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Osmotic stimulation of human dentine and the distribution of dental pain thresholds
Arc/uoralBiol. Vol.12,pp.417-426, 1967.Pergamon PressLtd. Printedin Gt. Britain.
OSMOTIC STIMULATION OF HUMAN DENTINE AND THE DISTRIBUTION OF DENTAL PAIN THRESHOLDS D. J. ANDERSON and B. MATTHEWS Dental School and Department of Physiology, University of Bristol, England Summary--It has been established
that there is a relationship between osmotic pressure and pain-producing power when CaC18 solutions in the range 200-2800 atm are applied to dentine (ANDERSONand RONN~NG,1962). Experiments have been performed in an attempt to explain previous failure to confirm this relationship with other solutions. The experiments fell into two groups: those with solutions in the range 25-700 atm and those in the range 200-2800 atm. A decline in sensitivity during an experiment was observed as previously but was found to be caused only by solutions in the high range of osmotic pressure. Because of this decline in sensitivity, only the first results of every sequence of stimulations with the high range of osmotic pressures is comparable with results from the low range of osmotic pressures. Comparable data over the entire range of osmotic pressures 25-2800 atm was obtained by selecting only the first results of every series in the high range and using all the results in the low range of osmotic pressures. When this selection was made, the points on a graph of pain-producing power and log osmotic pressure fell on a sigmoid curve. This curve can be considered to represent the distribution of pain thresholds within the group of subjects, defined in units of log osmotic pressures. Probit transformation has shown that this distribution is normal (Gaussian). Osmotic pressure can therefore be taken as the effective stimulus common to all the solutions used in evoking pain from dentine. INTRODUCTION
a wide variety of solutions, ANDERSON and RONNING (1962) investigated the possible relationship between the osmotic pressure of a solution and its ability to cause pain when applied to dentine. With CaCl, solutions in the range 200-2800 atm there appeared to be a straight-line relationship between osmotic pressure and the number of reports of pain. However, although other solutions caused pain with varying success, no clear-cut relationship based on osmotic pressure emerged and it therefore seemed possible that the relationship established might be due to some specific effect of CaCl,. In view of this, further experiments have been carried out to establish whether osmotic pressure or some other property of a solution might determine its ability to cause pain. If osmotic pressure is the effective stimulus, then painproducing power and osmotic pressure should be related over a wide range of osmotic pressures and irrespective of the chemical composition of the solute. The results of these more recent experiments will be presented and analysed together with those previously reported (ANDERSON and RONNING, 1962). USING
METHOD
The details of the experimental procedure have been described previously (ANDERSON and RONNING, 1962). The subjects were dental students within the age range 17-25 417 G
D. J. ANDERSONAND B. MATTHEWS
418
years. Solutions were applied in random order to dentine in an occlusal cavity cut in a premolar with minimal caries. Every solution was applied on a pledget of cotton wool at 37°C for 30 sec. After every application the cavity was rinsed with warm water and the subject was then asked to report any sensation he had experienced. The solutions were applied first to the freshly cut dentine and again after the cavity had been filled with gutta-percha for a week. The experiments fall into two groups; those in which a series of solutions within the range 200-2800 atm were used (group l), and those in which the range was 25-700 atm (group 2). Table 1 shows the solutions which have been tested, together with the TABLE 1
Approx. osmotic pressure (atm) at 37°C Group 1
200 700 :zE
Group 2
25
50-60
80-85
Solution
Number of applications
2 molal CaCl, Sugar syrup 6 molal CaCl 2 Sat. CaClz
314 314 314 313
1 molar 1 molar 1 molar 1 molar
dextrose urea glycerol ethanol
2 molar 1 molar 2 molar 2 molar 1 molar 2 molar
dextrose NH&l urea glycerol NaCl ethanol
2 4 4 2 4
200-250
4 molar NH&l Sat. urea 5 molar glycerol 4 molar NaCl 2 molar CaCl 2
700
104
3 molar glycerol 1 molar CaCl,
loo-125
300-350
56
molar molar molar molar molar
32
NH&l urea glycerol NaCl ethanol
56
90
5 molar NH&l 2.5 molar CaCl,
24
Sugar syrup
14 Total
No. of subjects: 102
1621
OSMOTICSTIMULAYIONOFHUhlAN
DENTINE
419
approximate osmotic pressures at 37°C. The Table also shows the total number of applications of every solution. RESULTS
The pooled results from the entire series of experiments, including those Of ANDERSONand RONNING(1962) are displayed in Fig. 1. No distinction is made between
0
2
4
6
8
10
12 14 16 18 20 22 24 26 28
osmotic pressure
in atmospheres
x 100
FIG. 1. The relationship between osmotic pressure of solutions and the % of applications which caused pain. Pooled results from group 1 (200-2800 atm) are shown by squares and from group 2 (25-700 atm) by solid circles. The line is that fitted by ANDERK~Nand RONNINO (1962) to their data.
