Mandibular rotation and enlargement J. M. H. Dibbets
Groningen, The Netherlands In a previous article, a theoretical mechanism for neutralization of condylar incremental growth was postulated. It was labeled counterbalancing rotation. The postulate resulted from the reasoning that condylar relocation along a segment of a circle around pogonion would be unable to enlarge the radius. In this article, the relationship between condylar relocation and mandibular enlargement is qL=antified. To this goal, counterbalancing proportion is defined as the percentage of condylar incremental growth, detected by implants that has contributed to the enlargement of the condyiion-to-pogonion dimension. This proportion proves to vary widely in the 21 cases documented by BjSrk and Skieller. In addition, a relationship between this proportion and the Angle classification is observed. It is concluded that counterbalancing rotation indeed must be considered a mechanism capable of neutralizing condylar incremental growth and may have clinical implications. (AM J ORTHOO DENTOFACORTHOP 1990;98:29-32.)
G r o w t h rotation of the mandible was first described by Bjrrk. t In 1983 Bj&k and Skieller3 took the initiative in framing operational definitions for different aspects of rotation. One of these is intramatrix rotation. However, according to Solow and Houston, 9 intramatrix rotation yields different values when an implant line is measured relative to the corpus rather than to the ramus. Therefore they suggest using the term angular remodeling of, followed by the anatomic reference in relation to where an implant line is measured. In a previous article 4 two hypothetical extreme and divergent patterns for mandibular growth were postulated. One was characterized by a circular growth direction of the condyle around a center on the contour of the chin that assumed "rotation" but no enlargement of the mandible. The other extreme pattern was characterized by a steady enlargement of the mandible but without "rotation." From this theoretical construct, the conclusion was that an implication of intramatrix rotation apparently was the capability of counterbalancing the condylar dimensional contribution to mandibular enlargement. To separate this aspect from others, it was labeled "counterbalancing rotation" and was operationally defined as follows: "Counterbalancing rotation pertains to circular condylar growth, accompanied by selective coordinated remodeling, which does not contribute to the incremental growth of the mandible." It was then stated that counterbalancing rotation incorporated the important attribute of being amenable to testing. The intention of this article is to test the postulate
811114400
of counterbalanced condylar incremental growth. In addition, the relationship between counterbalancing rotation and the Angle classification will be explored. MATERIAL AND METHODS
The material is adapted from Bj~rk and Skieller's 1972 article. 2 These investigators presented 21 cases, followed over 5 or 6 years and documented by various methods, such as mandibular tracings superimposed on stable metallic implants. All 21 tracings were photographically enlarged and measured as shown in Fig. 1. On a stable area of the chin, the landmark pogonion was chosen. Since condylion in the original article was constructed with a template, condylar incremental growth was consequently measured by the distance between the younger and older articulare. Mandibular size was represented by the diagonal from articulare to poo gonion. Mandibular enlargement during growth was determined by substracting the smaller diagonal from the larger one. The full documentation on 19 of the 21 cases was given to three experienced orthodontists, who were requested to determine the Angle classification independently and without knowledge of the specific goal of the exercise. Seventeen cases were unanimously assigned to one of the three Angle classes and two subdivisions. Two were classified as either Class I or Class II, indicating disagreement among the judges. Two cases were labeled "X" beforehand, showing a facial structure and mandibular growth pattern strikingly analogous to those seen in persons with deformed condyles, as documented in the Groningen TMJ dysfunction study. 5 The counterbalancing proportion is defined as the 29
30
Am. J. Orthod. Dentofac. Orthop. July 1990
Dibbets
Ar2
Finally, in Fig. 2 the 21 cases are arranged according to decreasing counterbalancing proportion from left to right, clearly displaying the relationship between facial structure and counterbalancing rotation. The vertical axis indicates the percentage. The horizontal bars at the bottom visualize the maximal range of the classes. DISCUSSION
