Calcium_Chow_1994 by amold

J Dent Res 73(1):26-32,January, 1994

Effects on Whole Saliva of Chewing Gums Containing Calcium Phosphates L.C. Chow, S. Takagi, Rj. Shern', T.H. Chow2, K.K. Takagi3, and B.A. Sieck American Dental Association Health Foundation, Paffenbarger Research Center, National Institute of Standards and Technology, Gaithersburg, Maryland 20899; 'National Institute of Dental Research, National Institutes of Health, Bethesda, Maryland; 2present address, University of Maryland, College Park, Maryland; and 3present address, Vanderbilt University, Nashville, Tennessee

Abstract. To evaluate chewing gums as a vehicle to increase salivary mineral saturation levels and enhance salivation, monocalcium phosphate monohydrate (MCPM) and an equimolar mixture of tetracalcium phosphate (TTCP) with dicalcium phosphate anhydrous (DCPA) were chosen as experimental chewing gum additives. Each of eight subjects chewed a commercial sugarless bubble gum (control) f or 16 min or the same gum to which 5 wt% of MCPM or the TTCPDCPA mixture had been added. The saliva samples collected every 2 min were analyzed for weight, pH, and total calcium (Ca) and phosphate (P) concentrations. Both experimental gums were found to increase significantly the Ca and P concentrations of saliva during the 16-minute period even more thanwithapreviouslyevaluatedgum that containeddicalcium phosphate dihydrate. The degree of saturation of tooth mineral was significantly increased by both experimental gums, with the greater increase being produced by the TTCP-DCPA gum. The MCPM gum produced a significantly greater saliva flow and a lower salivary pH than did the control and TTCPDCPA gums. The results suggest that the experimental gums may be useful for promoting remineralization in general and for inducing salivation in xerostomic patients. Key words. Saliva, Minerals, Salivation, Stimulation, Calcium Phosphates. Received March 9,1993; Accepted September 9,1993. Certain commercial materials and equipment are identified in this paper to specify the experimental procedure. In no instance does such identification imply recommendation or endorsement by the National Institute of Standards and Technology or the ADA Health Foundation or that the material or equipment identified is necessarily the best available for the purpose. This investigation was supported, in part, by USPHS Research Grant DE05354 to the American Dental Association Health Foundation from the National Institutes of Health-National Institute of Dental Research and is part of the dental research program conducted by the National Institute of Standards and Technology in cooperation with the American Dental Association Health Foundation.

Introduction Chewing gumshave the potential of being an effective vehicle for delivering therapeutic agents to dentition because they permit protracted contact of the agent with the teeth with minimal efforts on the part of the patient. A recent paper (Edgar and Geddes, 1990) reviewed studies that evaluated the effectiveness of a number of potentially anticarious agents in chewing gums. Among the agents that have received considerable attention was dicalcium phosphate dihydrate (DCPD), CaHPO4'2H20, which, at a dose of 7.5 wt%, was assessed for its effects on elevating the calcium (Ca) and phosphate (P) concentrations in saliva (Pickel and Bilotti, 1965). A chewing gum that contained 10 wt% DCPD was further assessed for its anticarious effects in two clinical studies (Finn and Jamison, 1967; Richardson et al., 1972). The results from the latter two studies indicate that while the sugar-DCPD gum produced a lower caries score than did the sugar gum, the cariogenicity of the sugar-DCPD gum was equivalent to that of the sugar-free gum. Based on the solubility phase diagram for calcium phosphates (Brown, 1973), it would appear that DCPD is not the most suitable calcium phosphate salt to be used as a chewing gum additive for the purpose of producing increased salivary Ca and P concentrations. There are other calcium phosphate compounds or mixtures of compounds that are more soluble and that may be more effective in modifying the salivary Ca and P concentrations than DCPD. Thus, the possibility exists that with the use of these other calcium phosphates, the anticarious effectiveness of calcium phosphate-containing chewing gum can be significantly improved over that produced by the DCPD-containing gums reported in previous studies. Monocalcium phosphate monohydrate (MCPM), Ca(H2PO4)2 H20, is an acidic salt that is considerably more

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lo0

Time, min

Figure 1. Mean salivary flow (mL/min) of subjects while chewing an experimental or the control gum. Bars denote standard errors (n = 8).