freshly cut dentine and dentine stimulated after the cavity had been filled with guttapercha for a week. The squares show the results from group 1 experiments (200-2800 atm) and the solid circles are from group 2 experiments (25-700 atm). The superimposed line is that fitted by ANDERSON and RONNING(1962) to their data obtained with CaCl, in the range 200-2800 atm and, although the group 1 data do not fall far from this line, it is clear that the group 2 data represents a different relationship. In Figs. 2A and B there has been a separation of the data; Fig. 2A shows all the results from freshly cut dentine and Fig. 2B shows the results from dentine after filling with gutta-percha. It is clear that the ability of a solution to cause pain is enhanced after filling the cavity with gutta-percha for 1 week. This confirms previous observations (ANDERSON,MATTHEWSand SHELTON,1967). DISCUSSION
AND
STATISTICAL
TREATMENT
The failure of the group 2 results to conform to the pattern of group 1 appeared seriously to undermine the hypothesis that osmotic pressure and pain-producing power are related. However, whether this hypothesis is correct or not, the results will have been complicated in a manner that has not previously been taken into consideration.
D. J. ANDERSONAND B. MATTHEWS
420
100 c 80 -
a 0
I,,
2
4
6
8
,
)
10
12
osmotic pressure
100
,
14
,
16
,
,
,
18 20
22
,
,
24
26
28
24
26
28
III atmospheres x 100
0
80
a
t
I
I
’
1
I”
0
2
4
6
8
1
11
10
12
osmotic pressure
14
16
’
18 20
in atmospheres
I”
22
I
x 100
FIG. 2. The relationship between osmotic pressure of solutions and the % applications which caused pain. Symbols as in Fig. 1. A, freshly cut dentine; B, dentine after filling with gutta-percha for 1 week.
OSMOTIC STIMULATION OF HUMAN DENTINE
421
It has been reported (ANDERSONet al., 1967) that, using a series of solutions within the range 200-2800 atm, the number of reports of pain declines during an experiment, although the solutions are applied randomly. Evidence has been presented (ANDERSON et al., 1967) in support of the view that this is due to a change in the sensory mechanisms at a peripheral level. It follows that the group 1 results, and possibly those from group II, will have been influenced by changing sensitivity of the receptor mechanism, and this will have complicated the relationship seen between osmotic pressure and pain-producing power. Since the solutions were applied in random order, every solution in a series will have appeared with approximately equal frequency in every position in the series. A change in sensitivity during a sequence of applications will therefore be demonstrated by arranging the results of all the applications, irrespective of the solution used, according to their position in the sequence of stimulations. Since it was customary to apply every solution twice, and to use four different solutions, the sequence usually consisted of eight applications. Figure 3A shows all the results arranged in this manner for group 1 experiments (200-2800 atm). Figure 3B shows a similar arrangement of group 2 results (25-700 atm). B
A
ol
0) 2
Position
4
6
8
in sequence
2 Position
4
6
a
in sequence
FIG. 3. The change in sensitivity as measured by the % response during a sequence of eight stimulations. Pooled results from freshly cut dentine and dentine after filling with gutta-percha for 1 week. A, group 1 experiments (200-2800 atm); B, group 2 experiments (25-700 atm).
The fall in the number of responses in Fig. 3A confirms previous findings with solutions in the 200-2800 atm range. However, it is clear from Fig. 3B that the position in the sequence does not affect the pain-producing power of solutions in the range 25700 atm, and this suggests that the cause of the inactivation of the sensory mechanisms is the use of solutions exerting more than 700 atm osmotic pressure. This conclusion is supported by the observation that the repeated application of saturated strontium chloride solution at 37°C (osmotic pressure approx. 700 atm) to a cavity does not produce a fall in sensitivity (ANDERSON et al., 1967). To obtain an undistorted picture of the role of osmotic pressure in pain production, it was necessary to exclude those results in the group 1 series obtained while the sensitivity was falling because of previous stimulation. By so doing, a large body of
422
D. J.
ANDERSON AND
B.
