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Principal component analysis of intercusp distances on the lower first molars of three human populations
ooo3-9969/H $3.00+ 0.00
heAs oralBid. Vol. 33,No. 8, pp. 53>541,1988 Printedin Great Britain. All rights reserved
Copyright0 1988Pergamon Press plc
PRINCIPAL COMPONENT ANALYSIS OF INTERCUSP DISTANCES ON THE LOWER FIRST MOLARS OF THREE HUMAN POPULATIONS ’ Department
M. SERIRAWA,’ E. KANAZAWA,’ T. OZAKI’ and T. BROWN* of Anatomy, Nihon University School of Dentistry at Matsudo, 2-870-1, Sakaecho Nishi,
Matsudo, Chiba 271, Japan and *Department of Dentistry, The University of Adelaide, G.P.O. Box 498, Adelaide, South Australia 5001, Australia (Accepted 17
March
1988)
Summary-The distances between the five main cusps of lower first molars were measured on moirk photographs 01‘ casts obtained from Japanese, Dutch and Australian Aboriginal children. Principal component analysis of the intercusp distances, log transformed and standardized so that average tooth size was held constant, revealed three sources of shape variation in cusp topography. All populations were similar for scores on component 1 which was concerned with variations in the position of the hypoconulid. The Dutch had lowest scores on component 2 indicating small buccolingual distances compared with mesiodistal, whereas the Australian Aboriginals had the lowest mean score on component 3, expressing the distances between metaconid, entoconid and hypoconulid.
INTRODUCTION
Intercusp distances have been measured on premolars and molars as an altelmative to the more conventional mesiodistal and buccolingual diameters of the crown (Gam, 1977; Brown and Townsend, 1984; Townsend, 1985). Intercusp distances are important in odontometry as enamel deposition is initiated at the ameloblast-odontoblast interface at the sites of future cusp tips. These dimensions are probably more useful than external crown diameters in relation to investigations of events taking place during odontogenesis. They also offer the potential for providing new insights into phylogenetic aspects of occlusal morphology. However, it is difficult to measure intercusp distances accurately, particularly if attrition has removed the cusp tips. We have developed fine moir&contour photography for quantification of occlusal features of molars. The technique has been applied to three-dimensional measurements of crowns including haights of cusp ridges and cusp areas (Kanazawa, Sekikawa and Ozaki, 1983, 1984; Kanazawa et al., 1985; Ozaki and Kanazawa, 1984; Ozaki et al., 1984, 1987; Sekikawa et al., 1983, 1986a, 1986b; Sekikawa, K.anazawa and Ozaki, 1987). Our purpose now was to investigate the occlusal shape variations of lower first molars between three populations based on intercusp distances using Healy and Tanner procedures (1981). MATERIALS AND METHODS
The study was made on the following sets of dental casts of attrition-free lower first molars from three populations: (1) Jalpanese, 75 casts of right molars from primary school children living in Ito city (39 males and 36 females); (2) Dutch, 43 casts (27 right and 16 left molars) :from the collection of the University of Amsterdam (sexes and ages of sample were 0.a.
33/a-A
535
unknown); and (3) Australian Aboriginals, 40 casts of left molars from the collection of the Department of Dentistry at Tlie University of Adelaide (24 males and 16 females from Yuendumu in Central Australia). Mesiodistal crown diameters were obtained from each first molar using digital calipers with an accuracy of 0.05 mm. The molar crowns were then photographed by moirt contourography following the technique described by Ozaki and Kanazawa (1984). Only casts were used where molars showed no obvious attrition; they were from children with approximate age range from 5 to 7 years in Japanese and Australian Aboriginals. The precise locations of the cusp tips were determined with the aid of moirC fringes (Plate Fig. 1). This technique provided an accurate and convenient method for measuring intercusp distances. The morphological analysis of the occlusal pentagons were slightly modified from the following procedure reported by Brown and Townsend (1984), who studied the shape of mandibular fist molars in Down syndrome by the log-transform method of Healy and Tanner (1981). First, the intercusp distances (Text Fig. 2) of all molars were transformed into common log distances, and then the generalized size of each tooth was obtained by averaging the 10 log distances. Next, each log distance was scaled by a factor that equated the generalized size of each tooth with the grand average computed from the log distances of all molars in the three populations. Details of the scaling procedures were given in Healy and Tanner (1981) and Brown and Townsend (1984). Shape variation was determined by a principal component analysis of the variance-covariance matrix computed from the scaled log distances of all molars. The principal components obtained indicated shape variation of the occlusal pentagons independent of overall tooth size which was scaled to the
536
M. SEKIKAWAet al.
grand average. Population comparisons of shape variations within the occlusal pentagons were carried out using Student’s t-test to assess the differences between mean values of component scores computed for each population.
Table 2 presents means and standard deviations of the log-transformed intercusp distances and the results of the Student’s t-test. With respect to the unscaled log distances used as a measure of generalized size of the occlusal pentagon, the smallest mean value was displayed by Dutch teeth and largest by the Aboriginals. There was no significant difference between generalized molar size in the Japanese and Aboriginals, but each of these was significantly greater than in the Dutch. Generally, the patterns of scaled log distances used to indicate shape of the molar pentagon were quite different from those displayed by the mean intercusp distances. Also there was a tendency for fewer differences between populations for the scaled distances. This was a consequence of the scaling procedure which brought all teeth to an average size of 0.776 so that the individual scaled log distances indicate the relative contribution of that distance to the grand average. Whereas, the Dutch molars displayed the smallest absolute values for all intercusp distances, 6 of the 10 scaled distances were larger than in the other populations. Four of the scaled distances, namely Prd-Med, Hld-Hnd, Hnd-Prd and Med-Hnd, representing buccal and mesial crown regions did not differ significantly between populations, indicating relative stability of these regions with respect to occlusal shape. In contrast the distance between the two distal
RESULTS
The mean mesiodistal diameters were 11.8 mm (SD 0.53) in Australian Aboriginals, 11.3 mm (SD0.35) in the Dutch and 11Smm (SDOSO) in Japanese. These mean values differed significantly at p < 0.05 between the three populations. Means for the 10 intercusp distances for the three populations are shown in Table 1. Among the three populations, the Dutch had the smallest mean values for all distances whereas, except for Med-End and Hld-Hnd, those in the Australian Aboriginals were largest. Significant differences were found for seven distances between the Dutch and Japanese and between Dutch and Australian Aboriginals. There were two significant differences between distances recorded in Japanese and Australian Aboriginals. These two distances, End-Hld and Med-Hld, also differed significantly between the three populations. However, there were no significant differences between populations for the distances between the two lingual cusps (Med-End) and the two buccal cusps (Hnd-Prd).
