Theoretical and computational tools that can be used in the clinic to predict
neoplastic progression and propose individualized optimal treatment strategies
to control cancer growth is desired. To develop such a predictive model, one
must account for the complex mechanisms involved in tumor growth. Here we
review resarch work that we have done toward the development of an "Ising
model" of cancer. The review begins with a description of a minimalist
four-dimensional (three in space and one in time) cellular automaton (CA) model
of cancer in which healthy cells transition between states (proliferative,
hypoxic, and necrotic) according to simple local rules and their present
states, which can viewed as a stripped-down Ising model of cancer. This model
is applied to model the growth of glioblastoma multiforme, the most malignant
of brain cancers. This is followed by a discussion of the extension of the
model to study the effect on the tumor dynamics and geometry of a mutated
subpopulation. A discussion of how tumor growth is affected by chemotherapeutic
treatment is then described. How angiogenesis as well as the heterogeneous and
confined environment in which a tumor grows is incorporated in the CA model is
discussed. The characterization of the level of organization of the invasive
network around a solid tumor using spanning trees is subsequently described.
Then, we describe open problems and future promising avenues for future
research, including the need to develop better molecular-based models that
incorporate the true heterogeneous environment over wide range of length and
time scales (via imaging data), cell motility, oncogenes, tumor suppressor
genes and cell-cell communication. The need to bring to bear the powerful
machinery of the theory of heterogeneous media to better understand the
behavior of cancer in its microenvironment is presented.Comment: 55 pages, 21 figures and 3 tables. To appear in Physical Biology.
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