MATTHEWS
comparable results was made available over the entire range 25-2800 atm. In group 1, only the first applications in every series were made to dentine unaffected by previous stimulation, and so, by selecting only the results from the first applications in the group 1 series, together with all the results from the group 2 series, the desensitizing effect was excluded. These results for freshly cut and for gutta-percha treated dentine are shown respectively in Figs. 4A and 4B and indicate that there is a curvilinear relation100
80
F
A
A
t A
A
A I
0
I
2
I
4
6
I,
8
,
,
10
12
osmotic pressure
14
I,
16
18
I
I,,
20
22
in atmospheres
,
24
26
28
x 100
A
II 0
2
I
t
1
11
4
6
8
10
12
osmotic pressure
1
”
14
16
1”’
18
in atmospheres
20
8
22
24
26
28
x 100
FIG. 4. The relationship between osmotic pressure and the % applications which caused pain. Pooled results from only the first applications of every solution in group 1 experiments and all applications in group 2 experiments. A, freshly cut dentine; B, dentine after filling with gutta-percha for 1 week.
OSMOTIC STIMULATION OF HUMAN DEhTINE
423
ship between the osmotic pressure of a solution and the frequency with which it causes pain. These results can also be interpreted as reflecting variation between subjects in their pain thresholds to osmotic stimulation of dentine. The pain thresholds for this form of stimulation can be defined as the minimum osmotic pressure which will cause pain. Considering first the results obtained from freshly cut dentine (Fig. 4A), the fact that a solution of, for example, 1400 atm osmotic pressure produced pain in approximately 85 per cent of applications indicates that about 85 per cent of the subjects tested with this solution had thresholds at or below this value. Similarly, approximately 30 per cent of subjects had thresholds at or below 200 atm. Thus, a curve fitted to the results would be an estimate of the cumulative frequency distribution curve of the pain thresholds of these subjects. If, as might be expected, the pain thresholds had a normal (Gaussian) distribution, then this curve would have a symmetrical sigmoid shape. Since the results in Figs. 4A and B do not appear to follow this pattern, the possibility was examined that the thresholds expressed as the log of osmotic pressure might have a normal distribution. Figure 5 shows the results, plotted in this way, appearing to follow a sigmoid curve. 100 A
A
80 1 I
m
A
60
ij ;
40
A
i
A A
20
A
A
A t 0 1.2
A
I
I
I
I
I
1.6
2.0
2.4
2.6
3.2
osmotic
pressure
log. FIG. 5. Data
I 3.6
from Fig. 4A plotted against log osmotic pressure.
The cumulative frequency distribution curve for a normal distribution can be converted to a straight line by probit transformation. In probit transformation, the % scale is converted to one in which the units are standard deviations of the normal distribution. Figure 6A shows the results from Fig. 5 plotted as the probit values against the log of osmotic pressure, together with the fitted line. The line was fitted using the method described by EMMENS (1948). With the xBtest it has been shown that the differences between the observed values and those predicted by the fitted line are
424
D. J. ANDUWW AND B. MATTHEWS
1.2
1.6
2.0
2.4
2.8
3.2
3.6
log. osmotic pressure
7.0 6.5
5.5
3.5
2.5 1.2
1
I
I
I
1. 6
2.0
2.4
2; 8
I
3.0
I
3.2
log. osmotic pressure FIG. 6. Probit transformation of results from only the first application of every solution in group 1 experiments and all applications in group 2 experiments. A, freshly cut dentine; B, dentine after filling with gutta-percha for 1 week. Lines fitted by method described by EMMENS(1948).
