Mathematical modelling of Pseudomonas aeruginosa biofilm growth and treatment in the cystic fibrosis lung.

Lung failure due to chronic bacterial infection is the leading cause of death for patients with cystic fibrosis (CF). It is thought that the chronic nature of these infections is, in part, due to the increased tolerance and recalcitrant behaviour of bacteria growing as biofilms. Inhalation of silver carbene complex (SCC) antimicrobial, either encased in polymeric biodegradable particles or in aqueous form, has been proposed as a treatment. Through a coordinated experimental and mathematical modelling effort, we examine this proposed treatment of lung biofilms. Pseudomonas aeruginosa biofilms grown in a flow-cell apparatus irrigated with an artificial CF sputum medium are analysed as an in vitro model of CF lung infection. A 2D mathematical model of biofilm growth within the flow-cell is developed. Numerical simulations demonstrate that SCC inactivation by the environment is critical in aqueous SCC, but not SCC-polymer, based treatments. Polymer particle degradation rate is shown to be an important parameter that can be chosen optimally, based on environmental conditions and bacterial susceptibility.

Nanoparticle deposition onto biofilms.

We develop a mathematical model of nanoparticles depositing onto and penetrating into a biofilm grown in a parallel-plate flow cell. We carry out deposition experiments in a flow cell to support the modeling. The modeling and the experiments are motivated by the potential use of polymer nanoparticles as part of a treatment strategy for killing biofilms infecting the deep passages in the lungs. In the experiments and model, a fluid carrying polymer nanoparticles is injected into a parallel-plate flow cell in which a biofilm has grown over the bottom plate. The model consists of a system of transport equations describing the deposition and diffusion of nanoparticles. Standard asymptotic techniques that exploit the aspect ratio of the flow cell are applied to reduce the model to two coupled partial differential equations. We perform numerical simulations using the reduced model. We compare the experimental observations with the simulation results to estimate the nanoparticle sticking coefficient and the diffusion coefficient of the nanoparticles in the biofilm. The distributions of nanoparticles through the thickness of the biofilm are consistent with diffusive transport, and uniform distributions through the thickness are achieved in about four hours. Nanoparticle deposition does not appear to be strongly influenced by the flow rate in the cell for the low flow rates considered.

Development of the Pseudomonas aeruginosa mushroom morphology and cavity formation by iron-starvation: a mathematical modeling study.

We present a mathematical model of mushroom-like architecture and cavity formation in Pseudomonas aeruginosa biofilms. We demonstrate that a proposed disparity in internal friction between the stalk and cap extracellular polymeric substances (EPS) leads to spatial variation in volumetric expansion sufficient to produce the mushroom morphology. The capability of diffusible signals to induce the formation of a fluid-filled cavity within the cap is then investigated. We assume that conversion of bacteria to the planktonic state within the cap occurs in response to the accumulation or depletion of some signal molecule. We (a) show that neither simple nutrient starvation nor signal production by one or more subpopulations of bacteria is sufficient to trigger localized cavity formation. We then (b) demonstrate various hypothetical scenarios that could result in localized cavity formation. Finally, we (c) model iron availability as a detachment signal and show simulation results demonstrating cavity formation by iron starvation. We conclude that iron availability is a plausible mechanism by which fluid-filled cavities form in the cap region of mushroom-like structures.