The transfer of occlusal forces through the maxillary molars: a finite element study

Orthodontic maxillary molar movement-induced zygomatic pillar remodeling and its consequences on occlusal characteristics and stress distribution

OBJECTIVE

We aimed to evaluate changes in the zygomatic pillar during orthodontic treatment involving premolar extraction, analyze the effects of maxillary first molar movement on zygomatic pillar remodeling, and examine occlusal characteristics and stress distribution after remodeling.

METHODS

Twenty-five patients who underwent premolar extraction were included in the study. The zygomatic pillar measurement range was defined, and cross-sectional areas, surface landmark coordinates, alveolar and cortical bone thicknesses, and density changes were assessed using Mimics software based on the cone-beam computed tomography scans taken before (T0) and after the treatment (T1). Multiple linear regression analysis was performed to determine the correlation between changes in the zygomatic pillar and maxillary first molar three-dimensional (3D) movement and rotation. Additionally, the correlation between pillar remodeling and occlusal characteristics was analyzed by Teetester. Pre- and post-reconstruction 3D finite element models were constructed and loaded with an average occlusal force of two periods.

RESULTS

The morphological and structural remodeling of the zygomatic pillar after orthodontic treatment involving premolar extraction showed a decreased cross-sectional area of the lower segment of the zygomatic pillar. The zygomatic process point moved inward and backward, whereas the zygomatico-maxillary suture point moved backward. The thicknesses of the zygomatic pillar alveolar and cortical bones were thinner, and reduced alveolar bone density was observed. Simultaneously, the movement and angle change of the maxillary first molar could predict zygomatic pillar reconstruction to a certain extent. With decreasing the total occlusal force and the occlusal force of the first molar, occlusal force distribution was more uniform. With zygomatic pillar remodeling, occlusal stress distribution in the zygomatic alveolar ridge decreased, and occlusal stress was concentrated at the junction of the vertical and horizontal parts of the zygomatic bone and the posterior part of the zygomatic arch.

CONCLUSIONS

Orthodontic treatment involving premolar extraction led to zygomatic pillar remodeling, making it more fragile than before and reducing the occlusal force of the maxillary first molar and the entire dentition with stress concentrated in weak areas.

CLINICAL RELEVANCE

No other study has focused on the effects of orthodontics on pillar structures. The present study indicates that the mesial movement of the maxillary first molar weakened the zygomatic pillar and reduced occlusal function, thereby providing insights for inserting anchorage screws and facial esthetics.

Stress Trajectory Variations During Occlusal Loading in Human Skull with a Maxillofacial Defect: A Finite Element Analysis

Background and Aim

Biting forces from the teeth are distributed to the facial bones and to the skull through the stress trajectories. The presence of a bony defect in either the maxilla or mandible might lead to variations in the stress distribution. The aim of this study was to evaluate the stress distribution and variations in stress trajectories from biting forces in a human skull with maxillofacial defect using a finite element (FE) model.

Methodology

In this study, a cone beam computed tomography (CBCT) of an adult male patient with a maxillectomy defect consequent to surgical treatment of mucormycosis is evaluated for the stress distribution from the biting forces of the remaining posterior teeth. Finite element model without the mandible was constructed from the patient's CBCT data. Occlusal loading forces of 600 N were applied on each side of the maxillary teeth. Stress trajectories were visualised through the stress distribution pattern.

Results

The results showed deviations in the normal stress distribution during occlusal loading and variations in zygomatic and pterygoid stress trajectories in the maxillofacial and skull regions in our FE model due to the bony defect.

Conclusion

We conclude that a skeletal maxillofacial defect should be reconstructed to resume proper stress distribution during functional forces to maintain a healthy craniofacial skeleton.

Three-dimensional location and distribution of the center of resistance in the maxillary first molar applied to occlusal force

We aimed to investigate the center of resistance (CRes) of the maxillary first molar to set the occlusal force through finite element analysis. The inclination of the molar was measured, with loading to the root on the crown, and the position and direction of the load that minimized the inclination were investigated. The CRes was defined as the set of midpoints of the minimum distances between the two lines. Nine hundred and ninety CRes points were estimated from forty-five lines. The CRes was estimated as the point 1.22 mm (Z), -0.74 mm (X), and 0.23 mm (Y) from the origin in the apical, distal, and buccal side directions, respectively, with an ellipsoid area of 1.578 (Z) mm×0.097 (X) mm×0.100 (Y) mm. Further research is required to make effective use of the CRes identified in this study for clinical applications.

Study on the Effects of Orthodontics on Anterior Tooth Displacement in Patients

Objective

The purpose of this study was to investigate the therapeutic effect of orthodontic treatment on anterior tooth displacement caused by periodontal disease.

Methods

A prospective study was performed in 86 patients with anterior tooth displacement caused by periodontal disease. These patients were divided into the experimental group and the control group according to the intervention methods. For the control group, patients were treated with conventional therapy. The experimental group used straight wire orthodontic technique for orthodontic treatment on the basis of conventional treatment. Comparisons were performed between two groups in term of bleeding index, alveolar bone height, anterior tooth coverage, periodontal pocket depth, probing depth, clinical crown length, tooth root length, inflammatory cytokines levels, and orthodontic satisfaction.

Results

Comparison of bleeding index, alveolar bone height, anterior tooth coverage, periodontal pocket depth, probing depth, clinical crown length, tooth root length, and inflammatory cytokines levels between two groups before treatment indicated that there were no statistical differences (all P > 0.05). After treatment, bleeding index, alveolar bone height, anterior tooth coverage, periodontal pocket depth, probing depth, clinical crown length, and serum levels of IL-6 and TNF-α in the experimental group were lower than those in the control group (all P < 0.05), while the serum level of IL-2 in the experimental group was more than that in the control group (P < 0.05). Also, there was no difference for tooth root length between two groups. Moreover, compared with the control group, orthodontic satisfaction in the experimental group was significantly increased.

Conclusion

The efficacy of orthodontic treatment in patients with anterior tooth displacement caused by periodontal disease is higher than that of only using conventional therapy, as it helps improve their periodontal health, alveolar bone height, clinical crown length, inflammatory factor levels, and orthodontic satisfaction of patients.

