CE: A.B.; SCS-17-0973; Total nos of Pages: 3;
SCS-17-0973
CLINICAL STUDY
Vertical Maxillary Measurements using a Virtual External Reference Point in Orthognathic Surgery: Technical Innovation Sebastia´n Espinosa S, DDS, OMS Abstract: It is extremely important to achieve vertical position of the upper jaw in orthognathic surgery. A common method used is measuring distances at surgery using external reference points. Unfortunately, surgeons have been making mistakes when calculating the goal distance of our external reference systems. A possible explanation is that when the author measure the baseline and goal vertical distances, the author usually do not consider the variations produced by the triangulation effect generated due the horizontal or/and transverse movements of the maxilla. A method is proposed to fix this phenomenon in an easy way through the virtual customization of the ERP in computer-assisted surgical simulation. The technique entails creating, in the planning software, the same reference system one will use at surgery. In this virtual system, one measures the difference between the baseline and target distances, and then uses them at surgery. Key Words: Computer-aided surgical simulation, external reference systems, LeFort I osteotomies, orthognathic surgery, vertical maxillary positioning (J Craniofac Surg 2017;00: 00–00)
O
rthognathic surgery involves the mobilization of the facial skeleton in order to achieve several goals with esthetic and functional implications. It is extremely important to transfer this process to the operative room (OR) by establishing precision and predictability in the position of the jaws. Many techniques have been published for intraoperative vertical repositioning of the maxilla. The most cited methods are the use of external and internal references. External reference points (ERPs)1 are currently the most accurate method described for vertical repositioning of the upper jaw.2,3 Although the use of ERP has proven to be more accurate than internal references,2,4 there is still a lack of accuracy in the 3 planes of space, especially during multidirectional movements commonly used in planning.5,6 Computer-assisted surgical simulation (CASS) has made a big contribution to orthognathic surgery, but there is another element to
be corrected that can further improve the results based on intraoperative vertical measurements. Since these measures seek to confirm the final vertical position of the maxilla, when we make such measurements, a triangulation effect is produced if the upper jaw is mobilized in the horizontal plane. Usually, the vertical measures that the software give us does not correlate with the real vertical measures we will obtain using ERPs in the OR. This is because the software calculates the vertical variations of the teeth based on a determined reference frame, which is not the same reference we use at surgery. Since our reference is a given anatomic point (ERP), the measurements that CASS gives us are perpendicular to a plane and are not equivalent to the measurements that we get in the OR. Therefore, every measurement obtained in the OR is a consequence from a triangulation effect that varies in relation to where the ERP is located, the magnitude of the movements and complexity of them as well. In practical terms, what we are measuring is the hypotenuse of a right triangle. If we decide to only make a maxillary advancement, the vertical position at the level of the teeth obviously should not vary. When this approach is put into practice at surgery, in an effort to maintain the vertical measurement in this advancement, what we are doing is positioning the maxilla (at the incisors level) in a more superior position. The explanation for this phenomenon is that our measurement is the distance between the ERP and the tooth (which is represented by the hypotenuse of a right triangle) and not a perpendicular distance from the tooth and a determined reference plane (what CASS give us) is the difference in the movement expressed in coordinates in each axis. If we want to maintain the level of the teeth, this distance (tooth-ERP) must increase in length at the incisors since this point is moving away from the ERP (Fig. 1). What usually happens is that we maintain the distance record achieved before the maxillary mobilization leaving the incisors in an upper position. To solve this problem, the author has developed a simple technique that calculates the goal distance from an external reference system (ERS). The technique entails creating—in the planning software—the same reference system one will use at surgery. In this virtual system, one measures the difference between the baseline and target distances, and then apply them at surgery.
METHOD From the Department of Oral and Maxillofacial Surgery, Hospital So´tero del Rı´o, Santiago, Chile. Received July 1, 2017. Accepted for publication August 30, 2017. Address correspondence and reprint requests to Dr Sebastia´n Espinosa, DDS, OMS, Hospital So´tero del Rı´o, Av Concha y Toro 3459, Puente Alto, Santiago, Chile 8207257; E-mail: [email protected] The author reports no conflicts of interest. Copyright # 2017 by Mutaz B. Habal, MD ISSN: 1049-2275 DOI: 10.1097/SCS.0000000000004170
The Journal of Craniofacial Surgery
The proposed method introduces corrected measurements based on the movements planned in the maxilla. The steps to achieving corrected vertical measurements through virtual orthognathic surgery are as follows: 1. Complete virtual surgical planning in the standard fashion. 2. Establish a virtual ERS. Digitize, on the computer model, the same external landmarks you will use at surgery—to establish the vertical position of the maxilla. This is done by placing a ‘‘virtual’’ ERP in the area where the surgeon decides is suitable, having in mind to place it in a round number distance for
Volume 00, Number 00, Month 2017
1
Copyright © 2017 Mutaz B. Habal, MD. Unauthorized reproduction of this article is prohibited.