Arl
Fig. 1. Two mandibular tracings of the same individual at age 11 years 7 months and 17 years 7 months, respectively, are superimposed on the images of implants. The originals were enlarged by a factor two. Pogonion is arbitrarily located on a stable area between the arrows. The dimension pogonion to articulare represents mandibular size. Mandibular growth is determined by subtracting Pg-Arl from Pg-Ar2. Condylar growth is represented by the dimension Art to Ar2. (Adapted with permission from plate 14 of Bjfrk and Skieller. 2)
quotient between mandibular and condylar incremental growth and expressed as a percentage. This proportion indicates what percentage of condylar relocation has contributed to the actual mandibular enlargement. The relationship between the proportion and the Angle classification is shown graphically. In addition, the average proportion for the Angle classes was assessed separately. RESULTS
The counterbalancing proportions for the 21 cases and the facial classification are presented in Table I. The proportion ranges from 50% to 97%. The relationship between the counterbalancing proportion and the facial classification is shown in Table II. The average proportion appears to differ among the groups presented. The proportion of 85% for Class III is in sharp contrast with the 59% for Class II Division 2. The average is 76% for cases exclusively labeled Class I and 65.5% for those labeled Class II.
It is apparent that an incongruity often exists between the condylar growth direction and the direction of enlargement of the anatomic mandible. ~4"6'8 Deposition, resorption, and endochondral ossification obviously seem to follow a pattern that is not readily anticipated from the textbook notion of almost parallel posterior relocation of the ramus. Originally, Bj6rk named this unexpected mechanism growth rotation. It became visible only after the superimpositioning of cephalograms on the stable reference images of implants. Unfortunately, growth rotation in the literature became associated with two separate mechanisms. One is remodeling of the mandibular contours in relation to implants; the other mechanism is displacement of the mandibular contours in relation to the anterior cranial base. Both create the impression of rotations and may be coincidental as well as antagonistic. The literature offers several accounts of the phenomenon of implants "rotating" in relation to mandibular contours. 3"6-8 Our contribution has been the formulation of a model that makes possible quantification and, thus, testing. The model was labeled counterbalancing rotation 4 and was based on the postulate of two theoretical extremes for mandibular growth without assuming a causative relationship between condylar and mandibular incremental growth. If this model is valid, during growth the effective contribution of the condyle to mandibular enlargement will vary among individual patients because of varying condylar growth directions and concomitant mandibular remodeling. The best documented and available implant material, as described in Bjrrk and Skieller's 1972 article, was adapted to our specific research goals. The dimensions measured are summarized in Fig. 1. It is not expected that other expressions will result in conclusions totally different from those obtained in the simple approximation presented here. Condylar growth and mandibular growth are weighted in relation to one another and labeled counterbalancing proportion. The operational definition is the quotient of mandibular diagonal gain and condylar incremental growth times 100%. It gives the percentage of condylar incremental growth that is converted into actual dimensional gain for the mandibular diagonal. The proportion is independent from the time span but assumes comparable
Volume98 Number 1
Mandibular rotation and enlargement % 100
% 100"
90
90" Q
80
80
70'
70
60
-6o
50
-50
,
J
4
2
18
X
III1 III
X
,
•
•
i
•
,
,
,
,
,
i
i
,
,
i
,
•
5
19
7
8
10
9
6
20
17
13
11
15
1
12
3
14
III 1/11 III
III
III
I11 I
III
I
I
I
I
II
II2
II
16 21
X
,
,
I
II ~ II 2 II 2
III IIII
Fig. 2. Mandibular enlargement as a percentage of condylar growth, arranged in decreasing order. The vertical axis denotes percentages; the horizontal axis denotes the 21 cases indicated by number. R o m a n numerals refer to the Angle classification of malocclusion. X denotes a specific growth type, IIII reveals disagreement among classification judges explained in Material and Methods section. The horizontal bars show m a x i m u m range of classes. Here 1/11 indicates total range for Class I and Class II (Adapted with permission from Bj~Srk and Skieller. 2)
Table
I. T h e c o u n t e r b a l a n c i n g
Case No. !
