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          Dr. Cogan's Research Page
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<h2>
N. G. Cogan - Research
<BR>
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This research was supported by  NSF Awards #0612467 and more recently
#1122378
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<b><font size = "+1">Overview</font></b>:
<font size = "3">
<ul>
<li> 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. 
<BR>
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.<BR><BR>

<BR><BR>
<li><B>Concepts in disinfection of bacterial populations</B> (Review Article)<BR>
Bacteria are responsible for a range of human diseases that are difficult to clear for a variety of reasons. Understanding the multilayered mechanisms that protect pathogens is of primary importance for developing effective treatments. Research over the past several decades has shown that bacteria can seek protected environments passively by avoiding deadly environments or actively by manipulating their phenotypic expression and gathering in structured biofilm communities. This article outlines the main tolerance mechanisms that have been studied and describes many of the mathematical models that indicate directions for new treatments. It is essential to understand that bacterial populations exploit a range of mechanisms to survive challenges and the mechanisms are often intertwined. This provides an opportunity for mathematical modeling to help provide insights into experiments that may uncouple particular mechanisms or optimize treatments.

<BR><BR>

<li><B>Pattern Formation Exhibited by Biofilm Formation within Microfluidic Chambers</B> (with M. Donahue, M. Whidden and L. De La Fuente<BR>

  This article investigates the dynamics of an important bacterial pathogen, Xylella fastidiosa, within artificial plant xylem. The bacterium is the causative agent of a variety of diseases that strike fruit-bearing plants including Pierce’s disease of grapevine. Biofilm colonization within microfluidic chambers was visualized in a laboratory setting, showing robust, regular spatial patterning. We also develop a mathematical model, based on a multiphase approach that is able to capture the spacing of the pattern and points to the role of the exopolymeric substance as the main source of control of the pattern dynamics. We concentrate on estimating the attachment/detachment processes within the chamber because these are two mechanisms that have the potential to be engineered by applying various chemicals to prevent or treat the disease.


<BR>
<BR>
<li><B>Effect of Periodic Disinfection on Persisters in a One-Dimensional Biofilm Model</B> (with B. Szomolay and M. Dindos) <BR>

It is well known that disinfection methods that successfully kill suspended bacterial populations often fail to eliminate bacterial biofilms. Recent efforts to understand biofilm survival have focused on the existence of small, but very tolerant, subsets of the bacterial population termed persisters. In this investigation, we analyze a mathematical model of disinfection that consists of a susceptible-persister population system embedded within a growing domain. This system is coupled to a reaction-diffusion system governing the antibiotic and nutrient.
We analyze the effect of periodic and continuous dosing protocols on persisters in a one-dimensional biofilm model, using both analytic and numerical method. We provide sufficient conditions for the existence of steady-state solutions and show that these solutions may not be unique. Our results also indicate that the dosing ratio (the ratio of dosing time to period) plays an important role. For long periods, large dosing ratios are more effective than similar ratios for short periods. We also compare periodic to continuous dosing and find that the results also depend on the method of distributing the antibiotic within the dosing cycle.
 <BR><BR><BR><BR> <b><font size = "+1">Publications </font></b>:
<BR><BR><BR>
<!--
20.) N.G. Cogan and Matt Donahue, Modeling Biofilm Development: PD, In
progress
<BR><BR> 
19.) Patrick DeLeenheer and N.G. Cogan, Replicator Dynamics of a Growing
Population of
Bacteria with Two Strategies, In Progress
<BR><BR>
--> 

26.) N.G. Cogan and S. Chellam (2013) A method for determining the optimal back-washing frequency and duration for dead-end microfiltration, Submitted. 
<BR><BR>

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

24.) N. G. Cogan (2013), Concepts in Bacterial Disinfection (Review), Mathematical Biosciences, 245(2), 111-125.
<BR><BR>


23.) N. G. Cogan, M. R. Donahue, Mark Whidden and Leonardo De La Fuente
(2013), Pattern Formation Exhibited by Biofilm Formation within
Microfluidic Chambers, Biophysical Journal, 104(9), 1867-1874.
<BR><BR>

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,75(1), 94-123
<BR><BR>

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

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.
<BR><BR>

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.
<BR><BR>


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
<BR><BR>

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?.
<BR><BR>

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

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). <BR><BR>

12.) Patrick DeLeenheer and N.G. Cogan,<a href="papers/persist3.pdf">
 Failure of antibiotic treatment
in microbial populations  </a>, Journal of
Mathematical
Biology, 59(4), 563-579 (2009).
<BR><BR>


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) <BR><BR>

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) <BR><BR>

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) 
<BR><BR>

8.) N. G. Cogan, <a href="papers/two_fluid_biofilm.pdf"> A Two-Fluid Model
of Biofilm Disinfection </a>, Bulletin of Mathematical Biology,
70(3) pp. 800-819 (2008) <BR><BR>

7.) Nicholas G.  Cogan, <a href="papers/two_fluid_post.pdf"> Hybrid Numerical
Treatment of Two Fluid Problems with Passive Interfaces </a>, COMM. APP. MATH. AND COMP. SCI. Vol 2., No. 1, pp. 117-133 2007  <br><br>

