Plaque Fluid and Diffusion: Study of the Cariogenic Challenge by Computer Modeling

Abstract

Every cariogenic challenge involves a mixture of convective transport, diffusive transport, and biochemical reactions, plus physico-chemical reactions (including charge-coupling of diffusion), all of which together require numerical methods for their analysis. This presentation describes a one-dimensional finite-difference computer model of the cariogenic process, and some conclusions obtained from it.

Sugar clearance from the mouth, together with site-dependent exchange between the bulk saliva and plaque surface via a salivary film, is combined with a finite-difference model of events occurring within the dental plaque. The latter includes: sugar diffusion and pH-dependent acid production; diffusion and dissociation equilibria for two acid end-products of fermentation and their anions (acetate and lactate); diffusion and dissociation equilibria of phosphate buffer; diffusion of potassium and chloride; diffusion of protons and simultaneous equilibration with fixed and mobile buffers. So that proper concentration distributions consistent with local charge neutrality can be ensured, an algorithm called Q-couple is used to impose charge-coupling between the fluxes of different ions including fixed charges. Mineral dissolution and precipitation are modeled as part of the same equilibrium calculations.

The predictions of the model are compared with those of an earlier, much simpler one, in which fixed buffers were not included. It is shown that the known concentration of fixed buffer greatly extends the low pH of a Stephan curve. The isoelectric point of the plaque bacteria also appears to be of importance. The effects of various concentrations of mobile buffers, including acetate, are investigated. It is also shown that varying plaque/saliva contact over the known range derived from published studies has a profound effect on the modeled cariogenic challenge.

Get full access to this article

View all access options for this article.

References

Albery, W.J. ; Greenwood, A.R. ; and Kibble, R.F. (1967): Diffusion Coefficients of Carboxylic Acids, Trans Faraday Soc 63:360-368.

Collins, L.M.C. and Dawes, C. (1987): The Surface Area of the Adult Human Mouth and Thickness of the Salivary Film Covering the Teeth and Oral Mucosa, J Dent Res 66:1300-1302.

Davies, C.W. (1962): Ion Association, 2nd ed., London: Butterworths.

Dawes, C. and Dibdin, G.H. (1986): A Theoretical Analysis of the Effect of Plaque Thickness and Initial Sucrose Concentration on Diffusion of Sucrose into Dental Plaque and its Conversion to Acid during Salivary Clearance, J Dent Res 65:89-94.

Dawes, C. and Watanabe, S. (1987): The Effect of Taste Adaptation on Salivary Flow Rate and Salivary Sugar Clearance, J Dent Res 66:740-744.

Dibdin, G.H. (1981): Diffusion of Sugars and Carboxylic Acids Through Human Dental Plaque in vitro, Arch Oral Biol 26 :515-523.

Dibdin, G.H. (1984): A Brief Survey of Recent in vitro Work on Diffusion of Small Ions and Molecules in Dental Plaque. In: Cariology Today, Int. Congr., Zurich (1983), B. Guggenheim , Ed., Basel: Karger , pp. 191-198.

Dibdin, G.H. (1989a): A Simple Add-on Algorithm to Extend One-dimensional Finite Difference Diffusion Calculations to Include Charge-coupling, Comput Appl Biosci 5:19-26.

Dibdin, G.H. (1989b): Computer Modelling of Stephan Curves with Saliva/Plaque Exchange via a Thin Salivary Film, Caries Res 23:441, Abst. No. 55.

10.

Dibdin, G.H. (1990): Effect on a Cariogenic Challenge of Saliva/ Plaque Exchange via a Thin Salivary Film Studied by Mathematical Modelling, Caries Res (in press).

11.

Dibdin, G.H. and Reece, G.L. (1984): Computer Simulation of Diffusion with Reaction in Dental Plaque, Caries Res 18:191-192, Abst. No. 110.

12.

Dibdin, G.H. and Shellis, R.P. (1988): Physical and Biochemical Studies of Streptococcus mutans Sediments Suggest New Factors Linking the Cariogenicity of Plaque with its Extracellular Polysaccharide Content, J Dent Res 67:890-895.

13.

Edgar, W.M. and Tatevossian, A. (1971): The Aqueous Phase of Plaque. In: Tooth Enamel II, R.W. Feamhead and M.V. Stack , Eds., Bristol, UK: John Wright, pp. 229-232.

14.

Goulet, D. and Brudevold, F. (1984): Salivary Glucose Clearance after Rinsing with Solutions of Different Concentrations of Glucose, Caries Res 18:481-487.

15.

Higuchi, W.I. ; Young, F. ; Lastra, J.L. ; and Koulour-Ides, T. (1970): Physical Model for Plaque Action in the Tooth-Plaque-Saliva System, J Dent Res 49:47-60.

16.

Lecomte, P. and Dawes, C. (1987): The Influence of Salivary Flow Rate on Diffusion of Potassium Chloride from Artificial Plaque at Different Sites in the Mouth , J Dent Res 66:1614-1618.

17.

Margolis, H.C. ; Moreno, E.C. ; and Murphy, B.J. (1985): Importance of High pKa Acids in Cariogenic Potential of Plaque, J Dent Res 64:786-792.

18.

Shellis, R.P. (1988): A Microcomputer Program to Evaluate the Saturation of Complex Solutions With Respect to Biominerals, Comput Appl Biosci 4:373-379.

19.

Shellis, R.P. and Dibdin, G.H. (1988): Analysis of the Buffering Systems in Human Dental Plaque, J Dent Res 67:436-446.

20.

Smith, G.D. (1985): Numerical Solutions of Partial Differential Equations. Finite Difference Methods, 3rd ed., Oxford: Clarendon Press.

21.

Stralfors, A. (1950): The Bacterial Chemistry of Dental Plaques, Odont Tidskr 58:155-341.

22.

Weatherell, J.A. ; Strong, M. ; Robinson, C. ; and Ralph, J.P. (1986): Fluoride Distribution in the Mouth after Fluoride Rinsing, Caries Res 20:111-119.