College of Engineering
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The College of Engineering at Montana State University will serve the State of Montana and the nation by fostering lifelong learning, integrating learning and discovery, developing and sharing technical expertise, and empowering students to be tomorrow's leaders.
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Item Viscoelastic fluid description of bacterial biofilm material properties(2002-09) Klapper, Isaac; Rupp, Cory J.; Cargo, R.; Purevdorj, B.; Stoodley, PaulA mathematical model describing the constitutive properties of biofilms is required for predicting biofilm deformation, failure and detachment in response to mechanical forces. Laboratory observations indicate that biofilms are viscoelastic materials. Likewise, current knowledge of biofilm internal structure suggests modeling biofilms as associated polymer viscoelastic systems. Supporting experimental results and a system of viscoelastic fluid equations with a linear Jeffreys viscoelastic stress-strain law are presented here. This system of equations is based on elements of associated polymer physics and is also consistent with presented and previous experimental results. A number of predictions can be made. One particularly interesting result is the prediction of an elastic relaxation time on the order of a few minutes: biofilm disturbances on shorter time scales produce an elastic response, biofilm disturbances on longer time scales result in viscous flow, i.e., non-reversible biofilm deformation. Although not previously recognized, evidence of this phenomenon is in fact present in recent experimental results.Item Biofilm material properties as related to shear-induced deformation and detachment phenomena(2002-12) Stoodley, Paul; Cargo, R.; Rupp, Cory J.; Wilson, Suzanne; Klapper, IsaacBiofilms of various Pseudomonas aeruginosa strains were grown in glass flow cells under laminar and turbulent flows. By relating the physical deformation of biofilms to variations in fluid shear, we found that the biofilms were viscoelastic fluids which behaved like elastic solids over periods of a few seconds but like linear viscous fluids over longer times. These data can be explained using concepts of associated polymeric systems, suggesting that the extracellular polymeric slime matrix determines the cohesive strength. Biofilms grown under high shear tended to form filamentous streamers while those grown under low shear formed an isotropic pattern of mound-shaped microcolonies. In some cases, sustained creep and necking in response to elevated shear resulted in a time-dependent fracture failure of the "tail" of the streamer from the attached upstream "head." In addition to structural differences, our data suggest that biofilms grown under higher shear were more strongly attached and were cohesively stronger than those grown under lower shears.Item Commonality of elastic relaxation times in biofilms(2004-08) Shaw, T.; Winston, Matthew T.; Rupp, Cory J.; Klapper, Isaac; Stoodley, PaulBiofilms, sticky conglomerations of microorganisms and extracellular polymers, are among the Earth's most common life forms. One component for their survival is an ability to withstand external mechanical stress. Measurements indicate that biofilm elastic relaxation times are approximately the same (about 18 min) over a wide sample of biofilms though other material properties vary significantly. A possible survival significance of this time scale is that it is the shortest period over which a biofilm can mount a phenotypic response to transient mechanical stress.Item Adaptive responses to antimicrobial agents in biofilms(2005-08) Szomolay, Barbara; Klapper, Isaac; Dockery, Jack D.; Stewart, Philip S.Bacterial biofilms demonstrate adaptive resistance in response to antimicrobial stress more effectively than corresponding planktonic populations. We propose here that, in biofilms, reaction-diffusion limited penetration may result in only low levels of antimicrobial exposure to deeper regions of the biofilm. Sheltered cells are then able to enter an adapted resistant state if the local time scale for adaptation is faster than that for disinfection. This mechanism is not available to a planktonic population. A mathematical model is presented to illustrate. Results indicate that, for a sufficiently thick biofilm, cells in the biofilm implement adaptive responses more effectively than do freely suspended cells. Effective disinfection requires applied biocide concentration that increases quadratically or exponentially with biofilm thickness.Item A multidimensional multispecies continuum model for heterogeneous biofilm development(2007-01) Alpkvist, Erik; Klapper, IsaacWe propose a multidimensional continuum model for heterogeneous growth of biofilm systems with multiple species and multiple substrates. The new model provides a deterministic framework for the study of the interactions between several species and their effects on biofilm heterogeneity. It consists of a system of partial differential equations derived on the basis of conservation laws and reaction kinetics. The derivation and key assumptions are presented. The assumptions used are a combination of those used in the established one