CE: A.B.; SCS-17-0973; Total nos of Pages: 3;
SCS-17-0973
The Journal of Craniofacial Surgery
Espinosa S
80 mm
Volume 00, Number 00, Month 2017
80mm
B
80,89 mm
80mm
10 mm advancement FIGURE 1. Geometric effect in the vertical measurements using an external reference point at the incisor level with 10 mm maxillary advancement. Although it is straightforward movement, the vertical measurement increased at the incisors. If the surgeon is not aware of this phenomenon, the maxilla will be fixated in an upper position in an attempt to maintain the initial measurement.
3.
4. 5.
6. 7. 8.
9.
convenience (ie, 70 mm, 80 mm, etc.). One landmark must be on the maxilla (dental points), the other on the midface (frontal midline region). For example, you may select soft-tissue nasion and the midpoint of the orthodontic arch wire (located between the brackets of the central incisors). You must record the distance of the ERP to the archwire, so as to reproduce it at surgery when you locate the ERP (Fig. 2). Measure and record baseline and goal distances with your CASS software. The baseline distance is the distance between the maxillary and midfacial landmarks, when the upper jaw is in its original position. The goal distance is the distance between the same landmarks, when the upper jaw is in final alignment. The distance between each point and the ERP can be corroborated (if needed) by applying the coordinates of each point measured to an Euclidian distance formula (H (x1 x2)2þ(y1 y2)2þ(z1 z2)2) (Fig. 3). Calculate the delta for each point measured in the software. That is the difference between goal and baseline distances. Pay attention to the sign of the difference. At surgery, locate as accurately as possible the maxillary and midfacial landmarks. For more precise location in the OR of the ERP, you can make vertical measurements from the canines so as to ‘‘triangulate’’ the position of the ERP. You may avoid movement of the soft-tissue landmark by placing a K-wire or a screw through the landmark into the underlying bone. Before cutting the upper jaw, measure and record the baseline distance. Calculate the goal distance by adding or subtracting the delta (calculated in step 4) to the baseline distance. Mobilize the maxilla, articulate it against the mandible, and wire it in maxillomandibular fixation. Rotate the maxilla and the mandible, around the condylar axis, until the distance between the maxillary landmark and the midfacial landmark reach the goal distance. In this way, the planned vertical movements will be reproduced based on the corrected measurements. Fixate the maxilla in this position.
80mm
A
C
FIGURE 2. Virtual external reference point (ERP) position. (A) Virtual ERP located in the frontal area. Note that it is located considering the soft tissue width. (B) Measurement without soft tissues in a round number. (C) Locating the ERP in the midline.
decrease or increase the fullness in the paranasal areas), the final position of the anterior nasal spine and the upper incisor exposure. All these errors are conditioned to the magnitude of the planned position of the maxilla. The traditional methodology has several limitations to avoid these errors. Projections are set in a 2-dimensional image, so is not possible to record the variations on each side of the maxilla. As well, when performing the measurements in the model block, there is no an anatomic reference point to achieve the vertical distances. What it does, is to take a certain horizontal reference plane, which does not reproduce the effect of triangulation using an ERP that is used in surgery. Computer-assisted surgical simulation reduces error margins, but they do not disappear. Stokbro et al7 found errors in the vertical position up to 0.75 mm not specifying whether a higher level error occurred in molars or incisors (they expressed an average of 3 dental points). There was a tendency to a lower position of the maxilla compared to what it was planned (they used the medial canthal region as ERP). Differences in pitch showed statistical significance, with a slightly greater decrease in the maxillary occlusal plane than CASS Surgery Placement of virtual ERP Obtain Coordinates for ERP Measure the distance between the virtual ERP and every point considered. Then calculate the difference between the baseline maxillary position and its final position.