Table 1. Means and SD of the intercusp distances of the lower first molars in three populations (mm) Dutch
Australian Aboriginals
Mean SD (?I = 43)
Mean SD (n =40)
Japanese ~___ Mean SD (n = 75) 1. 2. 3. 4. 5. 6. 7. 8. 9. 10.
Prd-Med Met-End End-Hld Hld-Hnd Hnd-Prd Prd-End Prd-Hld MedHnd Med-Hld End-Hnd
5.45 5.91 5.30 3.38 4.39 8.19 7.45 7.51 8.87 6.57
0.52 0.51 0.69 0.45 0.44 0.63 0.61 0.55 0.61 0.59
5.11 5.82 4.75 3.06 4.34 7.75 7.21 7.04 8.48 5.79
Table 2. The log-intercusp
distances
SD
Mean
log distance, unscaled) 0.781 0.030 0.754 Shape (scaled log distance) 1. Prd-Med 0.730 0.028 0.728 2. Me&End 0.766 0.028 0.785 3. End-Hld 0.716 0.043 0.696 4. Hld-Hnd 0.521 0.049 0.496 5. Hnd-Prd 0.635 0.034 0.653 6. Prd--End 0.907 0.014 0.914 7. Prd-Hld 0.865 0.022 0.881 8. Med-Hnd 0.869 0.016 0.871 9. Me&Hld 0.941 0.014 0.955 10. End-Hnd 0.811 0.017 0.783
5.60 5.90 5.85 3.30 4.49 8.38 7.59 7.62 9.19 6.73
0.48 0.41 0.76 0.63 0.55 0.51 0.71 0.48 0.61 0.53
J>D
D
JzD JrD
D
J>D
D
J>D J>D J>D
J
J
of the lower first molars Australian Aboriginals
Dutch
Japanese Mean
0.38 0.53 0.33 0.40 0.46 0.48 0.52 0.45 0.43 0.39
Population differences (p < 0.01)
SD
Mean
SD
0.021
0.791
0.024
0.026 0.035 0.027 0.054 0.042 0.014 0.022 0.019 0.015 0.021
0.733 0.756 0.749 0.501 0.637 0.905 0.862 0.865 0.945 0.811
0.029 0.030 0.047 0.073 0.050 0.017 0.025 0.022 0.018 0.021
Population differences (p < 0.01)
Size (average
J>D
D-CA
J
D
J
D>A
JD
D>A D
J
Intercusp lengths in lower first molars
cusp, End-Hld, displayed significant population differences. Table 3 summarizes the principal component analysis of the scaled intercusp distances; only the first three components which contributed 85.6 per cent to the total variance we:re retained for further analysis. Component coefficients, greater than 0.5 in absolute value, provided a guide for the interpretation of the components. On this, basis, component 1 was concerned with intercusp distances Hld-Hnd, Prd-Hld and MedHnd, component 2 had highest loading for End-Hld, Hnd-Prd, Prd-Hld and End-Hnd, whereas component 3 displayed strong associations with Prd-Med, Med.--End and End-Hld. Intercusp distances involved th.e distobuccal (Hnd), and distal (Hld) cusp were involved in the majority of these higher coefficients. In order to visualize and interpret each component, two contrasting occlusal pentagons were drawn for each component based on mean values for the highest 10 and lowest 10 component scores (Text Fig. 3). The pentagons were superimposed in two ways, by registering at Med and maligning on the line joining the two lingual cusps Med and End (left side of Fig. 3), and by a mathematical method for shape comparisons proposed by Siegel (1982) incorporating a robust fit by a repeated median procedure (right side of Fig. 3). Siegel’s approach is particularly useful as two homologous shapes are matched by selecting the optimal sub-set of homologous points for maximum
Fig. 2. Ten intercusp distances recorded on the occlusal surface. Table 3. Component loadings of the scaled log distances Component
Zl 1. Prd-Med 2. Med-End 3. End-Hld 4. Hld-Hnd 5. Hnd-Prd 6. Prd-End 7. Prd-Hld 8. Med-Hnd 9. Med-Hld 10. End-Hnd Eigen value (x10? Contribution (per cent)
22
23
0.346 0.365 0.411 - 0.980 0.185 0.391 - 0.552 0.594 0.399 -0.003
0.257 -0.299 0.736 0.185 -0.842 - 0.286 -0.689 -0.189 0.098 0.741
0.562 0.705 -0.531 0.032 -0.478 0.221 -0.309 0.405 0.325 -0.243
4.321
3.122
1.908
.39.57
28.59
17.46
23
Fig. 3. Schematic diagrams of the shape components in principal component analysis. Polygons are superimposed (left) on the line joining the lingual cusps and (right) mathematically by the robust repeated median procedure of Siegel (1982). Buccal and mesial sides are upper and left sides of polygons, respectively. Dotted area: high component scores. Clear area: low component scores.
congruence. This is achieved by taking repeated medians to calculate the required parameters for scaling, translation and rotation of shape 2 on shape 1. Because the repeated median procedure includes a scaling parameter, the superimposed occlusal pentagons have been matched in size, emphasizing shape differences. Consequently, the contrasting pairs representing high and low component scores are more readily identifiable with the component loadings shown in Table 3 than are the original unscaled intercusp distances. The first component, contributing 39.6 per cent to variance, was influenced particularly by variations in the position of the distal cusp Hld and the effect of this on crown shape. This interpretation was in accord with the finding that the loading for the scaled distance Hld-Hnd on this component was considerably higher than loadings for the other distances. The second component, contributing 28.6 per cent, was affected mainly by variations in the contributions of two pairs of intercusp distances to overall crown morphology. Subjects with high values for distances End-Hld and End-Hnd tended to have high component scores, whereas low component scores arose from higher values for distances Hnd-Prd and Prd-Hld. In relation to cusp topography, component 2 contrasted the relative positions of Prd and End, affecting the mesiodistal and buccolingual dimensions of the pentagon respectively. Component 3, which contributed 17.5 per cent to the total variance, contrasted variations in the relative contributions of the distances between the two lingual cusps, Med and End, and the two distal cusps Hld and End. The cusp End was common to each of these distances, and the construction in Fig. 3 illustrates the effect of positional variations in this cusp on crown shape.