Improvement of an additively manufactured subperiosteal implant structure design by finite elements based topological optimization

To design a new subperiosteal implant structure for patients suffering from severe Maxillary Atrophy that lowers manufacturing cost, shortens surgical time and reduces patient trauma with regard to current implant structures. A 2-phase finite-element-based topology optimization process was employed with implants made from biocompatible materials via additive manufacturing. Five bite loading cases related to standard chewing, critical chewing force, and worst conditions of fastening were considered along with each specific result to establish the areas that needed to be subjected to fatigue strength optimization. The 2-phase topological optimization tested in this study performed better than the reference implant geometry in terms of both the structural integrity of the implant under tensile-compressive and fatigue strength conditions and the material constraints related to implant manufacturing conditions. It returns a nearly 28% lower volumetric geometry and avoids the need to use two upper fastening screws that are required with complex surgical procedures. The combination of topological optimization methods with the flexibility afforded by additively manufactured biocompatible materials, provides promising results in terms of cost reduction, minimizing the surgical trauma and implant installation impact on edentulous patients.

Occlusal stress distribution in the human skull with permanent maxillary first molar extraction: A 3-dimensional finite element study

INTRODUCTION

The objective of this research was to analyze the effect of orthodontic treatment with maxillary permanent first molar extraction on the occlusal stress distribution and displacement in the human skull.

METHODS

A 3-dimensional finite element model was constructed on the basis of a computed tomography scan, and it was used as the pretreatment model. The software used for geometric modeling was Solid Works (Dassault Systèmes, Paris, France). For the extraction model, the maxillary permanent first molar was removed, followed by a repositioning of the anterior and posterior segments to create a space closure model. Stress distribution was evaluated under the simulation of 1000 N for occlusal forces and 400 N for masseter muscle force.

RESULTS

The highest von Mises stress was observed at the zygomatic process of the temporal bone across all 3 models (25 MPa), whereas stress at the pterygomaxillary suture area was almost 50% less. However, the stress in the pterygomaxillary suture area was lowest in the extraction model (18%) and space closure (30%). Stress in the zygomatic process of the frontal bone and frontal process of the maxilla increased from pretreatment to extraction model followed by space closure model.

CONCLUSIONS

The occlusal forces were transferred through maxillonasal, maxillozygomatic, and maxillopterygoid stress trajectories. The mesial displacement of the molars may weaken the role of maxillopterygoid stress trajectory while strengthening the role of maxillonasal stress trajectory.

Micro computed tomography evaluation of Invisalign aligner thickness homogeneity

OBJECTIVES

To measure the thickness homogeneity of Invisalign (Align Technology Inc, San José, Calif) aligners with micro-computed tomography (micro-CT) scans.

MATERIALS AND METHODS

Starting from micro-CT scanning of 20 different aligners, multiplanar reconstructions were obtained. An orthodontist blinded about the study measured aligner thickness in different regions (molar, canine, incisor) and in different sites (gingival-buccal, buccal, occlusal, lingual, and gingival-lingual). To assess various thicknesses in different aligner sites and regions, the sample was stratified into subgroups and linear regression analysis was performed.

RESULTS

Descriptive analysis showed that mean thickness of aligners in the incisor region ranged from 0.582 mm to 0.639 mm, in the canine region from 0.569 mm to 0.644 mm, and in the molar region from 0.566 mm to 0.634 mm. Student's t-tests showed no significant differences in the aligner thickness of different regions when data were stratified by different sites. Student's t-tests showed significant differences in thickness homogeneity for the molar region when the data were stratified by tooth (mean difference = 0.068 mm; 95% confidence interval, 0.009-0.126 mm; P = .024).

CONCLUSIONS

Invisalign aligner thickness is characterized by small differences. The only significant difference was revealed in the molar region where thickness of the gingival-lingual edge is significantly thinner than that measured at the occlusal aspect. From a clinical perspective, the results of the present study could be considered to explain the reduced predictability of several orthodontic tooth movements in the molar region.

Evaluation of condylar cortical bone thickness in patient groups with different vertical facial dimensions using cone-beam computed tomography

The aim of this study is to evaluate through computed tomography differences in cortical plate thickness of condyle in patients with a different facial vertical skeletal pattern. The final sample of this retrospective study included CBCT exams of 60 adult subjects (mean age 33.2 ± 5.6), selected from the digital archive of a private practice. The subjects were assigned to 3 different groups according to the values of the Frankfurt-mandibular plane angle: hyper-, normo-, and hypodivergent groups. The volume rendering of the mandible was obtained and three condylar points were marked on it: median pole, lateral pole and the most cranial point. For each considered reference point, the minimum distance between external and internal cortical surface was measured, obtaining three different outcomes: condylar cortical bone thickness of median pole (CCBToMP), lateral pole (CCBToLP) and cranial pole (CCBToCP). The measurements were executed by means of Mimics software by the same expert operator in specific scan views. The cortical bone thickness of hyperdivergent patients was found to be statistically thicker than normodivergent patients and hypodivergent patients. Cortical bone thickness of normodivergent patients was found thicker than hypodivergent patients. All the differences were statistically significant (p < 0.05). The Pearson correlation coefficient showed a statistically significant correlation (p < 0.001) between the Frankfurt-mandibular plane angle and the evaluated cortical bone thickness outcomes. Facial biotype characteristics that define vertical facial skeletal pattern affect the cortical bone thickness of mandibular condyle.

A REVIEW OF FINITE ELEMENT APPLICATIONS IN ORAL AND MAXILLOFACIAL BIOMECHANICS

Finite element method (FEM) is preferred to carry out mechanical analyses for many complex biomechanical structures. For most of the biomechanical models such as oral and maxillofacial structures or patient-specific dental instruments, including nonlinearities, complicated geometries, complex material properties, or loading/boundary conditions, it is not possible to accomplish an analytical solution. The FEM is the most widely used numerical approach for such cases and found a wide range of application fields for investigating the biomechanical characteristics of oral and maxillofacial structures that are exposed to external forces or torques. The numerical results such as stress or strain distributions obtained from finite element analysis (FEA) enable dental researchers to evaluate the bone tissues subjected to the implant or prosthesis fixation from the viewpoint of (i) mechanical strength, (ii) material properties, (iii) geometry and dimensions, (iv) structural properties, (v) loading or boundary conditions, and (vi) quantity of implants or prostheses. This review paper evaluates the process of the FEA of the oral and maxillofacial structures step by step as followings: (i) a general perspective on the techniques for creating oral and maxillofacial models, (ii) definitions of material properties assigned to oral and maxillofacial tissues and related dental materials, (iii) definitions of contact types between tissue and dental instruments, (iv) details on loading and boundary conditions, and (v) meshing process.

