An evaluation of the Pi analysis in the assessment of anteroposterior jaw relationship.

OBJECTIVE: This study has investigated two new cephalometric variables, the Pi angle and Pi linear in the evaluation of anteroposterior skeletal discrepancy. DESIGN: Retrospective cross-sectional study. SETTING: Manipal College of Dental Sciences, Manipal, India SUBJECTS AND METHOD: A sample of 155 subjects (mean age 19·7 years) were subdivided into skeletal class I, II and III groups based upon ANB angle. Descriptive data were calculated for each variable and group. Receiver operating characteristics curves were used to examine sensitivity and specificity of the Pi angle in the discrimination between different skeletal groups. Correlation coefficients were obtained for each of the parameters to compare their relationship with other parameters in the class I group. Coefficient of determination, regression coefficient, regression equation and standard error of estimate were also calculated from the parameters showing significant correlation with the Pi angle. RESULTS: Mean values for the Pi angle in skeletal class I, II and III subjects were 3·40 (±2·04), 8·94 (±3·16) and -3·57 (±1·61) degrees, respectively. For the Pi linear they were 3·40 (±2·20), 8·90 (±3·56) and -3·30 (±2·30) mm for class I, II and III subjects, respectively. Receiver operating characteristic curves showed that a Pi angle greater than 5 degrees had 89% sensitivity and 82% specificity for discriminating a skeletal class II group from class I. A Pi angle of less than 1·3 degrees had 100% sensitivity and 84% specificity in discriminating skeletal class III groups from class I. The overall accuracy for discriminating class II groups from class I was 85% and for class III from class I, 90%. Thus, a cut-off point between class I and II groups could be considered a Pi angle of approximately 5 degrees and between class I and class III, approximately 1·3 degrees. There were no statistically significant correlations found between Pi angle and ANB (0·07), Beta angle (-0·04) and WITS analysis (0·19). The highest level of correlation was obtained for the Pi angle and Pi linear (0·96). CONCLUSION: The anglar and linear components of the Pi analysis are a suitable method for assessing anteroposterior jaw discrepancy in daily clinical practice.

Biomechanical response of the maxillofacial skeleton to transpalatal orthopedic force in a unilateral palatal cleft.

OBJECTIVES: To assess the skeletal and dental effects of rapid maxillary expansion in a patient with unilateral cleft deformity of secondary palate and alveolus using the finite element method. MATERIALS AND METHODS: A patient-specific composite skull model was developed from a patient computed tomographic scan and a surface scan of the patient's maxillary cast using MIMICS imaging analysis software. For volumetric meshing and the finite element analysis, Abaqus (6.7) was used. RESULTS: The typical wedge-shaped opening that occurs after RME, seen in non-cleft patients, is not seen in cleft patients. A clockwise rotation of the maxilla as a result of maxillary expansion was evident. The areas of maximum stress were the intact primary palate region, inferior orbital foramen of the non-cleft and the cleft sides, and the zygomatic buttress of the cleft side. During expansion, the intact primary palate showed high stress and acted as a region of major resistance, followed by the zygomatic buttress on the cleft side. CONCLUSIONS: Clinicians should consider a need for customization of expansion therapy for cleft patients depending on the patient's age, the type of cleft present (primary or secondary palate), and the desired area of expansion (anterior or posterior).

Determining the osteotomy pattern in surgically assisted rapid maxillary expansion in a unilateral palatal cleft: a finite element model approach.

OBJECTIVES: To evaluate the stress pattern in the craniofacial skeleton in a patient with unilateral cleft deformity of the secondary palate and alveolus in response to various techniques of surgically assisted rapid maxillary expansion (SARME). MATERIALS AND METHODS: Three patient-specific composite skull models were developed for finite element model analysis. The details of the modeling procedure have been described in Part I of this series. The finite element analysis was performed on each model with a specified SARME technique in combination with RME using Abaqus (6.7). RESULTS: The ideal form of surgery in SARME for patients with unilateral cleft deformity of the secondary palate and alveolus would be complete unilateral LeFort I with pterygoid dysjunction in combination with midpalatal split, followed by isolated midpalatal split and zygomatic buttress osteotomies. CONCLUSIONS: A more invasive SARME technique can significantly reduce the resultant stresses. However, this benefit should be weighed against the risk of increasing complications associated with more extensive surgeries. When a more conservative surgical technique is selected, it would be preferable to perform a midpalatal split rather than zygomatic buttress osteotomies, as indicated by the stress-strain distribution and displacement pattern associated with different SARME techniques.

Maxillary protraction with and without maxillary expansion: a finite element analysis of sutural stresses.

INTRODUCTION: In this finite element study, we compared the stress patterns along the various craniofacial sutures with maxillary protraction with and without expansion. METHODS: Two 3-dimensional analytic models were developed, 1 simulating maxillary protraction and the other simulating maxillary protraction with expansion. The model consisted of 108799 10 node solid 92 elements (tetrahedron), 193633 nodes, and 580899 degrees of freedom. RESULTS: The overall stresses after maxillary protraction with maxillary expansion were significantly higher than with a facemask alone. The magnitude of stress on the craniofacial sutures with maxillary protraction alone was in the range of a few millinewtons per square millimeter, whereas, with maxillary protraction with maxillary expansion, the stresses ranged from a few newtons per square millimeter to a few hundred newtons per square millimeter. The pattern of stress distribution also differed with the 2 treatment modalities as did the sutures experiencing maximum and minimum stresses. CONCLUSIONS: The osteogenic potential of such low stresses after maxillary protraction can be questioned. High stresses generated in various craniofacial sutures after maxillary protraction with expansion are responsible for disrupting the circummaxillary sutural system and presumably facilitating the orthopedic effect of the facemask.

