Finite element method modeling of craniofacial growth

The Stress Concentration and Biomechanical Properties of the Intra-oral Distractors and the Extra-oral Distractors Used in Treatment of Post Ankylosis Facial Asymmetric Patients: A Finite Element Analysis Study

ABSTRACT

Assessment of stress and micromotions using finite element analysis along both the intraoral and the extraoral distractors devices used in the mandibular distraction of post temporomandibular joint ankylosis deformed mandible patients. The process of finite element analysis was carried out to assess distraction models. The first model was an extraoral mandibular distraction model and the second model was an intraoral mandibular distraction model. To analyze the stress state, 2 vertical loads were applied on the defective and normal side respectively by a 3D finite element ball model. The intraoral system observed lower stress (4.5 MPa) in the mandibular bone compared to the extra-oral system (11.5 MPa). The results revealed that the intraoral system observed higher stress on the distractor fixing points (392.21 MPa) compared to the extra-oral fixing points (12.62 MPa). The results revealed that the extra-oral system reflected higher displacement on the bone surrounding the screws of about 3720 μm compared to the intraoral system 1414.6 μm. Internal devices give better shielding to the bone and induce fewer stresses over the mandibular, so it is more advisable to be used. The external devices permit greater distraction length because the pins and the distractor main body are subjected to fewer stresses.

Geometric morphometric analysis of craniofacial growth between the ages of 12 and 14 in normal humans

Aim

There is great variation of growth among individuals. The question whether patients with different skeletal discrepancies grow differently is biologically interesting but also important in designing clinical trials. The aim of the present study was to evaluate whether growth direction depends on the initial craniofacial pattern.

Subjects and method

The sample consisted of 350 lateral cephalograms of 175 subjects (91 females and 84 males) followed during normal growth without any orthodontic treatment. The examined ages were 12 (T1) and 14 (T2) years. The cephalograms were obtained from the American Association of Orthodontists Foundation (AAOF) Craniofacial Growth Legacy Collection (Burlington, Fels, Iowa, and Oregon growth studies). We digitally traced 15 curves on each cephalogram, comprehensively covering the craniofacial skeleton, and located 127 points on the curves, 117 of which were sliding semilandmarks and 10 fixed. Procrustes alignment, principal component analysis and two-block partial least squares analysis were performed, after sliding the semilandmarks to minimize bending energy.

Results

The first 10 principal components (PCs) described approximately 71 per cent of the total shape variance. PC1 was related to shape variance in the vertical direction (low/high angle skeletal pattern) and PC2 was mainly related to shape variance in the anteroposterior direction (Class II/Class III pattern). PC3 was mainly related to the shape variance of the mandibular angle. All subjects shared a similar growth trajectory in shape space. We did not find any correlation between the initial shape and the magnitude of shape change between T1 and T2, but males showed a greater shape change than females. The direction of shape change was moderately correlated to the initial shape (RV coefficient: 0.14, P < 0.001).

Conclusions

The initial shape of the craniofacial complex covaried weakly with the direction of shape change during growth.

Effects of bracket slot size during en-masse retraction of the six maxillary anterior teeth using an induction-heating typodont simulation system

OBJECTIVE

To investigate how bracket slot size affects the direction of maxillary anterior tooth movement when en-masse retraction is performed in sliding mechanics using an induction-heating typodont simulation system.

METHODS

An induction-heating typodont simulation system was designed based on the Calorific Machine system. The typodont included metal anterior and resin posterior teeth embedded in a sticky wax arch. Three bracket slot groups (0.018, 0.020, and 0.022 inch [in]) were tested. A retraction force of 250 g was applied in the posterior-superior direction.

RESULTS

In the anteroposterior direction, the cusp tip of the canine in the 0.020-in slot group moved more distally than in the 0.018-in slot group. In the vertical direction, all six anterior teeth were intruded in the 0.018-in slot group and extruded in the 0.020- and 0.022-in slot groups. The lateral incisor was significantly extruded in the 0.020- and 0.022-in slot groups. Significant differences in the crown linguoversion were found between the 0.018- and 0.020-in slot groups and 0.018- and 0.022-in slot groups for the central incisor and between the 0.018- and 0.022-in slot groups and 0.020- and 0.022-in slot groups for the canine. In the 0.018-in slot group, all anterior teeth showed crown mesial angulation. Significant differences were found between the 0.018- and 0.022-in slot groups for the lateral incisor and between the 0.018- and 0.020-in slot groups and 0.018- and 0.022-in slot groups for the canine.

CONCLUSIONS

Use of 0.018-in slot brackets was effective for preventing extrusion and crown linguoversion of anterior teeth in sliding mechanics.

Construction of a three-dimensional finite element model of maxillary first molar and it's supporting structures

The finite element method (FEM) is a powerful computational tool for solving stress-strain problems; its ability to handle material inhomogeneity and complex shapes makes the FEM, the most suitable method for the analysis of internal stress levels in the tooth, periodontium, and alveolar bone. This article intends to explain the steps involved in the generation of a three-dimensional finite element model of tooth, periodontal ligament (PDL) and alveolar bone, as the procedure of modeling is most important because the result is based on the nature of the modeling systems. Finite element analysis offers a means of determining strain-stress levels in the tooth, ligament, and bone structures for a broad range of orthodontic loading scenarios without producing tissue damage.

Comparison of the Reliability of Anatomic Landmarks based on PA Cephalometric Radiographs and 3D CT Scans in Patients with Facial Asymmetry

Introduction

Conventional cephalometry is an inexpensive and well-established method for evaluating patients with dentofacial deformities. However, patients with major deformities and in particular asymmetric cases are difficult to evaluate by conventional cephalometry. Reliable and accurate evaluation in the orbital and midfacial region in craniofacial syndrome patients is difficult due to inherent geometric magnification, distortion and the superpositioning of the craniofacial structures on cephalograms. Both two- and three-dimensional computed tomography (CT) have been proposed to alleviate some of these difficulties.

Aims and objectives

The aim of our study is to compare the reliability of anatomic cephalometric points obtained from the two modalities: Conventional posteroanterior cephalograms and 3D CT of patients with facial asymmetry, by comparison of intra- and interobserver variation of points recorded from frontal X-ray to those recorded from 3D CT.

