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Pitfalls in orthognathic model surgery
Int..I. Oral Maxillofac. Surg. 1994; 23:11 15 Printed in Denmark. All rights reserved
Copyright © Munksgaard 1994 [ntemadonalJournal of
Oral& MaxillofacialSurgery ISSN 0901-5027
Pitfalls in orthognathic model surgery
A n d e r s Nattestad ~, Poul Vedtofte 2 1Department of Oral and Maxillofacial Surgery, School of Dentistry, Faculty of Health Sciences, University of Copenhagen, and 2Department of Oral and Maxillofacial Surgery, University Hospital (Rigshospitalet), Copenhagen, Denmark
The significance of using different reference lines and points during model surgery and operation A. Nattestad, R Vedtofte. Pi~alls in orthognathie model surgery. The significance of using different reference lines and points during model surgery and operation. Int. J. Oral Maxillofac. Surg. 1994; 23: 11-15. © Munksgaard, 1994 Abstract. The planning of orthognathic surgery usually involves a simulation of jaw movements in a semiadjustable articulator. The use of vertical and horizontal references during model surgery and operation have previously been described in great detail. The purpose of the present study was to quantify the errors resulting from using different reference lines and points in model surgery and operation. The results indicate that clinically significant differences between the planned and surgical jaw movement can result from the erroneous transfer of reference lines and points between model surgery and operation. Solutions to some of the problems discussed are suggested.
Several studies have described the results and stability of orthognathic surgery2'4'5'v'~3.However, only a few deal with the relation between the predicted result, based on model surgery in semiadjustable articulators, and the immediate result after surgery 1~'12't5'~6.POSPISIL 12 compared the prediction tracings with the immediate postoperative cephalometric radiographs in 40 patients and found that 83% differed between the planned and the surgical result by over 20% of the planned movement. POLIDO et al. H investigated the predictability of the maxillary central incisor position in 100 consecutive patients and found an average discrepancy of 2.2 mm vertically and 1.8 mm horizontally. VAN SicKEcs et al. ~6 reported a mean difference of 2.5 mm vertically and 3.6 mm horizontally in a group of 11 patients with the use of the intraoral measurement method. This was compared to another group of 11 patients, where an extraoral measurement device was used and a statistically significant improve-
ment in precision was found. Similar findings were reported by STANCH1NA et al. ~5. However, a later study by KAHNBERGet al. 6 with a similar design showed no statistically significant difference between the two measurement methods. A suggested explanation for the difference between the predicted and actual result of orthognathic surgery is a difference between the actual and simulated center of mandibular rotation 9,1°,14. Errors in model surgery done in the articulator have also been reported as a possible cause for this discrepancy3'17. The usual planning procedure for orthognathic surgery involves a cephalometric prediction tracing, followed by model surgery in a semiadjustable articulator8. Before model surgery, horizontal reference lines at a certain distance from the base of the upper and lower jaw models are usually drawn. The horizontal reference lines are often drawn parallel to the top and base of the articulator. Vertical reference lines are usually placed at the site of the first
Key words: orthognathic surgery; model surgery; prediction. Accepted for publication 16 September 1993
molar, the canine, and the central incisor, parallel to each other and perpendicular to the horizontal reference line. The cephalometric plan is reproduced in the models by cutting these in the desired fashion and is then transferred to the operation with an acrylic splint. At the operation, it is possible to compare the changes at the maxillary first molar and canine with the changes recorded at the models. WYLIE et al. 17 described a method of transferring the vertical reference lines at the canines and first molars from the articular to the patient during operation. This was done with a special instrument which also allowed transfer of the horizontal reference points above the first molars and canines. However, this method does not seem to have gained general acceptance, and its enhancement of the precision of surgery has not been documented. The purpose of the present investigation was to quantify the difference between the predicted and actual post-
12
Nattestad and Vedtofie
operative position of the maxilla as a result of using different reference lines and points in model surgery and operation. The different use of reference lines and points during model surgery and operation was evaluated by geometric considerations, the type of measurement error being correlated to the planned horizontal and vertical movement of the maxilla. Material and methods
The erroneous use of reference points and lines during model surgery and operation can be divided into four categories (A-D), depending on the measurement method (line or point) and the horizontal a n d vertical position of the reference point or line (Fig. 1). The errors could arise from measuring during model surgery perpendicular to a reference line and during operation to a fixed point (A), measuring to a fixed reference point in different horizontal positions (B), measuring to reference lines with different angulations
(C), and measuring to a fixed reference point with different vertical positions (D). These four different possibilities of error were analyzed only in mathematic models. The assumption of the mathematic model was that the m o v e m e n t of the maxillary first molar is two-dimensional (sagittal a n d vertical) and that no transverse or rotational m o v e m e n t of the maxilla takes place. These restrictions resulted in a similar horizontal and vertical movement of the maxillary first molars and incisors. Equations were developed to evaluate the vertical error in the position of the maxillary first molar arising from the specific erroneous measurement method. The error was described relative to a planned vertical and horizontal movement from 10 to l0 m m of the maxillary first molar in increments of 1 mm. All equations were based on two simple geometric relationships of the right triangle.
