This research was supported by NSF Awards #0612467, #1122378, #1510743 and #2210992

- 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, sensitivity/UQ 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, immune disease, micro filtration. I am also working on several other projects. Below I have listed some abstracts papers that have recently appeared or are to appear.

**Membrane aging effects on water recovery during full-scale potable reuse: Mathematical optimization of backwashing frequency for constant-flux microfiltration NG Cogan, D Ozturk, K Ishida, J Safarik, S Chellam Separation and Purification Technology 286, 120294**

One tool in efforts to tackle the ever growing problem of water scarcity is municipal wastewater reclamation to produce drinking water. Microfiltration (MF) is a central technology for potable reuse because it is highly effective in removing pathogenic protozoa, bacteria, and other colloids and for reverse osmosis pretreatment. However, as microfiltered materials accumulate at the membrane surface, its productivity is reduced requiring periodic removal of foulants. A mathematical model of MF is described in the context of hollow fiber filtration that focused on optimizing constant flux operation with backwashing. Design curves were also proposed for determining backwash timing. The model analysis is evaluated against real-world MF fouling for membranes that range in age from a few weeks to three years, observed at the world’s largest water reuse facility operated by the Orange County Water District. The presented model compares well with the full-scale operational data, and model parameters accurately capture variations in fouling kinetics with membrane age, providing clues to changes in optimal regeneration timing and frequency as membrane performance declines over long time scales.

**Physiological insights into electrodiffusive maintenance of gastric mucus through sensitivity analysis and simulations M Aggarwal, NG Cogan, OL Lewis Journal of Mathematical Biology 83 (3), 1-31**

It is generally accepted that the gastric mucosa and adjacent mucus layer are critical in the maintenance of a pH gradient from stomach lumen to stomach wall, protecting the mucosa from the acidic environment of the lumen and preventing auto-digestion of the epithelial layer. No conclusive study has shown precisely which physical, chemical, and regulatory mechanisms are responsible for maintaining this gradient. However, experimental work and modeling efforts have suggested that concentration dependent ion-exchange at the epithelial wall, together with hydrogen ion/mucus network binding, may produce the enormous pH gradients seen in vivo. As of yet, there has been no exhaustive study of how sensitive these modeling results are with respect to variation in model parameters, nor how sensitive such a regulatory mechanism may be to variation in physical/biological parameters. In this work, we perform sensitivity analysis (using Sobol’ Indices) on a previously reported model of gastric pH gradient maintenance. We quantify the sensitivity of mucosal wall pH (as a proxy for epithelial health) to variations in biologically relevant parameters and illustrate how variations in these parameters affects the distribution of the measured pH values. In all parameter regimes, we see that the rate of cation/hydrogen exchange at the epithelial wall is the dominant parameter/effect with regards to variation in mucosal pH. By careful sensitivity analysis, we also investigate two different regimes representing high and low hydrogen secretion with different physiological interpretations. By complementing mechanistic modeling and biological hypotheses testing with parametric sensitivity analysis we are able to conclude which biological processes must be tightly regulated in order to robustly maintain the pH values necessary for healthy function of the stomach.

**Data assimilation of synthetic data as a novel strategy for predicting disease progression in alopecia areata NG Cogan, F Bao, R Paus, A Dobreva Mathematical Medicine and Biology: A Journal of the IMA 38 (3), 314-332**The goal of patient-specific treatment of diseases requires a connection between clinical observations with models that are able to accurately predict the disease progression. Even when realistic models are available, it is very difficult to parameterize them and often parameter estimates that are made using early time course data prove to be highly inaccurate. Inaccuracies can cause different predictions, especially AQ5 when the progression depends sensitively on the parameters. In this study, we apply a Bayesian data assimilation method, where the data are incorporated sequentially, to a model of the autoimmune disease alopecia areata that is characterized by distinct spatial patterns of hair loss. Using synthetic data as simulated clinical observations, we show that our method is relatively robust with respect to variations in parameter estimates. Moreover, we compare convergence rates for parameters with different sensitivities, varying observational times and varying levels of noise. We find that this method works better for sparse observations, sensitive parameters and noisy observations. Taken together, we find that our data assimilation, in conjunction with our biologically inspired model, provides directions for individualized diagnosis and treatments.

