Lagrangian particle methods for biological systems

Solute transport coupled with biomass growth and/or mineral precipitation/dissolution is a complex and challenging nonlinear problem. Important applications in biomedical systems include tumor growth (Zheng et al. 2005); infection of prosthetic devices (Bandyk et al. 1991) and stents (Speer et al. 1988); dental plaque (Thomas and Nakaishi 2006); physiologic mineralization (Hartgerink et al. 2001) and demineralization (Holliday et al. 1997) in vertebrate bones (including cartilage), teeth, and otoconia; and ectopic calcification that occurs when mineral precipitates pathologically in soft tissues (Azari et al. 2008). In geological systems, microorganisms play an important role in the formation of iron mineral deposits in acid mine drainage (Karamanev 1991), in the precipitation of carbonates in hot springs (Riding 2000), in the growth of stromatolites (Reid 2000), and in weathering leading to the release of nutrients to the environment (Leyval and Berthelin 1991). Microorganisms also play an important role in corrosion (Beech and Gaylarde 1999), waste water treatment (Wagner et al. 1996), and blockage of water pipes (Brigmon et al. 1997) and heat exchangers. In the subsurface, microorganisms may significantly reduce permeability (Rittmann 1993), catalyze redox reactions relevant to contaminant remediation (Lensing et al. 1994), decompose organic contaminants (Zhang et al. 1995), and improve oil recovery (Van Hamme et al. 2003). Owing to the importance of these applications, there is a strong incentive to develop predictive numerical models.