diffusion fluxes of tritiated water across human enamel membranes

DIFFUSION FLUXES OF TRITIATED WATER ACROSS HUMAN ENAMEL MEMBRANES

E. J. BURKE and E. C. MORENO

Forsyth Dental Center, 140 Fenway, Boston, Mass. 02115. U.S.A.

Summary-Isothermal diffusion fluxes of tritiated water across human incisor and canine enamel membranes were measured using a small volume diaphragm cell in the temperature range 13-- 37°C. The plano-parallel intact enamel membranes were identified by geometric surface area, thickness, age and sex of donor. The calculated apparent diffusion coefficient values, D,, revealed that significant differences in the water fluxes exist between these two membranes, with the inci- sors displaying the larger 0, values. Diffusional activation energies, E,, calculated from the D, data obtained at three temperatures indicated an interaction between the diffusing water and the enamel pores, with the larger values observed for the canines. The data are discussed in terms of a uarallel pore model in which pore constrictions of the enamel serve as energy barriers to diffusion. 1

INTRODUCTION

A common feature of the several models advanced to explain the formation of incipient carious lesions is that a diffusion-limiting step controls the process (Gray, Francis and Griebstein, 1962; Holly and Gray, 1968; Higuchi et al., 1969; Moreno and Zahradnik, 1974). Actual diffusion coefficient data for dental enamel, however, are scant (Holly and Gray, 1968; Braden, Duckworth and Joyston-Bechal, 1971). The paucity of diffusion measurements is undoubtedly related to the difficulties encountered in designing experimental techniques that yield meaningful quantitative information. For example, the low porosity of enamel dictates the use of enamel sections with a large surface area, but the tooth morphology imposes a limi- tation to the fulfillment of this condition. Also, the preparation of a relatively thin enamel membrane suit- able for diffusion measurements (i.e. without cracks, lamellae, etc.) is a time-consuming operation and often unsuccessful. The restricted diffusion through the enamel membrane imposes the use of microdiffusion cells to avoid excessive dilution of the diffusing species with the consequent difficulties in analytical assessments; thus. the measurements involve all the problems inher- ent in the handling of small volumes.

In contrast with the lack of quantitative information on diffusion through dental enamel, there exists a plethora of data of a qualitative nature demonstrating either the molecular sieve behaviour of enamel (Berggren, 1947; Darling et al., 1961; Poole and Stack, 1965) or the anisotropy (preferential pathways) of this tissue for diffusion. This latter aspect has been studied by the use of both fluorescing dyes (Jansen and Visser, 1950) and non-fluorescing dyes (Berggren, 1947) through direct microscopical observation of fluid aggregation at particular structural sites (around the enamel prisms) in enamel (Linden, 1968), through polarized light microscopy (Gustafson and Gustafson, ’ 1967) as well as by studying the uptake of ultraviolet sensitive probe molecules (Tarbet and Fosdick, 1971).

The foregoing observations are useful to characterize qualitatively the nature of enamel as a diffusion medium. Quantitative diffusion measurements, however, yield parameters that can be used to predict

fluxes of matter through the tissue. In addition, information may be obtained on the interactions of the diffusing species with the enamel matrix, the effective porosity of the latter for diffusion purposes, and the properties of the water filling the enamel pores.

MATERIALS AND METHODS

The diffusion measurements were obtained by the use of a diaphragm cell constructed for the purpose. Details of the cell and supporting equipment as well as the procedure used for a typical experimental run have recently been reported (Moreno and Burke. 1974).

The enamel membranes were labially-transverse cut. plano-parallel sections obtained from either canine or incisor teeth selected because of their intact enamel and identified by age and sex of donor. The procedures used to measure the geometric surface area and thickness of these membranes as well as the method of seal- ing in place have previously been discussed (Moreno and Burke, 1974). The identification parameters for the enamel membranes used in this study are listed in Table 1. The parameter b, the cell factor, listed in column six, will be discussed below.

At the beginning of each run, the “hot” compartment of the diffusion cell contained tritiated water, HTO, of r 0.5 pCi/ml specific activity, and the “cold” side contained distilled water. After reaching steady state conditions, the cell compartments were emptied. refilled with their respective solutions, and diffusion was allowed to proceed for a specified period of time. The procedure was repeated using different diffusion times (usually 4 or more) for the same enamel membrane at each of the temperatures reported. The method used to establish the condition of steady-state has been reported (Moreno and Burke, 1974).

