Archs oral Bid.
Vol.
22. pp. 677 to 683
Pergamon Press 1977. Prmfed in Great Bntain
THE RELATIONSHIP BETWEEN THE SURFACE AREA OF TIHE ENAMEL CROWNS OF HUMAN TEETH AND THAT OF THE DENTINE-ENAMEL JUNCTION 0.
KIMURA*,E. DYKES and R. W. FURNHEAD
The London Hospital Medical College, Department of Dental Anatomy, Turner Street, London E.1, England
Summary-The surface area of the enamel and that of the dentine-enamel junction and the volume of enamel were calculated using a computer-based three-dimensional reconstruction technique. The surface area of the dentine+namel junction was compensated for its pitted nature. Different individual teeth had wide variation in surface areas but, for the same kind of tooth the: ratio between the surface area of the enamel and that of the dentin-name1 junction was very similar. Only a small amount (8-l 7 per cent) need be added to the thickness of crystals emerging normal to the enamel surface to account for the difference in surface areas. If it is assumed that crystals have uniform width and thickness, the angle of emergence of the crystals observed is sufficient to provide the required increase in the enamel surface area.
INTRODUaION It has been postulated from time to time that the apparent difference in the surface area between the
enamel crowns of teeth and the surface of dentine at the dentineaamel junction obliges the ameloblasts either to produce progressively wider rods as the surface of the enamel is reached (Pickerill, 1913; Williams, 1923; Chase, 1924; Heuser, 1956) or to produce extra rods (Mummery, 1916). The earlier work on this subject which has been reviewed by Fosse (1968) has been conoemed with the measurement of rod diameters or rod densities in different regions of the enamel but, as pointed out by Osbom (1973), with this approach a.11measurements are likely to be inaccurate unless the directions of the prism axes with respect to the plane of viewing can be taken into account. In other words, previous work has tended to calculate these surface areas from measurement of selected groups of ro,ds because presumably the direct measurement of the two surface areas presented serious technical difficulties. As far as we are aware, apart from the painstakingly careful wax and foil reconstructions prepared by Fosse (1964) there has been little effort to establish the precise magnitude of difference between these two surface areas which we believe is necessary before one can speculate on the mechanisms involved in accommodating this increase in surface area.. The model-making stage of the technique used by Fosse (1964) seemed to us to be the stage at which inaccuracies could be introduced and it should be noted that the ratios calculated from the two specimens he studied are considerably higher than those determined by our method. It is therefore our purpose to describe the initial results of a quantitative method using a computer-based three-dimensional reconstruction technique whereby detailed l Present address: Tokyo Medical and Dental University, School of Dentistry, Department of Pedodontics, l-5-45, Yushima, Bunkyo-Ku, Tokyo, Japan.
measurements are possible and surface areas and volumes of teeth can be accurately calculated directly from serial sections. We considered it important to avoid the pitfalls created by consideration of variations in rod size and densities. We tried to overcome this difficulty by adopting the crystal as the fundamental unit of the enamel structure. Moreover, we have assumed that enamel crystals and surrounding organic matrix have unvarying cross-sectional area throughout their lengths in order to establish whether in theoretical terms the accommodation of increase in surface area could be brought about simply by the angle of their emergence at the surface. MATERIALS AND METHODS
Ten extracted sound human teeth free from attrition were embedded in polyester resin, and two parallel grooves and one diagonal groove were milled into the surface of the block (Sullivan, 1972). The resulting grooves were filled with coloured resin. These markers are very important as they record the relative positions of each section in the block as well as a magnification scale factor. The distance between the two parallel markers and the angle of the diagonal marker to the parallel ones were accurately measured with a travelling microscope. Longitudinal serial sections were cut from the embedded teeth. Between 9-14 sections were obtained from each tooth, and these were ground to about 100~ thickness. The dentine in each section was stained with Van Gieson’s pi&c acid fuchsin solution for lOmin, in order to show up the dentine-name1 junction more clearly. The image of the stained section was projected at a magnification of about 15 times on to a D-Mac X-Y coordinate plotting table (Cetec Systems Limited (formerly D-Mac) Queen Elizabeth Avenue, Hillington, Glasgow G52 4SN) and the contours of the enamel surface and the dentin-name1 junction were traced and recorded on paper tape for each section. Typically, between 80-150 X-Y coordinates 677
678
0.
Kimura.
