Modeling cancer stem cell differentiation: reducing the complexity of agent-based models

Abstract

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 partial differential equations (PDEs).  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 of proliferation and  quiescence within the stem cell niche.

Unlike the original agent-based model, which required seven hours per simulation, the PDE model could be numerically evaluated in a few minutes, and our numerical simulations showed that the PDE model closely replicated the average behavior of the original agent-based model.  Furthermore, the PDE model was amenable to mathematical 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.

Thursday, November 18, 2010

2:30 – 3:30 P.M.

372 Science and Engineering Building

(Refreshments at 2:00-2:30 PM in the kitchen area adjacent to 368 SEB)