Materials and methods

The sample included nine patients (5 males and 4 females) with an age range of 14 to 21 years and a mean age of 17.11 years, whose treatment plan called for correction of facial asymmetry.

All CT scans were measured twice by two investigators with 2 weeks separation for determination of intraobserver and interobserver variability. Similarly, all measurement points on the frontal cephalograms were traced twice with 2 weeks separation. The tracings were superimposed and the average distance between replicate points readings were used as a measure of intra- and interobserver reliability. Intra-and interobserver variations are calculated for each method and the data were imported directly into the statistical program, SPSS 10.0.1 for windows.

Results

Intraobserver variations of points defined on 3D CT were small compared with frontal cephalograms. The intraobserver variations ranged from 0 (A1, B1) to 0.6 mm with the variations less than 0.5 mm for most of the points.

Interobserver variations of points between first and second tracings defined on PA Ceph and 3D CT were less than 1.5 mm for all the points.

A direct comparison of frontal cephalometry and 3D CT using intraobserver variation for the first observer showed that 3D CT was more reliable than frontal cephalometry for 11 points.

Direct comparison of frontal cephalometry and 3D CT for the second observer showed a similar tendency with 14 points significantly more reliable for 3D CT.

Comparison of frontal cephalometry and 3D CT using interobserver variation for the tracings showed that 3D CT was more reliable than frontal cephalometry.

Summary and conclusion

The study has shown that 3D CT is consistently more accurate and reliable than conventional frontal cephalometry. Unfortunately, the cost of a computerized tomography examination is considerable; this means that, at this stage, its use by surgeons and orthodontists is a last resort.

Transverse dentoskeletal features of anterior open bite in the mixed dentition

OBJECTIVE

To apply both conventional cephalometric analysis and morphometric analysis (thin-plate spline analysis) to posteroanterior (PA) cephalograms to test the hypothesis that the dentoskeletal features of subjects with anterior open bite in the mixed dentition are no different from those of normal controls.

MATERIALS AND METHODS

A group of 22 white subjects (6 males, 16 females; mean age, 8.7 +/- 0.7 years) with anterior open bite (AOBG) was compared with a control group (CG) of 22 white subjects (11 males, 11 females; mean age, 9.2 +/- 0.8 years) with Class I occlusal relationships, and without anterior open bite and sucking habits. Subjects of both groups were in the mixed dentition and had no history of orthodontic treatment. Between-group statistical comparisons were performed with independent sample t-tests and permutation tests.

RESULTS

AOBG exhibited statistically significant shape differences with respect to CG that consisted of a transverse contraction of the zygomatic region, of the maxilla (at both skeletal and dentoalveolar levels), and of the mandible (in both condylar and gonial regions), with a downward dislocation of point menton. With conventional cephalometrics, AOBG showed a statistically significant transverse deficiency in the zygomatic region (-4.8 mm), in the maxilla at both skeletal and dentoalveolar levels (-2.0 mm and -3.0 mm, respectively), and in the mandible in both condylar and gonial regions (-3.6 mm and -4.0 mm, respectively).

CONCLUSION

Subjects with anterior open bite showed transverse deficiencies in the zygomatic region, in the maxilla, and in the mandible when compared with normal subjects.

Analysis and visualization of growth-related and treatment-induced craniofacial changes

An analysis and visualization of craniofacial shape changes due to growth or orthodontic treatment is presented. The suggested method is based on an adapted Karhunen-Loève decomposition of time-discrete data based on landmarks in lateral X-rays of the skull. It allows for a reduction of the high-dimensional dynamic problem to a few spatial modes representing synchronous components of growth patterns with time-dependent mode coefficients. The growth-related shape changes as well as the orthodontic treatment effects are visualized by overdrawing the underlying shape changes. The results based on this technique give insight into the still controversially discussed question to which degree the craniofacial skeletal structures can be influenced by orthodontic appliances.

Finite element growth analysis for the craniofacial skeleton in patients with cleft lip and palate

The purpose of this study was to clarify the differences in the nature of craniofacial growth between subjects with normal occlusion and patients with unilateral cleft lip and palate (CLP) in terms of the size, shape and principal growth direction of craniofacial skeleton using finite element method (FEM). Lateral cephalograms were taken of 40 subjects as normal group and 178 patients as CLP group. These subjects were divided into seven developmental ages of 4-, 6-, 8-, 10-, 12-, 14- and 18-year-old. For the finite element analysis, the craniofacial complex was discretized into seven structures or elements with three nodal points in each after tracing each lateral cephalogram on acetate paper. For each stage, the growth parameters in CLP group were compared to those in normal group. The growth of upper facial skeleton and maxillary complex was more remarkably inhibited in CLP than in normal group. Especially, the growth inhibition of posterior maxillary complex in a vertical direction was remarkable in CLP group at any ages. Difference in the size and shape of entire mandibular skeleton between CLP and normal groups was not apparent. It is suggested that grow timing and peak velocity, an essential and key determinant to the success in orthodontic treatment, have been clarified in this study more clearly than in previous studies. It is hopefully anticipated to explore some key determinants to predict individual growth of the craniofacial skeleton near future.

Visualization of individual growth-related craniofacial changes based on cephalometric landmark data: a pilot study

OBJECTIVE

An approach based on Euclidean distances between cephalometric landmarks is presented (1) to visualize and localize the individual shape changes of the complex craniofacial skeleton during growth and (2) to depict the individual dynamic behavior of developmental size and shape changes.

PATIENTS AND METHOD

Growth-related craniofacial changes were investigated exemplarily for two male orthodontically untreated subjects from the Belfast Growth Study on the basis of lateral cephalograms at 7, 9, 11, 13, and 15 years. The interlandmark distances among seven skeletal cephalometric landmarks served as a database for the study. A modified Karhunen-Loève decomposition based on orthogonal modes and time-dependent scalar amplitudes was used to describe the growth process. The individual shape changes of the various craniofacial regions were visualized by allocation of colors to the respective distances, and overdrawn representations were reconstructed by means of multidimensional scaling.

