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Skeletal response to maxillary protraction with and without maxillary expansion: A finite element study
ORIGINAL ARTICLE
Skeletal response to maxillary protraction with and without maxillary expansion: A finite element study Pawan Gautam,a Ashima Valiathan,b and Raviraj Adhikaric Manipal, Karnataka, India Introduction: The purpose of this finite element study was to evaluate biomechanically 2 treatment modalities—maxillary protraction alone and in combination with maxillary expansion—by comparing the displacement of various craniofacial structures. Methods: Two 3-dimensional analytical models were developed from sequential computed tomography scan images taken at 2.5-mm intervals of a dry young skull. AutoCAD software (2004 version, Autodesk, San Rafael, Calif) and ANSYS software (version 10, Belcan Engineering Group, Cincinnati, Ohio) were used. The model consisted of 108,799 solid 10 node 92 elements, 193,633 nodes, and 580,899 degrees of freedom. In the first model, maxillary protraction forces were simulated by applying 1 kg of anterior force 30 downward to the palatal plane. In the second model, a 4-mm midpalatal suture opening and maxillary protraction were simulated. Results: Forward displacement of the nasomaxillary complex with upward and forward rotation was observed with maxillary protraction alone. No rotational tendency was noted when protraction was carried out with 4 mm of transverse expansion. A tendency for anterior maxillary constriction after maxillary protraction was evident. The amounts of displacement in the frontal, vertical, and lateral directions with midpalatal suture opening were greater compared with no opening of the midpalatal suture. The forward and downward displacements of the nasomaxillary complex with maxillary protraction and maxillary expansion more closely approximated the natural growth direction of the maxilla. Conclusions: Displacements of craniofacial structures were more favorable for the treatment of skeletal Class III maxillary retrognathia when maxillary protraction was used with maxillary expansion. Hence, biomechanically, maxillary protraction combined with maxillary expansion appears to be a superior treatment modality for the treatment of maxillary retrognathia than maxillary protraction alone. (Am J Orthod Dentofacial Orthop 2009;135:723-8)
M
axillary protraction is recommended for skeletal Class III patients with maxillary deficiency.1,2 The principle of maxillary protraction is to apply tensile force on the circummaxillary sutures and thereby stimulate bone apposition in the suture areas. Biomechanical studies on dry skulls have demonstrated that application of an anteriorly directed force results in forward movement of the maxilla.3,4 These investigations also showed that the direction of
a Assistant professor, Department of Orthodontics and Dentofacial Orthopedics, Manipal College of Dental Sciences, Manipal, Karnataka, India. b Professor and head, Director of Post Graduate Studies, Department of Orthodontics and Dentofacial Orthopedics, Manipal College of Dental Sciences, Manipal, Karnataka, India. c Reader, Department of Mechanical Engineering, Manipal Institute of Technology, Manipal, Karnataka, India. The authors report no commercial, proprietary, or financial interest in the products or companies described in this article. Reprint requests to: Ashima Valiathan, Department of Orthodontics and Dentofacial Orthopedics, Manipal College of Dental Sciences, Manipal, Karnataka, India, 576104; e-mail, [email protected]. Submitted, March 2007; revised and accepted, June 2007. 0889-5406/$36.00 Copyright Ó 2009 by the American Association of Orthodontists. doi:10.1016/j.ajodo.2007.06.016
the force is critical in controlling rotation of the maxilla. A force generated parallel to the maxilla or above the palatal plane produces counterclockwise rotation of the palatal plane. Maxillary protraction therapy often is supplemented with maxillary expansion. Maxillary expansion is commonly needed in the treatment of patients with Class III malocclusion, because of insufficient maxillary arch width. Rapid maxillary expansion is typically used in young patients and has been shown to help in Class III correction. Midfacial orthopedic expansion has been recommended with protraction forces on the maxilla because it supposedly disrupts the circummaxillary sutural system and presumably facilitates the orthopedic effect of the facemask.5-7 There is some evidence in the literature that maxillary expansion alone can be beneficial in the treatment of certain types of Class III malocclusion, particularly borderline malocclusions.7 The purposes of this finite element study were to evaluate the displacements of various craniofacial structures with maxillary protraction therapy and compare them with the pattern of displacement with combined rapid palatal expansion and maxillary protraction. 723
724
Gautam, Valiathan, and Adhikari
American Journal of Orthodontics and Dentofacial Orthopedics June 2009
Young’s modulus and Poisson’s ratio for various materials used in this study
Table I.
Material
Young’s modulus kg/mm2
Poisson’s ratio
1.37 3 103 7.9 3 102
0.3 0.3
Compact bone Cancellous bone Data from Tanne et al.9
Fig 1. Three-dimensional finite element method skull model of a 7-year-old child.
