ORIGINAL ARTICLE
Evaluation of stress changes in the mandible with a fixed functional appliance: A finite element study Anshul Chaudhry,a Maninder S. Sidhu,b Girish Chaudhary,c Seema Grover,d Nimisha Chaudhry,e and Ashutosh Kaushikf Ludhiana, Punjab, Gurgaon and Rohatak, Haryana, and Moradabad, Uttar Pradesh, India Introduction: The aim of this study was to evaluate the effects of a fixed functional appliance (Forsus Fatigue Resistant Device; 3M Unitek, Monrovia, Calif) on the mandible with 3-dimensional finite element stress analysis. Methods: A 3-dimensional finite element model of the mandible was constructed from the images generated by cone-beam computed tomography of a patient undergoing fixed orthodontic treatment. The changes were studied with the finite element method, in the form of highest von Mises stress and maximum principal stress regions. Results: More areas of stress were seen in the model of the mandible with the Forsus compared with the model of the mandible in the resting stage. Conclusions: This fixed functional appliance studied by finite element model analysis caused increases in the maximum principal stress and the von Mises stress in both the cortical bone and the condylar region of the mandible by more than 2 times. (Am J Orthod Dentofacial Orthop 2015;147:226-34)
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he aim of orthodontic treatment of children with malocclusions is to produce a well-balanced facial profile and an acceptable occlusion. Despite good treatment planning and patient selection, facial esthetics may not be ideal, and this can be compounded by relapse after an initially successful treatment. Dentofacial orthopedists believe that functional appliances train patients in maintaining correct oral and tongue postures. In the treatment of Class II malocclusion, an early phase of functional appliance treatment is
a Senior lecturer, Department of Orthodontics, Christian Dental College, Christian Medical College, Ludhiana, Punjab, India. b Director, postgraduate studies; professor and head, Department of Orthodontics, Shree Guru Gobind Singh Tricentenary Dental College, Hospital and Research Institute, Budhera, Gurgaon, Haryana, India. c Senior lecturer, Department of Orthodontics, Baba Jaswant Singh Dental College, Hospital & Research Institute, Ludhiana, Punjab, India. d Professor, Department of Orthodontics, Shree Guru Gobind Singh Tricentenary Dental College, Hospital and Research Institute, Budhera, Gurgaon, Haryana, India. e Formerly, postgraduate student, Department of Prosthodontics, Kothiwal Dental College, Moradabad, Uttar Pradesh, India. f Private practice, Rohatak, Haryana, India. All authors have completed and submitted the ICMJE Form for Disclosure of Potential Conflicts of Interest, and none were reported. Address correspondence to: Anshul Chaudhry, Department of Orthodontics, Christian Dental College, CMC, Ludhiana-141010, Punjab, India; e-mail, [email protected]. Submitted, March 2014; revised and accepted, September 2014. 0889-5406/$36.00 Copyright Ó 2015 by the American Association of Orthodontists. http://dx.doi.org/10.1016/j.ajodo.2014.09.020
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commonly used to simplify subsequent therapy and to optimize the development of the facial skeleton. McNamara1 reported mandibular retrusion as the most common characteristic of Class II malocclusion. Class II Division 1 malocclusions with mandibular deficiency have been treated for more than a century with different types of functional appliances. Woodside et al,2 Stockli and Willert,3 Vargervik and Harvold,4 and Ruf and Pancherz5 stated that typical muscular forces are generated by altering the mandibular position sagittally and vertically, resulting in orthodontic and orthopedic changes. The pressure created by stretching of the muscles and soft tissues is transmitted to the dental and skeletal structures, moving the teeth and modifying growth. Many removable functional appliances, such as activator, bionator, Fr€ankel, and Twin-block, have been used to correct Class II Division 1 malocclusions; however, few fixed functional appliances have been used. These fixed functional appliances for sagittal advancement of the mandible have certain advantages over removable functional appliances, such as less dependence on patient compliance, and these can be used concurrently with fixed mechanotherapy, thereby reducing treatment duration.3 Fixed functional appliances also enhance mandibular growth and tend to produce more horizontal condylar growth compared with removable appliances.6-8 The theoretical basis of functional treatment in general is the principle that a new pattern of function
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dictated by the appliance leads to the development of a correspondingly new morphologic pattern. This new pattern of function developed by wearing of functional appliances refers to different functional components of the orofacial system, including the tongue, lips, and facial and masticatory muscles: mainly the protracting muscles, ligaments, and periosteum. The new morphologic pattern includes a different arrangement of the teeth in the jaws, improvement of the occlusion, and an altered relationship of the jaws. The forces produced by the muscle contractions are transmitted to selected teeth and their periodontia, the jaws, and the temporomandibular joints. Anterior displacement of the mandible can induce altered postural activity in the pterygoid muscles, resulting in additional condylar growth.9 Removable functional appliances have some disadvantages; they are normally large, have unstable fixation, cause discomfort, lack tactile sensibility, exert pressure on the buccal mucosa, reduce space for the tongue, cause difficulty in deglutition and speech, and often affect the esthetic appearance. The lack of success with functional appliances has in some circumstance been attributed to a lack of patient compliance in wearing the appliance. This led to the development of fixed functional appliances. Fixed functional appliances—more appropriately termed “noncompliant Class II interarch correctors”— have gained significant ground. A fixed appliance is aimed at targeting the dentition and providing the following dental corrections: facilitating mandibular advancement by eliminating dental interferences, and consolidating the arches to minimize the adverse dental side-effects. A number of fixed functional appliances have gained popularity in recent years to help achieve better results in noncompliant patients: eg, the Herbst appliance and the Forsus Fatigue Resistant Device (3M Unitek, Monrovia, Calif). Remodeling changes in the condylar head and glenoid fossa been reported after functional appliance treatment for correction of Class II skeletal dysplasia with mandibular retrognathia. The posterior displacement of the condylar head and the anterior relocation of the glenoid fossa with functional appliances have been confirmed with numerous radiologic techniques.2,3,10-15 The remodeling changes in the condyle and dentofacial complex have been studied routinely with cephalometric analysis.16,17 The study of functional appliances using computed tomography has shown a double contour on the bony outline of the condylar head and fossa articularis,18 whereas single photon emission computerized tomography scans of the temporomandibular joint (TMJ) showed significant increases in