RESULTS AND CONCLUSIONS

This visualization technique allows anatomical regions to be characterized with respect to reduced or strengthened growth, compared with pure size changes. The clinically relevant mechanisms of craniofacial changes are visualized (e.g., shifts in the anteroposterior or vertical dimensions of the jaws in relation to cranial base and structural imbalances during development). In addition, overdrawing the effects of shape change on the skeletal structures gives a more readily comprehensible impression of the growth process. Taking account of the methodical limitations of this approach (e.g., the restrictions concerning the number of landmarks), the clinician may take advantage of this technique in orthodontic or surgical diagnostics to gain additional insight into the individual complex size and shape changes during development along with their dynamic behavior.

A three-dimensional, quantitative computed tomographic study of changes in distribution of bone mineralization in the developing human mandible

The three-dimensional distribution of highly mineralized cortical bone on the buccal surface of the mandible was evaluated using quantitative computed tomography. The study was completed in 34 living persons (21 females and 13 males) between the ages of 9 and 32 yr of age with symmetrical mandibles. The geometrical distribution of the highly mineralized areas (>1250 mg/cm(3)) was determined by three-dimensional reconstruction of images. The pattern of distribution was evaluated by superimposing a 9 by 9-mesh grid over the lateral view of the mandible and adapting it to the same anatomical landmarks for different aged participants. Individuals demonstrated four different patterns of distribution of highly mineralized buccal cortical bone. The youngest had highly mineralized bone in the corpus of the mandible and along the anterior ramal border. In older individuals, the mineralization changed to include the mid- and posterior ramus. Highly mineralized bone was not found within the condylar, coronoid, or gonial angle regions of any participant. A comparison of the mineralization pattern between the left and right lateral mandibular views showed bilateral symmetry with similar patterns of distribution. Comparison of the number of grids occupied by highly mineralized cortical bone with the age of the participant, mandibular length, gonial angle, and cross-sectional area of the masseter muscle produced the highest correlation coefficient with the size of the masseter muscle.

Changes in cortical bone mineralization in the developing mandible: a three-dimensional quantitative computed tomography study

Quantitative computed tomography (QCT) was completed in 34 subjects between the ages of 9 and 33 years with symmetrical mandibles in order to investigate the three-dimensional cortical bone mineral density (BMD) distribution in the mandible. The number and distribution of the pixels were determined at three levels: (1) representing the entire mandibular bone; (2) the cortical bone at 60% above the baseline defined as the segmentation level (around 1050 mg/cm3) and representative of only cortical bone; and (3) the highest mineralized cortical bone (>1250 mg/cm3). The geometrical distribution of the highest mineralized areas was evaluated by three-dimensional reconstruction of the images. The total number of pixels for the entire mandible increased significantly at each time point represented at four increasing ages groups (9-11 years of age, 12-14 years of age, 15-17 years of age, and >18 years of age). The male and female subjects had a similar total number of pixels for the entire mandible before the age of 11, but the male subjects showed a significantly larger total number of mandibular pixels after that age. Comparison of the number of pixels for pure cortical bone (60% segmentation level) and the highest mineralized cortical bone indicated a significant increase with maturation with the greatest change occurring between the 13-year and 16-year age groups. However, the ratio of cortical bone/total bone increased at a more rapid rate in the male subjects and reached a plateau by the 16-year age group, showing distinct differences in mineralization of the mandible between the sexes.

Methodologies for evaluating long-term stability of dental relationships after orthodontic treatment

A comprehensive review of literature which considers methodologies for studying long-term occlusal stability is presented. This article focuses on the evaluation of plaster study models because occlusal changes are best reflected in longitudinal casts. Of particular interest is the assessment of crowding in the dentition and the various physical and mathematical procedures used to evaluate the measurement of space available. Indices used to assess the overall occlusal results of treatment are also presented.

Morphologic determinants in the etiology of class III malocclusions: a review

Morphospatial disharmony of the craniomaxillary and mandibular complexes may yield apparent mandibular prognathism, but Class III malocclusions can exist with any number of aberrations of the craniofacial complex. Deficient orthocephalization of the cranial base allied with a smaller anterior cranial base component has been implicated in the etiology of Class III malocclusions. Whereas the more acute cranial base angle may affect the articulation of the condyles resulting in their forward displacement, the reduction in anterior cranial size may affect the position of the maxilla. As well, intrinsic skeletal elements of the maxillary complex may be responsible for maxillary hypoplasia that may exacerbate the anterior crossbite seen in the Class III condition. Conversely, with an orthognathic maxilla, condylar hyperplasia and anterior positioning of the condyles at the temporo-mandibular joint may produce an anterior crossbite. Aside from the skeletal components, soft tissue matrices, particularly labial pressure from the circumoral musculature, may influence the final outcome of craniofacial growth of a child skeletally predisposed to Class III conditions. Indeed, as some Asian ethnic groups demonstrate an increased prevalence of Class III malocclusions, it is likely that the skeletal components and soft tissues matrices are genetically determined. Presumably, the co-morphologies of the craniomaxillary and mandibular complexes are likely dependent upon candidate genes that undergo gene-environmental interactions to yield Class III malocclusions. The identification of such genes is a desirable step in unraveling the complexity of Class III malocclusions. With this knowledge, the clinician may elect an early course of dentofacial orthopedic and orthodontic treatments aimed at preventing the development of Class III malocclusions.

Automatic computerized radiographic identification of cephalometric landmarks

Computerized cephalometric analysis currently requires manual identification of landmark locations. This process is time-consuming and limited in accuracy. The purpose of this study was to develop and test a novel method for automatic computer identification of cephalometric landmarks. Spatial spectroscopy (SS) is a computerized method that identifies image structure on the basis of a convolution of the image with a set of filters followed by a decision method using statistical pattern recognition techniques. By this method, characteristic features are used to recognize anatomic structures. This study compared manual identification on a computer monitor and the SS automatic method for landmark identification on minimum resolution images (0.16 cm2 per pixel). Minimum resolution (defined as the lowest resolution at which a cephalometric structure could be identified) was used to reduce computational time and memory requirements during this development stage of the SS method. Fifteen landmarks were selected on a set of 14 test images. The results showed no statistical difference (p > 0.05) in mean landmark identification errors between manual identification on the computer display and automatic identification using SS. We conclude that SS shows potential for the automatic detection of landmarks, which is an important step in the development of a completely automatic cephalometric analysis.