Obtain coordinates for Baseline and Goal maxillary points
Complementary Measurements
To corroborate the distance measurements, calculate the distance from ERP coordinates and maxillary points coordinates through Euclidian formula:
( (x1-x2)2 + (y1-y2)2 + (z1-z2)2)
DISCUSSION The lack of precision in the final position of the maxilla determines several implications. An unplanned counterclockwise or clockwise rotation due to lack of vertical accuracy in the position of the incisors and/or molars could generate changes in the inclination of the planned occlusal plane, with the consecutive increase or decrease in the projection of the mandible. The same effect also generates a variation in the LeFort I osteotomy step (which can
2
Calculate Delta between baseline and goal distances obtained for every point selected
Apply the corrected vertical measurements at surgery
FIGURE 3. Algorithm proposed for corrected vertical measurements using a virtual external reference point.
#
2017 Mutaz B. Habal, MD
Copyright © 2017 Mutaz B. Habal, MD. Unauthorized reproduction of this article is prohibited.
CE: A.B.; SCS-17-0973; Total nos of Pages: 3;
SCS-17-0973
The Journal of Craniofacial Surgery
Volume 00, Number 00, Month 2017
the planned. They described a ‘‘decrease in the occlusal plane angulation’’ as a positive pitch which meant an upward movement of the central incisors. Xia et al8 described an average difference of 0.44 mm in the vertical level, measured at the midline between the preoperative and postoperative measurements (range 1.98, 0.47). In addition, they described a difference in 1 degree on the pitch of the maxilla. Kwon et al9 compared the accuracy between virtual model surgery and traditional model surgery (using a model block). They reported that in traditional model surgery, there was an 18.8% of the patients with more than 2 mm of discrepancy in the final results. Moreover, in the virtual surgery group, the same margin of error was observed in a 7% of the patients. This new technical proposal is to establish a customization of the ERP so as to accurately record the vertical distances in upper jaw fixation. It is evident that planned changes in vertical maxillary position change the goal distance of an ERS. This span, however, is also influenced by the size of the horizontal maxillary movement, the relative horizontal position between the ERS and the tooth landmarks, and the vertical distance between ERS and the landmarks used. It has to be considered that many times we make transversal and cant corrections in the upper jaw that may change even more the vertical measurements. Since we precisely determine the position of the ERP, we have no alterations in the sagittal or vertical position of the latter, and thus, changes in the measures taken in the computer will be reproduced in the patient. The author believes that with this simple method we strive for near perfect outcomes and gives us a tool to get closer.
#
2017 Mutaz B. Habal, MD
Measurements in Orthognathic Surgery
ACKNOWLEDGMENT The author would like to thank Dr Jaime Gateno for his help in developing this manuscript.
REFERENCES 1. Johnson DG. Intraoperative measurement of maxillary repositioning: an ancillary technique. Oral Surg Oral Med Oral Pathol 1985;60:266–268 2. Polido WD, Ellis E, Sinn DP. An assessment of the predictability of the maxillary surgery. J Oral Maxillofac Surg 1990;48:697–701 3. Polido WD, Ellis E, Sinn DP. An assessment of the predictability of the maxillary repositioning. Int J Oral Maxillofac Surg 1992;20:349–352 4. Van Sickels JK, Larsen AJ, Triplett RG. Predictability of maxillary surgery: a comparison of internal and external reference marks. Oral Surg 1986;61:542–545 5. Bryan DC, Hunt NP. Surgical accuracy in orthognathic surgery. Br J Oral Maxillofac Surg 1993;31:343–349 6. Ellis E. Bimaxillary surgery using an intermediate splint to position the maxilla. J Oral Maxillofac Surg 1999;57:53–56 7. Stokbro K, Aagaard E, Torkov P, et al. Surgical accuracy of threedimensional virtual planning: a pilot study of bimaxillary orthognathic procedures including maxillary segmentation. Int J Oral Maxillofac Surg 2016;45:8–18 8. Xia JJ, Gateno J, Teichgraeber JF, et al. Accuracy of the computer-aided surgical simulation (CASS) system in the treatment of patients with complex craniomaxillofacial deformity: a pilot study. J Oral Maxillofac Surg 2007;65:248–254 9. Kwon TG, Choi JW, Kyung HM, et al. Accuracy of maxillary repositioning in two-jaw surgery with conventional articulator model surgery versus virtual model surgery. Int J Oral Maxillofac Surg 2014;43:732–738
3
Copyright © 2017 Mutaz B. Habal, MD. Unauthorized reproduction of this article is prohibited.
