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Floating norms for the ANB angle as guidance for clinical considerations
Floating noms for the ANB angle as guidance for clinical considerations Seppo JBirvinen, Dr. Odont., Kuopio,
Finland
If the ANB angle is used in cephalometric analyses, its individual nature should be recognized. A method to interpret the measured values of the ANB angle has been recently presented by Hussels and Nanda. This article introduces another method to evaluate the appropriateneq of the measured values. A regression avalysis was applied to explain the individual variation of the ANB angle in a sample of 55 untreated orthodontic patients, aged 7 to 14 years, with Class I (Angle) malocclusion. Approximately 63% of the variation of the ANB angle could be explained by the variation of the SNA and NSL/ML angles. The regression produced a list of floating norms of the ANB angle for different facial types. The floating norms can help to interpret the individual normal variation of the ANB angle. (AM J ORTHOD DENTOFAC ORTHOP 90: 383-387, 1986.)
Key words: Cephalornetrics, sagittal ma!occlusions, apical base relationship, ANB angle, floating norms
I n orthodontic diagnosis and treatment planning, it is important to recognize the sag&al difference between the maxillary and mandibular apical bases. This difference has been generally measured by using the ANB angle, irrespective of the fact that the unreliability of the ANB angle has been convincingly documented. I-6 A specific measurement for the apical base difference should measure only this difference and nothing else. Unfortunately, such kind of measurement does not exist.’ When the ANB angle is used, its individual and multifactorial nature should be considered in clinical orthodontics. A method to interpret the measured value of the ANB angle has been recently presented by Hussels and Nanda.4 The method is based on geometric calculations and gives a number of individual norms for different skeletal forms. Another way to interpret the variability of cephalometric measurements is to study the associations between some suitable v&ables.* This procedure leads to the so-called floating norms.9 The aim of this study was to develop floating norms for the ANB angle by means of the regression model recently presented by the author.6 MATERIAL AND METHODS
The material for the study consisted of 55 lateral cephalometric radiographs of orthodontically untreated children, aged 7-14 years (mean age, 10.5 years), with Class I (Angle) malocclusion. They required some orthodontic treatment for dental or dentoalveolar anomalies (the Class I malocclusion group in an earlier study6).
The following dimensions were measured on tracings of the radiographs to the nearest 0.5” or 0.5 mm (Fig. 1): -ANB angle (y) -SNA angle (x,). In case of Class I malocclusions, it was assumed that this angle indicated the anteroposterior and vertical positions of the point N in relation to the jaws.“.* -NSL/ML angle (x,). It was assumed that this angle indicated the inclination of the jaws in relation to the anterior cranial base.6 -NSAr angle (x,). It was assumedthat this angle indicated the inclination of the cranial base.’
-N-S line (~4). This line indicated the anteroposterior position of the point N.
Means and standard deviations were computed for each measurement. When Bnalyzing the variation of the ANB angle, the following multiple regression was computed: y = b,x, + blx2 + b3x3 + b4x4 + a The independent variables (x,-h) were added to the regression in the above mentioned hierarchical order and the corresponding R* values were calculated. The statistical evaluation of the regression was made by means of the analysis of variance. The chosen level of significance was 1%. RESULTS
The means and standard deviations of the measurements are presented in Table I. The regression analysis indicated that 63.1% of the variation of the ANB angle could be explained by the 383
384
Am. J. Orthod.