Figure 2. Mean pH of saliva samples collected from subjects while chewing an experimental or the control gum. Bars denote standard errors (n = 8).

soluble than DCPD. Therefore, a MCPM-containing chewing gum may be expected to produce signif icantly greater increases in salivary Ca and P concentrations than those producible by DCPD. Such a gum may also cause a decrease in salivary pH due to the acidic nature of MCPM. An equimolar mixture of tetracalcium phosphate (TTCP), Ca4(PO4)20, and dicalcium phosphate anhydrous (DCPA), CaHPO4, in finely divided powder forms has been shown (Fukase et al., 1990) to convert completely to hydroxyapatite (OHAp) within 4 h (at 37'C) after the powder is mixed with a small amount of water or a dilute (20 mmol/L) phosphoric acid solution. The formation of OHAp in this system appears to be considerably faster than in systems where formation of OHAp was obtained by dissolution of DCPA or DCPD alone (Tung et al., 1985; Ishikawa and Eanes, 1992). This suggests that the dissolution of the TTCP-DCPA mixture must lead to a much higher level of supersaturation with respect to OHAp than that produced by dissolution of DCPD or DCPA. Therefore, such a mixture, when used as a chewing gum additive, may also be more effective in increasing the remineralizing potential of saliva than DCPD may be. In the present study, two experimental chewing gums that contained 5 wt% of either MCPM or the TTCP-DCPA mixture were evaluated for their effects on salivary pH, Ca and P concentrations, and the degree of saturation with respect to OHAp. The major purposes of the study were to determine the extent and duration of Ca and P concentration increases resulting from chewing the gums that contained the two calcium phosphate additives as compared with the control gum, which was the same gum without an additive. Since salivary flow is stimulated by gum chewing, the rate of salivary flow was also measured. The results from this study should provide information on the remineralization potential and on saliva stimulation effects of these gum additives.

Materials and methods Control and experimental chewing gums A commercially obtained sugar-free chewing gum (sugarless

BubbleYum,Planter'sLifesaverCo.,Winston-Salem,NC;grape-

flavored; nominal weight, 5 g per stick) was used as the gum base for formulation of the experimental chewing gums, and it also served as the control gum. Experimental gum A contained 5 g of the gum base and 0.25 g of MCPM. Experimental gum B contained 5 g of gum base and 0.25 g of the TTCP-DCPA mixture (0.182 g of TTCP and 0.068 g of DCPA). The calcium phosphate additives were uniformly blended into the gum base by hand-kneading. USP- or NF-grade MCPM and DCPA were used. We prepared TTCP, which was not commercially available, by heating an equimolar mixture of reagent-grade calcium carbonate and DCPA to 1500째 C for 6 h (Fukase et al., 1990). The DCPA and TTCP were ground in ethanol in a ball mill (Planetary ball mill model PM4, Brinkmann Instruments, Westbury, NY) to median particle sizes (Centrifugal Particle Size Analyzer, Model SA-CP3, Shimazu Instruments, Columbia, MD) of 0.8 and 1.2 mm, respectively. Recruitment of subjects Four male and four female volunteers (mean age, 37) who were in good general and dental health were recruited for the study. The subjects had normal salivary flow (> 0.2 mL/min) and did not wear orthodontic bands.

Experimental procedure Sample collection for all subjects was conducted 2 h after lunch (between 2:30 and 3:30 pm) on a weekday. Each subject was asked to spit into a pre-weighed test tube for a two-minute

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Table. Newman-Keuls multiple comparison summary Treatmenta

Volume

Control DCPA-TTCP

Time (min) 6 8

MCPM

Control DCPA-TTCP

MCPMI

[Cal

Control l MCPMI DCPA-TTCP

[P1

Controlii

DCPA-TTCP MCPMI

plAP

Control MCPMI DCPA-TTCPI

The order of treatment groups within each category varies for best presentation of the statistical ranking. Groups connected by a vertical line are not significantly different (p > 0.05). Control and MCPM groups are not significantly different.