The functional matrix hypothesis revisited. 4. The epigenetic antithesis and the resolving synthesis

In two interrelated articles, the current revision of the functional matrix hypothesis extends to a reconsideration of the relative roles of genomic and of epigenetic processes and mechanisms in the regulation (control, causation) of craniofacial growth and development. The dialectical method was chosen to analyze this matter, because it explicitly provides for the fuller presentation of a genomic thesis, an epigenetic antithesis, and a resolving synthesis. The later two are presented here, where the synthesis suggests that both genomic and epigenetic factors are necessary causes, that neither alone is also a sufficient cause, and that only the two, interacting together, furnish both the necessary and sufficient cause(s) of ontogenesis. This article also provides a comprehensive bibliography that introduces the several new, and still evolving, disciplines that may provide alternative viewpoints capable of resolving this continuing controversy; repetition of the present theoretical bases for the arguments on both sides of these questions seems nonproductive. In their place, it is suggested that the group of disciplines, broadly termed Complexity, would most likely amply repay deeper consideration and application in the study of ontogenesis.

The functional matrix hypothesis revisited. 2. The role of an osseous connected cellular network

Intercellular gap junctions permit bone cells to intercellularly transmit, and subsequently process, periosteal functional matrix information, after its initial intracellular mechanotransduction. In addition, gap junctions, as electrical synapses, underlie the organization of bone tissue as a connected cellular network, and the fact that all bone adaptation processes are multicellular. The structural and operational characteristics of such biologic networks are outlined and their specific bone cell attributes described. Specifically, bone is "tuned" to the precise frequencies of skeletal muscle activity. The inclusion of the concepts and databases that are related to the intracellular and intercellular bone cell mechanisms and processes of mechanotransduction and the organization of bone as a biologic connected cellular network permit revision of the functional matrix hypothesis, which offers an explanatory chain, extending from the epigenetic event of muscle contraction hierarchically downward to the regulation of the bone cell genome.

Reconstruction of three-dimensional anatomical landmark coordinates using video-based stereophotogrammetry

A method is described for reconstructing the 3-dimensional coordinates of anatomical landmarks from multiple video images. This method consists of 2 stages: (1) separate reconstructions of landmark coordinates visible in dorsal and ventral orientations using Direct Linear Transformation (Abdel-Aziz & Karara, 1972), and (2) least-squares alignment of the partial reconstructions using landmarks present in both. The repeatability of the overall reconstructions and of individual landmarks were assessed by performing multiple independent reconstructions of landmark coordinates for 2 camd specimens. Results indicate that the repeatability of interlandmark distances based on stereophotogrammetric reconstructions from standard-resolution video images is comparable to that of caliper measurement, and slightly superior to that of electronic 3-dimensional digitisation. At least 4 images should be available per landmark for optimal repeatability, but additional images allow only a slight increase in repeatability.

Comparison of numeric techniques in the analysis of cleft palate dental arch form change

OBJECTIVE

Quantitative descriptions of form (size and shape) changes are significant to the understanding of the development, treatment planning, and prognosis of patients born with cleft lip and palate. This study compared the results of traditional dental arch form change measurements, such as width, depth, perimeter, and area, with four numeric methods: finite element scaling analysis, macroelement method, Euclidean distance matrix analysis, and conventional least-squares and resistant-fit theta rho Procrustes analyses.

DESIGN

Using tooth cusp landmarks on maxillary study casts, form change measurements of a male with complete bilateral cleft lip and palate at ages 2, 5, and 6 years were made comparing each age to the next older.

RESULTS AND CONCLUSIONS

With the exception of the 2- to 5-year resistant-fit analysis, all numeric method: 1) provide comparable results, 2) provide more detailed descriptions than do traditional methods, and 3) provide results that correlate well with the reported effects of increased lip pressure due to lip closure surgery. The use of finite-element scaling analysis on study casts is somewhat limited since: 1) there is more than one solution at teeth shared by many finite elements, 2) gross averaging of form change occurs within triangular elements, and 3) solutions can vary with the choice of element location. The use of the macroelement method circumvented the above finite element limitations without compromising finite-element advantages. Procrustes results vary with the chosen superposition algorithm. The choice of the most appropriate Procrustes method required some a priori knowledge of form difference. The large number of results obtained by Euclidean distance matrix analysis and the nongraphic presentation of these results hamper quick interpretation but may be best suited for definitive statistical analysis. The graphic representation of both the magnitude and direction of: 1) landmark displacement in the Procrustes analyses (once size difference is eliminated), and 2) the rate of form change in the macroelement method provide an intuitive appreciation of how and where the casts differ.

Facial growth after primary periosteoplasty versus primary bone grafting in unilateral cleft lip and palate

A cephalometric evaluation of long-term changes resulting from two different surgical techniques for the correction of unilateral cleft lip and palate (UCLP) was undertaken on a sample of 19 males with primary bone grafting, and 42 males with primary periosteoplasty from the Science Academy of the Czech Republic, Prague. Lateral cephalometric radiographs collected at approximately 10 and 15 years of age were traced, digitized, and analyzed using the finite-element method. Facial growth and development between the two groups were compared. Significant differences between the two groups were found in the upper face, the posterior part of the maxilla, the anterior bony chin, and nasal bone areas. The periosteoplasty group demonstrated significantly greater vertical development between anterior cranial base and the maxilla. The bony chin was larger and a greater inferior displacement of the posterior palate were found in the periosteoplasty group. An increased proclination in the nasal bone was observed in the bone graft group. This investigation both confirms the findings of a previous study of these sample populations, and provides additional important details regarding the differences between the groups.