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bone count, indicating increased bone formation in the TMJ after mandibular anterior repositioning splint treatment.19 Magnetic resonance imaging studies have also shown that the mandibular condyle experiences tensile stresses in the posterosuperior aspect that explain condylar growth in that direction, whereas on the glenoid fossa, similar kinds of stresses are created in the posterior connective tissue region and are correlated with the increased cellular activity.17 The recent use of cone-beam computed tomography (CBCT) in creating the 3-dimensional (3D) model of the dentofacial skeleton has enhanced the precision and understanding of the region.20,21 The biomechanical response of bone to orthopedic forces is quite complex. The use of the finite element method (FEM) initially in medical orthopedics and later in dentistry, especially orthodontics, allowed precise analysis of the biomechanical effects of various treatment modalities. The FEM, which has been successfully applied to the study of stresses and strains in engineering,22,23 makes it possible to evaluate biomechanical components such as displacements, strains, and stresses induced in living structures from various external forces.24-27 The first finite element models described the tooth-bone structure 2 dimensionally using average geometric relationships and homogeneous and isotropic material models. The 3D finite element models were later introduced in 1973 by Farah et al.28 The FEM has numerous advantages in orthodontics.29 It is a noninvasive technique that measures the actual amount of stress experienced at any point on teeth, alveolar bones, periodontal ligaments, and craniofacial bones. It possibly can simulate the oral environment in vitro; the displacement of the tooth can be visualized graphically. The point of application, magnitude, and direction of a force may easily be varied to simulate the clinical situation; reproducibility does not affect the physical properties of the involved material, and the study can be repeated as many times as the operator wishes. Thus, the FEM has been introduced in orthodontics as a powerful research tool for solving various structural biomechanical problems. The FEM analyzes the biomechanical effects of various treatment modalities and is an approximation method to represent both the deformation and the 3D stress distribution in bodies that are exposed to stress. A pattern of stresses is created in the TMJ and orofacial complex when the mandible is protracted with a functional appliance. Whether this pattern remains the same during treatment and whether all biologic tissues respond in a similar predictable manner over time are not known. Previous FEM studies of functional appliances were on skulls or artificial models. Recently, Gupta
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et al20,21 used a CBCT model of a patient to check changes in the TMJs. Previous researchers did not study the stress changes produced in the orofacial complex using a 3D patient model with a fixed functional appliance. It is assumed that bone responds to mechanical stresses by showing particular kinds of compressive and tensile stresses. Since stress and strain in living tissues are thought to be key factors in biologic change, it is important to elucidate the stress or strain to understand its relationship to bone remodeling. In orthodontics, various techniques have been used to measure these biomechanical factors. However, it is not always possible with these methods to quantify the stress or strain in an internal area of a living structure.25 Therefore, a technique applicable to biomechanical investigation for stress or strain in biologic tissues is needed. The FEM is applicable to the biomechanical study of strains and stresses generated in internal structures. Other studies have reported the relationship between stresses analyzed by the FEM and biologic changes of bony structures.30-33 The limitation of an FEM study is that it can record only instantaneous stress patterns. In this study, the stress patterns in the mandible in the resting stage and the stress patterns created by simulated mandibular protraction of a fixed functional appliance were elucidated. The purpose of this study was to evaluate the stress pattern distribution in different parts of the mandible and associated structures with a fixed functional appliance (Forsus Fatigue Resistant Device) on a patient using the FEM with a CBCT-generated 3D image. MATERIAL AND METHODS
This study was designed to evaluate stress pattern distributions in different regions of the mandible with the Forsus appliance using the FEM. A 15-year-old girl with a typical Class II Division 1 malocclusion with an overjet of 11 mm was selected. Her chief complaint was an unpleasant appearance and backwardly positioned mandibular front teeth. After a clinical examination, the patient was planned to be treated with a fixed functional appliance, the Forsus. She had a skeletal Class II relationship with an almost normal maxilla, a retrognathic mandible, a positive visual treatment objective, an abnormal musculature, and a favorable growth pattern. All pretreatment records were taken for the patient including study models, photographs, CBCT scans, and interocclusal biting force recordings. The Forsus was planned to be given to the patient. Informed consent was obtained from the patient's parents for her to
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Fig 1. Mesh diagram of a complete mandible.
participate in the study. The DICOM images of the mandible, TMJ, and associated structures were generated using CBCT scans to construct the mesh diagram (Fig 1) for the finite element analysis with Mimics software (version 8.11; Materialise HQ, Leuven, Belgium) and HyperWorks software (version 9.0; Altair Engineering, Huntsville, Ala). Full bonding and banding of the maxillary and mandibular arches was done using a 0.022-in MBT (Mclaughlin Bennett Trevisi) prescription. After leveling and alignment, the arches were U-shaped but in a Class II relationship. When the rectangular wire stage reached 0.019 3 0.025-in stainless steel, the Forsus appliance was used in single-step advancement. The attachment of the appliance was at the canine and premolar interface. The horizontal force values were calculated with a Dontrix gauge (American Orthodontics, Sheboygan, Wis). The vertical forces were recorded with a custom-made pressure sensor by placing the sensor in the molar region. The muscles also exert forces on the mandible. Therefore, it is necessary to calculate the musculature forces for the assessment of the stress patterns on the mandible. The muscle areas were constructed by taking references from books of anatomy; however, interocclusal bite force recordings are specific for each patient. Muscle force in maximum intercuspation was calculated by multiplying the physiologic cross-sectional areas of the each masticatory muscle by 0.37 3 102 N. For the masseter, the calculated muscle force was 388.5 N; for the lateral pterygoid, it was 37 N; for the medial pterygoid, it was 432.9 N; and for the temporalis, it was 333 N, as shown in Figures 2 and 3 and Table I, as per the chart.34 The duration of treatment was 1 year 8 months.
