Perturbation method to model enamel caries progress

TL;DR

This paper presents a theoretical model of enamel caries progression based on diffusion-reaction equations, using a perturbation method to approximate acid diffusion and enamel demineralization, validated against numerical and experimental data.

Contribution

It introduces a novel perturbation-based analytical approach to model acid diffusion and enamel demineralization in caries development.

Findings

Analytical solutions closely match numerical results.

Model accurately reflects experimental data.

Provides insights into acid diffusion dynamics in enamel.

Abstract

We develop a theoretical model of the carious lesion progress caused by acids diffusing into the tooth enamel from the dental plaque. The acids react with static hydroxyapatite, which leads to demineralization of the enamel, and consequently to the development of the carious lesion. The model utilizes the diffusion-reaction equations with one static and one mobile reactant where the reaction term is proportional to the product of concentrations of acids and of mineral. The changes of concentrations are calculated approximately by means of a perturbation method. The analytical approximate solutions are compared with the numerical ones and experimental data.