M.
538
SEKIKAWA
et
Table 4. Comparison of the shape-component Japanese Component ZI 22 23
Mean 0.207 - 0.028 0.090
0.058 0.045 0.043
Mean 0.228 -0.073 0.105
The three populations are compared in Table 4 with respect to the average scores on each of the three major components retained. No significant population differences were found in the first component scores, indicating a similarity in general shape of the first molar. However, there were significant differences in the mean scores between the Dutch and the two other populations for component 2, and between the Australian Aboriginals and the two other populations for component 3. DISCUSSION
Most information on tooth-size characteristics of different populations has accrued from odontometric studies of overall tooth size using the conventional mesiodistal and buccolingual crown diameters. However, as Biggerstaff (1969) pointed out, crown diameters include many separate tooth components such as cusps and ridges. The size, shape and relative position of cusps to one another are fundamental elements of crown morphology in the molar series. Intercusp distances are particularly useful as an aid to interpreting ontogenetic phenomena because cusp tips are the sites of initial mineralization; positional variations in cusps often reflect development events (Townsend, 1985). Mesiodistal crown diameters of the lower first molars differed significantly between the three populations. However, there was greater uniformity between the intercusp distances, particularly for the Japanese and Australian Aboriginals. The population differences for intercusp distance were non-significant for all distances except End-Hld and Med-Hld, each of which included the variable distal cusp Hld. These two distances were the only ones showing differences in mean values that exceeded 0.2 mm between the Japanese and Aboriginals. Of the five peripheral intercusp distances, there were no significant differences between the three populations for lingual distance Med-End and buccal distance Hnd-Prd. On the other hand the distance between distal cusps End-Hld differed significantly, emphasizing the population variability in the distal crown component, particularly the distal cusp Hld. Our findings add to those of other studies comparing intercusp measures with conventional crown dimensions. For example, Gam (1977) studied these relationships in the premolars and molars of a large sample of North American children. Although buccolingual diameters were larger in males, there was no significant sex dimorphism in the intercusp dimensions. Townsend (1985) reported similar trends in the upper premolars of Australian Aboriginals. Thus it appears that the sex differences in overall crown size
scores among three populations Australian Aboriginals
Dutch SD
aI.
SD 0.061 0.047 0.039
Mean 0.233 -0.010 0.066
Population differences (p < 0.01)
SD 0.082 0.066 0.043
J>D
DA
J>A
are established after the positions of the cusp tips have been localized by spreading mineralization. Our findings for mesiodistal crown diameter were significantly different, but intercusp distances of mesiodistal directions Med-End and Hnd-Prd were insignificant among three populations; this suggests that the sequence and timing of initial cusp mineralization, with the possible exception of distal cusp Hld, was similar in the three populations, but the duration and rate of amelogenesis during subsequent crown formation, mainly mesiodistal direction, differed among populations. Size and shape of the occlusal pentagon as indicated by the intercusp distances and the scaled log distances respectively showed population differences, especially between the Dutch and the others. However, the Japanese and Australian Aboriginal groups were relatively similar in cusp topography. The major sources of variability in crown morphology were quantified by principal component analysis and depended to a large extent on the position of distal cusp Hld and its effect on buccal intercusp distances Hld-Hnd and End-Hld. The three populations did not differ in their scores on this component, an indicator of fundamental shape of lower fhst molars. The major source of variability in crown shape appeared to reside in the distal cusp, the last cusp to mineralize and the last molar cusp to develop phylogenetically. This observation accords with the finding of Brown and Townsend (1984) using principal component analysis of Healy-Tanner log transforms to assess crown shape in molars of Down-syndrome children; the position of the distal cusp and the intercusp distances involving this cusp differed in the Down-syndrome children compared with normal controls. They suggested that the growth retardation characteristics of Trisomy 21 led to the lingual displacement of the distal cusp. Scores on the second component were smaller in the Dutch than the other two groups which displayed no significant difference in mean values. This component contrasted some mesiodistal and buccolingual intercusp distances. The low mean score in the Dutch arose from a lower contribution to crown size from the buccolingual dimensions compared with the mesiodistal. As the distance between the two lingual cusps, Med-End, was similar in the three populations, component 2 expressed itself morphologically as variations in the relative lengths of the buccal and distal segments of the molar crown outline (Fig. 3, left). Morris (1986) contrasted buccolingual and mesiodistal intercusp distances on the upper molars of five human populations and concluded that there was twice as much variation in the buccolingual dimensions; mesiodistal intercusp distances varied little
