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Superimposition and structural analysis
POINT/COUNTE RPOINT
Superimposition and structural analysis Robert J. Isaacson, DDS, PhD
Richmond, Va.
This article is fundamentally concerned with the relative merits of referencing mandibular changes to parameters determined by surface skeletal landmarks versus referencing to metallic implants placed in the mandible. One of these approaches is not better than the other. They simply yield different information. All change is only change as compared with something else. If you are flying in an airplane at 300 MPH and walk to the rear of the plane at 3 MPH, how fast are you traveling? The answer is, of course, compared with what? The plane itself? The earth? The sun? The speeds of each are all different and it is all relative. Tooth positions referenced to cranial base structures, e.g., S-N, show changes relative to S-N. This represents the algebraic sum of changes at all of the potential intervening growth sites between the tooth and S-N. It is different information from implant information. To know about the total tooth movement relative to the cranial base, use S-N. To know about tooth movement only at the periodontium, use a measure such as the implants. What the S-N perspective and the article miss is the actual external remodeling changes of the surface of the mandible itself. These only show when the mandible is accurately superimposed on itself. When the mandible is superimposed on the mandibular plane, mandibular plane determinants, i.e., gonion and gnathion must be unchanged. In the common forward rotating growth pattern, remodeling along the lower border shows deposition anteriorly at gnathion and resorption posteriorly at gonion. The result is that the point originally called gnathion is covered with new bone and the definition of gnathion is now at a new and different point on the mandible. The point originally called gonion is resorbed away and the new gonion is located, by the same definition, at a more superior position on the mandible. The mandibular plane at time point 1 is not the same mandibular plane as present at time point 2. The terms gonion and gnathion do not AM J ORTHOD DENTOFAC ORTHOP 1996;109:193-5. Copyright © 1996 by the American Association of Orthodontists. 0889-5406/96/$5.00 + 0 8/8/612~)
change their definition, but the remodeling by the cells of the periosteum changes the precise points in the mandible that satisfy these definitions. This much is clear. What this article adds to our knowledge is the realization that a transition point between the resorption at gonion and the deposition at gnathion is present below the lower first molar. This has never been noted or reported before. Lacking implants, stable landmarks have been sought to superimpose the mandible on itself. Thus the finding of a stable point on the mandibular border below the first molar is of considerable importance. Since this point does not move, it is probably a valid point to use as a reference for (1) linear measurements of the vertical growth of the lower first molar and (2) superimposing the mandible on itself when used in conjunction with another nonchanging point on the mandible. The article is absolutely correct in its frequent assertion that mandibular implant data is totally incorporated into the S-N tracings. That is, all the data revealed by mandibular implant changes plus a lot of other data is revealed as a sum total by superimpositions on S-N. The point of mandibular implants is to understand changes that take place in the substance of the mandible itself by biologic activity in the mandible, not to study the displacement of the mandible relative to the cranial base. A S-N superimposition shows the displacement of the maxillary teeth relative to S-N. The maxillary teeth are changed relative to S-N because of displacement of the maxilla relative to S-N through growth at the maxillary sutures PLUS the changes at the cells of the periodontium of the maxillary teeth. The article notes the maxillary implants show the incisors move backward and downward. This change occurs at the periodontium. When referenced to S-N, the maxillary incisors clearly move forward and downward. This total change, relative to S-N, includes both the implant information of the periodontal changes, as well as the displacement and growth rotation of the maxilla. The quantitative contribution of the parts are not sorted out by an S-N reference. The same superimposition on S-N shows the 193
194
Isaacson