period. He/she then started chewingeither an experimental or the control gum. The subject was asked to continue to spit into a pre-weighed test tube that was replaced every 2 min as the saliva was produced. The saliva samples were collected for eight two-minute periods after the chewing started. Data on the effects of the two experimental gums and the control gum on saliva were obtained from all eight subjects on different days that were at least 3 days apart. Saliva sample analysis The weight of the saliva collected during the two-minute period just before chewing the gum and during the eight two-minute periods after the start of gum-chewing was determined. The weight was converted to volume, based on the assumption of a density value of 1.05 g/cm3 (Zipkin, 1970). The pH values of the saliva samples were measured with a pre-calibrated combination pH electrode (Orion Research, Cambridge, MA) immediately after collection, with the test tube capped to minimize the loss of CO2. The precision of the pH measurement was estimated to be 0.05 pH units. In order to determine the true Ca and P concentrations in the saliva samples, we first removed any mineral particles that might be suspended in the saliva. In a preliminary experiment, the 0-to-two-minute saliva samples were collected f rom two subjects for each of the two experimental gums and also from a DCPD-containing gum (see "Discussion"). Immediately after collection, each saliva sample was divided into

three portions and processed by (a) filtration through a 0.2,um pore-size filter, (b) centrifugation at 34,300 m/s2 for 15 min, and (c) centrifugation at 137,200 M/s2 for 15 min. The measured Ca concentrations in the three portions (a, b, and c) were norma.lized relative to the Ca concentration of portion b. The normalized Ca concentration values (mean + S.D.; n = 6) of the three portions a, b, and c were 1.11 Âą 0.12, 1.0 + 0.0, and 1.08 Âą 0.13, respectively. These values were numerically different by about 10%, but the differences were not statisticallysignif icant(p >0.05). The 0-to-two-minute saliva samples were chosen for this test because they would have the highest Ca and P concentrations from a given additive-containing gum formulation, and because these samples were also most likely to contain the largest amounts of suspended mineral particles. The results obtained in the preliminary study indicated that centrifugation at 34,300 M/s2 for 15 min was as effective for removing mineral particles as was filtration through the 0.2-,um filter, and that the Ca and P concentrations measured in the supernatant would represent the total soluble Ca and P concentrations in the original saliva sample. Thus, throughout the study, the saliva samples were centrifuged at 34,300 M/s2 for 15 min, 1 mL of the supernatant was transferred to a test tube, and 0.025 mL of 5 mol/L perchloric acid was added to each sample to prevent possible precipitation of calcium phosphates before the analyses for Ca and P concentrations were performed. The analyses were conducted with the use of previously described spectrophotometric

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Chewing Gums Containing Calcium Phosphates

Time, min

Time, min Figure 3. Mean calcium concentration (mmol/L) of saliva samples collected from subjects while chewing an experimental gum or the control gum. Bars denote standard errors (n = 8).

Figure 4. Mean phosphate concentration (mmol/L) of saliva samples collected from subjects while chewing an experimental gum or the control gum. Bars denote standard errors (n = 8).

methods (Vogel et al., 1983), with an estimated precision of 2.5% in each method.

The control gum produced a slight decrease in pH in the 0to-two-minute sample (Fig. 2). This was probably caused by the acidic flavoring agents in the gum. Starting from 2 min, the pH increased and remained above the baseline value throughout the experimental period. The pH values of the saliva samples in the MCPM gum group were significantly (p < 0.05) lower than those of the corresponding samples in the control group during the entire 16-minute period (Table). In contrast, the pH values of the saliva samples in the TTCP-DCPA gum group were not significantly different from those of the controls (Table). The control gum produced a slight increase in the Ca concentration in the two-minute sample but no significant effect in the subsequent samples (Fig. 3). Small but significant (p < 0.05) decreases in the P concentration from that of the unstimulated saliva (time 0 in Fig. 4) were observed in all the samples in this group. In contrast to the control gum, both experimental gums produced significant increases in the Ca and P concentrations (Table). The MCPM gum produced significant (p < 0.05) increases in the Ca concentrations over those of the controls during the two- to 12-minute period, while the TTCP-DCPA gum produced significant increases in the Ca concentrations over those of the controls for the entire experimental period (Table). The Ca concentrations in the TTCP-DCPA group were also significantly higher than those in the corresponding samples in the MCPM gum group between 6 and 16 min. Both experimental gums also produced significantly higher P concentrations when compared with the controls during the entire experimental period, with greater (p < 0.05) increases being produced by the MCPM gum during the time period from 2 to 10 min