Jiirvinen
Dentofac. Orthop. November 1986
Table I. Means (x) and standard deviations (SD) of the measurements
x SD
ANB
SNA
NSLIML
NSA r
N-S
2.80 2.21
84.12 3.64
31.24 5.29
120.56 4.50
70.52 3.19
Table II. Analysis of the variation of the ANB angle Independent variables added to the regression
I
SNA NSL/ML NSAr N-S Residual
SSR
I
107.54 166.72 174.11 174.18 90.04
R2
I
0.4070 0.6310 0.6590 0.6592 0.3408
RZ change
F
I
0.4070 0.2240 0.0280 0.0002 -
59.72 32.86 4.10 0.04 -
Table Ill. Floating norms for the ANB angle in relation to the SNA and NSL/ML
P
I
0.05 -
angles
SNA NSLIML 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40
77
78
79
80
81
82
83
84
85
86
87
88
-2.0 -1.8 -1.6 -1.4 - 1.2 -1.0 -0.8 -0.5 -0.3 -0.1 0.1 0.3 0.5 0.7 9.9 1.1
-1.5 - 1.3 -1.1 -0.9 -0.7 -0.5 -0.3 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6
- 1.0 -0.8 -0.6 -0.4 -0.2 0.0 0.2 0.4 0.6 0.8 1.0 1.3 1.5 1.7 1.9 2.1
-0.5 -0.3 -0.1 0.1 0.3 0.5 0.7 0.9 1.1 1.3 1.5 1.7 1.9 2.1 2.3 2.5
0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4 2.6 2.8 3.0
0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.1 2.3 2.5 2.7 2.9 3.1 3.3 3.5
0.9 1.1 1.3 1.5 1.7 1.9 2.1 2.3 2.5 2.7 2.9 3.1 3.3 3.5 3.8 4.0
1.4 1.6 1.8 2.0
1.8 2.0 2.2 2.5 2.7 2.9 3.1 3.3 3.5 3.7 3.9 4.1 4.3 4.5 4.7 4.9
2.3 2.5 2.7 2.9 3.1 3.3 3.5 3.7 3.9 4.1 4.4 4.6 4.8 5.0 5.2 5.4
2.8 3.0 3.2 3.4 3.6 3.8 4.0 4.2 4.4 4.6 4.8 5.0 5.2 5.4 5.6 5.8
3.3 3.5 3.7 3.9 4.1 4.3 4.5 4.7 4.9 5.1 5.3 5.5 5.7 5.9 6.1 6.3
variation of the SNA (P < 0.001) and NSL/ML angles (P < 0.001). The explanation power of the regression model increased to 65.9% by adding the NSAr angle to the model (0.01 < P < 0.05) and 65.92% by adding the N-S line (P < 0.05) (Table II). Thus, it seemed reasonable to derive floating norms for the ANB angle from the original equation6 y = 0.472 x, + 0.204 x2 - 43.386
The results are presented in Table III. DISCUSSION
As pointed out by Moyers and Bookstein,’ an angle has six degrees of freedom. A cephalometric angle like ANB has been formed by two lines drawn through three
2.2 2.4 2.6 2.8 3.0 3.2 3.4 3.6 3.8 4.0 4.2 4.4
points and all these points can move in every possible direction on the plane. The cephalometric theory of the ANB angle recognized only two degrees of freedomthe movements of the points A and B in the anteroposterior direction. Several studies have demonstrated the effects of the anteroposterior and vertical displacements of the point N and those of the vertical displacements of the points A and B on the ANB angle.le6 According to these reports, the ANB angle will increase when the relative length of the anterior cranial base decreases, when the anterior facial height decreases, or when the jaws rotate clockwise in relation to the cranial base. On the contrary, it will be decreased by opposite changes in the facial skeleton. Hussels and Nanda4 used a geometric model and
Vohu? 90 Number 5
Floating
norms for ANB angle as clinical
guidance
385
SNA.90.5’ SNS*67.SANa. 3. 70.5mm
Fig. 1. Cephalometric points, planes, and angles used in the study. Points: N (nasion)-The anterior limit of sutura nasofrontalis. S (sella)-Center of sella turcica. A (Down’s A point)The deepest point on the anterjor contour of the maxillary alveolar process. 6 (Down’s B point)-The deepest point on the anterior contour of the mandibular afveolar process. Gn (gnathion)-The deepest point of the chin. Ar (articulare)-The point of intersection of the posterior border of the mandible and the basis sphenoid. Planes: NSL-The line from N to S. ML (mandibular plane)-The tangent of the lower surface of the mandible through Gn. Angles: SNA, ANB, NSAr, and f$L/ML.
