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Title

Model surgery technique for Le Fort I osteotomy--

alteration in occlusal plane associated with upward

transposition of posterior maxilla

Author(s)

Yosano, A; Yamamoto, M; Shouno, T; Shiiki, S;

Hamase, M; Kasahara, K; Takaki, T; Takano, N;

Uchiyama, T; Shibahara, T

Journal Bulletin of Tokyo Dental College, 46(3): 67-78

URL http://hdl.handle.net/10130/240

Right

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Clinical Report

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Bull Tokyo Dent Coll (2005) 46 (3): 67–78

Model Surgery Technique for Le Fort I Osteotomy—Alteration in Occlusal Plane Associated with UpwardTransposition of Posterior Maxilla—

Akira Yosano, Masae Yamamoto, Takahiro Shouno,Sayaka Shiiki, Maki Hamase, Kiyohiro Kasahara, Takashi Takaki,Nobuo Takano, Takeshi Uchiyama and Takahiko Shibahara

Department of Oral and Maxillofacial Surgery, Tokyo Dental College,1-2-2 Masago, Mihama-ku, Chiba 261-8502, Japan

Received 15 July, 2005/Accepted for Publication 5 October, 2005

Abstract

It is difficult to translate analytical values into accurate model surgery by traditionalmethods, especially when moving the posterior maxilla. This is because cephalometricradiographic analysis generated information on movement of the posterior nasal spine(PNS) can not be recreated in model surgery.

Therefore, we propose a method that accurately reflects such analysis and simula-tion of movement using Quick Ceph® 2000 (Orthodontic Processing Corporation, USA).This will allow the enrichment of model surgery prior to actual surgery in cases whereupward movement of the posterior maxilla is involved.

All patients who participated in this study had skeletal mandibular prognathismcharacterized by a small occlusal plane angle in respect to the S-N plane. Cephalometricradiographs were taken and analyzed with the Quick Ceph® 2000. Pre- and post-surgicalevaluations were performed using Sassouni arc analysis and Ricketts analysis. Prior totransposition, we then prepared an anterior occlusal bite record on a model mounted onan articulator. This bite was then used as a reference when the molar parts were to betransposed upwards.

The use of a occlusal bite permitted an accurate translation of the preoperativecomputer simulation into model surgery, thus facilitating favorable surgical results.

Key words: Occlusal alteration—Model surgery—Bimaxillary surgery—Computer simulation—Occlusal bite record

Introduction

In orthognathic surgery, performing anoperation on the mandible alone does notallow satisfactory occlusal position of the max-illa and mandible. If there is an abnormalityin the inclination of the maxillary occlusal

plane, it is difficult to achieve stability of func-tional occlusion. The necessity of achieving aharmony of functional and esthetic aspects insuch cases requires bimaxillary surgery, as thisallows abnormal inclination of the maxillaryocclusal plane to be reformed and occlusionto be reconstructed4,5,8). For such complicated

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transposition of the maxilla, it is essential toestablish a plan of pre-surgery by modeling theprocedure in advance with a two-dimensionalrecreation of the movement by paper surgeryor a computer simulation. However, even whenpreoperative planning has been performedwith the greatest accuracy, any discrepancybetween the plan and the bite splint or basedon model surgery will lead to inaccuracies inactual surgery. It is consequently of criticalimportance that model surgery should bebased on an accurate translation of maxillarytransposition data from the analysis stage tothe model surgery stage. It is difficult, how-ever, to translate analytical values into accu-rate model surgery by traditional methods,especially when movement of the posteriormaxilla is involved. This is because cephalo-metric radiographic analysis generated infor-mation on movement on the posterior nasalspine (PNS) can not be recreated in modelsurgery. This is because it is impossible toreproduce transpositional information froma PNS cephalographic analysis into modelsurgery.

Therefore, we propose a method that accu-rately reflects such analysis and simulation ofmovement using Quick Ceph® 2000 (Ortho-dontic Processing Corporation, USA). Thiswill allow the enrichment of model surgeryprior to actual surgery in cases where upwardmovement of the posterior maxilla is involved.

Materials and Methods

1. PatientsThe patients who participated in this study

had skeletal mandibular prognathism charac-terized by a small angle of occlusal plane tothe S-N plane. They required bimaxillary sur-gery for alteration of the occlusal plane byupward movement of the molar part of themaxilla.

