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LETTERS TO THE EDITOR |
1 Center for Biofilm Engineering, and Department of Chemical and Biological Engineering, Montana State University-Bozeman, Bozeman, MT 59717-3980, USA, phil_s{at}erc.montana.edu
To the Editor:
A recent paper by Watson et al. (J Dent Res 84:451–455, 2005) reported ex vivo measurements of fluoride ion penetration into dental plaque formed on removable implants worn by human volunteers. These data showed that brief exposures—30 sec to 2 min—of plaque biofilms to 1000 ppm fluoride were insufficient to deliver the full concentration of fluoride throughout the depth of the biofilm. Here, I report the extraction of a numerical estimate of the effective diffusivity of fluoride in dental plaque from these valuable data. The reason to bother determining the diffusion coefficient is that this is an intrinsic parameter that can be compared between studies and can form the basis of predictive calculations.
Application of the diffusion equation to the data of Watson et al. yields a value of the effective diffusivity of fluoride ion in plaque of 5.5 x 10–6 cm2 s–1. This value is 43% of the diffusion coefficient of the ion in pure water at the measurement temperature of 20°C. This value of the fluoride diffusion coefficient in dental plaque is in reasonable agreement with the value reported by McNee et al. (Arch Oral Biol 25:819–823, 1980), which was 23% of the value of the fluoride ion diffusion coefficient in water.
Together, these studies suggest that the effective diffusion coefficient of fluoride in dental plaque is approximately one-third its value in water.
With this result, the transient penetration of fluoride to the tooth surface beneath biofilms of various thicknesses was solved, illustrating the highly non-linear nature of this transport process. In a 100-micron-thick plaque, a 20-second exposure will deliver 91% of the applied fluoride concentration to the tooth surface. In a 500-micron-thick plaque, the same application of 20 sec achieves only 0.14% of the applied fluoride concentration at the base of the biofilm. What these calculations illustrate is that the extent of fluoride penetration depends strongly on the thickness of the plaque. With a five-fold difference in the plaque thickness, fluoride penetration goes from being essentially complete to being insignificant.
2 Leeds Dental Institute, Clarendon Way, Leeds LS2 9LU, UK;
* corresponding author, c.robinson{at}leeds.ac.uk
We thank Dr. Stewart for taking the time and trouble to calculate diffusivity data from the information in our recent paper.
Similar calculations were performed and are published in Dr. Watson’s PhD Thesis (University of Leeds, UK, January, 2005). Results were similar at 1.5 x 10–6 cm2 s–1; differences may be due to the use of a slightly different diffusion constant for fluoride (Chu et al., 1989).
We were cautious in exploring diffusivity in this way for the reasons below, but perhaps we have been a little too strict and denied ourselves some element of prediction, which Dr. Stewart points out.
The predictions fit quite well for short exposure periods, but there is a large discrepancy between predicted and measured values in biofilms exposed to 1000 ppm fluoride ion for 30 min.
The non-linear nature of the transport process is due, we surmise, to interaction with the biomass. Such interaction will depend upon the nature of the diffusing species and the nature of the biomass itself. Both the nature of the biomass and its architecture may be related to the time period over which the biofilms form, as well as to biofilm thickness. We have not yet carried out detailed studies on the chemical nature of the biomass, and how this relates to architecture, thickness, and the period of plaque development. We avoid the use of the term "biofilm age", since this is a natural biofilm formed in vivo, and we would require data concerning turnover rate.
In this respect, the precise location of penetrating species with regard to biomass is important. With this in mind, we refer you to our recent publication in the Biofilm Club Proceedings for this year (Robinson and Watson, 2005). This indicates that some species may penetrate the biomass quite well, while others, more polar in nature, seem mainly to attach to the biomass surfaces which line relatively open channels.
With regard to biofilm thickness, Dr. Stewart’s point is well made, that plaque thickness is an extremely important determinant of fluoride penetration. However, while fluoride may penetrate thin biofilms more effectively, one of the aims behind the study was to simulate plaque biofilms at caries-prone sites, i.e., between the teeth and in molar fissures. Because they are difficult to remove, plaque biofilms at these sites tend to be relatively thick.
REFERENCES
Chu JS, Fox JL, Higuchi WI (1989). Quantitative study of fluoride transport during subsurface dissolution of dental enamel. J Dent Res 68:32–41.
Robinson C, Watson PS (2005), Penetration of therapeutic agents through natural plaque biofilms. In: Biofilms: persistence and ubiquity. McBain A, Allison D, Pratten J, Spratt D, Upton M, Verran J, eds. ISBN 0-955 1030-0-2. Manchester, UK: The Biofilm Club, School of Pharmacy and Pharmaceutical Sciences, University of Manchester.
This article has been cited by other articles:
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  P. Stoodley, J. Wefel, A. Gieseke, D. deBeer, and C. von Ohle Biofilm Plaque and Hydrodynamic Effects on Mass Transfer, Fluoride Delivery and Caries J Am Dent Assoc, September 1, 2008; 139(9): 1182 - 1190. [Abstract] [Full Text] [PDF]
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