Cell Mechanics of Craniosynostosis

Craniosynostosis is the premature fusion of the calvarial sutures that is associated with a number of physical and intellectual disabilities spanning from pediatric to adult years. Over the past two decades, techniques in molecular genetics and more recently, advances in high-throughput DNA sequencing have been used to examine the underlying pathogenesis of this disease. To date, mutations in 57 genes have been identified as causing craniosynostosis and the number of newly discovered genes is growing rapidly as a result of the advances in genomic technologies. While contributions from both genetic and environmental factors in this disease are increasingly apparent, there remains a gap in knowledge that bridges the clinical characteristics and genetic markers of craniosynostosis with their signaling pathways and mechanotransduction processes. By linking genotype to phenotype, outlining the role of cell mechanics may further uncover the specific mechanotransduction pathways underlying craniosynostosis. Here, we present a brief overview of the recent findings in craniofacial genetics and cell mechanics, discussing how this information together with animal models is advancing our understanding of craniofacial development.

Review of In Vivo Bone Strain Studies and Finite Element Models of the Zygomatic Complex in Humans and Nonhuman Primates: Implications for Clinical Research and Practice

The craniofacial skeleton is often described in the clinical literature as being comprised of vertical bony pillars, which transmit forces from the toothrow to the neurocranium as axial compressive stresses, reinforced transversely by buttresses. Here, we review the literature on bony microarchitecture, in vivo bone strain, and finite-element modeling of the facial skeleton of humans and nonhuman primates to address questions regarding the structural and functional existence of facial pillars and buttresses. Available bone material properties data do not support the existence of pillars and buttresses in humans or Sapajus apella. Deformation regimes in the zygomatic complex emphasize bending and shear, therefore conceptualizing the zygomatic complex of humans or nonhuman primates as a pillar obscures its patterns of stress, strain, and deformation. Human fossil relatives and chimpanzees exhibit strain regimes corroborating the existence of a canine-frontal pillar, but the notion of a zygomatic pillar has no support. The emerging consensus on patterns of strain and deformation in finite element models (FEMs) of the human facial skeleton corroborates hypotheses in the clinical literature regarding zygomatic complex function, and provide new insights into patterns of failure of titanium and resorbable plates in experimental studies. It is suggested that the "pillar and buttress" model of human craniofacial skeleton function be replaced with FEMs that more accurately and precisely represent in vivo function, and which can serve as the basis for future research into implants used in restoration of occlusal function and fracture repair. Anat Rec, 299:1753-1778, 2016. © 2016 Wiley Periodicals, Inc.

Relationship between molar occlusion and masticatory movement in lateral deviation of the mandible

INTRODUCTION

The relationship between molar occlusion and chewing patterns was examined in subjects with laterally deviated mandibles.

METHODS

Twenty-three patients with mandibular deviation from the midline (4 mm or more) and skeletal Class I (0° ≤ANB ≤4°) were divided into 2 groups: normal bite and crossbite. The chewing pattern was classified as normal, reversed, or crossover.

RESULTS

The normal bite group had a normal chewing pattern on the affected side 100% of the time and a reversed chewing pattern on the affected and unaffected sides 0% and 7.2% of the time, respectively. Additionally, the normal bite group showed no evidence of a crossover chewing pattern and also had significantly less axial inclination of the mandibular teeth on the affected side compared with the crossbite group; lingual inclination was also evident. The crossbite group had a normal chewing pattern on the affected and unaffected sides 0% and 55.6% of the time, respectively, and reversed and crossover chewing patterns on the affected side 55.6% and 44.4% of the time, respectively.

CONCLUSIONS

A normal chewing pattern tends to result in lingual axial inclination of the mandibular molars on the affected side, as well as a more consistent chewing pattern.

Dynamic finite element simulation of dental prostheses during chewing using muscle equivalent force and trajectory approaches

The long-term application of dental prostheses inside the bone has a narrow relation to its biomechanical performance. Chewing is the most complicated function of a dental implant as it implements different forces to the implant at various directions. Therefore, a suitable holistic modelling of the jaw bone, implant, food, muscles, and their forces would be deemed significant to figure out the durability as well as functionality of a dental implant while chewing. So far, two approaches have been proposed to employ the muscle forces into the Finite Element (FE) models, i.e. Muscle Equivalent Force (MEF) and trajectory. This study aimed at propounding a new three-dimensional dynamic FE model based on two muscle forces modelling approaches in order to investigate the stresses and deformations in the dental prosthesis as well as maxillary bone during the time of chewing a cornflakes bio. The results revealed that both contact and the maximum von Mises stress in the implant and bones for trajectory approach considerably exceed those of the MEF. The maximum stresses, moreover, are located around the neck of implant which should be both clinically and structurally strong enough to functionally maintain the bone-implant interface. In addition, a higher displacement due to compressive load is observed for the implant head in trajectory approach. The results suggest the benefits provided by trajectory approach since MEF approach would significantly underestimate the stresses and deformations in both the dental prosthesis and bones.

Maxillary Sinus Augmentation without Grafting Material with Simultaneous Implant Installation: A Three-Dimensional Finite Element Analysis

PURPOSE

The study aims to provide a theoretical guidance of postmaxillary implant in the augmented sinus without grafting materials by establishing a three-dimensional model of this new implant restorative technique, evaluating failure risk of sinus augmentation without grafting materials of different alveolar ridge heights, and analyzing stress distribution of different healing stage.

MATERIALS AND METHODS

Seventeen three-dimensional finite element models of a posterior maxillary region with sinus mucosa and different elevation heights were constructed according to anatomical data of sinus area, and the standard implant model based on Nobel Biocare implant system were created via computer-aided design software. All materials were assumed to be isotropic and linearly elastic. Axial force of 150 N was applied. The von Mises stress, stress distribution, and implant displacement were calculated with software.

RESULTS

With the height of the alveolar ridge reducing, the maximum von Mises stress of tissues and the displacement of the implant are on the rise, especially when the height of the bone is less than 7 mm. When the height decreased to 4 mm, the data may be doubled. After the stiff callus stage, the stress and displacement were close to the control model.

CONCLUSION

For maxillary sinus augmentation without grafting material implant technique, the stress of different tissues and the displacement of the implant were not increased much when the height of alveolar ridge is more than 7 mm. But if the alveolar bone height is less than 4 mm, this implant technique is not suggested. Immediately loading is not suggested and the loading opportunity should be after the stiff callus stage at least to improve the success rate.

