Caleif. Tiss. Res. 21, 17--28 (1976) 9 by Springer-Verlag 1976
Remineralization of Dentin in vitro D. B. B o y e r and F. R. Eirich Polytechnic Institute of New York, Brooklyn, New York Received June 17, 1975; accepted April 1, 1976 The remineralization of completely demineralized bovine dentin was studied in vitro by monitoring the velocities of fall of small particles through calcifying solutions. The density of a particle of dentin may be found from its velocity of fall through a fluid using Stokes' law. The minimum concentration product of calcium and acid phosphate ions of the solution in which remineralization would take place was 3.6 (raM)~ in the presence of 22 mM bicarbonate, pH 7.35, and ionic strength 0.1. This is just above the solubility product of brushite (CaHPO4- 2H20 ). Incubation of decalcified dentin in a phosphoprotein removed from dentin during demineralization, or in phosvitin, had no effect on remineralization. The rates of remineralization and of the fraction remineralized were inversely proportional to particle size. This inverse correlation may be due to deposition of mineral in a surface layer of constant depth irrespective of particle size. The fraction of a particle remineralized was greatly increased by the use of highly supersaturated calcifying solutions or by the incorporation of fluoride into the solutions. The empirical reaction order of remineralization for both calcium and phosphate ions was found to be unity, which is, within the error limits, equal to the order of growth of seed crystals of hydroxyapatite in calcifying solutions of the same composition. Key words: Calcification - - Dentin - - Nucleation - - Kinetics.
Introduction Decalcified dentin, like bone a n d cartilage, can be remineralized in supersaturated solutions. A n orderly deposition and g r o w t h of calcium phosphate salts within and a r o u n d its fibers is often seen. Studies of the remineralization of dental hard tissues have been concerned for the m o s t p a r t with partially demineralized enamel and dentin, and with the repair of incipient caries in enamel or the repair of carious dentin (Koulourides, 1968). Posteruptive changes in the composition of enamel, especially in hypomineralized areas, have been taken as evidence of remineralization in vivo (Brudevold et al., 1960). Microradiographie studies have shown carious dentin which has regained high density, an observation t h a t can be explained b y remineralization (Amprino and Camanni, 1956). I n laboratory studies, dental tissues are exposed either to calcifying solution, supersaturated in calcium and phosphate salts, or t o saliva. The extent of mineralization is determined b y direct techniques in which the a m o u n t of mineral t a k e n up b y the tissue or depleted from the solution is measured, or b y indirect techniques such as microradiography, polarizing microscopy, absorption of dyes, and measurement of surface hardness. Reviews on the remineralization of enamel
.~'or reprints: D. Boyer, College of Dentistry, University of Iowa, Iowa City, Iowa 52242, USA.
18
D.B. Boyer and F. R. Eirich
a n d d e n t i n have been given b y Wei (1967), Koulourides (1968), Poole a n d Silverstone (1973), a n d F r a n c i s et al. (1973). I n t h e present study, we sought to a p p l y a n e w t e c h n i q u e (Chan a n d Eirich, 1973) for t h e s t u d y of the r e m i n e r a l i z a t i o n of d e n t i n . This t e c h n i q u e m o n i t o r s the change i n d e n s i t y of a particle of hard tissue b y m e a s u r i n g its velocity of fall t h r o u g h a c o l u m n of calcifying solution.
Materials and Methods The sedimentation apparatus and its application have been described previously (Chan and Eirich, 1973). The apparatus consists of glass columns about 60 cm long, and a stand for mounting and rotating them in an air thermostat. Each column has a restricted channel near one end to center the falling particle within the column. The solution in the column is stirred at 1,000 rpm by a small stirring bar when readings are not being taken. The bar is held fixed to the side of the column by an external magnet during readings. An experiment is initiated by filling the column with 220 ml of calcifying solution and by equilibrating to 37~ C in the thermostat. The hard tissue sample is introduced into the column through a Teflon valve with a disposable pipette. The duration of fall of the particle between bench marks 30.5 cm apart is periodically measured with a stopwatch. Because calcification in solutions close to physiologic composition is a very slow process, readings were taken only once a day. An experiment usually lasted for 10 days, although in some instances, experiments were continued for 3 wk. This technique has the advantage that calcification can be followed for long periods of time without spontaneous precipitation or bacterial growth, since the columns are closed, air-flee and air-tight and need not be opened for sampling. Bovine dentin was used in the study. The lower jaws of calves were obtained from an abattoir on the day of slaughter. The teeth were removed, cleaned of soft tissue, and frozen until use. The roots were the source of dentin. The dentin was cut into small cubes with a scalpel under a dissection microscope. The dimensions of the cubes were measured to the nearest 5 ~m with a planimeter. The particles were generally about 0.03 cm in diameter because this proved to be the smallest size practical to cut and to observe. Small particles were desirable in order to shorten the duration of the experiments. The calcifying solution, prepared immediately before each experiment from three stock solutions, was that described by Hirschman and Sobel (1965). The desired amount of calcium stock solution was added dropwise to the phosphorus stock solution in 100 ml of basal salt solution and 600 ml of water. Before the calcium was added, the pH of the solution was lowered by bubbling CO2 through it. After the calcium was added and the solution adjusted to 1 l, the pH was raised by bubbling nitrogen through the solution. The final pH of the solutions was 7.35 =t=0.05. The amount of basal salt solution added was always 100 ml so that the calcifying solution contained 70 mM NaC1, 5 mM KC1, and 22 mM NaHC03; the ionic strength was 0.10. To prevent the loss of CO2, the solution was immediately poured into the glass columns. At the end of the experiments the pH was remeasured and found to be unchanged. Results
Nucleation. D e n t i n placed directly i n t o calcifying solution i n t h e columns would n o t calcify, even when i n c u b a t e d u p to a m o n t h . N u c l e a t i o n of fully demineralized d e n t i n was o b t a i n e d o n l y b y placing the d e n t i n i n calcifying solut i o n for 1 h, after which time it was removed, rinsed with distilled water, a n d transferred to the c o l u m n of calcifying solution. This t e c h n i q u e is similar to t h a t used b y Bachra a n d Fischer (1968) to nucleate certain tissues. The m i n i m u m c o n c e n t r a t i o n p r o d u c t a t which r e m i n e r a l i z a t i o n of freshly demineralized d e n t i n occurred was Ca • P ~ 3.6 (mM) 2 i n a solution with 22 m M b i c a r b o n a t e , ionic s t r e n g t h = 0.10, p H 7.4 a n d 37 ~ C.
