Mathematical modelling of tooth demineralisation and pH profiles in dental plaque

A mathematical model of dental plaque has been developed in order to investigate the processes leading to dental caries. The one-dimensional time-dependent model integrates existing knowledge on biofilm processes (mass transfer, microbial composition, microbial conversions and substrate availability) with tooth demineralisation kinetics. This work is based on the pioneering studies of Dibdin who, nearly two decades ago, build a mathematical model roughly describing the metabolic processes taking place in dental plaque. We extended Dibdin's model with: multiple microbial species (aciduric and non-aciduric Streptococci, Actinomyces and Veillonella), more metabolic processes (i.e., aerobic and anaerobic glucose conversion, low and high glucose uptake affinity pathways, formation and consumption of storage compounds), ion transport by Nernst–Planck equations, and we coupled the obtained pH and chemical component gradients inside the plaque with tooth demineralisation. The new model implementation was complemented with faster and more rigorous numerical methods for the model solution. Model results confirm the protective effect of Veillonella due to lactate consumption. Interestingly, on short term, the storage compounds may not necessarily have a negative effect on demineralisation. Individual feeding patterns can also be easily studied with this model. For example, slow (“social”) consumption of sugar-containing drinks proves to be more harmful than drinking the same amount over a short period of time.

► A one-dimensional time-dependent mathematical model of dental plaque is presented.
► The model integrates (bio)chemical processes in the plaque with tooth demineralisation.
► The model describes typical Stephan curves in different conditions.
► On short term storage compounds might not have a negative effect on demineralisation.
► Slow drinking of sugar containing drinks proves to be more harmful than gulping.