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Table I. Physiologic cross-sectional areas (PCS) of the
each masticatory muscle and calculated biting force Muscle Masseter Temporalis Medial pterygoid Lateral pterygoid
PCS (cm2) 10.5 9 11.7 1.0
Force (N) 388.5 333 432.9 37
Fig 2. Muscular forces exerted by the lateral and medial pterygoid muscles.
Fig 4. Von Mises stress contours in cortical bone.
Fig 3. Muscular forces exerted by the masseter and temporalis muscles.
For the finite element model construction, a CBCT scan of the tooth and the mandible was taken into the Mimics software. Surface data of the metal casting and the mandible were generated using Solid Edge 2004 software (Siemens, Plano, Tex). From the 3D image of the CBCT, a mesh diagram was generated using the HyperWorks software. Finite element models were constructed from the DICOM images of slices 1 mm thick generated by the DICOM software. The assembled finite element model of the mandible was imported into Ansys software (version 12.1; Canonsburg, Pa) for analysis. The material properties assigned were Young's modulus (or modulus of elasticity) and the Poisson ratio.20 A vertical biting force of 111.55 N was applied in the molar region, and a horizontal force of 1948.24 N was seen distal to the canine in the horizontal direction. The model was restricted at the outer part of the skull at its most posterosuperior edges. This allowed the visualization of deformation and stress generation in the mandible. RESULTS
The results showed changes in terms of von Mises stresses and principal stresses. The total number of
nodes was 462542, along with total elements numbering 92972. The color changes in terms of areas of maximum and minimum stresses were seen after the material properties were assigned. Red shows the maximum principal stress region, which is mainly tensile stress, and blue shows the minimum principal stress region, which is compressive stress. The results of this FEM analysis showed the areas of tension and compression in the mandible and associated structures. The results were calculated in terms of von Mises and principal stresses in the following regions: cortical bone, teeth, and condylar head. In the resting stage of the mandible, the highest von Mises stresses were 55.103 MPa in the cortical bone (Fig 4), 27.91 MPa in the teeth (Fig 5), and 4.098 MPa in the condyle (Fig 6). The maximum principal stresses were 65.066 MPa in the cortical bone (Fig 7), 20.96 MPa in the teeth (Fig 8), and 4.117 MPa in the condyle (Fig 9). There were changes with the fixed functional appliance. The highest von Mises stresses were 166.918 MPa in the cortical bone (Fig 10), 329.707 MPa in the teeth (Fig 11), and 10.559 MPa in the condyle (Fig 12). The maximum principal stresses were 145.016 MPa in the cortical bone (Fig 13), 187.077 MPa in the teeth (Fig 14), and 11.725 MPa in the condyle (Fig 15).
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Fig 5. Von Mises stress contours in teeth.
Fig 7. Principal stress contours in cortical bone in resting stage.
Fig 6. Von Mises stress contours in condyle.
Fig 8. Principal stress contours in teeth in resting stage.
DISCUSSION
The FEM is a computational technique used to obtain approximate solutions of boundary-value problems in engineering. The FEM makes it practicable to elucidate biomechanical components such as displacements, strains, and stresses induced in living structures from various external forces. Biomechanical studies have shown that the compressive and tensile stresses from functional orthopedic forces are the key determinants to remodeling of the bones.25,35 The limitation of an FEM study is that it can record only instantaneous stress patterns. In this study, the finite element model was constructed to evaluate the stress patterns on different parts of the mandible. Since we know that functional appliances bring the mandible forward, the muscles also get
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stretched, and there is some growth in the TMJs as well. Our findings suggest that the remodeling of the bone to mechanical forces might be correlated with the location of the tensile and compressive stress patterns. The mandible, the articular disc in the TMJ, and the condylar head are also affected during clenching of the teeth.36 In some previous FEM studies, the effects of the masticatory muscles were neglected; in other studies, muscle forces in different amounts and proportions were applied to the model. The mandible is not a static structure that carries only the loads that affect it. The mandibular position is maintained by the harmonious balance of muscles, connecting tissues, neural system, and facial skin. For this reason, we also considered the muscle forces acting on the mandible in the resting stage.
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Fig 9. Principal stress contours in condyle in resting stage.
Fig 11. Von Mises stress contours in teeth with Forsus.
Fig 10. Von Mises stress contours in cortical bone with Forsus.
Fig 12. Von Mises stress contours in condyle.
In the resting stage of the mandible, von Mises stress in the cortical bone is maximum at the neck of the condyle, probably because of the stretch of the lateral pterygoid muscle, the middle of the sigmoid notch, and a small part on the posterior border of the ramus, whereas the head of the condyle, the coronoid process, the angle of the mandible, and most of the body of the mandible show minimum stress (Table II). In an FEM study on mandibular first premolars, Tanne et al37 investigated the stress levels induced in the periodontal tissues by orthodontic forces and observed the highest stress, approximately 120 g/cm2, at the level of the cervix on the buccal and lingual points, with a gradual reduction to zero stress near the center of the root. In a similar study using the FEM, McGuinness et al38 determined the stress induced in the periodontal liga6ment in 3 dimensions when a maxillary canine was
subjected to an orthodontic force similar to that produced by an edgewise appliance. The maximum stress induced at the cervical margin of the periodontal ligament was 0.072 N/mm2. In the resting stage, the maximum principal stresses in the cortical bone were seen at the neck of the condyle and the middle of the sigmoid notch because of the attachments of the muscles in the corresponding areas (Table II). With a fixed functional appliance, the highest von Mises stresses in the cortical bone were from the canine to the premolar area and in the sigmoid notch (Table III). In the resting stage, it was maximum at the neck of the condyle, the middle of the sigmoid notch, and a small part on the posterior border of the ramus, whereas the head of the condyle, the coronoid process, the angle of the mandible, and most of the body of the mandible
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Fig 13. Principal stress contours in cortical bone with Forsus.
