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- to high-grade (glioblastoma). Whereas low-grade gliomas are weakly angiogenic, glioblastomas are among the most angiogenic 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. Furthermore, we investigated how proliferation and dispersal of glioma cells combine to induce increasing degrees of cellularity, mitoses, hypoxia-induced neoangiogenesis and necrosis, features that characterize increasing degrees of "malignancy," and we found that changes in the net rates of proliferation (ρ) 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.

Figure 1

Outline of the PIHNA mathematical model illustrating the interaction of glioma cells (normoxic and hypoxic) with the available vasculature which can be affected by the production of angiogenic factors.

Figure 2

Simulations illustrating each grade of glioma represented as a plot of density or concentration of the model variables (normoxic, hypoxic, and necrotic tissue, vasculature and VEGF) with respect to the distance from the center of the in silico tumor. Note the increasing cellularity, vasculature, hypoxia and necrosis with increasing grade.

Figure 3

In silico (survival) time from a typical diagnostic size of 1cm on T2 MRI to a typically fatal size of 4cm, as a function of D and ρ.

Figure 4

a) Maps of tumor grade as a function of tumor size (on T2 MRI) or of time. The blackened boxes indicate that the T2-visible portion of the simulated lesion has grown to a size sufficient to fill the whole brain. b) The * combination (high ρ, low D) produces a “primary” GBM (i.e., GBM from its first detectability), while comparatively c) the + combination (low ρ, high D – relative to *) produces a “secondary” GBM (i.e., “progressing” from lower grade).

Figure 5

A map of simulated “primary” (white) and “secondary” (grey) glioblastomas and gliomas that become fatal is size before malignant progression (black).

Figure 6

a) The total VEGF (integral amount of model TAF) normalized to the local glioma cell density for in silico Grade 3, sGBM and pGBM tumors showing increasing VEGF concentrations qualitatively consistent with the observations of (27). b) Increasing in silico expression of VEGF and hypoxia marker, HIF-1α, with increasing histological grade qualitatively consistent with the observations of (28, 29).

Figure 7

Connecting tissue level and imaging level model PIHNA model predictions of a) histological grade, b) fraction of cells that are hypoxic, and c) the radial size of central necrosis visible on T1-Gd MRI. Each grid cell represents a single virtual tumor with a specified combination of D and ρ, with in silico histologic grade, hypoxia and necrosis assessed within the virtual tumor and graphed separately. The PIHNA model accurately predicts relative amounts of hypoxia and necrosis as well as histologic grade for the 3 individual glioblastoma patients (stars). Each patient was approximately 2 cm in radius on T2 MRI with variable sizes on T1-Gd corresponding to the different D, ρ combinations graphed (quantified as in (25, 31)). Each patient was assessed for hypoxia quantified as the maximum HIF1α on immunohistochemistry (Patient 1: 30%, 2: 40%, 3: 40%) and a necrotic core radius on T1Gd MRI (Patient 1: 8mm, 2: 16mm, 3: 18mm).