MATERIAL AND METHODS
The details of the modeling procedure were described in a previous study.8 The analytical model was developed from sequential computed tomography scan images taken at 2.5-mm intervals of a dry young skull with dental age of 7 years. These computed tomography scan sections were traced by using AutoCAD software (2004 version, Autodesk, San Rafail, Calif). The next step was to generate geometric surfaces by joining lines together. These tracings were sequentially transferred to ANSYS software (version 10, Belcan Engineering Group, Cincinnati, Ohio). The complete geometry included an assemblage of discrete pieces called elements, connected at a finite number of points, called nodes; 10 node solid 92 elements (tetrahedron) were used for meshing. The solid 92 element has a quadratic displacement behavior, is well suited to model irregular solid geometry, and gives a better representation of the variable bone thickness that is characteristic of the craniofacial skeleton. Also, the use of solid 92 element gives better stress transmissibility and bending deformations. This tetrahedron element is defined by 10 nodes having 3 degrees of freedom at each unstrained node: 3 translations (x, y, and z). Our model consisted of 108,799 elements, 193,633 nodes, and 580,899 degrees of freedom. Hence, this model (Fig 1) is a better representation of the skull than previous models in which the sections were made at 10-mm sections.9-12 To avoid any inconsistencies associated with inaccuracy of modeling the teeth and the periodontal ligament through computed tomography, this study was restricted to the analysis of skeletal displacements.13,14 The teeth and the periodontal ligament were not modeled, and the model comprised the compact and cancellous bones of
the craniofacial skeleton. Nine craniofacial sutural systems were integrated into the model as described in the previous study.8 The mechanical properties of the compact and cancellous bones in the model were defined according to the experimental data in previous studies as shown in Table I.10 Restraints were established at all other nodes of the cranium lying on the symmetrical plane, and appropriate boundary conditions were imposed. In addition, zero-displacement and zero-rotation boundary conditions were imposed on the nodes along the foramen magnum. In the first model, 1 kg of force was directed anteriorly and 30 downward relative to the occlusal plane near the canine to simulate orthopedic maxillary protraction forces. In the second model, a known transversal (x) displacement with a magnitude of 2 mm was applied on the surface nodes of the intermaxillary suture in the first molar region to simulate the initial phase of maxillary expansion before maxillary protraction therapy. It was assumed that the 2 plates of the transversal orthopedic appliance moved apart by a total distance of 4 mm. After this, maxillary protraction forces were simulated by applying a 1-kg force directed anteriorly and 30 downward relative to the occlusal plane near the canine.
RESULTS
With maxillary protraction alone, Point A moved anteriorly and inferiorly by 0.33 and 0.056 mm, respectively. The inferior movement of the posterior nasal spine (PNS) was 0.20 mm, which was more than that of anterior nasal spine (ANS), indicating a slight tendency for upward rotation even with 30 of downward pull (Fig 2). Prosthion (or supradentale) moved anteriorly and inferiorly by 0.34 and 0.045 mm, respectively. With maxillary protraction alone, the total vector displacements of the medial and lateral pterygoid plates were 0.3 to 0.45 mm; the displacements of other areas of nasomaxillary region were 0.25 to 0.4 mm. Lateral bending of the medial and lateral pterygoid plates were evident with maxillary protraction (Table II). In response to maxillary protraction with maxillary expansion, Point A moved anteriorly and inferiorly by
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American Journal of Orthodontics and Dentofacial Orthopedics Volume 135, Number 6
Table II. Displacement of the craniofacial structures with maxillary protraction alone (mm) x
Fig 2. Maxillary protraction alone, causing counterclockwise rotation of the nasomaxillary complex.
0.15 and 0.68 mm, respectively. ANS moved anteriorly and inferiorly by 0.12 and 0.69 mm, respectively. The inferior movement of PNS was 0.57 mm (less than that of ANS), indicating downward and forward translation of the maxilla in response to maxillary protraction with maxillary expansion (Fig 3). Prosthion (or supradentale) moved anteriorly and inferiorly by 0.14 and 0.53 mm, respectively (Table III). Maxillary expansion resulted in a wedge-shaped opening in both the anteroposterior and superoinferior planes (Fig 4). Maximum displacement in response to maxillary protraction with maxillary expansion was observed in the nasomaxillary region followed by the body of the zygomatic bone. The overall displacements of the pterygoid plates were considerably less than the displacement of the zygomatic bone in maxillary protraction with maxillary expansion. This is different from the pattern of displacement with maxillary protraction alone in which the overall displacement of the pterygoid region was more than that of the zygomatic bone. The nasal cavity wall, the nasal bone, and the zygomatic bone were displaced medially, anteriorly, and inferiorly with maxillary protraction alone. Similarly, the zygomatic arch also was displaced in the medial, anterior, and inferior directions. With maxillary protraction alone, the orbital part of the greater wing of the sphenoid was displaced in the lateral direction, whereas the orbital part of the lesser wing of the sphenoid was displaced in the medial direction. The sphenoid bone as a whole was displaced in the anterior and inferior directions. With maxillary protraction with expansion, the zygomatic bone and the zygomatic process of the temporal bone were displaced laterally, posteriorly, and superiorly. The nasal cavity wall was displaced laterally,