tan (a) = bc ab
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The vertical measurements were m a d e perpendicular to the reference line during model surgery and to a fixed reference point (bur hole) during operation (Fig. 1A). The initial vertical position of the reference during model surgery and operation was identical. The vertical position of the maxillary first molar after model surgery and operation could be calculated by the following equations: MMODE L =
y
Mop = Yl
/(YI÷
Y)2÷(X,+X) 2
Use of reference point in different horizontal position (Fig. 1B)
l
/-%( cx,,v, ~
In all four categories, the error of the measurement method was the difference between the movement in model surgery and operation ( E R R O R = MMOOEL -- Moe). This movement at model surgery and operation was evaluated according to the m e a s u r e m e n t method by comparing the length of the dotted lines to the preoperative position of the molar (Fig. 1). The actual movement of the maxilla was the planned movement minus the error. This means that in cases of planned superior movement of the maxilla with a negative error, a further superior movement was taking place (planning @error) = planning + error). However, in cases of similar planned movement with a positive error, the resulting movement was smaller than planned.
Use of different reference systems (Fig. 1A)
Use of a reference point in different horizontal position,
\~
M = v e r t i c a l m o v e m e n t at molar; X and Y= horizontal and vertical m o v e m e n t of maxilla; X] and Y] = position of molar before movement of maxilla (0, -35); Ha=horizontal difference in reference point; Aa = difference in angulation of reference lines (in radians); Va= vertical difference in reference lines
I
REFERENCE MODEL
~F~
For each movement of the maxilla from 10 to 10 m m horizontally and vertically, respectively, the corresponding error in the vertical position of the maxillary first molar was derived from the equations. All equations were based on the coordinate system's being placed 35 m m superior to the molar and with the x-axis as the horizontal reference line. The variables used in the following equations are as follows:
f
O. Use of a reference point in different vertical position.
The vertical measurements during model surgery were made to a fixed reference point on the tooth axis placed 35 m m superior to the molar. Measurements during operation were done relative to a fixed reference point placed 35 m m superior to the molar and 10 m m anterior to the axis of the tooth (Fig. 1B). The vertical position of the maxillary first molar after model surgery and operation
Pitfalls in orthognathic m o d e l surgery
could be calculated by the following equations: MMODEL = / ( X l -~-X) 2@-( 111+ y)2 ~_ 111
Use of different angulation of reference lines (Fig. 1C)
The vertical measurements during model surgery were made to the reference line, which was placed perpendicular to the tooth axis of the molar. The measurements during operation were made to a reference line which formed an angle of 10° with the reference line used during model surgery. The center of rotation of the reference line was the preoperative reference point of the molar, and the rotation resulted in an anterior lift of the line of approximately 4.5 mm at the canine (Fig. IC). The vertical position of the maxillary first molar after model surgery and operation could be calculated by the following equations: MMoDer = y Mop = Y - (tan (As)" X)
Use of reference point in different vertical position (Fig. 1D)
The vertical measurements at model surgery were made relative to a fixed reference point located 45 mm superior to the molar along the tooth axis. A similar reference in the simulated operation was located 35 mm superior to the molar along the tooth axis (Fig. 1D). The vertical position of the maxillary first molar after model surgery and operation could be calculated by the following equations: MMODEL = ~(Y1 + Y + V~)2+ X ~
+ (YI-~ Y-~-g~) Mop = ]/(Y, + Y)2+X2+(Y, + Y)
Results
The results of the study show that the vertical positional error of the maxilla varied within the four categories and was closely correlated to the planned horizontal and vertical m o v e m e n t (Fig. 2). In general, the relationship between the vertical positioning error and the planned m o v e m e n t of the maxilla was that a larger horizontal a n d / o r vertical m o v e m e n t of the maxilla resulted in a larger positioning error. The relationship between the vertical positioning error and the planned maxillary movement was linear in categories B and C (Fig. 2B and C), whereas the error in categories A and D showed a hyperbolic
relationship (Fig. 2A and D). In categories A and D, only a positive error was found, whereas both positive and negative errors were found in categories B and C. The largest positioning error was found in category B, varying between -3.7 m m (at a maxillary m o v e m e n t of 10 m m posterior and 10 m m superior) to 3.3 m m (at a maxillary m o v e m e n t of 10 m m anterior and 10 m m inferior) (Fig. 2B). The vertical error in this category was found to depend mainly on the horizontal m o v e m e n t of the maxilla, whereas a vertical m o v e m e n t had little influence on the size of error when the maxilla was m o v e d in anterior and posterior directions. The pattern of error was similar in categories A and C, but the error was considerably smaller (Fig. 2A and C). In category D, the error was diminutive and mainly dependent on the vertical m o v e m e n t of the maxilla (Fig. 2D). The positioning error was close to 0 m m in all four categories when no horizontal maxillary m o v e m e n t t o o k place. The separation of errors into categories does not mean that only one measurement error can occur simultaneously. For example, error categories A and C could coincide, and if an anterior m o v e m e n t of the maxilla was planned, this would increase the error. On the other hand, if a posterior movement was planned, the two errors would tend to neutralize each other. Discussion