**Publications**:

59.) Membrane aging effects on water recovery during full-scale potable reuse: Mathematical optimization of backwashing frequency for constant-flux microfiltration NG Cogan, D Ozturk, K Ishida, J Safarik, S Chellam Separation and Purification Technology 286, 120294

58.) Physiological insights into electrodiffusive maintenance of gastric mucus through sensitivity analysis and simulations M Aggarwal, NG Cogan, OL Lewis Journal of Mathematical Biology 83 (3), 1-31

57.) Data assimilation of synthetic data as a novel strategy for predicting disease progression in alopecia areata NG Cogan, F Bao, R Paus, A Dobreva Mathematical Medicine and Biology: A Journal of the IMA 38 (3), 314-332

56.) Multiphase modelling of precipitation-induced membrane formation PS Eastham, MNJ Moore, NG Cogan, Q Wang, O Steinbock Journal of Fluid Mechanics 888

55.) Toward predicting the spatio-temporal dynamics of alopecia areata lesions using partial differential equation analysis A Dobreva, R Paus, NG Cogan Bulletin of mathematical Biology 82 (3), 1-32

54.) Growth Dynamics and Survival of Liberibacter crescens BT-1, an Important Model Organism for the Citrus Huanglongbing Pathogen “Candidatus Liberibacter … M Sena-Vélez, SD Holland, M Aggarwal, NG Cogan, M Jain, DW Gabriel, ... Applied and environmental microbiology 85 (21), e01656-19

53.) Where to look and how to look: combining global sensitivity analysis with fast/slow analysis to study multi-timescale oscillations M Aggarwal, N Cogan, R Bertram Mathematical Biosciences 314, 1-12

52.) Enhanced disinfection of bacterial populations by nutrient and antibiotic challenge timing N Acar, NG Cogan Mathematical Biosciences 313, 12-32

51.) The ups and downs of S. aureus nasal carriage AM Jarrett, NG Cogan Mathematical Medicine and Biology: A Journal of the IMA 36 (2), 157-177

50.) A framework for model analysis across multiple experiment regimes: Investigating effects of zinc on Xylella fastidiosa as a case study M Aggarwal, MY Hussaini, L De La Fuente, F Navarrete, NG Cogan Journal of theoretical biology 457, 88-100

49.) Computational investigation of ripple dynamics in biofilms in flowing systems NG Cogan, J Li, S Fabbri, P Stoodley Biophysical journal 115 (7), 1393-1400

48.) The ups and downs of S. aureus nasal carriage AM Jarrett, NG Cogan Mathematical medicine and biology: a journal of the IMA

47.) A mathematical model for the determination of mouse excisional wound healing parameters from photographic data NG Cogan, AP Mellers, BN Patel, BD Powell, M Aggarwal, KM Harper, ... Wound Repair and Regeneration

46.) Uncertainty propagation in a model of dead-end bacterial microfiltration using fuzzy interval analysis NG Cogan, MY Hussaini, S Chellam Journal of Membrane Science 546, 215-224

45.) Short-Term Antiretroviral Treatment Recommendations Based on Sensitivity Analysis of a Mathematical Model for HIV Infection of CD4+T Cells AM Croicu, AM Jarrett, NG Cogan, MY Hussaini Bulletin of mathematical biology 79 (11), 2649-2671

44.) Fluid‐driven interfacial instabilities and turbulence in bacterial biofilms S Fabbri, J Li, RP Howlin, A Rmaile, B Gottenbos, M De Jager, EM Starke, ... Environmental microbiology 19 (11), 4417-4431

43.) Combining two methods of global sensitivity analysis to investigate MRSA nasal carriage model AM Jarrett, NG Cogan, MY Hussaini Bulletin of mathematical biology 79 (10), 2258-2272