displacement of the mandibular teeth relative to S-N. The mandibular teeth are displaced relative to S-N because of mandibular growth rotation PLUS the changes at the periodontium of the mandibular teeth. Superimpositions on the implants reveal only mandibular tooth movements relative to the mandible itself that is only a part of the total tooth movements relative to S-N. The comparable information, gained by superimposing on the lower border of the mandible, is distorted by any remodeling that occurred at gonion and/or gnathion and gives a picture of the effects of change distorted by the new location of gonion and gnathion. 1 Mandibular rotation results from disproportionate vertical growth between the anterior and posterior regions of the jaws. The vertical growth anteriorly results from changes at the maxillary sutures and maxillary periodontal tooth areas PLUS vertical growth at the mandibular periodontal tooth regions. The vertical growth posteriorly results from vertical changes at the condyle and fossa. When mandibular rotation occurs, vertical growth of the teeth is a major contributor to increases in the anterior region of the jaws. Forward mandibular rotation can, and in the instance of case 14 clearly does, result in major forward movement of pogonion as well as major forward movement of the first molar and dentition relative to S-N. The precise amount of forward movement is a function of the location of the center of rotation relative to the point under analysis. Backwardly directed condylar growth has been demonstrated with backward rotational mandibular growth (Bjork case 2). Class II corrections generally do not result from backward condylar growth. Class II corrections result from robust vertical growth at the condyle producing significant forward mandibular rotations during treatment. In the absence of treatment, the teeth tend to compensate at the periodontium for disproportional jaw growth and the occlusion stays constant while the jaws change. This is most dramatic in skeletal patterns such as Bj6rk's case 14 or this article's Richard, Figs. 7 and 8. The extrapolation method has very real limitations. No doubt it gives an approximation for small changes. But it is impossible to relate accurately linear and angular measurements associated with rotational movements without factoring in the geometry and radii involved. The motion of any point on the mandible can be
American Journal of Orthodontics and Dentofacial Orthopedics Februa~ 1996
described by the arc of a circle with the center of the circle at the center of rotation. The distance any point travels is calculated by determining the chord of the arc of the circle traveled. In other words, the direction and magnitude of movement at pogonion is directly related to the distance and orientation of pogonion to the center of rotation. 2-5 Consider again case 14. The article reports an apparently primarily vertical change of lower molars, resulting in primarily a horizontal change when referenced to S-N. Again change compared with what? When referenced to the implants, the molars move mostly vertically at the periodontium. When referenced to S-N, the molars move some vertically and primarily horizontally. This is due to the displacements of the mandible relative to S-N due to mandibular rotation. The forward rotation is a question of proportionality of vertical growth increments where the vertical growth at the condyles and fossae is greater than the vertical increases at the facial sutures and periodontal areas of the teeth. In the interpretation of case 14, Bj6rk reports the condylar growth at 20 mm. It is not counted twice. The distance S-N to gonion was not measured by Bj6rk. Bj6rk measured the actual growth at the condyle as referenced to articulare with the mandible superimposed on the implants. This article measured the S-N to gonion distance and found 11.5 mm of condylar growth (Fig. 14). This must equal the algebraic sum of the vertical changes at the fossa, condyle and gonion. We agree S-N is not a site of major change. We agree the fossa remodeled downward relative to S-N increasing the S-N to gonion measurement. We agree the condyle grew and increased the S-N to gonion measurement. We agree gonion resorbed in case 14 reducing the S-N gonion measurement. When all potential sites of change are factored in, the values for condylar growth will closely agree with Bj6rk's data. Given that gonion biologically remodels, it is an inaccurate landmark. When condylar growth in S-N superimpositions is measured by S-N to gonion at T1 and compared with the same value at T2, the measurement must be corrected for the remodeling changes at gonion. In Bj6rk's case 14, the gonion of time point 1 has resorbed away. This results in a reduced measurement for the value S-N to gonion measured at time point 2 and, when time point 1 is subtracted, will make the condylar growth appear less than it really is. As the article notes in Table I, with marked
American Journal of Orthodontics and Dentofacial Orthopedics Volume 109, No. 2