OSMOTIC STIMULATION OF HUMAN
DENTINE
425
not statistically significant (p = > 0.8). It can be concluded, therefore, that for freshly cut dentine, the pain thresholds expressed as the log. of osmotic pressure have a normal distribution, with a mean value of 2.58 and a standard deviation of 0.66 log units. The mean value is equivalent to an osmotic pressure of 380 atm. A similar analysis of the results obtained after gutta-percha is shown in Fig. 6B. The x2 test in this case gave a value of p = > 0.6. It is therefore concluded that, after treatment with gutta-percha, the thresholds expressed as the log of the osmotic pressure have a normal distribution. In this case, the distribution has a mean value of 2.06 (I I5 atm) and standard deviation of 0.85 log units. Since it appears that the definition of pain thresholds in terms of the log of the osmotic pressure is valid, osmotic pressure may be taken as the effective stimulus common to all the various solutions used. The values for the mean and S.D. of the thresholds for freshly cut dentine will provide a basis for quantitating the effectiveness of measures designed to alter the sensitivity of dentine, using a similar group of subjects. Acknowledgement-This investigation was supported by U.S.P.H.S. Research Grant DE 01037-05 from the National Institute of Dental Research, National Institutes of Health, Bethesda, Maryland, U.S.A. R&&---Un rapport entre la pression osmotique et le pouvoir de provoquer de la douleur ii l’aide de solutions de CaCI,, appliquees entre 200-2800 atm a la dentine, a pu &tre Ctabli (ANDERSONet RONNING,1962). Des experiences ont ttC realisees pour expliquer l’&chec de la demonstration dun tel rapport avec d’autres solutions. Ces expbiences se divisent en deux groupes: celles effectuees avec des solutions variant entre 25-700 atm et celles variant de 200 a 2800 atm. Une baisse de sensibilite a BtCnotee dans une experience comme preddemment, mais elle semble due exclusivement a des solutions a pressions osmotiques &levees. Chaque serie de stimulations, saufla premiere, a la dentine en baisse de sensibilite et par suite les resultats de ces dernihes applications ne sont pas cornparables avec ceux obtenus avec des solutions a pression osmotique faible. Des rtsultats similaires sont obtenus avec des pressions osmotiques variant de 25-2800 atm, en choisissant seulement les premiers resultats pour chaque serie a valeur elev6e et en utilisant tous les resultats a pressions osmotiques faibles. Une fois ce choix effectue, les points sur un diagramme indiquant la potentialite a provoquer la douleur en fonction du log des pressions osmotiques sont disposes sur une courbe sigmoide. Cette courbe semble rep&enter la distribution des seuils douloureux dans un groupe de sujets, definis en unites de log de pressions osmotiques. La transformation “probit” a montre que cette distribution est normale (gaussienne). La pression osmotique peut par suite &re considerte comme le stimulus actif commun a toutes les solutions utilisees pour provoquer la douleur dentinaire. Zusammenfassung-Es wurde beobachtet, da8 eine Beziehung zwischen osmotischem Druck und schmerzverursachender Fahigkeit existiert, wenn CaCl,-Losungen im Bereich von 200-2800 atm auf Dentin angewandt werden (ANDERSONund RONNING, 1962). Versuchsweise wurden Experimente durchgeftihrt, urn den frtiheren MiRerfolg zu erkl%ren, diese Beziehung mit anderen Ldsungen zu bestatigen. Die Versuche teilten sich in zwei Gruppen: Solche mit Losungen im Bereich von 25-700 atm und andere im Bereich von 200-2800 atm. Wie zuvor wurde ein Sensibilitatsverlust wlhrend eines Experiments beobachtet, er wurdejedoch nur durch Liisungen mit hohem osmotischen Druck verursacht. Mit Ausnahme der ersten Stimulations-serie im
426
D. J. ANDERSONANDB. MA~WS hohen Bereich werden deshalballeweiterenan Dentin mit abnehmender Sensitivitat angcwandt worden sein; daher sind die Ergebnisse dieser splteren Applikationen nicht mit den mit Liisungen niedrigen osmotischen Druckes erhaltenen Resultaten vergleichbar. Vergleichbare Daten tiber den gesamten Bereich des osmotischen Druckes von 25-2800 atm wurden gewonnen, indem lediglich die ersten Ergebnisse jeder Serie im hohen Bereich ausgewlhlt und alle Ergebnisse bei niedrigem osmotischem Druck verwendet wurden. Bei dieser Auswahl fallen die graph&h dargestellten Punkte des schmerzverursachenden Druckes und der log des osmotischen Druckes im Sinne einer sigmoiden Kurve ab. Es kann angenommen werden, da8 diese Kurve die Verteilung von Schmerzreizen innerhalb der Probandengruppe, in Einheiten des log des osmitischen Druckes definiert, darstellt. Die Probit-Transformation hat erwiesen, da8 die Verteilung normal ist (Gaussian). Der osmotische Druck kann deshalb als der allein im Dentin allen schmerzverursachenden LSsungen gemeine, wirksame Reiz aufgefaBt werden.
REFERENCES ANDERSON,D. J. and RONNING, G. A. 1962. Osmotic excitants of pain in human dentine. Archs oral Biol. 7, 513-523. ANDERSON, D. J., MAI-I-HEWS,B. and SHELTON,L. E. 1967. Variations in the sensitivity to osmotic stimulation of human dentine. Archs oral Biol. 12,43-41. EMMENS,C. W. 1948. Principles of Biological Assay, p. 150. Chapman and Hall, London.