Fourier analysis of cephalometric shapes

Craniofacial growth and development involve both size and shape variations. Shape variations can be assessed independently from size using mathematical methods such as the Fourier series. A method for the reconstruction of outlines starting from selected landmarks and for their Fourier analysis has been developed and applied to analyze the age differences in shape in the tracings of the Bolton standards (lateral view) from 1 to 18 years of age. The size-independent shape of the Bolton standard at 18 years was larger at the chin, at the gonion, and in the anterior cranial base than the shape at 1 year of age. Conversely, the younger shape was larger in the middle part of face, corresponding roughly to the maxillary bone, than the older shape. When standardized for size, growth thus seemed to modify craniofacial shape with progressive lengthening and narrowing. This shape effect was largely overwhelmed by the very evident size increments, and it could be measured only using the proper mathematical methods.

Assessment of facial form modifications in orthodontics: proposal of a modified computerized mesh diagram analysis

A modified computerized mesh diagram analysis enables rapid, easy, and independent quantifications of facial size, shape, and head position. A lateral cephalometric radiograph is traced, positioned in natural head position (NHP) according to the NHP registered on a lateral photograph, and superimposed by the standard grid of rectangles determined by the patient's upper face height and face depth. The patient's tracing is compared with a reference tracing of a norm. The two tracings are registered at nasion in NHP, and the size difference of the patient's mesh rectangles from the norm is quantified by a size normalization. The shape discrepancies are evaluated by calculating relevant displacement vectors for each cephalometric landmark, and a global difference factor. This computerized method provides a rapid graphic evaluation of the patient's sagittal and vertical discrepancies and can also be applied to determine the effects of orthodontic therapy and/or growth on the skeletal and dental relationships in a single patient.

Asymmetric vault modification in Hopi crania

Cradleboarding was practiced by numerous prehistoric and historic populations, including the Hopi. In this group, one result of cradleboarding was bilateral or asymmetric flattening of the posterior occipital. We test whether cradleboarding had significant effects on the morphology of the cranial vault, cranial base, and face. Additionally, we examine associations between direction of flattening and asymmetric craniofacial growth. A skeletal sample of Hopi from the Old Walpi site includes both nonmodified (N = 43) and modified individuals (N = 39). Three-dimensional coordinates of 53 landmarks were obtained using a diagraph. Thirty-six landmarks were used to define nine finite elements in the cranial vault, cranial base, and face. Finite element scaling was used to compare average nonmodified individuals, with averages of bilaterally, right, and left modified individuals. The significance of variation among "treatment" groups was evaluated using a bootstrap test. Pearson product-moment correlations test the association of asymmetry with direction of modification. Hopi cradleboarding has a significant effect on growth of the cranial vault, but does not affect morphology of the cranial base or face. Bilateral flattening of the cranial vault leads to decreased length and increased width of the cranial vault. Flattening of the right or left cranial vault results in ipsilaterally decreased length and width coupled with a corresponding increased length and width on the contralateral side of the cranial vault. There is a significant correlation of size asymmetry with direction of modification in the cranial vault, but not with size or shape change in the cranial base or face.

Use of the boundary element method for biological morphometrics

Tensorial morphometric assessments of form difference can aid in the understanding of the cause of the form difference by providing reference frame independent, anisotropic, non-homogenous descriptions. The majority of biological and prosthetic structures cannot be adequately analyzed by current methods due to the paucity of anatomical landmarks and methodological requirements of subdivision through the domain. Internal subdivisions can be eliminated with the boundary element method (BEM). A non-landmark (NL) method can be developed by the combination of elliptical Fourier analysis (EFA) and BEM. The appropriateness of NL and BEM was investigated. The growth of the female rat neural skull from 7 to 14 postnatal days was calculated with respect to increase in area. Linear and quadratic BEM landmark analysis were made using 10 and 5 elements, respectively. Five hundred linear BEM elements were constructed from the EFA equations for NL. The form change tensors were obtained by the solution of the Laplace equation using boundary displacements as the essential boundary conditions. For comparison, simplex triangular finite element analysis (FEA), quadrilateral FEA and macroelement analysis were made on the same structure. Results correspond well to the two major growth process in this time period; (1) high cerebellar growth, and (2) relatively higher facial versus neural growth. The results in other regions are close to the biologically observed 36% increase in area. The average difference between BEM, NL versus FEA is 1.9 and 2.8%. Trends in results with position are almost identical for BEM, NL, MEM and quadrilateral FEA. The morphometric landmark BEM technique requires an additional numerical scheme to eliminate the singularities near the boundary.(ABSTRACT TRUNCATED AT 250 WORDS)

Effect of premature sagittal suture closure on craniofacial morphology in a prehistoric male Hopi

Scaphocephaly is caused by premature sagittal suture closure. It restricts medial-lateral growth of the cranial vault which appears longer and narrower than normal. We examined how this natural malformation affected morphology of the cranial base and face. A prehistoric adult male Hopi with scaphocephaly was compared to 19 normal male Hopi (Old Walpi Series, Field Museum of Natural History, Chicago, IL). Three-dimensional coordinates of 53 landmarks were recorded on the cranial vault, cranial base, and face. Finite element scaling analysis was used to test for significant differences between the scaphocephalic and normal individuals in craniofacial morphology. Finite element scaling results indicated that scaphocephaly has a profound effect on cranial vault morphology. However, morphology of the cranial base and face were only slightly affected and, typically, are within the normal range of variation for the sample. An abnormality in the cranial base is not associated with scaphocephaly in this individual.

An evaluation of growth changes and treatment effects in Class II, Division 1 malocclusion with conventional roentgenographic cephalometry and finite element method analysis

Conventional methods of roentgenographic cephalometry will yield differences in interpretation of growth or treatment changes depending on which methods of superimposition are used. The finite element method of analysis has been reported to have significant advantages since it does not require a reference frame to describe the changes that have taken place. This article describes the growth of a patient with a Class II, Division 1 malocclusion during approximately 2 years of orthodontic treatment with the use of conventional cephalometric growth and static analyses, as well as the finite element method. Thirty cephalometric points were digitized on the pretreatment and the posttreatment lateral cephalograms of a patient undergoing orthodontic treatment between the ages of 10 and 12 years. The finite element method provided a reference frame invariant description of the size, shape, change, and rotation of each of the 12 finite elements representing different anatomic structures.