E. Dykes and R. W. Feamhead
were used to define an outline. Also recorded were the X-Y coordinates of the three markers for each section (Plate Fig. 1). Five computer programs were written to process the data from the D-Mac tracings of the sections. Program 1
The data from the D-Mac tracings are scaled and rotated so that all the X-Y coordinates of the outlines have a common origin and magnification. The Z-parameters of each section (i.e. its relative position in the unsectioned block) are also calculated. A magnetic tape or disc file is written which contains all the corrected data and is suitable to be used as input for the following programs: Program 2
This program simply redraws the original outlines on microfilm. Program 3 The surface areas are calculated by dividing the same line in two adjacent sections into equal numbers of points. The program takes the first two points of that line in both sections, calculates the distance between the sections from the recorded positions of the diagonal markers and then calculates the area bounded by these four points. The procedure is then repeated for all the points around that outline. The whole procedure is then repeated for the second and third and successive sections. The accuracy of the calculations was checked by measuring the surface area of three sections representing a two-inch cube. The computed surface area was accurate to 0.5 per cent, Program 4 The volumes are calculated by first calculating the area enclosed by a particular outline in a section and then multiplying this area by a distance equal to half the distance from the preceding section plus half the distance to the succeeding section. This is repeated for each section that the outline appears in. The volume calculated for each section is summed to give the total volume.
Program 5
This program reassembles the traced outlines and draws stereo views of the original specimen in any desired orientation. The programs were written in standard Fortran and compiled and run on a CDC 6600 machine. When projected on to the D-Mac X-Y coordinate plotting table, the dentine-enamel junction appeared as a straight line because of the low magnification employed. The surface area calculated using this straight line approximation is termed the uncorrected surface area. When this junction was viewed at a higher magnification in section, it appeared scalloped (Plate Fig. 2). To correct for the increase in surface area at the junction which must naturally occur because of this pitting, high magnification photographs (x 200) of the junction in eight different regions for all teeth were taken (Plate Fig. 3). The two-dimensional scalloped outline and straight line approximation were traced and the ratio of their lengths calculated. As the dentine-enamel junction varied in complexity in different regions of the same tooth, the average ratio of the eight different positions was calculated for each tooth. The overall average value for each kind of tooth was squared and this ratio was then used to compensate the area of the dentine-name1 junction. The surface area thus calculated is termed the corrected surface area.
RESULTS
Comparison between the actual tooth sections and the computer-drawn tracings of the sections (Plate Fig. 1) showed that the contours of the enamel and the dentine-enamel junction were faithfully reproduced. Table 1 summarizes the results of all the calculations. Individual teeth show a wide variation in surface areas because of differing tooth size. However, for the same kind of tooth the ratio between the surface area of the enamel and that of the dentine-ename1 junction is remarkably similar. On average, the uncorrected ratio for the upper central incisor is 1.33,
Table 1. Computer calculations of volumes, surface areas and surface area ratios
Tooth Upper central incisor Upper central incisor Upper first premolar Upper first premolar Upper first premolar Lower first premolar Upper first molar Upper first molar Deciduous upper first molar Deciduous lower second molar
Volume of enamel cm3
Enamel
0.12 0.11 0.13 0.17 0.18 0.15 0.30 0.32 0.10
2.08 2.08 1.89 2.09 2.14 1.77 3.74 3.51 1.72
1.55 1.57 1.25 1.39 1.40 1.13 2.16 1.97 1.15
0.13
2.27
1.63
Surface area cm2 D.E.J uncorrected corrected 1.79 1.81 1.49
Ratio Enamel/D.E.J. corrected uncorrected
1.66 1.66 1.32 2.76 2.53 1.28
1.34 1.32 1.51 1.50 1.53 1.57 1.74 1.78 1.50
1.17 1.15 1.27 1.26 1.29 1.34 1.36 1.39 1.34
1.82
1.40
1.25
Surface area of the enamel crowns of human teeth
679
Table 2. Average squared ratios
Tooth Upper central incisor Upper first premolar Lower first premolar Upper first molar Deciduous upper first molar Deciduous lower second molar
the upper first premolars 1.51, the upper first molar 1.76. This means that the surface area of the enamel is about 33 per cent larger than that of the dentineenamel junction in the upper central incisor, 51 per cent larger in the upper first premolar and 76 per cent larger in the upper first molar. Table 2 gives the average squared ratios between the straight and scalloped contours of the dentineenamel junction. The ratios are slightly different for the different kinds of teeth. When the surface area UPPer
first
permanent
Enamel
nlO,Q,
actual length Straight line approximation
2
1.15 1.19 1.17 1.28 1.12 1.12
of the dentineenamel junction is corrected for its pitted nature (last column in Table 1) for all teeth, the difference between two surface areas is reduced by approximately one half. Thus for the upper central incisor the average corrected ratio is now 1.16 which means that the enamel surface area is now only 16 per cent larger than the dentineenamel surface area; for the upper first premolar, the corresponding corrected values are 1.27 and 27 per cent; for the upper first molar 1.38 and 38 per cent. Text Fig. 4 shows stereo-pairs of two of the teeth together with the corresponding stereo-pairs of the dentineenamel junction.
