Theory of effective drug release from medical implants based on the Higuchi model and physico-chemical hydrodynamics

[Display omitted] ► New theory of effective drug release from medical implants in surrounding tissues. ► Theory allows quantification needed to achieve therapeutic effectiveness. ► Role of convective diffusion in tissue using physicochemical hydrodynamics theory. ► Theory predicts duration of effective release using theories of colloid transport. ► Theory focuses on antibiotic release from implanted catheters. Combining the approach of colloid transport with the generalized Higuchi theory of drug release and with the concept of minimum inhibitory concentration (MIC) known in microbiology, the theory of effective drug release from implants has been developed. Effective release of an antibiotic at a concentration above MIC is a necessary condition to achieve protection against infection from implants such as central catheters. The Higuchi theory in its present form is not predictive of the therapeutic effect from medical implants. The theory of effective release presented in this paper specifies two release modes, namely: one with therapeutic usefulness (effective release) and another without therapeutic effect. Therapeutic usefulness may be achieved when the antibiotic concentration, Cti, on the implant surface kills the organisms of interest and prevents the formation and propagation of biofilm when Cti exceeds the corresponding MIC of the released antibiotic compound. Currently, neither the Higuchi theory nor any other theory can provide such prediction. The present approach requires quantification of the antibiotic transport from the drug–polymer blend implant surface into the tissue and accounts for its coupling with drug diffusion inside the blend, a task that has not been developed in existing theories. Our solution to this task resulted in the derivation of an equation for the time of duration of effective release, Te, which depends on MIC, the Higuchi invariant and the characteristics of convective diffusion within the tissue. The latter characteristics include: diffusivity Dti and diffusion layer thickness δ which is controlled by the velocity of the interstitial fluid in tissue. A smaller Dti is favorable because transport from the catheter surface is weaker, while a thinner diffusion layer is harmful because this transport is stronger. The influence of the tangential component of interstitial velocity in the tissue is especially harmful because the diffusion within the incision exit site (IES) will be extremely enhanced such that it may decrease