Prediction of coronal size of third molars by factor and multiple regression analyses

A new mathematical process for the calculation of average forms of teeth

STATEMENT OF PROBLEM

Qualitative visual inspections and linear metric measurements have been predominant methods for describing the morphology of teeth. No quantitative formulation exists for the description of dental features.

PURPOSE

The aim of this study was to determine and validate a mathematical process for calculation of the average form of first maxillary molars, including the general occlusal features.

MATERIAL AND METHODS

Stone replicas of 174 caries-free first maxillary molar crowns from young patients ranging from 6 to 9 years of age were measured 3-dimensionally with a laser scanning system at a resolution of approximately 100,000 points. Then, the average tooth was computed, which captured the common features of the molar's surface quantitatively. This new method adapts algorithms both from computer science and neuroscience to detect and associate the same features and same surface points (correspondences) between 1 reference tooth and all other teeth. In this study, the method was tested for 7 different reference teeth. The algorithm does not involve any prior knowledge about teeth and their features.

RESULTS

Irrespective of the reference tooth used, the procedure yielded average teeth that showed nearly no differences (less than +/-30 microm).

CONCLUSION

This approach provides a valid quantitative process for calculating 3-dimensional (3D) averages of occlusal surfaces of teeth even in the event of a high number of digitized surface points. Additionally, because this process detects and assigns point-wise feature correspondences between all library teeth, it may also serve as a basis for a more substantiated principal component analysis evaluating the main natural shape deviations from the 3D average.

Biogeneric tooth: a new mathematical representation for tooth morphology in lower first molars

A mathematical representation of tooth morphology may help to improve and automate restorative computer-aided design processes, virtual dental education, and parametric morphology. However, to date, no quantitative formulation has been identified for the description of dental features. The aim of this study was to establish and to validate a mathematical process for describing the morphology of first lower molars. Stone replicas of 170 caries-free first lower molars from young patients were measured three-dimensionally with a resolution of about 100,000 points. First, the average tooth was computed, which captures the common features of the molar's surface quantitatively. For this, the crucial step was to establish a dense point-to-point correspondence between all teeth. The algorithm did not involve any prior knowledge about teeth. In a second step, principal component analysis was carried out. Repeated for 3 different reference teeth, the procedure yielded average teeth that were nearly independent of the reference (less than +/- 40 microm). Additionally, the results indicate that only a few principal components determine a high percentage of the three-dimensional shape variability of first lower molars (e.g. the first five principal components describe 52% of the total variance, the first 10 principal components 72% and the first 20 principal components 83%). With the novel approach presented in this paper, surfaces of teeth can be described efficiently in terms of only a few parameters. This mathematical representation is called the 'biogeneric tooth'.

Single tooth bite forces in healthy young adults

The assessment of bite forces on healthy single tooth appears essential for a correct quantification of the actual impact of single implant oral rehabilitations. In the present study, a new single tooth strain-gauge bite transducer was used in 52 healthy young adults (36 men, 16 women) with a complete permanent dentition. The influences of tooth position along the dental arch, of side, and of sex, on maximum bite force were assessed by an ANOVA. No significant left-right differences were found. On average, in both sexes the lowest bite force was recorded on the incisors (40-48% of maximum single tooth bite force), the largest force was recorded on the first molar. Bite forces were larger in men than in women (P < 0.002), and increased monotonically along the arch until the first or second permanent molar (P < 0.0001). The present data can be used as reference values for the comparison of dental forces in patients.

[Assessment of effectiveness of the Tanaka-Johnston method for prediction of the mesiodistal diameter of unerupted canines and premolars]

In the present study, the authors evaluated the Tanaka-Johnston method of prediction, with the objective of verifying its effectiveness for the right and left sides, for both genders and for the white, light mulatto, medium mulatto, dark mulatto and black races in the city of Salvador, Bahia. The mesiodistal diameter of the inferior permanent incisors, canines and premolars that had already erupted was measured with the aid of a digital caliper rule in the oral cavity of 98 individuals (45 males and 53 females), aging from 13 to 29 years. The results obtained with the application of the Tanaka-Johnston formulas were compared with the real values through statistical tests. After the analysis of the results, it was observed that the correlation between the estimated values and the real values was greater for females than it was for males. As to race, the coefficients of correlation were satisfactory. They were greater in the superior arch for the dark mulatto race (0.67), and in the inferior arch for the light mulatto race (0.74). Considering the sides, the findings revealed a greater coefficient of correlation for the inferior arch on the left side (0.61). It was concluded that the Tanaka-Johnston method, in spite of originating from a sample of European descendants, is indicated for the prediction of the mesiodistal diameter of canines and premolars in the different races evaluated in this research. The effectiveness of the referred method was also checked for both genders and sides in the studied sample.

Size and shape of the human first permanent molar: a Fourier analysis of the occlusal and equatorial outlines

Form can be viewed as a combination of size and shape. Shape refers to the boundary outline independently from its orientation, relation to reference planes, and dimension (or size). Shape and its changes could be quantified by mathematical methods such as the Fourier series. In this investigation, Fourier analysis has been used to quantify the morphologic characteristics (size and shape) of the outline of the occlusal surface and maximum circumference (equator) in 259 normal, healthy human first permanent maxillary and mandibular molars and to assess the effect of sex. Large within-group variability was found in the Fourier coefficients. Both equatorial and occlusal molar areas were on average larger in male than in female homologous teeth, but the difference was statistically significant only for the equatorial areas. The mean ratios between equatorial and occlusal dental areas were independent from arch (maxillary and mandibular), side, or sex. Both equatorial and occlusal outlines of left and right homologous molars within sex and arch were similar, without size and shape differences. Similarly, no sex differences in shape were found in the comparison of homologous teeth. The method used in the present study could supply information about dental shape in both its entirety and local variations. In particular, the method is extremely sensitive to local variations in dental shape, and it could be usefully employed to compare single teeth to a standard.

Quantitative description of the morphology of the human palate by a mathematical equation

OBJECTIVE

To derive a three-dimensional mathematical description of normal human hard tissue palatal size and shape.

METHODS

The maxillary dental casts of 30 adolescents free from respiratory problems, who had a complete (28 teeth) permanent sound dentition with normal occlusion, were studied. The x, y, z coordinates of several standardized palatal and dental landmarks were obtained with a computerized three-dimensional digitizer. Palatal landmarks were used to derive a mathematical equation of palatal shape in the frontal and sagittal planes. Palatal width, length, frontal and sagittal heights, and sagittal slope, as well as dental arch transverse and anteroposterior dimensions, were computed.

RESULTS

Neither the size nor the shape of the palate was significantly influenced by gender. Only the intercanine distance was larger (p < .025) in males than in females.

CONCLUSIONS

Data collected in the present investigation could represent a first database for the quantitative description of normal human palatal morphology in subjects with a complete permanent dentition.