The aetiology of Class III malocclusion examined by tensor analysis

This study compares and contrasts the differences in facial pattern between groups of young people, employing a modified tensor analysis. One-hundred-and-thirty-eight children with Class III malocclusions were compared with 105 control individuals of similar ages: 126 subjects were prepubertal (age range 7 to 10 years), whilst the remaining 117 were between 15 and 22 years of age. Males and females were examined separately. The tensor analysis permitted the computation of differences in form (that is in size and shape) without specifically measuring either. Mean values for 18 conventional cephalometric landmarks were determined for each sub-group of control and Class III individuals. Customized programs were developed to assess the differences between 23 triads of points between the two occlusal groups.

The practicability of finite-element analysis for assessing changes in human craniofacial morphology from cephalographs

The usefulness of a finite-element analytical (FEA) method for studying changes in facial form was investigated. The material was lateral cephalographs of 19 patients who had undergone surgical correction of the chin. FEA was used to assess changes in bony form brought about by surgery. Replicate digitization of cephalographic landmarks was used to minimize measurement error. Random and systematic errors were examined and their influence on the finite-element method was assessed. However, the sensitivity of FEA is such that the level of residual measurement error affects the reliability of the method and makes the technique unsuitable for individual cases. However, for pooled data from a group of cases the effect of measurement error is reduced and the reliability of the analysis is satisfactory for intergroup comparison.

Human dental arch shape evaluated by euclidean-distance matrix analysis

Form differences between biological structures can be evaluated using several approaches. When landmark data are available, a recently proposed method (euclidean-distance matrix analysis) seems to be able to differentiate between size and shape differences. This method also localizes those areas which differ most between the two structures. We have applied it to analyze the sexual dimorphism in dental arch form in a sample of 50 men and 45 women. Subjects ranged in age between 20 and 27 years, and had sound dentitions. Fourteen landmarks, corresponding to the centers of gravity (centroids) of the occlusal surfaces of all permanent teeth (right second molar to left second molar), were individualized on the dental casts of subjects. All the possible linear distances between pairs of teeth were computed, thus creating four mean form matrices (one for each arch within sex). Gender differences were tested by using euclidean-distance matrix analysis. No significant differences were demonstrated in the shape of arches, while male arches proved to be slightly bigger than female arches.

Dental arch asymmetry in young healthy human subjects evaluated by Euclidean distance matrix analysis

Form differences between biological structures can be evaluated using several approaches. A recently proposed method (Euclidean distance matrix analysis; EDMA) seems to be able to differentiate between size and shape differences. Here it has been applied to study the asymmetry of mandibular and maxillary arches in 50 men and 45 women with sound dentitions. The centres of gravity (centroids) of the occlusal surfaces of all permanent teeth (right second molar to left second molar) were individualized on the dental casts of subjects. The form of the right and left maxillary and mandibular hemi-arches was separately assessed by calculating all the possible linear distances between pairs of teeth within arch and side. Side differences were tested by EDMA. In men, the maxillary and the mandibular arches were both symmetrical (i.e. there were no significant differences in size or shape between the left and right hemi-arches). In women, the mandibular arch was symmetrical, but in the maxillary arch the two antimeres had a significantly different shape. No size differences were found between the left and right female hemi-arches.

Effects of annular cranial vault modification on the cranial base and face

Artificial modification of the cranial vault was practiced by a number of prehistoric and protohistoric populations, frequently during an infant's first year of life. We test the hypothesis that, in addition to its direct effects on the cranial vault, annular cranial vault modification has a significant indirect effect on cranial base and facial morphology. Two skeletal series from the Pacific Northwest Coast, which include both nonmodified and modified crania, were used: the Kwakiutl (62 nonmodified, 45 modified) and Nootka (28 nonmodified, 20 modified). Three-dimensional coordinates of 53 landmarks were obtained using a diagraph, and 36 landmarks were used to define nine finite elements in the cranial vault, cranial base, and face. Finite element scaling was used to compare average nonmodified and average modified crania, and the significance of the results were evaluated using a bootstrap test. Annular modification of the cranial vault produces significant effects on the morphology of the cranial base and face. Annular modification in the Kwakiutl resulted in restrictions of the cranial vault in the medial-lateral and superior-inferior dimensions and an increase in anterior-posterior growth. Similar dimensional changes are observed in the cranial base. The Kwakiutl face is increased anterior-posteriorly and reduced anterior-laterally to posterior-medially. Similar effects of modification are observed in the Nootka cranial vault and cranial base, though not in the face. These results demonstrate the developmental interdependence of the cranial vault, cranial base, and face.

A preliminary study of craniofacial classification

Cephalographic evaluations often hinge on univariate statistical analyses of their component dimensions. These analyses generally depict a progressive increase in cephalometric form with age. Such analyses are, however, complicated by the varied inter-dimensional correlations. But when the cephalometric dimensions were combined together in cluster analysis, complex associations between various age groups were noted in the 1-18 year range. Such multivariate analyses revealed far more complex craniofacial age changes than traditionally envisaged. These data therefore indicated the need for further investigation of such "normocephalic gold standards" before their value in craniofacial evaluation can be established.

Effects of fronto-occipital artificial cranial vault modification on the cranial base and face

Artificial reshaping of the cranial vault has been practiced by many human groups and provides a natural experiment in which the relationships of neurocranial, cranial base, and facial growth can be investigated. We test the hypothesis that fronto-occipital artificial reshaping of the neurocranial vault results in specific changes in the cranial base and face. Fronto-occipital reshaping results from the application of pads or a cradle board which constrains cranial vault growth, limiting growth between the frontal and occipital and allowing compensatory growth of the parietals in a mediolateral direction. Two skeletal series including both normal and artificially modified crania are analyzed, a prehistoric Peruvian Ancon sample (47 normal, 64 modified crania) and a Songish Indian sample from British Columbia (6 normal, 4 modified). Three-dimensional coordinates of 53 landmarks were measured with a diagraph and used to form 9 finite elements as a prelude to finite element scaling analysis. Finite element scaling was used to compare average normal and modified crania and the results were evaluated for statistical significance using a bootstrap test. Fronto-occipitally reshaped Ancon crania are significantly different from normal in the vault, cranial base, and face. The vault is compressed along an anterior-superior to posterior-inferior axis and expanded along a mediolateral axis in modified individuals. The cranial base is wider and shallower in the modified crania and the face is foreshortened and wider with the anterior orbital rim moving inferior and posterior towards the cranial base. The Songish crania display a different modification of the vault and face, indicating that important differences may exist in the morphological effects of fronto-occipital reshaping from one group to another.