The present study illustrates that the actual result of orthognathic surgery may be different from the planned result because of the erroneous transition of reference lines and points between model surgery and operation. The results of the present study show that the possible inaccuracy from the erroneous use o f references has a magnitude similar to that o f the previously reported lack o f precision in clinical studies of orthognathic surgery6.11,12,16. The inaccuracy was measured as a variation in the vertical position of the maxillary molar and was found to depend on the type of error in the measurement method. The error varied between 3.7 and 3.3 m m for movements of the maxilla from - 1 0 to 10 m m horizontally and vertically. The most critical error occurred when a large horizontal movement of the maxilla was performed and the reference point at operation was in
13
a horizontal position 10 m m different from that at model surgery. For instance, the actual intrusion of the maxilla will be only 3.2 m m in a patient with a planned intrusion of 5 m m and a planned advancement of 8 mm, if the horizontal position of the reference point at operation is placed 10 m m anterior to the corresponding point during model surgery. A study describing the method of m o d e l surgery 1 supports the relevancy of the present study by choosing references during model surgery placed parallel to the upper arm of the articulator and close to the base of the model. This choice of references would probably differ from those chosen during operation by being in a higher vertical position (error category D), in a different horizontal position (error category B), and with a different angulation of the horizontal reference line (error category C). The present study has shown the effect o f various errors. However, a combination of incorrect measurement categories will probably be present and, as such, tend to aggravate or equalize the total error. The positional error will be aggravated if the maxilla is m o v e d anteriorly, since the errors in all categories are positive. On the other hand, a posterior m o v e m e n t will tend to equalize the error, since some categories introduce a positive error and other categories introduce a negative error. Several attempts to minimize the errors of surgery have been presented 6,15,16, including the use of an extraoral measurement device at surgery, but only STANCHINAet al. ~5and VAN SICKELS et al. 16 reported the improvement in precision to be statistically significant. This method is usually combined with the use of a composite splint to secure correct horizontal positioning of the maxilla, while the extraoral measure determines the vertical position of the maxilla. ELLlS 3 analyzed the precision of transferring the cephalometric prediction tracing to conventional model surgery, and found an unacceptably high degree of error, as compared with a new method involving precise three-dimensional measurements. EI.Hs 3 concluded that the conventional model surgery was not precise enough and advocated the use of a new instrument for measurement on the models. However, the instrument described by ELLIS 3 does not assist in the transferral of references from model surgery to operation. This still requires classical refer-
Nattestad and Vedtofte
14
Vertical error at maxillary molar (mm)
2.0
0.5 ....> 0.0 (~ Horizontal movement
of
tAntedor)
maxilla (ram)
HotizontaJ movement of moxifla
A. Use of different reference systems.
error at Vertical maxillary
1 molar (m~n)
.
.
.
(1) ~
-5 (ram)
10
B. Use of reference points in different h0riz0ntat positions, Vertical error at maxillary
~
molar (rnm) 2
"~-1
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(o)
1
(Suponor)
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0~" -2 1o
-5
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s
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-5 maxilla(ram)
-lo
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o ~'- Vertical
Vertical
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'
~
o -5 Horizontalmovementof maxilla(rnm)
movement
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-,o
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Fig. 2.
ences on the anterior maxilla a n d / o r a combination of extraoral measurement and composite splint. The horizontal positioning of the maxilla with a composite splint depends on the ability to predict the center of mandibular rotation, a procedure which has been shown to be difficult ~°. The transfer of reference lines from model surgery to operation, as described by WYLIE et al. 17, seems to be justified in all cases where a horizontal m o v e m e n t of some magnitude is planned. The use of extraoral references might increase the precision, but should be used in conjunction with the intraoral measures. A blind horizontal positioning of the maxilla with a composite splint, with the center of the condyle as the c e n t e r of mandibular rotation, is, at best, unreliable. In conclusion, the present study has shown the importance o f a correct transfer of references from the articulator to the operation. It is also suggested that the use of internal reference lines gives rise to errors, since there is no predictable method of transferring the reference lines from model surgery to operation. It is, however, likely that the instrument described by WYLIE et
a l l 7 could transfer the position of the bur holes from the models to the operation m o r e accurately. The recommended m e t h o d for both model surgery and operation is the use of bur holes in a reproducible vertical and horizontal position approximately 5 m m superior to the osteotomy line along the tooth axis. The use of a bur hole is relevant only for vertical measurements on the anterior maxilla, whereas the horizontal m o v e m e n t is best estimated by a vertical line on the bony surface of the maxilla. The angulation of these vertical lines can also be controlled with the instrument described by WYLIE et al. 17. We believe that precision in orthognathic surgery can still be improved. The application of current and future computer graphics systems to the planning procedure could be a major advance, but it presupposes the ability to achieve a strict coherence between the planning and immediate surgical result.
