Dentin Permeability: Determinants of Hydraulic Conductance 0. W. REEDER, JR., R. E. WALTON, M. J. LIVINGSTON, and D. H. PASHLEY
Departments of Endodontics, Oral Biology and Physiology, Medical College of Georgia, Augusta, Georgia 30902 A technique is described which permits ground dentin. This apparent discrepancy measurement of the ease with which fluid between the pressure required to induce permeates dentin. This value, the hydrau- fluid movement in these studies presumlic conductance of dentin, increased as sur- ably relates to differences in the surface face area increases and/or as dentin thick- characteristics of ground and fractured ness decreases. It increased 32-fold when dentin. Indeed, electron micrographs dentin was acid etched due to removal of showed that tubules in fractured dentin were "clean," whereas tubules from ground surface debris occluding the tubules. dentin were clogged with debris (Johnson J Dent Res 57(2): 187-193, February 1978. et al. I5). Polhagen and Brannstr6m8 found that fluid movement in dessicated dentin Several investigators have demonstrated was less than in rehydrated dentin. They fluid movement in dentin. Brannstrom's postulated that evaporation of water from groupl9 applied various stimuli to exposed tubular fluid leads to elevation in tubular dentin including hydrostatic pressure, a solute concentrations thereby blocking the stream of air, heat, cold, negative pres- cavity end of tubules with insoluble salts sure, and osmotic pressures. These stimuli and organic substances. Other investigacaused pain and also resulted in fluid flow tors have described increased sensitivity'5 through the dentinal tubules. Anderson, and, presumably, increased permeability Curwen, and Howard,'0 Anderson and of dentin'6"17 following treatment of Ronning" and Anderson and Matthews'2 ground dentin surfaces with citric acid, a provided further evidence of fluid move- procedure which clears the tubular aperment in dentin when applications of vari- tures of debris. These studies were not deous hyperosmotic solutions of CaCl2, su- signed to actually measure alterations in crose and other materials to exposed den- the rate of fluid flow through dentin, howtin caused pain. They also demonstrated in ever. A common deficiency in the previous vitro that these solutions produced fluid studies on fluid movement in dentin is that movement through dentin."3 The degree of occlusion of dentinal tu- flow was measured under poorly defined bules affects the rate of fluid flow through conditions and several variables were undentin. Br-innstrom, Johnson, and Lin- controlled. The thickness of the dentin was den'4 found that the hydrostatic pressure not uniform, nor was the area of the exnecessary to cause pain and to produce posed surface and its characteristics indifluid movement in ground dentin was 1 to cated. Scanning electron micrographs ob3 kg/cm2. Johnson et al.,15' using much viously do not give a quantitative descriplower pressures, observed slight flow tion of the overall dentin fluid permeabilthrough fractured dentin, while no flow ity. In order to resolve this problem, the was observed under similar pressures for hydraulic conductance of dentin must be quantitated to provide a description of the Received for publication on April 5, 1977. ability of fluid to pass through dentin. By 1977. Accepted for publicationJuly 28, definition, hydraulic conductance is a the from DE-03780 No. Grant This study was supported by measure of the ease with which fluid, unNIDR. 187
188
REEDER ET AL
j Dent
Res
February
1978
0 1' ,
111111
0
1
CENTIMETERS
RUBBER 0 RINGS
RUBBER DENTIN DISC
0
RINGS
FIG 1. -Schematic showing the origin of the dentin disk and the construction of the plastic split-chamber device. A buffer reservoir was connected via polyethylene tubing to the left side of the chamber. The second tube on both the right and left halves was
plugged. The outflow tube on the right half was connected to a microliter pipette to measure the rate of volume displacement. Filtration always occurred from left to right (i.e. from enamel to pulpal direction).
der hydrostatic or osmotic pressure, can pass through a permeable barrier (in this case, dentin) under defined conditions. 18 The purposes of this investigation were (1) to quantitatively determine the ease
placed in the chamber device described below. Ten disks were utilized in this experiment. CHAMBER DESIGN. - The design of the plastic, split chamber device is shown in Figure 1. Pairs of identical rubber "O" rings sealed the chamber to the disks and controlled the surface area of dentin to be studied. Hydrostatic pressure was applied to one side of the chamber to induce filtration through the dentin into the other side of the chamber. Thus, fluid filtration was measured as fluid displacement in a micropipette connected to the latter side of the chamber. Hydrostatic pressure was applied to the disk via a reservoir bottle of Krebs-Ringer phosphate buffer (KRP) connected to onehalf of the chamber device. Pressure was varied by regulating the height of the bottle above the disk. To insure a tight seal by the "O" rings and to check the system for leaks, a polyethylene disk was inserted in place of the dentin disk. No fluid movement (filtration) could be recorded even at the highest hydrostatic pressure (240 cm H20). During all experiments, the chamber was immersed in a constant temperature waterbathat25 + 1 C.