2 3 4 5 6 7 8 9 10 11
12 13 14 15 16 17 18 19 20 21
proportions and the facial classifications*
Mandibular growth (mm)
Condylar growth (ram)
12.8 11.3 10.3 10.7 8.1 18.0 14.0 10.8 10.9 14,1 14,4 10,7 14.2 11.7 15.9 18.2 16.0 13.7 14.1 14.6 14,8
18.4 11.9 17.8 11.0 9.1 22.4 16.7 13.2 13.3 17.3 20.1 17.8 18.9 23.6 22.5 20.3 21.0 14.9 16.2 19.0 16.7
Counterbalancing proportion (percent) 70 95 58 97 89 80 84 82 82 82
Angle classification 1I2 X 112 X l/II III III 111 I 111
72
I
60 75 50 71 90 76 92 87 77 89
It t 1 112 IP III 1 fill 111 I 111
Adapted with permission from Bj6rk A and Skieller V. Facial development and tooth eruption. AM J ORrlloD 1972;62:339-83. Grov, tb of articulare to pogonion *Counterbalancing proportion = × 100% Condylar incremental growth
31
32
Am. J. Orthod. Dentofac. Orthop. July 1990
Dibbets
Table II. Average counterbalancing proportion
for.Angle classes
xl'"l"l'
96%
90.5%
85%
I"1 76%
65.5%
//-" 59%
~;rowth between individuals. On the basis of the ages o f the persons in this study, this assumption may be regarded as valid. According to the concept of congruous mandibular growth, this proportion is expected to approximate 100%. From Table I it follows, however, that in reality the proportion varies from 5 0 % to 97%. Fig. 2 and Table I quantify the relationship between counterbalancing rotation and facial structure. Table II shows theaverage proportions for the different classes are shown. Because of the small numbers, statistical testing was not attempted, but ordering is obviously present. This order is even better visualized in Fig. 2. The typical growth pattern labeled X is the most efficient mode of mandibular enlargement. Every millimeter of condylar incremental growth contributes to the enlargement of the mandible. The two ambivalent diagnoses, classes I / I I , appear far left on the scale. The next, Class III, is clearly recognized as a cluster on the scale. The average proportion (85%) reveals a very efficient mechanism o f mandibular enlargement at work here as well. The Class I group adjacent to Class III in Fig. 2 is also recognized as a cluster in the illustration. There is an overlap for only one case. For Class I one quarter of the condylar dimensional gain is not expressed in gain for the diagonal. That is, an average of 24% of condylar incremental growth will not result in a larger mandible. Coordinated patterns of resorption and deposition will neutralize this growth. The effect of this neutralization is more pronounced in Class II, Divisions I and 2, constituting the far right end of the scale and indicating a low counterbalancing proportion. This is even more apparent for Class II, Division 2, where the group average is only 59%, indicating that a fair amount of tissue produced by the mandibular condyle did not contribute to mandibular enlargement. When one studies the tracings z of the original case 14 (Fig. I), it may become obvious why the idea of counterbalancing rotation was born. Too much growth of the condyle in this figure is neutralized by coordinated remodeling to be ignored. Too much remodeling activity is necessary to maintain or preserve form to be assigned to minor local adjustments only, or to reflect