References
1. ANWARM, HARRISM. Model surgery for orthognathic planning. Br J Oral Maxillofac Surg 1990: 28: 393-7.
2. BRAMMERJ, FINN R, BELLWH, SINN D, REISCH J, DANA K. Stability after bimaxillary surgery to correct vertical maxillary excess and mandibular deficiency. J Oral Surg 1980: 38: 664-70. 3. ELLIS E. Accuracy of model surgery: evaluation of an old technique and introduction of a new one. J Oral Maxillofac Surg 1990: 48: 1161-7. 4. HAYMOND c a , STOELINGA
PJW, BLIJDORP
PA, LEENENR J, MERKENSNM. Surgical orthodontic treatment of anterior skeletal open bite using small plate internal fixation. One to five year follow-up. Int J Oral Maxillofac Surg 1991: 20: 223-7. 5. IANNETTI G , CHIMENTI C, D~ PAOLO C. Five-year follow-up of Le Fort I osteotomies. J Cranio-Max-Fac Surg 1987: 15: 238 43. 6. KAHNBERGKE, SUNZEL B, ASTRANDP. Planning and control of vertical dimension in Le Fort I osteotomies. J CranioMax-Fac Surg 1990: 18: 267-70. 7. LABANCJP, KENDRICKJ. A custom acrylic template for the transfer of reference lines and osteotomy from model surgery to the patient: an adjunct for Le Fort I osteotomy. Int J Adult Orthod Orthogn Surg 1987: 2:215 20. 8. MARKOJV. Simple hinge and semi-adjustable articulators in orthognathic surgery. Am J Orthod Dentofacial Orthop 1986: 90: 3744. 9. NATTESTAD A, VEDTOFTE P, MOSEKILDE E.
Pitfalls in orthognathic model surgery The significance of an erroneous recording of the mandibular center of rotation on orthognathic surgery. J Cranio-MaxFac Surg 1991: 19: 25~9. 10. NATTESTAD A, VEDTOFTER Mandibular autorotation in orthognathic surgery. J Cranio-Max-Fac Surg 1992: 20: 16370. t 1. POLIDOWD, ELLISE, SrNNDR An assessment of predictability of maxillary surgery. J Oral Maxillofac Surg 1990: 48: 697-701. 12. POSPISILOA. Reliability and feasibility of prediction tracing in orthognathic surgery. J Cranio-Max-Fac Surg 1987: 15: 79-84. 13. PROFFIT WR, PHILLIPS C, TURVEY TA.
Stability following superior repositioning of the maxilla by Le Fort I osteotomy. Am J Orthod Dentofacial Orthop 1987: 92:151 61. 14. SPERRY TP, STEINBERG MJ, GANS BJ. Mandibular movement during autorotation as a result of maxillary impaction surgery. Am J Orthod 1982: 81:116 23. 15. STANCHINAR, ELLIS E, GALLOWJ, Fonseca RJ. A comparison of two measures for repositioning the maxilla during orthognathic surgery. Int J Adult Orthod Orthogn Surg 1988: 3: 149-54. 16. VAN SICKELSJE, LARSEN AJ, TRIPPLETT RG. Predictability of maxillary surgery: a comparison of internal and external reference marks. Oral Surg 1986: 61: 542-5.
15
17. WYLIE GA, EPKER BN, MossoP JR. A technique to improve the accuracy of total maxillary surgery. Int J Orthod Orthogn Surg 1988: 3: 143-7.
Address:
Anders Nattestad, DDS, PhD Senior Research Associate Department of Oral and Maxillofacial Surgery Faculty of Health Sciences University of Copenhagen Norre Alle 20 2200 Copenhagen Denmark
Copyright © Munksgaard 1994 [ntemadonalJournal of
Oral& MaxillofacialSurgery ISSN 0901-5027
Pitfalls in orthognathic model surgery
A n d e r s Nattestad ~, Poul Vedtofte 2 1Department of Oral and Maxillofacial Surgery, School of Dentistry, Faculty of Health Sciences, University of Copenhagen, and 2Department of Oral and Maxillofacial Surgery, University Hospital (Rigshospitalet), Copenhagen, Denmark
The significance of using different reference lines and points during model surgery and operation A. Nattestad, R Vedtofte. Pi~alls in orthognathie model surgery. The significance of using different reference lines and points during model surgery and operation. Int. J. Oral Maxillofac. Surg. 1994; 23: 11-15. © Munksgaard, 1994 Abstract. The planning of orthognathic surgery usually involves a simulation of jaw movements in a semiadjustable articulator. The use of vertical and horizontal references during model surgery and operation have previously been described in great detail. The purpose of the present study was to quantify the errors resulting from using different reference lines and points in model surgery and operation. The results indicate that clinically significant differences between the planned and surgical jaw movement can result from the erroneous transfer of reference lines and points between model surgery and operation. Solutions to some of the problems discussed are suggested.