with which fluid, at various hydrostatic pressures, can flow (hydraulic conductance) through ground and acid-etched dentin and (2) to determine the influence of dentin surface area and the thickness of rates of fluid filtration. Materials and Methods
PREPARATION OF DISKS. - Human, impacted maxillary third molars were extracted and stored for varying periods of time in isotonic 0.01 M phosphate buffer until the disks could be prepared. It has been determined that postextraction storage time was not a factor that affected dentin permeability. 20 With a high-speed handpiece, copious air-normal saline spray and #558 carbide fissure burs, the enamel was removed in a plane parallel to the occlusal surface of the teeth (Fig 1). Dentin disks were formed by cutting parallel to the flattened top of the tooth just above the tips of the pulp horns. All disks were made uniformly thick (0.99 + 0.03 mm, x + SEM) by sanding the "enamel" (occlusal) side with emery cloth. The disks were then
EXPERIMENTAL DESIGN AND MEASUREMENTS. -Measurements offiltration rate. - The amount of buffer which filtered through the disks during each period was measured as a volume displacement in the micropipettes. The data from three consecutive measurements were averaged. Mean values were compared using student's t test to determine statistically significant differences in filtration rates between the experimental groups. Control pressures. - Measurements of filtration rates were made on all disks during the application of zero hydrostatic pressure to determine if fluid movement could occur in the absence of a hydrostatic pressure gradient. Experimental pressures. -Unetched or ground disks were subjected to 60, 120, and 240 cm H20 of hydrostatic pressure for three consecutive 30-minute periods. Acid-etched disks were obtained by fill40
189
DENTIN PERMEABILITY: HYDRAULIC CONDUCTANCE
Vol. 5 7 No. 2
ing both sides of the chamber with 50% (w/v) citric acid for 2 minutes followed by immediate washing with large volumes of phosphate buffer. Each disk was again subjected to the same series of pressures for the same time periods as were the unetched disks; this permitted direct comparison between etched and ground surfaces in the same disks. Dentin thickness effects on filtration rate. - The effect of changes in dentin thickness on filtration rate was determined by reducing the disk thickness in steps from the original thickness of 0.99 ± 0.03 mm to 0.86, 0.74 and 0.61 mm by sanding just the enamel (occlusal) side of the disk with emery cloth. After each reduction and prior to measurement of filtration rate, the enamel side was reetched with acid in the chamber as described earlier. At each of the reduced thicknesses, surface area was varied as described below.
I
Kz
L4. (ZI
ZtZ
K:
ETCHED
0R K~ 0 tK
10
(10)
UN ETCHED (4)
0
(8)
(8)
120
240
1;
I
60
HYDROSTATIC PRESSURE IN cm OF H 20
This figure shows the relationship beFIG 2. tween filtration rate and hydrostatic pressure in unetched and etched dentin. The ordinates of the insert
are the same as the larger figure but the scale has been expanded. Numbers in parentheses indicate the number of disks utilized.
190
j Dent
REEDER ET AL
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February
1978
TABLE HYDRAULIC CONDUCTANCE OF DENTIN DISK (LP)* Thickness (mm)
Unetched Etched
0.61
0.74
3.90 x 10-1
1.85 x 10-1
0.079
0.178
0.86
1.21
x
0.99
10-'
2.86 x 10-3 6.67 x 10-2
Surface Area (cm')
Etched (0. 99 mm Thick) (0.86 mm Thick) (0.74 mm Thick) (0.61 mm Thick)
4.40 x 1.05 x 1.58 x 4.40 x
10-2 10-' 10-
10-'
7.02 x 1.40x 1.87 x 4.21 x
10-2 10-' 10-' 10-1
0.317
7.01 x 10-2 1.53 x 10-1 2.06 x 10-' 3.68 x 10-'
*Lp in ftl cm-2cm H,O-'minm'. The relationship betwen Lp (y) as a function of dentin thickness (x) is described by: y < 0.001.
=
4.833e-4 93,
r
-
0.978. P
Results This was to determine if the filtration rate per unit surface area was constant at any EFFECTS OF ACID ETCHING ON FILTRAgiven thickness, and to allow comparison TION RATE. - Control pressures. - Neiof the filtration rates per unit area at dif- ther ground nor acid-etched disks, when ferent thicknesses. subjected to zero hydrostatic pressure, exDentin surface area effects on filtration hibited fluid movement (filtration) (Fig 2). rate. - The effect of changes in dentin Unetched disks. - As the hydrostatic surface area available for filtration was de- pressure was increased from zero, the filtermined by varying the size of rubber "O" tration rate increased linearly (Fig 2, inrings on either side of the disk to give areas sert). From the filtration rates obtained, of 0.079, 0.178, or 0.317 cm2. Hydrostatic and using Equation I, a mean hydraulic pressure was maintained at 240 cm H20 conductance (Lp) for the disks was calcufor all of these determinations. lated (Table). Calculations. -Since the micropipettes Etched disks. -After acid etching both have constant bore diameters, dividing the sides, increases in hydrostatic pressure revolume of the pipette by its length gives a sulted in much greater filtration rates than proportionality constant which converts that found in the unetched disks. Similar linear displacement into volume displace- to the unetched disks, these rates also inment. These measurements can be excreased linearly as a function of pressure pressed as: (Fig 2). The calculated hydraulic conductances (Lp) were also significantly larger (P Lp = P(S.A.)' [I] < 0.001) for these disks (Table) and the filtration rates were 32 times greater than where Lp = hydraulic conductance of for unetched disks (Fig 2). DENTIN THICKNESS EFFECTS ON FILTRAdentin in It1 cm2 min' cm H20-', Q = filtration rate in y1 min-', S.A. = surface TION RATE. -When disks were reduced in thickness (Fig 3), there was an increase in area in cm2, P = hydrostatic pressure diffiltration rate. The larger graph in Figure ference across dentin in cm H20. 3 plots filtration rate on the ordinate against dentin thickness on the abscissa. In this graph, dentin surface area was held J S.AS. [II] constant at 0.317 cm2 and dentin thickness whereJv = filtration rate in t1 cm-2 min-'. varied in steps from 0.99 to 0.61 mm. This
DENTIN PERMEABILITY: HYDRAULIC CONDUCTANCE
Vol. 5 7 No. 2
191
30
100
80
FIG 3. -The larger figure demonstrates the relationship between filtration rate and dentin thickness. The insert shows the effects of changes in surface area on filtration rate. The number above each line indicates the thickness of the dentin
_ 60 z
0
n 40 z
disk.
