Research

My primary interest is the mathematical modeling of cancer. In particular, I develop mathematical models of various aspects of tumor growth, genetics, angiogenesis, the tumor microenvironment, and macroscopic tissue structures that combine to model the progression of cancer. I develop and adapt high-accuracy level set and ghost fluid methods to implement and study these mathematical models. I am interested in advancing the field of computational oncology by combining my expertise in mathematical modeling and high-performance computing.

In my M.S. thesis, I primarily worked on improving the accuracy and robustness of ghost fluid/level set methods, especially when dealing with evolving shapes that exhibit frequent morphological change. (e.g., splitting and merging regions) Part of that work led to improved curvature and normal vector discretizations. You can explore several publications on my numerical techniques here.

I am now focusing on the development and combination of continuum-based models of tumor genetic variation (with both spatial and stochastic temporal elements), the tumor microenvironment, complex macroscopic tissue structure, angiogenesis, and metastasis. In am particularly interested in the complex interaction between an evolving tumor and its surrounding microenvironment. This will be the primary focus of my Ph.D. dissertation.

My long-term goal is to develop an increasingly sophisticated, multiscale cancer simulator, with which experimental and clinical oncologists could systematically investigate the biophysical roots of cancer, understand how it spreads, and learn how best to treat it.

You can view animations of some of my work on the multimedia page.

Lastly, I have developed some open-source software tools, some of which may be helpful for scientific computation. Click here to view those tools.

Last Modified: February 19, 2007 at 06:24 PM (U.S. Pacific Time) Copyright © 2003-2007 Paul Macklin