6.) N. G. Cogan <a href="papers/persister2.pdf"> Incorporating Toxin
Hypothesis into a Mathematical Model of Persister Formation and Dynamics
</a>, Journal of Theoretical Biology 248 (2007): 340-349 <BR><BR>

5.) N.G. Cogan, <a href= "papers/persist.pdf"> Effects of Persister
Formation on Bacterial Response to Dosing </a>, Journal of Theoretical
Biology 238(3): 694-703 (2006) <BR><BR>


4.) N. G. Cogan and C.W. Wolgemuth, <a href= "papers/veil_pub.pdf"> Pattern Formation in Bacterial Veils,  </a> Biophysical Journal 88, 2525-2529 (2005)
<BR> <BR>

3.) N.G. Cogan, Ricardo Cortez and Lisa J. Fauci, <a href= "papers/resistance.pdf">Modeling Physiological Resistence in Bacterial Biofilms</a>,  Bulletin of Mathematical Biology 67 (4): 831-853 (2005)
<BR> <BR>

2.) N.G. Cogan and James P. Keener, <a href= "papers/channel1.pdf"> Channel Formation in Gels </a>, SIAM J. Appl. Math., Vol. 65, N0. 6, pp. 1839-1854.

<BR><BR>

1.) N.G. Cogan and James P. Keener, <a href= "papers/finger.pdf"> The Role of the Biofilm Matrix in  Structural Development </a>   Mathematical Medicine and Biology 21(2),147-166 (2004)
<BR><BR>

<BR><BR><BR><BR>
<b><font size = "+1">Simulations </font></b> (quicktime):
<BR><BR><BR>

<table border=1>

<tr>
<td width = "50%">
<b>Stripe 0</b>: Veil on the borderline of stripes 
</td>
<td>
<a href="movies/stripe1.avi"> Stripe0</a> 
</td>
</tr>

<tr>
<td width = "50%">
<b>Stripe 1</b>: Veil in stripe regime with tight colormap 
</td>
<td>
<a href="movies/roll2.avi"> Stripe1</a> 
</td>
</tr>
<tr>
<td width = "50%">
<tr>
<td width = "50%">
<b>Stripe 1a</b>: Same regime with broad colormap
</td>
<td>
<a href="movies/roll.avi"> Stripe 1a</a> 
</td>
</tr>
<tr>
<td width = "50%">
</td>
</tr>


<tr>
<td width = "50%">
<b>Fingering instability</b>: Production of polymer induces gradients in osmotic pressure. Expansion of the biofilm gel leads to a surface instability.
</td>
<td>
<a href="movies/mushroom.qt">  Mushroom </a> 
</td>
</tr>
<tr>
<td width = "50%">
<b>Disinfection</b>: Dynamic disinfection zones with  no external flow. The disifectant reacts with a component of the biofilm, destroying both the disinfectant and the nuetralizer.
</td>
<td>
<a href="movies/no_flow.qt">  No Flow </a> 
</td>
</tr>
<tr>
<td width = "50%">
<b>Fluid Visualization</b>: Movie showing advective transport of a passive marker dye. There is no explicit diffusion, although the numerical method is diffusive. 
</td>
<td>
<a href="movies/flow1.qt">  Fluid Visual </a> 
</td>
</tr>
<tr>
<td width = "50%">
<b>Disinfection</b>: Disinfection simulation indicating that physiological resistance cannot be the only resistance mechanism employed by biofilms.
</td>
<td>
<a href="movies/flow2.qt"> Disinfection</a> 
</td>


</tr>

<tr>
<td width = "50%">
<b>Moving Cluster</b> with advection of a dye. (NOTE: this is an animated GIF and takes a loooong time to load</b>: 
</td>
<td>
<a href="movies/cluster.gif"> Cluster</a> 
</td>
</tr>
<tr>
<td width = "50%">
<b>Moving Circle-centered</b>: Simulation of a blob of viscous fluid immeresed in water with a parabolic background flow. 
</td>
<td>
<a href="movies/movie_center_green.gif"> Circle - centered</a> 
</td>
</tr>
<tr>
<td width = "50%">
<b>Moving Circle-off center</b>: Simulation of a blob of viscous fluid immeresed in water with a parabolic background flow. 
</td>
<td>
<a href="movies/movie_off_center_green.gif"> Circle - off center</a> 
</td>
</tr>

<tr>
<td width = "50%">
<b>One Cluster</b>: One cluster in a parabolic background flow 
</td>
<td>
<a href="movies/cluster_green.gif"> Cluster</a> 
</td>
</tr>

<tr>
<td width = "50%">
<b>Two Clusters</b>:Two initially identical clusters in parabolic background flow 
</td>
<td>
<a href="movies/cluster_2_green.gif"> Two Clusters</a> 
</td>
</tr>
<tr>
<td width = "50%">
</td>
</tr>

<tr>
<td width = "50%">
<b>One Cluster</b>: Growth and response to fluid
</td>
<td>
<a href="movies/mush_small_40.avi"> Growing Biofilm</a> 
</td>
</tr>
<tr>
<td width = "50%">
<tr>
<td width = "50%">
<b>Two Clusters</b>: Growth and response to fluid
</td>
<td>
<a href="movies/mush_two_small_43.avi"> Growing Biofilm</a> 
</td>
</tr>
<tr>
<td width = "50%">
</td>
</tr>


</table>