In vitro measurement and computer modelling of the diffusion of antibiotic in bone cement

The diffusion coefficient for a particular antibiotic (benzyl penicillin) in various types of bone cement has been calculated from direct measurement of the passage of radio-labelled penicillin through thin sections of cement at intervals over a period of 90 days, assuming the transport processes to be Fickian. Since the concentration gradient across the test sample is not uniform in the earlier stages of the experiment, a finite-difference approximation to the diffusion equation was used to take account of the transient behaviour in determining the coefficient. This method of analysis may also be used to predict the release, as a function of time, from the surface of antibiotic-loaded bone cement and from implanted pre-loaded PMMA beads used to provide antibiotic cover following bone or joint surgery. Our computer-generated predictions appear to agree very well with previously published figures arising from in vivo and in vitro studies and we conclude therefore, that Fick's Law accurately describes the process, even when the cement mix is inhomogeneous. We have by this means a reliable method by which the diffusion coefficients for various combinations of cement, antibiotic and other additives may be retrospectively determined and compared.