Key rates for the grades and transformation ability of glioma: model simulations and clinical cases.

Tumor progression to higher grade is a fundamental property of cancer. The malignant advancement of the pathological features may either develop during the later stages of cancer growth (natural evolution) or it may necessitate new mutations or molecular events that alter the rates of growth, dispersion, or neovascularization (transformation). Here, we model the pathological and radiological features of grades 2-4 gliomas at the times of diagnosis and death and study grade development and the progression to higher grades. We perform a retrospective review of clinical cases based on model predictions. Simulations uncover two unusual patterns of glioma progression, which are supported by clinical cases: (1) some grades 2 and 3 gliomas lack the ability of progression to higher grades, and (2) grade 3 glioma may evolve to GBM in a few weeks. All 13 gliomas that recurred at the same grade carry either the IDH1-R132H or the ATRX mutation. All (five of five) grade 3 tumors are 1p/19q co-deleted, IDH1-R132H mutated and ATRX wt. Furthermore, three of seven grade 2 gliomas are both IDH1-R132H mutated and ATRX mutated. Simulations replicate the good prognosis of secondary GBM. The results support the hypothesis that constant rates of dispersion, proliferation, and angiogenesis prescribe either a natural evolution or the inability to progress to higher grades. Furthermore, the accrual of molecular events that change a tumor's ability to infiltrate, proliferate or neovascularize may transform the glioma either into a more aggressive tumor at the same grade or elevate its grade.

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

Glioblastoma (GBM) is a malignant brain tumor that continues to be associated with neurological morbidity and poor survival times. Brain invasion is a fundamental property of malignant glioma cells. The Go-or-Grow (GoG) phenotype proposes that cancer cell motility and proliferation are mutually exclusive. Here, we construct and apply a single glioma cell mathematical model that includes motility and angiogenesis and lacks the GoG phenotype. Simulations replicate key features of GBM including its multilayer structure (i.e.edema, enhancement, and necrosis), its progression patterns associated with bevacizumab treatment, and replicate the survival times of GBM treated or untreated with bevacizumab. These results suggest that the GoG phenotype is not a necessary property for the formation of the multilayer structure, recurrence patterns, and the poor survival times of patients diagnosed with GBM.

Computational Trials: Unraveling Motility Phenotypes, Progression Patterns, and Treatment Options for Glioblastoma Multiforme.

Glioblastoma multiforme is a malignant brain tumor with poor prognosis and high morbidity due to its invasiveness. Hypoxia-driven motility and concentration-driven motility are two mechanisms of glioblastoma multiforme invasion in the brain. The use of anti-angiogenic drugs has uncovered new progression patterns of glioblastoma multiforme associated with significant differences in overall survival. Here, we apply a mathematical model of glioblastoma multiforme growth and invasion in humans and design computational trials using agents that target angiogenesis, tumor replication rates, or motility. The findings link highly-dispersive, moderately-dispersive, and hypoxia-driven tumors to the patterns observed in glioblastoma multiforme treated by anti-angiogenesis, consisting of progression by Expanding FLAIR, Expanding FLAIR + Necrosis, and Expanding Necrosis, respectively. Furthermore, replication rate-reducing strategies (e.g. Tumor Treating Fields) appear to be effective in highly-dispersive and moderately-dispersive tumors but not in hypoxia-driven tumors. The latter may respond to motility-reducing agents. In a population computational trial, with all three phenotypes, a correlation was observed between the efficacy of the rate-reducing agent and the prolongation of overall survival times. This research highlights the potential applications of computational trials and supports new hypotheses on glioblastoma multiforme phenotypes and treatment options.

Effects of anti-angiogenesis on glioblastoma growth and migration: model to clinical predictions.

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.

Modeling of regulatory networks: theory and applications in the study of the Drosophila circadian clock.

Biological networks can be very complex. Mathematical modeling and simulation of regulatory networks can assist in resolving unanswered questions about these complex systems, which are often impossible to explore experimentally. The network regulating the Drosophila circadian clock is particularly amenable to such modeling given its complexity and what we call the clockwork orange (CWO) anomaly. CWO is a protein whose function in the network as an indirect activator of genes per, tim, vri, and pdp1 is counterintuitive--in isolated experiments, CWO inhibits transcription of these genes. Although many different types of modeling frameworks have recently been applied to the Drosophila circadian network, this chapter focuses on the application of continuous deterministic dynamic modeling to this network. In particular, we present three unique systems of ordinary differential equations that have been used to successfully model different aspects of the circadian network. The last model incorporates the newly identified protein CWO, and we explain how this model's unique mathematical equations can be used to explore and resolve the CWO anomaly. Finally, analysis of these equations gives rise to a new network regulatory rule, which clarifies the unusual role of CWO in this dynamical system.