Random walk calculations for bacterial migration in porous media

Bacterial migration is important in understanding many practical problems ranging from disease pathogenesis to the bioremediation of hazardous waste in the environment. Our laboratory has been successful in quantifying bacterial migration in fluid media through experiment and the use of population balance equations and cellular level simulations that incorporate parameters based on a fundamental description of the microscopic motion of bacteria. The present work is part of an effort to extend these results to bacterial migration in porous media. Random walk algorithms have been used successfully to date in nonbiological contexts to obtain the diffusion coefficient for disordered continuum problems. This approach has been used here to describe bacterial motility. We have generated model porous media using molecular dynamics simulations applied to a fluid with equal sized spheres. The porosity is varied by allowing different degrees of sphere overlap. A random walk algorithm is applied to simulate bacterial migration, and the Einstein relation is used to calculate the effective bacterial diffusion coefficient. The tortuosity as a function of particle size is calculated and compared with available experimental results of migration of Pseudomonas putida in sand columns. Tortuosity increases with decreasing obstacle diameter, which is in agreement with the experimental results.