A Multilayer Grow-or-Go Model for GBM: Effects of Invasive Cells and Anti-Angiogenesis on Growth

Abstract

The recent use of anti-angiogenesis (AA) drugs for the treatment of glioblastoma multiforme (GBM) has uncovered unusual tumor responses. Here, we derive a new mathematical model that takes into account the ability of proliferative cells to become invasive under hypoxic conditions; model simulations generate the multilayer structure of GBM, namely proliferation, brain invasion, and necrosis. The model is able to replicate and justify the clinical observation of rebound growth when AA therapy is discontinued in some patients. The model is interrogated to derive fundamental insights int cancer biology and on the clinical and biological effects of AA drugs. Invasive cells promote tumor growth, which in the long run exceeds the effects of angiogenesis alone. Furthermore, AA drugs increase the fraction of invasive cells in the tumor, which explain progression by fluid-attenuated inversion recovery (FLAIR) signal and the rebound tumor growth when AA is discontinued.

Self-organization in brain tumors: how cell morphology and cell density influence glioma pattern formation

“…Since the cells have an 30 ellipsoid shape, cell-cell avoidance leads to two possible effects: repulsion (i.e. cells move 31 away from each other) and steering (cells turn to avoid collision). The larger the 32 eccentricity of the cell, the larger the effect on steering.…”

On the preliminary design of hyperthermia treatments based on infusion and heating of magnetic nanofluids

“…Let us then address the propagation of the NPs concentration during the infusion. In particular, by recalling (18) and (19), let us consider the position r of the NPs concentration wave front, as a function of the infused nanofluid volume V in f . Illustrative trends are shown in Fig.…”

“…Indeed, many contributions focused on tumor growth [18], also accounting for chemotherapy [19] or radiotherapy [20] effects limiting proliferation. Moreover, valuable studies addressed the optimal control of cancer drug therapy [21], up to proposing multi-scale approaches [22].…”

A strongly degenerate diffusion‐haptotaxis model of tumour invasion under the go‐or‐grow dichotomy hypothesis

“…Motivated by the above-mentioned facts, we propose in this paper a model for tumour cell invasion, in which we account for the go-or-grow hypothesis and distinguish between migrating and proliferating (hence, nonmoving) cells. Several continuum mathematical models relying on the go-or-grow behaviour of tumour cells and explicitly accounting for the 2 subpopulations of migrating and proliferating cells, respectively, have been considered, eg, in Gerlee and Nelander 13 and Saut et al, 14 and featured reaction-(cross-)diffusion(-chemotaxis) equations. Using a 2-component continuous-time random walk along with a probabilistic approach based thereupon and involving switching with exponentially distributed waiting times between the proliferation and migration phenotypes, Fedotov and Iomin deduced 15 an ordinary differential equation-partial differential equation (ODE-PDE) system for the macroscopic dynamics of the 2 types of cancer cell densities, supporting the idea of tumour cells subdiffusivity instead of the more common Fickian diffusivity.…”