AMERICAN JOURNAL OF PHYSICAL ANTHROPOLOGY 55:443 -453 (1981) Dent n Apposition Rates as Markers of Primate Growth S. MOLNAR. T.R. PRZYBECK. i ~WILKERSON . D.G. GANTT. R.S. ELIZONDO. AND Washington University, St. Louis, Missouri 63130 (S.M., T.R.P.); Florida State University, Tallahassee, Florida (0. G.G.); and Indiana University, Bloornington, Indiana (R.S.E.,J.E.W.) KEY WORDS lines Primate growth, Primate teeth, Dentin, Incremental ABSTRACT The incremental lines of von Ebner frequently have been described as ultradian markers of dentin calcification. To determine the relationship between these lines and the quantity of dentin formed, reference was made to an in vivo marker of calcification, tetracycline. These markers were produced by injecting four juvenile rhesus monkeys periodically over a period of 175 days. These animals had been subjects in a heat stress study and were exposed to a series of heat stresses and cortisone injections. A t the end of the study, undecalcified thin sections of premolars and second molars were prepared by standard histological techniques. We found that linear apposition rates increased in a gradient toward the pulp chamber. These rates varied within each tooth but not in corresponding parts of different teeth. Also, we determined that dentin apposition can be temporarily depressed by certain metabolic stresses. Heat load and cortisone significantly slowed dentin formation. Each depression, however, was followed by a "catch-up'' period. Incremental line distances also increased as a function of the distance from the dentoenamel junction. There was, however, no systematic relationship between apposition rates and incremental line distance; these distances did not deviate from the observed trends during periods of slowed apposition. Incremental lines may be interpreted, not as natural growth markers, but as structural phenomena which are a function of dentin geometry and tubule bending. The incremental nature of tooth development has attracted the attention of researchers for many years. I t has been assumed that the apposition of the organic matrix and its mineralization proceed at a rate reflective of the biological rhythm of the organism. It is thought that disruptions of this rhythm, through metabolic depressions that affect mineralized tissues, should be indicated by structural changes that are visible through light microscopic examination of undecalcified thin sections. Dentin, in particular, has been described as especially prone to faulty calcification and is considered a more sensitive indicator of mineral metabolic fluctuation than enamel (Sognnaes, '61:727; Schour, '38:53). Faulty calcification may appear microscopically as interglobular dentin or as broad hypomineralized bands, which are referred to as Contour Lines of Owen (see Sicher and Bhaskar, '72109). 0002-948318115504-0443$03.50 0 1981 ALAN R. LISS, INC. Another feature of dentin which has received a great deal of attention is the alternating pattern of light and dark lines, the incremental lines of von Ebner (Fig. 1).These incremental lines, which represent alteration in the organization of the matrix, are presumed to be a record of dentinal apposition rates and constitute markers of circadian or ultradian rhythm (Schour and Massler, '40). The space between these lines has been measured in several mammalian species and the distances were reported to be 16 microns (pm)(seeSchour and Hoffman, '39a, b). Though this distance appears to be relatively constant between species, the time interval between lines varies considerably. Yilmaz et al. ('77) used lead acetate as an in vitro marker in the teeth of domestic pigs and Received September 10,1979: accepted February 13, 1981 444 S. MOLNAR ET AL. Fig. 1. Longitudinal undecalcified section of a lower second premolar of a rhesus monkey viewed under bright light microscopy to reveal incremental lines (original magnification 100 X). reported that there were 13 sets of alternating light and dark lines between markers injected at 2-week intervals. This indicated that each set of incremental lines represented a circadian unit of apposition. Calculations of dentinal apposition rates by reference of incremental lines to in vivo markers such as a alizarin and sodium fluoride were made by Schour and his co-workers, who reported that dentin is deposited at the rate of 4 pmlday in man and rhesus and 16 pmlday in rodent, cat, and dog. The interval between lines, 16 pm, was distinguished as a 4-day episode in man and rhesus but only a single day in the other species (Schour and Hoffman, '39b). In an earlier study, Schour and Poncher ('37) reported an apposition rate of 3.77 pmlday over a 115-day period in the central incisor of a human infant with inoperable hydrocephalus and meningocele. They used sodium fluoride