My general interests are in numerical mathematics
applied to problems in biology, with an emphasis on the physiologies of cancer and biofilm. 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
advise 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
work with Jason is done in collaboration with the Henry Lab
and the Stipp
Lab. The work with Stephanie is done in collaboration with the
Leddy Lab.
The main thrust of my research has been in physiologically 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-0914514.
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.
