Dr. Cogan's Research Page

N. G. Cogan - Research
Some of this research was supported by a an NSF Award #0612467
Joyously, some more of it will be supported by a new grant soon

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.
I have several students working on a variety of problems including spatial aspects of biofilm infections, host/bacteria interactions, stem cell modeling and the mechanics of muco-ciliary interactions in cystic fibrosis patients. I am also working on several other projects. Below I have listed some abstracts papers that have recently appeared or are to appear.
Biofilms and Infectious Diseases: Biology to Mathematics and Back again. (with J. S. Gunn and D. J. Wozniak)
There has been tremendous growth in biofilm research in the past three decades. This growth has been reflected in development of a wide variety of experimental, clinical and theoretical techniques and understanding. Keeping the theoretical developments abreast of the experimental understanding and ensuring that the theoretical results are disseminated to the experimental and clinical community is a major challenge. This manuscript provides an overview of recent developments in each scientific domain. More importantly, this manuscript aims to identify areas where the theory lags behind the experimental understanding (and vice versa). The major themes of the manuscript derive from discussions and presentations at a recent interdisciplinary workshop that brought together a variety of scientists whose underlying studies focus on biofilm processes.
An Extension of the Boundary Integral Method Applied to Periodic Disinfection of a Dynamic Biofilm
Several tolerance mechanisms have been introduced to explain how bacterial biofilms are protected from disinfection. One mechanism describes the transition between two sub-populations of bacteria, one of which consumes nutrients, divides and is susceptible to antimicrobial agents. The other sub-population consists of dormant bacteria that are insensitive to treatments. It has been shown that the presence of this persister sub-population can explain experimental observations of bacterial tolerance, at least in simplified domains. This investigation describes the development of a two-dimensional model of an established biofilm immersed in a flowing bulk fluid, where the biofilm influences the fluid dynamics and the fluid flow can deform the biofilm. We introduce several extensions to this model including the reaction between the biofilm and the antimicrobial agent, bacterial and EPS production and persister dynamics. The model and numerical methods are based on the boundary integral method (BIM) but require extensions to the standard formulation to account for the production of mass within the biofilm. Our simulations indicate that many results from batch culture models carry over to the extended spatial domain. In particular, alternating dosing can eventually eliminate the bacteria but on a time scale that is much longer than in batch culture. We also predict that there is a heterogeneous distribution of persister cells that depends on the geometry of the biofilm and the dosing protocol.
Computational Exploration of Disinfection of Bacterial Biofilms in Partially Blocked Channels
The failure of typical disinfectant protocols to eliminate bacterial biofilms is one of the major concerns in industrial, clinical and environmental biofilm control. Biofilms have a variety of mechanisms that protect the bacteria including physiological, physical and phenotypic mechanisms. This investigation focuses on an aspect of protection that exploits the combination of physiological tolerance and nutrient gradients. In particular, the fluid flow in a channel that is partially blocked introduces diffusion limited zones where the bacteria can evade the disinfectant challenge. These zones are both up- and down-stream of the obstacle. Using a computational study of a two-fluid system, this novel mechanism is explored. The model is numerically solved using a hybrid boundary integral method where boundary conditions are implemented using the free space Green's function to determine forces that are imparted on the fluid by the boundaries.

Multiphase flow models of biogels from crawling cells to bacterial biofilms (with R. D. Guy)
This article reviews multiphase descriptions of the fluid mechanics of cytoplasm in crawling cells and growing bacterial biofilms. These two systems involve gels which are mixtures composed of a polymer network permeated by water. The fluid mechanics of these systems is essential to their biological function and structure. Mathematical descriptions of them must account for the mechanics of the polymer, the water, and the interaction between these two phases. This review focuses on multiphase flow models because this framework is natural for including the relative motion between the phases, the exchange of material between phases, and additional stresses within the network that arise from nonspecific chemical interactions and the action of molecular motors. These models have been successful at accounting for how different forces are generated and transmitted to achieve cell motion and biofilm growth, and they have demonstrated how emergent structures develop though the interactions of the two phases.

Publications :

19.) Chellam, Shankararaman and Cogan, N.G. Colloidal and bacterial fouling during constant flux microfiltration: Comparison of classical blocking laws with a unified model combining pore blocking and EPS secretion In Press, Accepted Manuscript, Available online 5 August 2011

18.) Cogan, N. G. (2011), Computational exploration of disinfection of bacterial biofilms in partially blocked channels. International Journal for Numerical Methods in Biomedical Engineering. doi: 10.1002/cnm.1451

17.) Cogan, N. G., Gunn, J. S. and Wozniak, D. J. (2011), Biofilms and infectious diseases: biology to mathematics and back again. FEMS Microbiology Letters, 322: 1Ð7.

16.) R.D. Guy and N.G. Cogan, Multiphase flow models of biogels from crawling cells to bacterial biofilms. HFSP Journal, 4(11) (2010).

15.) N.G. Cogan and Charles W. Wolgemuth, Two-Dimensional Patterns in Bacterial Veils Arise from Self-generated, Three-Dimensional Fluid Flows, Bulletin of Mathematical Biology (2010).

14.) N. G. Cogan, An Extension of the Boundary Integral Method Applied to Periodic Disinfection of a Dynamic Biofilm, SIAM J. Appl. Math., 70(7), pp. 2281-2307 (2010).

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, 345(1-2), 81-89 (2009).

12.) Patrick DeLeenheer and N.G. Cogan, Failure of antibiotic treatment in microbial populations , Journal of Mathematical Biology, 59(4), 563-579 (2009).

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 Joyously, some more of it will be supported by a new grant soon

N. G. Cogan - Research
Some of this research was supported by a an NSF Award #0612467
Joyously, some more of it will be supported by a new grant soon