to delineate 20 growth intervals, and for these intervals apposition rates varied from 3.16 pm to 4.42 pmlday. They did not, however, note any systematic trends in the variation of these rates. Schour and Hoffman ('39b)found dentin apposition rates of between 3.68 pm and 4.40 pmlday in the gingival third and roots of premolars and molars in a series of 17 rhesus macaques. These animals ranged in age from 1.5 to 7.0 years. Though the authors gave no indication that the variation in rates was related to the ages of the animals, they noted gradient effects at different levels in a tooth. A rate of 12.2 pmlday was found in the cuspal portion of the third molars, and a rate of 2.4 was found at the apical level of the canines and premolars. Thus it is clear that this early work, while indicating an average rate of dentin apposition of 4 pmlday, does not demonstrate that apposition proceeds at a uniform rate as has been commonly assumed and stated. Nonetheless, the conclusions from these studies have become incorporated in many standard oral histology texts and the 4- and 16-pmintervals are usually accepted as indicative of biorhythm, and the incremental lines are frequently described as useful markers of time intervals (Sicher and Bhaskar '72:108; Symons, '67:311). However, statements about constant growth rate have not gone unchallenged. Kraus ('59) DENTIN APPOSITION RATES AS MARKERS OF PRIMATE GROWTH noted the discrepancy between tooth apposition rate and the calculated growth rates of other body tissues if the 4- and 16-pmintervals were accepted as a standard for tooth formation. He showed, through measurements of enamel of deciduous teeth from 76 human fetuses, that all areas of a tooth do not calcify a t a uniform rate and that growth proceeds more rapidly in some dimensions than in others; for example, mesiodistal diameter increases faster than cusp height. Further, when any one tooth dimension is plotted against age (in weeks),the regression is curvilinear indicating changing velocity in the calcification process. More recently, Kawasaki et al. ('77)reported that the rate of dentin formation changes continually. Their study of a series of human premolars and molars taken from individuals receiving therapeutic doses of tetracycline demonstrated that the rate of apposition slowly increases during the first third of dentinogenesis. During the second third the rate is relatively higher, and during the final third the rate declines steadily. Also, Melsen et al. ('77) reported that before eruption an apposition rate 3 1 pm per day is found in the teeth of both humans and Macaca mulatta. This rate decreases at eruption in the region over the pulp chamber but not in the roots. Finally, Rosenberg and Simmons ('80) examined incremental lines in the continually growing incisors of the rabbit and found that in decalcified sections of different thickness incremental lines of different widths were observable in-the dentin. Ebctron microprobe scans of calcium and sulfur distributions, indicative of the density of the mineral and organic phases, respectively, failed to reveal any systematic relationship between the pattern of the incremental lines and variation in calcium or sulfur distribution. The authors concluded that incremental lines are not a natural marker of growth but rather a structural phenomenon. These demonstrations, of course, raise questions about the nature of the rate of apposition and about the use of incremental lines as growth markers. In our study we have attempted to clarify the relationship between incremental lines and dentin apposition. Do the incremental lines demark episodes of growth? Is their spacing regular throughout the dentin? Also, can these naturally occurring lines be used to establish agrowth rhythm which would mark a normal pattern or identify depressed rates? * MATERIALS AND METHODS In order to examine the relationship between dentin apposition rates and the spacing of in- 445 cremental lines we studied teeth from two groups of rhesus monkeys (Macaca mulatta). One group was labeled with an in vivo marker, which permitted the measurement of apposition rates and incremental line spacing (Figs. 1 and 2). The second group was not labeled. Measurements of incremental lines in this group were used to assess possible effects of labeling on the incremental lines in the other group. Labeled group This group of four juvenile male rhesus, approximately 1.5 years old, were injected at intervals with tetracycline (6 mglkg, intravenously) over a 175-dayperiod in order to provide in vivo markers of dentin development. Tetracycline has proved effective as a marker of calcifying tissue and, at normal dosages, does not affect dentinogenesis according to recent reports by Yen and Shaw ('74) and Kawasaki ('75).Binding with the