Diagnosis of skeletal form on the lateral cephalogram with a finite element-based expert system

Orthodontic diagnosis depends largely on the current methods of cephalometric analysis and categorization. It is therefore unfortunate that such analyses tend to use inappropriate metrical systems that lack a rigorous scientific basis. As a consequence, the resultant data have questionable validity, as well as being subject to observer bias. In this study, an alternative, more rigorous, approach is described. A random sample of 126 pretreatment lateral cephalograms were analyzed with the finite element method. These data were then classified to form a training set or reference data base for the subsequent objective diagnosis of new, previously unclassified cases. This new case-classification system was based on matching the new cases to similar cases within the existing training set. The degree of concordance between such computer-matched cases was then evaluated by their subsequent conventional cephalometric analyses.

Comparison between two finite-element modelling methods for measuring change in craniofacial form

Finite-element modelling of form change is a useful morphometric technique for measuring differences between anatomical patterns. Two different finite-element algorithms currently are used. One method requires normalized coordinates as input data, while the second method uses globalized coordinates as input data. This study determines whether the two finite-element methods provide equivalent measures of three-dimensional form change when applied to the nasal septa of embryonic mice. Computer models of the nasal septa from mice of 15 and 17 days gestation were generated. Homologous landmarks were identified so that each nasal septum was represented by a tetrahedral finite-element. These elements were subjected to both finite-element modelling methods. Results show that the two algorithms use different interpolation functions and yield dissimilar intermediate results, but generate identical strain matrices as well as equivalent principal extensions, directions of form change, variables of form change, and graphical displays. Therefore, results are directly comparable from studies using either finite-element modelling method.

An evaluation of the changes in soft-tissue profile form induced by orthodontic therapy

In view of the growing concensus that traditional cephalometric appraisals yield data of dubious scientific value, the changes in soft-tissue profile forms were evaluated by an alternative technique. This involved dividing the soft-tissue profile form into a series of triangular finite elements spanning homologous datum points. With the use of techniques derived from continuum mechanics, the changes in soft-tissue profile form were evaluated by computing the degree of distortion in each triangle after treatment (target element) compared with the triangle before treatment (reference element) in terms of specific size and shape parameters. In a comparison of samples of patients with Class I and II malocclusion, varying patterns of facial profile change were noted, depending on the parameters analyzed. The results, therefore, showed that although such techniques offer rigorous cephalometric potential, further investigation is required to identify more appropriate datum points.

Computer-assisted location of reference points in three dimensions for radiographic cephalometry

A major obstacle to the derivation of three-dimensional data from lateral and coronal radiographs of the head has been the lack of precision in locating the same landmarks on each of the biplanar images. The method described herein uses radiographic equations based on the geometry of a biplanar system to predict the location of a reference point on one film from its location on the other. This technique, which differs from previously described systems, allows a pair of cephalometric films to be digitized by an on-line procedure controlled by a personal computer. Three-dimensional coordinates of reference points are calculated and stored for subsequent retrieval when they can be used for metric analysis or for the display of simple wire-frame models of the skull. Computing algorithms are provided to aid software development.

Biomechanical effect of anteriorly directed extraoral forces on the craniofacial complex: a study using the finite element method

This study was designed to investigate the biomechanical effect of protractive maxillary orthopedic forces on the craniofacial complex by use of the three-dimensional finite element method (FEM). The three-dimensional FEM model was developed on the basis of a dry skull of a young human being. The model consisted of 2918 nodes and 1776 solid elements. Eighteen cranial and facial sutural systems were integrated in the model. An anteriorly directed 1.0-kg force was applied on the buccal surfaces of the maxillary first molars in both a horizontal parallel direction and a 30 degree obliquely downward direction to the functional occlusal plane. The nasomaxillary complex showed a forward displacement with upward and forward rotation in a horizontal protraction case, whereas a downward force produced almost translatory repositioning of the complex in an anterior direction. High stress levels were observed in the nasomaxillary complex and its surrounding structures. However, the pattern of stress distributions within the complex was different in two force systems. A downward protraction force produced relatively uniform stress distributions, indicating the importance of the force direction in determining the stress distributions from various orthopedic forces.

A computer graphics program for measuring two- and three-dimensional form change in developing craniofacial cartilages using finite element methods

Allometric analysis of chondrocranial growth seeks to provide objective measures of morphogenetic form change during ontogeny of the primordial skull. Linear measures, typically employed to study differential growth, become problematic at the histological level since an external referencing system is impossible to achieve for microscopic anatomies in embryos. The purpose of this paper is to describe a computer graphics program which generates spatially invariant measures of two- and three-dimensional form change using finite element methods. Anatomical form change is viewed as a continuous deformation of an initial finite element representing an anatomical unit into a second configuration. The algorithm consists of isoparametric scaling of finite elements, strain matrix formulation, and size/shape variable derivation. The routine includes four segments serving to extract nodal data, generate the strain matrix relating the two morphologies as well as deriving corresponding size/shape variables, reference the major and minor axes of form change, and provide graphic display of the anatomical geometries. Applications are provided measuring two- and three-dimensional form change in the developing craniofacial cartilages of rats subjected to treatment with the known teratogen diazo-oxo-norleucine (DON). The finite element routine provides craniofacial form change variables which are expected in light of cellular alterations induced by DON administration. Finally, computational differences between this routine and similar approaches using finite element methods for analyzing biological form change are examined.

A retrospective cephalometric study of Class I patients

In view of the growing consensus that traditional cephalometric analyses yield data of dubious scientific validity, this study was undertaken using an alternative technique, termed finite element analysis (FEA). The study was based on 14 triangular finite elements spanning seven datum (nodal) points delineating cephalometric form. These points were delineated on lateral cephalographs taken immediately before and following the completion of orthodontic treatment for two samples of boys aged 12-16 years. Although both samples exhibited Class I molar occlusions with anterior over-crowding, one sample required bilateral maxillary and mandibular first premolar extraction prior to orthodontic treatment, while the other sample did not. FEA revealed greater cephalometric size and shape changes in the 'non-extraction' than 'extraction' samples. Such sample contrasts, however, varied depending upon the finite element included in the analysis. Further studies are therefore required to delineate the specific finite element configurations to provide precise descriptions of cephalometric change.