surface
DISCUSSION
Dentine-
Deciduous
enamel
ower
E:nomel
second
surface
molar
surface
Dentine-enamel
surface
Chase (1927) tried to measure the surface area of the enamel by transferring actual prints of the outlines drawn on the surface of the enamel with crayon to millimeter cross-section paper and counting the squares enclosed by the outlines (Table 3). The method we used of calculating surface areas by a computer-based three-dimensional technique using serial sections is more accurate than the one used by Chase (1927) and Fosse (1964). Moreover it was possible to calculate the surface area of the enamel and that of the dentine-enamel junction at the same time. As individual teeth have differing sizes, the surface area is different for each tooth and it is the ratio of the two areas that is important. The most interesting observation is that the ratios between the surface area of the enamel and that of the dentineenamel junction are quite similar for the same kind of tooth and that this ratio is independent of tooth size, suggesting that the ratios between the two areas depend on the morphology of the crowns. In other words, the ratios depend on the morphology of their fissures and on the numbers of the cusps. Molar crowns have a more complicated morphology than premolars and the premolars more than the incisors. The ratios, therefore, represent the complexity of the crowns. A comprehensive study of all the teeth Table 3. Surface area (cm2) of enamel calculated from Chase’s original data (Chase, 1927) Tooth
Fig. 4. Stereo views of the enamel and dentine-enamel junction surfaces of two teeth. Notice the similarity in morphology between the enamel surface and that of the den-’ tine-enamel junction.
Central incisors First premolars First molars
Upper
Lower
2.35 1.91 3.37
1.42 1.66 3.13
0. Kimura, E. Dykes and R. W. Feamhead
680
in the human dentition giving the ratios precisely would be capable of revealing morphological differences quantitatively. From the corrected ratios after compensating the surface area of the dentin-name1 junction for its pitted nature (Tables 1 and 2) it can be seen that the general trend of increasing ratio for increased complication in tooth morphology is maintained although the spread in value is somewhat reduced. These results suggest that posterior teeth have more complicated pitted dentine-enamel junction than anterior teeth, and this pitting makes the surface area of the dentin-name1 junction much larger. However, because of the thickness of the sections used and the limitations imposed by the field of view of the microscope, our corrections are not accurate enough. Ideally we would like to be able to magnify the section so that the whole scalloped dentineename1 junction could be traced at the same time. More accurate results could also be obtained perhaps by progressively grinding off small amounts of the tooth (say 10 pm at a time) and photographing the exposed surface. Thus more sections could be traced and increase the accuracy of the computed results. With improved accuracy the difference between the two surface areas would be further reduced. It is interesting to speculate on what factors are responsible in accommodating the increase in surface area from the dentineenamel junction to the enamel surface. It has been argued that this accommodation is brought about by the existence of additional prisms, branching or supplemental rods towards the outer surface of the enamel (Mummery, 1916) or by a gradual increase in the diameter of the enamel rods as they approach the surface (Pickerill, 1913; Williams, 1923; Chase, 1924; Heuser, 1956). Pickerill (1913) found the ratio of the diameter of the enamel rods near the dentine-enamel junction and tooth surface (1.183) to correspond well with the ratio of the surface areas of the dentineenamel junction and the enamel surface (1.176). Chase (1924) also found that the ratios between outer and inner enamel surface were 1.17 for the upper lateral incisor, 1.363 for the first molar. He mentioned that the relationship between increase in diameter of rods and increase in surface towards the outer enamel were very close. Both Pickerill and Chase obtained their ratios by comparing arbitarily chosen lengths of the enamel surface and the dentine-
enamel junction from a single section and ignoring the scalloped nature of the junction. In our opinion, their extrapolation from a measured length in one section to an overall surface area is questionable because of the variation in the ratio of the lengths of the enamel surface to the dentine-enamel junction in different planes of section of the same tooth. It is surprising, therefore, that their results compare favourably with ours (Table 1). Fosse (1964, 1968) who carefully measured and calculated the mean diameters of groups of rods in different regions of the crown, related these findings to total surface areas obtained from wax reconstructions. He obtained a ratio of 1.99 for an upper premolar which is much higher than we obtained for upper premolars; we believe this to be due to the difficulties inherent in obtaining surface area measurements from reconstructed wax models. Chase (1924) mentioned that the interprismatic substance is a negligible factor in the increase of the surface. However according to Motoyama (1973), the ratio of the diameter between the enamel rods and the interprismatic substance was quite different between the outer and inner surfaces of the enamel. Enamel rods often reach the surface of the enamel at an oblique angle and, as Osbom (1973) points out, accurate measurement of the diameter of enamel rods and the interprismatic regions depends critically on obtaining a true transverse section of the rod; any obliquity would introduce unacceptable errors. The errors inherent in making comparative measurements of the diameter of rods is further emphasized when we consider that the 17-39 per cent difference we found between the two surface areas means that the average increase in the diameter of a 4 pm enamel rod would be only 0.354.7 pm. In our opinion, such small changes in width cannot be detected with any reliability using light microscopy. We have looked at the problem of accommodating this increase in surface area from a different view point and have made some approximate measurements to see if the increase in the surface area from the dentine-enamel junction to the enamel surface could be accounted for without the necessity of increasing the size of the rods or the introduction of supplementary rods. If we assume that each rod starts off perpendicular to the dentineenamel junction, we can calculate at what average angle they should emerge at the surface to give the required surface area