SCS-17-0973
CLINICAL STUDY
Vertical Maxillary Measurements using a Virtual External Reference Point in Orthognathic Surgery: Technical Innovation Sebastia´n Espinosa S, DDS, OMS Abstract: It is extremely important to achieve vertical position of the upper jaw in orthognathic surgery. A common method used is measuring distances at surgery using external reference points. Unfortunately, surgeons have been making mistakes when calculating the goal distance of our external reference systems. A possible explanation is that when the author measure the baseline and goal vertical distances, the author usually do not consider the variations produced by the triangulation effect generated due the horizontal or/and transverse movements of the maxilla. A method is proposed to fix this phenomenon in an easy way through the virtual customization of the ERP in computer-assisted surgical simulation. The technique entails creating, in the planning software, the same reference system one will use at surgery. In this virtual system, one measures the difference between the baseline and target distances, and then uses them at surgery. Key Words: Computer-aided surgical simulation, external reference systems, LeFort I osteotomies, orthognathic surgery, vertical maxillary positioning (J Craniofac Surg 2017;00: 00–00)
O
rthognathic surgery involves the mobilization of the facial skeleton in order to achieve several goals with esthetic and functional implications. It is extremely important to transfer this process to the operative room (OR) by establishing precision and predictability in the position of the jaws. Many techniques have been published for intraoperative vertical repositioning of the maxilla. The most cited methods are the use of external and internal references. External reference points (ERPs)1 are currently the most accurate method described for vertical repositioning of the upper jaw.2,3 Although the use of ERP has proven to be more accurate than internal references,2,4 there is still a lack of accuracy in the 3 planes of space, especially during multidirectional movements commonly used in planning.5,6 Computer-assisted surgical simulation (CASS) has made a big contribution to orthognathic surgery, but there is another element to
be corrected that can further improve the results based on intraoperative vertical measurements. Since these measures seek to confirm the final vertical position of the maxilla, when we make such measurements, a triangulation effect is produced if the upper jaw is mobilized in the horizontal plane. Usually, the vertical measures that the software give us does not correlate with the real vertical measures we will obtain using ERPs in the OR. This is because the software calculates the vertical variations of the teeth based on a determined reference frame, which is not the same reference we use at surgery. Since our reference is a given anatomic point (ERP), the measurements that CASS gives us are perpendicular to a plane and are not equivalent to the measurements that we get in the OR. Therefore, every measurement obtained in the OR is a consequence from a triangulation effect that varies in relation to where the ERP is located, the magnitude of the movements and complexity of them as well. In practical terms, what we are measuring is the hypotenuse of a right triangle. If we decide to only make a maxillary advancement, the vertical position at the level of the teeth obviously should not vary. When this approach is put into practice at surgery, in an effort to maintain the vertical measurement in this advancement, what we are doing is positioning the maxilla (at the incisors level) in a more superior position. The explanation for this phenomenon is that our measurement is the distance between the ERP and the tooth (which is represented by the hypotenuse of a right triangle) and not a perpendicular distance from the tooth and a determined reference plane (what CASS give us) is the difference in the movement expressed in coordinates in each axis. If we want to maintain the level of the teeth, this distance (tooth-ERP) must increase in length at the incisors since this point is moving away from the ERP (Fig. 1). What usually happens is that we maintain the distance record achieved before the maxillary mobilization leaving the incisors in an upper position. To solve this problem, the author has developed a simple technique that calculates the goal distance from an external reference system (ERS). The technique entails creating—in the planning software—the same reference system one will use at surgery. In this virtual system, one measures the difference between the baseline and target distances, and then apply them at surgery.
METHOD From the Department of Oral and Maxillofacial Surgery, Hospital So´tero del Rı´o, Santiago, Chile. Received July 1, 2017. Accepted for publication August 30, 2017. Address correspondence and reprint requests to Dr Sebastia´n Espinosa, DDS, OMS, Hospital So´tero del Rı´o, Av Concha y Toro 3459, Puente Alto, Santiago, Chile 8207257; E-mail: [email protected] The author reports no conflicts of interest. Copyright # 2017 by Mutaz B. Habal, MD ISSN: 1049-2275 DOI: 10.1097/SCS.0000000000004170
The Journal of Craniofacial Surgery
The proposed method introduces corrected measurements based on the movements planned in the maxilla. The steps to achieving corrected vertical measurements through virtual orthognathic surgery are as follows: 1. Complete virtual surgical planning in the standard fashion. 2. Establish a virtual ERS. Digitize, on the computer model, the same external landmarks you will use at surgery—to establish the vertical position of the maxilla. This is done by placing a ‘‘virtual’’ ERP in the area where the surgeon decides is suitable, having in mind to place it in a round number distance for
Volume 00, Number 00, Month 2017
1
Copyright © 2017 Mutaz B. Habal, MD. Unauthorized reproduction of this article is prohibited.
