Biological fluids are complex with an variety of proteins and other particles suspended within and interacting with each other. Understanding microscopic diffusion through these biomaterials is important to understand biological function and create clinical strategies to treat disease, especially by quantifying the small scale movements of microscopic pathogens and drug delivery mechanisms.
My research has focused on finding techniques to efficiently simulate stochastic models for diffusion in complex fluids, such as the generalized Langevin equation, and methods for statistical inference for these models when observing the path of a single microscopic particle. Data is collected through high-speed video of tracer particles diffusing in the biofluid; the videos are analyzed to track the particles yielding multiple time series of position. Analysis of single time series is an initial step towards allowing us to study heterogeneity among paths induced by spatial variation across the biomaterial which will require a full analysis of the very high-dimensional multi-particle system. In addition, I have been creating statistical methods using hidden Markov models for particles which alternate between diffusing and binding, a phenomena known as caging.
This work is currently supported by the Biomathematics program of the Army Research Office.
- Analysis of single particle diffusion with transient binding using particle filtering
w Jason Bernstein
- On the Wavelet-based Simulation of Anomalous Diffusion
w Gustavo Didier
- Statistical Challenges in Microrheology
w Gustavo Didier, Scott A. McKinley, and David B. Hill
- Time-domain Methods for Diffusive Transport in Soft Matter
w Lingxing Yao, Timothy Elston, and Gregory Forest