dentin, tetracycline indicates the incremental pattern of growth of this tissue and can be seen under ultraviolet microscopy. Figure 2 shows the typical pattern of fluorescent banding provided by tetracycline labeling. The animals were part of a thermoregulation study. Each was subjected to three short periods (60-90 minutes) when it was exposed to ambient temperatures of 100-110°F at 20% humidity in a climatic chamber while held in a restraining chair. During these periods rectal temperatures increased from 3" to 5" above normal. On the 88th and 155th day of the study there were two longer heat stress periods. All four rhesus were kept in the climatic chamber for 48 hours at 100°F beginning on the 88th day and for 31 hours at 110°Fbeginning on the 155th day. In addition to the heat stress periods, two series of cortisone injections were given to determine its effect on dentin apposition. I t has been previously reported that cortisone inhibits bone growth and may also influence dentin apposition (Follis, '51; Moss, '55; Frost, '73). An injection of 4 mg of dexamethasone was given on each of 3 days beginning on the 125th day. Tetracycline markers were injected before and after this period. The dexamethasone injections were repeated for 5 days beginning on the 164th day. These physiological stresses were given with the intent of inducing disruptions in the normal pattern of dentinogenesis. Our initial expectations were that anomalies of development such as interglobular dentin (areas of hypocalcifica- 446 S. MOLNAR ET AL Fig. 2. Same field as shown in Figure 1. viewed under ultraviolet light demonstrating tetracycline labels. tion) might be associated with these disruptions and that the tetracycline markers would serve to identify the stress responsible for the observed anomaly. The stresses produced several problems with respect to the interpretation of apposition rates; this notwithstanding, a clear pattern emerged, indicating a resilience in the forming dental tissue. After 175 days the animals were terminated. The teeth were removed and prepared for histological analysis by standard methods. The premolars and second molars were extracted (12 teeth from each animal) and, after cleaning and drying in alcohol and acetone, were embedded in an epoxy resin. Undecalcified thin sections of 80-100 pm were made with a Gillings thin section diamond saw. The teeth were cut longitudinally in the buccolingual plane through the mesial cusps. After mounting on a glass slide under a coverslip, each section was examined under light microscopy for evidence of incremental lines and Contour Lines of Owen. When groups of incremental lines were located photographs were made at 1OOx magnification with Ektachrome film (ASA 125). The microscopic field was photographed again under ultraviolet light at the same magnification to reveal the fluorescent bands of tetracycline. This procedure was repeated for each area for each section where incremental lines were distinct. A photograph of a stage micrometer (2-mmscale) was made at the same magnification for calibration. The microphotographic slides (35-mmEktachrome)were projected by a Kodak carousel projector (50-mmlens) from a measured distance onto a specially prepared translucent screen. The 18" X 27" image permitted the easy measurement of the incremental line spacing from the reverse side of the screen with high precision (less than 3% difference in repeated measurements). The measurements were converted to microns by comparison to the stage micrometer image (a conversion of 1mm = 1.4 pm).This method provided more precise results than had been achieved by direct measurement of the thin section with a filar micrometer, which produced errors of 10-12%. The distance between incremental lines was measured according to the method of DENTIN APPOSITION RATES A S MARKERS OF PRIMATE GROWTH Schour and Hoffman ('39a) - that is, from the beginning of one dark band to the beginning of the next along the path of the dentinal tubules. The measurements of the tetracycline bands made by this method compared well with those previously obtained from enlargements of black and white photographs. The tetracycline bands were more regular and uniform in certain regions of each tooth section. In the 48 sections (12 from each animal) on the buccal and lingual sides, approximately half way between the dentinal horn and the cementoenamel junction (CEJ)was clearest. We refer to these areas as regions A2 and B2, respectively (see Fig. 3). These data comprise a large number of measurements which demonstrate clear patterns. For comparative purposes a similar, but much smaller, data set was generated for the region between the dentinal horns, the AB region, where the banding was less clear. While this smaller set of data does not, by itself, permit conclusions