Alexander R. A. Anderson

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.

Investigating prostate cancer tumour–stroma interactions: clinical and biological insights from an evolutionary game

Background:Tumours are made up of a mixed population of different types of cells that include normal structures as well as ones associated with the malignancy, and there are multiple interactions between the malignant cells and the local microenvironment. These intercellular interactions, modulated by the microenvironment, effect tumour progression and represent a largely under-appreciated therapeutic target. We use observations of primary tumour biology from prostate cancer to extrapolate a mathematical model. Specifically, it has been observed that in prostate cancer three disparate cellular outcomes predominate: (i) the tumour remains well differentiated and clinically indolent – in this case the local stromal cells may act to restrain the growth of the cancer; (ii) early in its genesis the tumour acquires a highly malignant phenotype, growing rapidly and displacing the original stromal population (often referred to as small cell prostate cancer) – these less common aggressive tumours are relatively independent of the local microenvironment and (iii) the tumour co-opts the local stroma – taking on a classic stromagenic phenotype where interactions with the local microenvironment are critical to the cancer growth.Methods:We present an evolutionary game theoretical construct that models the influence of tumour–stroma interactions in driving these outcomes. We consider three characteristic and distinct cellular populations: stromal cells, tumour cells that are self-reliant in terms of microenvironmental factors and tumour cells that depend on the environment for resources, but can also co-opt stroma.Results:Using evolutionary game theory we explore a number of different scenarios that elucidate the impact of tumour–stromal interactions on the dynamics of prostate cancer growth and progression, and how different treatments in the metastatic setting can affect different types of tumours.Conclusion:The tumour microenvironment has a crucial role in selecting the traits of the tumour cells that will determine prostate cancer progression. Equally important treatments like hormone therapy affect the selection of these cancer phenotypes making it very important to understand how they impact prostate cancers somatic evolution.

Computational Methods and Results for Structured Multiscale Models of Tumor Invasion

We present multiscale models of cancer tumor invasion with components at the molecular, cellular, and tissue levels. We provide biological justifications for the model components, present computati...

The role of IDH1 mutated tumour cells in secondary glioblastomas: an evolutionary game theoretical view

Recent advances in clinical medicine have elucidated two significantly different subtypes of glioblastoma which carry very different prognoses, both defined by mutations in isocitrate dehydrogenase-1 (IDH-1). The mechanistic consequences of this mutation have not yet been fully clarified, with conflicting opinions existing in the literature; however, IDH-1 mutation may be used as a surrogate marker to distinguish between primary and secondary glioblastoma multiforme (sGBM) from malignant progression of a lower grade glioma. We develop a mathematical model of IDH-1 mutated secondary glioblastoma using evolutionary game theory to investigate the interactions between four different phenotypic populations within the tumor: autonomous growth, invasive, glycolytic, and the hybrid invasive/glycolytic cells. Our model recapitulates glioblastoma behavior well and is able to reproduce two recent experimental findings, as well as make novel predictions concerning the rate of invasive growth as a function of vascularity, and fluctuations in the proportions of phenotypic populations that a glioblastoma will experience under different microenvironmental constraints.

The Role of Transforming Growth Factor-β–Mediated Tumor-Stroma Interactions in Prostate Cancer Progression: An Integrative Approach

We have implemented a hybrid cellular automata model based on the structure of human prostate that recapitulates key interactions in nascent tumor foci between tumor cells and adjacent stroma. Model simulations show how stochastic interactions between tumor cells and stroma may lead to a structural suppression of tumor growth, modest proliferation, or unopposed tumor growth. The model incorporates key aspects of prostate tumor progression, including transforming growth factor-beta (TGF-beta), matrix-degrading enzyme activity, and stromal activation. It also examines the importance of TGF-beta during tumor progression and the role of stromal cell density in regulating tumor growth. The validity of one of the key predictions of the model about the effect of epithelial TGF-beta production on glandular stability was tested in vivo. These experimental results confirmed the ability of the model to generate testable biological predictions in addition to providing new avenues of experimental interest. This work underscores the need for more pathologically representative models to cooperatively drive computational and biological modeling, which together could eventually lead to more accurate diagnoses and treatments of prostate cancer.

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.

Classifying the evolutionary and ecological features of neoplasms

Neoplasms change over time through a process of cell-level evolution, driven by genetic and epigenetic alterations. However, the ecology of the microenvironment of a neoplastic cell determines which changes provide adaptive benefits. There is widespread recognition of the importance of these evolutionary and ecological processes in cancer, but to date, no system has been proposed for drawing clinically relevant distinctions between how different tumours are evolving. On the basis of a consensus conference of experts in the fields of cancer evolution and cancer ecology, we propose a framework for classifying tumours that is based on four relevant components. These are the diversity of neoplastic cells (intratumoural heterogeneity) and changes over time in that diversity, which make up an evolutionary index (Evo-index), as well as the hazards to neoplastic cell survival and the resources available to neoplastic cells, which make up an ecological index (Eco-index). We review evidence demonstrating the importance of each of these factors and describe multiple methods that can be used to measure them. Development of this classification system holds promise for enabling clinicians to personalize optimal interventions based on the evolvability of the patients tumour. The Evo- and Eco-indices provide a common lexicon for communicating about how neoplasms change in response to interventions, with potential implications for clinical trials, personalized medicine and basic cancer research.

Perspectives on tissue interactions in development and disease.

From the morphogenetic movements of the three germ layers during development to the reactive stromal microenvironment in cancer, tissue interactions are vital to maintaining healthy organ morphologic architecture and function. The stromal compartment is thought to be complicit in tumor progression and, as such, represents an opportune target for disease therapies. However, recent developments in our understanding of the diversity of the stromal compartment and the lack of appropriate models to study its relevance in human disease have limited our further understanding of the role of tissue interactions in tumor progression. The failure any model to fully recapitulate the complexities of systemic biology continue to create a higher imperative for incorporating various perspectives into a broader understanding for the ultimate goal of designing interventional therapies. Understanding this potential, this review examines the biological models used to study stromal-epithelial interactions and includes an attempt to incorporate behavioral terminology to define and mathematically model ecological relationships in stromal-epithelial interactions. In addition, the current attempt to incorporate these diverse ecological perspectives into in silico mathematical models through cross-disciplinary coordination is reviewed, which will provide a fresh perspective on defining cell group behavior and tissue ecology in disease and hopefully lead to the generation of new hypotheses to be empirically validated.

In silico analysis suggests differential response to bevacizumab and radiation combination therapy in newly diagnosed glioblastoma.

Recently, two phase III studies of bevacizumab, an anti-angiogenic, for newly diagnosed glioblastoma (GBM) patients were released. While they were unable to statistically significantly demonstrate that bevacizumab in combination with other therapies increases the overall survival of GBM patients, there remains a question of potential benefits for subpopulations of patients. We use a mathematical model of GBM growth to investigate differential benefits of combining surgical resection, radiation and bevacizumab across observed tumour growth kinetics. The differential hypoxic burden after gross total resection (GTR) was assessed along with the change in radiation cell kill from bevacizumab-induced tissue re-normalization when starting therapy for tumours at different diagnostic sizes. Depending on the tumour size at the time of treatment, our model predicted that GTR would remove a variable portion of the hypoxic burden ranging from 11% to 99.99%. Further, our model predicted that the combination of bevacizumab with radiation resulted in an additional cell kill ranging from 2.6×107 to 1.1×1010 cells. By considering the outcomes given individual tumour kinetics, our results indicate that the subpopulation of patients who would receive the greatest benefit from bevacizumab and radiation combination therapy are those with large, aggressive tumours and who are not eligible for GTR.