Implications of reaction-diffusion theory for the disinfection of microbial biofilms by reactive antimicrobial agents

Abstract

A theoretical framework was developed for analyzing the efficacy of antimicrobial agents when applied to microbial biofilms with which they react. Reaction-diffusion theory was adapted to investigate the potential for transport limitation of the overall rate of biofilm disinfection and the rate of antimicrobial penetration into the biofilm. Disinfection efficacy was investigated with simulations that assumed catalytic reaction of the antimicrobial agent with live and dead cells in a uniformly thick slab with simultaneous transformation of live to dead cells by an independent rate process (disinfection). The intrinsic rate of disinfection was assumed to follow first-order dependence on antimicrobial concentration. Zero- and first-order reaction kinetics of antimicrobial agent with biomass were analyzed. Microbial growth and external mass transfer resistance were neglected. Results show that antimicrobial efficacy, defined as the ratio of the observed rate of biofilm disinfection to the rate that would prevail in the absence of mass transport limitation, decreases sharply as the Thiele modulus exceeds one. The reduction in efficacy worsens when the antimicrobial dose is more concentrated or longer. A second case examined the penetration of an antimicrobial agent into a biofilm with which it reacts stoichiometrically, as would be expected with an oxidizing biocide such as chlorine or ozone. The antimicrobial agent eventually penetrates the biofilm by depleting the reactive biomass constituent, but the time scale for penetration can exceed the time scale for transient diffusion in the absence of reaction by orders of magnitute. These results provide a theoretical basis for explaining experimentally observed resistance of biofilms to chemical disinfectants.