to be drawn, it does support the other data and suggests that the same trends exist in all parts of the tooth. The spacing of the tetracycline band groups over the 175-day study bracketed 13 intervals, and the distance between each marker was measured. The rate of dentin apposition during each interval was determined separately for each tooth and area in each animal. We determined the rates of dentin apposition in different parts of the teeth and measured the influences of the applied stresses on apposition rates. The distances between incremental lines were established and the two sets of data were compared to clarify the meaning and nature of incremental lines as natural markers of dentinogenesis. Unlabeled group This group consisted of four adult animals that had not been injected with tetracycline. Eight teeth from these animals were sectioned and photographed as described above. Measurements were made of the incremental lines in the A2 and AB regions. These measurements were compared to those of the labeled group to insure that incremental line distances were not influenced by the tetracycline injections. 447 Fig. 3. Schematic of tooth section. Buccal side of the tooth is to the right. The areas labeled A2. B2, and AB are those from which all measurements were taken, analysis of variance ( F = 2.98, P > 0.05) indicated that it would be appropriate to pool the measurements from the A2 and B2 areas in the four animals. This produced a data set consisting of up to 96 measurements per band interval, consisting of two measurements from each tooth, one buccal and one lingual, in a total of 1 2 teeth from each animal. Because some sections did not have all tetracycline bands clearly defined, the actual number of measurements for each interval ranged from 41 to 82. The results of these measurements are summarized in Table 1. The apposition rates in the A2 and B2 regions show a distinct temporal trend. During the first interval, which begins 300 pm from the dentoenamel junction (DEJ),the apposition rate is 2.91 pml day. Subsequent intervals show a steady inRESULTS crease until in the final interval a rate of 3.91 pmlper day is reached (Fig. 4). The rate of apApposition rates position averaged over the 175-day period is Comparisons of all teeth by class and by 3.27 pm per day, which is similar t o the area of measurement showed a greater than averages reported by several previous in0.9 c o r r e l a t i o n coefficient b e t w e e n vestigators. The small set of measurements from the AB tetracycline band intervals in isomeres and antimeres for each area. Q-mode correlation and region (the intercuspal area) indicate that ap- 448 S. MOLNAR ET AL. TABLE 1. Mean daily rates of apposition (labeled animals) Tetracycline interval 1 2 2 33 4 5 6 7 83 9 10 113 123 134 Length of interval (days) N' A2 and B2 area 17 22 16 18 22 22 12 4 10 7 3 15 7 67 78 80 82 82 81 78 75 74 66 62 60 41 AB area - XIpm) S.D. N X(&m) S.D. 2.91 2.71 3.10 3.27 3.26 3.50 3.52 3.22 3.92 3.57 3.34 3.75 3.91 0.575 0.459 0.572 0.542 0.529 0.547 0.567 0.600 0.687 0.597 0.770 0.604 0.512 2 4 6 6 7 5 2 1 1 1 2.87 2.90 3.86 4.52 4.54 4.91 4.58 5.37 4.27 4.66 0.665 0.273 0.900 1.05 0.983 1.03 0.375 - - 'Based on measurements from buccal and lingual areas in 12 teeth from each of four animals IN,,, 2300pm from DEJ. 31ntervalsduring which metabolic stress was induced. See text for discussion. '875 um from DEJ. - - - = 961. Y-2.75 + .006X / r = ,934 (P < ,011 3.5 I A Heat 1 Cortisone 1 A 0 No stress 25 0 Heat 2 Cortisone2 , I 1 1 I I 30 60 90 120 150 180 TIM€ (DAYS) Fig. 4. Plot of average apposition rates from A2 and B2 areas combined. Episodes of applied stress are indicated. hut were not used to calculate regression. Each point is at the midpoint of a tetracycline interval. Values are presented in Table I . See text for discussion. the animals were maintained for 31 hours at 110°F at the beginning of a 3-day interval (heat 11). The first heat episode (heat I) was longer (48 hours), b u t t h e ambient temperature was 10°F less. Possibly, the rhesus were better able to thermoregulate at 100" than at higher temperature. At least the metabolic processes suffered less disruption Response to stress as evidenced by the dentin rate during inHeat stress, applied over several hours, terval three (heat I). This distinction between caused a reduction in dentin apposition. This the two heat episodes may prove to be of was recorded during the 11th interval when significance and suggests a threshold in the position rates are, on the average about 1 pmlday greater than in the A2 or B2 regions. Finally, the teeth we examined were in a stage of development which corresponds to the second third of development as described by Kawasaki et al. ('77), and conform to their description of relative rates. 