Finite element analysis of three zygomatic implant techniques for the severely atrophic edentulous maxilla

STATEMENT OF PROBLEM

A variety of zygomatic implantation techniques currently exist; however, a consensus regarding the most suitable method has not yet been reached.

PURPOSE

The purpose of this study was to evaluate and compare 3 zygomatic implantation techniques and to clarify the optimal number and position of zygomatic and dental implants for the reconstruction of the severely atrophied edentulous maxilla.

MATERIAL AND METHODS

A 3-dimensional finite element analysis craniofacial model was constructed from the computed tomography data of a selected patient with a severely atrophic edentulous maxilla. Modeled zygomatic implants were inserted into the craniofacial model with 3 surgical techniques (classic Brånemark, exteriorized, and extramaxillary), and with 3 model variations that involved the number and position of zygomatic and dental implants. The zygomatic implants were loaded with a vertical force of 150 N and a lateral force of 50 N. The stresses on and deformations of the bones and implants were then observed and compared.

RESULTS

No obvious differences in the amount and distribution of stress on the external craniofacial bones were detected in the models. The lowest stresses on the zygomatic implants were observed in the exteriorized technique group. The lowest deformations of the bone that surrounds zygomatic implants and dental implants were observed in the exteriorized technique and classic Brånemark technique groups. For the exteriorized technique group, the model with 1 dental implant in the site of the maxillary lateral incisor exhibited the lowest stress on the zygomatic implants and the least deformation of the bone surrounding the zygomatic and dental implants.

CONCLUSIONS

All 3 zygomatic implant techniques resulted in more or less homogeneous transference of force and thus could reconstruct the edentulous maxilla; however, the exteriorized technique with 1 dental implant in the lateral incisor appeared to be the most appropriate reconstruction method for the severely atrophied edentulous maxilla.

Effect of bite force on orthodontic mini-implants in the molar region: Finite element analysis

Objective

To examine the effect of bite force on the displacement and stress distribution of orthodontic mini-implants (OMIs) in the molar region according to placement site, insertion angle, and loading direction.

Methods

Five finite element models were created using micro-computed tomography (microCT) images of the maxilla and mandible. OMIs were placed at one maxillary and two mandibular positions: between the maxillary second premolar and first molar, between the mandibular second premolar and first molar, and between the mandibular first and second molars. The OMIs were inserted at angles of 45° and 90° to the buccal surface of the cortical bone. A bite force of 25 kg was applied to the 10 occlusal contact points of the second premolar, first molar, and second molar. The loading directions were 0°, 5°, and 10° to the long axis of the tooth.

Results

With regard to placement site, the displacement and stress were greatest for the OMI placed between the mandibular first molar and second molar, and smallest for the OMI placed between the maxillary second premolar and first molar. In the mandibular molar region, the angled OMI showed slightly less displacement than the OMI placed at 90°. The maximum Von Mises stress increased with the inclination of the loading direction.

Conclusions

These results suggest that placement of OMIs between the second premolar and first molar at 45° to the cortical bone reduces the effect of bite force on OMIs.

Three-dimensional finite element analysis of occlusal stress distribution in the human skull with premolar extraction

Objective:

To analyze the effect of orthodontic treatment with premolar extraction on the stress distribution of the occlusal force in the human skull.

Materials and Methods:

A three-dimensional finite element (3D FE) model was constructed based on computed tomography scan data, and it served as the pretreatment model. For the extraction model simulating postorthodontic occlusion, the first premolar was removed in the pretreatment model, and the anterior and posterior segments were repositioned. Stress distribution was evaluated by 3D FE analysis in both models under the simulation of 1000 N for occlusal forces and 400 N for masseter muscle force.

Results:

The occlusal stresses were concentrated at the alveolar bone near the teeth, the infrazygomatic crest, the frontal process, the temporal process of the zygomatic bone, the infraorbital rim, the pyriform aperture region, and the pterygoid plate in both models. The von Mises stress at the pterygoid plate area was lower in the extraction model (3.53 MPa) than in the pretreatment model (5.57 MPa), while the stress at the frontal process of the maxilla was higher in the extraction model (2.32 MPa) than in the pretreatment model (2.16 MPa).

Conclusions:

The results indicated that the occlusal forces were transferred through the maxillonasal, maxillozygomatic, and maxillopterygoid stress trajectories and that stress distribution moved more “forward” with the orthodontic treatment with premolar extraction.

Accuracy of three-dimensional finite element modeling using two different dental cone beam computed tomography systems

The aim of this study is to evaluate the accuracy of dental ceramic object three dimensional (3D) finite element model constructed directly from two different dental cone beam computed tomography (CT) systems. CT scanned one 10.0 × 10.0 × 20.0 mm block and one 8.0 × 10.0 × 40.0 mm block of an 8-step wedge. All 3D finite element (FE) models were created from CT images. Each 3D FE model measured the length of the directions X, Y, and Z that corresponded to an original specimen using the measurement function between two points on the Mechanical Finder software package. The measurements and practical value were compared with the CT image and the accuracy of the reproduced measurements was examined. No significant differences were found between Alphard-3030 on the Z axis and ProMax 3D on the Y axis of the block. In addition, there were also no significant differences observed between Alphard-3030 on the Y axis and ProMax 3D on the X axis compared with Alphard-3030 on the Z axis and ProMax 3D on the Y axis for the step-wedge. The results suggest that measurement of the dimensions of cone beam CT images could be useful in applications where both good reproducibility and accuracy of FE models are required.

Finite element analysis of different surgical approaches in various occlusal loading locations for zygomatic implant placement for the treatment of atrophic maxillae

The aim of this study was to compare two different types of surgical approaches, intrasinus and extramaxillary, for the placement of zygomatic implants to treat atrophic maxillae. A computational finite element simulation was used to analyze the strength of implant anchorage for both approaches in various occlusal loading locations. Three-dimensional models of the craniofacial structures surrounding a region of interest, soft tissue and framework were developed using computed tomography image datasets. The implants were modelled using computer-aided design software. The bone was assumed to be linear isotropic with a stiffness of 13.4 GPa, and the implants were assumed to be made of titanium with a stiffness of 110 GPa. Masseter forces of 300 N were applied at the zygomatic arch, and occlusal loads of 150 N were applied vertically onto the framework surface at different locations. The intrasinus approach demonstrated more satisfactory results and could be a viable treatment option. The extramaxillary approach could also be recommended as a reasonable treatment option, provided some improvements are made to address the cantilever effects seen with that approach.