z U
20~
a
0.7
1.0
0.9
0.8 DENTIN THICKNESS (mm)
was associated with a curvilinear crease in filtration rate (Fig 3).
sixfold in-
DENTIN SURFACE AREA EFFECTS ON FILTRATION RATE. - At each of the dentin
thicknesses, the surface area available for filtration was varied from 0.079 to 0.317 cm2. The insert in Figure 3 shows the effect of changing surface area at each of the four different dentin thicknesses. The data demonstrate that at any given surface area, as thickness is reduced from the enamel side there is a progressive increase in filtration rate. Further, at any constant thickness, as surface area increases there is a linear increase in filtration rate. The data in Figures 2 and 3 are recalculated as hydraulic conductances (using Equation I) and shown in the Table. Discussion
Numerous investigators79,13 have attempted to quantitate fluid movement through dentin. Although many of them have attempted to define the area available for fluid movement, the surface area was usually described in terms of cavity dimensions rather than exposed dentinal surface area (wall plus floor). Furthermore, the variability of the morphology of pulp
chambers caused the thickness of the dentin between the cavity and the roof of the chamber to be highly variable from tooth to tooth. In the present experiments, the use of dentin disks permitted precise definition and control of both dentin surface area and thickness. Another critical variable that can affect fluid flow is the nature of the dentin surface. Johnson et al,9 using a much less sensitive system than ours, found that they could detect filtration through fractured dentin but not through ground dentin. They later demonstrated by scanning electron microscopy'5 that the apertures of fractured dentinal tubules were open while those of ground dentin were occluded with debris. They found that fractured dentin was clinically more sensitive to a variety of stimuli than ground dentin.'5 The authors implied that the increased sensitivity of fractured or acid-etched dentin compared to ground dentin was due to increased fluid in the former in response to stimuli. The results of the present study demonstrate that acid etching dentin resulted in increased filtration of fluid through dentin at a constant pressure (i.e. an increase in the hydraulic conductance of dentin) as shown in Figures 2 and 3 and
movement
192
REEDER ET AL
Table. This supports the observations and conclusions of in vivo studies15 that acid etching produces profound change in the dentin surface leading to a marked increase in fluid movement through dentinal tubules. Although other investigators"9.122 concluded that ground (unetched) dentin did not permit fluid filtration, our results suggest that the methods used in previous studies lacked adequate sensitivity. The fact that the unetched dentin in the present report permitted fluid filtration (Fig 2) indicated that the tubules were not totally occluded. The linearity of the increase in filtration rate with increasing hydrostatic pressure in both unetched and etched dentin (Fig 2) suggests that the fluid flow is nonturbulent and that little or no molecular sieving of buffer salts from the solvent occurred as has been previously described in other systems. 25,26 An examination of the variables (Equation I) determining hydraulic conductance (Lp) reveals that the variable of dentin thickness is not included, yet Figure 3 clearly demonstrated that filtration rate was very sensitive to changes in dentin thickness. Pappenheimer et a125 and Renkin26 attempted to correct for this by calculating the specific filtration coefficients for membranes, by multiplying the hydraulic conductance by the membrane thickness. Such a treatment assumes that there would be a linear increase in hydraulic conductance as dentin thickness is reduced. Examination of the data in Figure 3 reveals an exponential, rather than a linear relationship. While multiplying the hydraulic conductances by the membrane thicknesses tends to partially correct the data for thickness (not shown), the 38% reduction in thickness (from 0.99 to 0.61 mm) still would be associated with a 300% increase in filtration rate (rather than the 500% increase shown in the Table). Thus, expressing the ease with which fluid filters across dentin as a specific filtration coefficient (Kf), does not improve the ability to predict filtration rates under specific conditions. Presumably, this is due to the fact that as dentin thickness is reduced from the enamel side, the number of tubules per unit surface area increase.23'24 Outhwaite
j Dent Res February
1978
et al.22 obtained similar results when studying the rate of iodide diffusion across dentin disks. The data in the Table have been fitted to an exponential regression equation to permit more accurate estimates of Lp (y) as a function of dentin thickness (x). This relationship is described by y = 4.833e4l93x, r= 0.978, P < 0.001.
