Elucidating the complex interplay of factors regulating tissue level phenomena via lower level cell-cell and cell-matrix interactions has emerged as a major scientific challenge in the post-genomic era, generating a great deal of interest in what is now called “Systems Biology”. In this general area of research, mathematical modelling of cancer growth is now a well-established field in its own right. Predicting how cancers develop, grow and spread and how they are best treated is providing many challenging and novel problems for applied mathematicians.
The principal objective of this workshop, with its scientific and mathematical focus on the modelling and analysis of cancer invasion and metastasis, was to provide a deeper understanding of the links between intracellular processes and cancer cell population dynamics through the use of multiscale analysis, mathematical modelling and numerical/computational techniques.
With recent advances in analytical and computational tools and techniques, mathematical models of cancer growth are becoming ever more sophisticated, accurate, quantitative and predictive. The plenary talks at the Workshop demonstrated the “state-of-the-art” in this field and generated much fruitful discussion amongst the participants. Modelling in this area has evolved to a point where many of the mathematical models are capable of generating predictions which can be tested experimentally. The Workshop was highly stimulating for all participants and proved to be a success, both scientifically and “socially”.
Participants list and links to available presentations are further down this page.
Download the pdf file of the full report
Tea and coffee will be served during each of the breaks listed in the Programme.
Lunch will be provided between 12.30 and 14.00 from Monday to Friday in the restaurant of the West Park Centre.
On Thursday 29 March, there will a workshop dinner at Jimmy Chungs, a local Chinese Restaurant.
For all participants (excluding the 15 invited speakers), we are able to offer reimbursement, after the event, of up to 150.00 GBP to cover a portion of accommodation and travel costs. You will be given a claim form at the workshop. Please note that receipts are required for any items claimed – we are unable to reimburse any unreceipted items. Reimbursement will be in the currency of your choice, directly into your bank account, so you may wish to have a note of your bank details (including IBAN or routing number) with you, should you wish to submit your claim at the end of the workshop, rather than sending it to ICMS.
Information regarding collection of the 30.00 GBP ICMS registration fee will be sent to participants by email (excluding the 15 invited speakers).
| Presentation Details |
|
| Anderson, Alexander |
| Tumour morphology and mutation driven by microenvironment selection: insights from a hybrid mathematical model |
View Abstract
Hide Abstract
 
|
|
Cancer is a complex, multiscale process, in which genetic mutations occurring at a sub-cellular level manifest themselves as functional changes at the cellular and tissue scale. The importance of tumour cell/microenvironment interactions is currently of great interest - both the immediate microenvironment (cell-cell or cell-matrix interactions) and the extended microenvironment (e.g. vascular bed) are thought to play crucial roles in both tumour progression and suppression. <br /><br />In this talk we present a hybrid discrete-continuum (HDC) mathematical model of the invasion of healthy tissue by a solid tumour and examine how mutations in cell phenotypic attributes (e.g. proliferation, cell-cell adhesion, invasiveness) affect both tumour morphology and genetic makeup. The model focuses on four key variables implicated in the invasion process: tumour cells, host tissue (extracellular matrix), matrix-degradative enzymes and oxygen. The model is considered to be hybrid since the latter 3 variables are continuous (i.e. concentrations) and the tumour cells are discrete (i.e. individuals). Since the cells are considered as individuals we can assign each cell an individual life-cycle flow chart that takes into account both cell phenotype and microenvironmental influences. As the tumour grows mutations are allowed to occur leading to a heterogeneous tumour cell population with some cells having a greater ability to migrate, proliferate or degrade the surrounding tissue. All of these cell properties are closely controlled by cell-cell and cell-matrix interactions and as such the physical geometry of the whole tumour will be dependent on these individual cell interactions. We shall therefore examine how these individual-based cell interactions (with one another and the microenvironment) can affect tumour morphology and discuss which of these interactions is perhaps most crucial in influencing the tumours final structure. In addition we will discuss the evolutionary implications of tumour growth in either harsh/mild microenvironmental conditions.<br /><br />The HDC model is intrinsically multiscale, focusing here on the sub-cellular and cellular levels to produce computational simulations of tumour growth at the tissue scale. This technique, developed in previous models of angiogenesis and nematode migration, can easily incorporate a range of scales i.e. genetic, sub-cellular, cellular, tissue and organ.
|
| Aubert, Marine |
| Modelling the interactions between glioma cells during migration |
|
View Abstract
Hide Abstract
|
Malignant glioma cells are able not only to proliferate but also to migrate towards healthy tissues. The capacity to invade surrounding tissues makes glioblastoma particularly dangerous, because at the moment of diagnosis the tumour has already spread over large distances. To better understand the mechanisms governing the motility of glioma cells, we studied glioma cell migration in simple experimental conditions: migration in two dimensions over a substrate of collagen or an astrocyte monolayer. In order to model migration, we developed a cellular automaton which describes migration of tumour cells over time and compared our simulations with in vitro experimental results.
n our cellular automaton we introduce rules to model cell inertia or cell-cell interactions. In vivo cell-cell interactions can either be tumour cell-tumour cell (homotype) interactions or tumour cell-normal astrocytes (heterotype) interactions.