Three-dimensional finite-element analysis of a central lower incisor under labial and lingual loads

INTRODUCTION

The aim was to evaluate the differences between labial and lingual application of an orthodontic force. This was achieved using a three-dimensional CAD design software model of a real lower incisor surrounded by a prismatic representation of the mandibular bone. This model was subjected to various loading conditions, with finite-element analysis.

MATERIALS AND METHODS

Cone-beam computed tomography scanning was used to create a three-dimensional geometric model of a lower incisor, together with its simulated periodontal ligament. This model was then meshed and analysed with commercial finite-element code. Various single and combined forces and moments were applied to each side of the simulated lower incisor at the centre of the clinical crown. To evaluate the effects of the various forces considered, the instantaneous displacement and stress generated in the bone and the periodontal ligament were measured, as a comparison of the labial and lingual loading sites.

RESULTS

Dental movement was only influenced by the side of the force application when an intrusive component was present. The simulations showed larger displacement when a vertical force was present at the lingual surface. In general, this movement was of the tipping type when the combined forces were applied, while there was greater intrusion upon application of combined forces and an anticlockwise moment to the labial surface.

CONCLUSIONS

Application of an intrusive lingual force to a lower incisor appears to generate bodily movement, while the same intrusive labial force appears to lead to labial tipping. Subject to further study, this should be taken into consideration when devising treatment plans for fixed appliances.

Stress Analysis of a Class II MO-Restored Tooth Using a 3D CT-Based Finite Element Model

A computational method has been developed for stress analysis of a restored tooth so that experimental effort can be minimized. The objectives of this study include (i) developing a method to create a 3D FE assembly model for a restored tooth based on CT images and (ii) conducting stress analysis of the restored tooth using the 3D FE model established. To build up a solid computational model of a tooth, a method has been proposed to construct a 3D model from 2D CT-scanned images. Facilitated with CAD tools, the 3D tooth model has been virtually incorporated with a Class II MO restoration. The tooth model is triphasic, including the enamel, dentin, and pulp phases. To mimic the natural constraint on the movement of the tooth model, its corresponding mandible model has also been generated. The relative high maximum principal stress values were computed at the surface under loading and in the marginal region of the interface between the restoration and the tooth phases.

Cortical bone thickness at common miniscrew implant placement sites

INTRODUCTION

The purpose of this study was to assess age, sex, and regional differences in the cortical bone thickness of commonly used maxillary and mandibular miniscrew implant placement sites.

METHODS

Cone-beam computed tomography images, taken at 0.39-mm voxel size, of 52 patients, including 26 adolescents (13 girls, ages 11-13; 13 boys, ages 14-16) and 26 adults (13 men and 13 women, ages 20-45), were evaluated. The cone-beam computed tomography data were imported into 3-dimensional software (version 10.5, Dolphin Imaging Systems, Chatsworth, Calif); standardized orientations were used to measure cortical bone thickness at 16 sites representing the following regions: 3 paramedian palate sites, 1 infrazygomatic crest site, 4 buccal interradicular sites of the mandible, and 4 buccal and 4 lingual interradicular sites in the maxilla.

RESULTS

Multivariate analysis of variance (MANOVA) showed no significant differences in cortical bone thickness between the sexes. There were significant (P <0.05) differences between adolescents and adults, with adult cortices significantly thicker in all areas except the infrazygomatic crest, the mandibular buccal first molar-second molar site, and the posterior palate site. Cortical bone was thicker in the posterior than in the anterior mandibular sites. In the adults, interradicular bone in the maxillary first premolar-second premolar, and second premolar-first molar sites was thicker than bone at the lateral incisor-canine and first molar-second molar sites. Anterior paramedian palatal bone was significantly thicker than bone located more posteriorly. The mandibular buccal and infrazygomatic crest regions had the thickest cortical bone; differences between the maxillary buccal, the maxillary lingual, and the palatal regions were small.

CONCLUSIONS

Maxillary and mandibular cortical bones at commonly used miniscrew implant placement sites are thicker in adults than in adolescents. There are also differences in cortical bone thickness between and within regions of the jaws that must be considered when placing miniscrew implants.

Cross-sectional human mandibular morphology as assessed in vivo by cone-beam computed tomography in patients with different vertical facial dimensions

INTRODUCTION

The goal of this study was to look at mandibular cortical bone in live patients using cone-beam computed tomography (CBCT) to determine differences in cortical plate thicknesses and mandibular cross-sectional height and width in patients with different vertical facial dimensions.

METHODS

A total of 111 scanned patients were used. Of these subjects, 43 were included in the average vertical facial dimension group (average face), 34 in the high vertical facial group (long face), and 34 in the low vertical facial group (square short face). Cross-sectional slices of the mandible were developed with the cone-beam scans to evaluate the cortical bone between the dentition at 13 locations. Each section was then measured at 8 sites, which included 1 height and 2 width measures of the cross-sectional area and 5 cortical plate thicknesses. An analysis of variance (ANOVA) with a posthoc Bonferroni statistical analysis was used with a significance level of P  ≤0.0167.

RESULTS

The long-face group had slightly more narrow cortical bone than the other 2 facial groups at a few selected sites of the mandible. The height of the cross-sectional area of the mandible in the long-face group was shorter posteriorly than in the other 2 groups and became greater toward the symphysis.

CONCLUSIONS

Mandibular height and width differed more than cortical bone thickness among the 3 types of subjects with different vertical facial dimensions, but statistically significant differences were evident is some sites for cortical bone thickness.

Numerical fatigue 3D-FE modeling of indirect composite-restored posterior teeth

OBJECTIVE

In restored teeth, stresses at the tooth-restoration interface during masticatory processes may fracture the teeth or the restoration and cracks may grow and propagate. The aim was to apply numerical methodologies to simulate the behavior of a restored tooth and to evaluate fatigue lifetimes before crack failure.

MATERIALS AND METHODS

Using a CAD-FEM procedure and fatigue mechanic laws, the fatigue damage of a restored molar was numerically estimated. Tessellated surfaces of enamel and dentin were extracted by applying segmentation and classification algorithms, to sets of 2D image data. A user-friendly GUI, which enables selection and visualization of 3D tessellated surfaces, was developed in a MatLab(®) environment. The tooth-boundary surfaces of enamel and dentin were then created by sweeping operations through cross-sections. A class II MOD cavity preparation was then added into the 3D model and tetrahedral mesh elements were generated. Fatigue simulation was performed by combining a preliminary static FEA simulation with classical fatigue mechanical laws.