2. Methods1) Cephalometric analysis and interpretation

An operative plan for orthognathic surgerywas established by using frontal and lateral

cephalometric radiographs taken after pre-operative orthodontic procedure. To inputmeasurements and analyze the data obtainedfrom the cephalometric radiograph, we usedthe Quick Cepth® 2000. For pre- and post-operative evaluations, a Sassouni arc analysisand Ricketts analysis were used9,10) (Fig. 1A, B).Based on the results of the analysis, a simula-tion of maxillary and mandibular movementwas performed to determine the amountof movement required by using the QuickCeph® 2000 (The amount of the movementof the posterior maxilla was determined byestimating from the movement distance ofthe first molars with the Quick Ceph® 2000,too.)(Fig. 2). On performing maxillary trans-position simulation with the Quick Ceph®

2000, we rotated the occlusal plane clockwise,

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Fig. 1 Cephalometric analysisA: Sassouni arc analysisB: Ricketts analysis

69Model Surgery for Occlusal Plane Alteration

with the maxillary incisor as the center. Onestudy reports that “the extension line of theocclusal plane in subjects with normal occlu-sion passes through a fourth of the lengthof the dens from the center at the base ofthe dens”1). Based on these observations, werotated the occlusal plane clockwise, with themaxillary incisor tip or the anterior nasalspine (ANS) as the center.2) Measurement points and items

We used a total of 48 points of measure-ment in this study. These included the Corpusright, the topmost end-point of the dens, andthe basal center of the dental process, in addi-tion to the measurement points requiredfrom the Sassouni arc analysis of the profile.For the cephalometric porion, the anatomicalporion was used (Fig. 3).3) Model preparation and mount

After pre-surgical orthodontic surgery,impressions of the upper and lower teethwere taken and working models of each weremade with plaster. The height of the base ofeach of the working models was then deter-

lower arch: right left change

ALDincisors1st molarextractionexpansionstrippingE-space

Net change

mined in the following manner: to determinethe anterior base height of the maxillarymodel, the distance from the tip of the maxil-lary incisor to the ANS as determined by x-raycephalometry was measured using a lateralcephalometric radiograph. The anterior baseheight was then brought into alignment withthis distance from ANS to the incisor tip. Theposterior base height of the maxillary modelwas determined by using the frontal cephalo-metric radiograph and determining the dis-tance from the buccal cusp of the first maxil-lary molar on the left and right or the buccalbracket on the x-ray film to the zygomatico-maxillary suture (MX). The base height ofeach side of the model was then brought intoalignment with these distances. After deter-mining the height, this was then aligned withthe plane formed by the ANS and the left andright MX. The base surface of the maxillarymodel was then trimmed and flattenedaccordingly. Next, to determine the antero-posterior distance of the base of the maxillarymodel, we measured the horizontal distance

changes: X Y Rot

mx at ANS 1.6 �0.4 �3.2mx at A 1.2 �0.7mx at 1 crownmx at PNS 1.8 �3.4 �3.5mx at 6 crown 0.5 �2.5md ost. �5.6 �3.4 �1.5genioplasty �0.2 �0.2md at 1 crown �5.1 �2.3

Fig. 2 Repositioning simulationQuick Ceph® 2000 simulation of maxillary and mandibular movement to determine amount of movement.mx: maxilla, md: mandible

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means of paraffin wax (Fig. 5A�D). To mountthe maxillo-mandibular model, we woundpolivinyl tape around the base so that the seg-ment for the base of the model and the baseof the mounting cast ran flush against eachother. Baseline was applied to the base surfaceas a separating agent to facilitate separation ofthe base of the models and the base of themounting cast. Furthermore, an incisal guidepin was placed in position in alignment with 0line prior to mounting.4) Transposition of the model

After the model was mounted onto thearticulator, baselines were drawn on the baseof the maxillo-mandibular model and on thebase of the mounting cast. At least fourbaselines were drawn on both the maxilla andthe mandible, namely, the front, rear, left, andright baselines. Anteriorly, a baseline (line Aand A�) was drawn perpendicular to the basesurface in the median at the front of the max-illary and mandibular alignment of the teeth.At the left and right sides, baselines (lines B,B� and C, C�) were drawn perpendicularly tothe horizontal FH plane in the distal positionof the bracket of the first molars. Posteriorly,a baseline (line D and D�) was drawn perpen-dicular to the base surface in the median atthe dental arch. These baselines were drawnby marking with a saw, and used for measur-ing amount of movement (Fig. 6A�D).