Intercusp lengths in lower first molars between groups. Morris hypothesized that buccolingual size differences, were related to the transverse occlusal stroke of the mandible, an increase in this dimension being more effective in maintaining correct occlusal function than increased mesiodistal length. Our second component quantifies for the lower first molar the type of shape variations discussed by Morris for the maxillary first molar. Component 3, although contributing only 17 per cent to the total variance, represented an interesting source of shape variation concerned with the relative contributions the intercusp distances Med-End and End-Hld. Australian Aboriginals had the lowest mean score on this component, indicating a greater contribution by End-Hld to crown size. Macroscopitally, the crown of the lower first molar in Australian Aboriginals had a distinguishably large Hld and often a sixth cusp and well-developed bucca1 cingulum compared to the two other populations. This indicates that the talonid element of the lower molar was well-developed compared with the trigonid in the Aboriginals. Indeed. the cusp areas of talonid elements relative to whole crown area, except for End, were larger in Aboriginals than the Dutch and Japanese (Kanazawa et al., 1985). Wood and Abbott (1983) found that in fossil Plio-Pleistocene hominids the talonid cusps were larger than trigonid cusps. This suggests that the lower first molar Iof Australian Aboriginals may display the most primitive morphological characteristics of the three polpulations. When the occlusal pentagons were aligned on the two lingual cusps as in Fig. 3 (left), it becomes apparent that, in subjects with low scores on component 3, the mesiobuccal cusp Prd is located more mesially in relation to the lingual intercusp line. This tendency for a mesial location of Prd was also found in the deciduous lower second molar of Japanese (Sekikawa et al., 1986b). It has generally been accepted that the first component, contributing most to the total variance, in biometrical data represents variability in overall size, although the eigen vectors may sometimes be irregular in size (van Vork and Howells, 1984). Corruccini (1983) showed that the coefficients of the first component in a principal component analysis of body measurements were related to measures of body size allometrically rather than linearly. We believe that the log transformation and scaling procedures, described by Healy and Tanner (1981), are well suited for describing shape variation in occlusal morphology; they treat relationships additively rather than multiplicatively compared with other scaling procedures such as standardizing the area of the occlusal pentagon. Indeed, when principal component analysis was carried out on data scaled by pentagon area, the first three components concentrated about 77 per cent of total shape variation in contrast to 86 per cent when adopting the Healy-Tanner scaling. With the increasing availability of accurate measuring techniques, :such as moire photogrammetry and more penetrating analytic procedures, it has become feasible to describe the occlusal characteristics of the human dentition by methods that avoid the obvious limitations of conventional external crown dimensions. With furtheir development, it will be possible to
539
shed more light on the complex relationships between size, shape, developmental phenomena and masticatory function in the human dentition. REFERENCES
Biggerstaff R. H. (1969) The basal area of posterior tooth crown components: the assessment of within tooth varia-
tion of premolars and molars. Am. J. phys. Anrhrop. 31, 163-170.
Brown T. and Townsend G. C. (1984) Size and shape of mandibular first molars in Down syndrome. Ann. Hum. Biol. 11, 281-290. Corruccini R. S. (1983) Principal components for allometric analysis. Am. J. phys. Anthrop. 60, 451453. Gam S. M. (1977) Genetics of dental development. In: The Biology of Occlusal Developmeni (Edited by McNamara J. A.). Craniofacial Growth Series, Ann Arbor, Mich. Healy M. J. and Tanner J. M. (1981) Size and shape in relation to growthand form. Symp. Zool. Sot. Lond.46,1935. Kanazawa E.. Sekikawa M. and Ozaki T. (1983) Threedimensional measurements of the occlusal surface of upper first molars in a modem Japanese population. Acta anat. 116, 90-96. Kanazawa E., Sekikawa M. and Ozaki T. (1984) Threedimensional measurements of the occlusal surface of upper molars in a Dutch population. J. dent. Res. 63, 1298-1301. Kanazawa E., Sekikawa M., Akai J. and Ozaki T. (1985) Allometric variation on cuspal areas of the lower first molar in three racial populations. J. Anrhrop. Sot. Nippon 93, 425438.
Morris D. H. (1986) Maxillary molar occlusal polygons in five human samples. Am. J. phys. Anrhrop. 70, 333-338. Ozaki T. and Kanazawa E. (1984) An anolication of moire method to three-dimensional measure;dents of the occlusal aspects of molars. Acta morph. neel. stand. 22, 85-91. Ozaki T., Kanazawa E., Sekikawa M. and Sakurai S. (1984) Three-dimensional measurement of occlusal surface of upper first molars in Dutch population. Jap. J. oral Biol. 26, 241-248. Ozaki T., Kanazawa E., Sekikawa M. and Akai J. (1987) Three-dimensional measurement of occlusal surface of upper f%t molars in Australian Aboriginals. Ausr. dent. J. 32, 263-269. Sekikiwa M., Akai J., Nanbu J., Kanazawa E. and Ozaki T. (1983) Three-dimensional measurements of the occlusal surface of lower first molars in a modem Japanese population. Jap. J. oral Biol. 25, 737-744. Sekikawa M., Akai J., Kanazawa E. and Ozaki T. (1986a) Three-dimensional measurement of the occlusal surfaces of lower first molars of Australian Aboriginals. Am. J. phys. Anthrop. 71, 25-32.
Sekikawa M., Akai J., Kanazawa E. and Ozaki T. (1986b) Three-dimensional measurement of occlusal surface of deciduous second molar. J. dent. Res. 65, 743. Sekikawa M., Kanazawa E. and Ozaki T. (1987) Study of the cuspal ridges of the upper first molars in a modem Japanese population. Acta anat. 129, 159-164. Siegel A. F. (1982) Geometric data analysis: an interactive graphics program for shape comparisons. In: Modern Data Analysis (Edited by Launer R. L. and Siegel A. F.) pp. 103-122. Academic Press, New York. Townsend G. C. (1985) Intercuspal distances of maxillary premolar teeth in Australian Aboriginals. J. dent. Res. 64, 4434%. Vork G. N. van and Howells W. W. (1984) Multivariare Statistical Methoak in Physical Amhropology. Reidel, Holland. Wood B. A. and Abbott S. A. (1983) Analysis of the dental morphology of Plio-Pleistocene hominids. I. Mandibular molars: crown area measurements and morphological traits. J. Anat. 136, 197-219.
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M. SEKIKAWAet al.
Plate 1 Fig. 1.Moirk photographs of the lower right first molars in three populations. Cusps are indicated as Prd, protoconid; Med, metaconid; End, entoconid; Hnd, hypoconid; Hld, hypoconulid.