differential growth in anterior and posterior face heights .7 From Fig. 2 and Table II, it may be concluded that counterbalancing rotation is a mechanism capable of neutralizing condylar incremental growth. In addition, the conclusion is that the proportion by which counterbalancing rotation neutralizes this growth is strongly associated with facial structure, as expressed by the Angle classification. Further research has to clarify the diagnostic value of this concept for clinical use. SUMMARY
A method that makes possible the weighted quantification of condylar and mandibular incremental growth is presented. When applied to the 21 cases documented by Bj6rk and Skieller, the condylar endochondral tissue production appears to result in mandibular enlargement between 50% and 97% only. It is substantiated that there exists an association between this percentage and facial structure. I thank Prof. em. C. Booy, Dr. J. Boersma, and Dr. Tsj. de Jager for providing the morphologic classification, Drs. R. de Bruin and L.Th. van der Weele for their support and stimulating discussions, Mrs. Lilian Gaillard for providing secretarial assistance, and Dr. J. T. Wilmink for assisting in the final text preparation. Prof. A. Bj6rk kindly permitted adaptation of his publication. REFERENCES
1. Bjfrk A. Prediction of mandibular growthrotation. AMJ ORTHOD 1969;55:585-99. 2. Bjfrk A, Skieller V. Facial development and tooth eruption. AM J OR'moo 1972;62:339-83. 3. Bjfrk A, SKieller V. Norrr/al and abnormal growth of the mandible: a synthesis of longitudinal cephalometric implant studies over a period of 25 years. Eur J Orthod 1983;5:1-46. 4. Dibbets JMH. The puzzle of growth rotation. AM J ORTHOO 1985;87:473-80. 5. Dibbets JMH, van der Weele LTh, Uildriks AKJ. Symptoms of TMJ dysfunction: indicators of growth patterns? J Pedod 1985; 9:265-84. 6. Enlow DH. Handbookof facial growth. 2nd ed. Philadelphia: WB Saunders, 1982. 7. Houston WJB. Mandibular growth rotations--their mechanisms and importance. Eur J Orthod 1988;10:369-73. 8. Lavergne J, Gasson N. A metal impiant study of mandibular rotation. Angle Orthod 1976;46:144-50. 9. Solow B, Houston WJB. Mandibular rotations: concepts and terminology. Eur J Orthod 1988;10:177-9. Reprints requests to: Prof. J.M.H. Dibbets Department of Orthodontics School of Dentistry A. Deusinglaan I 9713 AV GRONINGEN The Netherlands
Groningen, The Netherlands In a previous article, a theoretical mechanism for neutralization of condylar incremental growth was postulated. It was labeled counterbalancing rotation. The postulate resulted from the reasoning that condylar relocation along a segment of a circle around pogonion would be unable to enlarge the radius. In this article, the relationship between condylar relocation and mandibular enlargement is qL=antified. To this goal, counterbalancing proportion is defined as the percentage of condylar incremental growth, detected by implants that has contributed to the enlargement of the condyiion-to-pogonion dimension. This proportion proves to vary widely in the 21 cases documented by BjSrk and Skieller. In addition, a relationship between this proportion and the Angle classification is observed. It is concluded that counterbalancing rotation indeed must be considered a mechanism capable of neutralizing condylar incremental growth and may have clinical implications. (AM J ORTHOO DENTOFACORTHOP 1990;98:29-32.)
