Dr. Cogan's Research Page

ô Dr. Cogan's Research Page

N. G. Cogan - Research
This research was supported by NSF Awards #0612467 and more recently #1122378

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.
Colloidal and Bacterial Fouling during Constant Flux Microfiltration: Comparison of Classical Blocking Laws with a Unified Model Combining Pore Blocking and EPS Secretion (with S. Chellam)
The instantaneous transmembrane pressure needs to be continuously increased to compensate for foulant accumulation during constant flux microfiltration. Herein, we compare predictions of a unified mathematical model and conventional blocking laws with laboratory data obtained during constant flux operation. Foulants employed included single species cultures of bacteria and coagulated natural colloids, both of which are known to form compressible cakes. The first principles model unifies fouling arising from pore blocking by individual cells, cake formation, as well as bacterial secretion of exopolymers. It also incorporates non-uniform spatial deposition patterns that have been observed during unstirred dead-end filtration. Mechanistically, these heterogeneities arise either from non-uniform membrane surface porosity or stochastic initial binding of foulants. Previous studies have shown that the initial patchy or uneven deposit morphology is magnified over longer time-scales during bacterial filtration by differential extracellular polymeric substances (EPS) secretion through quorum sensing. However, in this study, we are primarily interested in the averaged behavior (mainly flux and pressure). By spatially averaging the microscale variables we are able to compare with classical blocking law models. We show that blocking laws and the unified model both accurately model fouling under our experimental conditions. The unified model provides mechanistic insights into (bio)colloid deposition and associated fouling during constant flux microfiltration particularly since it obtained excellent predictive agreement with experimental data using parameters taken exclusively from our recent study of constant pressure filtration.
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.

Optimal Control Strategies for Disinfection of Bacterial Populations with Persister/Susceptible Dynamics (with Jason Brown, Kyle Darres, Katherine Petty)
It is increasingly clear that bacteria manage to evade killing by antibiotics and antimicrobials in a variety of ways including mutation, phenotypic variations and by forming biofilms. With recent advances in understanding the dynamics of the tolerance mechanisms, there have been subsequent advances in understanding how to manipulate the bacterial environments to eradicate the bacteria. This study focuses on using mathematical techniques to find the optimal disinfection strategy to eliminate the bacteria while managing the load of antibiotic that is applied. In this model, the bacterial population is separated into those that are tolerant to the antibiotic and those that are susceptible to disinfection. There are transitions between the two populations whose rates depend on the chemical environment. Our results extend previous mathematical studies to include more realistic methods of applying the disinfectant. The goal is to provide experimentally testable predictions that have been lacking in previous mathematical studies. In particular, we provide the optimal disinfection protocol under a variety of assumptions within the model that can be used to validate, or invalidate, our simplifying assumptions and experimental hypotheses we used to develop the model. We find that constant dosing is not the optimal method for disinfection. Rather, cycling between application and withdrawal of the antibiotic yields the fastest killing of the bacteria.

Publications :

24.) N. G. Cogan (2013), Concepts in Bacterial Disinfection, Submitted.

24.) Angela M. Jarret, N. G. Cogan and M. E. Shirtliff (2013), Model of Inflammatory Host Response to a Bacterial Infection, Submitted.

23.) N. G. Cogan, M. R. Donahue, Mark Whidden and Leonardo De La Fuente (2013), Pattern Formation Exhibited by Biofilm Formation within Microfluidic Chambers, Submitted.

22.) N. G. Cogan, Barbara Szomolay and Martin Dindos (2013), Effect of Periodic Disinfection on Persisters in a One-Dimensional Biofilm Model, Bulletin of Mathematical Biology, In Press.

21.) N. G. Cogan, Mathew Donahue and Mark Whidden (2012), Marginal Stability and Traveling Fronts in Two-Phase Mixtures, Phys. Rev. E., 86(5): 056204.

20.) N.G. Cogan, Jason Brown, Kyle Darres, Katherine Petty (2012), Optimal Control Strategies for Disinfection of Bacterial Populations with Persister/Susceptible Dynamics, Antimicrobial Agents and Chemotherapy, 56(9) pp: 4816-4826.

19.) Chellam, S. and N.G. Cogan (2011). Colloidal and Bacterial Fouling during Constant Flux Microfiltration: Comparison of Classical Blocking Laws with a Unified Model Combining Pore Blocking and EPS Secretion, Journal of Membrane Science, 382(1-2) 148-157.

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: 1?.

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 This research was supported by NSF Awards #0612467 and more recently #1122378

N. G. Cogan - Research
This research was supported by NSF Awards #0612467 and more recently #1122378