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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 the SwarmLab at the New Jersey Institute of Technology
Current projects: 

Mathematical aspects of collective behavior in social insects.  Social insects such as ants exhibit fascinating group behaviors where, from simple actions of individuals, emerges seemingly highly organized collective coordination in foraging and other activities important for colony survival. Over the past couple of years I have started collaborating with biologists Marc Seid at the University of Scranton and Simon Garnier at the New jersey Institute of Technology on problems that should lead to further understanding of often observed phenomena in the collective behavior of social insects. Through a combination of experiment and mathematical modeling we are learning more about how groups of insects work together to insure colony survival.       

Past 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 effects of such signaling on chondrocyte cell populations as pertaining to cartilage injury response.
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