Fig 15. Principal stress contours in condyle with Forsus. Table II. Resting stage of the mandible Part Cortical bone Teeth Condyle
Von Mises stress (MPa) 55.103 27.91 4.098
Principal stress (MPa) 65.066 20.96 4.117
Table III. Patient with the Forsus Part Cortical bone Teeth Condyle
Von Mises stress (MPa) 166.918 329.707 10.559
Principal stress (MPa) 145.016 187.077 11.725
Table IV. Maximum von Mises stresses in 2 models of
the Forsus Fig 14. Principal stress contours in teeth with Forsus.
showed minimum stresses. In the cortical bone, there was an increase by 3 times in the stress when the patient was wearing the Forsus. The teeth showed an increase in stress of almost 12 times with the Forsus because it is a tooth-borne appliance, whereas in the condyle, there was an increase of more than 2 times during appliance wear because of the constant sagittal positioning of the mandible (Table IV). Ulusoy and Darendeliler34 studied the stress region with the FEM in a dry human mandible with the Class II activator and the Class II activator and high-pull headgear combination. They found that the regions near the muscle attachments were affected the most. The inner part of the coronoid process and the gonial area had the maximum stress values. The stress regions formed by the Class II activator showed that the slope between the coronoid and condylar processes and the anterior
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Part Cortical bone Teeth Condyle
Resting stage of mandible (MPa) 55.103 27.91 4.098
With Forsus (MPa) 166.918 329.707 10.559
medial surface of the coronoid process were the most affected regions. A von Mises stress value of 8.556 MPa was recorded on the medial side of the coronoid process. The stress regions formed by the Class II activator high-pull headgear showed that the slopes between the coronoid and condylar processes and the anterior medial surface of the coronoid process were the most affected regions. In our study, the maximum principal stresses in the cortical bone were from the canine to the molar area, in the condylar neck, and in the sigmoid notch (Table III), whereas in the resting stage, the maximum principal stresses were seen at the neck of the condyle and the
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Table V. Maximum principal stresses in 2 models of
2.
the Forsus Part Cortical bone Teeth Condyle
Resting stage of mandible (MPa) 65.066 20.96 4.117
3. With Forsus (MPa) 145.016 187.077 11.725
With the appliance, the increases in the von Mises stress were by 3 times in the cortical bone and by more than 2 times in the condyle. With the appliance, the maximum principal stress increased by more than 2 times in the cortical bone and by more than 3 times in the condyle.
REFERENCES
middle of the sigmoid notch. In the teeth, these were seen in the roots of the canines; in the resting stage, the maximum stress was seen at the distal root of the first molar. In the condyle, it was in the posterior region of the superior surface. In the cortical bone, the principal stress increased by more than 2 times, and the teeth showed an increase in stress of 9 times when compared with the resting stage. The increase in stress in the condyle was 3 times (Table V). In a magnetic resonance imaging study, Gupta et al21 evaluated patterns of stress generation in the TMJ after mandibular protraction with different types of construction bites, where they changed the vertical opening but kept the sagittal advancement the same. Tensile stresses migrated more posteriorly on the condylar head with increased bite height. The locations of the tensile stresses in the glenoid fossa were similar in all simulations, and the TMJ as a whole showed increased loading with increasing vertical openings. In a similar study, we compared the stress generation in 3 models of the mandible with the Twin-block appliance.39 In the first model, the stress pattern in the resting stage—ie, only with the muscular forces—was seen. In the second and third models, with the Twin-block appliance, the vertical height of the bite was kept constant, and the horizontal advancement was changed. On checking the von Mises stress and principal stress pattern developed by the removable appliance, we found that the stress pattern generated by the Forsus was much higher. CONCLUSIONS
In this study, we ventured toward understanding the different biomechanical stresses produced in the various regions of mandible by a fixed functional appliance. When the mandible is protracted, a pattern of stresses is created in the TMJ and the mandible. The stress distribution in the whole mandible was determined using the finite element model constructed from a DICOM image generated by CBCT. 1.
With the Forsus, a tooth-supported appliance, both the von Mises and principal stresses increased many more times in the teeth than in the mandible at the resting stage.
