Model of ciprofloxacin subdiffusion in Pseudomonas aeruginosa biofilm formed in artificial sputum medium

We study theoretically and empirically ciprofloxacin antibiotic diffusion through a gel-like artificial sputum medium (ASM) mimicking physiological conditions typical for a cystic fibrosis layer, in which regions occupied by Pseudomonas aeruginosa bacteria are present. Our theoretical model is based on the subdiffusion-absorption equation with a fractional time derivative that describes molecules diffusion in a medium structured as Thompson9s plumpudding model; the pudding `background9 represents ASM and the plums represent the bacterial biofilm. We show that the process can be divided into three successive stages: (1) only antibiotic subdiffusion with constant biofilm parameters, (2) subdiffusion and absorption of antibiotic molecules with variable biofilm parameters, (3) subdiffusion and absorption in the medium but biofilm parameters are constant. Stage 2 is interpreted as the appearance of an intensive defence bulid--up of bacteria against the action of an antibiotic, in the stage 3 it is likely that the bacteria have been inactivated. Times at which stages change are determined from the experimentally obtained temporal evolution of the amount of substance that has diffused through the ASM with bacteria. Our analysis shows good agreement between experimental and our theoretical results.