Table 4. A comparison of the calculated and measured angles subtended at the enamel surface by the enamel rods. The calculated angles were derived from the surface area ratios given in Table 1, but the measured ones are the average values adjacent to the eight regions defined in Fig. 3 Tooth Upper central incisor Upper first premolar Lower first premolar Upper first molar Deciduous upper first molar Deciduous lower second molar
Calculated angle (degrees)
Average angle measured (degrees)
22 28 30 31 30 27
26 26 27 27 29 36
Surface area of the enan tel crowns of human teeth
ratio (Table 1). We have also measured the angles of emergence of the rods in all the sections of the teeth described here (Table 4). These approximate measurements
suggest
that
the increase
in surface
area could be accomplished solely by the increase in surface area brought about by the differing angles of emergence of the enamel rods or crystals at the enamel surface. In transverse sections the rods or crystals meet the surface at an angle close to 90”. To explain the observed increase in length between the enamel surface and the dentineenamel junction in this plane we have to postulate either an increase in the diameter of the rods or crystals and/or an increase in the number of rods or crystals. Our surface area measurements show that for an upper central incisor the increase in diameter for a rod or crystal needs’ to be only of the order of 8 per cent for the whole increase in surface area to be satisfactorily accounted for. Such an increase in diameter is too small to detect by conventional methods at present available. A plausible explanation (for transverse sections) is that there are more enamel rods or crystals at the surface than at the dentine-enamel junction. The concept of extra rods or crystals presents difficulties not only of detection but also of credibility. For example, in the case of both rods and crystals, it is necessary to postulate either the generation of new ameloblasts or the nucleation of new crystals. An alternative explanation is that additional rods or crystals could be added to a particular incremental layer of enamel by rods or crystals from a more cervically placed successive incremental layer. Although this introduces the concept of varying rates of migration of ameloblasts, which might be difficult to establish, it could at least in part account for the thinning down of the enamel at the cervical margin of the tooth.
Acknowledgements-We wish to acknowledge the financial support from the Japanese Ministry of Education and the Royal Society, and to thank Professors H. Yamashita and G. Hirai for their interest and support.
REFERENCES
Chase S. W. 1924. The absence of supplementary prisms in human enamel. Anat. Rec. 28, 79-98. Chase S. W. 1927. The number of enamel prisms in human teeth. J. Am. dent. Ass. 14. 491492. Fosse G. 1964. The number of prism bases on the inner and outer surfaces of the enamel mantle of human teeth. J. dent. Res. 43, 57-63. Fosse G. 1968. A quantitative analysis of the numerical density and the distributional pattern of prisms and ameloblasts in dental enamel and tooth germs. V. Prism density and pattern on the outer and inner surface of the enamel mantle of canines. Acta odont. stand. 26. 501-543.
Heuser V. H. 1956. Oberfllchenhistologische Untersuchungen iiber die GroiOe der Schmelzprismen in den einzelnen Schmelzschichten am menschlichen Zahn. Dr. zahniirztl. Z. 11, 705-711. Motoyama S. 1973. On the interprismatic substance of the human enamel. A scanning electron microscopic study. Jatx J. oral Viol. 15. 31-50 (In Jaoanese). Mummery J. H. 1916.‘On the‘structure and arrangement of the enamel prisms, especially as shown in the enamel of the elephant. Proc. R. Sot. Med. 9. 121-138. Osbom J. W. 1973. Variations in structure and development of enamel. Oral Sci. Rev. 3, 3-83. Pickerill H. P. 1913. The structure of enamel. Dent. Cosmos 55, 969-988. Sullivan P. G. 1972. A method for the study of jaw growth using a computer-based three dimensional recording technique. J. Anat. 112. 457-470. Williams J. L. 1923. Disputed points and unsolved problems in the normal and pathological histology of enamel. J. dent. Res. 5, 27-l 16.
Plate 1 overleaf
A.O.B. 22/12--c
681
682
0. Kimura,
E. Dykes
and R. W. Fearnhead
Plate
1
Fig. 1. A section projected on to the D-Mac plotting table showing the markers. The contours of the enamel surface and the dentine-enamel junction. which appeared as a straight line, were traced. The computer-drawn tracing of the section is on the right. The contours of the enamel and the dentineenamel junction are faithfully reproduced. Fig. 2. Scanning electron micrograph of a small part of the dentine-enamel junction of an upper first permanent molar (area 2, Fig. 3). The specimen was prepared by embedding the whole tooth in polyester resin and then deminerahsing the enamel. Fig. 3. High magnification photographs ( x 200) of the dentineenamel junction in three different regions of an upper first premolar showing the variety of scalloped outlines in different regions of the same tooth section (the scalloped outline actually traced has been overdrawn in pencil for clarity). The areas labelled 4. 5 and 6 were similar to that shown for area 3 whereas areas 8 and 7 were similar to areas 1 and 2.
