## Workshop 2: Metastasis and Angiogenesis

### Organizers

Mark Chaplain
Division of Mathematics, University of Dundee
Trachette Jackson
Department of Mathematics, University of Michigan
Lance Munn
Radiation Oncology, Massachusetts General Hospital & Harvard Medical School
Hans Othmer
School of Mathematics, University of Minnesota

Initially solid tumors are avascular, i.e., they do not have their own blood supply, and rely on diffusion from the surrounding vasculature to supply oxygen and nutrients. When the tumor becomes too large diffusion is too slow, growth in the core stops, and can resume only if the tumor becomes vascularized i.e. if it becomes permeated with a network of capillaries. Avascular tumors release growth factors into their environment to induce nearby blood vessels to grow new capillaries to vascularize the tumor through a process called angiogenesis. This results in the creation of a new capillary network that extends from a primary vessel into the growth-factor-secreting tumor, thereby bringing essential nutrients to the tumor and providing a shorter route for the spread of cancer cells to other parts of the body. Metastasis is the process by which tumor cells detach from a primary tumor and migrate to nearby blood vessels or the lymph system, and are thereby able to spread to other organs in the host. Cancer cells invade the surrounding tissue either as individuals or as small groups of cells, and may secrete enzymes that degrade the ECM to facilitate passage of cells. This workshop will address the mathematical and computational issues that arise from models of angiogenesis and metastasis. Such models are frequently hybrid models, that describe cells (either those building the vessel or those involved in metastasis) at a detailed level that treats their biochemical and mechanical responses to their environment, and couple this cell-based description with partial differential equations that describe the mechanics of the surrounding tissue and the reaction and transport of growth factors and chemotactic signals. Major topics to be treated are how to model the movement of single cells through the extracellular matrix, how to describe in sufficient detail the process by which new vessels grow toward a tumor, how to cope with the computational problems raised by such hybrid models, and what the implications are for our understanding of the underlying basic science and how that understanding can be translated into improved therapeutic regimens.

### Accepted Speakers

Jim Baish
Department of Biomedical Engineering, Bucknell University
Paul Bates
Biomolecular Modelling Laboratory, London Research Institute
Vincenzo Capasso
ADAMSS, Università degli Studi di Milano and "Gregorio Millan" Institute Escuela Politecnica Superior Universidad Carlos III de Madrid
Dirk Drasdo
Bioinformatics, Physical and Mathematical Biology, Institut National de Recherche en Informatique Automatique (INRIA)
Hermann Frieboes
Bionegineering, University of Louisville
Peter Friedl
Cell Biology, Radboud University Nijmegen
Alf Gerisch
Fachbereich Mathematik, Technische Universitat Darmstadt
Biomedical Engineering, The Ohio State University
Thomas Hillen
Mathematical and Statistical Sciences, University of Alberta
Petros Koumoutsakos
Computational Science, ETHZ
Pawan Kumar
Otolaryngology and Head and Neck Surgery, The Ohio State University
Tong Li
Mathematics, University of Iowa
John Lowengrub
Mathematics, University of California, Irvine
Aleksander Popel
Department of Biomedical Engineering, Johns Hopkins University
Shaurya Prakash
Mechanical and Aerospace Engineering, The Ohio State University
Luigi Preziosi
Department of Mathematical Sciences, Politecnico di Torino
Tim Secomb
Physiology, University of Arizona
Andy South
Dermatology & Cutaneous Biology, Thomas Jefferson University
Kristin Swanson
Neurological Surgery, Northwestern University
Alex Tyrrell
n/a, Thomson Reuters
Mike Watson
Institute of Petroleum Engineering, Heriot-Watt University
Monday, October 13, 2014
Time Session
08:00 AM

Shuttle to MBI

08:15 AM
09:00 AM

Breakfast

09:00 AM
09:15 AM

Greetings and info from MBI - Marty Golubitsky

09:15 AM
09:45 AM

Introduction by Organizers

09:45 AM
10:00 AM

Discussion of open questions

10:00 AM
10:30 AM

Break

10:30 AM
11:30 AM
Mike Watson - Tumours, Wounds and Retinae: Modelling Angiogenesis in Development and Disease

The ability of functional vascular networks to both grow and adapt is a crucial feature of many physiological processes, including organ growth, disease progression and tissue repair. Since the metabolic requirements of host tissue need to be served in each case, the manner of the spatio-temporal evolution of such vessel networks is an all-important regulator of tissue function. At a cellular level, the phenomenon of angiogenesis comprises a well?orchestrated sequence of events involving endothelial cell migration and proliferation; tissue degradation; capillary sprout emergence; anastomosis formation; and, finally, blood perfusion through the nascent network. The onset of blood flow is crucial to the subsequent evolution of the structure: by providing nutrients to the local tissue and introducing haemodynamic forces in flowing vessels, both individual capillary radii and the spatial distribution of migratory cues are dynamically modified. In this presentation I will discuss a hybrid discrete-continuum modelling approach that simultaneously couples vessel growth with blood flow through the vasculature, and provide an overview of results from its application to the study of solid tumour growth, wound healing and retinal development. Applying the model across this broad range of scenarios is found to be extremely beneficial, with the unique challenges posed in each case forcing a continual refinement of the approach. Retinal vascular growth, in particular, provides an extremely rigorous test, ultimately resulting in a model with strong potential for use in the investigation of ocular pathologies.

11:30 AM
12:30 PM
Andy South - Modelling squamous cell carcinoma invasion in vitro, in vivo and in silico

Squamous cell carcinomas (SCCs) collectively are the most common ectodermal cancers, resulting in >300,000 deaths per year. SCCs arise in renewable squamous epithelia which serve to create an environmental barrier in the skin, esophagus, lung, and cervix. In normal squamous epithelia, basal progenitors give rise to more superficial daughter cells that terminally differentiate into keratinized cells as they migrate toward the surface, coupling terminal differentiation with microanatomic position. An early feature of squamous neoplasia of all types is disrupted differentiation to variable degrees, typically associated with thickening of the epithelium and increased proliferation. Following on from this and as a first step towards metastatic dissemination and distant colonization, SCCs initiate the process of local invasion away from the surface and into the surrounding tissue comprised of extracellular matrix and cells such as cancer associated fibroblasts and macrophages. We model SCCs in vitro using tumor and normal cells derived from the skin. By reconstituting epithelial and mesenchymal cells together with a matrix (synthetic or cellular in origin) we are able to recapitulate normal cell differentiation and tumor cell invasion in a laboratory setting. By grafting these complex cultures to the backs of immune compromised mice we can model SCC invasion in vivo and test intervention strategies. Finally, mathematical modelling can simulate many aspects of cancer cell invasion and provide opportunity to interrogate parameters inaccessible to biological experimentation.

12:30 PM
02:15 PM

Lunch Break

02:15 PM
03:15 PM
Paul Bates - Multiscale Modelling of Cancer Cell Motility

Since Inhibiting metastasis is as crucial as minimizing tumour growth for efficient treatment of cancer, we constructed a multiscale model of cell motility, with our primary focus being on amoeboid type cell motility of metastasizing tumour cells in the extracellular matrix (ECM). Our 2D hybrid agent-based/finite-element model covers a wide parameter space and provides a deeper understanding of the conditions governing the motility of cancer cells on a multiscale level. Both the extracellular conditions (e.g. ECM density) and intrinsic cell properties (e.g. relative distribution of contractile and blebbing regions of the cell membrane) were investigated. The aim is to identify the combination of intrinsic properties metastasising cells are more likely to use under different extracellular conditions. After extensive benchmarking of the computational model, using in vitro data, we were able to predict cancer cell motility in vivo. Moreover, the model was successfully challenged to predict the effect of different combinations of kinase inhibitors and integrin depletion (Tozluoglu et al. Nat. Cell Biol. 2013).

03:15 PM
04:15 PM
Luigi Preziosi - Modelling Cell-Extracellular Matrix Interaction

Cell-extracellular matrix interaction and the mechanical properties of cell nucleus have been demonstrated to play a fundamental role in cell movement across fibre networks and micro-channels. In the talk, we will describe several mathematical models dealing with such a problem, starting from modelling cell adhesion mechanics to the inclusion of influence of nucleus stiffness in the motion of cells.

An energetic approach is used in order to obtain a necessary condition for which cells enter cylindrical structures. The nucleus of the cell is treated either (i) as an elastic membrane surrounding a liquid droplet or (ii) as an incompressible elastic material with Neo-Hookean constitutive equation. The results obtained highlight the importance of the interplay between mechanical deformability of the nucleus and the capability of the cell to establish adhesive bonds.

