Fig. 4

Schematic representation of the mathematical modeling of cancer at an intracellular, cellular and organ scale. Because tumors are heterogeneous entities in a changing microenvironment, development of new chemotherapeutics and understanding the sophisticated cancer redox biology are needed to address the importance of diversity in cancer cell populations and microenvironmental characteristics. Integrating information from multiple levels of biological complexity and multiscale models can potentially be more powerful than focusing solely on the well-developed molecular network level. In this framework, a system of ordinary differential equations could be developed to describe the dynamics of N species, [ROS]1(t), [ROS]2(t), [ROS]3(t) …[ROS]N(t), where the dynamics are governed by the production and decay terms for each ROS species, Pi(t) and Di(t), for i = 1,2,3…N, and t is time. In addition, each ROS species varies both temporally and spatially, such as at the organ-scale, it would be more appropriate to work with a system of partial differential equations. For this situation the mathematical model would predict the spatiotemporal distribution of N species, [ROS]1(x, t), [ROS]2(x,t), [ROS]3(x,t) …[ROS]N(x,t), where t is time and x is spatial position. In this case the spatial transport of each ROS species is governed by the flux J(x,t), which could be used to specify diffusive transport or some kind of directed transport if appropriate