Maxilla Point A ANS Supradentale Tuberosity Zygomatic buttress Inferior orbital rim Frontal process PNS Sphenoid bone medial pterygoid Inferior Superior Lateral pterygoid Inferior Superior Nasal cavity wall Lateral Inferior Superior Nasal bone Zygomatic bone Frontal Temporal Maxillary Body Frontal bone Zygomatic process Superior orbital ridge Temporal bone Zygomatic process Sphenoid bone Greater wing (orbital) Lesser wing (orbital)
y
0.45 3 10 0.43 3 10 0.23 3 10 0.78 3 10 0.11 3 10 0.86 3 10 0.38 3 10 0.27 3 10
7
0.14 3 10 0.10 3 10
4
0.80 3 10 0.12 3 10
5
0.77 3 10 0.43 3 10 0.45 3 10 0.37 3 10
5
0.14 3 10 0.12 3 10 0.26 3 10 0.26 3 10
5
0.24 3 10 0.40 3 10
7
0.64 3 10
z
0.33 3 10 0.30 3 10 0.34 3 10 0.32 3 10 0.36 3 10 0.25 3 10 0.20 3 10 0.33 3 10
3
0.32 3 10 0.32 3 10
3
0.30 3 10 0.32 3 10
3
0.28 3 10 0.30 3 10 0.23 3 10 0.20 3 10
3
0.20 3 10 0.19 3 10 0.29 3 10 0.28 3 10
3
0.19 3 10 0.15 3 10
3
4
0.19 3 10
0.59 3 10
5
0.53 3 10
6
7 5 5 4 6 6 7
4
4
7 7 5
3 5 5
5
0.56 3 10 0.68 3 10 0.45 3 10 0.22 3 10 0.17 3 10 0.18 3 10 0.21 3 10 0.20 3 10
4
0.25 3 10 0.23 3 10
3
0.38 3 10 0.26 3 10
3
0.86 3 10 0.67 3 10 0.48 3 10 0.65 3 10
4
0.13 3 10 0.20 3 10 0.13 3 10 0.15 3 10
3
0.21 3 10 0.55 3 10
3
3
0.16 3 10
3
0.19 3 10
3
0.20 3 10
3
0.19 3 10
3
0.22 3 10
3
3 3 3 3 3 3 3
3
4
3 3 3
3 3 3
3
4 4 3 3 3 3 3
3
3
4 4 4
3 3 3
4
whereas the nasal bone moved medially with maxillary protraction with expansion. The orbital part of the greater wing of the sphenoid was displaced laterally, posteriorly, and superiorly, whereas the orbital part of the lesser wing of the sphenoid was displaced laterally, anteriorly, and inferiorly. DISCUSSION
Several studies noted counterclockwise rotation of the maxilla with protraction headgear treatment.3,15,16 To minimize the counterclockwise rotation produced by the protraction forces, investigators changed the point of force application and the direction of the protraction forces. Some investigators applied the force from the canine region.17 Spolyar18 applied the force
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American Journal of Orthodontics and Dentofacial Orthopedics June 2009
Table III. Displacement of craniofacial structures with maxillary protraction with maxillary expansion (mm) x
Fig 3. Maxillary protraction with maxillary expansion (lateral view), causing the nasomaxillary complex to translate anteroinferiorly, approximating its growth direction.
at the premolar or the deciduous molar region. Other investigators moved the point of force application distal to the lateral incisors, and some changed the direction of force at an angle of 15 to 30 from the occlusal plane.19,20 A 1-kg force applied 30 downward to the palatal plane induced forward displacement of the nasomaxillary complex with upward and forward rotation. This is in contrast to the study by Tanne et al,10 who showed that the nasomaxillary complex repositioned in an almost translatory manner with a slight rotation in loading with a 30 downward force. Keles et al21 observed that the maxilla advanced forward with a counterclockwise rotation with 30 downward maxillary protraction. The counterclockwise rotational tendency of the maxilla was why maxillary protraction therapy in Class III patients with maxillary deficiency and open bite was contraindicated.22,23 A 1-kg force applied 30 downward to the palatal plane along with 4 mm of transverse expansion induced forward displacement of the nasomaxillary complex with no rotational tendency. This agrees with the findings of Yu et al,24 who demonstrated that the amounts of displacement and deformation when the midpalatal suture was opened showed decreases in upward-forward rotation of the maxilla and the zygomatic arch. This is a more favorable displacement pattern in patients with open bite or vertical growers. Hence, a combination of maxillary protraction with rapid maxillary expansion can be used in Class III maxillary retrognathic patients with open bite without the adverse effect of increasing lower anterior facial height.25 Contrary to this, Williams
Maxilla Point A 0.97 ANS 0.75 Supradentale 1.09 Tuberosity 0.61 Zygomatic buttress 0.79 Inferior orbital rim 0.20 Frontal process 0.12 3 10 PNS 0.67 Sphenoid bone medial pterygoid Inferior 0.55 Superior 0.67 Inferior 0.46 Superior 0.48 Nasal cavity wall Lateral 0.54 Inferior 0.75 Superior 0.89 3 10 Nasal bone 0.52 3 10 Zygomatic bone Frontal 0.19 Temporal 0.44 Maxillary 0.51 Body 0.49 Frontal bone Zygomatic 0.55 3 10 process Superior orbital 0.51 3 10 ridge Temporal bone Zygomatic 0.18 process Sphenoid bone Greater wing 0.40 3 10 (orbital) Lesser wing 0.29 3 10 (orbital)
y
1
0.15 0.12 0.14 0.29 3 10 0.10 0.54 3 10 0.11 0.16
0.36 3 10 0.37 3 10 0.27 3 10 0.37 3 10
5 2
0.66 3 10 0.12 0.13 3 10 0.87 3 10 0.17 0.11 0.53 3 10 0.10
5
1
z
1
2
1 1 1 1
1
1 1
1
0.12 0.18 3 10
1
0.60 3 10 0.12
0.14 0.19 0.60 3 10 0.71 3 10
1
1
1 1
0.29 0.69 0.37 0.28 0.40 0.50 0.28 0.46 0.24
1
0.15
2
0.68 0.69 0.53 0.38 3 10 0.43 0.93 3 10 0.21 0.57
0.37 3 10
1
0.28
1
0.11 0.22
et al26 and Baccetti et al27 observed backward and downward rotation of the mandible in patients undergoing maxillary protraction with palatal expansion. These findings suggest that the vertical dimension is difficult to control with maxillary protraction. Keles et al21 observed that the force applied extraorally 20 mm above the maxillary occlusal plane resulted in anterior translation of the maxilla without rotation; they recommended this method for Class III patients with anterior open bite. The displacement of various craniofacial structures was considerably more after maxillary protraction with maxillary expansion. This agrees with Yu et al,24 who showed greater displacements in the frontal,
Gautam, Valiathan, and Adhikari
American Journal of Orthodontics and Dentofacial Orthopedics Volume 135, Number 6
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and presumably facilitates the orthopedic effect of the facemask.6 This is supported by high stresses generated in various craniofacial sutures after rapid maxillary expansion.8 These results showed that maxillary protraction produced similar changes to normal downward and forward growth of the maxilla and was achieved with accompanying opening of the midpalatal suture. CONCLUSIONS
Fig 4. Maxillary protraction with maxillary expansion (inferior view), with wedge-shaped opening after maxillary expansion.