Several studies have described the results and stability of orthognathic surgery2'4'5'v'~3.However, only a few deal with the relation between the predicted result, based on model surgery in semiadjustable articulators, and the immediate result after surgery 1~'12't5'~6.POSPISIL 12 compared the prediction tracings with the immediate postoperative cephalometric radiographs in 40 patients and found that 83% differed between the planned and the surgical result by over 20% of the planned movement. POLIDO et al. H investigated the predictability of the maxillary central incisor position in 100 consecutive patients and found an average discrepancy of 2.2 mm vertically and 1.8 mm horizontally. VAN SicKEcs et al. ~6 reported a mean difference of 2.5 mm vertically and 3.6 mm horizontally in a group of 11 patients with the use of the intraoral measurement method. This was compared to another group of 11 patients, where an extraoral measurement device was used and a statistically significant improve-
ment in precision was found. Similar findings were reported by STANCH1NA et al. ~5. However, a later study by KAHNBERGet al. 6 with a similar design showed no statistically significant difference between the two measurement methods. A suggested explanation for the difference between the predicted and actual result of orthognathic surgery is a difference between the actual and simulated center of mandibular rotation 9,1°,14. Errors in model surgery done in the articulator have also been reported as a possible cause for this discrepancy3'17. The usual planning procedure for orthognathic surgery involves a cephalometric prediction tracing, followed by model surgery in a semiadjustable articulator8. Before model surgery, horizontal reference lines at a certain distance from the base of the upper and lower jaw models are usually drawn. The horizontal reference lines are often drawn parallel to the top and base of the articulator. Vertical reference lines are usually placed at the site of the first
Key words: orthognathic surgery; model surgery; prediction. Accepted for publication 16 September 1993
molar, the canine, and the central incisor, parallel to each other and perpendicular to the horizontal reference line. The cephalometric plan is reproduced in the models by cutting these in the desired fashion and is then transferred to the operation with an acrylic splint. At the operation, it is possible to compare the changes at the maxillary first molar and canine with the changes recorded at the models. WYLIE et al. 17 described a method of transferring the vertical reference lines at the canines and first molars from the articular to the patient during operation. This was done with a special instrument which also allowed transfer of the horizontal reference points above the first molars and canines. However, this method does not seem to have gained general acceptance, and its enhancement of the precision of surgery has not been documented. The purpose of the present investigation was to quantify the difference between the predicted and actual post-
12
Nattestad and Vedtofie
operative position of the maxilla as a result of using different reference lines and points in model surgery and operation. The different use of reference lines and points during model surgery and operation was evaluated by geometric considerations, the type of measurement error being correlated to the planned horizontal and vertical movement of the maxilla. Material and methods
The erroneous use of reference points and lines during model surgery and operation can be divided into four categories (A-D), depending on the measurement method (line or point) and the horizontal a n d vertical position of the reference point or line (Fig. 1). The errors could arise from measuring during model surgery perpendicular to a reference line and during operation to a fixed point (A), measuring to a fixed reference point in different horizontal positions (B), measuring to reference lines with different angulations
(C), and measuring to a fixed reference point with different vertical positions (D). These four different possibilities of error were analyzed only in mathematic models. The assumption of the mathematic model was that the m o v e m e n t of the maxillary first molar is two-dimensional (sagittal a n d vertical) and that no transverse or rotational m o v e m e n t of the maxilla takes place. These restrictions resulted in a similar horizontal and vertical movement of the maxillary first molars and incisors. Equations were developed to evaluate the vertical error in the position of the maxillary first molar arising from the specific erroneous measurement method. The error was described relative to a planned vertical and horizontal movement from 10 to l0 m m of the maxillary first molar in increments of 1 mm. All equations were based on two simple geometric relationships of the right triangle.
tan (a) = bc ab
REFERENCE I I
,
a
OSTEOTOM~
_
\ ' t '
\ 1'',
(-Ix I'\
\\ / \
xY
REFERENCE
_
I
\l
\
,;l / ,,/ I
[
", I
[
-- .-XI_ _.
\~.