449 DENTIN APPOSITION RATES AS MARKERS OF PRIMATE GROWTH sion of apposition rate would be averaged out by the “rebound effect,” which again indicates that without strategically placed in vivo markers it may be extremely difficult to discern depressions or disturbances of dentin growth since the tissue apparently has the ability to compensate for these depressions by later accelerated apposition. None of the stress periods induced the gross imperfections in dentin known as interglobular dentin (IGD).This lack of IGD in the rhesus teeth is consistent with previous reports on primate dental histology and our own observations of samples from other macaques (Molnar and Ward, ’75). But the failure to induce this imperfection in the dentin matrix by heat stress or cortisone treatment does not rule out the possibility that a pyrogenic agent might cause this defect. sensitivity of the dentin matrix to metabolic disturbances. The shorter heat stress periods during intervals 5 and 6 did not affect dentin development noticeably. The dentin apposition rate varied in the same way for all animals, and a pattern of response is clear; small increase in body temperature may cause slight depressions in dentin apposition rate, but these changes can only be detected if the period is closely bracketed by in vivo markers to exclude the “catch-up”period following this interval. The lack of response seen in interval 3 (heat I) may be related to this, since the heat strss fell at the beginning of the 22-day interVal. The first point of significant depression is seen during the second interval. No stresses were applied during this interval, which makes it difficult to explain the reduction in apposition rate. A suggestion is offered that the animals were still undergoing adjustment to their new quarters. Frost (’69:216) cautioned that animals must be preconditioned in the experimental environment for a time equal to “one sigma.” How this period, the time it takes for a basic bone unit to remodel, compares to dentin apposition rates we do not know. The first series of cortisone injections, though in normal therapeutic concentrations, caused detectable depressions in dentin apposition rates. Following the cortisone series a period of accelerated growth is seen as a “rebound effect” similar to that found in humans following treatment with corticosteroids (S. Teitelbaum, ’77, personal communication). The second period of cortisone (5 days a t 24-hour intervals) showed no response comparable to the first series. This may be due to the long period between tetracycline injections at this point in the study (15 days). Any depres- Incremental lines Interline measurements were made in three regions of the teeth as was done with the tetracycline measurements. Analysis of variance showed that there was no difference between teeth (PM3, PM4, M2),so all teeth were pooled as was done with the tetracycline band measurements. The mean incremental line distances are listed in Table 2 for each of the tooth regions, in correspondence to the tetracycline band intervals, a position relative to the dentoenamel junction. The first tetracycline marker is 300 p from the dentoenamel junction. The distance between lines in area A2 are not significantly different from comparable lines in the B2 area, but the incremental lines in the AB area are, on the average, farther apart. A total of 516 incremental line measurements were made on sections from the labeled animals. The mean distance between incremental lines was 16.87 pm. The average is approximately 1 pm TABLE 2. Incremental line distances for each area and group (labeled animals) Area ~- ~~ Band intervals 1 2 3 4 5 6 7 8 9 10. 11,123 13 Total 4‘(2)’ 10 (31 16 (6) 26 19) 49 (13) 47 (12) 31 113) 9 (6) 22 (11) 40 (91 10 (71 264 (14) ~~~~ 82 A2 Mean S.D. 13 76 15 04 15 70 14.99 15.21 15.33 16 72 17 34 17 29 17.98 17.74 16.15 1.OO 2.72 3.04 2.20 2.03 2.39 2.78 1.85 3.55 2.93 3.18 2.82 N 5 (1) 7 (2) 12(4) 13(4) 16 (6) 14(5) 8 (4) 4(4) lO(5) 1814) 7 (3) 114(7) Mean SD 1596 1656 1561 1506 1498 1599 1727 1547 1763 1848 1744 1633 096 160 288 283 309 313 235 259 2 18 200 292 279 AB Mean ~ SD 13.44 14.12 17.28 21.32 20.87 21.49 21.00 22.5 22.75 24.31 0.10 0.80 19.01 4.55 - 1.80 1.64 3.98 4.44 4.32 3.38 1.75 - - ‘Number of incremental lines. 2Numher of teeth. >Becauseintervals 10. 11, 12 were too short to include incremental lines in each. measurements were taken from the beginning of 10 to the end of 12. 