dimensional model, due to Wanner and Gujer, and for the viscous fluid model, of Dockery and Klapper. The work of Wanner and Gujer in particular has been extensively used through the years, and thus this new model is an extension to several spatial dimensions of an already proven working model. The model equations are solved using numerical techniques, for purposes of simulation and verification. The new model is applied to two different biofilm systems in several spatial dimensions, one of which is equivalent to a system originally studied by Wanner and Gujer. Dimensionless formulations for these two systems are given, and numerical simulation results with varying initial conditions are presented.Item Senescence can explain microbial persistence(2007-11) Klapper, Isaac; Gilbert, P.; Ayati, B. P.; Dockery, Jack D.; Stewart, Philip S.It has been known for many years that small fractions of persister cells resist killing in many bacterial colony–antimicrobial confrontations. These persisters are not believed to be mutants. Rather it has been hypothesized that they are phenotypic variants. Current models allow cells to switch in and out of the persister phenotype. Here, a different explanation is suggested for persistence, namely senescence. Using a mathematical model including age structure, it is shown that senescence provides a natural explanation for persistence-related phenomena, including the observations that the persister fraction depends on growth phase in batch culture and dilution rate in continuous culture.Item Description of mechanical response including detachment using a novel particle model of biofilm/flow interaction(2007-05) Alpkvist, Erik; Klapper, IsaacBacterial biofilms, while made up of microbial-scale objects, also function as meso- and macroscale materials. In particular, macro-scale material properties determine how biofilms respond to large-scale mechanical stresses, e.g. fluid shear. Viscoelastic and other constitutive properties influence biomass structure (through growth and fluid shear stresses) by erosion and sloughing detachment. In this paper, using the immersed boundary method, biofilm is modelled by a system of viscoelastic, breakable springs embedded in a fluid flow, evolving according to the basic physical laws of conservation of mass and momentum. We demonstrate in the context of computer simulation biofilm deformation and detachment under fluid shear stress.Item A multiscale model of biofilm as a senescence-structured fluid(2007-01) Ayati, B. P.; Klapper, IsaacWe derive a physiologically structured multiscale model for biofilm development. The model has components on two spatial scales, which induce different time scales into the problem. The macroscopic behavior of the system is modeled using growth-induced flow in a domain with a moving boundary. Cell-level processes are incorporated into the model using a so-called physiologically structured variable to represent cell senescence, which in turn affects cell division and mortality. We present computational results for our models which shed light on modeling the combined role senescence and the biofilm state play in the defense strategy of bacteria.Item Mathematical model of biofilm induced calcite precipitation(2010-08) Zhang, Tian-Yu; Klapper, IsaacMicrobially modulated carbonate precipitation is a fundamentally important phenomenon of both engineered and natural environments. In this paper, we propose a mixture model for biofilm induced calcite precipitation. The model consists of three phases—calcite, biofilm and solvent—which satisfy conservation of mass and momentum laws with addition of a free energy of mixing. The model also accounts for chemistry, mechanics, thermodynamics, fluid and electrodiffusion transport effects. Numerical simulations qualitatively capturing the dynamics of this process and revealing effects of kinetic parameters and external flow conditions are presented.Item Analysis of adaptive response to dosing protocols for biofilm control(2010-01) Szomolay, Barbara; Klapper, Isaac; Dindos, MartinBiofilms are sessile populations of microbes that live within a self-secreted matrix of extracellular polymers. They exhibit high tolerance to antimicrobial agents, and experimental evidence indicates that in many instances repeated doses of antimicrobials further reduce disinfection efficiency due to an adaptive stress response. In this investigation, a mathematical model of bacterial adaptation is presented consisting of an adapted-unadapted population system embedded within a moving boundary problem coupled to a reaction-diffusion equation. The action of antimicrobials on biofilms under different dosing protocols is studied both analytically and numerically. We find the limiting behavior of solutions under periodic and on-off dosing as the period is made very large or very small. High dosages often carry undesirable side effects so we specially consider low dosing regimes. Our results indicate that on-off dosing for small doses of biocide is more effective than constant dosing. Moreover, in a specific case, on-off dosing for short periods is again more effective regardless of the biocide dose. We also provide sufficient conditions for the eradication of biofilms under a constant dosing regime.