J',,
F,'-J
~"
_
i \ Y / ; 'i',, ',j / /
I ',
II II
I I
I/ ×,,v, |
/]
A. Use of different reference systems.
b
~1"10nlm-N
I
(
"AC
ac = ~ab2 + bc 2
B.
\,I
~\\ /\\
~
,
-- I----'
I
10 mm V~
'\.
Z
~,
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;" I
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~ t / / I \
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/~
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Fig. 1.
)
35mm I
REFERENCE OPERATION
\\
~q
/
/
/
/
OSTEOTOMY
/
V\ /\\
I
t--'~- 7 - - t
[
~
',',,, ,,
-m--
The vertical measurements were m a d e perpendicular to the reference line during model surgery and to a fixed reference point (bur hole) during operation (Fig. 1A). The initial vertical position of the reference during model surgery and operation was identical. The vertical position of the maxillary first molar after model surgery and operation could be calculated by the following equations: MMODE L =
y
Mop = Yl
/(YI÷
Y)2÷(X,+X) 2
Use of reference point in different horizontal position (Fig. 1B)
l
/-%( cx,,v, ~
In all four categories, the error of the measurement method was the difference between the movement in model surgery and operation ( E R R O R = MMOOEL -- Moe). This movement at model surgery and operation was evaluated according to the m e a s u r e m e n t method by comparing the length of the dotted lines to the preoperative position of the molar (Fig. 1). The actual movement of the maxilla was the planned movement minus the error. This means that in cases of planned superior movement of the maxilla with a negative error, a further superior movement was taking place (planning @error) = planning + error). However, in cases of similar planned movement with a positive error, the resulting movement was smaller than planned.
Use of different reference systems (Fig. 1A)
Use of a reference point in different horizontal position,
\~
M = v e r t i c a l m o v e m e n t at molar; X and Y= horizontal and vertical m o v e m e n t of maxilla; X] and Y] = position of molar before movement of maxilla (0, -35); Ha=horizontal difference in reference point; Aa = difference in angulation of reference lines (in radians); Va= vertical difference in reference lines
I
REFERENCE MODEL
~F~
For each movement of the maxilla from 10 to 10 m m horizontally and vertically, respectively, the corresponding error in the vertical position of the maxillary first molar was derived from the equations. All equations were based on the coordinate system's being placed 35 m m superior to the molar and with the x-axis as the horizontal reference line. The variables used in the following equations are as follows:
f
O. Use of a reference point in different vertical position.
The vertical measurements during model surgery were made to a fixed reference point on the tooth axis placed 35 m m superior to the molar. Measurements during operation were done relative to a fixed reference point placed 35 m m superior to the molar and 10 m m anterior to the axis of the tooth (Fig. 1B). The vertical position of the maxillary first molar after model surgery and operation
Pitfalls in orthognathic m o d e l surgery
could be calculated by the following equations: MMODEL = / ( X l -~-X) 2@-( 111+ y)2 ~_ 111
Use of different angulation of reference lines (Fig. 1C)
The vertical measurements during model surgery were made to the reference line, which was placed perpendicular to the tooth axis of the molar. The measurements during operation were made to a reference line which formed an angle of 10° with the reference line used during model surgery. The center of rotation of the reference line was the preoperative reference point of the molar, and the rotation resulted in an anterior lift of the line of approximately 4.5 mm at the canine (Fig. IC). The vertical position of the maxillary first molar after model surgery and operation could be calculated by the following equations: MMoDer = y Mop = Y - (tan (As)" X)
Use of reference point in different vertical position (Fig. 1D)
The vertical measurements at model surgery were made relative to a fixed reference point located 45 mm superior to the molar along the tooth axis. A similar reference in the simulated operation was located 35 mm superior to the molar along the tooth axis (Fig. 1D). The vertical position of the maxillary first molar after model surgery and operation could be calculated by the following equations: MMODEL = ~(Y1 + Y + V~)2+ X ~
+ (YI-~ Y-~-g~) Mop = ]/(Y, + Y)2+X2+(Y, + Y)
Results
The results of the study show that the vertical positional error of the maxilla varied within the four categories and was closely correlated to the planned horizontal and vertical m o v e m e n t (Fig. 2). In general, the relationship between the vertical positioning error and the planned m o v e m e n t of the maxilla was that a larger horizontal a n d / o r vertical m o v e m e n t of the maxilla resulted in a larger positioning error. The relationship between the vertical positioning error and the planned maxillary movement was linear in categories B and C (Fig. 2B and C), whereas the error in categories A and D showed a hyperbolic