The three-dimensional cephalogram: theory, technique, and clinical application

The Broadbent-Bolton cephalostat produces intrinsically three-dimensional information about cranial form. Yet in the clinical setting, this information has been used primarily two dimensions at a time in the separate study of lateral or posteroanterior cephalograms. In this article we demonstrate an expedient use of existing cephalostat-based data sets to derive certain analyses of three-dimensional form. The technique is essentially the same as that of the Broadbent-Bolton "Orientator," an exploitation of the geometry of the cephalostat to simulate stereophotogrammetry. The three-dimensional method supports the usual biometrics of landmark locations, and takes advantage of a normative data base that is suited for semiautomatic analysis of syndromic data. The principal drawback of the method is its inability to represent curving form in three dimensions. However, in comparison with computed tomography (CT), it involves low radiation dose, is simpler to obtain, has an available normative data base, and is more practical for quantitative or long-term serial analysis.

Three-dimensional finite element analysis for stress in the periodontal tissue by orthodontic forces

This study was designed to investigate the stress levels induced in the periodontal tissue by orthodontic forces using the three-dimensional finite element method. The three-dimensional finite element model of the lower first premolar was constructed on the basis of average anatomic morphology and consisted of 240 isoparametric elements. Principal stresses were determined at the root, alveolar bone, and periodontal ligament (PDL). In all loading cases for the buccolingually directed forces, three principal stresses in the PDL were very similar. At the surface of the root and the alveolar bone, large bending stresses acting almost in parallel to the root were generally observed. During tipping movement, stresses nonuniformly varied with a large difference from the cervix to the apex of the root. On the other hand, in case of movement approaching translation, the stresses induced were either tensile or compressive at all occlusogingival levels with some difference of the stress from the cervix to the apex. The pattern and magnitude of stresses in the periodontium from a given magnitude of force were markedly different, depending on the center of rotation of the tooth.

Comparative study of normal, Crouzon, and Apert craniofacial morphology using finite element scaling analysis

Finite element scaling analysis is used to study differences in morphology between the craniofacial complex of normal individuals and those affected with the syndromes of Apert and Crouzon. Finite element scaling quantifies the differences in shape and size between forms without reference to any fixed, arbitrary registration point or orientation line and measures the amount of form change required to deform one object into another. Two-dimensional coordinates of landmarks digitized from annual sets of cephalometric radiographs were used in the analysis. A simple tabulation shows no difference in variances between the normal and pathological samples. A test of mean differences depicts the Apert and Crouzon morphologies as significantly different from normal. The Apert palate differs from normal in shape in the older age groups analyzed, and palatal size differences are most common at the posterior nasal spine. The Apert pituitary fossa and basi-occiput are significantly larger than normal. The Crouzon pituitary fossa is also larger than normal, but the difference is not always significant. The typical morphology of the Crouzon nose is due more to differences in shape than size. The Crouzon basi-occiput is significantly smaller than normal. An age association of the differences between the normal and pathological craniofacies was found in Apert syndrome but not in Crouzon syndrome. Apert syndrome is characterized by a more homogeneous pattern of craniofacial dysmorphology from 6 months to 18 years of age than Crouzon syndrome.

Describing a craniofacial anomaly: finite elements and the biometrics of landmark locations

An intergroup comparison of cephalometric landmark configurations by the finite-element method elegantly depicts the algebra of some of the size and shape change measures that one may define by reference to those landmarks. In studies of mean differences between groups, the statistical analysis of these finite elements is equivalent to competent statistical analysis of the same data using any other geometric metaphor, such as properly standardized vector descriptions of landmark "movement" or scalar measures, size and shape variables, taken in sufficient variety. In applications to landmark data, the reality of finite-element depictions is purely statistical rather than phenomenological. In the absence of additional evidence, they should not be held either more or less biologically meaningful than other descriptions of the same landmark changes to which they lead. These propositions are exemplified using landmark data from 13 cases of Apert syndrome.

Quantitation of maxillary remodeling. 2. Masking of remodeling effects when an "anatomical" method of superimposition is used in the absence of metallic implants

We report the results of a study aimed at quantifying the differences in the perceived pattern of maxillary remodeling that are observed when different methods are used to superimpose maxillary images in roentgenographic cephalometrics. In a previous article, we reported cumulative changes in the positions of anterior nasal spine (ANS), posterior nasal spine (PNS), and Point A for a sample of 31 subjects with maxillary metallic implants. Measurements had been made on lateral cephalograms taken at annual intervals relative to superimposition on the implants. In the present article, we quantify the differences in the perceived displacement of the same landmarks in the same sample when a standard "anatomical best bit" rule was used in lieu of superimposition on the implants. The anatomical best fit superimposition as herein defined was found in this sample to lose important information on the downward remodeling of the superior surface of the maxilla that had been detected when the implant superimposition was used. In fact, we observed a small artifactual upward displacement of the ANS-PNS line. In the anteroposterior direction, the tendency toward backward displacement of skeletal landmarks through time that had been detected with the implant superimposition was replaced by a small forward displacement of ANS and Point A together with reduced backward displacement of PNS. To the extent that the implant superimposition is to be considered the true and correct one, the anatomical best fit superimposition appears to understate the true downward remodeling of the palate by an average of about 0.3 and 0.4 mm per year, although this value differs at different ages and timepoints. The anatomical best fit superimposition also misses entirely the small mean tendency toward backward remodeling that was observed when the implant superimposition was used. In situations in which there are no implants, clinicians and research workers must necessarily continue to use anatomically based superimpositions with definitions more or less similar to that of the anatomical best fit superimposition used here. When they do so, some systematic errors will be incurred. For grouped data, we believe that the best currently available estimates of the mean errors involved in using the anatomical best fit superimposition to approximate an implant superimposition are the "bias" values included in Table IIC. The secondary implications of these differences to the perceived displacements of the maxillary teeth will be considered in our next article.