Calculation of degree of saturation with respect to OHAp In order to estimate the degree of saturation with respect to OHAp of the saliva samples, we made the following assumptions: (1) 51.5% of the total Ca concentration was in ionized form (Matsuo and Lagerlof, 1991), (2) the ionic strength of saliva was 91 mmol/L (Lagerl6f, 1983) plus that produced by the dissolved Ca and P, and (3) all of the measured P is in the inorganic form (Lagerlof, 1983). With these assumptions, we computed the ion activity product (IAP) of OHAp using a previously described procedure that took into consideration ion pairs formation (Gregory et al., 1991). Statistical analysis of the data The mean and standard deviations of the experimentally measured values for each experimental group were computed, and a multiple-comparison t test (Newman-Keuls) procedure (Wall, 1986) was used to determine if significant differences existed among the study groups (Table).

Results Chewing any of the three gums leads to a significant increase in salivary flow throughout the 16 min over the baseline value (time 0 in Fig. 1). The mean salivary flow volumes in the MCPM group were numerically greater at all time points than the means of the control or the TTCP-DCPA gum groups. However, due to the relatively large standard deviations, only the four-minute samples were found to be significantly (p < 0.05) different (Table). The salivary flow volumes in the TTCPDCPA and the control groups were f ound not to be statistically different (Table).

(Table).

The mean -log(IAPOHAp) values (where IAP denotes ion activity product) of the saliva samples are shown in Fig. 5.

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J Dent Res 73(1) 1994

a,5o 045 0.4Q

,-~

"40 -

Time, min Figure 5. Mean degree of saturation with respect to OHAp, expressed as -Log(IAPOHAp), of saliva samples collected from subjects while chewing an experimental gum or the control gum. The dashed line represents solutions that are saturated. Bars denote standard errors (n = 8).

Also shown is a line that represents the solubility product constant of OHAp [-log(KspOHAp) = 58.5 (McDowell et al., 1977)]. Those points that are farther below the -log(KspOHAp) line represent solutions that are more supersaturated with respect to OHAp. The degrees of supersaturation in the samples from the MCPM gum group were found to be numerically greater than those from the controls throughout the experimental period. However, due to the relatively large standard deviations, the differences were significant (p < 0.05) only for the samples collected at time periods of 4,6,8, and 14 min. In contrast, the degrees of supersaturation in the samples from the TTCP-DCPA gum were significantly greater than the corresponding values in the control and the MCPM groups

throughout the experimental period (Table).

Discussion Pickel and Bilotti (1965) reported that nearly all of the measured Ca and P in the saliva samples f rom subjects who chewed a DCPD-containing gum can beattributed to mineral particles present in the saliva samples. As described in the "Methods" section, in the present study, three methods were evaluated for removal of the possible mineral suspensions in the saliva samples before the Ca and P analyses were conducted. The results show that samples processed by centrif ugation at 34,300 or 137,200 M/s2 for 15 min had the same Ca concentration value as that in the sample filtered through a 0.2-,um filter. Thus, unless the saliva samples contained microscopic mineral particles that were substantially smaller than 0.2 ,um, the Ca and P values reported in Figs. 3 and 4, respectively, would represent the solution Ca and P concentrations in the samples. If the centrifuged or filtered saliva samples did contain microscopic mineral suspensions, they were unlikely to have been from the powders dislodged from the gum, as suggested by

