
StotskyFrom MathBioContentsContact InformationEmail: Jay.Stotsky@colorado.edu http://amath.colorado.edu/people/jaystotsky AboutI am a fifth year graduate student in the Applied Mathematics Department. I am working with my advisor Dr. David Bortz on a project to model the physical and structural properties of bacterial biofilms. I am also a Dept. of Energy Computational Science Graduate Fellow. (https://www.krellinst.org/csgf/fellows/profile?n=stotsky2014) (Photo courtesy of the University of Colorado) PublicationsJ. A. Stotsky, J. F. Hammond, L. Pavlovsky, E. J. Stewart, J. G. Younger, M. J. Solomon, and D. M. Bortz. Variable Viscosity and Density Biofilm Simulations using an Immersed Boundary Method, Part II: Experimental Validation and the Heterogeneous RheologyIBM. Journal of Computational Physics, 317:204–222. (http://www.sciencedirect.com/science/article/pii/S0021999116300730) J. A. Stotsky, V. Dukic, and D. M. Bortz. (in revision) A Point Process Model for Generating Biofilms with Realistic Microstructure and Rheology. 2017 arXiv:1707.05739 (https://arxiv.org/abs/1707.05739) ResearchI am currently working on models and simulations of biofilms that can accurately capture the biomechanical response of biofilms to fluid flow. Biofilms are colonies of bacteria that grow on surfaces and are often interconnected through an extracellular matrix that contains cohesive polymers. Determining the material properties of biofilms, especially what leads to detachment and fragmentation of biofilms is an open question that has relevance to several application areas. Below is an image from a simulation of a biofilm immersed in a fluid that is undergoing shear deformation.
Experimental validation of the heterogeneous rheology Immersed Boundary MethodMy first work was to develop numerical validation tests to compare results from the biofilm model, called the heterogeneous rheology Immersed Boundary Method (hrIBM) model to experimental data. The hrIBM model consists of a equations governing fluid flow through a biofilm, positions of bacteria in a biofilm, and how the variable viscosity and forces vary over time and space. Features of this model are that it accounts for the highly heterogeneous rheology found in biofilms, and incorporates the motion of individual bacteria and viscoelastic linkages between bacteria. In Figure 2, a virtual biofilm is depicted.
In order to achieve this comparison, we used data collected by collaborators at the University of Michigan. This data consisted of frequency dependent measurements of the dynamic moduli of live biofilms undergoing oscillatory shear deformations, and time dependent measurements of the compliance of biofilms to a constant force.
A Point Process Model for BiofilmsThe heterogeneous rheology Immersed Boundary model described in the previous section works well when there is microscopy data to initialized the positions of bacteria in a biofilm. However, in many practical settings, such data is not available, and is expensive to obtain. Thus, it is of interest to have a way of understanding how bacteria are positioned in a biofilm. In this project, the goal was to develop a statistical model whose realizations are sets of points that correspond to realistic positions of bacteria in a biofilm. Towards this goal, we developed a pairwise interaction model (PIM). The probability is then related to a pairwise potential, and an external, or singlet potential. One of the key statistical characteristics in describing this data is the pair correlation function (PCF). The PCF quantifies how favorable it is for two bacteria to be separated by some distance. A comparison of the PCF computed from experimental data and the statistical model is shown in Figure 4
Comparisons of the dynamic moduli of virtual biofilms generated from the PIM model, several other statistical model, and the empirical data is shown in Figure 5.
PublicationsJ. A. Stotsky, J. F. Hammond, L. Pavlovsky, E. J. Stewart, J. G. Younger, M. J. Solomon, and D. M. Bortz. Variable Viscosity and Density Biofilm Simulations using an Immersed Boundary Method, Part II: Experimental Validation and the Heterogeneous RheologyIBM. Journal of Computational Physics, 317:204–222. (http://www.sciencedirect.com/science/article/pii/S0021999116300730) J. A. Stotsky, V. Dukic, and D. M. Bortz. (in revision) A Point Process Model for Generating Biofilms with Realistic Microstructure and Rheology. 2017 arXiv:1707.05739 (https://arxiv.org/abs/1707.05739) 