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19. Guner DD, Ozturk Y, Sayman HB. Evaluation of the effects of functional orthopedic treatment on temporomandibular joints with single-photon emission computerized tomography. Eur J Orthod 2003;25:9-12. 20. Gupta A, Kohli VS, Hazarey PV, Kharbanda OP, Gunjale A. Stress distribution in the temporomandibular joint after mandibular protraction: a 3-dimensional finite element method study. Part 1. Am J Orthod Dentofacial Orthop 2009;135:737-48. 21. Gupta A, Hazarey PV, Kharbanda OP, Kohli VS, Gunjal AS. Stress distribution in the temporomandibular joint after mandibular protraction: a 3-dimensional finite element study. Part 2. Am J Orthod Dentofacial Orthop 2009;135:749-56. 22. Desai CS, Abel JF. The introduction to the finite element analysis— a numerical method for engineering analysis. 1st ed. New York: Van Nostrand Reinhold; 1972. 23. Huiskes R, Chao EY. A survey of finite element analysis in orthopedic biomechanics: the first decade. J Biomech 1983;16:385-409. 24. Gautam P, Valiathan A, Adhikari R. Stress and displacement patterns in the craniofacial skeleton with rapid maxillary expansion: a finite element method study. Am J Orthod Dentofacial Orthop 2007;132:5.e1-11. 25. Tanne K, Sakuda M. Biomechanical and clinical changes of the craniofacial complex from orthopedic maxillary protraction. Angle Orthod 1991;61:145-52. 26. 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. 27. 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. 28. Farah JW, Craig RG, Sikarskei DL. Photoelastic and finite element stress analysis of a restored axisymmetric first molar. J Biomech 1973;6:511-20. 29. Jafari A, Shetty KS, Kumar M. Study of stress distribution and displacement of various craniofacial structures following applica-
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American Journal of Orthodontics and Dentofacial Orthopedics
Evaluation of stress changes in the mandible with a fixed functional appliance: A finite element study Anshul Chaudhry,a Maninder S. Sidhu,b Girish Chaudhary,c Seema Grover,d Nimisha Chaudhry,e and Ashutosh Kaushikf Ludhiana, Punjab, Gurgaon and Rohatak, Haryana, and Moradabad, Uttar Pradesh, India Introduction: The aim of this study was to evaluate the effects of a fixed functional appliance (Forsus Fatigue Resistant Device; 3M Unitek, Monrovia, Calif) on the mandible with 3-dimensional finite element stress analysis. Methods: A 3-dimensional finite element model of the mandible was constructed from the images generated by cone-beam computed tomography of a patient undergoing fixed orthodontic treatment. The changes were studied with the finite element method, in the form of highest von Mises stress and maximum principal stress regions. Results: More areas of stress were seen in the model of the mandible with the Forsus compared with the model of the mandible in the resting stage. Conclusions: This fixed functional appliance studied by finite element model analysis caused increases in the maximum principal stress and the von Mises stress in both the cortical bone and the condylar region of the mandible by more than 2 times. (Am J Orthod Dentofacial Orthop 2015;147:226-34)
T
he aim of orthodontic treatment of children with malocclusions is to produce a well-balanced facial profile and an acceptable occlusion. Despite good treatment planning and patient selection, facial esthetics may not be ideal, and this can be compounded by relapse after an initially successful treatment. Dentofacial orthopedists believe that functional appliances train patients in maintaining correct oral and tongue postures. In the treatment of Class II malocclusion, an early phase of functional appliance treatment is
a Senior lecturer, Department of Orthodontics, Christian Dental College, Christian Medical College, Ludhiana, Punjab, India. b Director, postgraduate studies; professor and head, Department of Orthodontics, Shree Guru Gobind Singh Tricentenary Dental College, Hospital and Research Institute, Budhera, Gurgaon, Haryana, India. c Senior lecturer, Department of Orthodontics, Baba Jaswant Singh Dental College, Hospital & Research Institute, Ludhiana, Punjab, India. d Professor, Department of Orthodontics, Shree Guru Gobind Singh Tricentenary Dental College, Hospital and Research Institute, Budhera, Gurgaon, Haryana, India. e Formerly, postgraduate student, Department of Prosthodontics, Kothiwal Dental College, Moradabad, Uttar Pradesh, India. f Private practice, Rohatak, Haryana, India. All authors have completed and submitted the ICMJE Form for Disclosure of Potential Conflicts of Interest, and none were reported. Address correspondence to: Anshul Chaudhry, Department of Orthodontics, Christian Dental College, CMC, Ludhiana-141010, Punjab, India; e-mail, [email protected]. Submitted, March 2014; revised and accepted, September 2014. 0889-5406/$36.00 Copyright Ó 2015 by the American Association of Orthodontists. http://dx.doi.org/10.1016/j.ajodo.2014.09.020
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commonly used to simplify subsequent therapy and to optimize the development of the facial skeleton. McNamara1 reported mandibular retrusion as the most common characteristic of Class II malocclusion. Class II Division 1 malocclusions with mandibular deficiency have been treated for more than a century with different types of functional appliances. Woodside et al,2 Stockli and Willert,3 Vargervik and Harvold,4 and Ruf and Pancherz5 stated that typical muscular forces are generated by altering the mandibular position sagittally and vertically, resulting in orthodontic and orthopedic changes. The pressure created by stretching of the muscles and soft tissues is transmitted to the dental and skeletal structures, moving the teeth and modifying growth. Many removable functional appliances, such as activator, bionator, Fr€ankel, and Twin-block, have been used to correct Class II Division 1 malocclusions; however, few fixed functional appliances have been used. These fixed functional appliances for sagittal advancement of the mandible have certain advantages over removable functional appliances, such as less dependence on patient compliance, and these can be used concurrently with fixed mechanotherapy, thereby reducing treatment duration.3 Fixed functional appliances also enhance mandibular growth and tend to produce more horizontal condylar growth compared with removable appliances.6-8 The theoretical basis of functional treatment in general is the principle that a new pattern of function