Skeletal response to maxillary protraction with and without maxillary expansion: a finite element study.

INTRODUCTION: The purpose of this finite element study was to evaluate biomechanically 2 treatment modalities-maxillary protraction alone and in combination with maxillary expansion-by comparing the displacement of various craniofacial structures. METHODS: Two 3-dimensional analytical models were developed from sequential computed tomography scan images taken at 2.5-mm intervals of a dry young skull. AutoCAD software (2004 version, Autodesk, San Rafael, Calif) and ANSYS software (version 10, Belcan Engineering Group, Cincinnati, Ohio) were used. The model consisted of 108,799 solid 10 node 92 elements, 193,633 nodes, and 580,899 degrees of freedom. In the first model, maxillary protraction forces were simulated by applying 1 kg of anterior force 30 degrees downward to the palatal plane. In the second model, a 4-mm midpalatal suture opening and maxillary protraction were simulated. RESULTS: Forward displacement of the nasomaxillary complex with upward and forward rotation was observed with maxillary protraction alone. No rotational tendency was noted when protraction was carried out with 4 mm of transverse expansion. A tendency for anterior maxillary constriction after maxillary protraction was evident. The amounts of displacement in the frontal, vertical, and lateral directions with midpalatal suture opening were greater compared with no opening of the midpalatal suture. The forward and downward displacements of the nasomaxillary complex with maxillary protraction and maxillary expansion more closely approximated the natural growth direction of the maxilla. CONCLUSIONS: Displacements of craniofacial structures were more favorable for the treatment of skeletal Class III maxillary retrognathia when maxillary protraction was used with maxillary expansion. Hence, biomechanically, maxillary protraction combined with maxillary expansion appears to be a superior treatment modality for the treatment of maxillary retrognathia than maxillary protraction alone.

Craniofacial displacement in response to varying headgear forces evaluated biomechanically with finite element analysis.

INTRODUCTION: The aim of this study was to evaluate biomechanically the displacement patterns of the facial bones in response to different headgear loading by using a higher-resolution finite element method model than used in previous studies. METHODS: An analytical model was developed from sequential computed tomography scan images taken at 2.5-mm intervals of a dry skull of a 7-year-old. Different headgear forces were simulated by applying 1 kg of posteriorly directed force in the first molar region to simulate cervical-pull, straight-pull, and high-pull headgear. Displacements (in mm) of various craniofacial structures were evaluated along the x, y, and z coordinates with different headgear loading. RESULTS: All 3 headgears demonstrated posterior displacement of the maxilla with clockwise rotation of the palatal plane. The distal displacement of the maxilla was the greatest with the straight-pull headgear followed by the cervical-pull headgear. The high-pull headgear had better control in the vertical dimensions. The midpalatal suture opening was evident and was more pronounced in the anterior region. The articular fossa and the articular eminence were displaced laterally and postero-superiorly with each headgear type. CONCLUSIONS: The high-pull headgear was most effective in restricting the antero-inferior maxillary growth vector. Midpalatal suture opening similar to rapid maxillary expansion was observed with all 3 headgear types. The center of rotation varied with the direction of headgear forces for both the maxilla and the zygomatic complex. A potential for chondrogenic and osteogenic modeling exists for the articular fossa and the articular eminence with headgear loading.

Stress and displacement patterns in the craniofacial skeleton with rapid maxillary expansion: a finite element method study.

INTRODUCTION: The purpose of this finite element study was to evaluate stress distribution along craniofacial sutures and displacement of various craniofacial structures with rapid maxillary expansion (RME) therapy. METHODS: The analytic model for this study was developed from sequential computed tomography scan images taken at 2.5-mm intervals of a dry young human skull. Subsequently, a finite element method model was developed from computed tomography images by using AutoCAD software (2004 version, Autodesk, Inc, San Rafael, Calif) and ANSYS software (version 10, Belcan Engineering Group, Downers Grove, Ill). RESULTS: The maxilla moved anteriorly and downward and rotated clockwise in response to RME. The pterygoid plates were displaced laterally. The distant structures of the craniofacial skeleton--zygomatic bone, temporal bone, and frontal bone--were also affected by transverse orthopedic forces. The center of rotation of the maxilla in the X direction was somewhere between the lateral and the medial pterygoid plates. In the frontal plane, the center of rotation of the maxilla was approximately at the superior orbital fissure. The maximum von Mises stresses were found along the frontomaxillary, nasomaxillary, and frontonasal sutures. Both tensile and compressive stresses could be demonstrated along the same suture. CONCLUSIONS: RME facilitates expansion of the maxilla in both the molar and the canine regions. It also causes downward and forward displacement of the maxilla and thus can contribute to the correction of mild Class III malocclusion. The downward displacement and backward rotation of the maxilla could be a concern in patients with excessive lower anterior facial height. High stresses along the deep structures and the various sutures of the craniofacial skeleton signify the role of the circummaxillary sutural system in downward and forward displacement of the maxilla after RME.