Abstract
Glioblastomas are highly diffuse, malignant tumors that have so far evaded clinical treatment. The strongly invasive behavior of cells in these tumors makes them very resistant to treatment, and for this reason both experimental and theoretical efforts have been directed toward understanding the spatiotemporal pattern of tumor spreading. Although usual models assume a standard diffusion behavior, recent experiments with cell cultures indicate that cells tend to move in directions close to that of glioblastoma invasion, thus indicating that a biased random walk model may be much more appropriate. Here we show analytically that, for realistic parameter values, the speeds predicted by biased dispersal are consistent with experimentally measured data. We also find that models beyond reaction–diffusion–advection equations are necessary to capture this substantial effect of biased dispersal on glioblastoma spread.
Highlights
Glioblastomas are highly diffuse, malignant tumors that have so far evaded clinical treatment
Fisher’s model assumes that cells behave as random walkers, but several aspects of cancer cell population dynamics depart from simple diffusion [13]
In order to provide an analytic estimate of this impact, here we present several increasingly realistic models of GLB spread with an outward dispersal preference by invasive cells
Summary
2(b) we plot the classical (Fisher) speed cFisher and the biased-model speed cRDA given by equation (10) as a function of the radial bias parameter x (for the value g = 0.1 day−1, which lies in the range 0 < g < 0.3 day−1 [14]). We observe that, according to the RDA model, within the experimentally observed speed range (hatched area in figure 2(b)), the bias effect (dotted line) is between 90 and 180%. This confirms that the effect of biased cell dispersal should be taken into account to understand GLB invasion rates
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