vertical, and lateral directions with midpalatal suture opening when compared with no midpalatal suture opening. The nodes in the anterior region of the maxilla were displaced medially with maxillary protraction alone, indicating the tendency for anterior maxillary constriction after maxillary protraction. A tendency for constriction at the anterior region of the maxilla was also noted previously.9 A wedge-shaped opening, as seen clinically, was evident both in the anteroposterior and the superoinferior directions.6 This suggests that maxillary expansion in conjunction with maxillary protraction tends to counteract the side effect of anterior constriction. Kapust et al28 showed that the treatment of Class III malocclusion with a bonded maxillary expander and a facemask in the early mixed dentition results in significant advancements of ANS, PNS, Point A, and the maxillary dentition. The anterior structures of the maxilla—Point A, ANS, and prosthion—were displaced more anteriorly with maxillary protraction and expansion than with maxillary protraction alone, with downward and forward translation of the maxilla, indicating that maxillary protraction with expansion yields more favorable results than maxillary protraction alone. This forward and downward displacement of the nasomaxillary complex with maxillary protraction with expansion more closely approximates the natural growth direction of the maxilla.29 Rapid palatal expansion has been recommended with protraction forces on the maxilla because it supposedly disrupts the circummaxillary sutural system
The amounts of displacement in the frontal, vertical, and lateral directions with midpalatal suture opening were more than those with no midpalatal suture opening. The amounts of displacement and deformation when the midpalatal suture was opened showed decreases in upward-forward rotation of the maxilla and the zygomatic arch. The forward and downward displacement of the nasomaxillary complex with maxillary protraction and maxillary expansion more closely approximates the natural growth direction of the maxilla. Hence, biomechanically, maxillary protraction combined with maxillary expansion appears to be a superior treatment modality for maxillary retrognathia than maxillary protraction alone.
REFERENCES 1. Nanda R. Biomechanical and clinical considerations of a modified protraction headgear. Am J Orthod 1980;78:125-39. 2. Nanda R, Hickory W. Zygomaticomaxillary suture adaptations incident to anteriorly-directed forces in rhesus monkeys. Angle Orthod 1984;54:199-210. 3. Itoh T, Chaconas SJ, Caputo AA, Matyas J. Photoelastic effects of maxillary protraction on the craniofacial complex. Am J Orthod 1985;88:117-24. 4. Miyasaka-Hiraga J, Tanne K, Nakamura S. Finite element analysis for stress in the craniofacial sutures produced by maxillary protraction forces applied at the upper canines. Br J Orthod 1994;21: 343-8. 5. Haas AJ. Palatal expansion: just the beginning of dentofacial orthopedics. Am J Orthod 1970;57:219-55. 6. Haas AJ. Treatment of maxillary deficiency by opening the midpalatal suture. Angle Orthod 1965;65:200-17. 7. McNamara JA Jr. An orthopedic approach to the treatment of Class III malocclusion in your patients. J Clin Orthod 1987;21: 598-608. 8. Gautam P, Valiathan A, Adhikari R. Stress and displacement patterns in craniofacial skeleton with rapid maxillary expansion: a finite element method study. Am J Orthod Dentofacial Orthop 2007;132:5.e1-11. 9. Tanne K, Sakuda M. Biomechanical and clinical changes of the craniofacial complex from orthopedic maxillary protraction. Angle Orthod 1991;61:145-52. 10. Tanne K, Hiraga J, Kakiuchi K, Yamagata Y, Sakuda M. Biomechanical effect of anteriorly directed extraoral forces on the craniofacial complex: a study using the finite element method. Am J Orthod Dentofacial Orthop 1989;95:200-7.