04:30 PM
05:00 PM

Break

05:00 PM
05:45 PM

Poster Introductions

05:45 PM
07:15 PM

Reception and Poster Session in MBI Lounge

Tuesday, October 14, 2014
Time Session
08:00 AM

Shuttle to MBI

08:15 AM
09:00 AM

Breakfast

09:00 AM
10:00 AM
10:00 AM
10:30 AM

Break

10:30 AM
11:30 AM
Aleksander Popel - Computational and experimental studies of breast cancer metastasis

I will present our recent experimental results on breast cancer metastasis with an emphasis on the tumor microenvironment and particularly the roles of blood and lymphatic vasculatures in metastatic organs [1,2]. We will analyze the roles of the stromal cells and their interactions with cancer cells in metastasis. We will then discuss our computational results on 3D reconstruction of tumor vasculature applicable to both primary and metastatic sites, and modeling of blood flow and molecular interactions and transport [3,4]. An agent-based model of tumor growth and metastasis will be presented that takes into account cancer stem cells [5]. Finally, we will discuss a framework for modeling cancer metastasis.

[1] E. Lee, E. Fertig, K. Jin, S. Sukumar, N.B. Pandey, and A.S. Popel. Breast cancer cells condition lymphatic endothelial cells within pre-metastatic niches to promote metastasis. Nature Communications, 5:4715, 2014.

[2] E. Lee, N.B. Pandey, and A.S. Popel. Lymphatic endothelial cells support tumor growth in breast cancer. Sci. Rep., 4:5853, 2014.

[3] S.K. Stamatelos, E. Kim, A.P. Pathak, and A.S. Popel. Bioimage informatics aided reconstruction of breast tumor microvasculature and computational predictions of blood flow. Microvasc. Res. 91:8-21, 2014.

[4] S.D. Finley and A.S. Popel. Effect of tumor microenvironment on tumor VEGF during anti-VEGF treatment: systems biology predictions. J Nat Cancer Inst., 105:802-811, 2013.

[5] K.A. Norton and A.S. Popel. An agent-based model of breast tumor growth, metastasis and seeding: the role of cancer stem cells. J. Roy. Soc. Interface, 11(100), 2014.

11:30 AM
12:30 PM
Alf Gerisch - Numerical challenges in models of tissue-scale tumour cell invasion

Firstly, the efficient simulation of nonlocal partial differential equation models where the nonlocal terms account for the effects of cell-cell and cell-matrix adhesion. Such models have been used in to simulate the process of tumor cell invasion but also in other applications. The repeated evaluation of the nonlocal term is a major computational bottleneck. We outline our FFT-based approach, discuss the inclusion of different boundary conditions, and comment on options and limitations.
Secondly, parameters appearing in mathematical models of tumor invasion are often difficult to assess experimentally and even if experimental values are available their accuracy might not be very good or they might have been obtained in a setting different from that what is modeled. Thus these parameters are uncertain and quantifying the effect of this uncertainty on the model solution or certain derived quantities of interest is beneficial for judging the value of the model and possibly for proposing required dedicated experiments. We present a framework for uncertainty quantification based on fast adaptive stochastic collocation on sparse grids. The advantage of this approach is that it can use an existing simulation environment for the model under investigation in a black-box fashion.

12:30 PM
01:30 PM

Lunch Break

01:30 PM
02:30 PM
Hans Othmer - Crawlers can also swim: new modes of movement in the ECM

Cell locomotion is essential for early development, angiogenesis, tissue regeneration, the immune response, and wound healing in multicellular organisms, and plays a very deleterious role in cancer metastasis in humans. Locomotion involves the detection and transduction of extracellular chemical and mechanical signals, integration of the signals into an intracellular signal, and the spatio-temporal control of the intracellular biochemical and mechanical responses that lead to force generation, morphological changes and directed movement. While many single-celled organisms use flagella or cilia to swim, there are two basic modes of movement used by eukaryotic cells that lack such structures -- mesenchymal and amoeboid. The former, which can be characterized as crawling' in fibroblasts or gliding' in keratocytes, involves the extension of finger-like filopodia or pseudopodia and/or broad flat lamellipodia, whose protrusion is driven by actin polymerization at the leading edge. This mode dominates in cells such as fibroblasts when moving on a 2D substrate. In the amoeboid mode, which does not rely on strong adhesion, cells are more rounded and employ shape changes to move -- in effect 'jostling through the crowd' or swimming'. Here force generation relies more heavily on actin bundles and on the control of myosin contractility. Leukocytes use this mode for movement through the extracellular matrix in the absence of adhesion sites, as does Dictyostelium discoideum when cells sort in the slug. However, recent experiments have shown that numerous cell types display enormous plasticity in locomotion in that they sense the mechanical properties of their environment and adjust the balance between the modes accordingly by altering the balance between parallel signal transduction pathways. Thus pure crawling and pure swimming are the extremes on a continuum of locomotion strategies, but many cells can sense their environment and use the most efficient strategy in a given context. We will discuss some of the mathematical and computational challenges that this diversity poses.

02:30 PM
03:30 PM
Alex Tyrrell - Transport, metabolic & shear stress effects in vascular remodeling

“Normalization” of tumor blood vessels has shown promise to improve the efficacy of subsequently-administered chemotherapeutics. In theory, anti-angiogenic drugs targeting VEGF signaling can improve vessel network structure and function, enhancing the transport of systemically-injected drugs. During normalization, a wide range of effects are observed on vessel diameters, tortuosity, permeability, and blood flow, eventually producing a more efficient network. Although not well-understood, it is likely that this type of adaptive remodeling depends on blood shear forces, transvascular pressure, upstream signals transmitted along the endothelium as well as growth factors such as VEGF.

In an effort to better analyze how blood vessels adapt and remodel, we have developed a physics model that simulates vascular structure and function from meso to macro scales, thereby capturing important dynamics that can be observed and measured using two-photon imaging and other experimental techniques. Though challenges remain, our model has helped better understand the complex, nonlinear processes involved in the normalization of tumor vasculature.

03:30 PM
04:00 PM

Break

04:00 PM
05:00 PM
Dirk Drasdo - How quantitative modelling can inform on disease pathogenesis: lessons from liver

Systems biology has opened up new ways of understanding disease processes based on close iterations between experimentation and mathematical modelling. So far, its focus has mainly been on molecular processes. The combination of modern imaging modalities with image processing and analysis (Hammad et. al. Arch. Toxicol. 2014; Hoehme and Drasdo, Bioinformatics 2010), and mathematical models opens up a promising new approach towards a quantitative understanding of pathologies and of disease processes that includes the multicellular tissue level. For illustration we will consider three examples of interdisciplinary approaches integrating biological models and mechanisms of processes contributing to disease progression at various scales within mathematical modelling frameworks. In the first example a multi-cellular spatial temporal model predicts within a systems biology approach a previously not recognized and subsequently validated order principle underlying liver regeneration after drug-induced damage, as it occurs for example after overdosing acetaminophen (paracetamol) (Hoehme et. al., PNAS, 2010). The second example will present a mathematical model integrating information from the spatial temporal model of the first example with the chemical reactions known to detoxify liver from ammonia in health liver during the destruction and subsequent regeneration process, that succeeded to indicate the lack of an important reaction (Schliess et. al., Hepatology, 2014). Experiments triggered by this model prediction led to finding of a so far unrecognized good candidate reaction that might be clinically utilized in case of hyperammonemia. The final example will address the spatial-temporal molecular control of the regeneration process within a mechanistic multi-scale model spanning the molecular, cellular, tissue and body scale. The tissue model involved in each of these examples represents each cell individually as biophysical entities and is hence able to integrate equally physical and biological information. The example demonstrates that multi-cellular models are so far able to falsify hypotheses and guide towards the most informative experimental design.

05:00 PM

Shuttle pick-up from MBI

Wednesday, October 15, 2014
Time Session
08:00 AM

Shuttle to MBI

08:15 AM
09:00 AM

Breakfast

09:00 AM
10:00 AM
Thomas Hillen - Mathematical Modelling with Fully Anisotropic Diffusion and Applications to Glioma Growth

Anisotropic diffusion describes random walk with different diffusion rates in different directions. I will present a form of anisotropic diffusion which is called "fully" anisotropic. The fully anisotropic diffusion model does not obey a maximum principle and can even lead to singularity formation in infinite time.

I will derive this model from biological principles, analyse some of its behavior and show how it can be used to model glioma spread.

