A Theoretical Analysis of the Effects of Plaque Thickness and Initial Salivary Sucrose Concentration on Diffusion of Sucrose into Dental Plaque and its Conversion to Acid During Salivary Clearance

Abstract

A mathematical model, written in FORTRAN, has been developed to simulate the interrelated processes of salivary sucrose clearance from the mouth, diffusion of sucrose into dental plaque, and conversion of sucrose to acid and glucan. Reaction of acid with enamel is not included in the model. A total of 28 parameters can be varied by the user, and the relative importance of the different factors affecting acid formation can be assessed. The output of the program gives sucrose and acid concentrations and pH at different depths within the plaque. The initial variables studied were plaque thickness, the salivary sucrose concentration, and the duration of exposure of the plaque to sucrose. Stephan curves typical of those recorded in vivo were generated by the model. With any particular salivary sucrose concentration, there was an optimum plaque thickness at which a minimum pH was achieved at the enamel surface, with very thin or thick plaque samples producing a smaller pH fall. With thick plaque, the minimum pH was often not achieved at the inner surface but at some intermediate depth, which may explain the location of early caries lesions in fissures. The extent of the pH fall at the inner surface and the duration of the pHminimum region of the Stephan curve were directly related to the initial salivary sucrose concentration and to the duration of exposure to sucrose prior to normal salivary clearance. Simulation of a water rinse at as short a time as two min after the beginning of normal salivary sugar clearance showed that this procedure had only a very small effect on the shape of the Stephan curve. Thus, the maximum salivary sucrose concentration achieved prior to normal salivary clearance appears to be a major factor which determines the extent of the pH fall at the enamel surface of the plaque.