developed a number of individual norms for the ANB angle: The method was based on the assumption that the A-B line should be at right angle to the occlusal line in normal occlusion.’ The ANB angle could thus be calculated from the formula ANB
= tan-l(b
aFczs
y)
where a = the distance between the points A and B b = the distance between the points N and B y = SNB + NSLIML
- 90”
However, the direction of the occlusal line is greatly dependent on the degree of eruption of the teeth. The A-B line is men not necessarily at right angle to the occlusal line. Therefore, the method includes a possibility of more or less significant errors in individual cases. In the present regression model, 63% of the variation of the ANB angle could be explained by the variation of the SNA and NSL/ML angles. The results seemed to give support to the assumption that the horizontal and vertical variations of the point N and the variation in the inclination between the jaws and the
Fig. 2. Cephalometric tracing of a 14-year-old girl with cleidocranial dysostosis.” The measured ANB angle is 3”, indicating a normal sagittal relation between the jaws. The floating individual norm (0.472x 90.5” + 0.204x 30” - 43.386”) is 5.5”. The difference, 3” - 5.5” = - 2.!?, indicates a Class Ill sagittal relationship.
cranial base, both of them having an effect upon the ANB angle, could be partly measured by these angles.6 There may be, however, some errors in the estimations. The location of point A can be affected by individual variations of the curvature between the points ANS and Pr, and the NSL/ML angle can be changed by individual variation in the form of the mandible. The NSAr angle was used in the regression model to better describe the inclination of the anterior cranial base.* The explanation power of the model was thereby increased to 65.9%. The NSAr angle measures vertical displacements of point N, but it can also be affected by displacements of point S and by those of the very artificial point Ar. In this connection, the variation of the point Ar is confusing. The variation of the point S has an effect upon the SNA, NSL/ML, and NSAr angles, but it has no effect on the ANB angle. This connection was assumed to be helpful in evaluating the confusing variation of the SNA and NSL/ML angles. Because of the weak explanation power (R* change = 2.8%), the NSAr angle was, however, excluded from the final model of regression. The S-N line was used in the regression model because it was assumed that the length of the anterior cranial base would indicate the anteroposterior position of the point N. However, the explanation power of the N-S line was very weak (R2 change = 0.02%). On the other hand, a result like this could have been predicted because absolute distances cannot be compared when the scales of the drawings are different in different persons. Only distance ratios are comparable. lo
366
Am. J. Orthod.
Jiirvinen
Dentofac. Orthop. November 1986
CASE 87 2s YEARS
CASE 87 s YEARS
Flg. 3. Cephalometric tracings of a female case presented by Hussels and Nanda? The readings of the cephalometric analysis are as follow: ANB SNA NSL/OL NSLIML
8 Yr 3.5 77.0” 22.0 42.0”
25 yr 3.0” 80.0” 12.5” 42.0”
At the age of 8 years, the geometrically calculated normal value’ for the ANB angle is 3.8”. The difference between the measured and calculated values is - 0.3”, indicating a normal relation between the jaws. The floating norm is 1.5”. The difference between the measured value and the floating norm is 2”, which indicates rather a slightly distal than a neutral relation between the jaws. At the age of 25 years, the geometrically caiculated normal value is - 0.4”. The difference (3” - - 0.4” = 3.4”) indicates a Class II relationship. The floating norm is 2.9”. The difference between the measured ANB and the floating norm Is O.l’, which indicates a normal relation between the jaws.
The regression model gave a number of floating norms for the ANB angle. These floating norms may be helpful in making better diagnoses in suspect cases. Fig. 2 shows tbe cephalometric tracing of a case with abnormal facial skeleton.” The measured ANB (3”) indicates a normal sag&al relation between the apical bases. The floating norm for this case is 5.5”. The difference between the measured ANB and the floating norm is -2.5”, which indicates a Class III sag&al relation. In this case, the measured ANB was obviously misleading. Fig. 3 shows a case presented by Hussels and Nar~da.~ At the age of 8 years, the measured ANB was 3.5”. The geometrically calculated4 normal value was 3.8”. The difference ( - 0.3”) indicates a normal sag&al relation between the jaws. The floating norm given by the present method is 1.5”. The difference, 3.5” - 1.5” = 2”, indicates a slightly distal rather than a neutral relation between the jaws (observe the labially inclined lower incisors). At the age of 25 years, the measured ANB was 3”. The geometrically calculated normal value was -0.4”. The difference (3.4”) indicates a Class II relationship. The floating norm was 2.9”. and the small difference (0.1”) indicates a neutral
sagittal relation between the jaws. In this case, the geometric method4 led to an erroneous evaluation because of the rotation of the occlusal line. In some other cases (for example, in cases with a morphogenic rotation of the mandibular line’*), the floating norm could be erroneous. If the ANB angle is used, its individual nature should be recognized. The floating norms, such as presented in this article, can offer the possibility of estimating individual normal values for the ANB angle. The method can be an alternative to the geometric method of Hussels and Nanda.4 However, both methods can give only estimates for tbe individually normal relationship; these estimates are suitable as guidance for diagnostic considerations, rather than an conclusive diagnostic norms. REFERENCES 1. Beatty EJ: A modified technique for evaluating apical base relationship. AM J ORTHOD68: 303-315, 1975. 2. Binder RE: The geometry of cephalometrics. J Clin Orthod 13: 258-263, 1979. 3. Bishara SE, Fahl J, Petersor! LC: Longitudinal changes in the
Volume90
Floating
norms for ANB angle as clinical
guidance
387
Number 5
4. 5. 6. 7. 8. 9.