The linear relationship between filtration rate and surface area, at any constant thickness (Fig 3, insert) suggests that the tubular density and dimensions are relatively constant across the disk surface. Had this relationship not been linear, it would have suggested that there were differences in tubular density and/or diameter within the same plane of the disk. The results of these studies should be regarded as setting an upper limit for dentin hydraulic conductance since the tubules in dentin disks apparently do not have odontoblastic processes on the pulpal side (unpublished observations). The hydraulic conductance of acid-etched disks probably represents a maximum value that could be obtained clinically in dentin that had been treated with acid-etching agents. Conclusions
The present report describes a method of measuring the ease with which fluid can filter across dentin (the hydraulic conductance) in a quantitative manner. Dentin surfaces that have been sanded have a measurable but low hydraulic conductance. Acid etching the dentin with 50% (w/v) citric acid for 2 minutes leads to a 32-fold increase in filtration rate. This was due to removal of surface debris partially occluding the tubule orifices. Since the degree of occlusion of dentinal tubules, the surface area, and the thickness of dentin vary widely depending upon experimental conditions, it is suggested that investigators report a hydraulic conductance value for the dentin under study to assist in future comparisons of interlaboratory data. References 1. BRXNNSTROM, M.: Dentinal and Pulpal Response. II. Application of an Air Stream to Exposed Dentine. Short Observation
DENTIN PERMEABILITY: HYDRAULIC CONDUCTANCE
Vol. 5 7 No. 2
Period, Acta Odont Scand 18:17-28, 1960. 2. BRXNNSTRbM, M.: Dentinal and Pulpal Response. V. Application of Pressure to Exposed Dentine, J Dent Res 40:960-970, 1961. 3. BRANNSTROM, M.: The Elicitation of Pain in Human Dentine and Pulp by Chemical Stimuli, Arch Oral Biol 7:59-62, 1962. 4. BRXNNSTROM, M., and ASTROM, A.: A Study on the Mechanism of Pain Elicited from the Dentin, J Dent Res 43:619-625, 1964. 5. LINDEN, L., and BRXNNSTR6M, M.: Fluid Movements in Dentine and Pulp. An In Vitro Study of Flow Produced by Chemical
14. BRXNNSTROSM, M.; JOHNSON, G.; and LIN-
DEN, L.: Fluid Flow and Pain Response in the Dentine Produced by Hydrostatic Pressure, Odont Revy 20:16-30, 1969. 15. JOHNSON, G., and BRXNNSTROM, M.: The
Sensitivity of Dentin: Changes in Relation to Conditions at Exposed Tubule Apertures, Acta Odont Scand 32:29-38, 1974. 16. STANLEY, H. R.; GORING, R. E.; and
17.
Solutions on Exposed Dentine, Odont Revy 18:227-236, 1976. 6. BRXNNSTROM,
M.;
LINDEN,
L.;
and
ASTRtM, A.: The Hydrodynamics of the
18.
Dental Tubule and of Pulp Fluid. A Discussion of its Significance in Relation to Dentinal Sensitivity, Caries Res 1:310-317, 1967.
19.
7. BRANNSTROM, M.; LINDEN, L.; and JOHN SON, G.: Movement of Dentinal and Pulpal
Fluid Caused by Clinical Procedures, J Dent Res 47:679-682, 1968. 8. POLHAGEN, L., and BRXNNSTROM, M.: The Liquid Movement in Desiccated and Rehydrated Dentine In Vitro, Acta Odont
20.
Scand29:95-102, 1971. 9. JOHNSON, G.; OLGART, L.; and BRXNN-
STROM, M.: Outward Fluid Flow in Dentin Under a Physiologic Pressure Gradient: Experiments In Vitro, Oral Surg 35(2):238-248, 1973. 10. ANDERSON, D. J.; CURWEN, M. P.; and HOWARD, L. V.: The Sensitivity of Human Dentin,JDent Res 37:669-677, 1958. 11. ANDERSON, D. J., and RONNING, G. A.: Osmotic Excitants of Pain in Human Den-
21.
22. 23.
tine, Arch Oral Biol 7:513-523, 1962. 12. ANDERSON, D. J., and MATTHEWS, B.: Os-
motic Stimulation of Human Dentine and the Distribution of Dental Pain Thresholds, Arch Oral Biol 12:417 -426, 1967. 13. ANDERSON, D. J.; MATTHEWS, B.; and GORRETTA, C.: Fluid Flow Through Human Dentine, Arch Oral Biol 12:209-216, 1967.
193
24.
CHAUNCEY, H. H.: Human Pulp Response to Acid Pretreatment of Dentin and to Composite Restoration, JADA 91:817-825, Oct 1975. VOJINOVIC, O.: NYBORG, H.; and BRXNNSTROM, M.: Acid Treatment of Cavities Under Resin Fillings: Bacterial Growth in Dentinal Tubules and Pulpal Reactions, J DentRes52:1189-1192, 1973. HOUSE, C. R.: Water Transport in Cells and Tissues, Baltimore: The William and Wilkins Company, 1974, p 88. UMBRIET, W. W.; BURRIS, R. H.; and STAUFFER, J. F.: 1972, Manometric and Biochemical Techniques (5th ed), Minneapolis, Minn.: Burgess Publishing Company, 1972, p 146. OUTHWAITE, W. C.; LIVINGSTON, M. J.; and PASHLEY, D. H.: Effects of Changes in Surface Area, Thickness, Temperature and Post-Extraction Time on Human Dentin Permeability, Arch Oral Biol 21:599-603, 1976. OLGART, L.; BRXNNSTROM, M.; andJOHNSON, G..: Invasion of Bacteria into Dentinal Tubules. Experiments In Vivo, Acta Odont Scand 32:61-70, 1974. STEVENSON, T. S.: Fluid Movement in Human Dentine, Arch Oral Biol 10:935-944, 1965. FORSSELL-AHLBERG, K.; BRANNSTROM, M.; and EDWALL, L.: The Diameter and Number of Dentinal Tubules in Rat, Cat, Dog, and Monkey. A Comparative Scanning Electron Microscopic Study, Acta Odont Scand 33:243-250, 1975. GARBEROGLIO, R., and BRXNNSTROM, M.: Scanning Electron Microscopic Investigation of Human Dentinal Tubules, Arch Oral Biol 21:355-362, 1976.