RESULTS

Regions with the shortest fatigue-life were located around the fillets of the class II MOD cavity, where the static stress was highest.

SIGNIFICANCE

The described method can be successfully adopted to generate detailed 3D-FE models of molar teeth, with different cavities and restorative materials. This method could be quickly implemented for other dental or biomechanical applications.

Análise do movimento inicial de molares superiores submetidos a forças extrabucais: estudo 3D

OBJETIVO: analisar pelo método dos elementos finitos o deslocamento dos molares superiores frente a três diferentes inclinações do arco externo do aparelho extrabucal na tração do tipo cervical. MÉTODOS: maxila, dentes montados em má oclusão de Classe II e aparelho foram modelados através de formulação variacional e seus valores reproduzidos em coordenadas X, Y e Z. Foram realizadas simulações em microcomputador tipo PC, utilizando o programa ANSYS versão 8.1. Cada modelo de arco externo reproduziu linhas de força que passaram (1) acima (AcCR), (2) abaixo (AbCR) e (3) no centro de resistência (CR) do molar permanente superior de um mesmo modelo portador de má oclusão de Classe II. A avaliação restringiu-se ao movimento inicial dos molares frente à força extrabucal de 4 Newtons. RESULTADOS: o movimento distal inicial dos molares, tendo como ponto de referência a mesial do tubo, foi maior na coroa do modelo AbCR (0,47x10-6), e maior na raiz do modelo AcCR (0,32x10-6), provocando inclinações da coroa para distal e mesial, respectivamente. No modelo CR, os pontos na coroa (0,15x10-6) e raiz (0,12x10-6) deslocaram-se para distal equilibradamente, resultando em movimento de translação. Em todos os modelos, numa vista oclusal, houve tendência de rotação distal inicial da coroa, porém no modelo CR esse movimento foi muito pequeno. No sentido vertical (Z), todos os modelos revelaram movimento extrusivo (AbCR= 0,18x10-6; CR= 0,62x10-6; AcCR= 0,72x10-6). CONCLUSÃO: a simulação computacional do uso de aparelho extrabucal com tração cervical revelou a ocorrência de movimento extrusivo e distal, podendo ser por inclinação distal de coroa, de raiz ou movimento de translação.

Current computational modelling trends in craniomandibular biomechanics and their clinical implications

Computational models of interactions in the craniomandibular apparatus are used with increasing frequency to study biomechanics in normal and abnormal masticatory systems. Methods and assumptions in these models can be difficult to assess by those unfamiliar with current practices in this field; health professionals are often faced with evaluating the appropriateness, validity and significance of models which are perhaps more familiar to the engineering community. This selective review offers a foundation for assessing the strength and implications of a craniomandibular modelling study. It explores different models used in general science and engineering and focuses on current best practices in biomechanics. The problem of validation is considered at some length, because this is not always fully realisable in living subjects. Rigid-body, finite element and combined approaches are discussed, with examples of their application to basic and clinically relevant problems. Some advanced software platforms currently available for modelling craniomandibular systems are mentioned. Recent studies of the face, masticatory muscles, tongue, craniomandibular skeleton, temporomandibular joint, dentition and dental implants are reviewed, and the significance of non-linear and non-isotropic material properties is emphasised. The unique challenges in clinical application are discussed, and the review concludes by posing some questions which one might reasonably expect to find answered in plausible modelling studies of the masticatory apparatus.

Maxillary expansion in customized finite element method models

INTRODUCTION

The aims of this study were to develop a method for constructing a 3-dimensional finite-element model (FEM) of the maxilla and to evaluate the effects of transverse expansion on the status of various midpalatal sutures.

METHODS

A 3-dimensional FEM of the craniofacial complex was developed by using computed-tomography images and Bionix modeling software (version 3.0, CANTIBio, Suwon, Korea). To evaluate the differences between transverse expansion forces in the solid model (maxilla without a midpalatal suture), the fused model (maxilla with suture elements), and the patent model (maxilla without suture elements), transverse expansion forces of 100 g were applied bilaterally to the maxillary first premolars and the first molars.

RESULTS

The fused model expressed a stress pattern similar to that of the solid model, except for the decreased first principal stress concentration in the incisive foramen area. The patent model, however, had a unique stress pattern, with the stress translated superiorly to the nasal area. The anterior nasal spine and the central incisors moved downward and backward in both solid and fused models but moved primarily downward with a slight backward movement of the anterior nasal spine in the patent model.

CONCLUSIONS

Clinical observations of maxillary expansion can be explained by different suture statuses. This efficient and customized FEM model can be used to predict craniofacial responses to biomechanics in patients.

Asymmetric headgear for differential molar movement: a study using finite element analysis

OBJECTIVE

To compare the effects of four different asymmetric headgear systems.

DESIGN

A mathematical method for three-dimensional data called finite element analysis.

SETTING

The Orthodontic Department, the Federal University of Rio de Janeiro and the Metallurgical Engineering Department of the Fluminense Federal University.

METHODS

Four systems of delivering an asymmetrical force to headgear were studied: using face-bow arms of different lengths, a symmetric face-bow with one of the arms bent outward in relation to the internal arch, a symmetric face-bow used in combination with a transpalatal arch activated to produce an asymmetric force, and a symmetric face-bow with the outer bow soldered to the inner bow on the side where a larger force will be applied.

RESULTS

All four systems were effective in promoting asymmetric distal movement of the molars. However, the symmetrical face-bow with the outer bow soldered to the inner bow (system 4) could be used in asymmetric mechanics if the bows are soldered on the opposite side to the proposed distalization. Lateral and occlusal displacing forces were observed in all systems as well as tip-back and rotational movements.

CONCLUSION

The simulated computer model used in this investigation suggests that a face-bow with a symmetrically soldered joint and arms of equal lengths used in combination with a transpalatal arch is the best headgear option when asymmetric movement of upper molars is desired.