Pickel and Bilotti (1965), because the particle sizes of the gum additives were considerably larger than 0.2 ,um. The possibility of the presence of some microscopic suspensions cannot be totally ruled out, because very high degrees of supersaturation (with respect to OHAp) were found in some of the saliva samples in the experimental gum groups (Fig. 5). The suspensions, if present, might form as a result of the high solubility of the gum additives, MCPM and the TTCP-DCPA mixture, making the saliva supersaturated with respect to OHAp, DCPD, octacalcium phosphate, or even amorphous calcium phosphate. In future studies it would be desirable to measure Ca2+ activities directly with the use of a calcium ion electrode (Lagerlof,1983;YankellandEmling,1990;MatsuoandLagerlof, 1991), in conjunction with measurement of total Ca concentration, to clarify the relationship between the two parameters. The Ca and P concentrations observed in the saliva before the start of chewing were similar in all three experimental groups and were in good agreement with the data reported in the literature for whole saliva (Matsuo and Lagerlof, 1991). In the control group, the salivary Ca concentration remained approximately the same during the 16-minute period of gum chewing, but the P concentrations were significantly (p < 0.05) lower than the P concentration in the baseline sample. The latter results are consistent with the previous finding (Suddick et al., 1980; Lagerlof, 1983) that the P concentration decreased with increasing parotid salivary flow. The salivary flow rates in the control group were found to follow a pattern similar to that reported previously (Dawes and Macpherson, 1992), i.e., a large initial increase followed by a smaller but significant elevation throughout the chewing period. The changes in salivary pH in the control group followed a pattern similar to that reported previously (Dawes and Macpherson, 1992) for a gum that contained some organic acids that caused a transient decrease in pH in the two-minute sample before the pH rose to a level that was slightly but significantly (p < 0.05) higher than the baseline value. In the present study, the initial decrease in pH is most probably a result of the flavoring agents of the gum used in the study. The degree of supersaturation is an important parameter in controlling the deposition of calcium phosphate mineral as in the mineralization of tooth enamel. Theresultsfrom the present study show that the salivary Ca and P concentrations and the degree of supersaturation with respect to OHAp were significantly increased by the gums that contained 5 wt% of either MCPM or the TTCP-DCPA mixture (Table). These findings are in contrast to the results obtained from a DCPD-containing gum reported previously (Pickel and Bilotti, 1965). Pilot work with DCPD-containing gum showed that the DCPD additive produced moderate but significant increases in salivary Ca and P levels only in the two- and four-minute samples. This finding suggests that, while in the twoclinical trials the DCPDcontaining gums were chewed f or 30 min, the mineral saturation level of saliva was likely to be elevated only during the first 4 min. The data also show that both the extent and duration of the increases in mineral concentration and degree of

J Dent Res 73(l) 1994

Chewing Gums Containing Calcium Phosphates

supersaturation obtained from the DCPD gum were much lower than those obtained from either the MCPM or TTCPDCPA gums. This is not surprising, because MCPM is much more soluble than any other calcium phosphate phases under neutral pH conditions (Chow and Brown, 1975; Takagi et al., 1987), and the TTCP-DCPA mixture has a unique dissolution property in that it produces a very high degree of supersaturation with respect to OHAp (Brown and Chow, 1987). Thus, the present f indings wouldsuggest that both the MCPM and TTCPDCPA gums have significantly greater remineralizing or anticarious potentials than does the DCPD gum. The mean salivary f low stimulated by the MCPM gum was greater than that stimulated by the control gum during the experimental period (Fig. 1). This was accompanied by the significantly (p < 0.05) lower pH values found in the saliva (Table). Despite the lower pH, the mineral saturation level was significantly (p < 0.05) greater than that of the corresponding samples in the control group during several time periods because of the significantly higher Ca and P concentrations produced by the MCPM gum. These results suggest that the MCPM gum might be an effective means for promoting salivation in dry-mouth patients and, at the same time, for providing a remineralizing condition rather than the demineralizing challenge often brought about by salivation enhancement regimens (Newbrun, 1981; Seward, 1984). The TTCP-DCPA gum produced a significantly (p < 0.05) greater increase in the mineral supersaturation level than did the MCPM gum (Table), suggesting that the TTCP-DCPA gum may have a remineralization potential greater than that obtainable from the MCPM gum. Such a gum therefore has the potential to produce a sufficiently large cariostatic effect to be used as a caries-preventive agent. An examination of the solubility isotherms of the various calcium phosphate phases (Brown, 1973; Brown and Chow, 1987) suggests that other calcium phosphate compounds (especially c -tricalcium phosphate, DCPD, and octacalcium phosphate), when used in combination with either MCPM or TTCP, can also produce mineral supersaturation levels close to those observed in the two experimental gums tested and significantly higher than that attainable from DCPD alone. Previous clinical studies that evaluated the DCPD-containing gums involved several hundred children and required a time of 2 years or more. The nature of these studies precluded the possibility of including more than one experimental gum formulation in the study. With the advent of recently developed experimental techniques, such as intra-oral demineraliza-

tion/remineralization modelsandmicro-analytical techniques

for studying plaque compositions, it is now possible to evaluate the potential anticarious effects of a range of gum additives systematically, with considerably less time and effort than the time and effort required in the previous clinical studies. The data from the present study indicate that both the MCPM and TTCP-DCPA gums produced significantly greater effects on saliva than did the DCPD gum, and these experimental gums warrant further evaluation for their effects on plaque composi-

tion and on enamel and root lesions in intra-oral models.