G r o w t h rotation of the mandible was first described by Bjrrk. t In 1983 Bj&k and Skieller3 took the initiative in framing operational definitions for different aspects of rotation. One of these is intramatrix rotation. However, according to Solow and Houston, 9 intramatrix rotation yields different values when an implant line is measured relative to the corpus rather than to the ramus. Therefore they suggest using the term angular remodeling of, followed by the anatomic reference in relation to where an implant line is measured. In a previous article 4 two hypothetical extreme and divergent patterns for mandibular growth were postulated. One was characterized by a circular growth direction of the condyle around a center on the contour of the chin that assumed "rotation" but no enlargement of the mandible. The other extreme pattern was characterized by a steady enlargement of the mandible but without "rotation." From this theoretical construct, the conclusion was that an implication of intramatrix rotation apparently was the capability of counterbalancing the condylar dimensional contribution to mandibular enlargement. To separate this aspect from others, it was labeled "counterbalancing rotation" and was operationally defined as follows: "Counterbalancing rotation pertains to circular condylar growth, accompanied by selective coordinated remodeling, which does not contribute to the incremental growth of the mandible." It was then stated that counterbalancing rotation incorporated the important attribute of being amenable to testing. The intention of this article is to test the postulate
811114400
of counterbalanced condylar incremental growth. In addition, the relationship between counterbalancing rotation and the Angle classification will be explored. MATERIAL AND METHODS
The material is adapted from Bj~rk and Skieller's 1972 article. 2 These investigators presented 21 cases, followed over 5 or 6 years and documented by various methods, such as mandibular tracings superimposed on stable metallic implants. All 21 tracings were photographically enlarged and measured as shown in Fig. 1. On a stable area of the chin, the landmark pogonion was chosen. Since condylion in the original article was constructed with a template, condylar incremental growth was consequently measured by the distance between the younger and older articulare. Mandibular size was represented by the diagonal from articulare to poo gonion. Mandibular enlargement during growth was determined by substracting the smaller diagonal from the larger one. The full documentation on 19 of the 21 cases was given to three experienced orthodontists, who were requested to determine the Angle classification independently and without knowledge of the specific goal of the exercise. Seventeen cases were unanimously assigned to one of the three Angle classes and two subdivisions. Two were classified as either Class I or Class II, indicating disagreement among the judges. Two cases were labeled "X" beforehand, showing a facial structure and mandibular growth pattern strikingly analogous to those seen in persons with deformed condyles, as documented in the Groningen TMJ dysfunction study. 5 The counterbalancing proportion is defined as the 29
30
Am. J. Orthod. Dentofac. Orthop. July 1990
Dibbets
Ar2
Finally, in Fig. 2 the 21 cases are arranged according to decreasing counterbalancing proportion from left to right, clearly displaying the relationship between facial structure and counterbalancing rotation. The vertical axis indicates the percentage. The horizontal bars at the bottom visualize the maximal range of the classes. DISCUSSION
Arl
Fig. 1. Two mandibular tracings of the same individual at age 11 years 7 months and 17 years 7 months, respectively, are superimposed on the images of implants. The originals were enlarged by a factor two. Pogonion is arbitrarily located on a stable area between the arrows. The dimension pogonion to articulare represents mandibular size. Mandibular growth is determined by subtracting Pg-Arl from Pg-Ar2. Condylar growth is represented by the dimension Art to Ar2. (Adapted with permission from plate 14 of Bjfrk and Skieller. 2)
quotient between mandibular and condylar incremental growth and expressed as a percentage. This proportion indicates what percentage of condylar relocation has contributed to the actual mandibular enlargement. The relationship between the proportion and the Angle classification is shown graphically. In addition, the average proportion for the Angle classes was assessed separately. RESULTS
The counterbalancing proportions for the 21 cases and the facial classification are presented in Table I. The proportion ranges from 50% to 97%. The relationship between the counterbalancing proportion and the facial classification is shown in Table II. The average proportion appears to differ among the groups presented. The proportion of 85% for Class III is in sharp contrast with the 59% for Class II Division 2. The average is 76% for cases exclusively labeled Class I and 65.5% for those labeled Class II.