relationship (Fig. 2A and D). In categories A and D, only a positive error was found, whereas both positive and negative errors were found in categories B and C. The largest positioning error was found in category B, varying between -3.7 m m (at a maxillary m o v e m e n t of 10 m m posterior and 10 m m superior) to 3.3 m m (at a maxillary m o v e m e n t of 10 m m anterior and 10 m m inferior) (Fig. 2B). The vertical error in this category was found to depend mainly on the horizontal m o v e m e n t of the maxilla, whereas a vertical m o v e m e n t had little influence on the size of error when the maxilla was m o v e d in anterior and posterior directions. The pattern of error was similar in categories A and C, but the error was considerably smaller (Fig. 2A and C). In category D, the error was diminutive and mainly dependent on the vertical m o v e m e n t of the maxilla (Fig. 2D). The positioning error was close to 0 m m in all four categories when no horizontal maxillary m o v e m e n t t o o k place. The separation of errors into categories does not mean that only one measurement error can occur simultaneously. For example, error categories A and C could coincide, and if an anterior m o v e m e n t of the maxilla was planned, this would increase the error. On the other hand, if a posterior movement was planned, the two errors would tend to neutralize each other. Discussion
The present study illustrates that the actual result of orthognathic surgery may be different from the planned result because of the erroneous transition of reference lines and points between model surgery and operation. The results of the present study show that the possible inaccuracy from the erroneous use o f references has a magnitude similar to that o f the previously reported lack o f precision in clinical studies of orthognathic surgery6.11,12,16. The inaccuracy was measured as a variation in the vertical position of the maxillary molar and was found to depend on the type of error in the measurement method. The error varied between 3.7 and 3.3 m m for movements of the maxilla from - 1 0 to 10 m m horizontally and vertically. The most critical error occurred when a large horizontal movement of the maxilla was performed and the reference point at operation was in
13
a horizontal position 10 m m different from that at model surgery. For instance, the actual intrusion of the maxilla will be only 3.2 m m in a patient with a planned intrusion of 5 m m and a planned advancement of 8 mm, if the horizontal position of the reference point at operation is placed 10 m m anterior to the corresponding point during model surgery. A study describing the method of m o d e l surgery 1 supports the relevancy of the present study by choosing references during model surgery placed parallel to the upper arm of the articulator and close to the base of the model. This choice of references would probably differ from those chosen during operation by being in a higher vertical position (error category D), in a different horizontal position (error category B), and with a different angulation of the horizontal reference line (error category C). The present study has shown the effect o f various errors. However, a combination of incorrect measurement categories will probably be present and, as such, tend to aggravate or equalize the total error. The positional error will be aggravated if the maxilla is m o v e d anteriorly, since the errors in all categories are positive. On the other hand, a posterior m o v e m e n t will tend to equalize the error, since some categories introduce a positive error and other categories introduce a negative error. Several attempts to minimize the errors of surgery have been presented 6,15,16, including the use of an extraoral measurement device at surgery, but only STANCHINAet al. ~5and VAN SICKELS et al. 16 reported the improvement in precision to be statistically significant. This method is usually combined with the use of a composite splint to secure correct horizontal positioning of the maxilla, while the extraoral measure determines the vertical position of the maxilla. ELLlS 3 analyzed the precision of transferring the cephalometric prediction tracing to conventional model surgery, and found an unacceptably high degree of error, as compared with a new method involving precise three-dimensional measurements. EI.Hs 3 concluded that the conventional model surgery was not precise enough and advocated the use of a new instrument for measurement on the models. However, the instrument described by ELLIS 3 does not assist in the transferral of references from model surgery to operation. This still requires classical refer-
Nattestad and Vedtofte
14
Vertical error at maxillary molar (mm)
2.0
0.5 ....> 0.0 (~ Horizontal movement
of
tAntedor)
maxilla (ram)
HotizontaJ movement of moxifla
A. Use of different reference systems.
error at Vertical maxillary
1 molar (m~n)
.
.
.
(1) ~
-5 (ram)
10
B. Use of reference points in different h0riz0ntat positions, Vertical error at maxillary
~
molar (rnm) 2
"~-1
10~(Super~°r)
(o)
1
(Suponor)
10 5
0~" -2 1o
-5
-T
(Anterior)
s
4' /
,~ ~o
Horizontal movement of
-5 maxilla(ram)
-lo
-10
C. Use of different angulation of reference lines,
o ~'- Vertical
Vertical
movement of maxilla /mm)
o-->:; 'o 1' (Anterior)
-5 t
'
~
o -5 Horizontalmovementof maxilla(rnm)
movement
of maxilla (mr'n)
-,o
-lo
D. U s e of r e f e r e n c e points in different vertical positions,
Fig. 2.