OSMOTIC STIMULATION OF HUMAN DENTINE AND THE DISTRIBUTION OF DENTAL PAIN THRESHOLDS D. J. ANDERSON and B. MATTHEWS Dental School and Department of Physiology, University of Bristol, England Summary--It has been established
that there is a relationship between osmotic pressure and pain-producing power when CaC18 solutions in the range 200-2800 atm are applied to dentine (ANDERSONand RONN~NG,1962). Experiments have been performed in an attempt to explain previous failure to confirm this relationship with other solutions. The experiments fell into two groups: those with solutions in the range 25-700 atm and those in the range 200-2800 atm. A decline in sensitivity during an experiment was observed as previously but was found to be caused only by solutions in the high range of osmotic pressure. Because of this decline in sensitivity, only the first results of every sequence of stimulations with the high range of osmotic pressures is comparable with results from the low range of osmotic pressures. Comparable data over the entire range of osmotic pressures 25-2800 atm was obtained by selecting only the first results of every series in the high range and using all the results in the low range of osmotic pressures. When this selection was made, the points on a graph of pain-producing power and log osmotic pressure fell on a sigmoid curve. This curve can be considered to represent the distribution of pain thresholds within the group of subjects, defined in units of log osmotic pressures. Probit transformation has shown that this distribution is normal (Gaussian). Osmotic pressure can therefore be taken as the effective stimulus common to all the solutions used in evoking pain from dentine. INTRODUCTION
a wide variety of solutions, ANDERSON and RONNING (1962) investigated the possible relationship between the osmotic pressure of a solution and its ability to cause pain when applied to dentine. With CaCl, solutions in the range 200-2800 atm there appeared to be a straight-line relationship between osmotic pressure and the number of reports of pain. However, although other solutions caused pain with varying success, no clear-cut relationship based on osmotic pressure emerged and it therefore seemed possible that the relationship established might be due to some specific effect of CaCl,. In view of this, further experiments have been carried out to establish whether osmotic pressure or some other property of a solution might determine its ability to cause pain. If osmotic pressure is the effective stimulus, then painproducing power and osmotic pressure should be related over a wide range of osmotic pressures and irrespective of the chemical composition of the solute. The results of these more recent experiments will be presented and analysed together with those previously reported (ANDERSON and RONNING, 1962). USING
METHOD
The details of the experimental procedure have been described previously (ANDERSON and RONNING, 1962). The subjects were dental students within the age range 17-25 417 G
D. J. ANDERSONAND B. MATTHEWS
418
years. Solutions were applied in random order to dentine in an occlusal cavity cut in a premolar with minimal caries. Every solution was applied on a pledget of cotton wool at 37°C for 30 sec. After every application the cavity was rinsed with warm water and the subject was then asked to report any sensation he had experienced. The solutions were applied first to the freshly cut dentine and again after the cavity had been filled with gutta-percha for a week. The experiments fall into two groups; those in which a series of solutions within the range 200-2800 atm were used (group l), and those in which the range was 25-700 atm (group 2). Table 1 shows the solutions which have been tested, together with the TABLE 1
Approx. osmotic pressure (atm) at 37°C Group 1
200 700 :zE
Group 2
25
50-60
80-85
Solution
Number of applications
2 molal CaCl, Sugar syrup 6 molal CaCl 2 Sat. CaClz
314 314 314 313
1 molar 1 molar 1 molar 1 molar
dextrose urea glycerol ethanol
2 molar 1 molar 2 molar 2 molar 1 molar 2 molar
dextrose NH&l urea glycerol NaCl ethanol
2 4 4 2 4
200-250
4 molar NH&l Sat. urea 5 molar glycerol 4 molar NaCl 2 molar CaCl 2
700
104
3 molar glycerol 1 molar CaCl,
loo-125
300-350
56
molar molar molar molar molar
32
NH&l urea glycerol NaCl ethanol
56
90
5 molar NH&l 2.5 molar CaCl,
24
Sugar syrup
14 Total
No. of subjects: 102
1621
OSMOTICSTIMULAYIONOFHUhlAN
DENTINE
419
approximate osmotic pressures at 37°C. The Table also shows the total number of applications of every solution. RESULTS
The pooled results from the entire series of experiments, including those Of ANDERSONand RONNING(1962) are displayed in Fig. 1. No distinction is made between
0
2
4
6
8
10
12 14 16 18 20 22 24 26 28
osmotic pressure
in atmospheres
x 100
FIG. 1. The relationship between osmotic pressure of solutions and the % of applications which caused pain. Pooled results from group 1 (200-2800 atm) are shown by squares and from group 2 (25-700 atm) by solid circles. The line is that fitted by ANDERK~Nand RONNINO (1962) to their data.