After the baselines were drawn, the occlu-sion of the maxillary and mandibular frontteeth (the distance from at least one canine tothe other canine of the maxilla has to bemarked off) before movement was obtainedon the model to prepare the bite of the frontteeth (referred to as “Occlusal Alteration Bite(OA bite)” below). Such OA bites are bestmade from materials that show little deforma-tion while being sufficiently flexible. In thisstudy, we used an EXTRA EXAFINE PUTTYTYPE® (GC Corp.). The top surface of theOA bite (i.e., the side on which the maxillarydentition has been marked off) should be asthin and flat as possible to the extent that thecutting margin and heads of the front teethare recorded (Fig. 7A�C).

After obtaining the bite, the base of the

Fig. 3 Cephalometric landmarksTotal points: 48. 1. Sella, 2. Porion, 3. Basion, 4. HingeAxis, 5. Pterygoid, 6. Nasion, 7. Orbitale, 8. ANS, 9. Apoint, 10. PNS, 11. B point, 12. PM, 13. Pogonion 14.Menton, 15. Corpus Left, 16. Ramus down, 17. Articulale,18. R3, 19. R1, 20. mx1 crown, 21. mx1 root, 22. md1crown, 23. md1 root, 24. mx4 crown, 25. mx6 crown, 26.mx6 root, 27. md6 crown, 28. md6 root, 29. Sella Poste-rior, 30. Sella Inferior, 31. Clinoidale, 32. Clibliform, 33.Temporale, 34. Floor of the orbitale, 35. Roof of theorbitale, 36. Supraorbitale, 37. Corpus right, 38. HyoidBone top, 39. Hyoid Bone prominent, 40. Hyoid Bonebottom, 41. CV2apex, 42. CV2tg, 43. CV2ip, 44. CV2base,45. CV2ia, 46. Dens Axis base, 47. CV3ip, 48. CV4ip

between the maxillary incisor and the ANSbased on the lateral cephalometric radio-graph. For the left-right distance of the baseof the model we measured from the mid-sagittal reference plane (MSR) to the left andright MX based on the posterior-anteriorcephalometric radiograph (Fig. 4A�D). Wereferenced a study by Motohashi et al. forselective of anatomical points (i.e. MX) formodel preparation7). The height of the baseof the mandibular model was trimmed andflattened so that the base was parallel with theocclusal plane. The sides of the base of themandible were then trimmed so that theywere perpendicular to the base surface.

The maxillary model was mounted on anarticulator by performing face-bow transferas reported in the literature and achievingocclusion in the mandibular rest position by

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maxillary model and the base of the mount-ing cast were separated and the maxillarymodel displaced. Movement of the maxillarymodel was performed to reproduce the move-ment simulated previously with the QuickCeph® 2000. First, the maxillary molar partwas moved in the upward direction. Themovement of the posterior part of the maxilla(i.e., the upward movement of the PNS) wasdetermined by estimating the movement dis-tance of the first molars on either side of themaxilla. This was because the PNS can not bereproduced on a model, and the movementdistance of the PNS can not be measuredin an actual operation. Thus, the computer-calculated distance of movement of the firstmaxillary molars was marked on the base ofthe mounting cast, and the base of the mount-

ing cast was then trimmed to this height inconjunction with the movement of the firstmaxillary molars (The base of the maxillarymodel must not be trimmed). This operationhad to be performed in such a manner thatthe height of the front part (i.e., ANS part)did not change. The base of the mountingcast was imparted with a cant from the front tothe rear. After this, the posterior part of themaxillary model was moved upwards to bringthe base of the model into close contact withthe base of the mounting cast. To do this, weused the OA bite of the front teeth obtainedprior to movement. First, the OA bite wasmade to fit on the mandible, and then themaxillary front teeth were made to fit with theOA bite. The maxillary front teeth of the OAbite served as the fulcrum or support point

Fig. 4 Length of model basea is vertical distance and b is horizontal distance from ANS to the tip of upperincisor. c and d are vertical distance from first molar of maxilla to MX. e and fare horizontal distance between MSR and MX. Length a�a�, b�b�, c�c�,d�d�, e�e� and f�f�.

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D

A

B

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Fig. 5 Mount of modelA, B: The maxillary model is mounted by performing face-bow transfer.C: Wax bite record taken in mandibular rest position.D: The mandibular model is mounted by using paraffin wax bite.