Departments of Endodontics, Oral Biology and Physiology, Medical College of Georgia, Augusta, Georgia 30902 A technique is described which permits ground dentin. This apparent discrepancy measurement of the ease with which fluid between the pressure required to induce permeates dentin. This value, the hydrau- fluid movement in these studies presumlic conductance of dentin, increased as sur- ably relates to differences in the surface face area increases and/or as dentin thick- characteristics of ground and fractured ness decreases. It increased 32-fold when dentin. Indeed, electron micrographs dentin was acid etched due to removal of showed that tubules in fractured dentin were "clean," whereas tubules from ground surface debris occluding the tubules. dentin were clogged with debris (Johnson J Dent Res 57(2): 187-193, February 1978. et al. I5). Polhagen and Brannstr6m8 found that fluid movement in dessicated dentin Several investigators have demonstrated was less than in rehydrated dentin. They fluid movement in dentin. Brannstrom's postulated that evaporation of water from groupl9 applied various stimuli to exposed tubular fluid leads to elevation in tubular dentin including hydrostatic pressure, a solute concentrations thereby blocking the stream of air, heat, cold, negative pres- cavity end of tubules with insoluble salts sure, and osmotic pressures. These stimuli and organic substances. Other investigacaused pain and also resulted in fluid flow tors have described increased sensitivity'5 through the dentinal tubules. Anderson, and, presumably, increased permeability Curwen, and Howard,'0 Anderson and of dentin'6"17 following treatment of Ronning" and Anderson and Matthews'2 ground dentin surfaces with citric acid, a provided further evidence of fluid move- procedure which clears the tubular aperment in dentin when applications of vari- tures of debris. These studies were not deous hyperosmotic solutions of CaCl2, su- signed to actually measure alterations in crose and other materials to exposed den- the rate of fluid flow through dentin, howtin caused pain. They also demonstrated in ever. A common deficiency in the previous vitro that these solutions produced fluid studies on fluid movement in dentin is that movement through dentin."3 The degree of occlusion of dentinal tu- flow was measured under poorly defined bules affects the rate of fluid flow through conditions and several variables were undentin. Br-innstrom, Johnson, and Lin- controlled. The thickness of the dentin was den'4 found that the hydrostatic pressure not uniform, nor was the area of the exnecessary to cause pain and to produce posed surface and its characteristics indifluid movement in ground dentin was 1 to cated. Scanning electron micrographs ob3 kg/cm2. Johnson et al.,15' using much viously do not give a quantitative descriplower pressures, observed slight flow tion of the overall dentin fluid permeabilthrough fractured dentin, while no flow ity. In order to resolve this problem, the was observed under similar pressures for hydraulic conductance of dentin must be quantitated to provide a description of the Received for publication on April 5, 1977. ability of fluid to pass through dentin. By 1977. Accepted for publicationJuly 28, definition, hydraulic conductance is a the from DE-03780 No. Grant This study was supported by measure of the ease with which fluid, unNIDR. 187
188
REEDER ET AL
j Dent
Res
February
1978
0 1' ,
111111
0
1
CENTIMETERS
RUBBER 0 RINGS
RUBBER DENTIN DISC
0
RINGS
FIG 1. -Schematic showing the origin of the dentin disk and the construction of the plastic split-chamber device. A buffer reservoir was connected via polyethylene tubing to the left side of the chamber. The second tube on both the right and left halves was
plugged. The outflow tube on the right half was connected to a microliter pipette to measure the rate of volume displacement. Filtration always occurred from left to right (i.e. from enamel to pulpal direction).
der hydrostatic or osmotic pressure, can pass through a permeable barrier (in this case, dentin) under defined conditions. 18 The purposes of this investigation were (1) to quantitatively determine the ease
placed in the chamber device described below. Ten disks were utilized in this experiment. CHAMBER DESIGN. - The design of the plastic, split chamber device is shown in Figure 1. Pairs of identical rubber "O" rings sealed the chamber to the disks and controlled the surface area of dentin to be studied. Hydrostatic pressure was applied to one side of the chamber to induce filtration through the dentin into the other side of the chamber. Thus, fluid filtration was measured as fluid displacement in a micropipette connected to the latter side of the chamber. Hydrostatic pressure was applied to the disk via a reservoir bottle of Krebs-Ringer phosphate buffer (KRP) connected to onehalf of the chamber device. Pressure was varied by regulating the height of the bottle above the disk. To insure a tight seal by the "O" rings and to check the system for leaks, a polyethylene disk was inserted in place of the dentin disk. No fluid movement (filtration) could be recorded even at the highest hydrostatic pressure (240 cm H20). During all experiments, the chamber was immersed in a constant temperature waterbathat25 + 1 C.