10:00 AM
10:15 AM

Break

10:15 AM
11:00 AM
Pawan Kumar - Role of Tumor-Associated Endothelial Cells in Tumor Metastasis

The metastatic spread of solid tumors is directly or indirectly responsible for most cancer-related deaths. Metastatic process is highly complex and it involves multiple steps including the release of tumor cells from the primary tumor, survival in circulation, interaction with vascular endothelium and invasion of target organs. Although our understanding of tumor cell biology has increased exponentially during the last couple of decades, we still know very little about the role tumor microenvironment plays in promoting tumor cell release from the primary tumor and metastasis to the distal organs. We have recently observed that primary tumor samples from head and neck cancer patients with metastasis show significantly higher Bcl-2 positive blood vessels as compared to cancer patients without metastasis. These results thereby suggest that Bcl-2 expression in tumor-associated endothelial cells may be involved in tumor cell metastasis. We tested this hypothesis using a SCID mouse model and indeed, enhanced Bcl-2 expression in tumor-associated endothelial cells promoted tumor metastasis to lungs. In the subsequent mechanistic study, we demonstrated that tumor-associated endothelial cells that express high levels of Bcl-2 significantly promoted tumor cell release by enhancing epithelial-mesenchymal transition (EMT)-related changes in tumor cells predominantly via the secretion of IL-6. It is well established that the early steps in metastasis are completed more efficiently than the later steps involving survival of cancer cells in circulation and extravasation into the target organ. This could be due to the fact that most of the cancer cells, particularly epithelial cells, undergo rapid cell death (anoikis) in harsh circulatory conditions. Interestingly, we also observed in our study that in addition to circulating tumor cells (CTCs), there is a marked increase in Bcl-2 positive circulating endothelial cells (CECs) in the blood samples of head and neck cancer patients. These results raised an intriguing question about the biological significance of these circulating endothelial cells. Our results suggest a novel role for CECs in binding to tumor cells, protecting them from anoikis and chaperoning them to distal sites.

11:00 AM
11:45 AM
Tong Li - Mathematical Analysis of PDE Models of Chemotaxis

We investigate local and global existence, blowup criterion and long time behavior of classical solutions for a system derived from the Keller-Segel model describing chemotaxis. We study the existence and the nonlinear stability of large-amplitude traveling wave solutions to the system.

11:45 AM
12:15 PM
Samir Ghadiali - Dynamic Changes in Cellular Mechanics Regulates Cancer Cell Migration/Invasion

Metastatic spread of tumor cells is responsible for a majority of cancer deaths. During metastasis, tumor cells acquire a highly motile phenotype in a process known as epithelial to mesenchymal transition (EMT). These motile cells detach from the primary tumor, invade into surrounding tissues, intravasate into the circulation and colonize distal tissues. Although investigators have recently characterized the biomechanical properties of circulating tumor cells (CTC), it is not known how changes in cell mechanics during EMT influence the initial tumor-detachment and invasion phases of metastasis. We have used a combination of computational techniques and in-vitro/in-vivo models to investigate how changes in both tumor cell and stromal cell mechanics influence metastasis. Contrary to the high compliance of CTCs, experiments in our lab indicate that tumor cells become significantly stiffer during EMT. However, detachment of these cells from the tumor results in a significant reduction in stiffness and this reduction in stiffness facilitates amoeboidal migration through the extracellular matrix (ECM). Furthermore, dynamic remodeling of the ECM by stromal fibroblasts facilitates additional invasion. Based on these results, we have used gene knockdown/mutation techniques to either reduce tumor cell stiffness or prevent ECM remodeling by stromal fibroblasts. Both of these manipulations significantly reduce the amount of tumor cell detachment and invasion. Therefore, altering the mechanical properties of tumor and stromal cells may be an effective way to prevent metastasis.

12:15 PM
02:00 PM

Pizza Lunch Provided by MBI

02:00 PM
03:00 PM
Petros Koumoutsakos - Uncertainty Quantification for Image Driven Modeling and Simulation

I will review our efforts to develop imaging, modeling and simulation tools for the study of angiogenesis. I will address the challenge of predictive simulations for Life Science applications and discuss a Bayesian uncertainty quantification and propagation framework that can help bridge experiments and simulations.

03:00 PM
03:30 PM

Break

03:30 PM
04:30 PM
Jim Baish - Quantifying Vascular Architecture: Relating Form to Function

Recent advances in our ability to manipulate blood vessels to therapeutic advantage have heightened our awareness that not all blood vessels are created equal. I will review recent efforts to improve upon traditional measures of vascular geometry such as vessel density and diameter. While retaining reasonable simplicity, the aim is to develop measures that better relate the geometry of the blood vessels to clinical outcomes. I will outline recent insights drawn from transport fundamentals, network science, percolation theory, reliability theory, system dynamics and fractal geometry that shed light on how the arrangement of blood vessels influences their ability to deliver nutrients and therapeutic agents in tumors. Special emphasis will be given to the similarities and differences between normal and tumor vasculature.

04:30 PM

Shuttle pick-up from MBI

Thursday, October 16, 2014
Time Session
09:00 AM

Shuttle pick-up from MBI

09:15 AM
10:30 AM

Breakfast

10:30 AM
11:30 AM
Vincenzo Capasso - Mathematical modeling of tumor-driven angiogenesis. A mean field model.

In the mathematical modeling of tumor-driven angiogenesis, the strong coupling between the kinetic parameters of the relevant stochastic branching-and-growth of the capillary network, and the family of interacting underlying fields is a major source of complexity from both the analytical and computational point of view.

Our main goal is thus to address the mathematical problem of reduction of the complexity of such systems by taking advantage of its intrinsic multiscale structure; the (stochastic) dynamics of cells will be described at their natural scale (the microscale), while the (deterministic) dynamics of the underlying fields will be described at a larger scale (the macroscale).

In this presentation, starting from a conceptual stochastic model including branching, elongation, and anastomosis of vessels, we derive a mean field approximation of the vessel densities, leading to deterministic partial differential equations for the underlying fields, driving the formation of the stochastic vessel network.

Outcomes of the relevant numerical simulations will be presented.

References

[1] Capasso, V., Morale, D.: Stochastic Modelling of Tumour-induced Angiogenesis.

J. Math. Biol., 58, 219{33 (2009)

[2] Capasso, V., Morale D., Facchetti, G.: The Role of Stochasticity for a

Model of Retinal Angiogenesis, IMA J. Appl. Math. (2012) ; 19 pages;

doi:10.1093/imamat/hxs050

[3] Bonilla, L., et al.: A mean field model for tumor-driven angiogenesis.

In preparation (2014).

11:30 AM
12:30 PM
Hermann Frieboes - Modeling the Effects of Dysregulated Angiogenesis on Tumor Nanotherapeutics Delivery

In addition to excessive cellular proliferation, solid tumors typically elicit irregular angiogenesis resulting in structurally abnormal and leaky vascular structures. The passive mechanism termed “enhanced permeability and retention” (EPR) effect enables systemically administered nanoparticles sized 10–400 nm to preferentially extravasate from the vasculature into the interstitial space of solid tumors. Additional factors contributing to nanoparticle pharmacodynamics and cytotoxicity include size, surface charge and morphology. These properties are typically tailored to design systems that exhibit optimal tumor tissue uptake. Drugs delivered via nanoparticles can thus increase treatment effectiveness while reducing systemic toxicity. However, heterogeneity in blood flow due to irregular angiogenesis and vascular remodeling at the tumor site promote tissue hypoxia and thus cell quiescence, presenting a physical barrier to cell-cycle dependent chemotherapeutics delivered by nanocarriers. Inadequate vascularization leads to further impediments that hinder optimal treatment, including insufficient drug dosages due to abnormally long inter-vascular diffusion distances, as well as disturbed convection and diffusion of molecules (glucose, oxygen) and nanoparticles in the interstitium, as we have recently explored through intravital microscopy and mathematical modeling. Cancerous tissue can contain almost twice the volume of interstitial space compared to normal tissue; an abundance of extracellular matrix proteins along with an increased interstitial pressure may further inhibit nanoparticle delivery and drug diffusion in under-vascularized tumor regions. These physical barriers, coupled with intrinsic resistance mechanisms at the cell-scale, often cause cancer drug therapies to fail. We present recent applications of engineering and modeling-based approaches to help tackle these challenges in cancer nanotherapy.

12:30 PM
02:00 PM

Lunch Break

02:00 PM
03:00 PM
John Lowengrub - Feedback, lineages and vascular tumor growth

Most tissues are hierarchically organized into lineages. Tumors arise when the carefully regulated balance of cell proliferation and programmed cell death (apoptosis) that ordinarily exists in normal homeostatic tissues breaks down. Traditionally, cancer cells are assumed to acquire a common set of traits. However, not all proliferating cells in a tumor matter seem to matter equally and tumor cells apparently progress through lineage stages regulated by feedback. The reasons for this are still not well established. In this talk, we will present new mathematical models to simulate the spatiotemporal dynamics of cell lineages in vascularized solid tumors. We account for protein signaling factors produced by tumor cells, and vascular endothelial cells in the microenvironment that direct self-renewal, differentiation and proliferation pathways. Our models demonstrate the development of heterogenous cell distributions and the formation of vascular niche-like environments for stem cells. We demonstrate that feedback processes play a critical role in tumor progression, heterogeneity, vascularity and the development of morphological instability.

