Abstract
Glioblastoma is a rapidly evolving high-grade astrocytoma that is distinguished pathologically from lower grade gliomas by the presence of necrosis and microvascular hyperplasia. Necrotic areas are typically surrounded by hypercellular regions known as “pseudopalisades” originated by local tumor vessel occlusions that induce collective cellular migration events. This leads to the formation of waves of tumor cells actively migrating away from central hypoxia. We present a mathematical model that incorporates the interplay among two tumor cell phenotypes, a necrotic core and the oxygen distribution. Our simulations reveal the formation of a traveling wave of tumor cells that reproduces the observed histologic patterns of pseudopalisades. Additional simulations of the model equations show that preventing the collapse of tumor microvessels leads to slower glioma invasion, a fact that might be exploited for therapeutic purposes.
Highlights
Malignant gliomas are the most common and lethal type of primary brain tumor
We model the hypercellular regions formation in glioblastoma multiforme (GBM) perinecrotic areas including the spatiotemporal interplay among normoxic and hypoxic tumor cell, a necrotic core, and the oxygen distribution
It is well known in biological contexts that some aspects of glioma dynamics can be understood in terms of two cell subpopulations corresponding to two dominant phenotypes (Giese et al 2003; DeBerardinis et al 2007; Keunen et al 2011; Onishi et al 2011; Hatzikirou et al 2012). This means that minimal mathematical models such as those based on Fisher–Kolmogorov type equations accounting for GBM progression (Frieboes et al 2007; Swanson et al 2008; Bondiau et al 2008; Eikenberry and Kuang 2009; Konukoglu et al 2010; Rockne et al 2010; Pérez-García et al 2011) may benefit from incorporating the two different phenotypes and necrosis as it is done in this paper
Summary
GBM is the most heterogeneous primary brain tumor. Studies by Anderson et al (2009), using three different discrete models, have shown that when low oxygen switch occurs, a large percentage of the populations become growth arrested or removed and the remaining cells are mainly dominated by a single aggressive phenotype. Our modeled system comprises three different compartments: two different coupled tumor cell subpopulations, competing for space and resources (oxygen), corresponding to the two dominant phenotypes, normoxic Cn and hypoxic Ch, well described in GBM (DeBerardinis et al 2007; Giese et al 2003; Keunen et al 2011; Onishi et al 2011). Necrosis represents a massive cell death and its degree is inversely related to patient survival (Nelson 1983 and Lacroix et al 2001) Since it happens at a different rate and occupies space, we incorporate Cd into the proliferation limiting terms in Eqs. Since it happens at a different rate and occupies space, we incorporate Cd into the proliferation limiting terms in Eqs. (1a) and (1b)
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