TRANSCRITO DO AM. J. ORTHOD.  September 1975

A modified technique for evaluating apical base relationships
 

Edward J. Beatty Lieutenant Colonel, DC, USA
Fort Benning, Ga.
 

One of the basic problems of othodontics has been the failure to develop a completely accurate cephalometric method of assessing apical base relationships. This method, of course, should use landmarks that are stable and easy to find. The popular ANB measurement usus four points to establish the position of maxilla to mandible and cranial base. These landmarks – sella turcica, point A, nasion, and point B, - were introduced by Down’s¹ and adapted by Riedel⁴ to reflect the discrepancy in apical base relationships. Today Riedel’s ANB measurement is the most commonly used; yet the literature is replete with references to the fact that points A and B are influenced by treatment. In addition, research has massed overwhelming evidence that nasion changes to a significant extent during treatment. There is need for a technique which will eliminate or reduce the innacuracies in the presently used landmarks. This study will demonstrate a revised method of establishing apical relationships. It will introduce an angular measurement and a number of linear measurements which originate from more stable landmarks.

Review of the literature

A review of the literature demonstrates just how far the science of orthodontics has progressed since Broadbent introduced a functional method of radiographic analysis in 1931. The development of the Broadbent – Bolton cephalometer and the history of its evolution to common usage are familiar to all orthodontists. It will be sufficient to mention here that the modern cephalometric head plate permits a critical analysis of attainable goals and results when the standard diagnostic procedures outlined by Down’s,¹ Riedel,⁴ etc. are carried out.
The literature agrees that the cephalometric landmarks used for a diagnostic analysis have certain limitations, but this subject is not a new one and it is not the purpose of this article to downgrade the credibility of cephalometrics. The fact is that, even trough the measurements made from cephalograms are not precise, the technical process itself is accurate. Hatton and Grainger³ studied the reliability of cephalometric measurements and concluded that despite a 10 per cent magnification error and variation introduced by growth, current techniques were acceptable for orthodontic purposes.
The important fact to consider is that certain landmarks are more reliable and easier to find than others. For example, Steiner, has long advocated the use of point D (the cross section of the sysmphysis of the mandible) as a reference point in our analysis. The advantages are clear cut since the landmark is surrounded by cortical bone and is isolated from the areas where tooth movement and growth changes occur.
Steiner’s interest in point D was directed at the use of this landmark for evaluating the anteroposterior position of the mandible. A logical development from this would be to use point D as a rerplacement for point B, incorporating the same advantages mentioned above. Point D would then be a factor in measuring apical base differences.
While considering the fact that certain landmarks are more reliable than others, subsequent developments in the science of cephalometrics must be evalueated. In 1950 Freeman² introduced some interesting observations in his thesis. In discussing the SNA measurement, he demonstrated the variation that could be introduced by the relative position of nasion. Bacause of growth at nasion and other geometric factors, he pointed out that the ANB difference might prove misleading in the evaluation of apical base differences.
In order to compensate for the amount of discrepancy introduced by the change in position of nasion. Freeman introduced his AXB angle, originating from Frankfort horizontal. A geometric perpendicular was extended from point A to Frankfort horizontal, with X marking the point of intersection. A line was then extended from point B to X, forming the angle AXB, which provides data similar to the ANB measurement but eliminates the problem of nasion.
The possible merit of this technique was emphasized by an article published in 1956 by Stoner and associates⁸ in which perpendiculars from points A and B to Frankfort horizontal were used as a basis for linear measurements of the apical base difference. However, credit for the originality of the idea must go to the Freeman thesis. By adapting this concept of using perpendiculars SN plane instead of Frankfort horizontal, we can eliminate the use of nasion except as a landmark to establish a plane. Point B is eliminated the use of nasion except as a landmark to establish a plane. Point B is eliminated by using Steiner’s point D. The resulting angular measurement (Fig. 1) would appear to have obvious advantages over the ANB technique.
Unfortunately, the study of angular cephalometric measurements reveals a rather basic geometric problem. Freeman pointed out that the variation in length of the face will prove to be a dominant factor. As the face lengthens with growth, the apical bases will become more divergent while the angular measurement (ANB or AXD) remains the same. A geometric triangle shows that the longer the lines are extended from an angle, the farther apart they become in relation to each other. Because of this, it is possible for two patients to have identical ANB values but a different horizontal distance between points A and B since the length of their faces may vary.

