A Mathematical Model for Dental Caries: A Coupled Dissolution-Diffusion Process

Demineralization of tooth mineral in the caries process was studied using a computer model that simulates a diffusion controlled dissolution process. The model consists of a two-compartment system. An acidic solution in the outer ("plaque") compartment was assumed to be large in volume so that its composition remained constant during the process. The solution in the inner ("lesion") compartment was in equilibrium with the tooth mineral, but its composition changed in response to diffusion of ions between the two solutions through an infinitely thin barrier. The permselectivity of the diffusion barrier to cations and anions can be modified as desired thus allowing the effects of membrane on the diffusion-dissolution process to be examined. Because the losses of calcium (Ca) and phosphate (P) from the "lesion" to the "plaque" generally does not occur at a molar ratio of 5/3, the Ca to P ratio of the dissolving mineral, the composition of the "lesion" fluid can change significantly from the starting composition, and this in turn modifies the Ca and P fluxes. A steady state condition is eventually reached under which the ratio of flux of Ca to that of P becomes 5/3. The results of the simulation show that for a given "plaque" pH, the rate of demineralization at steady state was the highest for cation and the lowest for anion permselective membranes. These results were in good agreement with those from an experimental study under comparable conditions.