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Research

I work, generally, in the field of applied mathematics, and more specifically, in mathematical biology. Most of my research revolves around developing mathematical models of biological phenomena of interest in current biomedical research. Below you can find a more detailed description of some of my projects, as well as links to some of my preprints available on the arXiv.  Recently I have started working with the excellent people at SwarmLab . 
Current projects:

Mathematical representations of bone remodeling.  Bone remodeling is the self-repair process for bone. It consists of two phases, resorption where old bone is removed, and formation where new bone is reformed. The remodeling process is carried out by two classes of specialized bone cells, the behaviors of which are regulated by complicated biochemical signaling. Irregular bone remodeling is associated with many degenerative bone diseases as well as some cancers. For this reason bone remodeling is a active topic of research in musculoskeletal biology and medicine. My collaborators and I are working to construct mathematical and computational representations of bone remodeling that can be used to explore various issues related to bone remodeling, and pathologies associated with irregular remodeling. 
   
Injury response in articular cartilage. Mechanical or chemical stress to articular cartilage kills chondrocytes, i.e. cartilage cells. This results in the appearance of lesions on the cartilage surface and is related to cartilage degeneration and development of post-traumatic osteoarthritis. The typical injury response, and inflammation in particular, can cause a certain amount of collateral damage resulting in the spread of cartilage lesions which in turn increases the potential for development of post-traumatic osteoarthritis. With collaborators I am working to develop a theoretical understanding of the interactions between pro- and anti-inflammatory biochemical signaling, and the eff.ects of such signaling on chondrocyte cell populations as pertaining to cartilage injury response.
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