Fig. 6 Baselines on castLines A and A� are drawn in median at front of maxillary and mandibular alignment of teeth.Lines B, B� and C, C� are drawn to horizontal surface FH in distal position of the bracket offirst molars. Lines D and D� are drawn posteriorly in median at dental arch.

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(i.e., the center of rotation) for when themaxillary molars were raised upward (Fig.8A�C). Since the maxillary incisors served asthe center of rotation in this, the position ofthe ANS protruded forward. Baselines B andC moved forward in a similar manner as aresult of the rotational movement. While thiswas being done, the position through whichthe baselines of the maxillary molar parts onthe base of the model moved (i.e., baselines Eand F) were recorded on the base of the

mounting cast. In this condition, the positionof the maxillary incisors showed no change inthe anterior-posterior or left-right directions(Fig. 9A�D). When there was not only move-ment in the perpendicular direction but alsomovement in the anterior-posterior direction,in other words, when anterior-posterior move-ment was required at the incisor tip position,the maxillary model had to be moved in theforward direction. This movement must bedone keeping the separate faces of the canted

Fig. 7 The material and method for makingocclusal alteration bite

A: EXAFINE PUTTY TYPE® used to make bite.B, C: Occlusion of maxillary and mandibular front teeth

is obtained on model. Area from at least onecanine other canine of maxilla is marked off.(B: Occlusal view, C: Saggital view)

Fig. 8 Occlusal alterationPosterior part of maxillary model is moved upwards tobring model base into close contact with mounting baseby using OA bite. At same time, maxillary front teeth ofOA bite serve as center of rotation. Amount of movementis computer-calculated movement distance of first maxil-lary molars.

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base of the mounting cast and the separatefaces of the maxillary model in contact.To ensure accurate anterior-posterior move-ment, the movement distance estimated frombaselines E and F was measured and the posi-tion recorded (lines G and H) before move-ment (Fig. 10). Next, the baseline on the base

of the model’s molar part was moved to thisposition. In order to prevent movement tothe left or right, it was necessary here to checkthat the baseline on the base of the model inthe median at the front teeth was in registerwith the baseline on the base of the mountingcast. After movement, the arrangement wasprovisionally fixed, and the OA bite was usedagain for a final check. The amount of move-ment estimated from the position of theincised mark of the maxillary incisor tip wasthen inscribed as a line on the top surface ofthe OA bite. Next, the maxillo-mandibularmodel was made to bite on the OA bite inter-vened. Accurate movement was achieved bychecking that the line marked off on theOA bite matched the central incisor tip ofthe maxillary model (Fig. 11A�C). After themodel was moved to the appropriate position,the model was then fixed on the base of themounting cast. Instantaneous adhesive and/or wax were used for fixing.

After movement of the maxillary model, afirst (intermediate) splint was made. Follow-

Fig. 9 Baseline after occlusal alterationLines E and F are recorded on mounting base when lines B and C moved after occlusal alteration. In thiscondition, position of maxillary incisors does not change in anterior-posterior or left-right directions.

Fig. 10 Technique for movement in anterior-posterior direction 1

Line G (and H) is position determined by measuring theamount of anterior-posterior movement from baseline E(and F). This distance was determined by computedsimulation.

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Fig. 11 Technique for movement in anterior-posterior direction 2

A: Amount of movement from upper incisor tip toplanned position is recorded on OA bite. When wedecided the planned position line, the vertical line atthe midline of upper incisor was used.

B, C: To check accuracy of movement, we must checkline marked off on OA bite matches upper incisoredge of maxillary model already moved in anterior-posterior direction.

Fig. 12 Surgical techniquePerpendicular line is drawn across osteotomy line at left-right maxillary first molar parts and the margin of leftand right piriform openings intraoperatively. We usedthese lines to accurately measure amounts of vertical andhorizontal movement of maxilla. Furthermore, moreaccurate surgery is not possible with stepping osteotomy.

ing this, the mandibular model was movedand fixed in the position previously deter-mined by the orthodontist as the position pro-viding stable occlusion with the maxillarymodel. When we received the maxillary andmandibular models from the orthodontist wehad the orthodontist mark off the final occlu-sion position from the lingual side of themaxillo-mandibular model with the bite of

EXAFINE PUTTY TYPE®. After movement ofthe mandibular model, the second (final)splint was made.5) Surgical procedure