03:00 PM
03:15 PM

Break

03:15 PM
04:15 PM
Tim Secomb - Generation of microvascular networks in normal and tumor tissues: A biological patterning problem

Formation of functionally adequate vascular networks by angiogenesis presents a problem in biological patterning. Generated without predetermined spatial patterns, networks must develop hierarchical tree-like structures for efficient convective transport over large distances, combined with dense space-filling meshes for short diffusion distances to every point in the tissue. Moreover, networks must be capable of restructuring in response to changing functional demands without interruption of blood flow. Here, theoretical simulations based on experimental data are used to demonstrate that this patterning problem can be solved through over-abundant stochastic generation of vessels in response to a growth factor generated in hypoxic tissue regions, in parallel with refinement by structural adaptation and pruning. Essential biological mechanisms for generation of adequate and efficient vascular patterns are identified and impairments in vascular properties resulting from defects in these mechanisms are predicted. The results provide a framework for understanding vascular network formation in normal or pathological conditions. With regard to tumor microcirculation, the simulations indicate possible factors leading to characteristic features including poor tissue oxygenation in the presence of adequate overall perfusion, and persistent instability of vessel structure and flow patterns.

04:15 PM
05:15 PM
Peter Friedl - Dimension of cancer invasion

Single-cell or collective invasion results from coordination of cell shape, deformability and actin dynamics relative to the tissue environment. Both, in vitro and in vivo models provide complementary insights into modes and mechanisms of cell movement. In monomorphic 3D invasion models in vitro, an obligate step of collective invasion is the degradation of extracellular matrix (ECM). Thereby, the density of the ECM determines the invasion mode of mesenchymal tumor cells. In 3D in vitro models, fibrillar, high porosity ECM enables single-cell dissemination, whereas dense matrix induces cell-cell interaction, leader-follower cell behavior and collective migration as an obligate protease-dependent process. Conversely, in vivo monitored by intravital multiphoton second and third harmonic generation microscopy, abundant tissue microniches provide invasion-promoting tracks that enable collective migration along tracks of least resistance. As main routes, non-destructive contact-guidance is mediated by preformed multi-interface perimuscular, vascular and –neural tracks of 1D, 2D and 3D topography. Whereas in vitro models predict a major role for beta1/beta3 integrins in sustaining invasion, in vivo targeting of intergrins induces unexpected plasticity of invasion, including collective and amoeboid single-cell dissemination, followed by enhanced micrometastasis, implicating integrin-independent dissemination as effective route to metastasis and challenging in vitro approaches. In conclusion, in vitro and in vivo models deliver diverse, often dedicated environments which impact the type, efficacy and mechanism of invasion. Computational modeling thus needs to take the physical and molecular organization of tissues into account.

05:30 PM

Shuttle pick-up from MBI

06:30 PM
07:15 PM

Cash Bar

07:15 PM
09:15 PM

Banquet in the Fusion Room at the Crowne Plaza

Friday, October 17, 2014
Time Session
08:00 AM

Shuttle to MBI

08:15 AM
09:00 AM

Breakfast

09:00 AM
09:30 AM
Lance Munn - Biomechanics of cancer invasion and vessel function

Mechanical forces control many processes in and around growing tumors. These forces can be transmitted by solid components of the tissue such as cell membranes, anchoring proteins and matrix components, or fluid components such as blood, plasma or lymph. Solid mechanical forces become important when uncontrolled growth compresses cells and matrix, directly affecting cancer cell proliferation and apoptosis. Compression of cancer cells can also induce more migration and invasion, potentially contributing to metastasis. Fluid forces, on the other hand, are central to development and function of tumor vascular systems (blood and lymphatic). Blood flow subjects vessel wall cells to shear stresses that drive blood vessel contractions or dilations to optimize flow, and plasma exchanged between vessels can direct the creation of additional blood vessel segments. Similarly, lymphatic pumping a process central to immune function and fluid homeostasis is sustained by cycles of fluid flow and shear stress-activated nitric oxide production. The flow is directed by one-way valves, and is often abnormal in tumor-associated lymphatic vessels. All of these processes involve the integration of mechanical signals by cells to direct biological processes. This interface between mechanics and biology is not well-explored, but contains many potential new control points for modulating tumor progression.

09:30 AM
10:00 AM
Shaurya Prakash - Impedance Spectroscopy for Imaging and Quantifying Tissue Properties

Over the past century, electrical or electrochemical impedance spectroscopy (EIS) has been used by chemists and biologists to study reaction rate kinetics, corrosion phenomena, battery aging, and tissue characteristics to name a few applications. EIS measures a current or voltage response of a system to an alternating voltage or current signal and records the response as complex impedance. The key idea is that the input is a small amplitude signal and therefore permits use of small-signal theory and linearization to analyze system response through data containing both magnitude and phase information.

In this talk, I will present the development of EIS as a new tool for imaging and quantifying tissue properties. EIS was used to generate images of morphologically distinct regions in excised human liver tissue to differentiate, based on differences in electrical conductivity and permittivity, the tumor and non-tumor regions. The impedance data can be reduced to equivalent tissue structure images showing the ability to use EIS as an imaging technique, with direct comparisons to visual representation by digital photography and clinical validation by histopathology images.

10:00 AM
10:30 AM

Break

10:30 AM
11:30 AM
Kristin Swanson - Towards Patient-Specific Modeling of Angiogenesis-driven Tumor-associated Edema in Gliomas

Glioblastoma, the most aggressive form of primary brain tumor, is predominantly assessed with gadolinium-enhancedT1-weighted (T1Gd) andT2-weighted magnetic resonance imag-ing (MRI). Pixel intensity enhancement on the T1Gd image is understood to correspond to the gadolinium contrast agent leaking from the tumor-induced neovasculature, while hyperintensity on theT2/FLAIR images corresponds with edema and infiltrated tumor cells. None of these modalities directly show tumor cells; rather, they capture abnormalities in the microenvironment caused by the presence of tumor cells. Thus, assessing disease response after treatments impacting the microenvironment remains challenging through the obscuring lens of MR imaging. Anti-angiogenic therapies have been used in the treat-ment of gliomas with spurious results ranging from no apparent response to significant imaging improvement with the potential for extremely diffuse patterns of tumor recurrence on imaging and autopsy. Anti-angiogenic treatment normalizes the vasculature, effectively decreasing vessel permeability and thus reducing tumor-induced edema, drastically alter-ing T2-weighted MRI. We extend a previously developed mathematical model of glioma growth to explicitly incorporate edema formation allowing us to directly characterize and potentially predict the effects of anti-angiogenics on imageable tumor growth. A compari-son of simulated glioma growth and imaging enhancement with and without bevacizumab supports the current understanding that anti-angiogenic treatment can serve as a surro-gate for steroids and the clinically driven hypothesis that anti-angiogenic treatment may not have any significant effect on the growth dynamics of the overall tumor cell popu-lations. However, the simulations do illustrate a potentially large impact on the level of edematous extracellular fluid, and thus on what would be imageable on T2/FLAIR MR. Additionally, by evaluating virtual tumors with varying growth kinetics, we see tumors with lower proliferation rates will have the most reduction in swelling from such treatments.

11:30 AM
12:00 PM

Wrap up panel: Major Challenges and Future Directions Moderator

12:00 PM
12:15 PM

Closing Remarks by Organizers

12:15 PM

Shuttle pick-up from MBI (One back to hotel and one to airport)