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11. Tanne K, Hiraga J, Sakuda M. Effects of directions of maxillary protraction forces on biomechanical changes in craniofacial complex. Eur J Orthod 1989;11:382-91. 12. Tanne K, Matsubara S, Sakuda M. Stress distributions in the maxillary complex from orthopedic headgear forces. Angle Orthod 1993;63:111-8. 13. Santler G, Karcher H, Ruda C. Indication and limitations of threedimensional models in cranio-maxillofacial surgery. J Craniomaxillofac Surg 1998;26:11-6. 14. Gateno J, Xia J, Teichgraeber JF, Rosen A. A new technique for the creation of a computerized composite skull model. J Oral Maxillofac Surg 2003;61:222-7. 15. Ngan P, Yiu C, Hu A, Ha¨gg U, Wei SHY, Gunel E. Cephalometric and occlusal changes following maxillary expansion and protraction. Eur J Orthod 1995;20:237-54. 16. Staggers JA, Germane N, Legan H. Clinical considerations in the use of protraction headgear. J Clin Orthod 1992;26:87-92. 17. Hickam JH. Maxillary protraction therapy: diagnosis and treatment. J Clin Orthod 1991;25:102-13. 18. Spolyar JL. The design, fabrication and use of full-coverage bonded rapid maxillary expansion appliance. Am J Orthod 1984;86:136-45. 19. Roberts CA, Subtelny JD. Use of the face mask in the treatment of maxillary skeletal retrusion. Am J Orthod Dentofacial Orthop 1988;93:388-94. 20. Wisth PJ, Tritrapunt A, Rygh P, Boe OE, Nordeval K. The effect of maxillary protraction on front occlusion and facial morphology. Acta Odontol Scand 1987;45:227-37.
American Journal of Orthodontics and Dentofacial Orthopedics June 2009
21. Keles A, Tokmak EC, Erverdi N, Nanda R. Effect of varying the force direction on maxillary orthopedic protraction. Angle Orthod 2002;72:387-96. 22. Merwin D, Ngan P, Ha¨gg U, Yiu C, Wei SHY. Timing for effective application of anteriorly directed orthopedic force to the maxilla. Am J Orthod Dentofacial Orthop 1997;112:292-9. 23. Ngan PW, Ha¨gg U, Yiu C, Wei SHY. Treatment response and long-term dentofacial adaptations to maxillary expansion and protraction. Semin Orthod 1997;3:255-64. 24. Yu HS, Baik HS, Sung SJ, Kim KD, Cho YS. Three-dimensional finite-element analysis of maxillary protraction with and without rapid palatal expansion. Eur J Orthod 2007;29:118-25. 25. Pangrazio-Kulbersh V, Berger J, Kersten G. Effects of protraction mechanics on the midface. Am J Orthod Dentofacial Orthop 1998;114:484-91. 26. Williams MD, Sarver DM, Sadowsky PL, Bradley E. Combined rapid maxillary expansion and protraction facemask in the treatment of Class III malocclusions in growing children: a prospective long-term study. Semin Orthod 1997;3:265-74. 27. Baccetti T, McGill JS, Franchi L, McNamara JA Jr, Tollaro I. Skeletal effects of early treatment of Class III malocclusion with maxillary expansion and face-mask therapy. Am J Orthod Dentofacial Orthop 1998;113:333-43. 28. Kapust AJ, Sinclair PM, Turley PK. Cephalometric effects of face mask/expansion therapy in Class III children: a comparison of three age groups. Am J Orthod Dentofacial Orthop 1998;113:204-12. 29. Enlow DH, Hans MG. Essentials of facial growth. Philadelphia: W.B. Saunders; 1996. p. 79-83.
Skeletal response to maxillary protraction with and without maxillary expansion: A finite element study Pawan Gautam,a Ashima Valiathan,b and Raviraj Adhikaric Manipal, Karnataka, India Introduction: The purpose of this finite element study was to evaluate biomechanically 2 treatment modalities—maxillary protraction alone and in combination with maxillary expansion—by comparing the displacement of various craniofacial structures. Methods: Two 3-dimensional analytical models were developed from sequential computed tomography scan images taken at 2.5-mm intervals of a dry young skull. AutoCAD software (2004 version, Autodesk, San Rafael, Calif) and ANSYS software (version 10, Belcan Engineering Group, Cincinnati, Ohio) were used. The model consisted of 108,799 solid 10 node 92 elements, 193,633 nodes, and 580,899 degrees of freedom. In the first model, maxillary protraction forces were simulated by applying 1 kg of anterior force 30 downward to the palatal plane. In the second model, a 4-mm midpalatal suture opening and maxillary protraction were simulated. Results: Forward displacement of the nasomaxillary complex with upward and forward rotation was observed with maxillary protraction alone. No rotational tendency was noted when protraction was carried out with 4 mm of transverse expansion. A tendency for anterior maxillary constriction after maxillary protraction was evident. The amounts of displacement in the frontal, vertical, and lateral directions with midpalatal suture opening were greater compared with no opening of the midpalatal suture. The forward and downward displacements of the nasomaxillary complex with maxillary protraction and maxillary expansion more closely approximated the natural growth direction of the maxilla. Conclusions: Displacements of craniofacial structures were more favorable for the treatment of skeletal Class III maxillary retrognathia when maxillary protraction was used with maxillary expansion. Hence, biomechanically, maxillary protraction combined with maxillary expansion appears to be a superior treatment modality for the treatment of maxillary retrognathia than maxillary protraction alone. (Am J Orthod Dentofacial Orthop 2009;135:723-8)
M
axillary protraction is recommended for skeletal Class III patients with maxillary deficiency.1,2 The principle of maxillary protraction is to apply tensile force on the circummaxillary sutures and thereby stimulate bone apposition in the suture areas. Biomechanical studies on dry skulls have demonstrated that application of an anteriorly directed force results in forward movement of the maxilla.3,4 These investigations also showed that the direction of
a Assistant professor, Department of Orthodontics and Dentofacial Orthopedics, Manipal College of Dental Sciences, Manipal, Karnataka, India. b Professor and head, Director of Post Graduate Studies, Department of Orthodontics and Dentofacial Orthopedics, Manipal College of Dental Sciences, Manipal, Karnataka, India. c Reader, Department of Mechanical Engineering, Manipal Institute of Technology, Manipal, Karnataka, India. The authors report no commercial, proprietary, or financial interest in the products or companies described in this article. Reprint requests to: Ashima Valiathan, Department of Orthodontics and Dentofacial Orthopedics, Manipal College of Dental Sciences, Manipal, Karnataka, India, 576104; e-mail, [email protected]. Submitted, March 2007; revised and accepted, June 2007. 0889-5406/$36.00 Copyright Ó 2009 by the American Association of Orthodontists. doi:10.1016/j.ajodo.2007.06.016