42.) Global parametric sensitivity analysis of a model for dead-end microfiltration of bacterial suspensions NG Cogan, S Chellam Journal of Membrane Science 537, 119-127

41.) Analysing the dynamics of a model for alopecia areata as an autoimmune disorder of hair follicle cycling A Dobreva, R Paus, NG Cogan Mathematical medicine and biology: a journal of the IMA

40.) Exploring an autoimmune hair loss condition through mathematical modeling and sensitivity analysis A Dobreva, R Paus, N Cogan

39.) Optimal backwashing in dead-end bacterial microfiltration with irreversible attachment mediated by extracellular polymeric substances production NG Cogan, J Li, AR Badireddy, S Chellam Journal of Membrane Science 520, 337-344

38.) Theoretical and experimental evidence for eliminating persister bacteria by manipulating killing timing NG Cogan, H Rath, N Kommerein, SN Stumpp, M Stiesch FEMS microbiology letters 363 (23)

37.) Predictive Computer Models for Biofilm Detachment Properties in Pseudomonas aeruginosa NG Cogan, JM Harro, P Stoodley, ME Shirtliff Mbio 7 (3), e00815-16

36.) Sensitivity analysis of a pharmacokinetic model of vaginal anti-HIV microbicide drug delivery AM Jarrett, Y Gao, MY Hussaini, NG Cogan, DF Katz Journal of pharmaceutical sciences 105 (5), 1772-1778

35.) Shocks and rarefactions arise in a two-phase model with logistic growth DA Ekrut, NG Cogan Applied Mathematics Letters 52, 4-8

34.) A Two-Dimensional Multiphase Model of Biofilm Formation in Microfluidic Chambers M Whidden, N Cogan, M Donahue, F Navarrete, L De La Fuente Bulletin of mathematical biology 77 (12), 2161-2179

33.) Mathematical model for alopecia areata A Dobreva, R Paus, NG Cogan Journal of theoretical biology 380, 332-345

32.) Mathematical model for MRSA nasal carriage AM Jarrett, NG Cogan, MY Hussaini Bulletin of mathematical biology 77 (9), 1787-1812

31.) Global sensitivity analysis used to interpret biological experimental results AM Jarrett, Y Liu, NG Cogan, MY Hussaini Journal of mathematical biology 71 (1), 151-170

30.) B Szomolay, NG Cogan (2015) Modelling mechanical and chemical treatment of biofilms with two phenotypic resistance mechanisms, Environmental microbiology

29.) A Dobreva, R Paus, NG Cogan (2015) Mathematical model for alopecia areata Journal of theoretical biology 380, 332-345

28.) DA Ekrut, NG Cogan (2015) A Particular Solutions for a Two-Phase Model with a Sharp Interface BIOMATH 4 (1), Article ID: 1503081

This one is sort of irritating - there are a couple of errors in this paper, most importantly the example is incorrect (although the methodology is correct). The journal will not accept errata, so I am posting one here. If you see people reference this paper, can you please point them to the corrections…

Errata for Shocks and Rarefactions Arise in a Two-Phase Model with Logistic Growth

27.) A. M. Jarrett, Y. Liu, N.G. Cogan and M. Y. Hussaini (2015) Global sensitivity analysis used to interpret biological experimental results, Journal of Mathematical Biology, in press.

26.) Angela M. Jarret, N. G. Cogan and M. E. Shirtliff (2014), Model of Inflammatory Host Response to a Bacterial Infection, Mathematical Medicine and Biology, in press. (Winner of the Best Paper Prize)

25.) N.G. Cogan and S. Chellam (2014) A method for determining the optimal back-washing frequency and duration for dead-end microfiltration, Journal of Membrane Science, 469, 410-417.

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

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.

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

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.

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 stripesStripe0 **Stripe 1**: Veil in stripe regime with tight colormapStripe1 **Stripe 1a**: Same regime with broad colormapStripe 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 flowCluster **Two Clusters**:Two initially identical clusters in parabolic background flowTwo Clusters **One Cluster**: Growth and response to fluidGrowing Biofilm **Two Clusters**: Growth and response to fluidGrowing Biofilm