Form difference computations in restorative dentistry utilizing the macroelement method

Lateral distribution of ultrasound velocity in horizontal layers of human teeth

The speed of ultrasound at 20 MHz differs inside human teeth depending on which tissues are involved. At least two out of four dental tissues exhibit variations in the longitudinal velocity (CL). The aim of this in vitro study is to describe the laterally varying propagation velocity of tangentially propagating longitudinal waves. At a distance of 5 mm from the crown reference, the CL is determined using longitudinal sections and a pulse-echo technique. Several graphs are combined to account for the corono-apical decrease in CL and the laterally varying CL distribution along horizontally adjacent relative tooth width portions. The laterally increasing CL of 21 specimens at radial locations rises from 2900 to 4000 m/s. A mathematical evaluation reveals an optimal horizontal formula of the form CL(5 mm) = a + bX2 ln(X), where X is the standardized lateral parameter relative to individual tooth width w, which is compensated for offsets. Individual residuals and a, b coefficients of the corresponding approximations are provided. Individual mean errors range from 7 m/s (SD=6 m/s) to 92 m/s (SD=79 m/s). The lower contour of the envelope curve of all CL distributions is described by taking up a formerly introduced equation [J. Acoust. Soc. Am. 116, 545 (2004)].

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.