Dr. Cogan's Research Page

N. G. Cogan - Research
Some of this research was supported by a an NSF Award #0612467

Overview:

The focus of my research is on mathematical biology. In particular, I am interested in fluid/solid interaction, chemical transport, bacterial physiology. I have spent the past several years researching biological processes where each of the topics above plays a fundamental role. As in many areas of applied mathematics, the mathematical methods that I use are very diverse. Deriving and analysing mathematical models requires familiarity with the biology of the problem, but also with multiphase flow, non-Newtonian fluid dynamics and nonlinear dynamics. I also employ computational methods, perturbation analysis and nonlinear PDE theory to answer specific, biologically motivated problems.
Currently I am working on several separate projects. Below I list abstracts of some of the papers that have recently appeared or are to appear.
Hybrid Numerical Treatment of Two Fluid Problems with Passive Interfaces
We consider the coupled motion of a passive interface separating two immiscible fluids of different viscosities. There are several applications where the velocity of the two fluids is needed everywhere within the domain. Examples include the transport of bacteria and diffusing substances within a biofilm matrix and the transport of cations throughout the mucociliary and peri-ciliary layer in the lung lining. In this investigation, we use a hybrid approach which employs the Boundary Integral Method to determine the interface velocity and the method of Regularized Stokeslets to determine the velocity elsewhere in the domain. Our approach capitalizes on the strengths of the two methods yielding an intuitive, efficient method for determining the velocity of a two-fluid system throughout the domain. The main result of the presented method is the extension to two-fluid systems with varying viscosity. We describe the results of three numerical simulations designed to test the numerical method and motivate its use.
Two-fluid Model of Biofilm Disinfection
We consider a dynamic model of biofilm disinfection in two dimensions. The biofilm is treated as a viscous fluid immersed in a fluid of less viscosity. The bulk fluid moves due to an imposed external parabolic flow. The motion of the fluid is coupled to the biofilm inducing motion of the biofilm. Both the biofilm and the bulk fluid are dominated by viscous forces, hence the Reynolds number is negligible and the appropriate equations are Stokes equations. The governing partial differential equations are recast as boundary integral equations using a version of the Lorenz reciprocal relationship. This allows for robust treatment of the simplified fluid/biofilm motions. The transport of nutrients and antimicrobials, which depends directly on the velocities of the fluid and biofilm, is also included. Disinfection of the bacteria is considered under the assumption that the biofilm grows slowly compared to the time-scale of diffusion/advection.
Field-Phase Models for Biofilms. II. 2-D Numerical Simulations of Biofilm-Flow Interaction
We study the biofilm-flow interaction resulting in growth and dispersal phenomena in a cavity and shear flows using the phase field model developed recently [27]. The growth of the biofilm and the solvent flow-biofilm interaction in various flow and geometrical conditions in 2-D are simulated using an extended Newtonian constitutive model for the biofilm. The model predicts growth patterns consistent with experimental findings with randomly distributed initial colonies in the biofilm. Shear induced dispersal detachment in biofilms is simulated in a shear cell with simple and oscillatory shear, predicting possible reattachment under oscillation. Dispersal due to the density variation is also investigated shedding light on the possible bacteria induced dispersal phenomenon.
Regularized Stokeslets Solution for 2-D Flow in Dead-end Microfiltration: Application to Bacterial Deposition and Fouling
Dead-end microfiltration is an effective method for removing particulate matter including protozoa and bacteria in a variety of settings. As the filtered components accumulate on the filter, the flux declines during constant pressure operation necessitating periodic backwashing. It as been recently reported emirically that the filtered components are not homogeneously distributed on the filter. This alters any mathematical theory describing the filtering process. We present a method for determining the coupled fluid dynamics and bacterial transport for dead-end filtration. Results of numerical simulations indicates that the model is able to closely cpture experimental data; moreover, the model predicts that the coupled system induces the experimentally observed patchy deposition patterns through spatial variablility in the pore structure and porosity of the membrane.
Failure of antibiotic treatment in microbial populations
The tolerance of bacterial populations to biocidal or antibiotic treatment has been well documented in both biofilm and planktonic settings. However, there is still very little known about the mechanisms that produce this tolerance. Evidence that small, non-mutant subpopulations of bacteria are not affected by antibiotic challenge has been accumulating and provides an attractive explanation for the failure of typical dosing protocols. Although a dosing challenge can kill all the susceptible bacteria, the remaining persister cells can serve as a source of population regrowth. We give a robust condition for the failure of a periodic dosing protocol for a general chemostat model, which supports the mathematical conclusions and simulations of an earlier, more specialized batch model. Our condition implies that the treatment protocol fails globally, in the sense that a mixed bacterial population will ultimately persist above a level that is independent of the initial composition of the population. We also give a sufficient condition for treatment success, at least for initial population compositions near the steady state of interest, corresponding to bacterial washout. Finally, we investigate how the speed at which the bacteria are wiped out depends on the duration of administration of the antibiotic. We find that this dependence is not necessarily monotone, implying that optimal dosing does not necessarily correspond to continuous administration of the antibiotic. Thus, genuine periodic protocols can be more advantageous in treating a wide variety of bacterial infections.