Surface area of the enamel crowns of human teeth
Parallel marker
Diagonal marker
Parallel marker
Plate I
683
Vol.
22. pp. 677 to 683
Pergamon Press 1977. Prmfed in Great Bntain
THE RELATIONSHIP BETWEEN THE SURFACE AREA OF TIHE ENAMEL CROWNS OF HUMAN TEETH AND THAT OF THE DENTINE-ENAMEL JUNCTION 0.
KIMURA*,E. DYKES and R. W. FURNHEAD
The London Hospital Medical College, Department of Dental Anatomy, Turner Street, London E.1, England
Summary-The surface area of the enamel and that of the dentine-enamel junction and the volume of enamel were calculated using a computer-based three-dimensional reconstruction technique. The surface area of the dentine+namel junction was compensated for its pitted nature. Different individual teeth had wide variation in surface areas but, for the same kind of tooth the: ratio between the surface area of the enamel and that of the dentin-name1 junction was very similar. Only a small amount (8-l 7 per cent) need be added to the thickness of crystals emerging normal to the enamel surface to account for the difference in surface areas. If it is assumed that crystals have uniform width and thickness, the angle of emergence of the crystals observed is sufficient to provide the required increase in the enamel surface area.
INTRODUaION It has been postulated from time to time that the apparent difference in the surface area between the
enamel crowns of teeth and the surface of dentine at the dentineaamel junction obliges the ameloblasts either to produce progressively wider rods as the surface of the enamel is reached (Pickerill, 1913; Williams, 1923; Chase, 1924; Heuser, 1956) or to produce extra rods (Mummery, 1916). The earlier work on this subject which has been reviewed by Fosse (1968) has been conoemed with the measurement of rod diameters or rod densities in different regions of the enamel but, as pointed out by Osbom (1973), with this approach a.11measurements are likely to be inaccurate unless the directions of the prism axes with respect to the plane of viewing can be taken into account. In other words, previous work has tended to calculate these surface areas from measurement of selected groups of ro,ds because presumably the direct measurement of the two surface areas presented serious technical difficulties. As far as we are aware, apart from the painstakingly careful wax and foil reconstructions prepared by Fosse (1964) there has been little effort to establish the precise magnitude of difference between these two surface areas which we believe is necessary before one can speculate on the mechanisms involved in accommodating this increase in surface area.. The model-making stage of the technique used by Fosse (1964) seemed to us to be the stage at which inaccuracies could be introduced and it should be noted that the ratios calculated from the two specimens he studied are considerably higher than those determined by our method. It is therefore our purpose to describe the initial results of a quantitative method using a computer-based three-dimensional reconstruction technique whereby detailed l Present address: Tokyo Medical and Dental University, School of Dentistry, Department of Pedodontics, l-5-45, Yushima, Bunkyo-Ku, Tokyo, Japan.
measurements are possible and surface areas and volumes of teeth can be accurately calculated directly from serial sections. We considered it important to avoid the pitfalls created by consideration of variations in rod size and densities. We tried to overcome this difficulty by adopting the crystal as the fundamental unit of the enamel structure. Moreover, we have assumed that enamel crystals and surrounding organic matrix have unvarying cross-sectional area throughout their lengths in order to establish whether in theoretical terms the accommodation of increase in surface area could be brought about simply by the angle of their emergence at the surface. MATERIALS AND METHODS
Ten extracted sound human teeth free from attrition were embedded in polyester resin, and two parallel grooves and one diagonal groove were milled into the surface of the block (Sullivan, 1972). The resulting grooves were filled with coloured resin. These markers are very important as they record the relative positions of each section in the block as well as a magnification scale factor. The distance between the two parallel markers and the angle of the diagonal marker to the parallel ones were accurately measured with a travelling microscope. Longitudinal serial sections were cut from the embedded teeth. Between 9-14 sections were obtained from each tooth, and these were ground to about 100~ thickness. The dentine in each section was stained with Van Gieson’s pi&c acid fuchsin solution for lOmin, in order to show up the dentine-name1 junction more clearly. The image of the stained section was projected at a magnification of about 15 times on to a D-Mac X-Y coordinate plotting table (Cetec Systems Limited (formerly D-Mac) Queen Elizabeth Avenue, Hillington, Glasgow G52 4SN) and the contours of the enamel surface and the dentin-name1 junction were traced and recorded on paper tape for each section. Typically, between 80-150 X-Y coordinates 677
678
0.
Kimura.