Intercusp
lengths Aus.
in lower
first
541
molars
Aboriginols
Japanese
Dutch
I Plate
1
5.0 mm
I
heAs oralBid. Vol. 33,No. 8, pp. 53>541,1988 Printedin Great Britain. All rights reserved
Copyright0 1988Pergamon Press plc
PRINCIPAL COMPONENT ANALYSIS OF INTERCUSP DISTANCES ON THE LOWER FIRST MOLARS OF THREE HUMAN POPULATIONS ’ Department
M. SERIRAWA,’ E. KANAZAWA,’ T. OZAKI’ and T. BROWN* of Anatomy, Nihon University School of Dentistry at Matsudo, 2-870-1, Sakaecho Nishi,
Matsudo, Chiba 271, Japan and *Department of Dentistry, The University of Adelaide, G.P.O. Box 498, Adelaide, South Australia 5001, Australia (Accepted 17
March
1988)
Summary-The distances between the five main cusps of lower first molars were measured on moirk photographs 01‘ casts obtained from Japanese, Dutch and Australian Aboriginal children. Principal component analysis of the intercusp distances, log transformed and standardized so that average tooth size was held constant, revealed three sources of shape variation in cusp topography. All populations were similar for scores on component 1 which was concerned with variations in the position of the hypoconulid. The Dutch had lowest scores on component 2 indicating small buccolingual distances compared with mesiodistal, whereas the Australian Aboriginals had the lowest mean score on component 3, expressing the distances between metaconid, entoconid and hypoconulid.
INTRODUCTION
Intercusp distances have been measured on premolars and molars as an altelmative to the more conventional mesiodistal and buccolingual diameters of the crown (Gam, 1977; Brown and Townsend, 1984; Townsend, 1985). Intercusp distances are important in odontometry as enamel deposition is initiated at the ameloblast-odontoblast interface at the sites of future cusp tips. These dimensions are probably more useful than external crown diameters in relation to investigations of events taking place during odontogenesis. They also offer the potential for providing new insights into phylogenetic aspects of occlusal morphology. However, it is difficult to measure intercusp distances accurately, particularly if attrition has removed the cusp tips. We have developed fine moir&contour photography for quantification of occlusal features of molars. The technique has been applied to three-dimensional measurements of crowns including haights of cusp ridges and cusp areas (Kanazawa, Sekikawa and Ozaki, 1983, 1984; Kanazawa et al., 1985; Ozaki and Kanazawa, 1984; Ozaki et al., 1984, 1987; Sekikawa et al., 1983, 1986a, 1986b; Sekikawa, K.anazawa and Ozaki, 1987). Our purpose now was to investigate the occlusal shape variations of lower first molars between three populations based on intercusp distances using Healy and Tanner procedures (1981). MATERIALS AND METHODS
The study was made on the following sets of dental casts of attrition-free lower first molars from three populations: (1) Jalpanese, 75 casts of right molars from primary school children living in Ito city (39 males and 36 females); (2) Dutch, 43 casts (27 right and 16 left molars) :from the collection of the University of Amsterdam (sexes and ages of sample were 0.a.
33/a-A
535
unknown); and (3) Australian Aboriginals, 40 casts of left molars from the collection of the Department of Dentistry at Tlie University of Adelaide (24 males and 16 females from Yuendumu in Central Australia). Mesiodistal crown diameters were obtained from each first molar using digital calipers with an accuracy of 0.05 mm. The molar crowns were then photographed by moirt contourography following the technique described by Ozaki and Kanazawa (1984). Only casts were used where molars showed no obvious attrition; they were from children with approximate age range from 5 to 7 years in Japanese and Australian Aboriginals. The precise locations of the cusp tips were determined with the aid of moirC fringes (Plate Fig. 1). This technique provided an accurate and convenient method for measuring intercusp distances. The morphological analysis of the occlusal pentagons were slightly modified from the following procedure reported by Brown and Townsend (1984), who studied the shape of mandibular fist molars in Down syndrome by the log-transform method of Healy and Tanner (1981). First, the intercusp distances (Text Fig. 2) of all molars were transformed into common log distances, and then the generalized size of each tooth was obtained by averaging the 10 log distances. Next, each log distance was scaled by a factor that equated the generalized size of each tooth with the grand average computed from the log distances of all molars in the three populations. Details of the scaling procedures were given in Healy and Tanner (1981) and Brown and Townsend (1984). Shape variation was determined by a principal component analysis of the variance-covariance matrix computed from the scaled log distances of all molars. The principal components obtained indicated shape variation of the occlusal pentagons independent of overall tooth size which was scaled to the
536
M. SEKIKAWAet al.
grand average. Population comparisons of shape variations within the occlusal pentagons were carried out using Student’s t-test to assess the differences between mean values of component scores computed for each population.
Table 2 presents means and standard deviations of the log-transformed intercusp distances and the results of the Student’s t-test. With respect to the unscaled log distances used as a measure of generalized size of the occlusal pentagon, the smallest mean value was displayed by Dutch teeth and largest by the Aboriginals. There was no significant difference between generalized molar size in the Japanese and Aboriginals, but each of these was significantly greater than in the Dutch. Generally, the patterns of scaled log distances used to indicate shape of the molar pentagon were quite different from those displayed by the mean intercusp distances. Also there was a tendency for fewer differences between populations for the scaled distances. This was a consequence of the scaling procedure which brought all teeth to an average size of 0.776 so that the individual scaled log distances indicate the relative contribution of that distance to the grand average. Whereas, the Dutch molars displayed the smallest absolute values for all intercusp distances, 6 of the 10 scaled distances were larger than in the other populations. Four of the scaled distances, namely Prd-Med, Hld-Hnd, Hnd-Prd and Med-Hnd, representing buccal and mesial crown regions did not differ significantly between populations, indicating relative stability of these regions with respect to occlusal shape. In contrast the distance between the two distal
RESULTS
The mean mesiodistal diameters were 11.8 mm (SD 0.53) in Australian Aboriginals, 11.3 mm (SD0.35) in the Dutch and 11Smm (SDOSO) in Japanese. These mean values differed significantly at p < 0.05 between the three populations. Means for the 10 intercusp distances for the three populations are shown in Table 1. Among the three populations, the Dutch had the smallest mean values for all distances whereas, except for Med-End and Hld-Hnd, those in the Australian Aboriginals were largest. Significant differences were found for seven distances between the Dutch and Japanese and between Dutch and Australian Aboriginals. There were two significant differences between distances recorded in Japanese and Australian Aboriginals. These two distances, End-Hld and Med-Hld, also differed significantly between the three populations. However, there were no significant differences between populations for the distances between the two lingual cusps (Med-End) and the two buccal cusps (Hnd-Prd).