freshly cut dentine and dentine stimulated after the cavity had been filled with guttapercha for a week. The squares show the results from group 1 experiments (200-2800 atm) and the solid circles are from group 2 experiments (25-700 atm). The superimposed line is that fitted by ANDERSON and RONNING(1962) to their data obtained with CaCl, in the range 200-2800 atm and, although the group 1 data do not fall far from this line, it is clear that the group 2 data represents a different relationship. In Figs. 2A and B there has been a separation of the data; Fig. 2A shows all the results from freshly cut dentine and Fig. 2B shows the results from dentine after filling with gutta-percha. It is clear that the ability of a solution to cause pain is enhanced after filling the cavity with gutta-percha for 1 week. This confirms previous observations (ANDERSON,MATTHEWSand SHELTON,1967). DISCUSSION
AND
STATISTICAL
TREATMENT
The failure of the group 2 results to conform to the pattern of group 1 appeared seriously to undermine the hypothesis that osmotic pressure and pain-producing power are related. However, whether this hypothesis is correct or not, the results will have been complicated in a manner that has not previously been taken into consideration.
D. J. ANDERSONAND B. MATTHEWS
420
100 c 80 -
a 0
I,,
2
4
6
8
,
)
10
12
osmotic pressure
100
,
14
,
16
,
,
,
18 20
22
,
,
24
26
28
24
26
28
III atmospheres x 100
0
80
a
t
I
I
’
1
I”
0
2
4
6
8
1
11
10
12
osmotic pressure
14
16
’
18 20
in atmospheres
I”
22
I
x 100
FIG. 2. The relationship between osmotic pressure of solutions and the % applications which caused pain. Symbols as in Fig. 1. A, freshly cut dentine; B, dentine after filling with gutta-percha for 1 week.
OSMOTIC STIMULATION OF HUMAN DENTINE
421
It has been reported (ANDERSONet al., 1967) that, using a series of solutions within the range 200-2800 atm, the number of reports of pain declines during an experiment, although the solutions are applied randomly. Evidence has been presented (ANDERSON et al., 1967) in support of the view that this is due to a change in the sensory mechanisms at a peripheral level. It follows that the group 1 results, and possibly those from group II, will have been influenced by changing sensitivity of the receptor mechanism, and this will have complicated the relationship seen between osmotic pressure and pain-producing power. Since the solutions were applied in random order, every solution in a series will have appeared with approximately equal frequency in every position in the series. A change in sensitivity during a sequence of applications will therefore be demonstrated by arranging the results of all the applications, irrespective of the solution used, according to their position in the sequence of stimulations. Since it was customary to apply every solution twice, and to use four different solutions, the sequence usually consisted of eight applications. Figure 3A shows all the results arranged in this manner for group 1 experiments (200-2800 atm). Figure 3B shows a similar arrangement of group 2 results (25-700 atm). B
A
ol
0) 2
Position
4
6
8
in sequence
2 Position
4
6
a
in sequence
FIG. 3. The change in sensitivity as measured by the % response during a sequence of eight stimulations. Pooled results from freshly cut dentine and dentine after filling with gutta-percha for 1 week. A, group 1 experiments (200-2800 atm); B, group 2 experiments (25-700 atm).
The fall in the number of responses in Fig. 3A confirms previous findings with solutions in the 200-2800 atm range. However, it is clear from Fig. 3B that the position in the sequence does not affect the pain-producing power of solutions in the range 25700 atm, and this suggests that the cause of the inactivation of the sensory mechanisms is the use of solutions exerting more than 700 atm osmotic pressure. This conclusion is supported by the observation that the repeated application of saturated strontium chloride solution at 37°C (osmotic pressure approx. 700 atm) to a cavity does not produce a fall in sensitivity (ANDERSON et al., 1967). To obtain an undistorted picture of the role of osmotic pressure in pain production, it was necessary to exclude those results in the group 1 series obtained while the sensitivity was falling because of previous stimulation. By so doing, a large body of
422
D. J.
ANDERSON AND
B.