Name Email Affiliation
Avendano, Alex avendano.8@osu.edu Mechanical and Aerospace Engineering, The Ohio State University
Baish, Jame baish@bucknell.edu Department of Biomedical Engineering, Bucknell University
Bates, Paul paul.bates@cancer.org.uk Biomolecular Modelling Laboratory, London Research Institute
Bates, Dan bates@math.colostate.edu Department of Mathematics, Colorado State University
Bentley, Katie kbentley@bidmc.harvard.edu pathology, Beth Israel Hospital, Harvard Medical School
Capasso, Vincenzo vincenzo.capasso@unimi.it ADAMSS, Università degli Studi di Milano and "Gregorio Millan" Institute Escuela Politecnica Superior Universidad Carlos III de Madrid
Cebulla, Colleen colleen.cebulla@osumc.edu Ophthalmology and Visual Science, The Ohio State University
Chen, Zhan chen2724@umn.edu Department of Mathematical science, Georgia Southern University
Cheng, Yougan yxc283@case.edu Mathematics, University of Minnesota
Connor, Anthony anthony.connor@keble.ox.ac.uk Computer Science, University of Oxford
Drasdo, Dirk dirk.drasdo@inria.fr Bioinformatics, Physical and Mathematical Biology, Institut National de Recherche en Informatique Automatique (INRIA)
Ewool, Richard rce2m@mtmail.mtsu.edu Computational Science, Middle Tennessee State University
Flores Castillo, Nicolas nicolas@rice.edu Department of Statistics, Rice University
Frieboes, Hermann hbfrie01@louisville.edu Bionegineering, University of Louisville
Friedl, Peter P.Friedl@ncmls.ru.nl Cell Biology, Radboud University Nijmegen
Gerisch, Alf gerisch@mathematik.tu-darmstadt.de Fachbereich Mathematik, Technische Universitat Darmstadt
Ghadiali, Samir ghadiali.1@osu.edu Biomedical Engineering, The Ohio State University
Govinder, Kesh govinder@ukzn.ac.za Mathematics, Statistics and Computer Science, University of KwaZulu-Natal
Hansford, Derek hansford.4@osu.edu Biomedical Engineering, The Ohio State University
Hillen, Thomas thillen@ualberta.ca Mathematical and Statistical Sciences, University of Alberta
Jiang, Yi yjiang12@gsu.edu Mathematics and Statistics, Georgia State University
Klimov, Sergey sklimov3@gmail.com Interdisciplinarity Biology and Mathematics, Georgia State University
Koumoutsakos, Petros petros@ethz.ch Computational Science, ETHZ
Kumar, Pawan pawan.kumar@osumc.edu Otolaryngology and Head and Neck Surgery, The Ohio State University
Li, Tong tong-li@uiowa.edu Mathematics, University of Iowa
Long, Quan quan.long@brunel.ac.uk Brunel Institute for Bioengineering, Brunel University
Lowengrub, John lowengrb@math.uci.edu Mathematics, University of California, Irvine
Munn, Lance lance@steele.mgh.harvard.edu Radiation Oncology, Massachusetts General Hospital & Harvard Medical School
Norton, Kerri-Ann knorton4@jhmi.edu Biomedical engineering, Johns Hopkins University
Othmer, Hans othmer@math.umn.edu School of Mathematics, University of Minnesota
Ponce de Leon, Marco ponce018@umn.edu Mathematics, University of Minnesota
Popel, Aleksander apopel@jhu.edu Department of Biomedical Engineering, Johns Hopkins University
Prakash, Shaurya prakash.31@osu.edu Mechanical and Aerospace Engineering, The Ohio State University
Preziosi, Luigi luigi.preziosi@polito.it Department of Mathematical Sciences, Politecnico di Torino
Rambani, Komal komal.rambani@osumc.edu IBGP, OSU
Ramis-Conde, Ignacio ignacio.ramis@uclm.es Instituto de Matematica Aplicada a la Ciencia y la Ingenieria, Universidad de Castilla La Mancha
Rezaei Yousefi, Mohammadmahdi rezaeiyousefi.1@osu.edu Electrical and Computer Engineering, The Ohio State University
Sanft, Kevin kevin@kevinsanft.com Mathematics, University of Minnesota
Secomb, Timothy secomb@u.arizona.edu Physiology, University of Arizona
Sinkala, Zachariah Zachariah.Sinkala@mtsu.edu Mathematical Sciences, Middle Tennessee State University
Sivaloganathan, Siv ssivalog@math.uwaterloo.ca Applied Mathematics, University of Waterloo
South, Andy a.p.south@dundee.ac.uk Dermatology & Cutaneous Biology, Thomas Jefferson University
Stolarska, Magdalena mastolarska@stthomas.edu Mathematics,
Subramaniam, Vish subramaniam.1@osu.edu Mechanical & Aerospace Engineering, The Ohio State University
Sun, Yi yisun@math.sc.edu Mathematics, University of South Carolina
Swanson, Kristin kristin.swanson@northwestern.edu Neurological Surgery, Northwestern University
Tang, Min tangmin@sjtu.edu.cn Department of Mathematics, Shanghai Jiaotong University
Taslim, Cenny taslim.2@osu.edu Comprehensive Cancer Center , The Ohio State University
Tyrrell, Alex james.tyrrell@thomsonreuters.com n/a, Thomson Reuters
Wang, Qixuan qixuanw@math.uci.edu math, University of California, Irvine
Watson, Michael Michael.Watson@pet.hw.ac.uk Institute of Petroleum Engineering, Heriot-Watt University
Yun, Ana ana7123@korea.ac.kr Mathematics, Korea University
Quantifying Vascular Architecture: Relating Form to Function

Recent advances in our ability to manipulate blood vessels to therapeutic advantage have heightened our awareness that not all blood vessels are created equal. I will review recent efforts to improve upon traditional measures of vascular geometry such as vessel density and diameter. While retaining reasonable simplicity, the aim is to develop measures that better relate the geometry of the blood vessels to clinical outcomes. I will outline recent insights drawn from transport fundamentals, network science, percolation theory, reliability theory, system dynamics and fractal geometry that shed light on how the arrangement of blood vessels influences their ability to deliver nutrients and therapeutic agents in tumors. Special emphasis will be given to the similarities and differences between normal and tumor vasculature.

Multiscale Modelling of Cancer Cell Motility

Since Inhibiting metastasis is as crucial as minimizing tumour growth for efficient treatment of cancer, we constructed a multiscale model of cell motility, with our primary focus being on amoeboid type cell motility of metastasizing tumour cells in the extracellular matrix (ECM). Our 2D hybrid agent-based/finite-element model covers a wide parameter space and provides a deeper understanding of the conditions governing the motility of cancer cells on a multiscale level. Both the extracellular conditions (e.g. ECM density) and intrinsic cell properties (e.g. relative distribution of contractile and blebbing regions of the cell membrane) were investigated. The aim is to identify the combination of intrinsic properties metastasising cells are more likely to use under different extracellular conditions. After extensive benchmarking of the computational model, using in vitro data, we were able to predict cancer cell motility in vivo. Moreover, the model was successfully challenged to predict the effect of different combinations of kinase inhibitors and integrin depletion (Tozluoglu et al. Nat. Cell Biol. 2013).

Mathematical modeling of tumor-driven angiogenesis. A mean field model.

In the mathematical modeling of tumor-driven angiogenesis, the strong coupling between the kinetic parameters of the relevant stochastic branching-and-growth of the capillary network, and the family of interacting underlying fields is a major source of complexity from both the analytical and computational point of view.

Our main goal is thus to address the mathematical problem of reduction of the complexity of such systems by taking advantage of its intrinsic multiscale structure; the (stochastic) dynamics of cells will be described at their natural scale (the microscale), while the (deterministic) dynamics of the underlying fields will be described at a larger scale (the macroscale).

In this presentation, starting from a conceptual stochastic model including branching, elongation, and anastomosis of vessels, we derive a mean field approximation of the vessel densities, leading to deterministic partial differential equations for the underlying fields, driving the formation of the stochastic vessel network.

Outcomes of the relevant numerical simulations will be presented.

References

[1] Capasso, V., Morale, D.: Stochastic Modelling of Tumour-induced Angiogenesis.

J. Math. Biol., 58, 219{33 (2009)

[2] Capasso, V., Morale D., Facchetti, G.: The Role of Stochasticity for a

Model of Retinal Angiogenesis, IMA J. Appl. Math. (2012) ; 19 pages;

doi:10.1093/imamat/hxs050

[3] Bonilla, L., et al.: A mean field model for tumor-driven angiogenesis.

In preparation (2014).

How quantitative modelling can inform on disease pathogenesis: lessons from liver

Systems biology has opened up new ways of understanding disease processes based on close iterations between experimentation and mathematical modelling. So far, its focus has mainly been on molecular processes. The combination of modern imaging modalities with image processing and analysis (Hammad et. al. Arch. Toxicol. 2014; Hoehme and Drasdo, Bioinformatics 2010), and mathematical models opens up a promising new approach towards a quantitative understanding of pathologies and of disease processes that includes the multicellular tissue level. For illustration we will consider three examples of interdisciplinary approaches integrating biological models and mechanisms of processes contributing to disease progression at various scales within mathematical modelling frameworks. In the first example a multi-cellular spatial temporal model predicts within a systems biology approach a previously not recognized and subsequently validated order principle underlying liver regeneration after drug-induced damage, as it occurs for example after overdosing acetaminophen (paracetamol) (Hoehme et. al., PNAS, 2010). The second example will present a mathematical model integrating information from the spatial temporal model of the first example with the chemical reactions known to detoxify liver from ammonia in health liver during the destruction and subsequent regeneration process, that succeeded to indicate the lack of an important reaction (Schliess et. al., Hepatology, 2014). Experiments triggered by this model prediction led to finding of a so far unrecognized good candidate reaction that might be clinically utilized in case of hyperammonemia. The final example will address the spatial-temporal molecular control of the regeneration process within a mechanistic multi-scale model spanning the molecular, cellular, tissue and body scale. The tissue model involved in each of these examples represents each cell individually as biophysical entities and is hence able to integrate equally physical and biological information. The example demonstrates that multi-cellular models are so far able to falsify hypotheses and guide towards the most informative experimental design.

