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

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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.