Remineralization of Dentin
19
1.0
d = .030 .8
d = .038
d = .064
.2
~i~-.,=..,~..~-40
I 80
I 120 TIME
I 160 (HOURS)
I 200
I 240
i 280
Fig. 1. Effect of particle size of dentin on fraction mineralized with time. Calcifying solution: Tea ~ 2.25 mM, Tp= 1.61 mM, ionic strength ~ 0.1, 37~ C; d is edge length in cm Other methods of nucleation were Mso tried. I t has been suggested t h a t a noncollagenous phosphoprotein in the matrix might be responsible for nucleation in vivo (Veis-and Perry, 1967). This protein (a sialoglycoprotein) was isolated b y dialysis of an E D T A solution which had just been used to decalcify samples of dentin, and was used in a 0.1% solution to incubate dentin. No improvement in nucleation of this dentin was seen. Dentin was also preincubated in phosvitin, a phosphoprotein, with negative results. E//ect of Particle Size. The effect of particle size on the rate of remineralization of dentin was studied in solutions of constant composition, i.e., total calcium added, T c a = 2.25 mM, and total phosphorus added, T v = 1.61 mM. The data are plotted in Figure 1 as fraction mineralized vs. time. The fraction mineralized, (1-~)t, is (1-~)~_ ~t-~ (1) QD-- ~r where ~ is the fraction unmineralized, ~t, is the density at a given time, and the subscripts D and C stand for dentin and demineralized dentin (collagen). The density, Qt, is determined from the velocity, u, with the relationship t = u (//Vg) + ~s
(2)
where [ is the frictional coefficient, V is the volume of the particle, y is the acceleration of gravity, and ~s is the density of the fluid. The curves are S-shaped, indicating an initial lag period, followed by a period of rapid growth, and finally by a long period of slow mineralization. The steepest slope was taken as the rate of mineralization, R~ (hr-1). As can be seen in Figure 1, the rate is inversely proportional to particle size.
20
D.B. Boyer and F. R. Eirich 1.0
.9
%
~.8 t~
tu
~.s i
.5
I
!
I
I
10
20
301 cm-
40
l/d,
Fig. 2. Calculated depth of remineralization [(1--fraction mineralized)l/a] vs. the reciprocal of particle size (l/d)
The reminerahzed particles, when sectioned and viewed under a polarizing microscope, showed a highly birefringent surface layer. The depth of this layer ranged from 30-60 l~m for various particles, with an average of 47. This observation correlated with the slowing of the rate of reminerahzation long before the particles were totally remineralized. The point of intersection of the tangents to the steep and to the final slopes of the remineralization curves was defined as the fraction minerahzed when the rate slows (1-~)s. The hypothetical depth of mineralization, w, was calculated from this point for 13 particles assuming t h a t the layer had been remineralized to the original density of fully calcified dentin when the rate slowed. The relationship between the volume fraction, qs, of a surface layer of a cube of edge length, d, and width of the layer, w, is: ~s = 1 - - (1 - - 2 w / d )
3 --
(1 -- ~)~
(3)
~]),'/,.
(4)
w -----(d/2) - - (d/2)(1 - - (1 --
The average hypothetical depth of remineralization, 46 {zm, is in good agreement with the average value measured with a planimeter on six samples, 47 ~m. The calculated depth of remineralization is plotted against the reciprocal of the particle size in Figure 2. The constant value of the slope indicates, again, a single value of the depth regardless of particle size. Figure 2 includes the data from the experiments on size variation, and from experiments at various supersaturations and temperatures. The extent of mineralization can be rewritten in terms of the fraction of the surface layer which is remineralized, (1 --})w, rather than as the fraction of the
Remineralization of Dentin
21
1.0 Sample 44 45 I"I 50
O Z~ .8
Tea (mM) 2.70 2.70 2.48
0
51
2.48
0
47
2.25
~
0 -
/ Y
~
~/""~'-
A '
~ /
~
0
~
.6
.4
0
.2
-
9
40
80
120
160
200
240
280
320
360
O0
TIME (HOURS)
Fig. 3. Effect of calcium concentration on remineralization of dentin. Fraction mineralized vs. time. All runs: T~ ~ 1.61 mM, Tee ~=23.4 raM, I = 0 . i , 37~ C
entire particle, (1 - - ~) t: (1 -
~)w =
((1i -- ~)t ~)~
(5)
where (1--~)s is the volume fraction of the particle included in the surface layer, ~P8 (see Eq. 3). The application of this correction leads to rates independent of particle size. EHect of Supersaturation. The dependence of the rate of remineralization on calcium and phosphate concentrations was determined by fixing the concentration of one ion and varying the other. Experimental data for calcium variation are plotted in Figure 3, and for phosphate variation in Figure 4. The range of concentrations used was very restricted because, at calcium concentrations higher than 2.70 mM with 1.61 mM phosphorus, the experiments were terminated by spontaneous precipitation of the solution after 6-8 days. Two runs were conducted at higher concentration (Fig. 5). I n this case, the rates were greatly accelerated and the particles were 90 % remineralized before the process slowed. The empirical reaction orders were determined with resepct to calcium and acid phosphate b y plotting--log (rate) from their respective experiments versus log ((Ca 2+) -- (Ca 2+)oo) or -- log ( (HP042-)- (HP042-)oo) in Figure 6. The rates were corrected for variation in particle size. The saturation values, (Ca2+)oo ~0.875 and (HP042-)oo z 0 . 5 7 5 , were determined from experiments of the growth of hydroxyapatite seed crystals in the same calcifying solutions using the procedures of Nancollas and Mohan (1970). The actual ionic concentrations were calculated taking into account the phosphate multiple equilibria, calcium-phosphate complex formation, calcium-carbonate complex formation, p i t and ionic strength. Calculating for the calcifying solution at 37 ~ C and I = 0 . 1 , we found (Ca2+) ~ (0.78) -
-
22
D . B . Boyer and F. R. Eirich 1.0
Sample A .8
56
Tp (mM) 2.25
0
57
2.25
0
60
1.93
61
1.93
z
.2
0
I 40
A
80
I 120
i 160 T I ME
I 200 (HOURS)
I 240
I 280
I 320
Fig. 4. Effect of phosphate concentration on remineralization of dentin. Fraction mineralized vs. time. All runs: Tc~ ~ 2.70 mM, Too ~ = 2 3 . 4 raM, I = 0 . I , 37 ~ C
1,0
.8
N
i .o z .4
0
O
Sample
27
~
Sample
38
I
40
80
I
120 TIME
160 (HOURS)
I
I
200
240
Fig. 5. Effect of high concentration of calcium and phosphate on remineralization of dentin vs. time. T c a ~ 3 . 1 5 mM, T~ = 1.93 raM, T e e ~= 2 3 . 4 mM, I = 0 . 1 , 37 ~ C
Tea, (HPO~ 2-)-- (0.65) T~, and (HC03-) ~ (0.92) Tee ,. Although the variation in the rates is large, the best value of the reaction orders seems to be 1.0 =k 0.3 with respect to both c a l c i u m a n d a c i d phosphate.