CE: A.B.; SCS-17-0973; Total nos of Pages: 3;
SCS-17-0973
The Journal of Craniofacial Surgery
Espinosa S
80 mm
Volume 00, Number 00, Month 2017
80mm
B
80,89 mm
80mm
10 mm advancement FIGURE 1. Geometric effect in the vertical measurements using an external reference point at the incisor level with 10 mm maxillary advancement. Although it is straightforward movement, the vertical measurement increased at the incisors. If the surgeon is not aware of this phenomenon, the maxilla will be fixated in an upper position in an attempt to maintain the initial measurement.
3.
4. 5.
6. 7. 8.
9.
convenience (ie, 70 mm, 80 mm, etc.). One landmark must be on the maxilla (dental points), the other on the midface (frontal midline region). For example, you may select soft-tissue nasion and the midpoint of the orthodontic arch wire (located between the brackets of the central incisors). You must record the distance of the ERP to the archwire, so as to reproduce it at surgery when you locate the ERP (Fig. 2). Measure and record baseline and goal distances with your CASS software. The baseline distance is the distance between the maxillary and midfacial landmarks, when the upper jaw is in its original position. The goal distance is the distance between the same landmarks, when the upper jaw is in final alignment. The distance between each point and the ERP can be corroborated (if needed) by applying the coordinates of each point measured to an Euclidian distance formula (H (x1 x2)2þ(y1 y2)2þ(z1 z2)2) (Fig. 3). Calculate the delta for each point measured in the software. That is the difference between goal and baseline distances. Pay attention to the sign of the difference. At surgery, locate as accurately as possible the maxillary and midfacial landmarks. For more precise location in the OR of the ERP, you can make vertical measurements from the canines so as to ‘‘triangulate’’ the position of the ERP. You may avoid movement of the soft-tissue landmark by placing a K-wire or a screw through the landmark into the underlying bone. Before cutting the upper jaw, measure and record the baseline distance. Calculate the goal distance by adding or subtracting the delta (calculated in step 4) to the baseline distance. Mobilize the maxilla, articulate it against the mandible, and wire it in maxillomandibular fixation. Rotate the maxilla and the mandible, around the condylar axis, until the distance between the maxillary landmark and the midfacial landmark reach the goal distance. In this way, the planned vertical movements will be reproduced based on the corrected measurements. Fixate the maxilla in this position.
80mm
A
C
FIGURE 2. Virtual external reference point (ERP) position. (A) Virtual ERP located in the frontal area. Note that it is located considering the soft tissue width. (B) Measurement without soft tissues in a round number. (C) Locating the ERP in the midline.
decrease or increase the fullness in the paranasal areas), the final position of the anterior nasal spine and the upper incisor exposure. All these errors are conditioned to the magnitude of the planned position of the maxilla. The traditional methodology has several limitations to avoid these errors. Projections are set in a 2-dimensional image, so is not possible to record the variations on each side of the maxilla. As well, when performing the measurements in the model block, there is no an anatomic reference point to achieve the vertical distances. What it does, is to take a certain horizontal reference plane, which does not reproduce the effect of triangulation using an ERP that is used in surgery. Computer-assisted surgical simulation reduces error margins, but they do not disappear. Stokbro et al7 found errors in the vertical position up to 0.75 mm not specifying whether a higher level error occurred in molars or incisors (they expressed an average of 3 dental points). There was a tendency to a lower position of the maxilla compared to what it was planned (they used the medial canthal region as ERP). Differences in pitch showed statistical significance, with a slightly greater decrease in the maxillary occlusal plane than CASS Surgery Placement of virtual ERP Obtain Coordinates for ERP Measure the distance between the virtual ERP and every point considered. Then calculate the difference between the baseline maxillary position and its final position.
