values were positive and we could predict them 28 percent of the time. Both these figures are statistically significant but clinically irrelevant. Further studies are needed to determine the exact nature of these interrelationships. We thank Dr. Russi K. Gheewalla for his guidance during the study and in the preparation of the cephalometric tracings. We also thank R. Ernest Clark, Ph.D., for his help in the statistical analysis of our data. Finally, we would like to thank Ms. Linda S. Johnson for her typing of the manuscript. REFERENCES I. Baber. W. E., and Meredith, H. V.: Childhood change in depth and height of the face, with special reference to Downs’ A point, AM. J. ORTHOD. 51: 913, 1965. 2. Binder, R. C.: The geometry of cephalometrics, J. Clin. Orthod. 13: 258, 1979. 3. Bjork, A.: The face in profile, Sven. Tandlak. Tidskr. 40: 5 B, 1947. 4. Buchnin, Irving D.: An appraisal of the effect of the edgewise arch appliance in modifying the dentofacial profile, AM. J. ORTHOD. 43: 801-818, 1957. 5. Downs, W. B.: Variations in facial relationship: Their significanoe in treatment and prognosis, AM. J. ORTHOD. 34: 812-840,
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6. Dreyer, C. J., and Joffe, B. M.: A concept of cephalometric interpretation, Angle Orthod. 33: 123, 1963. 7. Enlow, Donald H.: A morphogenetic analysis of facial growth, AM. J. ORTHOD. 52: 283, 1966. 8. Freeman, R. S.: A radiographic method of analysis of the relation of the structures of the lower face to each other and to the occlusal plane of the teeth, M. S. D. thesis, Northwestern University Dental School, 1950. 9. Graber, T. M.: Roentgenographic cephalometric workshop, AM. J. ORTHOD. 44: 928, 1958. 10. Hatton, M. E., and Grainger, R. M.: Reliability of measurements from cephalograms at the Burlington Orthodontic Research Center, J. Dent. Res. 37: 853.859, 1958. 11. Holdaway, Reed A.: Changes in relationship of points A and B during orthodontic treatment. AM. I. ORTHOD. 42: 176, 1956.
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Jacobson, A.: The “Wits” appraisal of jaw disharmony, AM. J. ORTHOD. 67: 125-138. 1975. Jacobson, A.: Application of the “Wits” appraisal, AM. J. ORTHOD. 70: 179-189, 1976. Jacobson, A.: The proportionate template as a diagnostic aid, AM. J. ORTHOD. 75: 156. 1979. Moore, Alton W.: Observations on facial growth and itsclinical significance, AM. J. ORTHOD. 45: 399-423, 1959. Riedel, Richard A.: The relation of maxillary structures to cranium in malocclusion and in normal occlusion, Angle Orthod. 22: 140-145, 1952. Salzmann, J. A.: The Research Workshop on Cephalometrics, AM. J. ORTHOD. 46: 834, 1960. Schudy, F. F.: Cant of the occlusal plane and axial inclination of teeth, Angle Orthod. 33: 69, 1963. Sperry, T. P.: Differential treatment planning for mandibular prognathism, AM. J. ORTHOD. 71: 531, 1977. Taylor, C. M.: Changes in the relationship of nasion, point A, and point B and the effect upon ANB, AM. J. ORTHOD. 56: 143, 1969.
21. Sassouni, V., and Sotereanos, G. C.: Diagnosis and treatment of dentofacial abnormalities, Springfield, Ill., 1974, Charles C Thomas Publisher. 83 speen St