ences on the anterior maxilla a n d / o r a combination of extraoral measurement and composite splint. The horizontal positioning of the maxilla with a composite splint depends on the ability to predict the center of mandibular rotation, a procedure which has been shown to be difficult ~°. The transfer of reference lines from model surgery to operation, as described by WYLIE et al. 17, seems to be justified in all cases where a horizontal m o v e m e n t of some magnitude is planned. The use of extraoral references might increase the precision, but should be used in conjunction with the intraoral measures. A blind horizontal positioning of the maxilla with a composite splint, with the center of the condyle as the c e n t e r of mandibular rotation, is, at best, unreliable. In conclusion, the present study has shown the importance o f a correct transfer of references from the articulator to the operation. It is also suggested that the use of internal reference lines gives rise to errors, since there is no predictable method of transferring the reference lines from model surgery to operation. It is, however, likely that the instrument described by WYLIE et
a l l 7 could transfer the position of the bur holes from the models to the operation m o r e accurately. The recommended m e t h o d for both model surgery and operation is the use of bur holes in a reproducible vertical and horizontal position approximately 5 m m superior to the osteotomy line along the tooth axis. The use of a bur hole is relevant only for vertical measurements on the anterior maxilla, whereas the horizontal m o v e m e n t is best estimated by a vertical line on the bony surface of the maxilla. The angulation of these vertical lines can also be controlled with the instrument described by WYLIE et al. 17. We believe that precision in orthognathic surgery can still be improved. The application of current and future computer graphics systems to the planning procedure could be a major advance, but it presupposes the ability to achieve a strict coherence between the planning and immediate surgical result.
References
1. ANWARM, HARRISM. Model surgery for orthognathic planning. Br J Oral Maxillofac Surg 1990: 28: 393-7.
2. BRAMMERJ, FINN R, BELLWH, SINN D, REISCH J, DANA K. Stability after bimaxillary surgery to correct vertical maxillary excess and mandibular deficiency. J Oral Surg 1980: 38: 664-70. 3. ELLIS E. Accuracy of model surgery: evaluation of an old technique and introduction of a new one. J Oral Maxillofac Surg 1990: 48: 1161-7. 4. HAYMOND c a , STOELINGA
PJW, BLIJDORP
PA, LEENENR J, MERKENSNM. Surgical orthodontic treatment of anterior skeletal open bite using small plate internal fixation. One to five year follow-up. Int J Oral Maxillofac Surg 1991: 20: 223-7. 5. IANNETTI G , CHIMENTI C, D~ PAOLO C. Five-year follow-up of Le Fort I osteotomies. J Cranio-Max-Fac Surg 1987: 15: 238 43. 6. KAHNBERGKE, SUNZEL B, ASTRANDP. Planning and control of vertical dimension in Le Fort I osteotomies. J CranioMax-Fac Surg 1990: 18: 267-70. 7. LABANCJP, KENDRICKJ. A custom acrylic template for the transfer of reference lines and osteotomy from model surgery to the patient: an adjunct for Le Fort I osteotomy. Int J Adult Orthod Orthogn Surg 1987: 2:215 20. 8. MARKOJV. Simple hinge and semi-adjustable articulators in orthognathic surgery. Am J Orthod Dentofacial Orthop 1986: 90: 3744. 9. NATTESTAD A, VEDTOFTE P, MOSEKILDE E.
Pitfalls in orthognathic model surgery The significance of an erroneous recording of the mandibular center of rotation on orthognathic surgery. J Cranio-MaxFac Surg 1991: 19: 25~9. 10. NATTESTAD A, VEDTOFTER Mandibular autorotation in orthognathic surgery. J Cranio-Max-Fac Surg 1992: 20: 16370. t 1. POLIDOWD, ELLISE, SrNNDR An assessment of predictability of maxillary surgery. J Oral Maxillofac Surg 1990: 48: 697-701. 12. POSPISILOA. Reliability and feasibility of prediction tracing in orthognathic surgery. J Cranio-Max-Fac Surg 1987: 15: 79-84. 13. PROFFIT WR, PHILLIPS C, TURVEY TA.
Stability following superior repositioning of the maxilla by Le Fort I osteotomy. Am J Orthod Dentofacial Orthop 1987: 92:151 61. 14. SPERRY TP, STEINBERG MJ, GANS BJ. Mandibular movement during autorotation as a result of maxillary impaction surgery. Am J Orthod 1982: 81:116 23. 15. STANCHINAR, ELLIS E, GALLOWJ, Fonseca RJ. A comparison of two measures for repositioning the maxilla during orthognathic surgery. Int J Adult Orthod Orthogn Surg 1988: 3: 149-54. 16. VAN SICKELSJE, LARSEN AJ, TRIPPLETT RG. Predictability of maxillary surgery: a comparison of internal and external reference marks. Oral Surg 1986: 61: 542-5.
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17. WYLIE GA, EPKER BN, MossoP JR. A technique to improve the accuracy of total maxillary surgery. Int J Orthod Orthogn Surg 1988: 3: 143-7.
Address:
Anders Nattestad, DDS, PhD Senior Research Associate Department of Oral and Maxillofacial Surgery Faculty of Health Sciences University of Copenhagen Norre Alle 20 2200 Copenhagen Denmark