the force is critical in controlling rotation of the maxilla. A force generated parallel to the maxilla or above the palatal plane produces counterclockwise rotation of the palatal plane. Maxillary protraction therapy often is supplemented with maxillary expansion. Maxillary expansion is commonly needed in the treatment of patients with Class III malocclusion, because of insufficient maxillary arch width. Rapid maxillary expansion is typically used in young patients and has been shown to help in Class III correction. Midfacial orthopedic expansion has been recommended with protraction forces on the maxilla because it supposedly disrupts the circummaxillary sutural system and presumably facilitates the orthopedic effect of the facemask.5-7 There is some evidence in the literature that maxillary expansion alone can be beneficial in the treatment of certain types of Class III malocclusion, particularly borderline malocclusions.7 The purposes of this finite element study were to evaluate the displacements of various craniofacial structures with maxillary protraction therapy and compare them with the pattern of displacement with combined rapid palatal expansion and maxillary protraction. 723
724
Gautam, Valiathan, and Adhikari
American Journal of Orthodontics and Dentofacial Orthopedics June 2009
Young’s modulus and Poisson’s ratio for various materials used in this study
Table I.
Material
Young’s modulus kg/mm2
Poisson’s ratio
1.37 3 103 7.9 3 102
0.3 0.3
Compact bone Cancellous bone Data from Tanne et al.9
Fig 1. Three-dimensional finite element method skull model of a 7-year-old child.
MATERIAL AND METHODS
The details of the modeling procedure were described in a previous study.8 The analytical model was developed from sequential computed tomography scan images taken at 2.5-mm intervals of a dry young skull with dental age of 7 years. These computed tomography scan sections were traced by using AutoCAD software (2004 version, Autodesk, San Rafail, Calif). The next step was to generate geometric surfaces by joining lines together. These tracings were sequentially transferred to ANSYS software (version 10, Belcan Engineering Group, Cincinnati, Ohio). The complete geometry included an assemblage of discrete pieces called elements, connected at a finite number of points, called nodes; 10 node solid 92 elements (tetrahedron) were used for meshing. The solid 92 element has a quadratic displacement behavior, is well suited to model irregular solid geometry, and gives a better representation of the variable bone thickness that is characteristic of the craniofacial skeleton. Also, the use of solid 92 element gives better stress transmissibility and bending deformations. This tetrahedron element is defined by 10 nodes having 3 degrees of freedom at each unstrained node: 3 translations (x, y, and z). Our model consisted of 108,799 elements, 193,633 nodes, and 580,899 degrees of freedom. Hence, this model (Fig 1) is a better representation of the skull than previous models in which the sections were made at 10-mm sections.9-12 To avoid any inconsistencies associated with inaccuracy of modeling the teeth and the periodontal ligament through computed tomography, this study was restricted to the analysis of skeletal displacements.13,14 The teeth and the periodontal ligament were not modeled, and the model comprised the compact and cancellous bones of
the craniofacial skeleton. Nine craniofacial sutural systems were integrated into the model as described in the previous study.8 The mechanical properties of the compact and cancellous bones in the model were defined according to the experimental data in previous studies as shown in Table I.10 Restraints were established at all other nodes of the cranium lying on the symmetrical plane, and appropriate boundary conditions were imposed. In addition, zero-displacement and zero-rotation boundary conditions were imposed on the nodes along the foramen magnum. In the first model, 1 kg of force was directed anteriorly and 30 downward relative to the occlusal plane near the canine to simulate orthopedic maxillary protraction forces. In the second model, a known transversal (x) displacement with a magnitude of 2 mm was applied on the surface nodes of the intermaxillary suture in the first molar region to simulate the initial phase of maxillary expansion before maxillary protraction therapy. It was assumed that the 2 plates of the transversal orthopedic appliance moved apart by a total distance of 4 mm. After this, maxillary protraction forces were simulated by applying a 1-kg force directed anteriorly and 30 downward relative to the occlusal plane near the canine.
RESULTS
With maxillary protraction alone, Point A moved anteriorly and inferiorly by 0.33 and 0.056 mm, respectively. The inferior movement of the posterior nasal spine (PNS) was 0.20 mm, which was more than that of anterior nasal spine (ANS), indicating a slight tendency for upward rotation even with 30 of downward pull (Fig 2). Prosthion (or supradentale) moved anteriorly and inferiorly by 0.34 and 0.045 mm, respectively. With maxillary protraction alone, the total vector displacements of the medial and lateral pterygoid plates were 0.3 to 0.45 mm; the displacements of other areas of nasomaxillary region were 0.25 to 0.4 mm. Lateral bending of the medial and lateral pterygoid plates were evident with maxillary protraction (Table II). In response to maxillary protraction with maxillary expansion, Point A moved anteriorly and inferiorly by
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American Journal of Orthodontics and Dentofacial Orthopedics Volume 135, Number 6
Table II. Displacement of the craniofacial structures with maxillary protraction alone (mm) x
Fig 2. Maxillary protraction alone, causing counterclockwise rotation of the nasomaxillary complex.