Amount of movement was ultimately deter-mined and the prepared bite splint was usedto perform actual surgical procedure basedon the model operation method describedabove. In addition, a perpendicular line wasdrawn intraoperatively across the osteotomyline with respect to the left-right maxillaryfirst molar parts; also, perpendicular lineswere drawn in the same manner on the mar-gin of the left and right piriform openings.The length of these perpendicular lines wasmeasured before separation, and with this theamounts of vertical and horizontal movementof maxilla were measured. Certain devicessuch as the provision of steps in the design ofthe separating line may also be useful to someextent in permitting accurate measurementof the amount of movement during an opera-tion. This would make the transition fromanalysis to model operation and from there toactual surgery more accurate, leading to moresatisfactory postoperative results (Fig. 12).

Results

The use of an OA bite permitted accurate

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inscription of baselines by suitably devisedmethods. Most new methods, however, aresubstantially the same as the classic methods,and when a model operation is performed bya classic method, there is the possibility oferrors occurring in various areas. The areasmost prone to error are the perpendicularposition and horizontal position of the maxil-lary molar part. Perhaps the most commoninaccuracy in performing maxillary modelsurgery in the cases of bimaxillary surgery is inthe mediolateral positioning of the posteriormaxilla. The perpendicular positioning ofthe maxilla is made difficult by the action ofgravity. The horizontal positioning of themaxillary molar part presents difficulties, inthat horizontal rotation toward the center caneasily occur, even when the median of themaxilla is aligned3) (Fig. 13). If the maxilla isskewed to one side to correct the posteriorarea and occlusion, the mandible will alsobe skewed in the same direction. This is themost important factor in a model operation.Therefore, in order to achieve greater accu-racy in the perpendicular and horizontalpositioning of the maxillary molar part, wehave made some modifications to the classicmodel operation method. By inscribing thefront teeth on the bite, it is possible to obtainperpendicular movement of the maxillarymolars, rotating the maxilla with the edges ofthe upper incisors as the pivotal center, and

modeling of the operation as the directionand amount of movement could be trans-posed from the preoperative computer simu-lation to model surgery. By using the bitesplint prepared from this during actual sur-gery, it was possible to reproduce a movementplan in an accurate manner. As a result, it waspossible to achieve not only satisfactory func-tional occlusion but also an esthetically favor-able outcome. Alteration in occlusal plane byrotation of the maxillo-mandibular complexcaused the point of the chin to move back-ward and downward in relation to the lowerincisor tips. Therefore, the postoperative pro-file view revealed the establishment of a betterharmony between the chin, lips, cheeks andnose than in the case of operation on themandibule alone. The results have revealedstable in all patients more than 12 monthsfollowing sargery.

Discussion

Surgery to correct deformities of the jawbegins with diagnostic procedure, whichinvolves performing cephalometric and softtissue analysis. After establishing a plan ofsurgery and after pre-surgical orthodonticcorrection, surgery is performed. For success-ful orthognathic correction to be achieved,operative accuracy is critical in the course ofthe above procedure. This procedure involvessimulation of movement based on the analysisof cephalometric radiographs. Although suchsimulations will determine the amount ofmovement required, the accuracy of the move-ment by the estimated amount will depend, toa large extent, on the experience of the sur-geon in taking measurements during theactual operation2,6). This often presents signifi-cant difficulties. For this reason, it is impor-tant to conduct a model operation prior toactual surgery. Errors in model operationswill have a direct effect on surgical outcome,and therefore it is important to ensure thegreatest possible accuracy in model surgerywhen making an actual splint. There are vari-ous approaches to model surgery such as the

Fig. 13 Horizontal rotation of maxillaRotation to one side or other of posterior maxillacan easily occur, while maxillary dental midlinesare coincident with facial midline.

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without that center itself undergoing any shiftin position. In this manner it is also possible toprevent displacement in the horizontal direc-tion. Even when it is necessary to move thefront dentition in the anterior-posterior direc-tion, precision can be achieved by checkingagainst the baseline at the center of the frontteeth using the marking on the OA bite.