450 S. MOLNAR ET AL. greater than the mean of 15.85 pm reported by Schour and Massler (’40) for the rhesus monkey. A series of 144 incremental line distances on the tooth sections of the unlabeled animals is consistent with the data from the labeled group, giving a mean of 16.81 pm. The differences between our data and Schour and Hoffman’s (’39a)are not readily explicable. The most probable cause is that our measurements were taken from all regions of the teeth. If we separate the measurements according to region (aswith the tetracycline measurements) (see Tables 2 and 3), it can be seen that the means for the A2 and B2 regions in both the labeled and unlabeled groups are very close to Schour and Hoffman’s findings. The labeled group has means of 16.15 and 16.37 pm for the A2 and B2 regions, respectively; the unlabeled group has a mean of 16.3 pm for the A2 region (no B2 measurements were taken). In both groups, however, the mean in the AB region is larger, 19.01 in the labeled group and 17.36 in the unlabeled group. Further, since Schour and Hoffman used transverse sections for their study, the level of sectioning may have limited the variation of their measurements. This is probable in light of the fact that we see a difference in the average interline distance in different regions of the same tooth. Although there is no indication of the level at which they made their sections, it is most likely that they more closely approximate the level corresponding to our A2 and B2 regions in the cervical rather than intercuspal region, since sections here would not expose the pulp chamber if taken transversely. As a result of these considerations, there appears to be no great disparity in the results of the Schour and Hoffman study and our results. The validity of an approximately 16-pm average distance between incremental lines in the cervical portion of the tooth is confirmed. While our average distance is in agreement with previous work, we noticed that the variation around that mean is not random; in fact, the lines are spaced farther apart near the pulp chamber, and there is a high correlation between distance from the DEJ and distance between incremental lines. This relationship is illustrated in Figures 5 and 6. Figure 5 is a plot of incremental line distance in the A2 region from the labeled group. Each point is the mean incremental line distance for each of the tetracycline band intervals. This plot represents the best fit of the four we calculated (A2 and AB regions from both groups of animals). Figure 6 is a plot of the mean incremental line distances A 2 A R E A (915) 19.0 ~1 W r z . 9 2 3 . P<.OI W a I 13.01 Q I c u) 6 1201 200 400 600 DISTANCE FROM 1st TC MARKER(y1 Fig. 5. Plot of average incremental line spacing in A2 area in labeled animals. The initial tetracycline label was 300 pm from the cementaenamel junction in this area of the tooth. Values are presented in Table 2. See text for discussion. TABLE 3. Incremental line distance for each area (unlabeled animals) Area Distance from DEJ (pm) 0-100 100-200 200-300 300-400 400-500 500-600 600-700 700-800 800-900 Total ‘Number of incremental lines lNumber of teeth. A2 N AB Mean S.D. N Mean S.D. - - 14.78 14.57 14.54 15.23 17.20 19.10 23.81 24.71 16.37 1.35 2.80 1.84 1.59 3.36 2.46 1.67 1.41 3.63 9 (2) 12 12) 6 (21 7 (2) 9 (2) 8 (2) 13.55 15.39 18.32 18.77 16.05 19.01 18.19 22.19 22.88 17.36 2.09 3.38 6.37 4.27 2.54 3.48 2.97 0.60 1.62 4.14 6 12) 5 (1) 2 11) 64 (4) 451 DENTIN APPOSITION RATES A S MARKERS O F PRIMATE GROWTH TABLE 4. Comparison of regression analysis in labeled and unlabeled animals for relationship between incremental line distance (Y) and distance from DEJ (X) A2 Labeled Unlabeled r = 0.916 ( P < 0.01) . 100 ' 400 + + -- Area ___ Band intervals 1 ' AB Y = 13.93 0.06 X r = 0.912 ( P < 0.01) Y = 13.93 0.01 X r = 0.872 (P < 0.01) TABLE 5. Periodicity of incremental lines' / I3L + 0.01 X r = 0.923 ( P < 0.01) Y = 10.17 + 0.02 X Y = 13.95 800 600 DISTANCE FROM DEJ (PI Fig. 6. Plot of average incremental line spacing in AB area in unlabeled animals. Interline distances are grouped in increments of 100 pm starting from the cementoenameljunction. Values are given in Table 3. See text for discussion. in each 100-micron increment traversed from the DEJ to the pulp chamber. This plot represents our poorest fit of the four, but the correlation is still high (r = 0.872). The regression equations and correlation coefficients for all four regions are given in Table 4. There is some inconsistency in the slopes of these regressions, but we believe that this is due to the rather narrow range over which the regressions were calculated and that the least reliable means (due to rather small numbers of measurements) were obtained for the extremes of the x axis, thus distorting the slopes slightly. Nonetheless, the high correlations indicate that a large percentage of the variance in incremental line distance is explained by the distance from the DEJ. Periodicity of incremental lines The actual time interval (in days) betwen incremental lines was determined, in the labeled animals. Incremental line distances were divided by the apposition rate for that location, which had been calculated by the tetyracycline band measurements as listed in Table 1. The results established the time, in days, needed to form the space between two incremental lines. This time period, frequently described as a growth rhythm, varied considerably with a range of 4.19 to 5.83 days (see Table 5). There was no significant correlation between this rhythm and distance from the DEJ (r = 0.38, 2 3 4 5 6 7 8 9 10, 1 1 . 