forward rotation of the mandible the values for mandibular growth shown with implants are much larger than shown by S-N to gonion measures. This is because the more forward rotation, the more lower border remodeling occurs. The resorption pattern at the mandibular plane is usually in the opposite direction of the rotation and usually is about half the magnitude. There is no question that Bj6rk is correct on this. Bj6rk's higher value is not evidence of duplication, but the absence of accounting for the bone resorbed at gonion at T2 when using the gonion to S-N measure. Including the bone lost to remodeling increases the value of S-N to gonion at T2 and makes the condylar growth measurement bigger and comparable to Bj6rk's implant measurement. In case 14, Bj6rk reports forward rotation of 16° as measured by the lower implant line to S-N. This article reports forward rotation of 8°. This does not suggest that the condylar growth was double counted. It does mean that measurements of forward rotation, which use mandibular plane relative to S-N, will be in error the amount gonion and gnathion have remodeled. The lower border remodeling attempts to mask the rotation and occurs in the opposite direction of the rotation. The changes in tooth positions revealed by implant superimposition are the same data mandibular plane superimpositions and ANS-PNS try to show. Both are tyring to reveal tooth changes at
Isaacson
1 95
the periodontium. The problem with mandibular plane and ANS-PNS superimpositions is that the mandibular plane and ANS-PNS landmarks are remodeled by surface changes. Implants are not influenced by surface remodeling changes and this is one of the key advantages and contributions of implants. I join Dr. Schudy in his recognition of the major debt of gratitude owed to Dr. Bj6rk for his enormous visionary contribution. But I also insist that, among those with visionary contributions, Dr. Schudy is sine qua non. His original contributions in the recognition of the critical role of vertical growth profoundly influenced the evolution of orthodontics today. REFERENCES 1. Isaacson R J, Worms FW, Speidel TM. Measurement of tooth movement. AM J ORTHOD 1976;70:290-303. 2. Hultgren BW, Isaacson RJ, Erdman AG, et al. Mechanics, growth, and Class II corrections. AM J ORTHOD 1978;74:38895. 3. Hultgren BW, Isaacson R J, Erdman AG, et al. Growth contributions to Class ]I corrections based on models of mandibular morphology. AM J ORTHOD 1980;78:310-20. 4. Isaacson RJ, Zapfel RJ, Worms FW, et al. Some effects of mandibular growth on the dental occlusion and profile. Angle Orthod 1977;47:97-106. 5. Isaacson RJ, Zapfel RJ, Worms FW, et al. Effects of rotational jaw growth on the occlusion and profile. AM J ORTHOD 1977;72:276-86.
Superimposition and structural analysis Robert J. Isaacson, DDS, PhD
Richmond, Va.
This article is fundamentally concerned with the relative merits of referencing mandibular changes to parameters determined by surface skeletal landmarks versus referencing to metallic implants placed in the mandible. One of these approaches is not better than the other. They simply yield different information. All change is only change as compared with something else. If you are flying in an airplane at 300 MPH and walk to the rear of the plane at 3 MPH, how fast are you traveling? The answer is, of course, compared with what? The plane itself? The earth? The sun? The speeds of each are all different and it is all relative. Tooth positions referenced to cranial base structures, e.g., S-N, show changes relative to S-N. This represents the algebraic sum of changes at all of the potential intervening growth sites between the tooth and S-N. It is different information from implant information. To know about the total tooth movement relative to the cranial base, use S-N. To know about tooth movement only at the periodontium, use a measure such as the implants. What the S-N perspective and the article miss is the actual external remodeling changes of the surface of the mandible itself. These only show when the mandible is accurately superimposed on itself. When the mandible is superimposed on the mandibular plane, mandibular plane determinants, i.e., gonion and gnathion must be unchanged. In the common forward rotating growth pattern, remodeling along the lower border shows deposition anteriorly at gnathion and resorption posteriorly at gonion. The result is that the point originally called gnathion is covered with new bone and the definition of gnathion is now at a new and different point on the mandible. The point originally called gonion is resorbed away and the new gonion is located, by the same definition, at a more superior position on the mandible. The mandibular plane at time point 1 is not the same mandibular plane as present at time point 2. The terms gonion and gnathion do not AM J ORTHOD DENTOFAC ORTHOP 1996;109:193-5. Copyright © 1996 by the American Association of Orthodontists. 0889-5406/96/$5.00 + 0 8/8/612~)