Table 1. Means and SD of the intercusp distances of the lower first molars in three populations (mm) Dutch
Australian Aboriginals
Mean SD (?I = 43)
Mean SD (n =40)
Japanese ~___ Mean SD (n = 75) 1. 2. 3. 4. 5. 6. 7. 8. 9. 10.
Prd-Med Met-End End-Hld Hld-Hnd Hnd-Prd Prd-End Prd-Hld MedHnd Med-Hld End-Hnd
5.45 5.91 5.30 3.38 4.39 8.19 7.45 7.51 8.87 6.57
0.52 0.51 0.69 0.45 0.44 0.63 0.61 0.55 0.61 0.59
5.11 5.82 4.75 3.06 4.34 7.75 7.21 7.04 8.48 5.79
Table 2. The log-intercusp
distances
SD
Mean
log distance, unscaled) 0.781 0.030 0.754 Shape (scaled log distance) 1. Prd-Med 0.730 0.028 0.728 2. Me&End 0.766 0.028 0.785 3. End-Hld 0.716 0.043 0.696 4. Hld-Hnd 0.521 0.049 0.496 5. Hnd-Prd 0.635 0.034 0.653 6. Prd--End 0.907 0.014 0.914 7. Prd-Hld 0.865 0.022 0.881 8. Med-Hnd 0.869 0.016 0.871 9. Me&Hld 0.941 0.014 0.955 10. End-Hnd 0.811 0.017 0.783
5.60 5.90 5.85 3.30 4.49 8.38 7.59 7.62 9.19 6.73
0.48 0.41 0.76 0.63 0.55 0.51 0.71 0.48 0.61 0.53
J>D
D
JzD JrD
D
J>D
D
J>D J>D J>D
J
J
of the lower first molars Australian Aboriginals
Dutch
Japanese Mean
0.38 0.53 0.33 0.40 0.46 0.48 0.52 0.45 0.43 0.39
Population differences (p < 0.01)
SD
Mean
SD
0.021
0.791
0.024
0.026 0.035 0.027 0.054 0.042 0.014 0.022 0.019 0.015 0.021
0.733 0.756 0.749 0.501 0.637 0.905 0.862 0.865 0.945 0.811
0.029 0.030 0.047 0.073 0.050 0.017 0.025 0.022 0.018 0.021
Population differences (p < 0.01)
Size (average
J>D
D-CA
J
D
J
D>A
J
D>A D
J
Intercusp lengths in lower first molars
cusp, End-Hld, displayed significant population differences. Table 3 summarizes the principal component analysis of the scaled intercusp distances; only the first three components which contributed 85.6 per cent to the total variance we:re retained for further analysis. Component coefficients, greater than 0.5 in absolute value, provided a guide for the interpretation of the components. On this, basis, component 1 was concerned with intercusp distances Hld-Hnd, Prd-Hld and MedHnd, component 2 had highest loading for End-Hld, Hnd-Prd, Prd-Hld and End-Hnd, whereas component 3 displayed strong associations with Prd-Med, Med.--End and End-Hld. Intercusp distances involved th.e distobuccal (Hnd), and distal (Hld) cusp were involved in the majority of these higher coefficients. In order to visualize and interpret each component, two contrasting occlusal pentagons were drawn for each component based on mean values for the highest 10 and lowest 10 component scores (Text Fig. 3). The pentagons were superimposed in two ways, by registering at Med and maligning on the line joining the two lingual cusps Med and End (left side of Fig. 3), and by a mathematical method for shape comparisons proposed by Siegel (1982) incorporating a robust fit by a repeated median procedure (right side of Fig. 3). Siegel’s approach is particularly useful as two homologous shapes are matched by selecting the optimal sub-set of homologous points for maximum
Fig. 2. Ten intercusp distances recorded on the occlusal surface. Table 3. Component loadings of the scaled log distances Component
Zl 1. Prd-Med 2. Med-End 3. End-Hld 4. Hld-Hnd 5. Hnd-Prd 6. Prd-End 7. Prd-Hld 8. Med-Hnd 9. Med-Hld 10. End-Hnd Eigen value (x10? Contribution (per cent)
22
23
0.346 0.365 0.411 - 0.980 0.185 0.391 - 0.552 0.594 0.399 -0.003
0.257 -0.299 0.736 0.185 -0.842 - 0.286 -0.689 -0.189 0.098 0.741
0.562 0.705 -0.531 0.032 -0.478 0.221 -0.309 0.405 0.325 -0.243
4.321
3.122
1.908
.39.57
28.59
17.46
23
Fig. 3. Schematic diagrams of the shape components in principal component analysis. Polygons are superimposed (left) on the line joining the lingual cusps and (right) mathematically by the robust repeated median procedure of Siegel (1982). Buccal and mesial sides are upper and left sides of polygons, respectively. Dotted area: high component scores. Clear area: low component scores.
congruence. This is achieved by taking repeated medians to calculate the required parameters for scaling, translation and rotation of shape 2 on shape 1. Because the repeated median procedure includes a scaling parameter, the superimposed occlusal pentagons have been matched in size, emphasizing shape differences. Consequently, the contrasting pairs representing high and low component scores are more readily identifiable with the component loadings shown in Table 3 than are the original unscaled intercusp distances. The first component, contributing 39.6 per cent to variance, was influenced particularly by variations in the position of the distal cusp Hld and the effect of this on crown shape. This interpretation was in accord with the finding that the loading for the scaled distance Hld-Hnd on this component was considerably higher than loadings for the other distances. The second component, contributing 28.6 per cent, was affected mainly by variations in the contributions of two pairs of intercusp distances to overall crown morphology. Subjects with high values for distances End-Hld and End-Hnd tended to have high component scores, whereas low component scores arose from higher values for distances Hnd-Prd and Prd-Hld. In relation to cusp topography, component 2 contrasted the relative positions of Prd and End, affecting the mesiodistal and buccolingual dimensions of the pentagon respectively. Component 3, which contributed 17.5 per cent to the total variance, contrasted variations in the relative contributions of the distances between the two lingual cusps, Med and End, and the two distal cusps Hld and End. The cusp End was common to each of these distances, and the construction in Fig. 3 illustrates the effect of positional variations in this cusp on crown shape.