12 13 A2 AB 5.11 days 5.83 days 5.05 days 4.68 days 4.63 days 4.47 days 4.83 days 5.09 days 4.45 days 5.06 days 4.50 days 4.68 days 4.86 days 4.47 days 4.71 days 4.59 days 4.37 days 4.58 days 4.19 days 5.32 days 5.22 days - 'Growth rhythm was calculated by dividing the average incremental line distance in a tetracycline interval by the apposition rate for that interval. P > 0.05), and we see no apparent pattern in the calculated values of the rhythm. No change in the incremental line distances was seen during the intervals 2 and 8, which were the intervals exhibiting depressed apposition rates, as determined by the tetracycline measurements. This lack of deviation from expected incremental line distance produced calculated growth rhythms that were greater because of the division of distance by a lower apposition rate figure (see Table 5). Further, there is no concordancebetween rhythms in the different areas. DISCUSSION AND CONCLUSIONS Our results provided strong evidence that the pattern of dentinogenesis is a complex process that cannot be reduced to simple characterizations such as the often cited 4 pmlday apposition rate and 4-day 16-pm calcification rhythm. Over the course of the study, which spans the middle one-third of dentin development, we were able to document a steady increase in the rate of dentin apposition from 2.6 to 3.9 pmlday in the cervical portion of the crown. In the intercuspal area a similar increase was noted, and rates were approximately 1 pmlday higher than in the cervical region. Because our study does not span the entire growth period, we cannot make definite statements about the rate of apposition during the entire sequence. However, bearing in mind the 452 S. MOLNAR ET AL. results of Kawasaki et al. ('77),it is reasonable to expect that the entire growth of the dentin probably conforms to the common s-shaped growth curve and that we are sampling from the middle of it. Additionally, regional differences in apposition rates are apparent. There are two factors that can explain these regional differences. One is differential cell activity; the second is the unique geometry of the dentin. We have argued elsewhere (Przybecket al., '79)that an understanding of the cellular dynamics of dentin formation must include a consideration of the increased crowding of the odontoblasts as they migrate toward the final contour of the pulp chamber. Indeed, for the span of our study we were able to document a declining rate of cell activity in spite of the increasing linear apposition rates. This leads to the conjecture that geometric considerations may play a paramount role in the tempo of dentin formation. The phenomenon of cell crowding among odontoblasts as they migrate toward the pulp chamber may cause a simple reduction in efficiency of the cells by diminution of surface area. Thus the uptake of materials and production of the dentinal matrix may be progressively reduced. This purely mechanical scenario has as its chief advantage the fact that it does not require consideration of complex hormonal processes or other factors which would regulate odontoblast productivity. In contrast, a nonmechanical model would have to explain both the change in rate of apposition in any one region of the tooth and the variation in rate in different regions of the tooth. The latter aspect, in particular, would be difficult to model since we would have to posit differential sensitivity to controlling factors within a single population of cells. A mechanistic interpretation of dentinogenesis does not imply that the developing tooth is immune to metabolic fluctuation. Our data show that, at least in some instances, agents of metabolic stress (heat load and cortisone) do cause depressions in apposition rates. However, where we noted growth depressions, they were succeeded by periods of compensating acceleration. In the cases in which no growth depressions were recorded, either the stress was of insufficient intensity to disrupt normal dentinogenesis (in the case of the short-term heat stress), or the tissue markers were administered so as to bracket both the period of growth depression and the episode of catch-up growth. (Thisprobably is the case for one of the cortisone stresses and possibly so for one of the longer heat stresses.) The response to stress agents indicates that the forming dentin has resilience which