Effects of Anti-Angiogenesis on Glioblastoma Growth and Migration: Model to Clinical Predictions

Abstract

Glioblastoma multiforme (GBM) causes significant neurological morbidity and short survival times. Brain invasion by GBM is associated with poor prognosis. Recent clinical trials of bevacizumab in newly-diagnosed GBM found no beneficial effects on overall survival times; however, the baseline health-related quality of life and performance status were maintained longer in the bevacizumab group and the glucocorticoid requirement was lower. Here, we construct a clinical-scale model of GBM whose predictions uncover a new pattern of recurrence in 11/70 bevacizumab-treated patients. The findings support an exception to the Folkman hypothesis: GBM grows in the absence of angiogenesis by a cycle of proliferation and brain invasion that expands necrosis. Furthermore, necrosis is positively correlated with brain invasion in 26 newly-diagnosed GBM. The unintuitive results explain the unusual clinical effects of bevacizumab and suggest new hypotheses on the dynamic clinical effects of migration by active transport, a mechanism of hypoxia-driven brain invasion.

Fast and high temperature hyperthermia coupled with radiotherapy as a possible new treatment for glioblastoma

“…All the three more complete GBM models mentioned in the text [47, 48, 51] predict that in the evolution of the disease, the biologically active region (proliferating and infiltrating) is pushed toward the periphery of the tumor, while the central part becomes progressively larger and necrotic. Therefore, it seems reasonable to concentrate in this peripheral region both radiation and HT.…”

“…To solve this gap, more detailed models, with five or more equations describing the main tumor elements (such as normal, necrotic and hypoxic tumor cells, vascularity, nutrients, etc.) were subsequently proposed [45–51]. …”

Single Cell Mathematical Model Successfully Replicates Key Features of GBM: Go-Or-Grow Is Not Necessary

“…The authors have recently reported a system of partial differential equations (PDE) that models GBM at the scale of MRI; the equations model replication, brain invasion, angiogenesis, and hypoxia [4, 5]. Here, we modify the system of equations to eliminate the GoG phenotype, thus reducing the system to a single glioma cell model; the equations are shown in Table 1, and the parameter values and units are displayed in Table 2.…”

“…necrosis, enhancing ring and edema, but also reproduces specific tumor progression patterns and their associated average patient survival times [4, 5]. This model incorporates the GoG phenotype by including two specific cell types, Invasive (I) cells and Proliferative (P) cells, which can switch back and forth between one phenotype or another depending on the nutrient environment in the brain.…”

“…As suggested by their names, I cells move throughout the brain but do not divide, and P cells divide but do not move; under the assumption of the GoG phenotype, a single tumor cell will never move and divide at the same time. The equations in [4, 5] also include an angiogenic term.…”