Mathematic Modeling of Macromolecular Diffusion through in vivo Oral Biofilm

Objectives: The aim of this study was to examine the diffusion mode of macromolecules through in vivo oral biofilm with mathematical description. Methods: Plastic slabs were placed on intra-oral devices by healthy volunteers (n=20) for 24h to collect in vivo dental plaque biofilm, then biofilms were removed and incubated at room temperature for 30 mins with fluorescent marked dextrans  with molecular weights(3KD,10KD,40KD,70KD,2000KD), dynamical recordings of macromolecules diffusion through dental plaque biofilm were conducted by confocal laser scanning microscopy. Results: Compared with diffusion in bulk water, diffusion in dental plaque biofilm was markedly slower. The diffusion rate of each dextran appeared to be constant, and the dextran with lower molecular weight diffused much faster than that of higher molecular weight. Based on the following assumptions: the velocity of molecular diffusion is equal at any time, the probability of molecular diffusion direction is equal at any time and there are no external forces to interfere with the molecular diffusion. A mathematical modeling of biofilm diffusion was derived with the following equations to describe the mode :

Conclusion: Mathematical description of biofilm diffusion might be a better method for further understanding macromolecular diffusion through dental plaque biofilm.