At the conclusion of each diffusion run, aliquots ot the solution contained in each cell compartment were prepared in triplicate for counting in a liquid scintillation spectrometer (Tri-Garb 3375, Packard Instrument Co.). Counting efficiencies of ~28 per cent were obtained at 8.8”C using a 3 per cent (v/v) water to scintillation solution. The liquid scintillation “cocktail” was prepared using 700ml toluene, 300 ml absolute

327

328 E. J. Burke and E. C. Moreno

Table 1. Identification parameter of enamel membranes

Tooth type

Incisor Incisor Incisor Incisor Incisor Incisor Incisor Canine Canine Canine Canine

Age (yr)

17 18 20 28 59 62 63 17 17 58 59

Sex

M F F F F F F M F M F

Thickness Area P (w) (cm’ x 10’) (cm-* x 10)

371 6.32 6.74 435 15.9 15.1 371 13.6 14.2 350 10.8 12.2 399 9.95 9.97 322 10.3 12.6 465 21.9 19.1 315 5.61 7.37 361 6.98 8.01 320 7.53 9.74 345 6.24 7.49

ethanol, 4 g of PPO and 100 mg of POPOP. Absolute activities were calculated from a plot of per cent effi- ciency vs degree of sample quench. Sample count rate was corrected for background.

Apparent diffusion coefficient, D,, values were determined from a linear regression of the left-hand term of equation (1) (Gordon, 1945) on experimental time, t.

The cell constant /I (cf. Table 1 for values) is defined in terms of the geometric surface area, S, of the enamel membrane, its thickness, L, and the volumes VA and V, of the two compartments. Thus,

fi- ’ ln(ACJAC,) = DJ. (1)

The quantities /3, ACi, and ACJ represent respectively the cell factor, the initial, and the final differences in solution specific activities. The uncertainties in the D, values are expressed as the standard deviation in the slope of the best fit line.

(2)

The volumes VA and V, were approximately 5 cm3 in the cells used; their actual values were accurately determined by standard gravimetric methods.

The diffusion experiments reported here were con- ducted at three different temperatures using thermo- stated water baths (+0005”C). The values of D, obtained at the three temperatures were used to calculate activation energy values, E,, for diffusion. This latter calculation involved a linear regression of the left- hand term of the equation InD, = 1nK - EJRT on the reciprocal of the absolute temperature, T. A value for R of 1.987 cal deg- ’ mole- ’ was used in the calculations. The uncertainties in the E, values were calculated from the standard deviation in the slope of the best fit line.

The bulk water diffusion coefficient values, D,, used for comparison purposes in this work were those of Wang, Robinson and Edelman (1953) determined using the capillary tube technique and HTO as tracer. For convenience the D, values (cm’ x sec_I x 105) reported or interpolated from their data for the temperatures of interest in this study are listed here: 1.75 (13.O”C), 244 (25VC), 2.72 (3OOC), 3.21 (37.O”C). For these data E, = 4.46 + 0.11 kcal mole- ‘.

RESULTS

Typical plots of equation (1) obtained in the present investigation are shown in Fig. 1 for one enamel mem-

e- 25 0°C

6-

13 0 “C

Tame, set x 10-5

Fig. 1. Plot of left-hand side of equation (1) versus time,

I 0

t, for three temperatures. The slope of each line yields the

2

apparent diffusion coefficient, D,. (Membrane: 63 yr.

3 4 5 6 7

female, incisor).

brane at three temperatures. The good linearity of the plots indicates that the measurements were taken un- der steady-state conditions and that the apparent diffusion coefficients obtained from them constitute reliable values for the enamel membranes studied. In Table 2 is shown the set of calculated D, values, at three temperatures, for the enamel membranes from incisor teeth used in the present work. There appears to be a trend of lower apparent diffusion coefficients with increasing age of the enamel over the three experimental temperatures. The overlapping of values and the limited number of data, however, preclude the attach- ment of significance to this trend.

The increase in the D, values with increasing temperature was anticipated; however, the actual increases are several fold higher than those observed for diffusion of bulk water in the temperature range of 1%37”C (Wang, Robinson and Edelman, 1953). In fact, the activation energies calculated from the data in Table 2 and shown in Table 3 reflect this particular behaviour. Although the statistical uncertainties reported in Table 3 are rather large, the E, values for water diffusion through the enamel of incisor teeth are consistently higher than the E, value for diffusion of bulk water. This observation suggests that the enamel is not a simple porous diffusion medium. The activation energy values in Table 3 are consistent with an interaction between the diffusing water and the enamel structure, the nature of which will be elucidated in the Discus- sion.