Remineralization of Dentin
23
8.4
8.3
i s.2
8.1
v 8.0 t
7.9 E
-
log
2.92+ ((Ca ) -
3. + ( C a ~ )~e)
3.1 or -
log
3.~ ((HP042-)
-
3.3 23.4 (HPO 4 )ga)
Fig. 6. R a t e of mineralization (--log) vs. concentration of calcium or acid phosphate at supersaturation levels. Short vertical lines represent ~ 1 S.D.
1.0 B .8 ~
Sample 71
Temperature 45
~
45
Q
72
]k
66
37 -
25
l-]
69
37 -
25
O
70
37 - 25
i' .2
0
w
|
t
40
80
S 120
I
160 TIME
200 (HOURS)
!
I
240
280
I
320
Fig. 7. Temperature dependence of remineralization. Fraction mineralized vs. time. All runs: Tea = 2.70 mM, Tp= 1.61 raM, TCo ' = 23.4 m ~ . For samples 66, 69, 70, the runs were begun at 37 ~ C. After remineralization was under way the temperature was lowered to 25 ~ C
24
D.B. Boyer and F. R. Eirich
~s z
~4
~2 t
I .0031
I .0034
I I .0032 .0033 1/TEMPERATURE ~
Fig. 8. Activation energy of remineralization. - - l n (rate of remineralization) vs. 1/temperature 1.0
.8
9
s9
o
4o
0
48
/4/
g z
2
.4
.2
40
80
120
160 T I ME
200 ( HOURS )
240
280
320
I 360
Fig. 9. Effect of fluoride on remineralization of dentin. Fraction mineralized vs. time; 1 ppm F- as NaF. T e a = 2.70 raM, T v = 1.61 mM, Tco, = 23.4 mM, 37~ C
Temperature Dependence. The t e m p e r a t u r e dependence of r e m i n e r a l i z a t i o n was s t u d i e d to clarify w h e t h e r the process is diffusion or surface-controlled. I t was found, a t c o n c e n t r a t i o n s of 2.70 mM Tca a n d 1.61 m M Tp, t h a t n u c l e a t i o n would n o t occur a t 25 ~ C. Therefore, the experiments a t this t e m p e r a t u r e were carried o u t b y first setting the t e m p e r a t u r e a t 37 ~ C. After m i n e r a l i z a t i o n was well u n d e r way, the t e m p e r a t u r e was r a p i d l y reduced to 25 ~ C a n d t h e r u n was continued. The e x p e r i m e n t s are shown i n F i g u r e 7, where corrections have been m a d e for changes i n t h e viscosity with t e m p e r a t u r e .
Remineralization of Dentin
25
1.0
.8
2k
Sample
58
0
Sample
59
~.4
.2
0
l 40
80
I 120
| 160 TIME
I 200 (HOURS)
I 240
I 280
I 320
Fig. 10. Effect of strontium on remineralization of dentin. Fraction mineralized vs. time. 1 ppm Sr+2 as SrCI~. Tea = 2,70 mM, T~ = 1.61 mM:, Tco ~ 23.4 mM, 37~ C =
The apparent activation energy of remineralization was determined from the plot of In k = - - E a / R T + constant to be 28.1 kcal/mole (Fig. 8). E//ect o/Fluoride. The effect of fluoride ion on the remineralization of dentin was studied b y including 1 p p m F - (5.26 • 10 -5 M NaF) in the calcifying solution, Tea =- 2.70 mM, Tv ~ 1.61 mM (data shown in Fig. 9). The significant findings are t h a t the rate of remineralization does not change; e.g., the average value of the steepest slopes of samples 54 and 55 is 0.0068 h -1 compared to the average of 0.0065 h -1 for samples 44 and 45 from Figure 3. However, the process continues until the samples are about 90% remineralized before the rate slows. The samples become nearly completely remineralized in 4 - 5 days after calcification begins. The effect of strontium ion was studied b y adding 1 p p m Sr 2+ (1.14 • 10 -5 M SrC12-6H20 ) to the calcifying solution with T c a = 2 . 7 0 mM and T v = l . 6 1 mM (data are shown in Fig. 10). The rate of remineralization increased. The average of the steepest slopes of samples 58 and 59 is 0.0103 h -1 compared to 0.0065 h -1 for samples 44 and 45, the runs at a corresponding saturation without strontium.
