Modeling of Diffusion Transport through Oral Biofilms with the Inverse Problem Method

Abstract

Aim

The purpose of this study was to develop a mathematical model to quantitatively describe the passive transport of macromolecules within dental biofilms.

Methodology

Fluorescently labeled dextrans with different molecular mass (3 kD, 10 kD, 40 kD, 70 kD, 2 000 kD) were used as a series of diffusion probes. Streptococcus mutans, Streptococcus sanguinis, Actinomyces naeslundii and Fusobacterium nucleatum were used as inocula for biofilm formation. The diffusion processes of different probes through the in vitro biofilm were recorded with a confocal laser microscope.

Results

Mathematical function of biofilm penetration was constructed on the basis of the inverse problem method. Based on this function, not only the relationship between average concentration of steady‐state and molecule weights can be analyzed, but also that between penetrative time and molecule weights.

Conclusion

This can be used to predict the effective concentration and the penetrative time of anti‐biofilm medicines that can diffuse through oral biofilm. Furthermore, an improved model for large molecule is proposed by considering the exchange time at the upper boundary of the dental biofilm.

Keywords

oral biofilm / diffusion model / boundary condition / inverse problem method