A tensor analysis to evaluate the effect of high-pull headgear on Class II malocclusions

Longitudinal evaluation of growth changes in Class II division 1 subjects

Longitudinal records from the Ohio State University Growth Study were used to compare the skeletal growth changes between Class II division 1 and Class I female subjects between ages 7 and 14. Tensor analysis was used to determine the yearly growth rate and direction. No significant difference was found in cranial base dimension between the Class I and Class II subjects. In Class II subjects, the maxilla (S-N-A) was found to be normally related to the cranial base. However, mandibular position (S-N-B and S-N-Pog) was found to be significantly more retrusive in Class II when compared with Class I subjects. Mandibular length (Ar-Gn) and corpus length (Go-Gn) were found to be shorter in Class II subjects. The ratio of PFH to AFH was found to be smaller in Class II subjects. This is particularly apparent during the pubertal growth period. The y-axis and mandibular plane angle were more open in Class II subjects which also contributed to the retrusive position of the mandible. Maxillo-mandibular difference (A-N-B) between Class I and II subjects was present at age 7 and persisted through puberty, maintaining a greater angle of convexity (A-N-Pg) in Class II subjects. These results suggest that Class II malocclusion can be detected early. The majority of the Class II cases showed mandibular skeletal retrusion or a combination of horizontal and vertical abnormalities of the mandible rather than maxillary protrusion. These skeletal differences remain through puberty without orthodontic intervention. Individual variations were found within each type of malocclusion.

Shape-coordinate and tensor analysis of skeletal changes in children with treated Class III malocclusions

The current study was undertaken to evaluate both maxillary and mandibular shape/size changes in children with Class III malocclusions, treated with a functional appliance (removable mandibular retractor). Nonconventional cephalometric methods (Bookstein's shape coordinate analysis, centroid size analysis, and tensor analysis) were applied to a maxillary triangle (T-FMN-A) and to a mandibular triangle (Co-Go-Pg). A group of 30 children with treated Class III malocclusions were compared with a matched group of 30 children with untreated Class III malocclusions. Treatment with the functional appliance produced a significantly increased growth of the maxilla, featuring a more downward and forward displacement of the region of point A and a significantly more upward and forward direction of condylar growth, leading to a "shrinkage" of total mandibular length. The biologic significance of some conventional cephalometric measurements used for the assessment of both maxillary and mandibular position and structure was tested.

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.

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)