Combined finite element and multibody dynamics analysis of biting in a Uromastyx hardwickii lizard skull

Lizard skulls vary greatly in shape and construction, and radical changes in skull form during evolution have made this an intriguing subject of research. The mechanics of feeding have surely been affected by this change in skull form, but whether this is the driving force behind the change is the underlying question that we are aiming to address in a programme of research. Here we have implemented a combined finite element analysis (FEA) and multibody dynamics analysis (MDA) to assess skull biomechanics during biting. A skull of Uromastyx hardwickii was assessed in the present study, where loading data (such as muscle force, bite force and joint reaction) for a biting cycle were obtained from an MDA and applied to load a finite element model. Fifty load steps corresponding to bilateral biting towards the front, middle and back of the dentition were implemented. Our results show the importance of performing MDA as a preliminary step to FEA, and provide an insight into the variation of stress during biting. Our findings show that higher stress occurs in regions where cranial sutures are located in functioning skulls, and as such support the hypothesis that sutures may play a pivotal role in relieving stress and producing a more uniform pattern of stress distribution across the skull. Additionally, we demonstrate how varying bite point affects stress distributions and relate stress distributions to the evolution of metakinesis in the amniote skull.

Predicting skull loading: applying multibody dynamics analysis to a macaque skull

Evaluating stress and strain fields in anatomical structures is a way to test hypotheses that relate specific features of facial and skeletal morphology to mechanical loading. Engineering techniques such as finite element analysis are now commonly used to calculate stress and strain fields, but if we are to fully accept these methods we must be confident that the applied loading regimens are reasonable. Multibody dynamics analysis (MDA) is a relatively new three dimensional computer modeling technique that can be used to apply varying muscle forces to predict joint and bite forces during static and dynamic motions. The method ensures that equilibrium of the structure is maintained at all times, even for complex statically indeterminate problems, eliminating nonphysiological constraint conditions often seen with other approaches. This study describes the novel use of MDA to investigate the influence of different muscle representations on a macaque skull model (Macaca fascicularis), where muscle groups were represented by either a single, multiple, or wrapped muscle fibers. The impact of varying muscle representation on stress fields was assessed through additional finite element simulations. The MDA models highlighted that muscle forces varied with gape and that forces within individual muscle groups also varied; for example, the anterior strands of the superficial masseter were loaded to a greater extent than the posterior strands. The direction of the muscle force was altered when temporalis muscle wrapping was modeled, and was coupled with compressive contact forces applied to the frontal, parietal and temporal bones of the cranium during biting.

Early treatment with a maxillary lip bumper-bite plateau combination

OBJECTIVE

To evaluate the intra-arch displacements of the molars and the change in molar relationship following the use of a maxillary lip bumper combined with a bite plate.

MATERIALS AND METHODS

The material comprised study casts taken before and after the treatment of 40 consecutive patients with mixed dentition. The sagittal and transversal displacements were evaluated by a three-dimensional digitizer using the palatal rugae as an indirect fixed reference. The displacements were expressed as translation mesiodistally and buccolingually and rotation around the long axis and tipping mesiodistally. The change in molar relationship was measured to the nearest millimeter at the level of the occlusal plane.

RESULTS

The tooth movements were predominantly of distal rotation (mean, 9.7 degrees ; range, 6.5 degrees to 26 degrees ) and distal tipping (mean, 5 degrees ; range, 5.8 degrees to 18 degrees ). The distal displacement was a modest mean (mean, 0.3 mm; SD, 1.6 mm) and more pronounced to the buccal (mean 1.6 mm; SD, 1.5 mm). The molar relationship improved in all but four sites, and a full Class I was obtained in 65 of 80 sites.

CONCLUSIONS

The early treatment with the lip bumper and bite plate can be recommended from a cost-benefit point of view.

An experimentally calibrated finite element study of maxillary trauma

A baseball injury to an instrumented human cadaver maxillae was simulated with a regulation (142 g) baseball traveling at 14 m s(-1). Measurements of strain were obtained with three-axis strain gauge rosettes located at the medial palate and both canine fossae. A three-dimensional finite element (FE) model of a dentate human maxilla was constructed from computed tomography scans of the skull of an adolescent. This three-dimensional mathematical model of the maxilla was deemed geometrically accurate by convergence testing when the model's degrees of freedom approximated 74 000. The simulated load case involved a transient dynamic impact to the medial maxilla with boundary conditions imposed at skeletal buttresses of the model. The model was calibrated through direct comparison with the displacements and principal strains gathered from experimental and epidemiological data. The comparison of experimental and calculated principal strains as a result of the simulated impacts revealed a 1.7-11.4% difference.

Three-dimensional finite elemental analysis of zygomatic implants in craniofacial structures

The objective of this study was to analyse stress distribution in craniofacial structures around zygomatic osseointegrated implants. An integrated system for Digital Imaging and Communications in Medicine (DICOM) data were utilized to create a three-dimensional model of craniofacial structures. The amount and distribution of the main stresses were compared using three-dimensional finite elemental analysis. The system allowed visual confirmation and analysis of stress distribution as well as the convenient and simple construction of a digital biomechanical model that provided details of anatomical structures in the regions of interest. Zygomatic implants with or without connected implants supporting the superstructure were compared. Stresses in severely resorbed maxillae with connected implants were not concentrated around the alveolar bone supporting the zygomatic implants. Stresses where there were no connected implants tended to be generated in the zygomatic bone, at the middle part of the zygomatic implant and at the joint of the fixture-abutment. Stress due to occlusal forces is mainly supported by the zygomatic bone, is transferred predominantly through the infrazygomatic crest, and is divided between the frontal and temporal processes of the zygomatic bone in different directions.

Efficient 3D finite element analysis of dental restorative procedures using micro-CT data

OBJECTIVES

This investigation describes a rapid method for the generation of finite element models of dental structures and restorations.

METHODS

An intact mandibular molar was digitized with a micro-CT scanner. Surface contours of enamel and dentin were fitted following tooth segmentation based on pixel density using an interactive medical image control system. Stereolithography (STL) files of enamel and dentin surfaces were then remeshed to reduce mesh density and imported in a rapid prototyping software, where Boolean operations were used to assure the interfacial mesh congruence (dentinoenamel junction) and simulate different cavity preparations (MO/MOD preparations, endodontic access) and restorations (feldspathic porcelain and composite resin inlays). The different tooth parts were then imported in a finite element software package to create 3D solid models. The potential use of the model was demonstrated using nonlinear contact analysis to simulate occlusal loading. Cuspal deformation was measured at different restorative steps and correlated with existing experimental data for model validation and optimization.