change their definition, but the remodeling by the cells of the periosteum changes the precise points in the mandible that satisfy these definitions. This much is clear. What this article adds to our knowledge is the realization that a transition point between the resorption at gonion and the deposition at gnathion is present below the lower first molar. This has never been noted or reported before. Lacking implants, stable landmarks have been sought to superimpose the mandible on itself. Thus the finding of a stable point on the mandibular border below the first molar is of considerable importance. Since this point does not move, it is probably a valid point to use as a reference for (1) linear measurements of the vertical growth of the lower first molar and (2) superimposing the mandible on itself when used in conjunction with another nonchanging point on the mandible. The article is absolutely correct in its frequent assertion that mandibular implant data is totally incorporated into the S-N tracings. That is, all the data revealed by mandibular implant changes plus a lot of other data is revealed as a sum total by superimpositions on S-N. The point of mandibular implants is to understand changes that take place in the substance of the mandible itself by biologic activity in the mandible, not to study the displacement of the mandible relative to the cranial base. A S-N superimposition shows the displacement of the maxillary teeth relative to S-N. The maxillary teeth are changed relative to S-N because of displacement of the maxilla relative to S-N through growth at the maxillary sutures PLUS the changes at the cells of the periodontium of the maxillary teeth. The article notes the maxillary implants show the incisors move backward and downward. This change occurs at the periodontium. When referenced to S-N, the maxillary incisors clearly move forward and downward. This total change, relative to S-N, includes both the implant information of the periodontal changes, as well as the displacement and growth rotation of the maxilla. The quantitative contribution of the parts are not sorted out by an S-N reference. The same superimposition on S-N shows the 193
194
Isaacson
displacement of the mandibular teeth relative to S-N. The mandibular teeth are displaced relative to S-N because of mandibular growth rotation PLUS the changes at the periodontium of the mandibular teeth. Superimpositions on the implants reveal only mandibular tooth movements relative to the mandible itself that is only a part of the total tooth movements relative to S-N. The comparable information, gained by superimposing on the lower border of the mandible, is distorted by any remodeling that occurred at gonion and/or gnathion and gives a picture of the effects of change distorted by the new location of gonion and gnathion. 1 Mandibular rotation results from disproportionate vertical growth between the anterior and posterior regions of the jaws. The vertical growth anteriorly results from changes at the maxillary sutures and maxillary periodontal tooth areas PLUS vertical growth at the mandibular periodontal tooth regions. The vertical growth posteriorly results from vertical changes at the condyle and fossa. When mandibular rotation occurs, vertical growth of the teeth is a major contributor to increases in the anterior region of the jaws. Forward mandibular rotation can, and in the instance of case 14 clearly does, result in major forward movement of pogonion as well as major forward movement of the first molar and dentition relative to S-N. The precise amount of forward movement is a function of the location of the center of rotation relative to the point under analysis. Backwardly directed condylar growth has been demonstrated with backward rotational mandibular growth (Bjork case 2). Class II corrections generally do not result from backward condylar growth. Class II corrections result from robust vertical growth at the condyle producing significant forward mandibular rotations during treatment. In the absence of treatment, the teeth tend to compensate at the periodontium for disproportional jaw growth and the occlusion stays constant while the jaws change. This is most dramatic in skeletal patterns such as Bj6rk's case 14 or this article's Richard, Figs. 7 and 8. The extrapolation method has very real limitations. No doubt it gives an approximation for small changes. But it is impossible to relate accurately linear and angular measurements associated with rotational movements without factoring in the geometry and radii involved. The motion of any point on the mandible can be
American Journal of Orthodontics and Dentofacial Orthopedics Februa~ 1996
