Session B-3
Cancer (1:30 - 3:30)

1:30 - 2:00 : Khain, Evgeniy (Physics, Oakland University)
-Authors: E. Khain, C. M. Schneider-Mizell, M. O. Nowicki, E. A. Chiocca, S. E. Lawler and L. M. Sander
-Title: Clustering of brain tumor cells: theory and experiment
We investigate clustering of malignant glioma cells [1]. In vitro experiments in collagen gels identified a cell line that formed clusters in a region of low cell density, whereas a very similar cell line (which lacks an important mutation) did not cluster significantly. We hypothesize that the mutation affects the strength of cell-cell adhesion. We investigate this effect in a new experiment, which follows the clustering dynamics of glioma cells on a surface. We interpret our results in terms of a stochastic model and identify two mechanisms of clustering. First, there is a critical value of the strength of adhesion; above the threshold, large clusters grow from a homogeneous suspension of cells; below it, the system remains homogeneous, similarly to the ordinary phase separation. Second, when cells form a cluster, we have evidence that they increase their proliferation rate. We have successfully reproduced the experimental findings and found that both mechanisms are crucial for cluster formation and growth.
Ref. E. Khain, C. M. Schneider-Mizell, M. O. Nowicki, E. A. Chiocca, S. E. Lawler and L. M. Sander, EPL (Europhysics Letters) 88, 28006 (2009).

2:00 - 2:30 : Jain, Harsh (Mathematical Biosciences Institute, Ohio State University)
-Title: A Biochemical Perspective to an Agent-based Model of VEGF-induced Capillary Formation
I present a hybrid model of VEGF-induced capillary network formation, based on the theory of reinforced random walks. A major component of such a model is endothelial cell (EC) chemotaxis. I therefore begin with simulating the motion of a single EC under the influence of a gradient of VEGF. In this model, the cell responds by polarizing itself in response to VEGF bound to cell-surface receptors. This is in contrast to the classical modeling approach that approximates motion as a function of free VEGF concentrations. A novel chemotactic sensitivity function is proposed for cellular motion, incorporating biological details hitherto ignored by the phenomenological sensitivity functions in current literature. Biologically observed phenomena such as the ability of endothelial cells to sense a chemical gradient as low as 1-2% across their lengths, and their resulting polarization and movement is captured by this model. Later, the model for the motion of a single cell is modified to simulate capillary network formation under the influence of VEGF. Empirically observed proliferative regions behind developing sprout tips match those in our simulations, thereby validating this model. To our knowledge, this is the first instance of the inclusion of this level of molecular detail in a spatial model of VEGF-induced angiogenesis. It provides a basic framework for the addition of further cellular and sub-cellular events in such models, in order to elucidate the mechanisms of chemokine mediated vasculogenesis.

2:30 - 3:00 : Mikhaylov, Jessica (Mathematical Sciences, United States Military Academy)
-Title: Evaluating an improved two-compartment model to determine tumor angiogenesis parameters using contrast-enhanced dynamic imaging data
-Abstract: The most common methods for determining the efficacy of cancer treatments against tumors involves a pair of pre/post-treatment contrast-enhanced medical image sequences, such as MRI or CT. Currently, this data is often analyzed using static images to do a visual size comparison. Unfortunately, the time between image sequences must be large, on the order of months, to see a meaningful potential change in tumor size. With the goal of reducing the time between tests to a time scale of weeks, radiologists and mathematicians have explored methods of using the dynamic data available from the tests to see if blood flow parameters (perfusion, permeability, volume compartment sizes for the plasma and the interstitial space) can be estimated and if these measurements can in turn provide insight about the efficacy of the treatment. In previous work, it was shown that a fundamental assumption regarding capillary re-uptake was flawed, and current work attempts to recover the parameters without this assumption. Using model data sets and sampled model data sets, two of the parameters can be recovered, however, in the presence of noise, these methods show weakness. This talk will give an overview of the background research and will show the current results using model data sets subjected to Gaussian noise (with and without smoothing) and a fixed bias.

3:00 - 3:30 : Zheng, Xiaoming (Mathematics, Central Michigan University)
-Authors: Trachette Jackson (Mathematics, University of Michigan), Gou Young Koh (National Research Laboratory of Vascular Biology, Korea Advanced Institute of Science and Technology)
-Title: A continuous model of angiogenesis: initiation, extension and maturation
Angiogenesis, formation of new blood vessels, is essential to many physiological and pathological processes, such as wound healing and tumor growth. Angiogenesis is one of the fastest growing biomedical research disciplines in the past 20 years. However, there are very few mathematical models of angiogenesis compared with the explosion in experimental data. In this talk, we will present a brand new mathematical model of angiogenesis, which covers three critical events: endothelial cell activation (or the new blood vessel initiation), sprout extension, and maturation of new blood vessels. We investigate the regulating mechanisms of three families of growth factors: Vascular Endothelial Growth Factor (VEGF), Angiopoietins (including Ang1 and Ang2), and Platelet-Derived Growth Factor (PDGF-B). The biochemical and biophysical properties of two types of cells, endothelial cells that line the inner wall of blood vessels and perictyes that coat the outer surface of blood vessels, will be examined. These growth factors and cells form a complex multiscale system composed of molecular reactions, cellular responses and tissue growth. The numerical simulations of the mathematical model will be presented along with the main results of the study, which include: demonstrating how the balance of the angiopoietin system serves as angiogenic switch; highlighting that a proper mechanical model is necessary to address the blood vessel extension; showing that pericytes and angiopoietins are central to the maturation process.