On the posterior-anterior cephalometricradiograph, the occlusal plane connectingthe first molars on the left and right of themaxilla was skewed, and our method can alsobe used for patients with this kind of maxillaryasymmetry. This type of deformity arises fromthe perpendicular positions of the molarparts on either side of the maxilla being dif-ferent. In such cases it is necessary to movethe molar parts upwards, and the first step inachieving this is to correct the perpendicularpositioning of the maxillary molar parts onboth sides. In this manner, the upward ordownward movement of the molar part onone side brings it in alignment with the heightof the molar part on the opposite side. Thismust be accomplished in such a manner thatthe other parts will not move in the anterior-posterior or horizontal directions and thatthe ANS will not move in the perpendiculardirection. Provisional fixation is made whenthe skew of the maxillary occlusal planeappears to be improved in the frontal viewof the face. In our method, after improvingmaxillary asymmetry, the upper incisors areinscribed in the OA bite (Fig. 14A�C). Then,the OA bite is used to achieve upward move-ment of the maxillary molar parts and,if necessary, anterior-posterior movementalso. Since the molars on one side have beenmoved perpendicularly in order to correctthe asymmetry of the maxilla, however, it isnecessary to subtract this amount of move-ment from the upward movement of the max-illary molar parts, and this will be planned foron the basis of the analysis.

To ensure accuracy in actual surgery, pre-cise modeling of operations is vital. Suchmodeling can address the difficulties thatarise from the three-dimensional positioningthat is required by actual surgery. However,

inaccuracies in modeling can lead to inaccu-rate maxillary-mandibular positioning. This isbecause of the complexity of modeling andthe impossibility of accurately translatingmeasurements derived from cephalometricimages. It is, therefore, important to be ableto simply and accurately translate the move-ments and positioning of the maxillary modelinto actual orthognathic surgery. In this study,we simulated movement using a computer. Bymaking an OA bite on the model derivedfrom this movement, and by using that OAbite, we were able to transpose the perpen-

Fig. 14 Technique in case of maxillary asymmetryUpward or downward movement of molar part on oneside brings it in alignment with height of molar part onopposite side. After maxillary asymmetry is improved,edges of upper incisors are inscribed in OA bite.

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dicular movement of the maxillary molarparts in a simple and accurate manner toachieve accurate positioning. This allowedsurgery to be performed in an easy and accu-rate manner, making it possible to obtainfavorable results. The proposed method usescephalometric radiographs and the transposi-tion of simulated two-dimensional movementin the modeling of operations. In the future,use of advanced diagnostic techniques suchas CT will provide three-dimensional simula-tion data that can be transposed to modeloperations in order to achieve even greateraccuracy.

References

1) Akimoto Y, Noma Y, Takaki T (2000) A study ofrelationship between the occlusal plane andthe dens of the axis, by lateral cephalography,regarding individual-normal-occlusion personsand patients with jaw deformity. Japanese Jour-nal of Jaw Deformity 10:80–98.

2) David AC, Larry MW (1994) Altered orthogna-thic surgical a modified approach to modelsurgery. J Oral Maxillofac Surg 52:1010–1020.

3) Edward E III (1990) Accuracy of model sur-gery: Evaluation of an old technique and in-troduction of a new one. J Oral MaxillofacSurg 48:1161–1167.

4) Johan PR, William GE (1990) Surgical mani-

pulation of the occlusal plane. The Interna-tional Journal of Adult Orthodontics andOrthognathic Surgery 5:99–110.

5) Larry MW, Peter DC, Frank H (1994) Occlusalplane alteration in orthognathic surgery—part I: Effect on function and esthetics. Ameri-can Journal of Orthodontics and DentofacialOrthopedics 106:304–316.

6) Mohammad A, Malcolm H (1990) Model sur-gery for orthognathic planning. Br J OralMaxillofac Surg 28:393–397.

7) Motohashi K, Kameda A, Kondo E (1972)Some elementary facts to be considered instudying of posteroanterior cephalogram.Journal of Japan Orthodontic Society 31:105–116.

8) Peter DC, Larry MW, Peter HB (1994)Occlusal plane alteration in orthognathic sur-gery—part II: Long-term stability of results.Am J Orthod Dentofacial Orthop 106:434–440.

9) Ricketts RM, Bench RW, Hilgers JJ, Schulhof R(1972) An overview of computerized cephalo-metrics. Am J Orthod 61:1– 28.

10) Sassouni V (1955) A roentgenographic cepha-lometric analysis of cephalo-faciodental rela-tionships. Am J Orthod 41:735–764.

Reprint requests to:Dr. Akira YosanoDepartment of Oral andMaxillofacial Surgery,Tokyo Dental College,1-2-2 Masago, Mihama-ku,Chiba 261-8502, JapanE-mail: yosano@tdc.ac.jp

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