ANB angle and Wits appraisal: Clinical implication. AM J ORTHOD84: 133-136, 1983. Hussels W, Nanda RS: Analysis of the factors affecting angle ANB. AM J ORTHOD85: 41 l-423, 1984. Jacobson A: The “Wits” appraisal of jaw disharmony. AM J ORTHOD67: 125138, 1975. Jiirvinen S: An analysis of the variation of the ANB angle. A statistical appraisal. AM J ORTHOD87: 144-146, 1985. Moyers RE, Bookstein FL: The inappropriateness of conventional cephalometrics. AM J ORTHOD75: 599-617, 1979. Jlrvinen S: Saddle angle and maxillary prognathism. A radiological analysis of the association between the NSAr and SNA angles. Br J Orthod 11: 209-213, 1984. Hasund A, Biie OE: Floating norms as guidance for the position of the lower incisors. Angle Orthod 50: 165-168, 1980.
10. Bookstein FL: On the cephalometrics of skeletal change. AM J ORTHOD82: 177-198, 1982. 11. Jarvmen S: Cephalometric findings in three casesof cleidocranial dysostosis. AM J ORTHOD79: 184-191, 1981. 12. Lavergne J, Gasson N: Analysis and classification of the rotational growth pattern without implants. Br J Orthod 9: 51-56, 1982. Reprint requests to: Dr. Seppo J%rvinen Karjusaari SF-15240 Lahti, Finland
Finland
If the ANB angle is used in cephalometric analyses, its individual nature should be recognized. A method to interpret the measured values of the ANB angle has been recently presented by Hussels and Nanda. This article introduces another method to evaluate the appropriateneq of the measured values. A regression avalysis was applied to explain the individual variation of the ANB angle in a sample of 55 untreated orthodontic patients, aged 7 to 14 years, with Class I (Angle) malocclusion. Approximately 63% of the variation of the ANB angle could be explained by the variation of the SNA and NSL/ML angles. The regression produced a list of floating norms of the ANB angle for different facial types. The floating norms can help to interpret the individual normal variation of the ANB angle. (AM J ORTHOD DENTOFAC ORTHOP 90: 383-387, 1986.)
Key words: Cephalornetrics, sagittal ma!occlusions, apical base relationship, ANB angle, floating norms
I n orthodontic diagnosis and treatment planning, it is important to recognize the sag&al difference between the maxillary and mandibular apical bases. This difference has been generally measured by using the ANB angle, irrespective of the fact that the unreliability of the ANB angle has been convincingly documented. I-6 A specific measurement for the apical base difference should measure only this difference and nothing else. Unfortunately, such kind of measurement does not exist.’ When the ANB angle is used, its individual and multifactorial nature should be considered in clinical orthodontics. A method to interpret the measured value of the ANB angle has been recently presented by Hussels and Nanda.4 The method is based on geometric calculations and gives a number of individual norms for different skeletal forms. Another way to interpret the variability of cephalometric measurements is to study the associations between some suitable v&ables.* This procedure leads to the so-called floating norms.9 The aim of this study was to develop floating norms for the ANB angle by means of the regression model recently presented by the author.6 MATERIAL AND METHODS
The material for the study consisted of 55 lateral cephalometric radiographs of orthodontically untreated children, aged 7-14 years (mean age, 10.5 years), with Class I (Angle) malocclusion. They required some orthodontic treatment for dental or dentoalveolar anomalies (the Class I malocclusion group in an earlier study6).