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dictated by the appliance leads to the development of a correspondingly new morphologic pattern. This new pattern of function developed by wearing of functional appliances refers to different functional components of the orofacial system, including the tongue, lips, and facial and masticatory muscles: mainly the protracting muscles, ligaments, and periosteum. The new morphologic pattern includes a different arrangement of the teeth in the jaws, improvement of the occlusion, and an altered relationship of the jaws. The forces produced by the muscle contractions are transmitted to selected teeth and their periodontia, the jaws, and the temporomandibular joints. Anterior displacement of the mandible can induce altered postural activity in the pterygoid muscles, resulting in additional condylar growth.9 Removable functional appliances have some disadvantages; they are normally large, have unstable fixation, cause discomfort, lack tactile sensibility, exert pressure on the buccal mucosa, reduce space for the tongue, cause difficulty in deglutition and speech, and often affect the esthetic appearance. The lack of success with functional appliances has in some circumstance been attributed to a lack of patient compliance in wearing the appliance. This led to the development of fixed functional appliances. Fixed functional appliances—more appropriately termed “noncompliant Class II interarch correctors”— have gained significant ground. A fixed appliance is aimed at targeting the dentition and providing the following dental corrections: facilitating mandibular advancement by eliminating dental interferences, and consolidating the arches to minimize the adverse dental side-effects. A number of fixed functional appliances have gained popularity in recent years to help achieve better results in noncompliant patients: eg, the Herbst appliance and the Forsus Fatigue Resistant Device (3M Unitek, Monrovia, Calif). Remodeling changes in the condylar head and glenoid fossa been reported after functional appliance treatment for correction of Class II skeletal dysplasia with mandibular retrognathia. The posterior displacement of the condylar head and the anterior relocation of the glenoid fossa with functional appliances have been confirmed with numerous radiologic techniques.2,3,10-15 The remodeling changes in the condyle and dentofacial complex have been studied routinely with cephalometric analysis.16,17 The study of functional appliances using computed tomography has shown a double contour on the bony outline of the condylar head and fossa articularis,18 whereas single photon emission computerized tomography scans of the temporomandibular joint (TMJ) showed significant increases in
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bone count, indicating increased bone formation in the TMJ after mandibular anterior repositioning splint treatment.19 Magnetic resonance imaging studies have also shown that the mandibular condyle experiences tensile stresses in the posterosuperior aspect that explain condylar growth in that direction, whereas on the glenoid fossa, similar kinds of stresses are created in the posterior connective tissue region and are correlated with the increased cellular activity.17 The recent use of cone-beam computed tomography (CBCT) in creating the 3-dimensional (3D) model of the dentofacial skeleton has enhanced the precision and understanding of the region.20,21 The biomechanical response of bone to orthopedic forces is quite complex. The use of the finite element method (FEM) initially in medical orthopedics and later in dentistry, especially orthodontics, allowed precise analysis of the biomechanical effects of various treatment modalities. The FEM, which has been successfully applied to the study of stresses and strains in engineering,22,23 makes it possible to evaluate biomechanical components such as displacements, strains, and stresses induced in living structures from various external forces.24-27 The first finite element models described the tooth-bone structure 2 dimensionally using average geometric relationships and homogeneous and isotropic material models. The 3D finite element models were later introduced in 1973 by Farah et al.28 The FEM has numerous advantages in orthodontics.29 It is a noninvasive technique that measures the actual amount of stress experienced at any point on teeth, alveolar bones, periodontal ligaments, and craniofacial bones. It possibly can simulate the oral environment in vitro; the displacement of the tooth can be visualized graphically. The point of application, magnitude, and direction of a force may easily be varied to simulate the clinical situation; reproducibility does not affect the physical properties of the involved material, and the study can be repeated as many times as the operator wishes. Thus, the FEM has been introduced in orthodontics as a powerful research tool for solving various structural biomechanical problems. The FEM analyzes the biomechanical effects of various treatment modalities and is an approximation method to represent both the deformation and the 3D stress distribution in bodies that are exposed to stress. A pattern of stresses is created in the TMJ and orofacial complex when the mandible is protracted with a functional appliance. Whether this pattern remains the same during treatment and whether all biologic tissues respond in a similar predictable manner over time are not known. Previous FEM studies of functional appliances were on skulls or artificial models. Recently, Gupta
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et al20,21 used a CBCT model of a patient to check changes in the TMJs. Previous researchers did not study the stress changes produced in the orofacial complex using a 3D patient model with a fixed functional appliance. It is assumed that bone responds to mechanical stresses by showing particular kinds of compressive and tensile stresses. Since stress and strain in living tissues are thought to be key factors in biologic change, it is important to elucidate the stress or strain to understand its relationship to bone remodeling. In orthodontics, various techniques have been used to measure these biomechanical factors. However, it is not always possible with these methods to quantify the stress or strain in an internal area of a living structure.25 Therefore, a technique applicable to biomechanical investigation for stress or strain in biologic tissues is needed. The FEM is applicable to the biomechanical study of strains and stresses generated in internal structures. Other studies have reported the relationship between stresses analyzed by the FEM and biologic changes of bony structures.30-33 The limitation of an FEM study is that it can record only instantaneous stress patterns. In this study, the stress patterns in the mandible in the resting stage and the stress patterns created by simulated mandibular protraction of a fixed functional appliance were elucidated. The purpose of this study was to evaluate the stress pattern distribution in different parts of the mandible and associated structures with a fixed functional appliance (Forsus Fatigue Resistant Device) on a patient using the FEM with a CBCT-generated 3D image. MATERIAL AND METHODS
This study was designed to evaluate stress pattern distributions in different regions of the mandible with the Forsus appliance using the FEM. A 15-year-old girl with a typical Class II Division 1 malocclusion with an overjet of 11 mm was selected. Her chief complaint was an unpleasant appearance and backwardly positioned mandibular front teeth. After a clinical examination, the patient was planned to be treated with a fixed functional appliance, the Forsus. She had a skeletal Class II relationship with an almost normal maxilla, a retrognathic mandible, a positive visual treatment objective, an abnormal musculature, and a favorable growth pattern. All pretreatment records were taken for the patient including study models, photographs, CBCT scans, and interocclusal biting force recordings. The Forsus was planned to be given to the patient. Informed consent was obtained from the patient's parents for her to
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Fig 1. Mesh diagram of a complete mandible.