Modeling the Effects of Dysregulated Angiogenesis on Tumor Nanotherapeutics Delivery

In addition to excessive cellular proliferation, solid tumors typically elicit irregular angiogenesis resulting in structurally abnormal and leaky vascular structures. The passive mechanism termed “enhanced permeability and retention” (EPR) effect enables systemically administered nanoparticles sized 10–400 nm to preferentially extravasate from the vasculature into the interstitial space of solid tumors. Additional factors contributing to nanoparticle pharmacodynamics and cytotoxicity include size, surface charge and morphology. These properties are typically tailored to design systems that exhibit optimal tumor tissue uptake. Drugs delivered via nanoparticles can thus increase treatment effectiveness while reducing systemic toxicity. However, heterogeneity in blood flow due to irregular angiogenesis and vascular remodeling at the tumor site promote tissue hypoxia and thus cell quiescence, presenting a physical barrier to cell-cycle dependent chemotherapeutics delivered by nanocarriers. Inadequate vascularization leads to further impediments that hinder optimal treatment, including insufficient drug dosages due to abnormally long inter-vascular diffusion distances, as well as disturbed convection and diffusion of molecules (glucose, oxygen) and nanoparticles in the interstitium, as we have recently explored through intravital microscopy and mathematical modeling. Cancerous tissue can contain almost twice the volume of interstitial space compared to normal tissue; an abundance of extracellular matrix proteins along with an increased interstitial pressure may further inhibit nanoparticle delivery and drug diffusion in under-vascularized tumor regions. These physical barriers, coupled with intrinsic resistance mechanisms at the cell-scale, often cause cancer drug therapies to fail. We present recent applications of engineering and modeling-based approaches to help tackle these challenges in cancer nanotherapy.

Dimension of cancer invasion

Single-cell or collective invasion results from coordination of cell shape, deformability and actin dynamics relative to the tissue environment. Both, in vitro and in vivo models provide complementary insights into modes and mechanisms of cell movement. In monomorphic 3D invasion models in vitro, an obligate step of collective invasion is the degradation of extracellular matrix (ECM). Thereby, the density of the ECM determines the invasion mode of mesenchymal tumor cells. In 3D in vitro models, fibrillar, high porosity ECM enables single-cell dissemination, whereas dense matrix induces cell-cell interaction, leader-follower cell behavior and collective migration as an obligate protease-dependent process. Conversely, in vivo monitored by intravital multiphoton second and third harmonic generation microscopy, abundant tissue microniches provide invasion-promoting tracks that enable collective migration along tracks of least resistance. As main routes, non-destructive contact-guidance is mediated by preformed multi-interface perimuscular, vascular and –neural tracks of 1D, 2D and 3D topography. Whereas in vitro models predict a major role for beta1/beta3 integrins in sustaining invasion, in vivo targeting of intergrins induces unexpected plasticity of invasion, including collective and amoeboid single-cell dissemination, followed by enhanced micrometastasis, implicating integrin-independent dissemination as effective route to metastasis and challenging in vitro approaches. In conclusion, in vitro and in vivo models deliver diverse, often dedicated environments which impact the type, efficacy and mechanism of invasion. Computational modeling thus needs to take the physical and molecular organization of tissues into account.

Numerical challenges in models of tissue-scale tumour cell invasion

Firstly, the efficient simulation of nonlocal partial differential equation models where the nonlocal terms account for the effects of cell-cell and cell-matrix adhesion. Such models have been used in to simulate the process of tumor cell invasion but also in other applications. The repeated evaluation of the nonlocal term is a major computational bottleneck. We outline our FFT-based approach, discuss the inclusion of different boundary conditions, and comment on options and limitations.
Secondly, parameters appearing in mathematical models of tumor invasion are often difficult to assess experimentally and even if experimental values are available their accuracy might not be very good or they might have been obtained in a setting different from that what is modeled. Thus these parameters are uncertain and quantifying the effect of this uncertainty on the model solution or certain derived quantities of interest is beneficial for judging the value of the model and possibly for proposing required dedicated experiments. We present a framework for uncertainty quantification based on fast adaptive stochastic collocation on sparse grids. The advantage of this approach is that it can use an existing simulation environment for the model under investigation in a black-box fashion.

Dynamic Changes in Cellular Mechanics Regulates Cancer Cell Migration/Invasion

Metastatic spread of tumor cells is responsible for a majority of cancer deaths. During metastasis, tumor cells acquire a highly motile phenotype in a process known as epithelial to mesenchymal transition (EMT). These motile cells detach from the primary tumor, invade into surrounding tissues, intravasate into the circulation and colonize distal tissues. Although investigators have recently characterized the biomechanical properties of circulating tumor cells (CTC), it is not known how changes in cell mechanics during EMT influence the initial tumor-detachment and invasion phases of metastasis. We have used a combination of computational techniques and in-vitro/in-vivo models to investigate how changes in both tumor cell and stromal cell mechanics influence metastasis. Contrary to the high compliance of CTCs, experiments in our lab indicate that tumor cells become significantly stiffer during EMT. However, detachment of these cells from the tumor results in a significant reduction in stiffness and this reduction in stiffness facilitates amoeboidal migration through the extracellular matrix (ECM). Furthermore, dynamic remodeling of the ECM by stromal fibroblasts facilitates additional invasion. Based on these results, we have used gene knockdown/mutation techniques to either reduce tumor cell stiffness or prevent ECM remodeling by stromal fibroblasts. Both of these manipulations significantly reduce the amount of tumor cell detachment and invasion. Therefore, altering the mechanical properties of tumor and stromal cells may be an effective way to prevent metastasis.

Mathematical Modelling with Fully Anisotropic Diffusion and Applications to Glioma Growth

Anisotropic diffusion describes random walk with different diffusion rates in different directions. I will present a form of anisotropic diffusion which is called "fully" anisotropic. The fully anisotropic diffusion model does not obey a maximum principle and can even lead to singularity formation in infinite time.

I will derive this model from biological principles, analyse some of its behavior and show how it can be used to model glioma spread.

Uncertainty Quantification for Image Driven Modeling and Simulation

I will review our efforts to develop imaging, modeling and simulation tools for the study of angiogenesis. I will address the challenge of predictive simulations for Life Science applications and discuss a Bayesian uncertainty quantification and propagation framework that can help bridge experiments and simulations.

Role of Tumor-Associated Endothelial Cells in Tumor Metastasis

The metastatic spread of solid tumors is directly or indirectly responsible for most cancer-related deaths. Metastatic process is highly complex and it involves multiple steps including the release of tumor cells from the primary tumor, survival in circulation, interaction with vascular endothelium and invasion of target organs. Although our understanding of tumor cell biology has increased exponentially during the last couple of decades, we still know very little about the role tumor microenvironment plays in promoting tumor cell release from the primary tumor and metastasis to the distal organs. We have recently observed that primary tumor samples from head and neck cancer patients with metastasis show significantly higher Bcl-2 positive blood vessels as compared to cancer patients without metastasis. These results thereby suggest that Bcl-2 expression in tumor-associated endothelial cells may be involved in tumor cell metastasis. We tested this hypothesis using a SCID mouse model and indeed, enhanced Bcl-2 expression in tumor-associated endothelial cells promoted tumor metastasis to lungs. In the subsequent mechanistic study, we demonstrated that tumor-associated endothelial cells that express high levels of Bcl-2 significantly promoted tumor cell release by enhancing epithelial-mesenchymal transition (EMT)-related changes in tumor cells predominantly via the secretion of IL-6. It is well established that the early steps in metastasis are completed more efficiently than the later steps involving survival of cancer cells in circulation and extravasation into the target organ. This could be due to the fact that most of the cancer cells, particularly epithelial cells, undergo rapid cell death (anoikis) in harsh circulatory conditions. Interestingly, we also observed in our study that in addition to circulating tumor cells (CTCs), there is a marked increase in Bcl-2 positive circulating endothelial cells (CECs) in the blood samples of head and neck cancer patients. These results raised an intriguing question about the biological significance of these circulating endothelial cells. Our results suggest a novel role for CECs in binding to tumor cells, protecting them from anoikis and chaperoning them to distal sites.

Mathematical Analysis of PDE Models of Chemotaxis

We investigate local and global existence, blowup criterion and long time behavior of classical solutions for a system derived from the Keller-Segel model describing chemotaxis. We study the existence and the nonlinear stability of large-amplitude traveling wave solutions to the system.