with which fluid, at various hydrostatic pressures, can flow (hydraulic conductance) through ground and acid-etched dentin and (2) to determine the influence of dentin surface area and the thickness of rates of fluid filtration. Materials and Methods
PREPARATION OF DISKS. - Human, impacted maxillary third molars were extracted and stored for varying periods of time in isotonic 0.01 M phosphate buffer until the disks could be prepared. It has been determined that postextraction storage time was not a factor that affected dentin permeability. 20 With a high-speed handpiece, copious air-normal saline spray and #558 carbide fissure burs, the enamel was removed in a plane parallel to the occlusal surface of the teeth (Fig 1). Dentin disks were formed by cutting parallel to the flattened top of the tooth just above the tips of the pulp horns. All disks were made uniformly thick (0.99 + 0.03 mm, x + SEM) by sanding the "enamel" (occlusal) side with emery cloth. The disks were then
EXPERIMENTAL DESIGN AND MEASUREMENTS. -Measurements offiltration rate. - The amount of buffer which filtered through the disks during each period was measured as a volume displacement in the micropipettes. The data from three consecutive measurements were averaged. Mean values were compared using student's t test to determine statistically significant differences in filtration rates between the experimental groups. Control pressures. - Measurements of filtration rates were made on all disks during the application of zero hydrostatic pressure to determine if fluid movement could occur in the absence of a hydrostatic pressure gradient. Experimental pressures. -Unetched or ground disks were subjected to 60, 120, and 240 cm H20 of hydrostatic pressure for three consecutive 30-minute periods. Acid-etched disks were obtained by fill40
189
DENTIN PERMEABILITY: HYDRAULIC CONDUCTANCE
Vol. 5 7 No. 2
ing both sides of the chamber with 50% (w/v) citric acid for 2 minutes followed by immediate washing with large volumes of phosphate buffer. Each disk was again subjected to the same series of pressures for the same time periods as were the unetched disks; this permitted direct comparison between etched and ground surfaces in the same disks. Dentin thickness effects on filtration rate. - The effect of changes in dentin thickness on filtration rate was determined by reducing the disk thickness in steps from the original thickness of 0.99 ± 0.03 mm to 0.86, 0.74 and 0.61 mm by sanding just the enamel (occlusal) side of the disk with emery cloth. After each reduction and prior to measurement of filtration rate, the enamel side was reetched with acid in the chamber as described earlier. At each of the reduced thicknesses, surface area was varied as described below.
I
Kz
L4. (ZI
ZtZ
K:
ETCHED
0R K~ 0 tK
10
(10)
UN ETCHED (4)
0
(8)
(8)
120
240
1;
I
60
HYDROSTATIC PRESSURE IN cm OF H 20
This figure shows the relationship beFIG 2. tween filtration rate and hydrostatic pressure in unetched and etched dentin. The ordinates of the insert
are the same as the larger figure but the scale has been expanded. Numbers in parentheses indicate the number of disks utilized.
190
j Dent
REEDER ET AL
Res
February
1978
TABLE HYDRAULIC CONDUCTANCE OF DENTIN DISK (LP)* Thickness (mm)
Unetched Etched
0.61
0.74
3.90 x 10-1
1.85 x 10-1
0.079
0.178
0.86
1.21
x
0.99
10-'
2.86 x 10-3 6.67 x 10-2
Surface Area (cm')
Etched (0. 99 mm Thick) (0.86 mm Thick) (0.74 mm Thick) (0.61 mm Thick)
4.40 x 1.05 x 1.58 x 4.40 x
10-2 10-' 10-
10-'
7.02 x 1.40x 1.87 x 4.21 x
10-2 10-' 10-' 10-1
0.317
7.01 x 10-2 1.53 x 10-1 2.06 x 10-' 3.68 x 10-'
*Lp in ftl cm-2cm H,O-'minm'. The relationship betwen Lp (y) as a function of dentin thickness (x) is described by: y < 0.001.
=
4.833e-4 93,
r
-
0.978. P
Results This was to determine if the filtration rate per unit surface area was constant at any EFFECTS OF ACID ETCHING ON FILTRAgiven thickness, and to allow comparison TION RATE. - Control pressures. - Neiof the filtration rates per unit area at dif- ther ground nor acid-etched disks, when ferent thicknesses. subjected to zero hydrostatic pressure, exDentin surface area effects on filtration hibited fluid movement (filtration) (Fig 2). rate. - The effect of changes in dentin Unetched disks. - As the hydrostatic surface area available for filtration was de- pressure was increased from zero, the filtermined by varying the size of rubber "O" tration rate increased linearly (Fig 2, inrings on either side of the disk to give areas sert). From the filtration rates obtained, of 0.079, 0.178, or 0.317 cm2. Hydrostatic and using Equation I, a mean hydraulic pressure was maintained at 240 cm H20 conductance (Lp) for the disks was calcufor all of these determinations. lated (Table). Calculations. -Since the micropipettes Etched disks. -After acid etching both have constant bore diameters, dividing the sides, increases in hydrostatic pressure revolume of the pipette by its length gives a sulted in much greater filtration rates than proportionality constant which converts that found in the unetched disks. Similar linear displacement into volume displace- to the unetched disks, these rates also inment. These measurements can be excreased linearly as a function of pressure pressed as: (Fig 2). The calculated hydraulic conductances (Lp) were also significantly larger (P Lp = P(S.A.)' [I] < 0.001) for these disks (Table) and the filtration rates were 32 times greater than where Lp = hydraulic conductance of for unetched disks (Fig 2). DENTIN THICKNESS EFFECTS ON FILTRAdentin in It1 cm2 min' cm H20-', Q = filtration rate in y1 min-', S.A. = surface TION RATE. -When disks were reduced in thickness (Fig 3), there was an increase in area in cm2, P = hydrostatic pressure diffiltration rate. The larger graph in Figure ference across dentin in cm H20. 3 plots filtration rate on the ordinate against dentin thickness on the abscissa. In this graph, dentin surface area was held J S.AS. [II] constant at 0.317 cm2 and dentin thickness whereJv = filtration rate in t1 cm-2 min-'. varied in steps from 0.99 to 0.61 mm. This
DENTIN PERMEABILITY: HYDRAULIC CONDUCTANCE
Vol. 5 7 No. 2
191
30
100
80
FIG 3. -The larger figure demonstrates the relationship between filtration rate and dentin thickness. The insert shows the effects of changes in surface area on filtration rate. The number above each line indicates the thickness of the dentin
_ 60 z
0
n 40 z
disk.