E. Dykes and R. W. Feamhead
were used to define an outline. Also recorded were the X-Y coordinates of the three markers for each section (Plate Fig. 1). Five computer programs were written to process the data from the D-Mac tracings of the sections. Program 1
The data from the D-Mac tracings are scaled and rotated so that all the X-Y coordinates of the outlines have a common origin and magnification. The Z-parameters of each section (i.e. its relative position in the unsectioned block) are also calculated. A magnetic tape or disc file is written which contains all the corrected data and is suitable to be used as input for the following programs: Program 2
This program simply redraws the original outlines on microfilm. Program 3 The surface areas are calculated by dividing the same line in two adjacent sections into equal numbers of points. The program takes the first two points of that line in both sections, calculates the distance between the sections from the recorded positions of the diagonal markers and then calculates the area bounded by these four points. The procedure is then repeated for all the points around that outline. The whole procedure is then repeated for the second and third and successive sections. The accuracy of the calculations was checked by measuring the surface area of three sections representing a two-inch cube. The computed surface area was accurate to 0.5 per cent, Program 4 The volumes are calculated by first calculating the area enclosed by a particular outline in a section and then multiplying this area by a distance equal to half the distance from the preceding section plus half the distance to the succeeding section. This is repeated for each section that the outline appears in. The volume calculated for each section is summed to give the total volume.
Program 5
This program reassembles the traced outlines and draws stereo views of the original specimen in any desired orientation. The programs were written in standard Fortran and compiled and run on a CDC 6600 machine. When projected on to the D-Mac X-Y coordinate plotting table, the dentine-enamel junction appeared as a straight line because of the low magnification employed. The surface area calculated using this straight line approximation is termed the uncorrected surface area. When this junction was viewed at a higher magnification in section, it appeared scalloped (Plate Fig. 2). To correct for the increase in surface area at the junction which must naturally occur because of this pitting, high magnification photographs (x 200) of the junction in eight different regions for all teeth were taken (Plate Fig. 3). The two-dimensional scalloped outline and straight line approximation were traced and the ratio of their lengths calculated. As the dentine-enamel junction varied in complexity in different regions of the same tooth, the average ratio of the eight different positions was calculated for each tooth. The overall average value for each kind of tooth was squared and this ratio was then used to compensate the area of the dentine-name1 junction. The surface area thus calculated is termed the corrected surface area.
RESULTS
Comparison between the actual tooth sections and the computer-drawn tracings of the sections (Plate Fig. 1) showed that the contours of the enamel and the dentine-enamel junction were faithfully reproduced. Table 1 summarizes the results of all the calculations. Individual teeth show a wide variation in surface areas because of differing tooth size. However, for the same kind of tooth the ratio between the surface area of the enamel and that of the dentine-ename1 junction is remarkably similar. On average, the uncorrected ratio for the upper central incisor is 1.33,
Table 1. Computer calculations of volumes, surface areas and surface area ratios
Tooth Upper central incisor Upper central incisor Upper first premolar Upper first premolar Upper first premolar Lower first premolar Upper first molar Upper first molar Deciduous upper first molar Deciduous lower second molar
Volume of enamel cm3
Enamel
0.12 0.11 0.13 0.17 0.18 0.15 0.30 0.32 0.10
2.08 2.08 1.89 2.09 2.14 1.77 3.74 3.51 1.72
1.55 1.57 1.25 1.39 1.40 1.13 2.16 1.97 1.15
0.13
2.27
1.63
Surface area cm2 D.E.J uncorrected corrected 1.79 1.81 1.49
Ratio Enamel/D.E.J. corrected uncorrected
1.66 1.66 1.32 2.76 2.53 1.28
1.34 1.32 1.51 1.50 1.53 1.57 1.74 1.78 1.50
1.17 1.15 1.27 1.26 1.29 1.34 1.36 1.39 1.34
1.82
1.40
1.25
Surface area of the enamel crowns of human teeth
679
Table 2. Average squared ratios
Tooth Upper central incisor Upper first premolar Lower first premolar Upper first molar Deciduous upper first molar Deciduous lower second molar
the upper first premolars 1.51, the upper first molar 1.76. This means that the surface area of the enamel is about 33 per cent larger than that of the dentineenamel junction in the upper central incisor, 51 per cent larger in the upper first premolar and 76 per cent larger in the upper first molar. Table 2 gives the average squared ratios between the straight and scalloped contours of the dentineenamel junction. The ratios are slightly different for the different kinds of teeth. When the surface area UPPer
first
permanent
Enamel
nlO,Q,
actual length Straight line approximation
2
1.15 1.19 1.17 1.28 1.12 1.12
of the dentineenamel junction is corrected for its pitted nature (last column in Table 1) for all teeth, the difference between two surface areas is reduced by approximately one half. Thus for the upper central incisor the average corrected ratio is now 1.16 which means that the enamel surface area is now only 16 per cent larger than the dentineenamel surface area; for the upper first premolar, the corresponding corrected values are 1.27 and 27 per cent; for the upper first molar 1.38 and 38 per cent. Text Fig. 4 shows stereo-pairs of two of the teeth together with the corresponding stereo-pairs of the dentineenamel junction.