Discussion The minimum concentration product at which nucleation occurred was Ca • P = 3.6 (mM) 2 in a solution with a physiologic concentration of bicarbonate, 22 raM, ionic strength 0.10, 37 ~ C, and p H 7.4.1The activity product, aca 2+. a~eo, 2-, for this solution is 2.67 X 10 -7, which is just above the solubility product of brushite, 2.32 x 10 -7 (Gregory et al., 1970). Using serum ultrafiltrate, Solomons and Neuman (1960) found t h a t dentin nudeated solutions above 3.2 (raM) 2, in
26
D.B. Boyer and F. R. Eirich
approximate agreement with the results obtained here. B y comparison, Chan (1971) found t h a t rachitie rat cartilage was an effective nucleator at 2.8 (raM) 2 in the same calcifying solutions as used here. Nucleation was obtained only by the technique of renewal of the calcifying solution after intermediate rinsing with distilled water. This technique has been used b y Bachra and Fischer (1968a) to initiate nucleation in tissues which are poor nucleation catalysts. They showed (1968b) t h a t such renewal causes a loss of CO 2 from the solution entrapped within the tissue during rinsing and leads to a rise in the p H which facilitates nucleation. The lag time between immersion of a dentin particle in calcifying solution and the first detecion of mineralization was proportional to the supersaturation of the calcifying solution. The rates of remineralization, i.e., the fractions remineralized, were inversely proportional to particle size. This relationship was observed at several levels of supersaturation, temperature, and strontium concentration. This relationship m a y be due to deposition of mineral in a surface layer of constant depth regardless of particle size. Apparently, when the surface has become heavily mineralized, the diffusion pathways to the interior become blocked so t h a t further mineralization proceeds very slowly. An alternative explanation m a y be that only the surface layer has been nucleated and is calcifying.The agreement of the calculated and measured depths of remineralization m a y to some degree be due to offsetting errors in the assumptions t h a t the intersection of the tangents to the slopes is the fraction mineralized and t h a t the layer is mineralized to its original density. Two exceptions to the usual pattern of mineralization of a surface layer were found with high supersaturation, 5.07 (mM) 2, and the presence of 1 p p m F at low supersaturation. I n these cases the rate proceeded at its m a x i m u m value until the particles were about 90% remineralized. I t appears t h a t here the entire particle is mineralizing simultaneously, rather than only a surface layer. I n a study of calcification of demineralized sheep bone matrix, Bachra (1972) predicted an inverse dependence of the rate on the particle size. However, he found no dependence on particle size of either mineralization rate, or per cent mineralization. His results m a y be compatible with those of this study because he used a calcifying solution of high supersaturation, Ca • P : 6.26 (raM) 2. As shown here, the high metastability of this solution would lead to rapid mineralization throughout the tissue. A comparison of the present study with t h a t of Baehra shows t h a t bovine dentin can be remineralized to a greater degree than sheep bone. The per cent by weight of mineral deposited in dentin was 50-70% compared to 35% in bone obtained by Baehra. This finding m a y be due to the presence of dentinal tubules which give greater access to the interior of the particle. The activation energy of remineralization found in this study~ 28 kcal/mole, indicates a surface-controlled process, since diffusion-limited reactions have low activation energies in the range 2-10 kcal/mole (Satterfield, 1970). The m a x i m u m rate of remineralization in the presence of fluoride was the same as without fluoride. I t might have been expected t h a t the rate would be higher, since apparently the entire particle mineralizes. Coupling the latter observation with the finding t h a t the rates of hydroxyapatite (HAP) seed crystal
Remineralization of Dentin
27
growth were reduced in the same calcifying solution in the presence of 1 p p m F (Boyer and Eirich, in preparation), it might be concluded t h a t the lack of a change in rate is due to an averaging of the two opposing effects. The effect of fluoride on the mineralization of decalcified bovine dentin has been studied by DeSteno et al. (1973). They found t h a t the presence of 0.05 mM N a F inhibited remineralization in solutions containing 22 mM bicarbonate, and reduced the amount of mineral deposited in 2 days b y 50%. This result m a y be consistent with the present study because they used highly supersaturated calcifying solutions containing Ca • P ~ 6.26 (raM) ~. At this supersaturation, mineralization m a y occur throughout the dentin, so t h a t the only effect of fluoride is to inhibit crystal growth. They also found t h a t fluoride added to HCO3-free buffer increased the rate of mineralization of partially decalcified sections. This finding is in contrast to the results of our studies of the growth of H A P seed crystals (Boyer and Eirich, in preparation) where crystal growth was inhibited b y fluoride in the presence and absence of carbonate. The findings of DeSteno et al. (1973) could perhaps be explained b y the formation of new nucleation sites in the tissue by CaF~ in the absence of HCO3. I n an a t t e m p t to clarify the role of the organic matrix in the precipitation of calcium phosphates, the empirical reaction orders of the rate of mineralization for calcium and phosphate were determined. These orders were found to be 1 ~= 0.3, for both calcium and acid phosphate, compared to the values of 1.29 and 1.28 for H A P growth in the same solutions. The saturation values of calcium and acid phosphate used in determining these reaction orders were determined from the H A P seed crystal growth experiments. These values are thought to be valid for crystal growth in dentin because the order for total calcium was similar in both cases. Saturation values could not be determined in the remineralization experiments because the concentrations remained constant due to a large excess of calcifying solution. The similarity of reaction orders, together with the finding of a high apparent energy of activation, leads to the conclusion t h a t crystal growth in the organic matrix is essentially the same process as t h a t in solutions containing seed crystals. The present study suggests t h a t the results of studies of the deposition of calcium phosphate salts from solution (Termine and Posner, 1970; Nancollas and Mohan 1970) can be extrapolated to the more physiologic situation of mineral deposition in an organic matrix. Such studies have shown t h a t precipitates reflect the solution composition, temperature, and pH.
References Amprino, R., Camanni, F. : ~Iistoradiographic and autoradiographic researches of hard dental tissues. Acta anat. (Basel) 28, 217-258 (1956) Baehra, B.N.: Calcification in vitro of demineralized bone matrix. Caleif. Tiss. Res. 8, 287-303 (1972) Baehra, B. N., Fischer, H. R. A. : Mineral deposition in collagen in vitro. Calcif. Tiss. Res. 2, 343-352 (1968a) Bachra, B. N., Fischer, H. R. A. : Calcification in model systems. Proc. of the Fifth European Syrup. on Calcified Tissues, pp. 53-58. Bordeaux 1968b
28
D.B. Boyer and F. R. Eirich
