Georgia Institute of Technology College of Sciences

We improved a computational model of leukemia development from stem cells to terminally differentiated cells by replacing the probabilistic, agent-based model of Roeder et al. (2006) with a system of deterministic, difference equations. The model is based on the relatively recent theory that cancer originates from cancer stem cells that reside in a microenvironment, called the stem cell niche. Depending on a stem cell’s location within the stem cell niche, the stem cell may remain quiescent or begin proliferating. This emerging theory states that leukemia (and potentially other cancers) is caused by the misregulation of the cycle ofproliferation and quiescence within the stem cell niche.Unlike the original agent-based model, which required seven hours per simulation, our model could be numerically evaluated in less than five minutes. The results of our numerical simulations showed that our model closely replicated the average behavior of the original agent-based model. We then extended our difference equation model to a system of age-structured partial differential equations (PDEs), which also reproduced the behavior of the Roeder model. Furthermore, the PDE model was amenable to mathematical stability analysis, which revealed three modes of behavior: stability at 0 (cancer dies out), stability at a nonzero equilibrium (a scenario akin to chronic myelogenous leukemia), and periodic oscillations (a scenario akin to accelerated myelogenous leukemia).The PDE formulation not only makes the model suitable for analysis, but also provides an effective mathematical framework for extending the model to include other aspects, such as the spatial distribution of stem cells within the niche.