z U
20~
a
0.7
1.0
0.9
0.8 DENTIN THICKNESS (mm)
was associated with a curvilinear crease in filtration rate (Fig 3).
sixfold in-
DENTIN SURFACE AREA EFFECTS ON FILTRATION RATE. - At each of the dentin
thicknesses, the surface area available for filtration was varied from 0.079 to 0.317 cm2. The insert in Figure 3 shows the effect of changing surface area at each of the four different dentin thicknesses. The data demonstrate that at any given surface area, as thickness is reduced from the enamel side there is a progressive increase in filtration rate. Further, at any constant thickness, as surface area increases there is a linear increase in filtration rate. The data in Figures 2 and 3 are recalculated as hydraulic conductances (using Equation I) and shown in the Table. Discussion
Numerous investigators79,13 have attempted to quantitate fluid movement through dentin. Although many of them have attempted to define the area available for fluid movement, the surface area was usually described in terms of cavity dimensions rather than exposed dentinal surface area (wall plus floor). Furthermore, the variability of the morphology of pulp
chambers caused the thickness of the dentin between the cavity and the roof of the chamber to be highly variable from tooth to tooth. In the present experiments, the use of dentin disks permitted precise definition and control of both dentin surface area and thickness. Another critical variable that can affect fluid flow is the nature of the dentin surface. Johnson et al,9 using a much less sensitive system than ours, found that they could detect filtration through fractured dentin but not through ground dentin. They later demonstrated by scanning electron microscopy'5 that the apertures of fractured dentinal tubules were open while those of ground dentin were occluded with debris. They found that fractured dentin was clinically more sensitive to a variety of stimuli than ground dentin.'5 The authors implied that the increased sensitivity of fractured or acid-etched dentin compared to ground dentin was due to increased fluid in the former in response to stimuli. The results of the present study demonstrate that acid etching dentin resulted in increased filtration of fluid through dentin at a constant pressure (i.e. an increase in the hydraulic conductance of dentin) as shown in Figures 2 and 3 and
movement
192
REEDER ET AL
Table. This supports the observations and conclusions of in vivo studies15 that acid etching produces profound change in the dentin surface leading to a marked increase in fluid movement through dentinal tubules. Although other investigators"9.122 concluded that ground (unetched) dentin did not permit fluid filtration, our results suggest that the methods used in previous studies lacked adequate sensitivity. The fact that the unetched dentin in the present report permitted fluid filtration (Fig 2) indicated that the tubules were not totally occluded. The linearity of the increase in filtration rate with increasing hydrostatic pressure in both unetched and etched dentin (Fig 2) suggests that the fluid flow is nonturbulent and that little or no molecular sieving of buffer salts from the solvent occurred as has been previously described in other systems. 25,26 An examination of the variables (Equation I) determining hydraulic conductance (Lp) reveals that the variable of dentin thickness is not included, yet Figure 3 clearly demonstrated that filtration rate was very sensitive to changes in dentin thickness. Pappenheimer et a125 and Renkin26 attempted to correct for this by calculating the specific filtration coefficients for membranes, by multiplying the hydraulic conductance by the membrane thickness. Such a treatment assumes that there would be a linear increase in hydraulic conductance as dentin thickness is reduced. Examination of the data in Figure 3 reveals an exponential, rather than a linear relationship. While multiplying the hydraulic conductances by the membrane thicknesses tends to partially correct the data for thickness (not shown), the 38% reduction in thickness (from 0.99 to 0.61 mm) still would be associated with a 300% increase in filtration rate (rather than the 500% increase shown in the Table). Thus, expressing the ease with which fluid filters across dentin as a specific filtration coefficient (Kf), does not improve the ability to predict filtration rates under specific conditions. Presumably, this is due to the fact that as dentin thickness is reduced from the enamel side, the number of tubules per unit surface area increase.23'24 Outhwaite
j Dent Res February
1978
et al.22 obtained similar results when studying the rate of iodide diffusion across dentin disks. The data in the Table have been fitted to an exponential regression equation to permit more accurate estimates of Lp (y) as a function of dentin thickness (x). This relationship is described by y = 4.833e4l93x, r= 0.978, P < 0.001.