Feedback, lineages and vascular tumor growth

Most tissues are hierarchically organized into lineages. Tumors arise when the carefully regulated balance of cell proliferation and programmed cell death (apoptosis) that ordinarily exists in normal homeostatic tissues breaks down. Traditionally, cancer cells are assumed to acquire a common set of traits. However, not all proliferating cells in a tumor matter seem to matter equally and tumor cells apparently progress through lineage stages regulated by feedback. The reasons for this are still not well established. In this talk, we will present new mathematical models to simulate the spatiotemporal dynamics of cell lineages in vascularized solid tumors. We account for protein signaling factors produced by tumor cells, and vascular endothelial cells in the microenvironment that direct self-renewal, differentiation and proliferation pathways. Our models demonstrate the development of heterogenous cell distributions and the formation of vascular niche-like environments for stem cells. We demonstrate that feedback processes play a critical role in tumor progression, heterogeneity, vascularity and the development of morphological instability.

Biomechanics of cancer invasion and vessel function

Mechanical forces control many processes in and around growing tumors. These forces can be transmitted by solid components of the tissue such as cell membranes, anchoring proteins and matrix components, or fluid components such as blood, plasma or lymph. Solid mechanical forces become important when uncontrolled growth compresses cells and matrix, directly affecting cancer cell proliferation and apoptosis. Compression of cancer cells can also induce more migration and invasion, potentially contributing to metastasis. Fluid forces, on the other hand, are central to development and function of tumor vascular systems (blood and lymphatic). Blood flow subjects vessel wall cells to shear stresses that drive blood vessel contractions or dilations to optimize flow, and plasma exchanged between vessels can direct the creation of additional blood vessel segments. Similarly, lymphatic pumping a process central to immune function and fluid homeostasis is sustained by cycles of fluid flow and shear stress-activated nitric oxide production. The flow is directed by one-way valves, and is often abnormal in tumor-associated lymphatic vessels. All of these processes involve the integration of mechanical signals by cells to direct biological processes. This interface between mechanics and biology is not well-explored, but contains many potential new control points for modulating tumor progression.

Crawlers can also swim: new modes of movement in the ECM

Cell locomotion is essential for early development, angiogenesis, tissue regeneration, the immune response, and wound healing in multicellular organisms, and plays a very deleterious role in cancer metastasis in humans. Locomotion involves the detection and transduction of extracellular chemical and mechanical signals, integration of the signals into an intracellular signal, and the spatio-temporal control of the intracellular biochemical and mechanical responses that lead to force generation, morphological changes and directed movement. While many single-celled organisms use flagella or cilia to swim, there are two basic modes of movement used by eukaryotic cells that lack such structures -- mesenchymal and amoeboid. The former, which can be characterized as crawling' in fibroblasts or gliding' in keratocytes, involves the extension of finger-like filopodia or pseudopodia and/or broad flat lamellipodia, whose protrusion is driven by actin polymerization at the leading edge. This mode dominates in cells such as fibroblasts when moving on a 2D substrate. In the amoeboid mode, which does not rely on strong adhesion, cells are more rounded and employ shape changes to move -- in effect 'jostling through the crowd' or swimming'. Here force generation relies more heavily on actin bundles and on the control of myosin contractility. Leukocytes use this mode for movement through the extracellular matrix in the absence of adhesion sites, as does Dictyostelium discoideum when cells sort in the slug. However, recent experiments have shown that numerous cell types display enormous plasticity in locomotion in that they sense the mechanical properties of their environment and adjust the balance between the modes accordingly by altering the balance between parallel signal transduction pathways. Thus pure crawling and pure swimming are the extremes on a continuum of locomotion strategies, but many cells can sense their environment and use the most efficient strategy in a given context. We will discuss some of the mathematical and computational challenges that this diversity poses.

Computational and experimental studies of breast cancer metastasis

I will present our recent experimental results on breast cancer metastasis with an emphasis on the tumor microenvironment and particularly the roles of blood and lymphatic vasculatures in metastatic organs [1,2]. We will analyze the roles of the stromal cells and their interactions with cancer cells in metastasis. We will then discuss our computational results on 3D reconstruction of tumor vasculature applicable to both primary and metastatic sites, and modeling of blood flow and molecular interactions and transport [3,4]. An agent-based model of tumor growth and metastasis will be presented that takes into account cancer stem cells [5]. Finally, we will discuss a framework for modeling cancer metastasis.

[1] E. Lee, E. Fertig, K. Jin, S. Sukumar, N.B. Pandey, and A.S. Popel. Breast cancer cells condition lymphatic endothelial cells within pre-metastatic niches to promote metastasis. Nature Communications, 5:4715, 2014.

[2] E. Lee, N.B. Pandey, and A.S. Popel. Lymphatic endothelial cells support tumor growth in breast cancer. Sci. Rep., 4:5853, 2014.

[3] S.K. Stamatelos, E. Kim, A.P. Pathak, and A.S. Popel. Bioimage informatics aided reconstruction of breast tumor microvasculature and computational predictions of blood flow. Microvasc. Res. 91:8-21, 2014.

[4] S.D. Finley and A.S. Popel. Effect of tumor microenvironment on tumor VEGF during anti-VEGF treatment: systems biology predictions. J Nat Cancer Inst., 105:802-811, 2013.

[5] K.A. Norton and A.S. Popel. An agent-based model of breast tumor growth, metastasis and seeding: the role of cancer stem cells. J. Roy. Soc. Interface, 11(100), 2014.

Impedance Spectroscopy for Imaging and Quantifying Tissue Properties

Over the past century, electrical or electrochemical impedance spectroscopy (EIS) has been used by chemists and biologists to study reaction rate kinetics, corrosion phenomena, battery aging, and tissue characteristics to name a few applications. EIS measures a current or voltage response of a system to an alternating voltage or current signal and records the response as complex impedance. The key idea is that the input is a small amplitude signal and therefore permits use of small-signal theory and linearization to analyze system response through data containing both magnitude and phase information.

In this talk, I will present the development of EIS as a new tool for imaging and quantifying tissue properties. EIS was used to generate images of morphologically distinct regions in excised human liver tissue to differentiate, based on differences in electrical conductivity and permittivity, the tumor and non-tumor regions. The impedance data can be reduced to equivalent tissue structure images showing the ability to use EIS as an imaging technique, with direct comparisons to visual representation by digital photography and clinical validation by histopathology images.

Modelling Cell-Extracellular Matrix Interaction

Cell-extracellular matrix interaction and the mechanical properties of cell nucleus have been demonstrated to play a fundamental role in cell movement across fibre networks and micro-channels. In the talk, we will describe several mathematical models dealing with such a problem, starting from modelling cell adhesion mechanics to the inclusion of influence of nucleus stiffness in the motion of cells.

An energetic approach is used in order to obtain a necessary condition for which cells enter cylindrical structures. The nucleus of the cell is treated either (i) as an elastic membrane surrounding a liquid droplet or (ii) as an incompressible elastic material with Neo-Hookean constitutive equation. The results obtained highlight the importance of the interplay between mechanical deformability of the nucleus and the capability of the cell to establish adhesive bonds.

Generation of microvascular networks in normal and tumor tissues: A biological patterning problem

Formation of functionally adequate vascular networks by angiogenesis presents a problem in biological patterning. Generated without predetermined spatial patterns, networks must develop hierarchical tree-like structures for efficient convective transport over large distances, combined with dense space-filling meshes for short diffusion distances to every point in the tissue. Moreover, networks must be capable of restructuring in response to changing functional demands without interruption of blood flow. Here, theoretical simulations based on experimental data are used to demonstrate that this patterning problem can be solved through over-abundant stochastic generation of vessels in response to a growth factor generated in hypoxic tissue regions, in parallel with refinement by structural adaptation and pruning. Essential biological mechanisms for generation of adequate and efficient vascular patterns are identified and impairments in vascular properties resulting from defects in these mechanisms are predicted. The results provide a framework for understanding vascular network formation in normal or pathological conditions. With regard to tumor microcirculation, the simulations indicate possible factors leading to characteristic features including poor tissue oxygenation in the presence of adequate overall perfusion, and persistent instability of vessel structure and flow patterns.

Modelling squamous cell carcinoma invasion in vitro, in vivo and in silico

Squamous cell carcinomas (SCCs) collectively are the most common ectodermal cancers, resulting in >300,000 deaths per year. SCCs arise in renewable squamous epithelia which serve to create an environmental barrier in the skin, esophagus, lung, and cervix. In normal squamous epithelia, basal progenitors give rise to more superficial daughter cells that terminally differentiate into keratinized cells as they migrate toward the surface, coupling terminal differentiation with microanatomic position. An early feature of squamous neoplasia of all types is disrupted differentiation to variable degrees, typically associated with thickening of the epithelium and increased proliferation. Following on from this and as a first step towards metastatic dissemination and distant colonization, SCCs initiate the process of local invasion away from the surface and into the surrounding tissue comprised of extracellular matrix and cells such as cancer associated fibroblasts and macrophages. We model SCCs in vitro using tumor and normal cells derived from the skin. By reconstituting epithelial and mesenchymal cells together with a matrix (synthetic or cellular in origin) we are able to recapitulate normal cell differentiation and tumor cell invasion in a laboratory setting. By grafting these complex cultures to the backs of immune compromised mice we can model SCC invasion in vivo and test intervention strategies. Finally, mathematical modelling can simulate many aspects of cancer cell invasion and provide opportunity to interrogate parameters inaccessible to biological experimentation.