0.15 and 0.68 mm, respectively. ANS moved anteriorly and inferiorly by 0.12 and 0.69 mm, respectively. The inferior movement of PNS was 0.57 mm (less than that of ANS), indicating downward and forward translation of the maxilla in response to maxillary protraction with maxillary expansion (Fig 3). Prosthion (or supradentale) moved anteriorly and inferiorly by 0.14 and 0.53 mm, respectively (Table III). Maxillary expansion resulted in a wedge-shaped opening in both the anteroposterior and superoinferior planes (Fig 4). Maximum displacement in response to maxillary protraction with maxillary expansion was observed in the nasomaxillary region followed by the body of the zygomatic bone. The overall displacements of the pterygoid plates were considerably less than the displacement of the zygomatic bone in maxillary protraction with maxillary expansion. This is different from the pattern of displacement with maxillary protraction alone in which the overall displacement of the pterygoid region was more than that of the zygomatic bone. The nasal cavity wall, the nasal bone, and the zygomatic bone were displaced medially, anteriorly, and inferiorly with maxillary protraction alone. Similarly, the zygomatic arch also was displaced in the medial, anterior, and inferior directions. With maxillary protraction alone, the orbital part of the greater wing of the sphenoid was displaced in the lateral direction, whereas the orbital part of the lesser wing of the sphenoid was displaced in the medial direction. The sphenoid bone as a whole was displaced in the anterior and inferior directions. With maxillary protraction with expansion, the zygomatic bone and the zygomatic process of the temporal bone were displaced laterally, posteriorly, and superiorly. The nasal cavity wall was displaced laterally,
Maxilla Point A ANS Supradentale Tuberosity Zygomatic buttress Inferior orbital rim Frontal process PNS Sphenoid bone medial pterygoid Inferior Superior Lateral pterygoid Inferior Superior Nasal cavity wall Lateral Inferior Superior Nasal bone Zygomatic bone Frontal Temporal Maxillary Body Frontal bone Zygomatic process Superior orbital ridge Temporal bone Zygomatic process Sphenoid bone Greater wing (orbital) Lesser wing (orbital)
y
0.45 3 10 0.43 3 10 0.23 3 10 0.78 3 10 0.11 3 10 0.86 3 10 0.38 3 10 0.27 3 10
7
0.14 3 10 0.10 3 10
4
0.80 3 10 0.12 3 10
5
0.77 3 10 0.43 3 10 0.45 3 10 0.37 3 10
5
0.14 3 10 0.12 3 10 0.26 3 10 0.26 3 10
5
0.24 3 10 0.40 3 10
7
0.64 3 10
z
0.33 3 10 0.30 3 10 0.34 3 10 0.32 3 10 0.36 3 10 0.25 3 10 0.20 3 10 0.33 3 10
3
0.32 3 10 0.32 3 10
3
0.30 3 10 0.32 3 10
3
0.28 3 10 0.30 3 10 0.23 3 10 0.20 3 10
3
0.20 3 10 0.19 3 10 0.29 3 10 0.28 3 10
3
0.19 3 10 0.15 3 10
3
4
0.19 3 10
0.59 3 10
5
0.53 3 10
6
7 5 5 4 6 6 7
4
4
7 7 5
3 5 5
5
0.56 3 10 0.68 3 10 0.45 3 10 0.22 3 10 0.17 3 10 0.18 3 10 0.21 3 10 0.20 3 10
4
0.25 3 10 0.23 3 10
3
0.38 3 10 0.26 3 10
3
0.86 3 10 0.67 3 10 0.48 3 10 0.65 3 10
4
0.13 3 10 0.20 3 10 0.13 3 10 0.15 3 10
3
0.21 3 10 0.55 3 10
3
3
0.16 3 10
3
0.19 3 10
3
0.20 3 10
3
0.19 3 10
3
0.22 3 10
3
3 3 3 3 3 3 3
3
4
3 3 3
3 3 3
3
4 4 3 3 3 3 3
3
3
4 4 4
3 3 3
4
whereas the nasal bone moved medially with maxillary protraction with expansion. The orbital part of the greater wing of the sphenoid was displaced laterally, posteriorly, and superiorly, whereas the orbital part of the lesser wing of the sphenoid was displaced laterally, anteriorly, and inferiorly. DISCUSSION
Several studies noted counterclockwise rotation of the maxilla with protraction headgear treatment.3,15,16 To minimize the counterclockwise rotation produced by the protraction forces, investigators changed the point of force application and the direction of the protraction forces. Some investigators applied the force from the canine region.17 Spolyar18 applied the force
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Table III. Displacement of craniofacial structures with maxillary protraction with maxillary expansion (mm) x
Fig 3. Maxillary protraction with maxillary expansion (lateral view), causing the nasomaxillary complex to translate anteroinferiorly, approximating its growth direction.