The linear relationship between filtration rate and surface area, at any constant thickness (Fig 3, insert) suggests that the tubular density and dimensions are relatively constant across the disk surface. Had this relationship not been linear, it would have suggested that there were differences in tubular density and/or diameter within the same plane of the disk. The results of these studies should be regarded as setting an upper limit for dentin hydraulic conductance since the tubules in dentin disks apparently do not have odontoblastic processes on the pulpal side (unpublished observations). The hydraulic conductance of acid-etched disks probably represents a maximum value that could be obtained clinically in dentin that had been treated with acid-etching agents. Conclusions
The present report describes a method of measuring the ease with which fluid can filter across dentin (the hydraulic conductance) in a quantitative manner. Dentin surfaces that have been sanded have a measurable but low hydraulic conductance. Acid etching the dentin with 50% (w/v) citric acid for 2 minutes leads to a 32-fold increase in filtration rate. This was due to removal of surface debris partially occluding the tubule orifices. Since the degree of occlusion of dentinal tubules, the surface area, and the thickness of dentin vary widely depending upon experimental conditions, it is suggested that investigators report a hydraulic conductance value for the dentin under study to assist in future comparisons of interlaboratory data. References 1. BRXNNSTROM, M.: Dentinal and Pulpal Response. II. Application of an Air Stream to Exposed Dentine. Short Observation
DENTIN PERMEABILITY: HYDRAULIC CONDUCTANCE
Vol. 5 7 No. 2
Period, Acta Odont Scand 18:17-28, 1960. 2. BRXNNSTRbM, M.: Dentinal and Pulpal Response. V. Application of Pressure to Exposed Dentine, J Dent Res 40:960-970, 1961. 3. BRANNSTROM, M.: The Elicitation of Pain in Human Dentine and Pulp by Chemical Stimuli, Arch Oral Biol 7:59-62, 1962. 4. BRXNNSTROM, M., and ASTROM, A.: A Study on the Mechanism of Pain Elicited from the Dentin, J Dent Res 43:619-625, 1964. 5. LINDEN, L., and BRXNNSTR6M, M.: Fluid Movements in Dentine and Pulp. An In Vitro Study of Flow Produced by Chemical
14. BRXNNSTROSM, M.; JOHNSON, G.; and LIN-
DEN, L.: Fluid Flow and Pain Response in the Dentine Produced by Hydrostatic Pressure, Odont Revy 20:16-30, 1969. 15. JOHNSON, G., and BRXNNSTROM, M.: The
Sensitivity of Dentin: Changes in Relation to Conditions at Exposed Tubule Apertures, Acta Odont Scand 32:29-38, 1974. 16. STANLEY, H. R.; GORING, R. E.; and
17.
Solutions on Exposed Dentine, Odont Revy 18:227-236, 1976. 6. BRXNNSTROM,
M.;
LINDEN,
L.;
and
ASTRtM, A.: The Hydrodynamics of the
18.
Dental Tubule and of Pulp Fluid. A Discussion of its Significance in Relation to Dentinal Sensitivity, Caries Res 1:310-317, 1967.
19.
7. BRANNSTROM, M.; LINDEN, L.; and JOHN SON, G.: Movement of Dentinal and Pulpal
Fluid Caused by Clinical Procedures, J Dent Res 47:679-682, 1968. 8. POLHAGEN, L., and BRXNNSTROM, M.: The Liquid Movement in Desiccated and Rehydrated Dentine In Vitro, Acta Odont
20.
Scand29:95-102, 1971. 9. JOHNSON, G.; OLGART, L.; and BRXNN-
STROM, M.: Outward Fluid Flow in Dentin Under a Physiologic Pressure Gradient: Experiments In Vitro, Oral Surg 35(2):238-248, 1973. 10. ANDERSON, D. J.; CURWEN, M. P.; and HOWARD, L. V.: The Sensitivity of Human Dentin,JDent Res 37:669-677, 1958. 11. ANDERSON, D. J., and RONNING, G. A.: Osmotic Excitants of Pain in Human Den-
21.
22. 23.
tine, Arch Oral Biol 7:513-523, 1962. 12. ANDERSON, D. J., and MATTHEWS, B.: Os-
motic Stimulation of Human Dentine and the Distribution of Dental Pain Thresholds, Arch Oral Biol 12:417 -426, 1967. 13. ANDERSON, D. J.; MATTHEWS, B.; and GORRETTA, C.: Fluid Flow Through Human Dentine, Arch Oral Biol 12:209-216, 1967.
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24.
CHAUNCEY, H. H.: Human Pulp Response to Acid Pretreatment of Dentin and to Composite Restoration, JADA 91:817-825, Oct 1975. VOJINOVIC, O.: NYBORG, H.; and BRXNNSTROM, M.: Acid Treatment of Cavities Under Resin Fillings: Bacterial Growth in Dentinal Tubules and Pulpal Reactions, J DentRes52:1189-1192, 1973. HOUSE, C. R.: Water Transport in Cells and Tissues, Baltimore: The William and Wilkins Company, 1974, p 88. UMBRIET, W. W.; BURRIS, R. H.; and STAUFFER, J. F.: 1972, Manometric and Biochemical Techniques (5th ed), Minneapolis, Minn.: Burgess Publishing Company, 1972, p 146. OUTHWAITE, W. C.; LIVINGSTON, M. J.; and PASHLEY, D. H.: Effects of Changes in Surface Area, Thickness, Temperature and Post-Extraction Time on Human Dentin Permeability, Arch Oral Biol 21:599-603, 1976. OLGART, L.; BRXNNSTROM, M.; andJOHNSON, G..: Invasion of Bacteria into Dentinal Tubules. Experiments In Vivo, Acta Odont Scand 32:61-70, 1974. STEVENSON, T. S.: Fluid Movement in Human Dentine, Arch Oral Biol 10:935-944, 1965. FORSSELL-AHLBERG, K.; BRANNSTROM, M.; and EDWALL, L.: The Diameter and Number of Dentinal Tubules in Rat, Cat, Dog, and Monkey. A Comparative Scanning Electron Microscopic Study, Acta Odont Scand 33:243-250, 1975. GARBEROGLIO, R., and BRXNNSTROM, M.: Scanning Electron Microscopic Investigation of Human Dentinal Tubules, Arch Oral Biol 21:355-362, 1976.