M.
538
SEKIKAWA
et
Table 4. Comparison of the shape-component Japanese Component ZI 22 23
Mean 0.207 - 0.028 0.090
0.058 0.045 0.043
Mean 0.228 -0.073 0.105
The three populations are compared in Table 4 with respect to the average scores on each of the three major components retained. No significant population differences were found in the first component scores, indicating a similarity in general shape of the first molar. However, there were significant differences in the mean scores between the Dutch and the two other populations for component 2, and between the Australian Aboriginals and the two other populations for component 3. DISCUSSION
Most information on tooth-size characteristics of different populations has accrued from odontometric studies of overall tooth size using the conventional mesiodistal and buccolingual crown diameters. However, as Biggerstaff (1969) pointed out, crown diameters include many separate tooth components such as cusps and ridges. The size, shape and relative position of cusps to one another are fundamental elements of crown morphology in the molar series. Intercusp distances are particularly useful as an aid to interpreting ontogenetic phenomena because cusp tips are the sites of initial mineralization; positional variations in cusps often reflect development events (Townsend, 1985). Mesiodistal crown diameters of the lower first molars differed significantly between the three populations. However, there was greater uniformity between the intercusp distances, particularly for the Japanese and Australian Aboriginals. The population differences for intercusp distance were non-significant for all distances except End-Hld and Med-Hld, each of which included the variable distal cusp Hld. These two distances were the only ones showing differences in mean values that exceeded 0.2 mm between the Japanese and Aboriginals. Of the five peripheral intercusp distances, there were no significant differences between the three populations for lingual distance Med-End and buccal distance Hnd-Prd. On the other hand the distance between distal cusps End-Hld differed significantly, emphasizing the population variability in the distal crown component, particularly the distal cusp Hld. Our findings add to those of other studies comparing intercusp measures with conventional crown dimensions. For example, Gam (1977) studied these relationships in the premolars and molars of a large sample of North American children. Although buccolingual diameters were larger in males, there was no significant sex dimorphism in the intercusp dimensions. Townsend (1985) reported similar trends in the upper premolars of Australian Aboriginals. Thus it appears that the sex differences in overall crown size
scores among three populations Australian Aboriginals
Dutch SD
aI.
SD 0.061 0.047 0.039
Mean 0.233 -0.010 0.066
Population differences (p < 0.01)
SD 0.082 0.066 0.043
J>D
DA
J>A
are established after the positions of the cusp tips have been localized by spreading mineralization. Our findings for mesiodistal crown diameter were significantly different, but intercusp distances of mesiodistal directions Med-End and Hnd-Prd were insignificant among three populations; this suggests that the sequence and timing of initial cusp mineralization, with the possible exception of distal cusp Hld, was similar in the three populations, but the duration and rate of amelogenesis during subsequent crown formation, mainly mesiodistal direction, differed among populations. Size and shape of the occlusal pentagon as indicated by the intercusp distances and the scaled log distances respectively showed population differences, especially between the Dutch and the others. However, the Japanese and Australian Aboriginal groups were relatively similar in cusp topography. The major sources of variability in crown morphology were quantified by principal component analysis and depended to a large extent on the position of distal cusp Hld and its effect on buccal intercusp distances Hld-Hnd and End-Hld. The three populations did not differ in their scores on this component, an indicator of fundamental shape of lower fhst molars. The major source of variability in crown shape appeared to reside in the distal cusp, the last cusp to mineralize and the last molar cusp to develop phylogenetically. This observation accords with the finding of Brown and Townsend (1984) using principal component analysis of Healy-Tanner log transforms to assess crown shape in molars of Down-syndrome children; the position of the distal cusp and the intercusp distances involving this cusp differed in the Down-syndrome children compared with normal controls. They suggested that the growth retardation characteristics of Trisomy 21 led to the lingual displacement of the distal cusp. Scores on the second component were smaller in the Dutch than the other two groups which displayed no significant difference in mean values. This component contrasted some mesiodistal and buccolingual intercusp distances. The low mean score in the Dutch arose from a lower contribution to crown size from the buccolingual dimensions compared with the mesiodistal. As the distance between the two lingual cusps, Med-End, was similar in the three populations, component 2 expressed itself morphologically as variations in the relative lengths of the buccal and distal segments of the molar crown outline (Fig. 3, left). Morris (1986) contrasted buccolingual and mesiodistal intercusp distances on the upper molars of five human populations and concluded that there was twice as much variation in the buccolingual dimensions; mesiodistal intercusp distances varied little
