Kevin Murgas (Biomedical Engineering, Class 2017), started working on this project during a Research Experience for Undergraduates (REU) program in mathematical biology in the summer of 2015. Together with his research mentor, Dr. Marc Ryser, they developed a new approach to modeling the dynamics of physiological bone remodeling – the process responsible for keeping our bones strong and healthy. By describing the process of bone remodeling in the language of evolutionary game theory, they developed and analyzed a three-dimensional model of the interactions between bone tissue and the cells responsible for its maintenance. With their model, Kevin and Marc were able to show that the cyclic renewal dynamics and spatial patterns typical for human bone can arise naturally from the complex interactions between the different cell types. Over the past year, Kevin learned exciting new mathematics, ranging from spatial stochastic processes to partial differential equations. He also developed software to simulate the evolutionary game under different conditions and to visualize the results. Kevin enthused, "I really enjoyed the Duke Math-Bio REU; it was an incredible opportunity to begin applying my abilities in research. From the start of the program, we dove into advanced mathematical theory to produce an analytical model and simulation for the dynamic process of bone remodeling. Replaying the simulations and seeing spatially coordinated behavior arise was breathtaking because we had only actually defined the direct neighbor-neighbor interactions. It was surreal to realize we had done the work to establish a novel understanding of spatial EGT."
Dr. Marc Ryser spoke highly of Kevin's work. "Kevin had to learn several advanced mathematical concepts for this project, and got a good insight into real-life research. It was a pleasure to see how quickly he assimilated new theory and was able to translate it into practice. Using advanced mathematical concepts to model biological processes is very challenging, and Kevin did an excellent job. In the future, we hope to couple this biological model with mechanical models of bone loading and adaptation to develop an integrated description of how mechanical loading leads to different structural patterns in our bone tissue."
http://www.sciencedirect.com/science/article/pii/S0022519317300218