participate in the study. The DICOM images of the mandible, TMJ, and associated structures were generated using CBCT scans to construct the mesh diagram (Fig 1) for the finite element analysis with Mimics software (version 8.11; Materialise HQ, Leuven, Belgium) and HyperWorks software (version 9.0; Altair Engineering, Huntsville, Ala). Full bonding and banding of the maxillary and mandibular arches was done using a 0.022-in MBT (Mclaughlin Bennett Trevisi) prescription. After leveling and alignment, the arches were U-shaped but in a Class II relationship. When the rectangular wire stage reached 0.019 3 0.025-in stainless steel, the Forsus appliance was used in single-step advancement. The attachment of the appliance was at the canine and premolar interface. The horizontal force values were calculated with a Dontrix gauge (American Orthodontics, Sheboygan, Wis). The vertical forces were recorded with a custom-made pressure sensor by placing the sensor in the molar region. The muscles also exert forces on the mandible. Therefore, it is necessary to calculate the musculature forces for the assessment of the stress patterns on the mandible. The muscle areas were constructed by taking references from books of anatomy; however, interocclusal bite force recordings are specific for each patient. Muscle force in maximum intercuspation was calculated by multiplying the physiologic cross-sectional areas of the each masticatory muscle by 0.37 3 102 N. For the masseter, the calculated muscle force was 388.5 N; for the lateral pterygoid, it was 37 N; for the medial pterygoid, it was 432.9 N; and for the temporalis, it was 333 N, as shown in Figures 2 and 3 and Table I, as per the chart.34 The duration of treatment was 1 year 8 months.
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Table I. Physiologic cross-sectional areas (PCS) of the
each masticatory muscle and calculated biting force Muscle Masseter Temporalis Medial pterygoid Lateral pterygoid
PCS (cm2) 10.5 9 11.7 1.0
Force (N) 388.5 333 432.9 37
Fig 2. Muscular forces exerted by the lateral and medial pterygoid muscles.
Fig 4. Von Mises stress contours in cortical bone.
Fig 3. Muscular forces exerted by the masseter and temporalis muscles.
For the finite element model construction, a CBCT scan of the tooth and the mandible was taken into the Mimics software. Surface data of the metal casting and the mandible were generated using Solid Edge 2004 software (Siemens, Plano, Tex). From the 3D image of the CBCT, a mesh diagram was generated using the HyperWorks software. Finite element models were constructed from the DICOM images of slices 1 mm thick generated by the DICOM software. The assembled finite element model of the mandible was imported into Ansys software (version 12.1; Canonsburg, Pa) for analysis. The material properties assigned were Young's modulus (or modulus of elasticity) and the Poisson ratio.20 A vertical biting force of 111.55 N was applied in the molar region, and a horizontal force of 1948.24 N was seen distal to the canine in the horizontal direction. The model was restricted at the outer part of the skull at its most posterosuperior edges. This allowed the visualization of deformation and stress generation in the mandible. RESULTS
The results showed changes in terms of von Mises stresses and principal stresses. The total number of
nodes was 462542, along with total elements numbering 92972. The color changes in terms of areas of maximum and minimum stresses were seen after the material properties were assigned. Red shows the maximum principal stress region, which is mainly tensile stress, and blue shows the minimum principal stress region, which is compressive stress. The results of this FEM analysis showed the areas of tension and compression in the mandible and associated structures. The results were calculated in terms of von Mises and principal stresses in the following regions: cortical bone, teeth, and condylar head. In the resting stage of the mandible, the highest von Mises stresses were 55.103 MPa in the cortical bone (Fig 4), 27.91 MPa in the teeth (Fig 5), and 4.098 MPa in the condyle (Fig 6). The maximum principal stresses were 65.066 MPa in the cortical bone (Fig 7), 20.96 MPa in the teeth (Fig 8), and 4.117 MPa in the condyle (Fig 9). There were changes with the fixed functional appliance. The highest von Mises stresses were 166.918 MPa in the cortical bone (Fig 10), 329.707 MPa in the teeth (Fig 11), and 10.559 MPa in the condyle (Fig 12). The maximum principal stresses were 145.016 MPa in the cortical bone (Fig 13), 187.077 MPa in the teeth (Fig 14), and 11.725 MPa in the condyle (Fig 15).
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Fig 5. Von Mises stress contours in teeth.
Fig 7. Principal stress contours in cortical bone in resting stage.
Fig 6. Von Mises stress contours in condyle.
Fig 8. Principal stress contours in teeth in resting stage.
DISCUSSION
The FEM is a computational technique used to obtain approximate solutions of boundary-value problems in engineering. The FEM makes it practicable to elucidate biomechanical components such as displacements, strains, and stresses induced in living structures from various external forces. Biomechanical studies have shown that the compressive and tensile stresses from functional orthopedic forces are the key determinants to remodeling of the bones.25,35 The limitation of an FEM study is that it can record only instantaneous stress patterns. In this study, the finite element model was constructed to evaluate the stress patterns on different parts of the mandible. Since we know that functional appliances bring the mandible forward, the muscles also get
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stretched, and there is some growth in the TMJs as well. Our findings suggest that the remodeling of the bone to mechanical forces might be correlated with the location of the tensile and compressive stress patterns. The mandible, the articular disc in the TMJ, and the condylar head are also affected during clenching of the teeth.36 In some previous FEM studies, the effects of the masticatory muscles were neglected; in other studies, muscle forces in different amounts and proportions were applied to the model. The mandible is not a static structure that carries only the loads that affect it. The mandibular position is maintained by the harmonious balance of muscles, connecting tissues, neural system, and facial skin. For this reason, we also considered the muscle forces acting on the mandible in the resting stage.
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Fig 9. Principal stress contours in condyle in resting stage.
Fig 11. Von Mises stress contours in teeth with Forsus.