The following dimensions were measured on tracings of the radiographs to the nearest 0.5” or 0.5 mm (Fig. 1): -ANB angle (y) -SNA angle (x,). In case of Class I malocclusions, it was assumed that this angle indicated the anteroposterior and vertical positions of the point N in relation to the jaws.“.* -NSL/ML angle (x,). It was assumed that this angle indicated the inclination of the jaws in relation to the anterior cranial base.6 -NSAr angle (x,). It was assumedthat this angle indicated the inclination of the cranial base.’
-N-S line (~4). This line indicated the anteroposterior position of the point N.
Means and standard deviations were computed for each measurement. When Bnalyzing the variation of the ANB angle, the following multiple regression was computed: y = b,x, + blx2 + b3x3 + b4x4 + a The independent variables (x,-h) were added to the regression in the above mentioned hierarchical order and the corresponding R* values were calculated. The statistical evaluation of the regression was made by means of the analysis of variance. The chosen level of significance was 1%. RESULTS
The means and standard deviations of the measurements are presented in Table I. The regression analysis indicated that 63.1% of the variation of the ANB angle could be explained by the 383
384
Am. J. Orthod.
Jiirvinen
Dentofac. Orthop. November 1986
Table I. Means (x) and standard deviations (SD) of the measurements
x SD
ANB
SNA
NSLIML
NSA r
N-S
2.80 2.21
84.12 3.64
31.24 5.29
120.56 4.50
70.52 3.19
Table II. Analysis of the variation of the ANB angle Independent variables added to the regression
I
SNA NSL/ML NSAr N-S Residual
SSR
I
107.54 166.72 174.11 174.18 90.04
R2
I
0.4070 0.6310 0.6590 0.6592 0.3408
RZ change
F
I
0.4070 0.2240 0.0280 0.0002 -
59.72 32.86 4.10 0.04 -
Table Ill. Floating norms for the ANB angle in relation to the SNA and NSL/ML
P
I
angles
SNA NSLIML 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40
77
78
79
80
81
82
83
84
85
86
87
88
-2.0 -1.8 -1.6 -1.4 - 1.2 -1.0 -0.8 -0.5 -0.3 -0.1 0.1 0.3 0.5 0.7 9.9 1.1
-1.5 - 1.3 -1.1 -0.9 -0.7 -0.5 -0.3 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6
- 1.0 -0.8 -0.6 -0.4 -0.2 0.0 0.2 0.4 0.6 0.8 1.0 1.3 1.5 1.7 1.9 2.1
-0.5 -0.3 -0.1 0.1 0.3 0.5 0.7 0.9 1.1 1.3 1.5 1.7 1.9 2.1 2.3 2.5
0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4 2.6 2.8 3.0
0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.1 2.3 2.5 2.7 2.9 3.1 3.3 3.5
0.9 1.1 1.3 1.5 1.7 1.9 2.1 2.3 2.5 2.7 2.9 3.1 3.3 3.5 3.8 4.0
1.4 1.6 1.8 2.0
1.8 2.0 2.2 2.5 2.7 2.9 3.1 3.3 3.5 3.7 3.9 4.1 4.3 4.5 4.7 4.9
2.3 2.5 2.7 2.9 3.1 3.3 3.5 3.7 3.9 4.1 4.4 4.6 4.8 5.0 5.2 5.4
2.8 3.0 3.2 3.4 3.6 3.8 4.0 4.2 4.4 4.6 4.8 5.0 5.2 5.4 5.6 5.8
3.3 3.5 3.7 3.9 4.1 4.3 4.5 4.7 4.9 5.1 5.3 5.5 5.7 5.9 6.1 6.3
variation of the SNA (P < 0.001) and NSL/ML angles (P < 0.001). The explanation power of the regression model increased to 65.9% by adding the NSAr angle to the model (0.01 < P < 0.05) and 65.92% by adding the N-S line (P < 0.05) (Table II). Thus, it seemed reasonable to derive floating norms for the ANB angle from the original equation6 y = 0.472 x, + 0.204 x2 - 43.386
The results are presented in Table III. DISCUSSION
As pointed out by Moyers and Bookstein,’ an angle has six degrees of freedom. A cephalometric angle like ANB has been formed by two lines drawn through three
2.2 2.4 2.6 2.8 3.0 3.2 3.4 3.6 3.8 4.0 4.2 4.4
points and all these points can move in every possible direction on the plane. The cephalometric theory of the ANB angle recognized only two degrees of freedomthe movements of the points A and B in the anteroposterior direction. Several studies have demonstrated the effects of the anteroposterior and vertical displacements of the point N and those of the vertical displacements of the points A and B on the ANB angle.le6 According to these reports, the ANB angle will increase when the relative length of the anterior cranial base decreases, when the anterior facial height decreases, or when the jaws rotate clockwise in relation to the cranial base. On the contrary, it will be decreased by opposite changes in the facial skeleton. Hussels and Nanda4 used a geometric model and