at the premolar or the deciduous molar region. Other investigators moved the point of force application distal to the lateral incisors, and some changed the direction of force at an angle of 15 to 30 from the occlusal plane.19,20 A 1-kg force applied 30 downward to the palatal plane induced forward displacement of the nasomaxillary complex with upward and forward rotation. This is in contrast to the study by Tanne et al,10 who showed that the nasomaxillary complex repositioned in an almost translatory manner with a slight rotation in loading with a 30 downward force. Keles et al21 observed that the maxilla advanced forward with a counterclockwise rotation with 30 downward maxillary protraction. The counterclockwise rotational tendency of the maxilla was why maxillary protraction therapy in Class III patients with maxillary deficiency and open bite was contraindicated.22,23 A 1-kg force applied 30 downward to the palatal plane along with 4 mm of transverse expansion induced forward displacement of the nasomaxillary complex with no rotational tendency. This agrees with the findings of Yu et al,24 who demonstrated that the amounts of displacement and deformation when the midpalatal suture was opened showed decreases in upward-forward rotation of the maxilla and the zygomatic arch. This is a more favorable displacement pattern in patients with open bite or vertical growers. Hence, a combination of maxillary protraction with rapid maxillary expansion can be used in Class III maxillary retrognathic patients with open bite without the adverse effect of increasing lower anterior facial height.25 Contrary to this, Williams
Maxilla Point A 0.97 ANS 0.75 Supradentale 1.09 Tuberosity 0.61 Zygomatic buttress 0.79 Inferior orbital rim 0.20 Frontal process 0.12 3 10 PNS 0.67 Sphenoid bone medial pterygoid Inferior 0.55 Superior 0.67 Inferior 0.46 Superior 0.48 Nasal cavity wall Lateral 0.54 Inferior 0.75 Superior 0.89 3 10 Nasal bone 0.52 3 10 Zygomatic bone Frontal 0.19 Temporal 0.44 Maxillary 0.51 Body 0.49 Frontal bone Zygomatic 0.55 3 10 process Superior orbital 0.51 3 10 ridge Temporal bone Zygomatic 0.18 process Sphenoid bone Greater wing 0.40 3 10 (orbital) Lesser wing 0.29 3 10 (orbital)
y
1
0.15 0.12 0.14 0.29 3 10 0.10 0.54 3 10 0.11 0.16
0.36 3 10 0.37 3 10 0.27 3 10 0.37 3 10
5 2
0.66 3 10 0.12 0.13 3 10 0.87 3 10 0.17 0.11 0.53 3 10 0.10
5
1
z
1
2
1 1 1 1
1
1 1
1
0.12 0.18 3 10
1
0.60 3 10 0.12
0.14 0.19 0.60 3 10 0.71 3 10
1
1
1 1
0.29 0.69 0.37 0.28 0.40 0.50 0.28 0.46 0.24
1
0.15
2
0.68 0.69 0.53 0.38 3 10 0.43 0.93 3 10 0.21 0.57
0.37 3 10
1
0.28
1
0.11 0.22
et al26 and Baccetti et al27 observed backward and downward rotation of the mandible in patients undergoing maxillary protraction with palatal expansion. These findings suggest that the vertical dimension is difficult to control with maxillary protraction. Keles et al21 observed that the force applied extraorally 20 mm above the maxillary occlusal plane resulted in anterior translation of the maxilla without rotation; they recommended this method for Class III patients with anterior open bite. The displacement of various craniofacial structures was considerably more after maxillary protraction with maxillary expansion. This agrees with Yu et al,24 who showed greater displacements in the frontal,
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and presumably facilitates the orthopedic effect of the facemask.6 This is supported by high stresses generated in various craniofacial sutures after rapid maxillary expansion.8 These results showed that maxillary protraction produced similar changes to normal downward and forward growth of the maxilla and was achieved with accompanying opening of the midpalatal suture. CONCLUSIONS
Fig 4. Maxillary protraction with maxillary expansion (inferior view), with wedge-shaped opening after maxillary expansion.
vertical, and lateral directions with midpalatal suture opening when compared with no midpalatal suture opening. The nodes in the anterior region of the maxilla were displaced medially with maxillary protraction alone, indicating the tendency for anterior maxillary constriction after maxillary protraction. A tendency for constriction at the anterior region of the maxilla was also noted previously.9 A wedge-shaped opening, as seen clinically, was evident both in the anteroposterior and the superoinferior directions.6 This suggests that maxillary expansion in conjunction with maxillary protraction tends to counteract the side effect of anterior constriction. Kapust et al28 showed that the treatment of Class III malocclusion with a bonded maxillary expander and a facemask in the early mixed dentition results in significant advancements of ANS, PNS, Point A, and the maxillary dentition. The anterior structures of the maxilla—Point A, ANS, and prosthion—were displaced more anteriorly with maxillary protraction and expansion than with maxillary protraction alone, with downward and forward translation of the maxilla, indicating that maxillary protraction with expansion yields more favorable results than maxillary protraction alone. This forward and downward displacement of the nasomaxillary complex with maxillary protraction with expansion more closely approximates the natural growth direction of the maxilla.29 Rapid palatal expansion has been recommended with protraction forces on the maxilla because it supposedly disrupts the circummaxillary sutural system
The amounts of displacement in the frontal, vertical, and lateral directions with midpalatal suture opening were more than those with no midpalatal suture opening. The amounts of displacement and deformation when the midpalatal suture was opened showed decreases in upward-forward rotation of the maxilla and the zygomatic arch. The forward and downward displacement of the nasomaxillary complex with maxillary protraction and maxillary expansion more closely approximates the natural growth direction of the maxilla. Hence, biomechanically, maxillary protraction combined with maxillary expansion appears to be a superior treatment modality for maxillary retrognathia than maxillary protraction alone.
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