Diffusion of water in dental enamel

Table 2. D, for HTO diffusion in incisor enamel

Incisor sample (age, sex)

D, (cm’ x set’ x 109) 13.0 (“C) 25.0 37.0

17M 4.3 f 0.3* 8.4 * 0.4 144 & I.3 18F 13.9 +_ 0.1 17.1 * 0.6 276 +_ 0.5 20F 6.5 f 0.4 12~0 k 0.6 14.4 + 20 2X F 4.9 f 0.1 9.6 i @2 lY.2 + 0.4 59 F 2.0 _+ 0.1 5.X & @2 7.7 _t 0 I 62 F 5.6 k 0.1 X.3 5 0.7 63 F 7.3 & 0.2 II.6 f 0.5 17.x * 0.5

* k Sample standard deviation of regression line slope.

The apparent diffusion coefficients calculated from experiments with enamel membranes from canine teeth are shown in Table 4. It is apparent that, in general, the D, values obtained with these membranes are smaller than those obtained with enamel from incisor teeth (Table 2). Perhaps more important, the activation energies derived from the data in Table 4, and reported in Table 5, are significantly higher for the canine enamel than for the incisor enamel (Table 3). Thus, it appears that the water-enamel interaction is much stronger for the canine than for the incisor enamel membranes.

DISCUSSION

The data obtained in the present investigation indi- cate that the transport of water across dental enamel in vitro is not a simple diffusion process in which enamel behaves as an inert porous medium. Rather, the enamel tissue apparently offers significant energy barriers for water diffusion which result in higher activation energies for this process compared with that for diffusion in bulk water. This phenomenon is more pro- nounced in the enamel of canine than in the enamel of incisor teeth (Tables 3 and 5).

The present results could be explained on the basis that the water in the enamel pores (or a significant fraction of it) has thermodynamic properties different from those of bulk water. A higher degree of organization in the water structure might be induced by sites of alter- nating polarities on the pore surfaces and interactions with the organic matter of enamel; certainly, diffusion of water through a more ordered structure would require higher activation energies than diffusion in bulk water. The operational terms “loosely bound” water and “firmly bound” water have been advanced in the literature presumably to identify two kinds of water in dental enamel although no satisfactory quantitative criteria have underlined this distinction. On the

basis of changes in the birefringence of enamel heated up to 400°C the content of firmly bound water has been reported (Carlstrom, Glas and Angmar, 1963) to be in the order of 80 per cent of the total water present; other reports (Myers, 1965) based on NMR spectra of samples heated up to 200°C disagree markedly with this finding. Recent work (Dibdin, 1972) casts doubt on the earlier NMR results in that the narrow resonance in the NMR spectrum of enamel (indicative of free water) disappears when the sample is exposed to low relative humidities (4 per cent) at 20’C provided that contamination with air moisture is avoided; the resi- dual broad resonance could be accounted for by the protons in the hydroxyl ions of the crystalline lattice although a contribution from firmly bound water cannot be discarded. The observation that a portion of enamel water does not freeze at temperatures as low as -40 to -6O’C (Myers and Myrberg, 1965; Myrberg. 1968) would suggest that water is present in enamel in at least two different states. However, it has been indicated (Hagymassy, Brunauer and Mikhail. 1969) that

Table 3. E, values calculated for HTO diffusion in incisor enamel

Incisor sample (age, sex) E, (kcal x mole _ ‘)

17M 8.9 I_ 1,4* 18F 5.2 _+ 1.1 20 F 5.9 &- 1.7 28 F 10.1 * I.0 59 F 10.1 * 3.1 62 F 5.9 * 0.5t 63 F 6.5 i 0. I

* f Sample standard deviation of regression line slope.

t f Propagated error in D,.

Table 4. D, for HTO diffusion in canine enamel

Canine sample D, (cm2 x sec. ’ x 10’) (age, sex) 25.0 (“C) 30.0

17M 35 * 0.1* 5.7 f 0.2 17F 5.4 * 0.2 7.4 + 0.2 58 M 3.9 * 0.1 5.0 * 0.1 59 F 49 * 0.1 6.9 + 0.1

* f Sample standard deviation of regression line slope.