Vohu? 90 Number 5
Floating
norms for ANB angle as clinical
guidance
385
SNA.90.5’ SNS*67.SANa. 3. 70.5mm
Fig. 1. Cephalometric points, planes, and angles used in the study. Points: N (nasion)-The anterior limit of sutura nasofrontalis. S (sella)-Center of sella turcica. A (Down’s A point)The deepest point on the anterjor contour of the maxillary alveolar process. 6 (Down’s B point)-The deepest point on the anterior contour of the mandibular afveolar process. Gn (gnathion)-The deepest point of the chin. Ar (articulare)-The point of intersection of the posterior border of the mandible and the basis sphenoid. Planes: NSL-The line from N to S. ML (mandibular plane)-The tangent of the lower surface of the mandible through Gn. Angles: SNA, ANB, NSAr, and f$L/ML.
developed a number of individual norms for the ANB angle: The method was based on the assumption that the A-B line should be at right angle to the occlusal line in normal occlusion.’ The ANB angle could thus be calculated from the formula ANB
= tan-l(b
aFczs
y)
where a = the distance between the points A and B b = the distance between the points N and B y = SNB + NSLIML
- 90”
However, the direction of the occlusal line is greatly dependent on the degree of eruption of the teeth. The A-B line is men not necessarily at right angle to the occlusal line. Therefore, the method includes a possibility of more or less significant errors in individual cases. In the present regression model, 63% of the variation of the ANB angle could be explained by the variation of the SNA and NSL/ML angles. The results seemed to give support to the assumption that the horizontal and vertical variations of the point N and the variation in the inclination between the jaws and the
Fig. 2. Cephalometric tracing of a 14-year-old girl with cleidocranial dysostosis.” The measured ANB angle is 3”, indicating a normal sagittal relation between the jaws. The floating individual norm (0.472x 90.5” + 0.204x 30” - 43.386”) is 5.5”. The difference, 3” - 5.5” = - 2.!?, indicates a Class Ill sagittal relationship.
cranial base, both of them having an effect upon the ANB angle, could be partly measured by these angles.6 There may be, however, some errors in the estimations. The location of point A can be affected by individual variations of the curvature between the points ANS and Pr, and the NSL/ML angle can be changed by individual variation in the form of the mandible. The NSAr angle was used in the regression model to better describe the inclination of the anterior cranial base.* The explanation power of the model was thereby increased to 65.9%. The NSAr angle measures vertical displacements of point N, but it can also be affected by displacements of point S and by those of the very artificial point Ar. In this connection, the variation of the point Ar is confusing. The variation of the point S has an effect upon the SNA, NSL/ML, and NSAr angles, but it has no effect on the ANB angle. This connection was assumed to be helpful in evaluating the confusing variation of the SNA and NSL/ML angles. Because of the weak explanation power (R* change = 2.8%), the NSAr angle was, however, excluded from the final model of regression. The S-N line was used in the regression model because it was assumed that the length of the anterior cranial base would indicate the anteroposterior position of the point N. However, the explanation power of the N-S line was very weak (R2 change = 0.02%). On the other hand, a result like this could have been predicted because absolute distances cannot be compared when the scales of the drawings are different in different persons. Only distance ratios are comparable. lo
366
Am. J. Orthod.