It seems obvious that the technical solution to the geometric problem would be the introduction of linear measurements. Stoner and his colleagues ⁵ used linear measurements in 1956 when they studied Tweed’s cases. Perpendiculars were dropped from Frankfort horizontal to points A and B in order to measure the horizontal distance between the apical bases. In 1969 Taylor⁹ demonstrated just how enlightening linear measurements could be. His linear measurement was derived by dropping perpendiculars from SN to points A and B. He also measured from the midpoint of sella to nasion and the point B intercept on the SN plane. These measurements revealed information about the amount of growth which ocurred during treatment.
The linear measurements introduced by Stoner, Taylor, etc. are enlightening and definitely not complex. They demonstrate the evolution of the science of cephalometrics toward a method which will assimilate all treatment factors and correlate them in a logical manner.
The many analyses designed by the various contributors attempt to evaluate completely the effects of growth and treatement mechanics of the patient. The challenge to the science of cephalometrics rests in the fact it is not and never can be an exact science. However, it does appear that certain techniques can be refined to allow us to derive all the information that our cephalograms contain and in many ways hide from us.

Materials, methods, and procedures

The material for this study consisted of cephalometric roentgenograms which were taken with the Broadbent-Bolton type of cephalometer. The films were exposed, processed, and traced by a standard technique.

Pantient selections was limited to Class II, Division 1 cases since their divergent apical base relationship graphically demonstrates the changes taking place as a result of growth and influenced by orthodontic treatment.
Specifically, cephalometric roentgenograms were taken before and after treatment of fifty patients over a period of approximately 24 months. No control group was indicated, since the study was based on individual landmarks changes occurring during treatment. No consideration was given to sex, extraction or nonextraction of teeth, growth trend, etc. The project was specifically aimed at the relative changes in certain landmarks and their relationships to apical base measurements in current use. The information was investigated as follows:
1. The questionable reliability of the ANB measurement as opposed to an angular apical base measurement using geometric projections to less variable landmarks.
2. The introduction and use of linear measurements between the apical bases to compensate for errors inherent in angular measurements.
3. Over-all comparison of the linear and angular measurements to determine their usefullness.
Tracings were made on the before- and after-treatment roentgenograms, drawn from the anatomic landmarks as illustrated in Figs. 1 and 2. For the sake of brevity, only the unfamiliar landmarks and reference planes will be defined:
1. Point X — A geometrically constructed perpendicular from point A to the sella-nasion plane.
2. Angle AXD — The interior angle formed by the intersection of lines extending from point A and point D at the X intercept on the SN plane.

3. D’ — A geometrically constructed perpendicular from point D to the sella-nasion plane.
4. S-D’ — A line segment along the sella-nasion plane, extending from the center of sella turcica to the intersection of the perpendicular drawn from point D to the S-N plane.
5. A-D’ — A line segment along the sella-nasion plane, extending from the center of sella turcica to the intersection of the perpendicular drawn from point A to the S-N plane.
The linear measurements used were as follows:
1. The distance from the center of sella turcica to nasion.
2. The distance from the center of sella turcica to D’ and A’.
3. The distance from point A to D’, drawn horizontal and parallel to the S-N plane.

The data for all linear and angular measurements were recorded as pretreatment and posttreatment figures and placed in Tables I and II.
The linear measurements were designed to illustrate the changes which occurred when the relationship of the apical bases was changed. For example, one case demonstrated a classic change from a Class II molar and canine relationship to Class I. ANB went from 7 degrees to 3.5 degrees during treatment. A study of the linear measurements allows us to determine exactly what occurred:
 
 

It is obvious that this patient is what we call a “good grower”. The A-D’ measurement has decreased 4.5 mm. and is directly related to the 4 mm. of growth which ocurred at S-D’. It obvious that treatment mechanics were under control as S-A’ increased by only 1 mm. as S-N was growing a total of 4 mm.

Findings

Angular apical base measurements (Table I). In this phase of the investigation two methods which evaluated the anteroposterior relationship of the apical bases were compared. The first was the technique introduced by Riedel10 which uses the ANB difference. The second method was discussed and illustrated under “Materials, Methods, and Procedures” and will be referred to as the AXD method. This consists of constructing a perpendicular from point A to the SN plane, X marking the point of intersection. A line was then extended from point D to the X intercept, forming an inner angle — AXD. This technique eliminates two of the variables present in the ANB method, namely, point B and nasion. The elimination of nasion is of particular importance, since this anatomic landmark is susceptible to considerable growth during the average 2-year treatment time. Taylor’s study indicated that nasion was moving away from sella approximately 1 mm. per year.

