We present a model aiming at the description of intercellular communication on the invasive character of gliomas. We start from a previous model of ours based on a cellular automaton and develop a new version of it in a three-dimensional geometry. Introducing the hydrodynamic limit of the automaton we obtain a macroscopic model involving a nonlinear diffusion equation. We show that this macroscopic model is quite adequate for the description of realistic situations. Comparison of the simulations with experimental results shows agreement with the finding that the inhibition of intercellular communication (through gap junctions) tends to decrease migration. As an application of our model we estimated the possible increase in life expectancy, due to reduced cell migration mediated by the inhibition of intercellular communication, on patients suffering from gliomas. We find that the obtained increase may amount to a 20% gain in the case of unresectable tumours.