References Brown WE (1973). Solubility of calcium phosphate and other sparingly soluble compounds. In: Environmental phosphorus handbook. Griffith EJ, Beeton JM, Spencer, Mitchell DT, editors. New York: Wiley & Sons, pp. 203-239. Brown WE, Chow LC (1987). A new calcium phosphate, water-setting cement. In: Cements research progress. Brown PW, editor. Westerville, OH: American Ceramic Society, pp. 352-379. Chow LC, Brown WE (1975). Formation of CaHPO4'2H2O in tooth enamel as an intermediate product of topical fluoride treatments. J Dent Res 54:65-76. Dawes C, Macpherson LMD (1992). Effects of nine different chewinggums and lozenges on salivary flow rate and pH. Caries Res 26:176182. Edgar WM, Geddes DMA (1990). Chewing gum and dental health-a review. Br DentJ 24:173-176. Finn SB, Jamison HC (1967). The effect of a dicalcium phosphate chewing gum on caries incidence in children: 30-month results.] Am Dent Assoc 74:987-995. Fukase Y, Eanes E, Takagi S, Chow LC, Brown WE (1990). Setting reactions and compressive strengths of calcium phosphate cements.J Dent Res 69:1852-1856. Gregory TM, Chow LC, Carey CM (1991). A mathematical model for dental caries: a coupled dissolution-diffusion process.J Res Natl Inst Stand Technol 96:593-604. Ishikawa K, Eanes ED (1993). The hydrolysis of anhydrous dicalcium phosphate into hydroxyapatite.J Dent Res 72:474-480. Lagerlof F (1983). Effects of flow rate and pH on calcium phosphate saturation in human parotid saliva. Caries Res 17:403-411. McDowell H, Gregory TM, Brown WE (1977). Solubility of Ca5(PO4)3OH in the system Ca(OH)2-H3PO4-H20 at 5,15, 25 and 37째C.] Res Nati Bur Stand (US) Part A Phys Chem 81A:273-281. Matsuo S, Lagerlof F (1991). Relationship between total and ionized calcium concentrations in human whole saliva and dental plaque

fluid. Arch Oral Biol 36:525-527. Newbrun E (1981). Xerostomia. Oral SurgOral Med Oral Pathol 51:262. Pickel FD, Bilotti A (1965). The effects of a chewing gum containing dicalcium phosphate on salivary calcium and phosphatejAL Med Soc 2:286-287. Richardson AS, Hole IW, Mccombie F, Kolthammer J (1972). Anticariogenic effect of dicalcium phosphate dihydrate chewing gum: results after two years.J Can Dent Assoc (no. 6):213-218. Seward GR (1984). Sialagogues for patients with sicca syndrome. Br

MedJ 228:407. Suddick RP, Hyde RJ, Feller RP (1980). Salivary water and electrolytes and oral health. In: The biologic basis of dental caries. Menaker L, editor. New York: Harper & Row, p. 132. Takagi S, Chow LC, Yamada EM, Brown WE (1987). Enhanced enamel F uptake bymonocalcium phosphate monohydrate gelsjDent Res 66:1523-1526. Tung MS, Chow LC, Brown WE (1985). Hydrolysis of dicalcium phosphate dihydrate in the presence or absence of calcium fluoride.j

Chow et al.

Dent Res 64:2-5. Vogel GL, Chow LC, Brown WE (1983). A microanalytical procedure forthedeterminationof calcium, phosphateandfluoride inenamel biopsy samples. Caries Res 17:23-31.

WallFJ(1986).Statisticaldataanalysishandbook.NewYork:McGrawHill, pp. 4.1-5.36.

J Dent Res 73(1)1994 Yankell SL, Emling RC (1989). Clinical study to evaluate the effects of three marketed sugarless chewing gum products on plaque pH, pCa, and swallowing rates.JClin Dent 1:70-74. Zipkin 1(1970). Biology of oral environment. In: Dental science handbook. Morrey LW, Nelsen RJ, editors. US DHEW Publication No. (NIH)72-336.three parameters (Weibull, 1951).