Fig 10. Von Mises stress contours in cortical bone with Forsus.
Fig 12. Von Mises stress contours in condyle.
In the resting stage of the mandible, von Mises stress in the cortical bone is maximum at the neck of the condyle, probably because of the stretch of the lateral pterygoid muscle, the middle of the sigmoid notch, and a small part on the posterior border of the ramus, whereas the head of the condyle, the coronoid process, the angle of the mandible, and most of the body of the mandible show minimum stress (Table II). In an FEM study on mandibular first premolars, Tanne et al37 investigated the stress levels induced in the periodontal tissues by orthodontic forces and observed the highest stress, approximately 120 g/cm2, at the level of the cervix on the buccal and lingual points, with a gradual reduction to zero stress near the center of the root. In a similar study using the FEM, McGuinness et al38 determined the stress induced in the periodontal liga6ment in 3 dimensions when a maxillary canine was
subjected to an orthodontic force similar to that produced by an edgewise appliance. The maximum stress induced at the cervical margin of the periodontal ligament was 0.072 N/mm2. In the resting stage, the maximum principal stresses in the cortical bone were seen at the neck of the condyle and the middle of the sigmoid notch because of the attachments of the muscles in the corresponding areas (Table II). With a fixed functional appliance, the highest von Mises stresses in the cortical bone were from the canine to the premolar area and in the sigmoid notch (Table III). In the resting stage, it was maximum at the neck of the condyle, the middle of the sigmoid notch, and a small part on the posterior border of the ramus, whereas the head of the condyle, the coronoid process, the angle of the mandible, and most of the body of the mandible
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Fig 13. Principal stress contours in cortical bone with Forsus.
Fig 15. Principal stress contours in condyle with Forsus. Table II. Resting stage of the mandible Part Cortical bone Teeth Condyle
Von Mises stress (MPa) 55.103 27.91 4.098
Principal stress (MPa) 65.066 20.96 4.117
Table III. Patient with the Forsus Part Cortical bone Teeth Condyle
Von Mises stress (MPa) 166.918 329.707 10.559
Principal stress (MPa) 145.016 187.077 11.725
Table IV. Maximum von Mises stresses in 2 models of
the Forsus Fig 14. Principal stress contours in teeth with Forsus.
showed minimum stresses. In the cortical bone, there was an increase by 3 times in the stress when the patient was wearing the Forsus. The teeth showed an increase in stress of almost 12 times with the Forsus because it is a tooth-borne appliance, whereas in the condyle, there was an increase of more than 2 times during appliance wear because of the constant sagittal positioning of the mandible (Table IV). Ulusoy and Darendeliler34 studied the stress region with the FEM in a dry human mandible with the Class II activator and the Class II activator and high-pull headgear combination. They found that the regions near the muscle attachments were affected the most. The inner part of the coronoid process and the gonial area had the maximum stress values. The stress regions formed by the Class II activator showed that the slope between the coronoid and condylar processes and the anterior
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Part Cortical bone Teeth Condyle
Resting stage of mandible (MPa) 55.103 27.91 4.098
With Forsus (MPa) 166.918 329.707 10.559
medial surface of the coronoid process were the most affected regions. A von Mises stress value of 8.556 MPa was recorded on the medial side of the coronoid process. The stress regions formed by the Class II activator high-pull headgear showed that the slopes between the coronoid and condylar processes and the anterior medial surface of the coronoid process were the most affected regions. In our study, the maximum principal stresses in the cortical bone were from the canine to the molar area, in the condylar neck, and in the sigmoid notch (Table III), whereas in the resting stage, the maximum principal stresses were seen at the neck of the condyle and the
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Table V. Maximum principal stresses in 2 models of
2.
the Forsus Part Cortical bone Teeth Condyle
Resting stage of mandible (MPa) 65.066 20.96 4.117
3. With Forsus (MPa) 145.016 187.077 11.725
With the appliance, the increases in the von Mises stress were by 3 times in the cortical bone and by more than 2 times in the condyle. With the appliance, the maximum principal stress increased by more than 2 times in the cortical bone and by more than 3 times in the condyle.
REFERENCES
middle of the sigmoid notch. In the teeth, these were seen in the roots of the canines; in the resting stage, the maximum stress was seen at the distal root of the first molar. In the condyle, it was in the posterior region of the superior surface. In the cortical bone, the principal stress increased by more than 2 times, and the teeth showed an increase in stress of 9 times when compared with the resting stage. The increase in stress in the condyle was 3 times (Table V). In a magnetic resonance imaging study, Gupta et al21 evaluated patterns of stress generation in the TMJ after mandibular protraction with different types of construction bites, where they changed the vertical opening but kept the sagittal advancement the same. Tensile stresses migrated more posteriorly on the condylar head with increased bite height. The locations of the tensile stresses in the glenoid fossa were similar in all simulations, and the TMJ as a whole showed increased loading with increasing vertical openings. In a similar study, we compared the stress generation in 3 models of the mandible with the Twin-block appliance.39 In the first model, the stress pattern in the resting stage—ie, only with the muscular forces—was seen. In the second and third models, with the Twin-block appliance, the vertical height of the bite was kept constant, and the horizontal advancement was changed. On checking the von Mises stress and principal stress pattern developed by the removable appliance, we found that the stress pattern generated by the Forsus was much higher. CONCLUSIONS
In this study, we ventured toward understanding the different biomechanical stresses produced in the various regions of mandible by a fixed functional appliance. When the mandible is protracted, a pattern of stresses is created in the TMJ and the mandible. The stress distribution in the whole mandible was determined using the finite element model constructed from a DICOM image generated by CBCT. 1.
With the Forsus, a tooth-supported appliance, both the von Mises and principal stresses increased many more times in the teeth than in the mandible at the resting stage.
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