Jiirvinen
Dentofac. Orthop. November 1986
CASE 87 2s YEARS
CASE 87 s YEARS
Flg. 3. Cephalometric tracings of a female case presented by Hussels and Nanda? The readings of the cephalometric analysis are as follow: ANB SNA NSL/OL NSLIML
8 Yr 3.5 77.0” 22.0 42.0”
25 yr 3.0” 80.0” 12.5” 42.0”
At the age of 8 years, the geometrically calculated normal value’ for the ANB angle is 3.8”. The difference between the measured and calculated values is - 0.3”, indicating a normal relation between the jaws. The floating norm is 1.5”. The difference between the measured value and the floating norm is 2”, which indicates rather a slightly distal than a neutral relation between the jaws. At the age of 25 years, the geometrically caiculated normal value is - 0.4”. The difference (3” - - 0.4” = 3.4”) indicates a Class II relationship. The floating norm is 2.9”. The difference between the measured ANB and the floating norm Is O.l’, which indicates a normal relation between the jaws.
The regression model gave a number of floating norms for the ANB angle. These floating norms may be helpful in making better diagnoses in suspect cases. Fig. 2 shows tbe cephalometric tracing of a case with abnormal facial skeleton.” The measured ANB (3”) indicates a normal sag&al relation between the apical bases. The floating norm for this case is 5.5”. The difference between the measured ANB and the floating norm is -2.5”, which indicates a Class III sag&al relation. In this case, the measured ANB was obviously misleading. Fig. 3 shows a case presented by Hussels and Nar~da.~ At the age of 8 years, the measured ANB was 3.5”. The geometrically calculated4 normal value was 3.8”. The difference ( - 0.3”) indicates a normal sag&al relation between the jaws. The floating norm given by the present method is 1.5”. The difference, 3.5” - 1.5” = 2”, indicates a slightly distal rather than a neutral relation between the jaws (observe the labially inclined lower incisors). At the age of 25 years, the measured ANB was 3”. The geometrically calculated normal value was -0.4”. The difference (3.4”) indicates a Class II relationship. The floating norm was 2.9”. and the small difference (0.1”) indicates a neutral
sagittal relation between the jaws. In this case, the geometric method4 led to an erroneous evaluation because of the rotation of the occlusal line. In some other cases (for example, in cases with a morphogenic rotation of the mandibular line’*), the floating norm could be erroneous. If the ANB angle is used, its individual nature should be recognized. The floating norms, such as presented in this article, can offer the possibility of estimating individual normal values for the ANB angle. The method can be an alternative to the geometric method of Hussels and Nanda.4 However, both methods can give only estimates for tbe individually normal relationship; these estimates are suitable as guidance for diagnostic considerations, rather than an conclusive diagnostic norms. REFERENCES 1. Beatty EJ: A modified technique for evaluating apical base relationship. AM J ORTHOD68: 303-315, 1975. 2. Binder RE: The geometry of cephalometrics. J Clin Orthod 13: 258-263, 1979. 3. Bishara SE, Fahl J, Petersor! LC: Longitudinal changes in the
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ANB angle and Wits appraisal: Clinical implication. AM J ORTHOD84: 133-136, 1983. Hussels W, Nanda RS: Analysis of the factors affecting angle ANB. AM J ORTHOD85: 41 l-423, 1984. Jacobson A: The “Wits” appraisal of jaw disharmony. AM J ORTHOD67: 125138, 1975. Jiirvinen S: An analysis of the variation of the ANB angle. A statistical appraisal. AM J ORTHOD87: 144-146, 1985. Moyers RE, Bookstein FL: The inappropriateness of conventional cephalometrics. AM J ORTHOD75: 599-617, 1979. Jlrvinen S: Saddle angle and maxillary prognathism. A radiological analysis of the association between the NSAr and SNA angles. Br J Orthod 11: 209-213, 1984. Hasund A, Biie OE: Floating norms as guidance for the position of the lower incisors. Angle Orthod 50: 165-168, 1980.
10. Bookstein FL: On the cephalometrics of skeletal change. AM J ORTHOD82: 177-198, 1982. 11. Jarvmen S: Cephalometric findings in three casesof cleidocranial dysostosis. AM J ORTHOD79: 184-191, 1981. 12. Lavergne J, Gasson N: Analysis and classification of the rotational growth pattern without implants. Br J Orthod 9: 51-56, 1982. Reprint requests to: Dr. Seppo J%rvinen Karjusaari SF-15240 Lahti, Finland