RESULTS

Five different models were validated by existing experimental data. Cuspal widening (between mesial cusps) at 100 N load ranged from 0.4 microm for the unrestored tooth, 9-12 microm for MO, MOD cavities, to 12-21 microm for endodontic access cavities. Placement of an MOD adhesive restoration in porcelain resulted in 100% cuspal stiffness recovery (0.4 microm of cuspal widening at 100 N) while the composite resin inlay allowed for a partial recuperation of cusp stabilization (1.3 microm of cuspal widening at 100 N).

SIGNIFICANCE

The described method can generate detailed and valid three dimensional finite element models of a molar tooth with different cavities and restorative materials. This method is rapid and can readily be used for other medical (and dental) applications.

Biomechanical finite-element investigation of the position of the centre of resistance of the upper incisors

The position of the centre of resistance (CR) is an essential parameter regarding the planning of orthodontic tooth movements. In the present investigation, the combined CR of the upper four incisors was determined numerically using the finite-element (FE) method. Based on a commercially available three-dimensional data set of a maxilla, including all 16 teeth, as well as known and earlier determined material parameters, FE models of the upper incisors and their surrounding tooth-supporting structures were generated. In the FE system, the model of the anterior segment was loaded with torques of 10 Nmm each at the lateral incisors. The FE model indicated that the individual incisors moved independently, although they were blocked with a steel wire of dimension 0.46 x 0.65 mm(2). The individual CRs were located at 5 mm distal and 9 and 12 mm apical to the centre of the lateral brackets. Thus, the classical view of a combined CR for the anterior segment was disproved and the planning of orthodontic tooth movements of the upper incisors should no longer be based on that concept.

Evaluation of Class II treatment by cephalometric regional superpositions versus conventional measurements

INTRODUCTION

The aims of this study were (1) to evaluate cephalometric changes in subjects with Class II Division 1 malocclusion who were treated with headgear (HG) or Fränkel function regulator (FR) and (2) to compare findings from regional superpositions of cephalometric structures with those from conventional cephalometric measurements.

METHODS

Cephalographs were taken at baseline, after 1 year, and after 2 years of 65 children enrolled in a prospective randomized clinical trial. The spatial location of the landmarks derived from regional superpositions was evaluated in a coordinate system oriented on natural head position. The superpositions included the best anatomic fit of the anterior cranial base, maxillary base, and mandibular structures.

RESULTS

Both the HG and the FR were effective in correcting the distoclusion, and they generated enhanced differential growth between the jaws. Differences between cranial and maxillary superpositions regarding mandibular displacement (Point B, pogonion, gnathion, menton) were noted: the HG had a more horizontal vector on maxillary superposition that was also greater (.0001 < P < .05) than the horizontal displacement observed with the FR. This discrepancy appeared to be related to (1) the clockwise (backward) rotation of the palatal and mandibular planes observed with the HG; the palatal plane's rotation, which was transferred through the occlusion to the mandibular plane, was factored out on maxillary superposition; and (2) the interaction between the inclination of the maxillary incisors and the forward movement of the mandible during growth.

CONCLUSIONS

Findings from superpositions agreed with conventional angular and linear measurements regarding the basic conclusions for the primary effects of HG and FR. However, the results suggest that inferences of mandibular displacement are more reliable from maxillary than cranial superposition when evaluating occlusal changes during treatment.

Comparison of relative mandibular growth vectors with high-resolution 3-dimensional imaging

INTRODUCTION

The mandibular rami and their endochondrally growing condyles develop in many directions relative to the variable anatomic patterns of the nasomaxilla and middle cranial fossae during growth and response to orthopedic treatment.

METHODS

High-resolution magnetic resonance images were used to compare 3-dimensional (3D) growth vectors of skeletal displacement and bone remodeling in 25 untreated subjects with Class II malocclusions, 28 subjects with Class II malocclusions who were treated with Fränkel appliance therapy, and 25 subjects with normal occlusions. Marked differences were noted over an 18-month observation period. The 3D coordinates of anatomic landmarks were registered by Procrustes fit to control for rotation, translation, and scale differences.

RESULTS

Compared with untreated Class II and normal-occlusion subjects, the treated group showed highly significant differences in the 3D displacement/remodeling vectors of gonion and pterygomaxillary fissure relative to condylion and middle cranial fossae bilateral skeletal landmarks, by using both permutation tests ( P < .001) and a general linear multivariate model ( P < .0001).

CONCLUSIONS

In a prospective and systematically controlled study, we quantitatively described significant 3D rami skeletal compensations in the structural assembly of facial morphogenesis at the beginning of the adolescent growth spurt using novel modeling techniques. These techniques have facilitated quantification of relative 3D growth vectors to illustrate skeletal changes with Fränkel appliance therapy. Future studies are required to assess the long-term clinical significance of our findings.

Modeling elastic properties in finite-element analysis: how much precision is needed to produce an accurate model?

The influence of elastic properties on finite-element analysis was investigated using a finite-element model of a Macaca fascicularis skull. Four finite-element analyses were performed in which the model was assigned different sets of elastic properties. In analysis 1, elastic properties were modeled isotropically using published data obtained from human limb bones. Analyses 2-4 used data obtained from skulls of a closely allied species, M. mulatta, but varied as to how those data were incorporated into the model. In analysis 2, the model was assigned a single set of isotropic elastic properties. In analysis 3, each region within the model was assigned its own set of isotropic elastic properties. Finally, in analysis 4, each region received its own set of orthotropic elastic properties. Although a qualitative assessment indicates that the locations of strain concentrations across the model are broadly similar in all analyses, a quantitative assessment of strain indicates some differences between the analyses. When strain data from the finite-element analyses were compared to strain data derived from in vivo experiments, it was found that the model deformed most realistically using the orthotropic elastic properties employed in analysis 4. Results suggest that finite-element analyses can be adversely affected when elastic properties are modeled imprecisely, and that modelers should attempt to obtain elastic properties data about the species and skeletal elements that are the subjects of their analyses.

Distal molar movement with Kloehn headgear: is it stable?

The aim of this study was to evaluate intramaxillary molar movement after 8 months of cervical traction and posttreatment displacement 7 years later. The total molar displacements in relation to stable intraosseous reference points were compared with those observed in an untreated control group that also had intraosseous reference indicators inserted. During the headgear period, the type of molar displacement could be predicted by the direction of the force system acting on the teeth. It was noted, however, that the variation in the vertical development was related more to each patient's growth pattern than to the force system applied. After cessation of the headgear, intramaxillary displacement of the molars was noted, and the total displacement of the molars did not differ from that of the untreated group. The indication for intramaxillary displacement of the molars by means of extraoral traction is therefore questioned.