It is apparent that an incongruity often exists between the condylar growth direction and the direction of enlargement of the anatomic mandible. ~4"6'8 Deposition, resorption, and endochondral ossification obviously seem to follow a pattern that is not readily anticipated from the textbook notion of almost parallel posterior relocation of the ramus. Originally, Bj6rk named this unexpected mechanism growth rotation. It became visible only after the superimpositioning of cephalograms on the stable reference images of implants. Unfortunately, growth rotation in the literature became associated with two separate mechanisms. One is remodeling of the mandibular contours in relation to implants; the other mechanism is displacement of the mandibular contours in relation to the anterior cranial base. Both create the impression of rotations and may be coincidental as well as antagonistic. The literature offers several accounts of the phenomenon of implants "rotating" in relation to mandibular contours. 3"6-8 Our contribution has been the formulation of a model that makes possible quantification and, thus, testing. The model was labeled counterbalancing rotation 4 and was based on the postulate of two theoretical extremes for mandibular growth without assuming a causative relationship between condylar and mandibular incremental growth. If this model is valid, during growth the effective contribution of the condyle to mandibular enlargement will vary among individual patients because of varying condylar growth directions and concomitant mandibular remodeling. The best documented and available implant material, as described in Bjrrk and Skieller's 1972 article, was adapted to our specific research goals. The dimensions measured are summarized in Fig. 1. It is not expected that other expressions will result in conclusions totally different from those obtained in the simple approximation presented here. Condylar growth and mandibular growth are weighted in relation to one another and labeled counterbalancing proportion. The operational definition is the quotient of mandibular diagonal gain and condylar incremental growth times 100%. It gives the percentage of condylar incremental growth that is converted into actual dimensional gain for the mandibular diagonal. The proportion is independent from the time span but assumes comparable
Volume98 Number 1
Mandibular rotation and enlargement % 100
% 100"
90
90" Q
80
80
70'
70
60
-6o
50
-50
,
J
4
2
18
X
III1 III
X
,
•
•
i
•
,
,
,
,
,
i
i
,
,
i
,
•
5
19
7
8
10
9
6
20
17
13
11
15
1
12
3
14
III 1/11 III
III
III
I11 I
III
I
I
I
I
II
II2
II
16 21
X
,
,
I
II ~ II 2 II 2
III IIII
Fig. 2. Mandibular enlargement as a percentage of condylar growth, arranged in decreasing order. The vertical axis denotes percentages; the horizontal axis denotes the 21 cases indicated by number. R o m a n numerals refer to the Angle classification of malocclusion. X denotes a specific growth type, IIII reveals disagreement among classification judges explained in Material and Methods section. The horizontal bars show m a x i m u m range of classes. Here 1/11 indicates total range for Class I and Class II (Adapted with permission from Bj~Srk and Skieller. 2)
Table
I. T h e c o u n t e r b a l a n c i n g
Case No. !
2 3 4 5 6 7 8 9 10 11
12 13 14 15 16 17 18 19 20 21
proportions and the facial classifications*
Mandibular growth (mm)
Condylar growth (ram)
12.8 11.3 10.3 10.7 8.1 18.0 14.0 10.8 10.9 14,1 14,4 10,7 14.2 11.7 15.9 18.2 16.0 13.7 14.1 14.6 14,8
18.4 11.9 17.8 11.0 9.1 22.4 16.7 13.2 13.3 17.3 20.1 17.8 18.9 23.6 22.5 20.3 21.0 14.9 16.2 19.0 16.7
Counterbalancing proportion (percent) 70 95 58 97 89 80 84 82 82 82
Angle classification 1I2 X 112 X l/II III III 111 I 111
72
I
60 75 50 71 90 76 92 87 77 89
It t 1 112 IP III 1 fill 111 I 111
Adapted with permission from Bj6rk A and Skieller V. Facial development and tooth eruption. AM J ORrlloD 1972;62:339-83. Grov, tb of articulare to pogonion *Counterbalancing proportion = × 100% Condylar incremental growth
31
32
Am. J. Orthod. Dentofac. Orthop. July 1990
Dibbets
Table II. Average counterbalancing proportion
for.Angle classes
xl'"l"l'
96%
90.5%
85%
I"1 76%
65.5%
//-" 59%