Publications :

18.) N.G. Cogan, Donald A. French, Sookkyung Lim, Mauricio Osorio, M. Kupferle, Distributions of Bacteria and Biofilms in Urban Pipes, In Progress.

17.) R.D. Guy and N.G. Cogan, A Review of Multiphase Models in Biology, Submitted

16.) N.G. Cogan and C. Avalos, Run and Reverse Chemotactic Strategies in the Presence of Structured Fluid Flow: 1 and 2 Dimensional Studies, Submitted

15.) N.G. Cogan and Charles W. Wolgemuth, Instability of a two-dimensional bacterial veil in a three-dimensional fluid, Submitted.

14.) N. G. Cogan, Persister Distribution in a two-dimensional Model of a Dynamic Biofilm, In Revision

13.) N.G. Cogan and Shankar Chellam, Incorporating pore blocking, cake filtration and EPS production in a model for constant pressure bacterial fouling during dead-end microfiltration, Journal of Membrane Science, In Press

12.) Patrick DeLeenheer and N.G. Cogan, Failure of antibiotic treatment in microbial populations, Accepted, Journal of Mathematical Biology

11.) N. G. Cogan and Shankar Chellam, Regularized Stokeslets Solution for 2-D Flow in Dead-end Microfiltration: Application to Bacterial Deposition and Fouling, Journal of Membrane Science 318(1-2) pp: 379-386 (2008)

10.) Tianyu Zhang, N. G. Cogan and Qi Wang, Field-Phase Models for Biofilms. II. 2-D Numerical Simulations of Biofilm-Flow Interaction, Communications in Computational Physics, 4(1) pp: 72-101 (2008)

9.) Tianyu Zhang, N. G. Cogan and Qi Wang, Phase-Field Models for Biofilm. I. Theory and 1-D Simulations, SIAM J. Appl. Math 69(3), pp. 641-669 (2008)

8.) N. G. Cogan, A Two-Fluid Model of Biofilm Disinfection , Bulletin of Mathematical Biology, 70(3) pp. 800-819 (2008)

7.) Nicholas G. Cogan, Hybrid Numerical Treatment of Two Fluid Problems with Passive Interfaces , COMM. APP. MATH. AND COMP. SCI. Vol 2., No. 1, pp. 117-133 2007

6.) N. G. Cogan Incorporating Toxin Hypothesis into a Mathematical Model of Persister Formation and Dynamics , Journal of Theoretical Biology 248 (2007): 340-349

5.) N.G. Cogan, Effects of Persister Formation on Bacterial Response to Dosing , Journal of Theoretical Biology 238(3): 694-703 (2006)

4.) N. G. Cogan and C.W. Wolgemuth, Pattern Formation in Bacterial Veils, Biophysical Journal 88, 2525-2529 (2005)

3.) N.G. Cogan, Ricardo Cortez and Lisa J. Fauci, Modeling Physiological Resistence in Bacterial Biofilms, Bulletin of Mathematical Biology 67 (4): 831-853 (2005)

2.) N.G. Cogan and James P. Keener, Channel Formation in Gels , SIAM J. Appl. Math., Vol. 65, N0. 6, pp. 1839-1854.

1.) N.G. Cogan and James P. Keener, The Role of the Biofilm Matrix in Structural Development Mathematical Medicine and Biology 21(2),147-166 (2004)

Simulations (quicktime):

Stripe 0: Veil on the borderline of stripes	Stripe0
Stripe 1: Veil in stripe regime with tight colormap	Stripe1

Stripe 1a: Same regime with broad colormap	Stripe 1a

Fingering instability: Production of polymer induces gradients in osmotic pressure. Expansion of the biofilm gel leads to a surface instability.	Mushroom
Disinfection: Dynamic disinfection zones with no external flow. The disifectant reacts with a component of the biofilm, destroying both the disinfectant and the nuetralizer.	No Flow
Fluid Visualization: Movie showing advective transport of a passive marker dye. There is no explicit diffusion, although the numerical method is diffusive.	Fluid Visual
Disinfection: Disinfection simulation indicating that physiological resistance cannot be the only resistance mechanism employed by biofilms.	Disinfection
Moving Cluster with advection of a dye. (NOTE: this is an animated GIF and takes a loooong time to load:	Cluster
Moving Circle-centered: Simulation of a blob of viscous fluid immeresed in water with a parabolic background flow.	Circle - centered
Moving Circle-off center: Simulation of a blob of viscous fluid immeresed in water with a parabolic background flow.	Circle - off center
One Cluster: One cluster in a parabolic background flow	Cluster
Two Clusters:Two initially identical clusters in parabolic background flow	Two Clusters

One Cluster: Growth and response to fluid	Growing Biofilm

Two Clusters: Growth and response to fluid	Growing Biofilm

N. G. Cogan - Research Some of this research was supported by a an NSF Award #0612467

N. G. Cogan - Research
Some of this research was supported by a an NSF Award #0612467