Brudevold, F., Steadman, L. T., Smith, F. A. : Inorganic and organic components of tooth structure. Arm. N.Y. Acad. Sci. 85, 110-132 (1960) Chan, 1~I.S. : On the rates of calcification and decalcification of bone in vitro. Ph.D. Dissertation, Polytechnic Institute of Brooklyn, Brooklyn: 1971 Chan, M. S., Eirich, F. R. : Calcification and decalcification rates in vitro. A new technique. Proc. Soc. exp. Biol. (N.Y.) 143, 919-924 (1973) Desteno, C. V., Feagin, F. F., Taylor, R. E., Jr. : Effect of fluoride on the mineralization of decalcified and partially recalcified bovine dentin. (Abstract 581, IADR Programs and Abstracts of Papers). J. dent. Res. 52 (Special Issue) 204 (1973) Francis, M. D., Briner, W. W., Gray, J. A.: Chemical agents in the control of calcification processes in biological systems. In: Ciba Foundation Symposium II: Hard tissue growth, repair, and remineralization, pp. 57-90. Amsterdam: Elsevier 1973 Gregory, T. M., Moreno, E. C., Brown, W. E. : Solubility of calcium monohydrogen phosphate dihydrate in the system calcium hydroxide-orthophosphoric acid~water at 5, 15, 25, and 37.5~ J. Res. nat. Bur. Std. 74 (A), 461475 (1970) Hirshman, A., Sobel, A. E. : Composition of the mineral deposited during in vitro calcification in relation to the fluid phase. Arch. Biochem. Biophys. 110, 237-243 (1965) Koulourides, T. : Remineralization methods. Ann. N.Y. Acad. Sci. 153, 84-101 (1968) Nancollas, G. H., Mohan, M. S. : The growth of hydroxyapatite crystals. Arch. oral Biol. 15, 731-745 (1970) Poole, D. F. G., Silverstone, L. M. : Remineralization of enamel. In: Ciba Foundation Symposium II: Hard tissue growth, repair, and remineralization, pp. 35-56. Amsterdam: Elsevier 1973 Satterfield, C.N.: Mass transfer in heterogeneous catalysis, Chap. 1. Cambridge: M.I.T. Press 1970 Solomons, C. C., Neuman, W. F. : On the mechanism of calcification: The remineralization of dentin. J. biol. Chem. 285, 2502-2506 (1960) Termine, J. D., Posner, A. S. : Calcium phosphate formation in vitro. Arch. Biochem. Biophys. 140, 307-317 (1970) Veis, A., Perry, A.: The phosphoprotein of the dentin matrix. Biochemistry. (Wash.) 6, 2409-2416 (1967) Wei, S. H. Y. : l~emineralizationof enamel and dentine---a review. J. Dent. Child. 84, 444-451 (1967)
Remineralization of Dentin in vitro D. B. B o y e r and F. R. Eirich Polytechnic Institute of New York, Brooklyn, New York Received June 17, 1975; accepted April 1, 1976 The remineralization of completely demineralized bovine dentin was studied in vitro by monitoring the velocities of fall of small particles through calcifying solutions. The density of a particle of dentin may be found from its velocity of fall through a fluid using Stokes' law. The minimum concentration product of calcium and acid phosphate ions of the solution in which remineralization would take place was 3.6 (raM)~ in the presence of 22 mM bicarbonate, pH 7.35, and ionic strength 0.1. This is just above the solubility product of brushite (CaHPO4- 2H20 ). Incubation of decalcified dentin in a phosphoprotein removed from dentin during demineralization, or in phosvitin, had no effect on remineralization. The rates of remineralization and of the fraction remineralized were inversely proportional to particle size. This inverse correlation may be due to deposition of mineral in a surface layer of constant depth irrespective of particle size. The fraction of a particle remineralized was greatly increased by the use of highly supersaturated calcifying solutions or by the incorporation of fluoride into the solutions. The empirical reaction order of remineralization for both calcium and phosphate ions was found to be unity, which is, within the error limits, equal to the order of growth of seed crystals of hydroxyapatite in calcifying solutions of the same composition. Key words: Calcification - - Dentin - - Nucleation - - Kinetics.
Introduction Decalcified dentin, like bone a n d cartilage, can be remineralized in supersaturated solutions. A n orderly deposition and g r o w t h of calcium phosphate salts within and a r o u n d its fibers is often seen. Studies of the remineralization of dental hard tissues have been concerned for the m o s t p a r t with partially demineralized enamel and dentin, and with the repair of incipient caries in enamel or the repair of carious dentin (Koulourides, 1968). Posteruptive changes in the composition of enamel, especially in hypomineralized areas, have been taken as evidence of remineralization in vivo (Brudevold et al., 1960). Microradiographie studies have shown carious dentin which has regained high density, an observation t h a t can be explained b y remineralization (Amprino and Camanni, 1956). I n laboratory studies, dental tissues are exposed either to calcifying solution, supersaturated in calcium and phosphate salts, or t o saliva. The extent of mineralization is determined b y direct techniques in which the a m o u n t of mineral t a k e n up b y the tissue or depleted from the solution is measured, or b y indirect techniques such as microradiography, polarizing microscopy, absorption of dyes, and measurement of surface hardness. Reviews on the remineralization of enamel
.~'or reprints: D. Boyer, College of Dentistry, University of Iowa, Iowa City, Iowa 52242, USA.
18
D.B. Boyer and F. R. Eirich
a n d d e n t i n have been given b y Wei (1967), Koulourides (1968), Poole a n d Silverstone (1973), a n d F r a n c i s et al. (1973). I n t h e present study, we sought to a p p l y a n e w t e c h n i q u e (Chan a n d Eirich, 1973) for t h e s t u d y of the r e m i n e r a l i z a t i o n of d e n t i n . This t e c h n i q u e m o n i t o r s the change i n d e n s i t y of a particle of hard tissue b y m e a s u r i n g its velocity of fall t h r o u g h a c o l u m n of calcifying solution.
Materials and Methods The sedimentation apparatus and its application have been described previously (Chan and Eirich, 1973). The apparatus consists of glass columns about 60 cm long, and a stand for mounting and rotating them in an air thermostat. Each column has a restricted channel near one end to center the falling particle within the column. The solution in the column is stirred at 1,000 rpm by a small stirring bar when readings are not being taken. The bar is held fixed to the side of the column by an external magnet during readings. An experiment is initiated by filling the column with 220 ml of calcifying solution and by equilibrating to 37~ C in the thermostat. The hard tissue sample is introduced into the column through a Teflon valve with a disposable pipette. The duration of fall of the particle between bench marks 30.5 cm apart is periodically measured with a stopwatch. Because calcification in solutions close to physiologic composition is a very slow process, readings were taken only once a day. An experiment usually lasted for 10 days, although in some instances, experiments were continued for 3 wk. This technique has the advantage that calcification can be followed for long periods of time without spontaneous precipitation or bacterial growth, since the columns are closed, air-flee and air-tight and need not be opened for sampling. Bovine dentin was used in the study. The lower jaws of calves were obtained from an abattoir on the day of slaughter. The teeth were removed, cleaned of soft tissue, and frozen until use. The roots were the source of dentin. The dentin was cut into small cubes with a scalpel under a dissection microscope. The dimensions of the cubes were measured to the nearest 5 ~m with a planimeter. The particles were generally about 0.03 cm in diameter because this proved to be the smallest size practical to cut and to observe. Small particles were desirable in order to shorten the duration of the experiments. The calcifying solution, prepared immediately before each experiment from three stock solutions, was that described by Hirschman and Sobel (1965). The desired amount of calcium stock solution was added dropwise to the phosphorus stock solution in 100 ml of basal salt solution and 600 ml of water. Before the calcium was added, the pH of the solution was lowered by bubbling CO2 through it. After the calcium was added and the solution adjusted to 1 l, the pH was raised by bubbling nitrogen through the solution. The final pH of the solutions was 7.35 =t=0.05. The amount of basal salt solution added was always 100 ml so that the calcifying solution contained 70 mM NaC1, 5 mM KC1, and 22 mM NaHC03; the ionic strength was 0.10. To prevent the loss of CO2, the solution was immediately poured into the glass columns. At the end of the experiments the pH was remeasured and found to be unchanged. Results
Nucleation. D e n t i n placed directly i n t o calcifying solution i n t h e columns would n o t calcify, even when i n c u b a t e d u p to a m o n t h . N u c l e a t i o n of fully demineralized d e n t i n was o b t a i n e d o n l y b y placing the d e n t i n i n calcifying solut i o n for 1 h, after which time it was removed, rinsed with distilled water, a n d transferred to the c o l u m n of calcifying solution. This t e c h n i q u e is similar to t h a t used b y Bachra a n d Fischer (1968) to nucleate certain tissues. The m i n i m u m c o n c e n t r a t i o n p r o d u c t a t which r e m i n e r a l i z a t i o n of freshly demineralized d e n t i n occurred was Ca • P ~ 3.6 (mM) 2 i n a solution with 22 m M b i c a r b o n a t e , ionic s t r e n g t h = 0.10, p H 7.4 a n d 37 ~ C.