Towards Patient-Specific Modeling of Angiogenesis-driven Tumor-associated Edema in Gliomas

Glioblastoma, the most aggressive form of primary brain tumor, is predominantly assessed with gadolinium-enhancedT1-weighted (T1Gd) andT2-weighted magnetic resonance imag-ing (MRI). Pixel intensity enhancement on the T1Gd image is understood to correspond to the gadolinium contrast agent leaking from the tumor-induced neovasculature, while hyperintensity on theT2/FLAIR images corresponds with edema and infiltrated tumor cells. None of these modalities directly show tumor cells; rather, they capture abnormalities in the microenvironment caused by the presence of tumor cells. Thus, assessing disease response after treatments impacting the microenvironment remains challenging through the obscuring lens of MR imaging. Anti-angiogenic therapies have been used in the treat-ment of gliomas with spurious results ranging from no apparent response to significant imaging improvement with the potential for extremely diffuse patterns of tumor recurrence on imaging and autopsy. Anti-angiogenic treatment normalizes the vasculature, effectively decreasing vessel permeability and thus reducing tumor-induced edema, drastically alter-ing T2-weighted MRI. We extend a previously developed mathematical model of glioma growth to explicitly incorporate edema formation allowing us to directly characterize and potentially predict the effects of anti-angiogenics on imageable tumor growth. A compari-son of simulated glioma growth and imaging enhancement with and without bevacizumab supports the current understanding that anti-angiogenic treatment can serve as a surro-gate for steroids and the clinically driven hypothesis that anti-angiogenic treatment may not have any significant effect on the growth dynamics of the overall tumor cell popu-lations. However, the simulations do illustrate a potentially large impact on the level of edematous extracellular fluid, and thus on what would be imageable on T2/FLAIR MR. Additionally, by evaluating virtual tumors with varying growth kinetics, we see tumors with lower proliferation rates will have the most reduction in swelling from such treatments.

Transport, metabolic & shear stress effects in vascular remodeling

“Normalization” of tumor blood vessels has shown promise to improve the efficacy of subsequently-administered chemotherapeutics. In theory, anti-angiogenic drugs targeting VEGF signaling can improve vessel network structure and function, enhancing the transport of systemically-injected drugs. During normalization, a wide range of effects are observed on vessel diameters, tortuosity, permeability, and blood flow, eventually producing a more efficient network. Although not well-understood, it is likely that this type of adaptive remodeling depends on blood shear forces, transvascular pressure, upstream signals transmitted along the endothelium as well as growth factors such as VEGF.

In an effort to better analyze how blood vessels adapt and remodel, we have developed a physics model that simulates vascular structure and function from meso to macro scales, thereby capturing important dynamics that can be observed and measured using two-photon imaging and other experimental techniques. Though challenges remain, our model has helped better understand the complex, nonlinear processes involved in the normalization of tumor vasculature.

Tumours, Wounds and Retinae: Modelling Angiogenesis in Development and Disease

The ability of functional vascular networks to both grow and adapt is a crucial feature of many physiological processes, including organ growth, disease progression and tissue repair. Since the metabolic requirements of host tissue need to be served in each case, the manner of the spatio-temporal evolution of such vessel networks is an all-important regulator of tissue function. At a cellular level, the phenomenon of angiogenesis comprises a well?orchestrated sequence of events involving endothelial cell migration and proliferation; tissue degradation; capillary sprout emergence; anastomosis formation; and, finally, blood perfusion through the nascent network. The onset of blood flow is crucial to the subsequent evolution of the structure: by providing nutrients to the local tissue and introducing haemodynamic forces in flowing vessels, both individual capillary radii and the spatial distribution of migratory cues are dynamically modified. In this presentation I will discuss a hybrid discrete-continuum modelling approach that simultaneously couples vessel growth with blood flow through the vasculature, and provide an overview of results from its application to the study of solid tumour growth, wound healing and retinal development. Applying the model across this broad range of scenarios is found to be extremely beneficial, with the unique challenges posed in each case forcing a continual refinement of the approach. Retinal vascular growth, in particular, provides an extremely rigorous test, ultimately resulting in a model with strong potential for use in the investigation of ocular pathologies.

### Posters

A 3-D Composite Hybrid Model of Angiogenesis in the Cornea

We study angiogenesis in the context of a highly controllable experimental environment: the cornea micropocket assay. Using a multidisciplinary approach that combines experiments, image processing and analysis, and mathematical modelling we aim to provide mechanistic insight into the action of vascular endothelial growth factor A (VEGF-A) and other angiogenic factors. Image analysis techniques have been used to extract quantitative data, which are both spatially and temporally resolved, from experimental images, and complementary one-dimensional continuum and three-dimensional composite hybrid models of VEGF-A induced angiogenesis have been developed. The experimental data have been used for model parametrisation, while the mathematical models have been used to assess the utility of the cornea micropocket assay and to provide insight into phenomena underlying angiogenesis in the cornea [1].

In this poster we introduce our three-dimensional composite hybrid model of angiogenesis in the cornea. Our model extends existing on-lattice models of angiogenesis by incorporating an abstract representation of tip cell filopodia which enables tip cells to sense nearby vessels (or other tip cells) and facilitates the formation of anastomoses and thus the formation of well-perfused, functional vascular networks. When model parameters are selected from a biologically feasible regime we demonstrate that our model can capture quantitatively the dynamics of in vivo experiments; model results are consistent with the experimental data in terms of the observed neovascular density and the rate of neovascular growth towards the VEGF-A source. The simplicity of our experimental system and model geometry also allow us to examine the relationship between the migrating fronts of perfused and unperfused vessels, which are not observable in our experimental images.

Modeling Distributions of Reads from Leukemic Cells DNA through Mixture of Poisson Distributions

Prof. Yuriy Fofanov and his team from the University of Houston sequenced DNA material obtained from the laboratory of Dr. Michael Andreeff at MD Anderson Cancer Center from different types of cells in patients with leukemia. In this poster, I will present a method to model number of left-hand end reads Y that cover a random site in a nucleotide contained in a region of interest of the sequencing project for different samples. Specifically, I modeled the distribution of Y using a Mixture of Truncated Poisson Distributions.

Modelling of a brain tumour initiation and early development: A coupled model of glioblastoma growth, pre-existing vessel co-option, angiogenesis and blood perfusion

We propose a coupled mathematical modelling system to investigate glioblastoma growth in response to dynamic chemical and haemodynamic microenvironments caused by pre-existing vessel co-option, remodelling, collapse and angiogenesis. A typical tree-like architecture network with different orders for vessel diameter is designed to model pre-existing vasculature in host tissue. The chemical substances including oxygen, VEGF, extra-cellular matrix and matrix degradation enzymes are calculated based on the haemodynamic environment which is obtained by coupled modelling of intravascular blood flow with interstitial fluid flow. The haemodynamic changes, including vessel diameter and wall permeability, are introduced to reflect a series of pathological characteristics of abnormal tumour vessels such as vessel dilation, leakage, angiogenesis, regression and collapse. Migrating cells are developed as a special proliforation tumour cell phenotype to describe the migration behaviour of malignant tumour cells. The simulation focuses on the avascular phase of tumour development and stops at an early phase of angiogenesis. The model is able to demonstrate the main features of glioblastoma growth in this phase such as the formation of pseudopalisades, cell migration along the host vessels, the pre-existing vasculature co-option, angiogenesis and remodelling. The model also enables us to examine the influence of initial conditions and local environment to the early phase of glioblastoma growth.

A Continuum Mechanics Model for Modeling Tumor Spheroid Growth and Cell Spreading

I present a mathematical model that can be applied to various biological phenomena in which growth and motion and its affect on mechanics stresses play a significant role. This model is based on concepts in continuum mechanics in which the rate of deformation tensor is additively decomposed into an active and passive part. In the two presented applications of this model, stress-dependent tumor growth and cell-substrate interaction in cell spreading, the active component represents deformation due to growth and cytoskeletal rearrangement. In both applications, it is assumed that materials are hypoelastic, i.e. the stress rate is proportional to the strain rate. Such a constitutive relation is proposed by Rajagopal and Srinivasa(2007) because it captures large strain elastic deformations while not requiring the concept of a reference configuration, which may be meaningless for the constant growth and remodeling present in biological materials. Finite element simulations of the model equations shed insight into the complexity of the stress feedback mechanism present in tumor growth and the effect of substrate elasticity on intracellular stresses.

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