__.

37.0

9.1 * 0.2 Il.1 * 02 8.4 * 0.3

12.0 f @4


Table 5. E, values calculated for HTO diffusion in canine enamel

Canine sample

(age, sex) E, (kcal x mole-‘)

17M 14.6 f 1.4* 17F 1 I.1 * 0.1 58M 11.6 + I.4 59 F 13.6 + 0%

* + Sample standard deviation of regression line slope.

the resistance to freezing of water in small spaces is not necessarily related to a different thermodynamic state but rather to a hindrance in the formation of nuclei for crystal growth. Although the bulk of the enamel pores appears to have radii between 3 nm and 6 nm (Moreno and Zahradnik, 1973; Zahradnik and Moreno, 1975) their size alone probably does not determine the presence of “anomalous” water; in other materials, it has been shown (Anderson and Quinn, 1971) that water in pores as small as 3-5.6 nm in radius is virtually identi- cal to bulk water. Specific interactions with the enamel constituents, however, cannot be ruled out. In the light of the discussion in this paragraph it is apparent that, although the present results would be consistent with the presence of water in a state different from the bulk, there is considerable uncertainty as to the extent to which this phenomenon actually occurs in dental enamel. Therefore, it seems appropriate to consider other possible explanations.

An alternative or complementary explanation for the high activation energies derived from the present measurements concerns structural features of dental enamel which introduce energy barriers for the diffusion process. The pertinent feature in this respect is the presence of constrictions in the enamel pores (Moreno and Zahradnik, 1973). Indeed, it has been shown (Zdh- radnik and Moreno, 1975) that, because of these constrictions extending down to molecular dimensions, enamel displays the phenomenon of activated diffusion. Thus, at the constriction sites, strong interactions with the enamel constituents (particularly the organic matter) hinder the movement of the water molecules. When temperature is increased, the augmented kinetic energy overcomes the movement hindrance and the water molecules can pass into the pore body; as a result of this mechanism, enamel porosities determined by water vapour adsorption increase with increasing temperature. The present observations per se neither prove nor disprove that the foregoing mechanism is applicable to the diffusion of water through the enamel

sections. Nevertheless, barring evidence to the con- trary, it is KdSOmbk to assume that the enamel constrictions constitute energy barriers responsible for the high activation energies calculated for the diffusion process. It is pertinent then to examine the consistency of the diffusion data with the pore constriction model; in particular, we shall examine the temperature depen- dence of effective porosites calculated on the basis of the apparent diffusion coefficients reported for the various experimental temperatures. In order to per- form these calculations some simplifying assumptions have to be made. If the pores in the enamel membrane are considered to be parallel capillaries of uniform radius, it can be shown (Wheeler, 1951) that the apparent diffusion flux, J,. would be given by

J, = E x (L/L,)2 x J, (3)

in which E is the porosity of the enamel, L, is the actual length of the diffusion path, L is the thickness of the enamel membrane, and J, is the “true” flux inside the capillaries. The pores of a real substance seldom run “straight through” the material but rather are somewhat twisting and tortuous (Everett and Stone, 1958); for this reason, a parameter called tortuosity, T, is in- troduced to characterize this aspect of a porous material. The tortuosity is defined by T = (L,/L)2 although it has also been defined by the first power of this ratio (Fatt, 1959; Scheidegger, 1960). Using the definition of T and substituting Fick’s first law in equation (3) the following is obtained

D, = (c/r)D, (4)

in which D, is the actual diffusion coefficient of water in the enamel capillaries. Equation (4) was used in the present investigation to calculate effective enamel porosities. In the absence of information concerning the tortuosity of the enamel pores, two limiting values were used in these calculations. When 7 = 1, the model regards the diffusion pathways equal to the thickness of the enamel membrane; when t = 2, the model con- siders an angle of 45’ between the enamel diffusion pathways and the normal to the surface of the membrane. The values used for D, were the water self-diffusion coefficients reported (Wang, Robinson and Edel- man, 1953) for the various temperatures used in the present experiments.