~;rowth between individuals. On the basis of the ages o f the persons in this study, this assumption may be regarded as valid. According to the concept of congruous mandibular growth, this proportion is expected to approximate 100%. From Table I it follows, however, that in reality the proportion varies from 5 0 % to 97%. Fig. 2 and Table I quantify the relationship between counterbalancing rotation and facial structure. Table II shows theaverage proportions for the different classes are shown. Because of the small numbers, statistical testing was not attempted, but ordering is obviously present. This order is even better visualized in Fig. 2. The typical growth pattern labeled X is the most efficient mode of mandibular enlargement. Every millimeter of condylar incremental growth contributes to the enlargement of the mandible. The two ambivalent diagnoses, classes I / I I , appear far left on the scale. The next, Class III, is clearly recognized as a cluster on the scale. The average proportion (85%) reveals a very efficient mechanism o f mandibular enlargement at work here as well. The Class I group adjacent to Class III in Fig. 2 is also recognized as a cluster in the illustration. There is an overlap for only one case. For Class I one quarter of the condylar dimensional gain is not expressed in gain for the diagonal. That is, an average of 24% of condylar incremental growth will not result in a larger mandible. Coordinated patterns of resorption and deposition will neutralize this growth. The effect of this neutralization is more pronounced in Class II, Divisions I and 2, constituting the far right end of the scale and indicating a low counterbalancing proportion. This is even more apparent for Class II, Division 2, where the group average is only 59%, indicating that a fair amount of tissue produced by the mandibular condyle did not contribute to mandibular enlargement. When one studies the tracings z of the original case 14 (Fig. I), it may become obvious why the idea of counterbalancing rotation was born. Too much growth of the condyle in this figure is neutralized by coordinated remodeling to be ignored. Too much remodeling activity is necessary to maintain or preserve form to be assigned to minor local adjustments only, or to reflect
differential growth in anterior and posterior face heights .7 From Fig. 2 and Table II, it may be concluded that counterbalancing rotation is a mechanism capable of neutralizing condylar incremental growth. In addition, the conclusion is that the proportion by which counterbalancing rotation neutralizes this growth is strongly associated with facial structure, as expressed by the Angle classification. Further research has to clarify the diagnostic value of this concept for clinical use. SUMMARY
A method that makes possible the weighted quantification of condylar and mandibular incremental growth is presented. When applied to the 21 cases documented by Bj6rk and Skieller, the condylar endochondral tissue production appears to result in mandibular enlargement between 50% and 97% only. It is substantiated that there exists an association between this percentage and facial structure. I thank Prof. em. C. Booy, Dr. J. Boersma, and Dr. Tsj. de Jager for providing the morphologic classification, Drs. R. de Bruin and L.Th. van der Weele for their support and stimulating discussions, Mrs. Lilian Gaillard for providing secretarial assistance, and Dr. J. T. Wilmink for assisting in the final text preparation. Prof. A. Bj6rk kindly permitted adaptation of his publication. REFERENCES
1. Bjfrk A. Prediction of mandibular growthrotation. AMJ ORTHOD 1969;55:585-99. 2. Bjfrk A, Skieller V. Facial development and tooth eruption. AM J OR'moo 1972;62:339-83. 3. Bjfrk A, SKieller V. Norrr/al and abnormal growth of the mandible: a synthesis of longitudinal cephalometric implant studies over a period of 25 years. Eur J Orthod 1983;5:1-46. 4. Dibbets JMH. The puzzle of growth rotation. AM J ORTHOO 1985;87:473-80. 5. Dibbets JMH, van der Weele LTh, Uildriks AKJ. Symptoms of TMJ dysfunction: indicators of growth patterns? J Pedod 1985; 9:265-84. 6. Enlow DH. Handbookof facial growth. 2nd ed. Philadelphia: WB Saunders, 1982. 7. Houston WJB. Mandibular growth rotations--their mechanisms and importance. Eur J Orthod 1988;10:369-73. 8. Lavergne J, Gasson N. A metal impiant study of mandibular rotation. Angle Orthod 1976;46:144-50. 9. Solow B, Houston WJB. Mandibular rotations: concepts and terminology. Eur J Orthod 1988;10:177-9. Reprints requests to: Prof. J.M.H. Dibbets Department of Orthodontics School of Dentistry A. Deusinglaan I 9713 AV GRONINGEN The Netherlands