described by the arc of a circle with the center of the circle at the center of rotation. The distance any point travels is calculated by determining the chord of the arc of the circle traveled. In other words, the direction and magnitude of movement at pogonion is directly related to the distance and orientation of pogonion to the center of rotation. 2-5 Consider again case 14. The article reports an apparently primarily vertical change of lower molars, resulting in primarily a horizontal change when referenced to S-N. Again change compared with what? When referenced to the implants, the molars move mostly vertically at the periodontium. When referenced to S-N, the molars move some vertically and primarily horizontally. This is due to the displacements of the mandible relative to S-N due to mandibular rotation. The forward rotation is a question of proportionality of vertical growth increments where the vertical growth at the condyles and fossae is greater than the vertical increases at the facial sutures and periodontal areas of the teeth. In the interpretation of case 14, Bj6rk reports the condylar growth at 20 mm. It is not counted twice. The distance S-N to gonion was not measured by Bj6rk. Bj6rk measured the actual growth at the condyle as referenced to articulare with the mandible superimposed on the implants. This article measured the S-N to gonion distance and found 11.5 mm of condylar growth (Fig. 14). This must equal the algebraic sum of the vertical changes at the fossa, condyle and gonion. We agree S-N is not a site of major change. We agree the fossa remodeled downward relative to S-N increasing the S-N to gonion measurement. We agree the condyle grew and increased the S-N to gonion measurement. We agree gonion resorbed in case 14 reducing the S-N gonion measurement. When all potential sites of change are factored in, the values for condylar growth will closely agree with Bj6rk's data. Given that gonion biologically remodels, it is an inaccurate landmark. When condylar growth in S-N superimpositions is measured by S-N to gonion at T1 and compared with the same value at T2, the measurement must be corrected for the remodeling changes at gonion. In Bj6rk's case 14, the gonion of time point 1 has resorbed away. This results in a reduced measurement for the value S-N to gonion measured at time point 2 and, when time point 1 is subtracted, will make the condylar growth appear less than it really is. As the article notes in Table I, with marked
American Journal of Orthodontics and Dentofacial Orthopedics Volume 109, No. 2
forward rotation of the mandible the values for mandibular growth shown with implants are much larger than shown by S-N to gonion measures. This is because the more forward rotation, the more lower border remodeling occurs. The resorption pattern at the mandibular plane is usually in the opposite direction of the rotation and usually is about half the magnitude. There is no question that Bj6rk is correct on this. Bj6rk's higher value is not evidence of duplication, but the absence of accounting for the bone resorbed at gonion at T2 when using the gonion to S-N measure. Including the bone lost to remodeling increases the value of S-N to gonion at T2 and makes the condylar growth measurement bigger and comparable to Bj6rk's implant measurement. In case 14, Bj6rk reports forward rotation of 16° as measured by the lower implant line to S-N. This article reports forward rotation of 8°. This does not suggest that the condylar growth was double counted. It does mean that measurements of forward rotation, which use mandibular plane relative to S-N, will be in error the amount gonion and gnathion have remodeled. The lower border remodeling attempts to mask the rotation and occurs in the opposite direction of the rotation. The changes in tooth positions revealed by implant superimposition are the same data mandibular plane superimpositions and ANS-PNS try to show. Both are tyring to reveal tooth changes at
Isaacson
1 95
the periodontium. The problem with mandibular plane and ANS-PNS superimpositions is that the mandibular plane and ANS-PNS landmarks are remodeled by surface changes. Implants are not influenced by surface remodeling changes and this is one of the key advantages and contributions of implants. I join Dr. Schudy in his recognition of the major debt of gratitude owed to Dr. Bj6rk for his enormous visionary contribution. But I also insist that, among those with visionary contributions, Dr. Schudy is sine qua non. His original contributions in the recognition of the critical role of vertical growth profoundly influenced the evolution of orthodontics today. REFERENCES 1. Isaacson R J, Worms FW, Speidel TM. Measurement of tooth movement. AM J ORTHOD 1976;70:290-303. 2. Hultgren BW, Isaacson RJ, Erdman AG, et al. Mechanics, growth, and Class II corrections. AM J ORTHOD 1978;74:38895. 3. Hultgren BW, Isaacson R J, Erdman AG, et al. Growth contributions to Class ]I corrections based on models of mandibular morphology. AM J ORTHOD 1980;78:310-20. 4. Isaacson RJ, Zapfel RJ, Worms FW, et al. Some effects of mandibular growth on the dental occlusion and profile. Angle Orthod 1977;47:97-106. 5. Isaacson RJ, Zapfel RJ, Worms FW, et al. Effects of rotational jaw growth on the occlusion and profile. AM J ORTHOD 1977;72:276-86.