MATTHEWS
comparable results was made available over the entire range 25-2800 atm. In group 1, only the first applications in every series were made to dentine unaffected by previous stimulation, and so, by selecting only the results from the first applications in the group 1 series, together with all the results from the group 2 series, the desensitizing effect was excluded. These results for freshly cut and for gutta-percha treated dentine are shown respectively in Figs. 4A and 4B and indicate that there is a curvilinear relation100
80
F
A
A
t A
A
A I
0
I
2
I
4
6
I,
8
,
,
10
12
osmotic pressure
14
I,
16
18
I
I,,
20
22
in atmospheres
,
24
26
28
x 100
A
II 0
2
I
t
1
11
4
6
8
10
12
osmotic pressure
1
”
14
16
1”’
18
in atmospheres
20
8
22
24
26
28
x 100
FIG. 4. The relationship between osmotic pressure and the % applications which caused pain. Pooled results from only the first applications of every solution in group 1 experiments and all applications in group 2 experiments. A, freshly cut dentine; B, dentine after filling with gutta-percha for 1 week.
OSMOTIC STIMULATION OF HUMAN DEhTINE
423
ship between the osmotic pressure of a solution and the frequency with which it causes pain. These results can also be interpreted as reflecting variation between subjects in their pain thresholds to osmotic stimulation of dentine. The pain thresholds for this form of stimulation can be defined as the minimum osmotic pressure which will cause pain. Considering first the results obtained from freshly cut dentine (Fig. 4A), the fact that a solution of, for example, 1400 atm osmotic pressure produced pain in approximately 85 per cent of applications indicates that about 85 per cent of the subjects tested with this solution had thresholds at or below this value. Similarly, approximately 30 per cent of subjects had thresholds at or below 200 atm. Thus, a curve fitted to the results would be an estimate of the cumulative frequency distribution curve of the pain thresholds of these subjects. If, as might be expected, the pain thresholds had a normal (Gaussian) distribution, then this curve would have a symmetrical sigmoid shape. Since the results in Figs. 4A and B do not appear to follow this pattern, the possibility was examined that the thresholds expressed as the log of osmotic pressure might have a normal distribution. Figure 5 shows the results, plotted in this way, appearing to follow a sigmoid curve. 100 A
A
80 1 I
m
A
60
ij ;
40
A
i
A A
20
A
A
A t 0 1.2
A
I
I
I
I
I
1.6
2.0
2.4
2.6
3.2
osmotic
pressure
log. FIG. 5. Data
I 3.6
from Fig. 4A plotted against log osmotic pressure.
The cumulative frequency distribution curve for a normal distribution can be converted to a straight line by probit transformation. In probit transformation, the % scale is converted to one in which the units are standard deviations of the normal distribution. Figure 6A shows the results from Fig. 5 plotted as the probit values against the log of osmotic pressure, together with the fitted line. The line was fitted using the method described by EMMENS (1948). With the xBtest it has been shown that the differences between the observed values and those predicted by the fitted line are
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D. J. ANDUWW AND B. MATTHEWS
1.2
1.6
2.0
2.4
2.8
3.2
3.6
log. osmotic pressure
7.0 6.5
5.5
3.5
2.5 1.2
1
I
I
I
1. 6
2.0
2.4
2; 8
I
3.0
I
3.2
log. osmotic pressure FIG. 6. Probit transformation of results from only the first application of every solution in group 1 experiments and all applications in group 2 experiments. A, freshly cut dentine; B, dentine after filling with gutta-percha for 1 week. Lines fitted by method described by EMMENS(1948).