Remineralization of Dentin
19
1.0
d = .030 .8
d = .038
d = .064
.2
~i~-.,=..,~..~-40
I 80
I 120 TIME
I 160 (HOURS)
I 200
I 240
i 280
Fig. 1. Effect of particle size of dentin on fraction mineralized with time. Calcifying solution: Tea ~ 2.25 mM, Tp= 1.61 mM, ionic strength ~ 0.1, 37~ C; d is edge length in cm Other methods of nucleation were Mso tried. I t has been suggested t h a t a noncollagenous phosphoprotein in the matrix might be responsible for nucleation in vivo (Veis-and Perry, 1967). This protein (a sialoglycoprotein) was isolated b y dialysis of an E D T A solution which had just been used to decalcify samples of dentin, and was used in a 0.1% solution to incubate dentin. No improvement in nucleation of this dentin was seen. Dentin was also preincubated in phosvitin, a phosphoprotein, with negative results. E//ect of Particle Size. The effect of particle size on the rate of remineralization of dentin was studied in solutions of constant composition, i.e., total calcium added, T c a = 2.25 mM, and total phosphorus added, T v = 1.61 mM. The data are plotted in Figure 1 as fraction mineralized vs. time. The fraction mineralized, (1-~)t, is (1-~)~_ ~t-~ (1) QD-- ~r where ~ is the fraction unmineralized, ~t, is the density at a given time, and the subscripts D and C stand for dentin and demineralized dentin (collagen). The density, Qt, is determined from the velocity, u, with the relationship t = u (//Vg) + ~s
(2)
where [ is the frictional coefficient, V is the volume of the particle, y is the acceleration of gravity, and ~s is the density of the fluid. The curves are S-shaped, indicating an initial lag period, followed by a period of rapid growth, and finally by a long period of slow mineralization. The steepest slope was taken as the rate of mineralization, R~ (hr-1). As can be seen in Figure 1, the rate is inversely proportional to particle size.
20
D.B. Boyer and F. R. Eirich 1.0
.9
%
~.8 t~
tu
~.s i
.5
I
!
I
I
10
20
301 cm-
40
l/d,
Fig. 2. Calculated depth of remineralization [(1--fraction mineralized)l/a] vs. the reciprocal of particle size (l/d)
The reminerahzed particles, when sectioned and viewed under a polarizing microscope, showed a highly birefringent surface layer. The depth of this layer ranged from 30-60 l~m for various particles, with an average of 47. This observation correlated with the slowing of the rate of reminerahzation long before the particles were totally remineralized. The point of intersection of the tangents to the steep and to the final slopes of the remineralization curves was defined as the fraction minerahzed when the rate slows (1-~)s. The hypothetical depth of mineralization, w, was calculated from this point for 13 particles assuming t h a t the layer had been remineralized to the original density of fully calcified dentin when the rate slowed. The relationship between the volume fraction, qs, of a surface layer of a cube of edge length, d, and width of the layer, w, is: ~s = 1 - - (1 - - 2 w / d )
3 --
(1 -- ~)~
(3)
~]),'/,.
(4)
w -----(d/2) - - (d/2)(1 - - (1 --
The average hypothetical depth of remineralization, 46 {zm, is in good agreement with the average value measured with a planimeter on six samples, 47 ~m. The calculated depth of remineralization is plotted against the reciprocal of the particle size in Figure 2. The constant value of the slope indicates, again, a single value of the depth regardless of particle size. Figure 2 includes the data from the experiments on size variation, and from experiments at various supersaturations and temperatures. The extent of mineralization can be rewritten in terms of the fraction of the surface layer which is remineralized, (1 --})w, rather than as the fraction of the
Remineralization of Dentin
21
1.0 Sample 44 45 I"I 50
O Z~ .8
Tea (mM) 2.70 2.70 2.48
0
51
2.48
0
47
2.25
~
0 -
/ Y
~
~/""~'-
A '
~ /
~
0
~
.6
.4
0
.2
-
9
40
80
120
160
200
240
280
320
360
O0
TIME (HOURS)
Fig. 3. Effect of calcium concentration on remineralization of dentin. Fraction mineralized vs. time. All runs: T~ ~ 1.61 mM, Tee ~=23.4 raM, I = 0 . i , 37~ C
entire particle, (1 - - ~) t: (1 -
~)w =
((1i -- ~)t ~)~
(5)
where (1--~)s is the volume fraction of the particle included in the surface layer, ~P8 (see Eq. 3). The application of this correction leads to rates independent of particle size. EHect of Supersaturation. The dependence of the rate of remineralization on calcium and phosphate concentrations was determined by fixing the concentration of one ion and varying the other. Experimental data for calcium variation are plotted in Figure 3, and for phosphate variation in Figure 4. The range of concentrations used was very restricted because, at calcium concentrations higher than 2.70 mM with 1.61 mM phosphorus, the experiments were terminated by spontaneous precipitation of the solution after 6-8 days. Two runs were conducted at higher concentration (Fig. 5). I n this case, the rates were greatly accelerated and the particles were 90 % remineralized before the process slowed. The empirical reaction orders were determined with resepct to calcium and acid phosphate b y plotting--log (rate) from their respective experiments versus log ((Ca 2+) -- (Ca 2+)oo) or -- log ( (HP042-)- (HP042-)oo) in Figure 6. The rates were corrected for variation in particle size. The saturation values, (Ca2+)oo ~0.875 and (HP042-)oo z 0 . 