This work started as a result of a small grant from the National Institutes of Health Grant CA 84509. This was a joint grant between the Harvard Medical School and Princeton University.
Currently, the dynamics of malignant brain tumor growth is a medical mystery. The incidence of primary malignant brain tumors is already 8/100,000 persons per year and is still increasing. The vast majority consists of high-grade malignant tumors such as glioblastoma multiforme (GBM) (see Figure 1). In spite of aggressive conventional and advanced treatments, the prognosis remains uniformly fatal with a median survival time for patients with GBM of 8 months.
The rapid growth and resilience of tumors make it difficult to believe that they behave as random, disorganized and diffuse cell masses and suggest that they are emerging opportunistic systems, that not only adapt to their environment but also change their environment for survival purposes. If this hypothesis holds true, a growing tumor must be investigated and treated as a self-organizing complex dynamical system. This cannot be done with currently available in vitro/in vivo models or common modeling approaches.
Figure 1. Left panel: The tumor is located in the upper left portion of the image. The white rim around the tumor is composed of highly active cells, corresponding to the red rim in the right panel. Right panel: The outer, red rim corresponds to cells that are dividing rapidly. The middle, yellow region are cells that are alive but are not dividing. The innermost, black region are cells that are necrotic (dead).
The aim of the project is to show that we can model the growth (proliferation and invasion) of brain tumors using concepts from statistical physics, materials science and dynamical systems, as well as data from novel oncological experiments. We expect the work not only to increase our understanding of tumorigenesis, but to provide insight into novel ways to treat malignant brain tumors.
We have developed a novel and versatile three-dimensional cellular automaton model of brain tumor growth [1]. We showed that macroscopic tumor behavior can be realistically modeled using microscopic parameters. Using only four parameters, this model simulates Gompertzian growth for a tumor growing over nearly three orders of magnitude in radius. It also predicts the composition and dynamics of the tumor at selected time points in agreement with medical literature. We also demonstrated the flexibility of the model by showing the emergence, and eventual dominance, of a second tumor clone with a different genotype. The model incorporates several important and novel features, both in the rules governing the model and in the underlying structure of the model. Among these are a new definition of how to model proliferative and non-proliferative cells, an isotropic lattice, and an adaptive grid lattice.
Malignant brain tumors consist of a number of distinct subclonal populations. Each of these subpopulations may be characterized by its own behaviors and properties. These subpopulations arise from the constant genetic and epigenetic alteration of existing cells in the rapidly growing tumor. However, since each single cell mutation only leads to a small number of offspring initially, very few newly arisen subpopulations survive more than a short time. In a subsequent work [2], we quantified ``emergence,'' i.e., the likelihood of an isolated subpopulation surviving for an extended period of time. Only competition between clones was considered; there are no cooperative effects included. The probability that a subpopulation emerges under these conditions was found to be a sigmoidal function of the degree of change in cell division rates. This function has a non-zero value for mutations that confer no advantage in growth-rate, which represents the emergence of a distinct subpopulation with an advantage that has yet to be selected for, such as hypoxia tolerance or treatment resistance. A logarithmic dependence on the size of the mutated population was also observed. A significant probability of emergence was found for subpopulations with any growth advantage that comprise even 0.1% of the proliferative cells in a tumor. The impact of even two clonal populations within a tumor was shown to be sufficient such that a prognosis based on the assumption of a monoclonal tumor can be markedly inaccurate.
We also extended the cellular automaton to study the effects of treatment [3]. By varying three treatment parameters, we simulated tumors that display clinically plausible survival times. Much of our work is dedicated to heterogeneous tumors with both treatment-sensitive and treatment-resistant cells. First, we investigated two-strain systems in which resistant cells are initialized within predominantly sensitive tumors. We found that when resistant cells are not confined to a particular location, they competed more effectively with the sensitive population. Moreover, in this case, the fraction of resistant cells within the tumor was a less important indicator of patient prognosis. In additional simulations, we studied tumors that are initially monoclonal and treatment-sensitive, but that undergo resistance-mutations in response to treatment. Here, the tumors with both very frequent and very infrequent mutations developed with more spherical geometries. Tumors with intermediate mutational responses exhibited multi-lobed geometries, as mutant strains develop at localized points on the tumor's surfaces.
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