Slide 1
In this example calculation, we'll estimate the time it takes for an antimicrobial mouthwash to penetrate a patch of dental plaque.
Slide 2
More specifically we want to address the question of how long must one rinse with mouthwash containing chlorhexidine, a common antimicrobial agent, to have this agent penetrate right down to the tooth surface.
Slide 3
Our starting point is this equation, which gives us the time required to attain, at the deepest part of this hemispherical patch of dental plaque-the center point of the sphere, 90% of the applied bulk fluid concentration.
Slide 4
There are just two parameters required in this calculation: R, the radius of this patch of biofilm, and De, the effective diffusion coefficient of chlorhexidine in the biofilm. The radius, we're going to take as given as 280 microns.
Slide 5
Our starting point for estimating the diffusion coefficient of chlorhexidine in the biofilm is the value of the diffusion coefficient of chlorhexidine in water, Daq, here estimated using the Wilke-Chang correlation at 30 degrees Celsius.
Slide 6
Now, in the dental plaque, the diffusion coefficient is reduced due to the presence of cells and polymers and precipitates. From looking at the literature on measurements of diffusion coefficients in dental plaque, we can estimate that a solute the size of chlorhexidine will only diffuse at about 20% of its rate in water, and so, to calculate De, we just take one-fifth of Daq, and here is that number.
Slide 7
When these numbers are plugged into the equation, the only trick is that we need to make sure that the distance units will cancel-so we've put the radius in centimeters. Now the centimeters squared in the numerator, and the centimeters squared in the denominator will cancel and give us an answer in units of seconds.
Slide 8
The answer is 289 seconds. Try rinsing with mouthwash for 5 minutes for a new appreciation of just how long 300 seconds is!
This calculation is telling us that, in a pretty healthy patch of dental plaque two- or three-hundred microns thick, a typical rinse of 20 or 30 seconds probably is not adequate to deliver the full concentration of the antimicrobial in the mouthwash to the interior of the plaque.