Quantifying the Role of Angiogenesis in Malignant Progression of Gliomas: In Silico Modeling Integrates Imaging and Histology

Abstract

Gliomas are uniformly fatal forms of primary brain neoplasms that vary from low-grade to high-grade (glioblastoma). While low-grade gliomas are weakly angiogenic, glioblastomas are among the most angiogenic of tumors. Thus, interactions between glioma cells and their tissue microenvironment may play an important role in aggressive tumor formation and progression. To quantitatively explore how tumor cells interact with their tissue microenvironment, we incorporated the interactions of normoxic glioma cells, hypoxic glioma cells, vascular endothelial cells, diffusible angiogenic factors, and necrosis formation into a first-generation, biologically-based mathematical model for glioma growth and invasion. Model simulations quantitatively described the spectrum of in vivo dynamics of gliomas visualized with medical imaging. Further, we investigated how proliferation and dispersal of glioma cells combine to induce increasing degrees of cellularity, mitoses, hypoxia-induced neo-angiogenesis and necrosis, features that characterize increasing degrees of “malignancy”, and we found that changes in the net rates of proliferation ({lower case rho}) and invasion (D) are not always necessary for malignant progression. Thus, although other factors, including the accumulation of genetic mutations, can change cellular phenotype (e.g. proliferation and invasion rates), this study suggests that these are not required for malignant progression. Simulated results are placed in the context of the current clinical World Health Organization grading scheme for studying specific patient examples. This study suggests that through the application of the proposed model for tumor-microenvironment interactions, predictable patterns of dynamic changes in glioma histology distinct from changes in cellular phenotype (e.g. proliferation and invasion rates) may be identified, thus providing a powerful clinical tool.

Applying a patient-specific bio-mathematical model of glioma growth to develop virtual [18F]-FMISO-PET images

“…Our previous successes with the PI model combined with the need for more information on the molecular level dynamics of tumour growth has led us to explore an expanded model, which we will refer to as the proliferation-invasion-hypoxia-necrosis-angiogenesis (PIHNA) model (Swanson et al, 2011). The PIHNA model characterizes GBM evolution by partitioning the malignant tumour cells into subpopulations based on fundamental histological characteristics of GBM including normoxic GBM cells, hypoxic GBM cells, necrotic tissue, neo-angiogenic vasculature and angiogenic factors ((5)-(10)).…”

“…It was designed in order to consider the complex interplay of essential histological characteristics of GBM and has already provided insights into the grading of GBM (Swanson et al, 2011). The PIHNA model partitions the tumour cell populations into three classes: well-oxygenated 'normoxic' tumour cells (c), hypoxic tumour cells (h) and dead or necrotic tumour cells (n) along with angiogenic factors (a), density of vasculature (v) and total tumour cell density (T ).…”

“…Parameter values and references are listed in Table 2. Further discussion regarding the form and justification of the equations can be found elsewhere (Swanson et al, 2011). Patient-specific PI model parameters (D PI , ρ PI ) were determined from pre-treatment MRI tumour volumes (Harpold et al, 2007;Szeto et al, 2009; and were converted using a one-toone mapping of PIHNA model parameters D c and ρ (Fig.…”

Mathematical modelling: Forecasting cancer

“…Such models are starting to have an impact in the clinic. Alexander Anderson, a mathematical and computer modeller at the Moffitt centre and one of the team who worked on the glioma study, is using the model to investigate how cancer moves and spreads 1 . His lab has built computer models that focus on the changes to individual cancer cells.…”

Some Novel Exponential and Complex Structural Properties of the Fisher Equation Arising in Mathematical Bioscience

“…M. Beren et al one characteristic of glioblastoma cells which has gained considerable attention is the 'go or grow'-hypotesis, which states that proliferation and migration are mutually exclusive phenotypes of glioblastoma cells [3]. Many different models of glibastoma growth have been proposed by D.Basanta et al have searched for game theoretical models [4], and K.R.Swanson et al sytems of partial differantial equaitons [5], E. Khain et al to individual-based models [6]. The effects of the density driven swithcing have observed by Pham et al [7].…”