5 7 5 , were determined from experiments of the growth of hydroxyapatite seed crystals in the same calcifying solutions using the procedures of Nancollas and Mohan (1970). The actual ionic concentrations were calculated taking into account the phosphate multiple equilibria, calcium-phosphate complex formation, calcium-carbonate complex formation, p i t and ionic strength. Calculating for the calcifying solution at 37 ~ C and I = 0 . 1 , we found (Ca2+) ~ (0.78) -
-
22
D . B . Boyer and F. R. Eirich 1.0
Sample A .8
56
Tp (mM) 2.25
0
57
2.25
0
60
1.93
61
1.93
z
.2
0
I 40
A
80
I 120
i 160 T I ME
I 200 (HOURS)
I 240
I 280
I 320
Fig. 4. Effect of phosphate concentration on remineralization of dentin. Fraction mineralized vs. time. All runs: Tc~ ~ 2.70 mM, Too ~ = 2 3 . 4 raM, I = 0 . I , 37 ~ C
1,0
.8
N
i .o z .4
0
O
Sample
27
~
Sample
38
I
40
80
I
120 TIME
160 (HOURS)
I
I
200
240
Fig. 5. Effect of high concentration of calcium and phosphate on remineralization of dentin vs. time. T c a ~ 3 . 1 5 mM, T~ = 1.93 raM, T e e ~= 2 3 . 4 mM, I = 0 . 1 , 37 ~ C
Tea, (HPO~ 2-)-- (0.65) T~, and (HC03-) ~ (0.92) Tee ,. Although the variation in the rates is large, the best value of the reaction orders seems to be 1.0 =k 0.3 with respect to both c a l c i u m a n d a c i d phosphate.
Remineralization of Dentin
23
8.4
8.3
i s.2
8.1
v 8.0 t
7.9 E
-
log
2.92+ ((Ca ) -
3. + ( C a ~ )~e)
3.1 or -
log
3.~ ((HP042-)
-
3.3 23.4 (HPO 4 )ga)
Fig. 6. R a t e of mineralization (--log) vs. concentration of calcium or acid phosphate at supersaturation levels. Short vertical lines represent ~ 1 S.D.
1.0 B .8 ~
Sample 71
Temperature 45
~
45
Q
72
]k
66
37 -
25
l-]
69
37 -
25
O
70
37 - 25
i' .2
0
w
|
t
40
80
S 120
I
160 TIME
200 (HOURS)
!
I
240
280
I
320
Fig. 7. Temperature dependence of remineralization. Fraction mineralized vs. time. All runs: Tea = 2.70 mM, Tp= 1.61 raM, TCo ' = 23.4 m ~ . For samples 66, 69, 70, the runs were begun at 37 ~ C. After remineralization was under way the temperature was lowered to 25 ~ C
24
D.B. Boyer and F. R. Eirich
~s z
~4
~2 t
I .0031
I .0034
I I .0032 .0033 1/TEMPERATURE ~
Fig. 8. Activation energy of remineralization. - - l n (rate of remineralization) vs. 1/temperature 1.0
.8
9
s9
o
4o
0
48
/4/
g z
2
.4
.2
40
80
120
160 T I ME
200 ( HOURS )
240
280
320
I 360
Fig. 9. Effect of fluoride on remineralization of dentin. Fraction mineralized vs. time; 1 ppm F- as NaF. T e a = 2.70 raM, T v = 1.61 mM, Tco, = 23.4 mM, 37~ C
Temperature Dependence. The t e m p e r a t u r e dependence of r e m i n e r a l i z a t i o n was s t u d i e d to clarify w h e t h e r the process is diffusion or surface-controlled. I t was found, a t c o n c e n t r a t i o n s of 2.70 mM Tca a n d 1.61 m M Tp, t h a t n u c l e a t i o n would n o t occur a t 25 ~ C. Therefore, the experiments a t this t e m p e r a t u r e were carried o u t b y first setting the t e m p e r a t u r e a t 37 ~ C. After m i n e r a l i z a t i o n was well u n d e r way, the t e m p e r a t u r e was r a p i d l y reduced to 25 ~ C a n d t h e r u n was continued. The e x p e r i m e n t s are shown i n F i g u r e 7, where corrections have been m a d e for changes i n t h e viscosity with t e m p e r a t u r e .
Remineralization of Dentin
25
1.0
.8
2k
Sample
58
0
Sample
59
~.4
.2
0
l 40
80
I 120
| 160 TIME
I 200 (HOURS)
I 240
I 280
I 320
Fig. 10. Effect of strontium on remineralization of dentin. Fraction mineralized vs. time. 1 ppm Sr+2 as SrCI~. Tea = 2,70 mM, T~ = 1.61 mM:, Tco ~ 23.4 mM, 37~ C =
The apparent activation energy of remineralization was determined from the plot of In k = - - E a / R T + constant to be 28.1 kcal/mole (Fig. 8). E//ect o/Fluoride. The effect of fluoride ion on the remineralization of dentin was studied b y including 1 p p m F - (5.26 • 10 -5 M NaF) in the calcifying solution, Tea =- 2.70 mM, Tv ~ 1.61 mM (data shown in Fig. 9). The significant findings are t h a t the rate of remineralization does not change; e.g., the average value of the steepest slopes of samples 54 and 55 is 0.0068 h -1 compared to the average of 0.0065 h -1 for samples 44 and 45 from Figure 3. However, the process continues until the samples are about 90% remineralized before the rate slows. The samples become nearly completely remineralized in 4 - 5 days after calcification begins. The effect of strontium ion was studied b y adding 1 p p m Sr 2+ (1.14 • 10 -5 M SrC12-6H20 ) to the calcifying solution with T c a = 2 . 7 0 mM and T v = l . 6 1 mM (data are shown in Fig. 10). The rate of remineralization increased. The average of the steepest slopes of samples 58 and 59 is 0.0103 h -1 compared to 0.0065 h -1 for samples 44 and 45, the runs at a corresponding saturation without strontium.