OSMOTIC STIMULATION OF HUMAN
DENTINE
425
not statistically significant (p = > 0.8). It can be concluded, therefore, that for freshly cut dentine, the pain thresholds expressed as the log. of osmotic pressure have a normal distribution, with a mean value of 2.58 and a standard deviation of 0.66 log units. The mean value is equivalent to an osmotic pressure of 380 atm. A similar analysis of the results obtained after gutta-percha is shown in Fig. 6B. The x2 test in this case gave a value of p = > 0.6. It is therefore concluded that, after treatment with gutta-percha, the thresholds expressed as the log of the osmotic pressure have a normal distribution. In this case, the distribution has a mean value of 2.06 (I I5 atm) and standard deviation of 0.85 log units. Since it appears that the definition of pain thresholds in terms of the log of the osmotic pressure is valid, osmotic pressure may be taken as the effective stimulus common to all the various solutions used. The values for the mean and S.D. of the thresholds for freshly cut dentine will provide a basis for quantitating the effectiveness of measures designed to alter the sensitivity of dentine, using a similar group of subjects. Acknowledgement-This investigation was supported by U.S.P.H.S. Research Grant DE 01037-05 from the National Institute of Dental Research, National Institutes of Health, Bethesda, Maryland, U.S.A. R&&---Un rapport entre la pression osmotique et le pouvoir de provoquer de la douleur ii l’aide de solutions de CaCI,, appliquees entre 200-2800 atm a la dentine, a pu &tre Ctabli (ANDERSONet RONNING,1962). Des experiences ont ttC realisees pour expliquer l’&chec de la demonstration dun tel rapport avec d’autres solutions. Ces expbiences se divisent en deux groupes: celles effectuees avec des solutions variant entre 25-700 atm et celles variant de 200 a 2800 atm. Une baisse de sensibilite a BtCnotee dans une experience comme preddemment, mais elle semble due exclusivement a des solutions a pressions osmotiques &levees. Chaque serie de stimulations, saufla premiere, a la dentine en baisse de sensibilite et par suite les resultats de ces dernihes applications ne sont pas cornparables avec ceux obtenus avec des solutions a pression osmotique faible. Des rtsultats similaires sont obtenus avec des pressions osmotiques variant de 25-2800 atm, en choisissant seulement les premiers resultats pour chaque serie a valeur elev6e et en utilisant tous les resultats a pressions osmotiques faibles. Une fois ce choix effectue, les points sur un diagramme indiquant la potentialite a provoquer la douleur en fonction du log des pressions osmotiques sont disposes sur une courbe sigmoide. Cette courbe semble rep&enter la distribution des seuils douloureux dans un groupe de sujets, definis en unites de log de pressions osmotiques. La transformation “probit” a montre que cette distribution est normale (gaussienne). La pression osmotique peut par suite &re considerte comme le stimulus actif commun a toutes les solutions utilisees pour provoquer la douleur dentinaire. Zusammenfassung-Es wurde beobachtet, da8 eine Beziehung zwischen osmotischem Druck und schmerzverursachender Fahigkeit existiert, wenn CaCl,-Losungen im Bereich von 200-2800 atm auf Dentin angewandt werden (ANDERSONund RONNING, 1962). Versuchsweise wurden Experimente durchgeftihrt, urn den frtiheren MiRerfolg zu erkl%ren, diese Beziehung mit anderen Ldsungen zu bestatigen. Die Versuche teilten sich in zwei Gruppen: Solche mit Losungen im Bereich von 25-700 atm und andere im Bereich von 200-2800 atm. Wie zuvor wurde ein Sensibilitatsverlust wlhrend eines Experiments beobachtet, er wurdejedoch nur durch Liisungen mit hohem osmotischen Druck verursacht. Mit Ausnahme der ersten Stimulations-serie im
426
D. J. ANDERSONANDB. MA~WS hohen Bereich werden deshalballeweiterenan Dentin mit abnehmender Sensitivitat angcwandt worden sein; daher sind die Ergebnisse dieser splteren Applikationen nicht mit den mit Liisungen niedrigen osmotischen Druckes erhaltenen Resultaten vergleichbar. Vergleichbare Daten tiber den gesamten Bereich des osmotischen Druckes von 25-2800 atm wurden gewonnen, indem lediglich die ersten Ergebnisse jeder Serie im hohen Bereich ausgewlhlt und alle Ergebnisse bei niedrigem osmotischem Druck verwendet wurden. Bei dieser Auswahl fallen die graph&h dargestellten Punkte des schmerzverursachenden Druckes und der log des osmotischen Druckes im Sinne einer sigmoiden Kurve ab. Es kann angenommen werden, da8 diese Kurve die Verteilung von Schmerzreizen innerhalb der Probandengruppe, in Einheiten des log des osmitischen Druckes definiert, darstellt. Die Probit-Transformation hat erwiesen, da8 die Verteilung normal ist (Gaussian). Der osmotische Druck kann deshalb als der allein im Dentin allen schmerzverursachenden LSsungen gemeine, wirksame Reiz aufgefaBt werden.
REFERENCES ANDERSON,D. J. and RONNING, G. A. 1962. Osmotic excitants of pain in human dentine. Archs oral Biol. 7, 513-523. ANDERSON, D. J., MAI-I-HEWS,B. and SHELTON,L. E. 1967. Variations in the sensitivity to osmotic stimulation of human dentine. Archs oral Biol. 12,43-41. EMMENS,C. W. 1948. Principles of Biological Assay, p. 150. Chapman and Hall, London.