gives it a certain immunity from long-term effects resulting from a series of short-term growth disruptions. The limit of this resilience clearly was not reached in this study. Further evidence of this is provided by the lack of any structural abnormalities in any of the teeth. The stress response data raise severalproblematic issues, all of which indicate that conclusions regarding the causes of imperfections of the dentin may be premature. The intensity, duration, and mechanism of metabolic stresses and individual constitution are all probably ingredients in the production of histological defects in teeth. However, further study must be undertaken to determine how these factors interact. We cannot distinguish the contribution of each in our data. For example, would cortisone produce permanent effects if administered for longer periods or in larger dose? Given these difficulties, it is thus obvious that the interpretation of the presence of microstructural defects in dentin requires extreme care, contingent on a more precise definition of the etiology of those defects. The incremental lines of von Ebner appear to behave independently of the metabolic fluctuations we observed. During both periods of depressed growth and accelerated growth, we were not able to notice any quantitative or qualitative abnormalities in the spacing of the alternating light and dark bands of the incremental lines. This indicates that the incremental lines represent structural markers of dentin growth and are not directly affected by alterations in the physiological environment of the tooth and also do not represent the growth tempo of the tooth to any significant degree. The exact nature of the structural features which produce incremental lines is not totally clear. Schmidt and Keil ('71:lOO) suggested that the alternating light and dark bands reflect changes in the orientation of collagen fibers in the organic phase of the dentin. They point out that incremental lines can be seen in decalcified as well as undecalcified sections, indicating that the mineral phase of the dentin is not involved. It should be noted that Vincentelli ('78) reached similar conclusions concerning the laminar structure of the secondary osteon in bone. This interpretation is consistent with our data, but here again we must refer to the unique geometry of the dentin. The crowding phenomenon of the odontoblasts and thus the increased density of the dentinal tubules probably exerts an influence on the spacing of incremental lines. The fact that these lines are more widely spaced near the pulp may be related to either the primary or DENTIN APPOSITION RATES AS MARKERS O F PRIMATE GROWTH secondary curvatures of the tubules. In the former case, we would suggest that changes in matrix orientation occur regularly and each incremental line set is produced by an identical or nearly identical volume of matrix. In the latter case the secondary curvatures or apparent "buckling" of the odontoblast processes may be sufficient to cause slight changes in collagen fiber direction, which cause the optical phenomenon of the incremental line. If this is true, then the increasing density of odontoblasts nearer the pulp could mechanically inhibit the secondary curvature of the tubules and thus cause the wider spacing of the incremental lines. In either case the differential odontoblast crowding in the cervical and intercuspal regions would account for the observed regional differences. In sum, we determined that dentin is sensitive to metabolic fluctuation. Variations in apposition rates are detectable by use of an in vivo marker of the calcification front. The naturally occurring incremental lines of von Ebner do not reflect with accuracy the variations in dentin apposition that are revealed by tetracycline markers and, thus, are not useful in detecting apposition rates. The lines do not vary in width, and there are no changes in optical density during those periods of reduced apposition rates. However, before definite conclusions can be reached regarding the usefulness of incremental lines, more study is required to determine the precise influence of tubule density and curvature, and a model should be employed that treats the tissue as a three-dimensional object. Such a model would provide the opportunity to assess tubule density (and thus cell density) as well as allowing the examination of volumetric relationships, which may be the most accurate way to study the complex process of dentinogenesis. ACKNOWLEDGMENTS We gratefully acknowledge the support and encouragement of Dr. Steven Horvath, the Institute for Environmental Stress, University of California, Santa Barbara. We wish to thank Mr. William Sawyer and Mrs. Sue Easley for their technical assistance. 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