surface
DISCUSSION
Dentine-
Deciduous
enamel
ower
E:nomel
second
surface
molar
surface
Dentine-enamel
surface
Chase (1927) tried to measure the surface area of the enamel by transferring actual prints of the outlines drawn on the surface of the enamel with crayon to millimeter cross-section paper and counting the squares enclosed by the outlines (Table 3). The method we used of calculating surface areas by a computer-based three-dimensional technique using serial sections is more accurate than the one used by Chase (1927) and Fosse (1964). Moreover it was possible to calculate the surface area of the enamel and that of the dentine-enamel junction at the same time. As individual teeth have differing sizes, the surface area is different for each tooth and it is the ratio of the two areas that is important. The most interesting observation is that the ratios between the surface area of the enamel and that of the dentineenamel junction are quite similar for the same kind of tooth and that this ratio is independent of tooth size, suggesting that the ratios between the two areas depend on the morphology of the crowns. In other words, the ratios depend on the morphology of their fissures and on the numbers of the cusps. Molar crowns have a more complicated morphology than premolars and the premolars more than the incisors. The ratios, therefore, represent the complexity of the crowns. A comprehensive study of all the teeth Table 3. Surface area (cm2) of enamel calculated from Chase’s original data (Chase, 1927) Tooth
Fig. 4. Stereo views of the enamel and dentine-enamel junction surfaces of two teeth. Notice the similarity in morphology between the enamel surface and that of the den-’ tine-enamel junction.
Central incisors First premolars First molars
Upper
Lower
2.35 1.91 3.37
1.42 1.66 3.13
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in the human dentition giving the ratios precisely would be capable of revealing morphological differences quantitatively. From the corrected ratios after compensating the surface area of the dentin-name1 junction for its pitted nature (Tables 1 and 2) it can be seen that the general trend of increasing ratio for increased complication in tooth morphology is maintained although the spread in value is somewhat reduced. These results suggest that posterior teeth have more complicated pitted dentine-enamel junction than anterior teeth, and this pitting makes the surface area of the dentin-name1 junction much larger. However, because of the thickness of the sections used and the limitations imposed by the field of view of the microscope, our corrections are not accurate enough. Ideally we would like to be able to magnify the section so that the whole scalloped dentineename1 junction could be traced at the same time. More accurate results could also be obtained perhaps by progressively grinding off small amounts of the tooth (say 10 pm at a time) and photographing the exposed surface. Thus more sections could be traced and increase the accuracy of the computed results. With improved accuracy the difference between the two surface areas would be further reduced. It is interesting to speculate on what factors are responsible in accommodating the increase in surface area from the dentineenamel junction to the enamel surface. It has been argued that this accommodation is brought about by the existence of additional prisms, branching or supplemental rods towards the outer surface of the enamel (Mummery, 1916) or by a gradual increase in the diameter of the enamel rods as they approach the surface (Pickerill, 1913; Williams, 1923; Chase, 1924; Heuser, 1956). Pickerill (1913) found the ratio of the diameter of the enamel rods near the dentine-enamel junction and tooth surface (1.183) to correspond well with the ratio of the surface areas of the dentineenamel junction and the enamel surface (1.176). Chase (1924) also found that the ratios between outer and inner enamel surface were 1.17 for the upper lateral incisor, 1.363 for the first molar. He mentioned that the relationship between increase in diameter of rods and increase in surface towards the outer enamel were very close. Both Pickerill and Chase obtained their ratios by comparing arbitarily chosen lengths of the enamel surface and the dentine-
enamel junction from a single section and ignoring the scalloped nature of the junction. In our opinion, their extrapolation from a measured length in one section to an overall surface area is questionable because of the variation in the ratio of the lengths of the enamel surface to the dentine-enamel junction in different planes of section of the same tooth. It is surprising, therefore, that their results compare favourably with ours (Table 1). Fosse (1964, 1968) who carefully measured and calculated the mean diameters of groups of rods in different regions of the crown, related these findings to total surface areas obtained from wax reconstructions. He obtained a ratio of 1.99 for an upper premolar which is much higher than we obtained for upper premolars; we believe this to be due to the difficulties inherent in obtaining surface area measurements from reconstructed wax models. Chase (1924) mentioned that the interprismatic substance is a negligible factor in the increase of the surface. However according to Motoyama (1973), the ratio of the diameter between the enamel rods and the interprismatic substance was quite different between the outer and inner surfaces of the enamel. Enamel rods often reach the surface of the enamel at an oblique angle and, as Osbom (1973) points out, accurate measurement of the diameter of enamel rods and the interprismatic regions depends critically on obtaining a true transverse section of the rod; any obliquity would introduce unacceptable errors. The errors inherent in making comparative measurements of the diameter of rods is further emphasized when we consider that the 17-39 per cent difference we found between the two surface areas means that the average increase in the diameter of a 4 pm enamel rod would be only 0.354.7 pm. In our opinion, such small changes in width cannot be detected with any reliability using light microscopy. We have looked at the problem of accommodating this increase in surface area from a different view point and have made some approximate measurements to see if the increase in the surface area from the dentine-enamel junction to the enamel surface could be accounted for without the necessity of increasing the size of the rods or the introduction of supplementary rods. If we assume that each rod starts off perpendicular to the dentineenamel junction, we can calculate at what average angle they should emerge at the surface to give the required surface area
