## 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

Tomas Alarcon
Computational & Mathematical Biology,
Jim Baish
Department of Biomedical Engineering, Bucknell University
Paul Bates
Biomolecular Modelling Laboratory, London Research Institute
Katie Bentley
pathology, Beth Israel Hospital, Harvard Medical School
Vincenzo Capasso
ADAMSS, Università degli Studi di Milano and "Gregorio Millan" Institute Escuela Politecnica Superior Universidad Carlos III de Madrid
Vittorio Cristini
School of Health Information Sciences, University of Texas
Dirk Drasdo
Bioinformatics, Physical and Mathematical Biology, Institut National de Recherche en Informatique Automatique (INRIA)
Hermann Frieboes
Bionegineering, University of Louisville
Peter Friedl
Alf Gerisch
Thomas Hillen
Mathematical and Statistical Sciences, University of Alberta
Petros Koumoutsakos
Computational Science, ETHZ
John Lowengrub
Mathematics, University of California, Irvine
Aleksander Popel
Department of Biomedical Engineering, Johns Hopkins 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 Introductory talk by an organizer

09:45 AM
10:00 AM

Discussion of open questions

10:00 AM
10:30 AM

Break

10:30 AM
11:30 AM
Zuzanna Szymańska - Large-scale computational simulation of cancer invasion

Abstract not submitted.

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

Abstract not submitted.

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
Peter Friedl - Multi-scale analysis of cell migration in vitro and in vivo

Abstract not submitted.

10:00 AM
10:30 AM

Break

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

Abstract not submitted.

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

Boxed Lunch at MBI

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
Triantafyllos Stylianopoulos - Dissecting tumor mechanical microenvironment through mathematical modeling

Abstract not submitted.

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

Abstract not submitted.

10:00 AM
10:30 AM

Break

10:30 AM
11:30 AM
Tomas Alarcon - Multiscale modelling of tumour growth and angiogenesis

Abstract not submitted.

11:30 AM
12:30 PM
Vittorio Cristini - Predictive modeling of cancer patient drug response

Abstract not submitted.

12:30 PM
02:00 PM

Lunch Break

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

Abstract not submitted.

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
08:00 AM

Shuttle to MBI

08:15 AM
09:00 AM

Breakfast

09:00 AM
10:00 AM
Katie Bentley - Uncovering mechanistic switches in tumour angiogenesis with an in silico/in vivo approach

Through integrated agent-based computational modeling with in vitro and in vivo experimentation we have uncovered a fundamental switch that occurs in endothelial cell (EC) behavior during blood vessel growth (angiogenesis) between normal and pathologically high VEGF tissue environments, such as tumors. In normal conditions, a VEGF-Dll4-Notch signaling feedback loop generates a “salt and pepper pattern” of alternating migratory or inhibited EC phenotypes throughout newly extending vessels, critical to normal branch spacing and elongation. Simulations predicted that if the VEGF levels rise then this same pathway can become overloaded, switching ECs to collectively oscillate their Notch signaling, in-phase with each other, such that large clusters of adjacent cells oscillate between trying to migrate at once or remain still at once, hugely disrupting the branching process. We have now observed first evidence of this temporal patterning switch in vivo and in vitro.

We also recently identified that the entire sprouting process is more dynamic than previously thought, with ECs interchanging positions and migratory phenotypes as new vessels form. Predictive simulations led to the discovery that Notch regulates VE-cadherin turnover, the major adhesion molecule of ECs. Simulations further predict that differential adhesion is required to drive EC intercalation; the clustering of Notch signaling caused by high VEGF levels was found to entirely abrogate intercalation in silico. We subsequently observed first evidence for these predictions in vitro and in vivo with a switch observed in mouse glioblastoma tumor vessels. Together, providing a new explanation for enlarged and poorly branched tumor vessels as a result of a spatiotemporal shift in collective EC signaling and movement dynamics.

K. Bentley, et al. Nature Cell Biology (2014)

K Bentley, et al. Developmental Cell. (2014)

K. Bentley, et al. PLoS Computational Biology (2009)

10:00 AM
10:30 AM

Break

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 of tumor microenvironment heterogeneity resulting from dysregulated angiogenesis

Abstract not submitted.

12:30 PM
02:00 PM

Lunch Break

02:00 PM
03:00 PM
John Lowengrub
03:00 PM
03:30 PM

Break

03:30 PM
04:30 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.

04:30 PM
05:30 PM

Panel discussion / breakout session

05:30 PM

Shuttle pick-up from MBI

06:30 PM
07:15 PM

Cash Bar

07:15 PM
07:15 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
10:00 AM

TBD

10:00 AM
10:30 AM

Break

10:30 AM
11:30 AM
Kristin Swanson
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
Alarcon, Tomas talarcon@crm.cat Computational & Mathematical Biology,
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
Cristini, Vittorio VCristini@salud.unm.edu School of Health Information Sciences, University of Texas
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
Govinder, Kesh govinder@ukzn.ac.za Mathematics, Statistics and Computer Science, University of KwaZulu-Natal
Hillen, Thomas thillen@ualberta.ca Mathematical and Statistical Sciences, University of Alberta
Jiang, Yi yjiang12@gsu.edu Mathematics and Statistics, 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
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
Multiscale modelling of tumour growth and angiogenesis

Abstract not submitted.

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).

Uncovering mechanistic switches in tumour angiogenesis with an in silico/in vivo approach

Through integrated agent-based computational modeling with in vitro and in vivo experimentation we have uncovered a fundamental switch that occurs in endothelial cell (EC) behavior during blood vessel growth (angiogenesis) between normal and pathologically high VEGF tissue environments, such as tumors. In normal conditions, a VEGF-Dll4-Notch signaling feedback loop generates a “salt and pepper pattern” of alternating migratory or inhibited EC phenotypes throughout newly extending vessels, critical to normal branch spacing and elongation. Simulations predicted that if the VEGF levels rise then this same pathway can become overloaded, switching ECs to collectively oscillate their Notch signaling, in-phase with each other, such that large clusters of adjacent cells oscillate between trying to migrate at once or remain still at once, hugely disrupting the branching process. We have now observed first evidence of this temporal patterning switch in vivo and in vitro.

We also recently identified that the entire sprouting process is more dynamic than previously thought, with ECs interchanging positions and migratory phenotypes as new vessels form. Predictive simulations led to the discovery that Notch regulates VE-cadherin turnover, the major adhesion molecule of ECs. Simulations further predict that differential adhesion is required to drive EC intercalation; the clustering of Notch signaling caused by high VEGF levels was found to entirely abrogate intercalation in silico. We subsequently observed first evidence for these predictions in vitro and in vivo with a switch observed in mouse glioblastoma tumor vessels. Together, providing a new explanation for enlarged and poorly branched tumor vessels as a result of a spatiotemporal shift in collective EC signaling and movement dynamics.

K. Bentley, et al. Nature Cell Biology (2014)

K Bentley, et al. Developmental Cell. (2014)

K. Bentley, et al. PLoS Computational Biology (2009)

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).

Predictive modeling of cancer patient drug response

Abstract not submitted.

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 of tumor microenvironment heterogeneity resulting from dysregulated angiogenesis

Abstract not submitted.

Multi-scale analysis of cell migration in vitro and in vivo

Abstract not submitted.

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.

Mathematical Modelling with Fully Anisotropic Diffusion and Applications to Glioma Growth

Abstract not submitted.

Uncertainty Quantification for Image Driven Modeling and Simulation

Abstract not submitted.

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

Abstract not submitted.

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

Abstract not submitted.

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