ABSTRACT
The complexity of cancer as a disease state is a reflection of the inherent complexity of the molecular interactions that govern cell metabolism, growth, and division. This is further complicated by the underlying heterogeneity of tumor tissue and the dependence of tumor growth on surrounding support cells (Burkert, Wright, and Alison 2006). Therefore, understanding the initiation, growth, and spread of cancer requires the use of mathematical and computational tools that can help researchers visualize and model these complex interactions both within and between cells. Modeling cancer is not new. Efforts aimed at mathematically modeling certain features of tumor growth date back to the 1920s but it is Burton who is largely credited with developing one of the first accurate tumor models (Burton 1966). His work not only explained the observed distribution of oxygen in a solid tumor (i.e., the necrotic core), but also the characteristic Gompertzian growth curve seen in solid tumors. Subsequent efforts in the 1970s and 1980s focused on modeling tumor invasion and metastasis using simplified cellular diffusion models or the examination of mechanical stress on tumor shape (Araujo and McElwain 2004). With the increasing availability of computers and with our improved understanding of molecular biology, cancer modeling during the late 1990s evolved to have a greater focus on simulating (albeit crudely) the molecular etiology of different cancers. Over the past decade, with the explosion of quantitative data coming from genomic, proteomic, and metabolomic experiments along with equally impressive data coming from advanced cellular and tissue imaging techniques, we have now reached the point where far more realistic computational modeling of both the molecular and cellular events (i.e., the systems biology) in tumor development is becoming a possibility (Alberghina Chiaradonna, and Vanoni 2004; Bugrim, Nikolskaya, and Nikolsky 2004; Hollywood, Brison, and Goodacre 2006; Ideker et al. 2001; Jares 2006).