Intercusp lengths in lower first molars between groups. Morris hypothesized that buccolingual size differences, were related to the transverse occlusal stroke of the mandible, an increase in this dimension being more effective in maintaining correct occlusal function than increased mesiodistal length. Our second component quantifies for the lower first molar the type of shape variations discussed by Morris for the maxillary first molar. Component 3, although contributing only 17 per cent to the total variance, represented an interesting source of shape variation concerned with the relative contributions the intercusp distances Med-End and End-Hld. Australian Aboriginals had the lowest mean score on this component, indicating a greater contribution by End-Hld to crown size. Macroscopitally, the crown of the lower first molar in Australian Aboriginals had a distinguishably large Hld and often a sixth cusp and well-developed bucca1 cingulum compared to the two other populations. This indicates that the talonid element of the lower molar was well-developed compared with the trigonid in the Aboriginals. Indeed. the cusp areas of talonid elements relative to whole crown area, except for End, were larger in Aboriginals than the Dutch and Japanese (Kanazawa et al., 1985). Wood and Abbott (1983) found that in fossil Plio-Pleistocene hominids the talonid cusps were larger than trigonid cusps. This suggests that the lower first molar Iof Australian Aboriginals may display the most primitive morphological characteristics of the three polpulations. When the occlusal pentagons were aligned on the two lingual cusps as in Fig. 3 (left), it becomes apparent that, in subjects with low scores on component 3, the mesiobuccal cusp Prd is located more mesially in relation to the lingual intercusp line. This tendency for a mesial location of Prd was also found in the deciduous lower second molar of Japanese (Sekikawa et al., 1986b). It has generally been accepted that the first component, contributing most to the total variance, in biometrical data represents variability in overall size, although the eigen vectors may sometimes be irregular in size (van Vork and Howells, 1984). Corruccini (1983) showed that the coefficients of the first component in a principal component analysis of body measurements were related to measures of body size allometrically rather than linearly. We believe that the log transformation and scaling procedures, described by Healy and Tanner (1981), are well suited for describing shape variation in occlusal morphology; they treat relationships additively rather than multiplicatively compared with other scaling procedures such as standardizing the area of the occlusal pentagon. Indeed, when principal component analysis was carried out on data scaled by pentagon area, the first three components concentrated about 77 per cent of total shape variation in contrast to 86 per cent when adopting the Healy-Tanner scaling. With the increasing availability of accurate measuring techniques, :such as moire photogrammetry and more penetrating analytic procedures, it has become feasible to describe the occlusal characteristics of the human dentition by methods that avoid the obvious limitations of conventional external crown dimensions. With furtheir development, it will be possible to
539
shed more light on the complex relationships between size, shape, developmental phenomena and masticatory function in the human dentition. REFERENCES
Biggerstaff R. H. (1969) The basal area of posterior tooth crown components: the assessment of within tooth varia-
tion of premolars and molars. Am. J. phys. Anrhrop. 31, 163-170.
Brown T. and Townsend G. C. (1984) Size and shape of mandibular first molars in Down syndrome. Ann. Hum. Biol. 11, 281-290. Corruccini R. S. (1983) Principal components for allometric analysis. Am. J. phys. Anthrop. 60, 451453. Gam S. M. (1977) Genetics of dental development. In: The Biology of Occlusal Developmeni (Edited by McNamara J. A.). Craniofacial Growth Series, Ann Arbor, Mich. Healy M. J. and Tanner J. M. (1981) Size and shape in relation to growthand form. Symp. Zool. Sot. Lond.46,1935. Kanazawa E.. Sekikawa M. and Ozaki T. (1983) Threedimensional measurements of the occlusal surface of upper first molars in a modem Japanese population. Acta anat. 116, 90-96. Kanazawa E., Sekikawa M. and Ozaki T. (1984) Threedimensional measurements of the occlusal surface of upper molars in a Dutch population. J. dent. Res. 63, 1298-1301. Kanazawa E., Sekikawa M., Akai J. and Ozaki T. (1985) Allometric variation on cuspal areas of the lower first molar in three racial populations. J. Anrhrop. Sot. Nippon 93, 425438.
Morris D. H. (1986) Maxillary molar occlusal polygons in five human samples. Am. J. phys. Anrhrop. 70, 333-338. Ozaki T. and Kanazawa E. (1984) An anolication of moire method to three-dimensional measure;dents of the occlusal aspects of molars. Acta morph. neel. stand. 22, 85-91. Ozaki T., Kanazawa E., Sekikawa M. and Sakurai S. (1984) Three-dimensional measurement of occlusal surface of upper first molars in Dutch population. Jap. J. oral Biol. 26, 241-248. Ozaki T., Kanazawa E., Sekikawa M. and Akai J. (1987) Three-dimensional measurement of occlusal surface of upper f%t molars in Australian Aboriginals. Ausr. dent. J. 32, 263-269. Sekikiwa M., Akai J., Nanbu J., Kanazawa E. and Ozaki T. (1983) Three-dimensional measurements of the occlusal surface of lower first molars in a modem Japanese population. Jap. J. oral Biol. 25, 737-744. Sekikawa M., Akai J., Kanazawa E. and Ozaki T. (1986a) Three-dimensional measurement of the occlusal surfaces of lower first molars of Australian Aboriginals. Am. J. phys. Anthrop. 71, 25-32.
Sekikawa M., Akai J., Kanazawa E. and Ozaki T. (1986b) Three-dimensional measurement of occlusal surface of deciduous second molar. J. dent. Res. 65, 743. Sekikawa M., Kanazawa E. and Ozaki T. (1987) Study of the cuspal ridges of the upper first molars in a modem Japanese population. Acta anat. 129, 159-164. Siegel A. F. (1982) Geometric data analysis: an interactive graphics program for shape comparisons. In: Modern Data Analysis (Edited by Launer R. L. and Siegel A. F.) pp. 103-122. Academic Press, New York. Townsend G. C. (1985) Intercuspal distances of maxillary premolar teeth in Australian Aboriginals. J. dent. Res. 64, 4434%. Vork G. N. van and Howells W. W. (1984) Multivariare Statistical Methoak in Physical Amhropology. Reidel, Holland. Wood B. A. and Abbott S. A. (1983) Analysis of the dental morphology of Plio-Pleistocene hominids. I. Mandibular molars: crown area measurements and morphological traits. J. Anat. 136, 197-219.
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M. SEKIKAWAet al.
Plate 1 Fig. 1.Moirk photographs of the lower right first molars in three populations. Cusps are indicated as Prd, protoconid; Med, metaconid; End, entoconid; Hnd, hypoconid; Hld, hypoconulid.
Intercusp
lengths Aus.
in lower
first
541
molars
Aboriginols
Japanese
Dutch
I Plate
1
5.0 mm
I