A representative set of calculated effective porosities is shown in Table 6. It is apparent that the effective porosity increases with increasing temperature in the enamel from incisor and canine teeth, a result which is consistent with the occurrence of activated diffusion in the enamel membranes. The figures in Table 6 also in- dicate that the effective porosities for incisor are larger than those for canine enamel suggesting a smaller pore

Table 6. Porosity calculated for incisor and canine enamel membranes

Enamel sample (age, sex, tooth type)

5°C x 10’ t=l T=2

13.0 (“C) 25.0 30.0 37.0 13.0 25.0 30.0 37.0

28 F, Incisor 2.8 3.9 6.0 5.6 7.8 - 12.0 59 F, Incisor I.1 2.4 2.4 2.2 4.8 4.8 17 F, Canine 2.2 2.6 35 4.4 5.2 7.0 59 F. Canine - 2.1 2.5 3.7 - 4.2 5.0 7.4

Diffusion of water in dental enamel 331

volume available for diffusion in the latter case. Recent work (Zahradnik and Moreno, 1975) shows that the pore volume distribution functions are bimodal for both incisor and canine enamel but that the pore radii are displaced toward smaller values in the canine enamel. Thus, it appears that canine enamel is probably mineralized to a larger extent than incisor enamel which ,may be related to the longer pre-eruption time of the former, 10 vs 7.5 yr (Krogh-Poulsen, 1945). It is reasonable to assume that smaller pore sizes are asso- ciated with smaller pore constrictions; therefore, a stronger interaction between the diffusing water and the constriction sites should be expected for canine than for incisor teeth. The significantly higher diffusion activation energies calculated from the experimental results with canine enamel membranes seem to bear out this assumption. The present results may have clinical implications in that the differences in effective porosity may be a partial explanation for the lower cariesexperience in canine as compared to incisor teeth (Marthaler, 1966).

in human enamel, it is fully recognized and appreciated that the barriers to diffusion and the driving forces of diffusion in oivo within this tissue are more complex and remain as yet not fully explored. Indeed, although it has been demonstrated that the acquired enamel pellicle modifies the behaviour of an enamel surface in solubility studies, presumably by retarding the attack of acids on teeth (Meckel, 1965), there does not appear to be available irt oitro data representing the rates of diffusion through enamel membranes covered with this pellicle. Further, the effect of the plaque on teeth must eventually be examined as a diffusion barrier. Ulti- mately, it may not be possible to establish and study in an in vitro model simultaneously all the driving forces which exist in uiuo. However, it is felt that from a step- by-step investigation of the effect of the acquired pellicle and finally the pellicle and plaque on the in vitro diffusion rates in enamel, a better understanding of the nature of the enamel-pellicle-plaque composite as a diffusion medium may be obtained.

The effective porosities given in Table 6 ( z 0.05 per cent) are but a fraction of the porosities (2 I.5 per cent) obtained from water vapour sorption studies (Zahrad- nik and Moreno, 1975). The present results are consistent with the findings of other investigators. Thus, Holly and Gray ( l968), based on diffusion measure- mcnts of electrolytes across enamel membranes, esti- mated an effective porosity in the order of 0.1 per cent. It appears then that a very substantial portion of the porosity measured through sorption studies does not contribute to the observed diffusion fluxes. This phenomenon is probably related to the pore constrictions present in enamel; these constrictions may form blind pores for the diffusion process. An additional consideration is that diffusion may occur preferentially through some parts of the enamel structure. Thus, whereas intra- and inter-prismatic spaces might be measured by water vapour sorption, there are indica- tions that diffusion takes place primarily through inter-prismatic spaces (Lindkn, 1968).

Ackno,vled~rmrrlt-This work was partially supported by U.S. Public Health Service Grant N.I.D.R.. DE-03187.

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In view of the assumptions made in the calculation of affective porosities, the figures in Table 6 should be taken cautiously. The values used for 7 encompass two limiting conditions applicable to the membranes used in the present study. Also the use of water diffusion coefficients for the parameter D, may be open to ques- tion. In fact. the activated transport phenomenon pre- supposes that, at least in some regions of the enamel, the diffusion ofwater is impaired and, therefore, its diffusion coefficient cannot be the same as that for bulk water. Thus. although the values in Table 6 are useful for a gross analysis of the diffusion data, they only represent the minimum pore volume available for diffusion in the enamel membranes (see equation 4). In addition. it is recognized that with the present experimental results, individual quantities for the porosity and the tortuosity cannot be obtained. Obviously. set- ting an invariant tortuosity instead of porosity with lempcrature for computational purposes is somewhat arbitrary. The justification for this procedure, however, resides in the fact that, in independent studies (Zahrad- nik and Moreno. 1975). it has been shown that the apparent porosity of dental enamel does vary with

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diffusion fluxes of tritiated water across human enamel membranes

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