Of course, this estimative is a statistical mean computed from a representative number of cases of all ages. In the actively growing patient the rate could and should exceed 1 mm. per year; this fact will be enlarged on later in the investigation.
In the fifty cases recorded, the ANB went from a pretreatment mean of 6.5 degrees to a posttreatment mean of 3.7 degrees, which results in a treatment change pf 2.8 degreess. This can also be stated as a 43.1 per cent change in the apical base relationship of points A and B.
The AXD angle went from a pretreatment mean of 12.7 degrees to a posttreatment mean of 10.4 degrees. The treatment change in apical base relationship was 2.3 degrees, or 18.4 per cent.
The significant difference between the two methods is quite obvious. However, the mechanism of this difference between the ANB and AXD methods is not so apparent unless other factors are considered. As mentioned before, growth and treatment mechanics can influence cephalometric landmarks considerably. For example, growth at nasion can produce a considerable reduction in SNA. The schematic drawing presented in Fig. 3 enlarges on this point. It demonstrates that as nasion grows forward, angle SNA will decrease if point A remains in the same position. Since our Class II treatment mechanics are designed to inhibit forward growth of point A, this is a frequent ocurrence. Therefore, as angle SNA is reduced in value, ANB can also decrease, even though there has been no change in the relationship of point A to point B. This interesting conclusion is demonstrated in Fig. 4 and is taken from one of the cases in this study. In situations such as this, ANB is misrepresenting the true apical base relationship as demonstrated by the fact that, despite a rotation of the mandible, ANB went from 8 degrees to 5.5 degrees during treatment. Angle SNA changed from a pretreatment reading of 88 degrees to 84 degrees, and growth at nasion would account for most of this. The linear S-N measurement increased 3 mm. and would, by necessity, reduce the angle since point A was controlled by Class II mechanics. The AXD angle, which does not use nasion as a landmark, went from 11 degrees to 10 degrees and, in this case, more accuratelly reflects the existing apical base relationship. A further check on the statistics of this case shows that the horizontal linear measurement of the apical base difference (A-D’) did not change significantly. Prior to treatment the apical bases were 18.5 mm. apart; after treatment the difference between the maxilla (point A) and the mandible (point D) decreased 0.5 mm.
The fifty cases analyzed in this study demonstrate conclusively that the AXD method discloses a more accurate representation of the apical base relationship than does the ANB method. The point to consider here is whether the ANB technique was designed to demonstrate actual apical base relationships. The ANB measurements informs us of how much the angular measurement between point A and point B has been changed. This change has been brought about by a number of factors (for example, mandibular growth, distal “en masse movement” of the maxilla, distal repositioning of the maxillary incisors, etc.). The ANB measurement combines all these factors, and in the average Class II case the ANB measurement is decreased and points A and B are closer together in the horizontal plane. However, the ANB method can never trully reflect the apical base difference, since the landmarks are directly affected by treatment mechanics and growth.
The problem has been one of attempting to find more representative landmarks which would disclose the relationship of the apical bases to each other and which would appear to be impossible to replace. The AXD method demonstrates a change in apical base relationships of less than half of that disclosed by the ANB method (43.1 per cent as opposed to 18.4 per cent). A logical question as this point is: How much of this apical base change, represented by AXD, was caused by the variable that could not to be eliminated, point A? One of the linear measurement recorded was S-A’, defined as a line segment along the SN plane, extending from the center of sella turcica to the intersection of the perpendicular drawn from point A to the SN plane. The mean pretreatment and posttreatment difference of this measurement was less than 1 mm., and this would not alter the mean AXD measurement significantly.
Iniatially, one might consider discouraging the fact that 2 years of active treatment can effect only an 18.4 per cent change in the apical bases of Class II cases. Prime consideration should be given here to the more important reflection
 
 