Discussion The minimum concentration product at which nucleation occurred was Ca • P = 3.6 (mM) 2 in a solution with a physiologic concentration of bicarbonate, 22 raM, ionic strength 0.10, 37 ~ C, and p H 7.4.1The activity product, aca 2+. a~eo, 2-, for this solution is 2.67 X 10 -7, which is just above the solubility product of brushite, 2.32 x 10 -7 (Gregory et al., 1970). Using serum ultrafiltrate, Solomons and Neuman (1960) found t h a t dentin nudeated solutions above 3.2 (raM) 2, in
26
D.B. Boyer and F. R. Eirich
approximate agreement with the results obtained here. B y comparison, Chan (1971) found t h a t rachitie rat cartilage was an effective nucleator at 2.8 (raM) 2 in the same calcifying solutions as used here. Nucleation was obtained only by the technique of renewal of the calcifying solution after intermediate rinsing with distilled water. This technique has been used b y Bachra and Fischer (1968a) to initiate nucleation in tissues which are poor nucleation catalysts. They showed (1968b) t h a t such renewal causes a loss of CO 2 from the solution entrapped within the tissue during rinsing and leads to a rise in the p H which facilitates nucleation. The lag time between immersion of a dentin particle in calcifying solution and the first detecion of mineralization was proportional to the supersaturation of the calcifying solution. The rates of remineralization, i.e., the fractions remineralized, were inversely proportional to particle size. This relationship was observed at several levels of supersaturation, temperature, and strontium concentration. This relationship m a y be due to deposition of mineral in a surface layer of constant depth regardless of particle size. Apparently, when the surface has become heavily mineralized, the diffusion pathways to the interior become blocked so t h a t further mineralization proceeds very slowly. An alternative explanation m a y be that only the surface layer has been nucleated and is calcifying.The agreement of the calculated and measured depths of remineralization m a y to some degree be due to offsetting errors in the assumptions t h a t the intersection of the tangents to the slopes is the fraction mineralized and t h a t the layer is mineralized to its original density. Two exceptions to the usual pattern of mineralization of a surface layer were found with high supersaturation, 5.07 (mM) 2, and the presence of 1 p p m F at low supersaturation. I n these cases the rate proceeded at its m a x i m u m value until the particles were about 90% remineralized. I t appears t h a t here the entire particle is mineralizing simultaneously, rather than only a surface layer. I n a study of calcification of demineralized sheep bone matrix, Bachra (1972) predicted an inverse dependence of the rate on the particle size. However, he found no dependence on particle size of either mineralization rate, or per cent mineralization. His results m a y be compatible with those of this study because he used a calcifying solution of high supersaturation, Ca • P : 6.26 (raM) 2. As shown here, the high metastability of this solution would lead to rapid mineralization throughout the tissue. A comparison of the present study with t h a t of Baehra shows t h a t bovine dentin can be remineralized to a greater degree than sheep bone. The per cent by weight of mineral deposited in dentin was 50-70% compared to 35% in bone obtained by Baehra. This finding m a y be due to the presence of dentinal tubules which give greater access to the interior of the particle. The activation energy of remineralization found in this study~ 28 kcal/mole, indicates a surface-controlled process, since diffusion-limited reactions have low activation energies in the range 2-10 kcal/mole (Satterfield, 1970). The m a x i m u m rate of remineralization in the presence of fluoride was the same as without fluoride. I t might have been expected t h a t the rate would be higher, since apparently the entire particle mineralizes. Coupling the latter observation with the finding t h a t the rates of hydroxyapatite (HAP) seed crystal
Remineralization of Dentin
27
growth were reduced in the same calcifying solution in the presence of 1 p p m F (Boyer and Eirich, in preparation), it might be concluded t h a t the lack of a change in rate is due to an averaging of the two opposing effects. The effect of fluoride on the mineralization of decalcified bovine dentin has been studied by DeSteno et al. (1973). They found t h a t the presence of 0.05 mM N a F inhibited remineralization in solutions containing 22 mM bicarbonate, and reduced the amount of mineral deposited in 2 days b y 50%. This result m a y be consistent with the present study because they used highly supersaturated calcifying solutions containing Ca • P ~ 6.26 (raM) ~. At this supersaturation, mineralization m a y occur throughout the dentin, so t h a t the only effect of fluoride is to inhibit crystal growth. They also found t h a t fluoride added to HCO3-free buffer increased the rate of mineralization of partially decalcified sections. This finding is in contrast to the results of our studies of the growth of H A P seed crystals (Boyer and Eirich, in preparation) where crystal growth was inhibited b y fluoride in the presence and absence of carbonate. The findings of DeSteno et al. (1973) could perhaps be explained b y the formation of new nucleation sites in the tissue by CaF~ in the absence of HCO3. I n an a t t e m p t to clarify the role of the organic matrix in the precipitation of calcium phosphates, the empirical reaction orders of the rate of mineralization for calcium and phosphate were determined. These orders were found to be 1 ~= 0.3, for both calcium and acid phosphate, compared to the values of 1.29 and 1.28 for H A P growth in the same solutions. The saturation values of calcium and acid phosphate used in determining these reaction orders were determined from the H A P seed crystal growth experiments. These values are thought to be valid for crystal growth in dentin because the order for total calcium was similar in both cases. Saturation values could not be determined in the remineralization experiments because the concentrations remained constant due to a large excess of calcifying solution. The similarity of reaction orders, together with the finding of a high apparent energy of activation, leads to the conclusion t h a t crystal growth in the organic matrix is essentially the same process as t h a t in solutions containing seed crystals. The present study suggests t h a t the results of studies of the deposition of calcium phosphate salts from solution (Termine and Posner, 1970; Nancollas and Mohan 1970) can be extrapolated to the more physiologic situation of mineral deposition in an organic matrix. Such studies have shown t h a t precipitates reflect the solution composition, temperature, and pH.
References Amprino, R., Camanni, F. : ~Iistoradiographic and autoradiographic researches of hard dental tissues. Acta anat. (Basel) 28, 217-258 (1956) Baehra, B.N.: Calcification in vitro of demineralized bone matrix. Caleif. Tiss. Res. 8, 287-303 (1972) Baehra, B. N., Fischer, H. R. A. : Mineral deposition in collagen in vitro. Calcif. Tiss. Res. 2, 343-352 (1968a) Bachra, B. N., Fischer, H. R. A. : Calcification in model systems. Proc. of the Fifth European Syrup. on Calcified Tissues, pp. 53-58. Bordeaux 1968b
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D.B. Boyer and F. R. Eirich
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