title: Modeling of diffusion transport through oral biofilms with the inverse problem method.
abstract: OBJECTIVE
  The purpose of this study was to develop a mathematical model to quantitatively describe the passive transport of macromolecules within dental biofilms.
  
  
  METHODS
  Fluorescently labeled dextrans with different molecular mass (3 kD, 10 kD, 40 kD, 70 kD, 2000 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.
  
  
  CONCLUSIONS
  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.
authors.affiliation: Department of Endodontics, Ninth People's Hospital, Shanghai Jiao Tong University School of Medicine, Shanghai Key Laboratory of Stomatology, Shanghai, China.
authors.forename: Rui
authors.initials: R
authors.lastname: Ma
authors.forename: Jie
authors.initials: J
authors.lastname: Liu
authors.forename: Yun-tao
authors.initials: YT
authors.lastname: Jiang
authors.forename: Zheng
authors.initials: Z
authors.lastname: Liu
authors.forename: Zi-sheng
authors.initials: ZS
authors.lastname: Tang
authors.forename: Dong-xia
authors.initials: DX
authors.lastname: Ye
authors.forename: Jin
authors.initials: J
authors.lastname: Zeng
authors.forename: Zheng-wei
authors.initials: ZW
authors.lastname: Huang
mesh_terms: D000190:Actinomyces / Q000254:growth & development; D000465:Algorithms; D018441:Biofilms / Q000254:growth & development; D001692:Biological Transport; D003773:Dental Plaque / Q000382:microbiology*; D003911:Dextrans / Q000493:pharmacokinetics; D004058:Diffusion; D005456:Fluorescent Dyes / Q000493:pharmacokinetics; D016967:Fusobacterium nucleatum / Q000254:growth & development; D046911:Macromolecular Substances / Q000493:pharmacokinetics; D018613:Microscopy, Confocal; D008954:Models, Biological; D015336:Molecular Probe Techniques; D013295:Streptococcus mutans / Q000254:growth & development; D013298:Streptococcus sanguis / Q000254:growth & development
chemical_list: D003911:Dextrans; D005456:Fluorescent Dyes; D046911:Macromolecular Substances