that Class II cases can be and are corrected when the apical bases are shifted this amount.
Linear apical base measurements (Table II). The study of angular cephalometric measurements uncovers a rather basic geometric problem. It is not unusual to find cases in which the angular measurement ANB is small and yet visual inspection shows that the apical bases are widely divergent (Fig. 5). In these cases, angular measurements alone would not give as a true picture of the complexity of the case. The longer the lines are extended from an angle, the farther apart thay become in relation to each other. From this, we can see that as the vertical distances between nasion and points A and B increase in length, the linear measurement between the sides of the triangle also increases. Because of this, it is possible for two patients to have identical ANB values but a different horizontal distance between points A and B, since the length of their faces (vertical height) may vary.
Another consideration which demonstrates this problem is the fact that as nasion moves forward (growth), angle SNA is reduced in value if point A remains in the same position (Fig. 4). This was explained in detail previously and leads to the conclusion that a reduction in SNA can produce a smaller ANB, even though the actual relationship of point A to point B is unchanged.
The factors mentioned above emphasize the need for linear measurements relating the apical bases in the horizontal plane.
Sella nasion (mm.). This linear measurement has been used by many authors, including Ricketts5, 6 and Taylor,9 to name the most recent. As originally intended in this study, the measurement would disclose how much growth had ocurred in the average 2-year treatment time.
Ricketts, in this study of more than 2,000 cases, determined that the SN measurement increased approximately 1 mm. per year in the active growing child. In this study the mean pre- and postreatment change was 2.2 mm., ocurring over an average 2-year treatment time.
This study of mean changes of a population can be misleading when one is dealing with the specific cases of an orthodontic practice. A review of individual cases in this study shows that, while certain patients grew not at all, others had a change of 3 to 4 mm. per year at SN. These large ocurred in the actively growing patients whom orthodontics are interested in treating. When the mean change at SN is computed for the 11- to 13-year-old children in this study, we find that there is an average of 1.6 mm. of growth per year.
Sella-D’ (mm.). This measurement originates at the midpoint of sella and extends to the perpendicular projection of point D at the SN plane. The mean chagne for all cases was 2.5 mm., demonstrating that point D moved forward, a change which would reduce ANB or AXD. This measurement and others using mandibular landmarks would be susceptible to vertical changes taking place in the lower third of the face. This would primarily involve mandibular rotation, and this factor can be evaluated in a number of ways. In this study there was no significant change between pre- and postreatment FMA, which indicates that the mean S-D’ change of 2.5 mm. is essentially accurate. An evaluation of specific cases demonstrated situations in which the mandible was rotated during treatment and the S-D’ measurement was therefore decreased, resulting in greater apical base divergence. Since can be considered an undesirable aspect in the correction of ClassII cases, treatment mechanics are designed to bypass this potential problem. In the fifty cases reviewed fot this study, rotation of the mandible did not prove to be a significantly factor. With the spector of manibular rotation, it would appear that most of the change taking place at S-D’ is mandibular repositioning or growth. The S-D’ measurement accurately reflects this change, and therefore allows us to place proper emphasis on favorable growth or treatment mechanics. Other implications concerning the S-D’ measurement will be discussed in the following sections.
Sella-A’ (mm.). This measurement originates at the midpoint of sella and extends to the perpendicular projection of point A at the SN plane. The pretreatment mean of 63.9 mm. and the measurement descreased to a posttreatment mean of 63.1 mm., a change of 0.8 mm., which is not statistically significant. An evaluation of the fifty cases in this study determined that this measurement remained remarkably constant during orthodontic treatment. In fact, even in those cases in which considerable growth was ocurring at nasion and in the mandible, that A’ projection to SN remained in relatively the same position. It would appear from this that treatment mechanics do not actively relocate point A but actually hold it in position, while the middle face is growing forward. This observation is a result of comparing the pre- and posttreatment S-A’ means. A review of the specific cases reveals situations in which point A moved 2 to 3 mm. backward or forward in response to treatment mechanics or growth; however, this did not occur frequently enough to alter the mean value.
It would seem from the statements above that the conclusion concerning this landmark directly contradicts previous research. Ricketts,5, 6 Stoner and his associates,8 and others have demonstrated retraction of point A in vigorous Class II treatment. Careful reflection on this subject leads to the conclusion that all the studies are reviewing similar results concerning point A. The apparent contradiction arises from different perspectives of evaluating results. For example, Ricketts superimposes his tracings at SN and then eliminates vertical and horizontal growth. From this viewpoint, it would appear as if point A were relocated. In the present study the superimposition technique was not used; a linear pre- and posttreatment measurement was evaluated. When the same cephalograms were superimposed, point A did indeed appear to undergo retraction. It is my opinion that active retraction does not occur as frequently as we are led to believe by the superimposition technique. To repeat, in this study, point A was held in position int the great majority of cases by treatment mechanics while the middle face was growing forward.
A-D’ (mm.). This linear measurement is concerned with the actual distance between the apical base landmarks (in this study, point A and point D). During the course of treatment this value showed a mean decrease of 3.6 mm. which, of course, was not unexpected. This linear measurement closely paralleled the angular assessment AXD. The mean linear change of 3.6 mm. indicated a 15.8 per cent reduction in the horizontal distance between the apical bases.
The linear measurement A-D’ should prove to be relatively immune to the effects of treatment mechanics. There are two factors which could influence this value— rotation of the mandible and relocation of point A through treatment. In the fifty cases studied, mandibular rotation proved to be infrequent and, when it does occur, quickly becomes apparent. The relocation of point A by orthodontic means appears to be a factor which will constantly plague an apical base analysis. In the discussion of the S-A’ measurement it was pointed out that point A remains in a relatively constant position. The mean change of the point A projection to the SN plane was less than 1 mm. This change of less than 1 mm. cannot be considered statistically significant. However, as mentioned previously, the review of specific cases reveals situations in which point A was relocated 2 or 3 mm. in a posterior direction. In an individual case this is a desirable change, but unfortunately the method of ocurrence does not reveal itself in a predictable pattern. Over-all, one must be impressed by the fact that point A is not moved horizontally in the amount previously expected but held int the same position by treatment mechanics.
The A-D’ linear measurement offers an accurate method of assessing the actual horizontal distance between the apical bases. It does not have the liabilities inherent in any angular measurement and is simple to determine. The landmarks used are relatively stable, except for point A, but it does not appear that any replacement for this landmark will ever be found.
In conclusion, an attempt has been made to justify the use of linear measurements in the analysis of apical base divergence. The resutls of this study would indicate that, while linear measurements are not essential, they certainly can simplify an evaluation of the influence of growth and treatment mechanics on our cases.

