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

Glioblastoma multiforme (GBM) is a class of primary brain tumours characterized by their ability to rapidly proliferate and diffusely infiltrate surrounding brain tissue. The aggressive growth of GBM leads to the development of regions of low oxygenation (hypoxia), which can be clinically assessed through [18F]-fluoromisonidazole (FMISO) positron emission tomography (PET) imaging. Building upon the success of our previous mathematical modelling efforts, we have expanded our model to include the tumour microenvironment, specifically incorporating hypoxia, necrosis and angiogenesis. A pharmacokinetic model for the FMISO-PET tracer is applied at each spatial location throughout the brain and an analytical simulator for the image acquisition and reconstruction methods is applied to the resultant tracer activity map. The combination of our anatomical model with one for FMISO tracer dynamics and PET image reconstruction is able to produce a patient-specific virtual PET image that reproduces the image characteristics of the clinical PET scan as well as shows no statistical difference in the distribution of hypoxia within the tumour. This work establishes proof of principle for a link between anatomical (magnetic resonance image [MRI]) and molecular (PET) imaging on a patient-specific basis as well as address otherwise untenable questions in molecular imaging, such as determining the effect on tracer activity from cellular density. Although further investigation is necessary to establish the predicitve value of this technique, this unique tool provides a better dynamic understanding of the biological connection between anatomical changes seen on MRI and biochemical activity seen on PET of GBM in vivo.

Quantifying the role of angiogenesis in malignant progression of gliomas: in silico modeling integrates imaging and histology.

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.

A spatial model of tumor-host interaction: application of chemotherapy.

In this paper we consider chemotherapy in a spatial model of tumor growth. The model, which is of reaction-diffusion type, takes into account the complex interactions between the tumor and surrounding stromal cells by including densities of endothelial cells and the extra-cellular matrix. When no treatment is applied the model reproduces the typical dynamics of early tumor growth. The initially avascular tumor reaches a diffusion limited size of the order of millimeters and initiates angiogenesis through the release of vascular endothelial growth factor (VEGF) secreted by hypoxic cells in the core of the tumor. This stimulates endothelial cells to migrate towards the tumor and establishes a nutrient supply sufficient for sustained invasion. To this model we apply cytostatic treatment in the form of a VEGF-inhibitor, which reduces the proliferation and chemotaxis of endothelial cells. This treatment has the capability to reduce tumor mass, but more importantly, we were able to determine that inhibition of endothelial cell proliferation is the more important of the two cellular functions targeted by the drug. Further, we considered the application of a cytotoxic drug that targets proliferating tumor cells. The drug was treated as a diffusible substance entering the tissue from the blood vessels. Our results show that depending on the characteristics of the drug it can either reduce the tumor mass significantly or in fact accelerate the growth rate of the tumor. This result seems to be due to complicated interplay between the stromal and tumor cell types and highlights the importance of considering chemotherapy in a spatial context.