My research work revolve around the development of theoretical and numerical models for studying the bio-mechanical systems, and complex flows. Physics of fluids in these systems are important to a variety of applications, including: 1) bacterial community and biofilm formation, where biofilm can be modeled as a multi-scale system, 2) cell-biomechanics, where the focus is on the behavior of single cells, cell mechanical properties and interactions between cells in extracellular environment, and 3) complex flows which exhibit rheological behavior.

In the case of such complex systems, where the physics is not fully explored, mathematical models can be coupled with experiments to better predict and optimize the relevant parameters involved in the problem. Parameter estimates are fundamental for a range of predictive analysis including optimal control, sensitivity and uncertainty. However, these data assimilation techniques are much less widespread in biomathematics applications where the challenges are unique. I develop numerical platforms based on Bayesian statistics to assimilate observational data to estimate parameters in a variety of settings, primarily in mechanics where the topic is underdeveloped.

During my postdoctoral career at the Florida State University, I had the opportunity to work closely with Dr. Cogan and Dr. Huusani on mathematical modeling and uncertainty quantification of biofilm mechanics. The heterogeneity of the biofilm composition and its dynamic behavior require detiled investigations. The bacteria colony in the biofilm produce various types of extracellular polymeric substances such as Psl, Pel, and alginate, which are involved in biofilm development, attachment to the surface and structure integrity. The viscoelastic characteristics of such polysaccharides are not fully explored in literature due to their complexity, and is the subject of my research. At the same time, there is renewed interest in the biomechanics of biofilms due recent advances in understanding of the key signaling pathways controlling polymer production. I have estimated mechanical parameters of biofilms, along with our experimental collaborators, Dr. Stoodley and Dr. Gloag (Ohio state University). For the next step of this work, I will use dynamical systems and PDE viscoelastic models to build a robust mathematical model for development and spatiotemporal arrangement of biofilm components, including rheological and kinetics models. The mathematical model will be coupled with stochastic Bayesian algorithms to quantify the uncertainty and estimate the relevant model parameters. This understanding will be useful for targeted treatments designed to manipulate the biofilm, making it easier to remove.

During my master’s study at the Koc University and Ph.D. at the University of Central Florida, I had the opportunity to work on various projects and collaborated with amazing research teams. My work was focused specifically on numerical simulations of complex rheological and biological flows in droplet based microfluidic systems. For these projects, I modeled the governing fluid flow equations by an incompressible Navier-Stokes equations which were solved in the framework of a one-field formulation on an Eulerian grid for all fluids. The FENE-CR viscoelastic convective term were treated by a fifth-order upwind WENO-Z scheme along with a log-conformation method to overcome high Weissenberg number to preserve the positive-definiteness of the conformation tensor. Using these numerical methods, I simulated formation of droplets, deposition of cell-loaded droplets in bio-printing systems, and migration and encapsulation of cells in microfluidic channels.