Conclusions

1. The ANB difference is not always an accurate method of establishing the actual ammount of apical base divergence. In addition to the geometric shortcomings previously pointed out, the results of this study indicate that the ANB landmarks are subject to growth and treatment mechanics which cause corresponding variations in the measurements used.
2. The AXD method described in this study demonstrates a method of relating apical bases which eliminates two of the variables, nasion and point B. The AXD angle is a more critical evaluation and was found to correspond significantly with a linear measurement of the actual apical base difference.
3. This study and others have demonstrated conclusively that angular measurements cannot compensate for divergence of apical bases resulting from variations in vertical facial height. For this reason, a set of linear measurements was proposed which would offer an accurate method of evaluating the pre- and posttreatment changes taking place.
4. The linear measurements introduced in this study demonstrate an accurate method of assessing apical base relationships. The use of these measurements provides a critical evaluation of treatment and places proper emphasis on favorable growth and treatment mechanics.
5. The study of the pre- and posttreatment linear measurement concerning point A determined that this landmark remained remarkably constant during orthodontic treatment. It would appear from this study that treatment mechanics for Class II cases do not actively relocate from point A but actually hold it in position while the middle face is growing forward.
6. The A-D’ measurement is concerned with the actual distance, in millimeters, between the apical base landmarks. In the fifty cases studied, the mean pretreatment measurement of A-D’ was reduced 15.8 per cent as the Class II malocclusion was corrected. The mean pretreatment ANB underwent a reduction of 43.1 per cent on the same cases. While the A-D’ pre- and posttreatment change may not be as dramatic as the ANB evaluation, the major point to consider is the critical degree of accuracy which this measurement brings into an analysis.
The author wishes to extend special thanks to Donald A. Closson, Gene Thompson, and Don Thompson of the University of Missouri at Kansas City fot their assistance in this study. He also acknowledges the guidance and technical assistance of Robert S. Freeman in the preparation of this manuscript.

REFERENCES

1. Downs, W. B.: Variations in facial relationship: Their significance in treatment and prognosis, AM. J. ORTHOD. 34: 812-840, 1948.
2. 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.
3. Hatton, M. E., and Grainger, R. M.: Reliability of measurements from cephalograms at the Burlington Orthodontic Reasearch Center, J. D. Res. 37: 853-859, 1958.
4. Riedel, Richard A.: The relation of maxillary structures to cranium in malocclusion and in normal occlusion, Angle Orthod. 22: 140-145, 1952.
5. Ricketts, Robert M.: Planning treatment on the basis of the facial pattern and an estimate of its growth, Angle Orthod. 27: 14-37, 1957.
6. Ricketts, Robert M.: Cephalometric aynthesis: An exercise in stading objetives and planning treatment with tracings of the head roentgenogram, AM. J. ORTHOD. 46: 647-673, 1960.
7. Steiner, Cecil C.: Cephalometrics in clinical practice, Angle Orthod. 29: 8-30, 1959.
8. Stoner, Morris M, Lindquist, J. T., Vorhies, J. M., Hanes, Rolenzo A., Hapak, F. M., and Haynes, Edgar T.: A cephalometric evaluation of fifty-seven cases treated by Dr. Charles H. Tweed, Angle Orthod. 26: 68,1956.
9. Taylor, Charles M.: Changes in the relationship of nasion, point A, and point B and the effect upon ANB, AM. J. ORTHOD. 56: 143-163, 1969.

         Alguns aspectos da História da Cefalometria ( I ) (em construção) 

         Alguns aspectos da História da Cefalometria ( II ) (em construção) 
         Alguns aspectos da História da Cefalometria ( I ) (em construção)