A mathematical model for the progression of dental caries

TL;DR

This paper develops a mathematical model for dental caries progression, incorporating microscopic processes, anisotropic diffusion, and geometric changes, and validates it through numerical simulations and experimental comparisons.

Contribution

It introduces a novel macroscopic model derived from microscopic reactions, accounting for anisotropic diffusion and enamel melting effects in dental caries progression.

Findings

Anisotropic diffusion significantly affects caries progression rates.

Numerical simulations align with experimental observations.

The model predicts geometric changes in enamel during decay.

Abstract

A model for the progression of dental caries is derived. The analysis starts at the microscopic reaction and diffusion process. The local equations are averaged to derive a set of macroscopic equations. The global system includes features such as anisotropic diffusion and local changes in the geometry due to the enamel melting. The equations are then solved numerically. The simulations highlight the effect of anisotropy. In addition we draw conclusions on the progression rate of caries, and discuss them in light of a number of experiments.