Research Interests

My general interests are in numerical mathematics applied to problems in biology. I am a member of the Mathematical & Computational Biology and Numerical Analysis groups within the Department of Mathematics. I am also on the faculty of the Applied Mathematical and Computational Sciences program of the Graduate College. I currently supervise two AMCS students. I am working with Jason Graham on the representation of cellular motion involved in tumor invasion and metastasis, and Stephanie Schmidt on a model of a Nafion fuel cell.

The main thrust of my research has been in structured multiscale modeling and simulation. I have worked on applications such as tumor invasion, biofilm growth and persistence, and Proteus mirabilis swarm-colony development. I refer to these systems as "structured multiscale" because they link mechanisms at the macroscopic or population scale with mechanisms at the individual scale using so-called structured variables such as age or size. The different spatial scales induce different time scales into the problem.

A major focus of my research is the development of software that will allow modelers to incorporate physiological structure more easily into their study of various biological systems. This effort is partially supported by the NSF under award DMS-0802609.

My other major projects are the modeling and simulation of multiple myeloma, with collaborators at Vanderbilt University, and phenotypic diversity in bacterial biofilms, with collaborators at Montana State University.

Tumor Invasion

Biofilm Growth

Proteus mirabilis

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Last revision: June 17, 2009.