Table 4. A comparison of the calculated and measured angles subtended at the enamel surface by the enamel rods. The calculated angles were derived from the surface area ratios given in Table 1, but the measured ones are the average values adjacent to the eight regions defined in Fig. 3 Tooth Upper central incisor Upper first premolar Lower first premolar Upper first molar Deciduous upper first molar Deciduous lower second molar
Calculated angle (degrees)
Average angle measured (degrees)
22 28 30 31 30 27
26 26 27 27 29 36
Surface area of the enan tel crowns of human teeth
ratio (Table 1). We have also measured the angles of emergence of the rods in all the sections of the teeth described here (Table 4). These approximate measurements
suggest
that
the increase
in surface
area could be accomplished solely by the increase in surface area brought about by the differing angles of emergence of the enamel rods or crystals at the enamel surface. In transverse sections the rods or crystals meet the surface at an angle close to 90”. To explain the observed increase in length between the enamel surface and the dentineenamel junction in this plane we have to postulate either an increase in the diameter of the rods or crystals and/or an increase in the number of rods or crystals. Our surface area measurements show that for an upper central incisor the increase in diameter for a rod or crystal needs’ to be only of the order of 8 per cent for the whole increase in surface area to be satisfactorily accounted for. Such an increase in diameter is too small to detect by conventional methods at present available. A plausible explanation (for transverse sections) is that there are more enamel rods or crystals at the surface than at the dentine-enamel junction. The concept of extra rods or crystals presents difficulties not only of detection but also of credibility. For example, in the case of both rods and crystals, it is necessary to postulate either the generation of new ameloblasts or the nucleation of new crystals. An alternative explanation is that additional rods or crystals could be added to a particular incremental layer of enamel by rods or crystals from a more cervically placed successive incremental layer. Although this introduces the concept of varying rates of migration of ameloblasts, which might be difficult to establish, it could at least in part account for the thinning down of the enamel at the cervical margin of the tooth.
Acknowledgements-We wish to acknowledge the financial support from the Japanese Ministry of Education and the Royal Society, and to thank Professors H. Yamashita and G. Hirai for their interest and support.
REFERENCES
Chase S. W. 1924. The absence of supplementary prisms in human enamel. Anat. Rec. 28, 79-98. Chase S. W. 1927. The number of enamel prisms in human teeth. J. Am. dent. Ass. 14. 491492. Fosse G. 1964. The number of prism bases on the inner and outer surfaces of the enamel mantle of human teeth. J. dent. Res. 43, 57-63. Fosse G. 1968. A quantitative analysis of the numerical density and the distributional pattern of prisms and ameloblasts in dental enamel and tooth germs. V. Prism density and pattern on the outer and inner surface of the enamel mantle of canines. Acta odont. stand. 26. 501-543.
Heuser V. H. 1956. Oberfllchenhistologische Untersuchungen iiber die GroiOe der Schmelzprismen in den einzelnen Schmelzschichten am menschlichen Zahn. Dr. zahniirztl. Z. 11, 705-711. Motoyama S. 1973. On the interprismatic substance of the human enamel. A scanning electron microscopic study. Jatx J. oral Viol. 15. 31-50 (In Jaoanese). Mummery J. H. 1916.‘On the‘structure and arrangement of the enamel prisms, especially as shown in the enamel of the elephant. Proc. R. Sot. Med. 9. 121-138. Osbom J. W. 1973. Variations in structure and development of enamel. Oral Sci. Rev. 3, 3-83. Pickerill H. P. 1913. The structure of enamel. Dent. Cosmos 55, 969-988. Sullivan P. G. 1972. A method for the study of jaw growth using a computer-based three dimensional recording technique. J. Anat. 112. 457-470. Williams J. L. 1923. Disputed points and unsolved problems in the normal and pathological histology of enamel. J. dent. Res. 5, 27-l 16.
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Fig. 1. A section projected on to the D-Mac plotting table showing the markers. The contours of the enamel surface and the dentine-enamel junction. which appeared as a straight line, were traced. The computer-drawn tracing of the section is on the right. The contours of the enamel and the dentineenamel junction are faithfully reproduced. Fig. 2. Scanning electron micrograph of a small part of the dentine-enamel junction of an upper first permanent molar (area 2, Fig. 3). The specimen was prepared by embedding the whole tooth in polyester resin and then deminerahsing the enamel. Fig. 3. High magnification photographs ( x 200) of the dentineenamel junction in three different regions of an upper first premolar showing the variety of scalloped outlines in different regions of the same tooth section (the scalloped outline actually traced has been overdrawn in pencil for clarity). The areas labelled 4. 5 and 6 were similar to that shown for area 3 whereas areas 8 and 7 were similar to areas 1 and 2.
Surface area of the enamel crowns of human teeth
Parallel marker
Diagonal marker
Parallel marker
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