Obtain coordinates for Baseline and Goal maxillary points
Complementary Measurements
To corroborate the distance measurements, calculate the distance from ERP coordinates and maxillary points coordinates through Euclidian formula:
( (x1-x2)2 + (y1-y2)2 + (z1-z2)2)
DISCUSSION The lack of precision in the final position of the maxilla determines several implications. An unplanned counterclockwise or clockwise rotation due to lack of vertical accuracy in the position of the incisors and/or molars could generate changes in the inclination of the planned occlusal plane, with the consecutive increase or decrease in the projection of the mandible. The same effect also generates a variation in the LeFort I osteotomy step (which can
2
Calculate Delta between baseline and goal distances obtained for every point selected
Apply the corrected vertical measurements at surgery
FIGURE 3. Algorithm proposed for corrected vertical measurements using a virtual external reference point.
#
2017 Mutaz B. Habal, MD
Copyright © 2017 Mutaz B. Habal, MD. Unauthorized reproduction of this article is prohibited.
CE: A.B.; SCS-17-0973; Total nos of Pages: 3;
SCS-17-0973
The Journal of Craniofacial Surgery
Volume 00, Number 00, Month 2017
the planned. They described a ‘‘decrease in the occlusal plane angulation’’ as a positive pitch which meant an upward movement of the central incisors. Xia et al8 described an average difference of 0.44 mm in the vertical level, measured at the midline between the preoperative and postoperative measurements (range 1.98, 0.47). In addition, they described a difference in 1 degree on the pitch of the maxilla. Kwon et al9 compared the accuracy between virtual model surgery and traditional model surgery (using a model block). They reported that in traditional model surgery, there was an 18.8% of the patients with more than 2 mm of discrepancy in the final results. Moreover, in the virtual surgery group, the same margin of error was observed in a 7% of the patients. This new technical proposal is to establish a customization of the ERP so as to accurately record the vertical distances in upper jaw fixation. It is evident that planned changes in vertical maxillary position change the goal distance of an ERS. This span, however, is also influenced by the size of the horizontal maxillary movement, the relative horizontal position between the ERS and the tooth landmarks, and the vertical distance between ERS and the landmarks used. It has to be considered that many times we make transversal and cant corrections in the upper jaw that may change even more the vertical measurements. Since we precisely determine the position of the ERP, we have no alterations in the sagittal or vertical position of the latter, and thus, changes in the measures taken in the computer will be reproduced in the patient. The author believes that with this simple method we strive for near perfect outcomes and gives us a tool to get closer.
#
2017 Mutaz B. Habal, MD
Measurements in Orthognathic Surgery
ACKNOWLEDGMENT The author would like to thank Dr Jaime Gateno for his help in developing this manuscript.
REFERENCES 1. Johnson DG. Intraoperative measurement of maxillary repositioning: an ancillary technique. Oral Surg Oral Med Oral Pathol 1985;60:266–268 2. Polido WD, Ellis E, Sinn DP. An assessment of the predictability of the maxillary surgery. J Oral Maxillofac Surg 1990;48:697–701 3. Polido WD, Ellis E, Sinn DP. An assessment of the predictability of the maxillary repositioning. Int J Oral Maxillofac Surg 1992;20:349–352 4. Van Sickels JK, Larsen AJ, Triplett RG. Predictability of maxillary surgery: a comparison of internal and external reference marks. Oral Surg 1986;61:542–545 5. Bryan DC, Hunt NP. Surgical accuracy in orthognathic surgery. Br J Oral Maxillofac Surg 1993;31:343–349 6. Ellis E. Bimaxillary surgery using an intermediate splint to position the maxilla. J Oral Maxillofac Surg 1999;57:53–56 7. Stokbro K, Aagaard E, Torkov P, et al. Surgical accuracy of threedimensional virtual planning: a pilot study of bimaxillary orthognathic procedures including maxillary segmentation. Int J Oral Maxillofac Surg 2016;45:8–18 8. Xia JJ, Gateno J, Teichgraeber JF, et al. Accuracy of the computer-aided surgical simulation (CASS) system in the treatment of patients with complex craniomaxillofacial deformity: a pilot study. J Oral Maxillofac Surg 2007;65:248–254 9. Kwon TG, Choi JW, Kyung HM, et al. Accuracy of maxillary repositioning in two-jaw surgery with conventional articulator model surgery versus virtual model surgery. Int J Oral Maxillofac Surg 2014;43:732–738
3
Copyright © 2017 Mutaz B. Habal, MD. Unauthorized reproduction of this article is prohibited.