In our first model tumour cells migrate on a passive substrate (thus only homotype interactions are involved). In the model the strength of the attraction between cells can vary substantially, a stronger attraction leading to a reduced migration and thus to a limited spreading of glioma cells. With this model, we find that the best agreement between simulations and experimental results for migration over a substrate of collagen is obtained for a maximum cell-cell attraction while inertia is not necessary [1]. In experiments where gap junctions (communication channels between cells) are inhibited, cells migrate further [2] and it corresponds to a decreased attraction in the model [3].
Our second model simulates the migration of glioma cells onto an astrocyte monolayer. Homotype and heterotype interactions are involved in this case. As in experiments [2], and opposite to what happen on collagen, the migration is reduced when gap junctions are inhibited. Both in the model and in experiments, astrocytes seem to promote migration of tumour cells.
In conclusion for these models, by tuning only two parameters (the strength of the attraction between cells and the density of heterotype contacts), we are able to reproduce experimental observations on the migration of glioma cells on two different substrates and the role of homotype and heterotype communication through gap junctions in each case [3].
Finally we study the effect that a lump of cells can have on the migration of cells from neighbouring spheroids. A motivation for this study can be found in the results of Werbowetski et al. [4] who postulate that larger glioma spheroids secrete a chemorepellent factor that orients cells migration (an effect which could correspond to our cell inertia) and also affects cells from the adjacent spheroid by repelling them. We use our cellular automaton model in order to investigate whether local cell interactions may reproduce the effects observed by Werbowetski et al [4].
1 IMNC, Universite Paris VII-Paris XI, CNRS, UMR 8165, Bat. 104, 91406 Orsay, France
2 Institut Mondor de Medecine Moleculaire and INSERM E0011, Universite Paris XII, Creteil, France
References
[1] M. Aubert, M. Badoual, S. Fereol, C. Christov, B. Grammaticos, 2006, A cellular automaton model for the migration of glioma cells, Phys. Biol. 3, 93-100.
[2] R. Oliveira, C. Christov, J.S. Guillamo, S. De Bouard, S. Palfi, L. Venance, M. Tardy, M. Peschanski, 2005, Contribution of gap junctional communication between tumour cells and astroglia to the invasionof the brain parenchyma by human glioblastomas, BMC Cell Biol. 6, 7-23.
[3] M. Aubert, M. Badoual, C. Christov, B. Grammaticos, A model for glioma cell migration on collagen and astrocytes, submitted 2007.
[4] T. Werbowetski, R. Bjerkvig and R. Del Maestro, 2004, Evidence for a secreted chemorepellent that direct glioma cell invasion, J Neurobiol. 60, 71-88.
|
| Bellomo, Nicola |
| From the theory of modules to multiscale cancer modelling |
|
View Abstract
Hide Abstract
|
|
Multiscale cancer modelling definitely identifies an highly complex field of interaction between mathematics and biology, with the additional motivation that cancer is one of the greatest killer in our society. This lecture analyzes some conceptual issues concerning multiscale aspects of cancer modelling based on an intepretation and application of Hartwell’s theory of modules [1]. The cellular scale is chosen as the reference scale to describe the system by mathematical equations. Then it is shown how the analysis at the lower scale [2] (molecular and genetics) may provide information to identify the expression of biological functions at the cell scale, while suitable asymptotic methods [3], [4], are developed to recover macroscopic equations at the level of tissues. The above analysis is then viewed as a conceptualbackground to look at two challenging topics: Modelling living tissues as a large system of several interconnected systems, and developing a mathematical theory for multicellular systems [5].<p>[1] H.L. Hartwell, J.J. Hopfield, S. Leibner, and A.W. Murray, From molecular to modular cell biology, <em>Nature</em>, 402, c47-c52, (1999). </p><p>[2] C.R. Woese, A new biology for a new century, <em>Microbiology and Molecular Biology Reviews</em>, 68, 173-186, (2004).</p> <p>[3] A. Bellouquid and M. Delitala, <strong>Modelling Complex Biological Systems - A Kinetic Theory Approach</strong>, Birkhauser, Boston, (2006).</p> <p>[4] N. Bellomo and A. Bellouquid, On the onset of nonlinearity for diffusion models of binary mixtures of biological materials by asymptotic analysis, <em>Int. J. Nonlinear Mechanics</em>, 41, 281-293, (2006).</p> <p>[5] Bellomo N., and Forni G., Looking for new paradigms towards a biological-mathematical theory of complex multicellular systems, <em>Math. Mod. Meth. Appl. Sci.</em>, 16, 1001-1029, (2006).</p>
|
| Byrne, Helen |
| Multiscale modelling of colorectal cancer |
|
View Abstract
Hide Abstract
|
|
Colorectal cancer (CRC) is one of the best characterised cancers, with extensive data documenting the sequential gene mutations that underlie its development. Complementary datasets are also being generated describing changes in protein and RNA expression, tumour biology and clinical outcome. Increases in the quantity and variety of information that can be collected are stimulating the development of multiscale mathematical models that can integrate these highly disparate datasets. In this talk we will introduce the approach that we are using to build such a multiscale model of CRC. We will illustrate the type of insight that such modelling can provide by presenting results from submodels that are being developed to describe phenomena occurring at different spatial scales.
|
| Enderling, Heiko |
| Novel mathematical models of breast cancer development - implications for treatment design |
|
View Abstract
Hide Abstract
|
|
We have developed a multi-scale mathematical model that incorporates new oncological findings to describe the development of breast tumours. In an individual-cell based approach we implement a sequential mutation pathway that allows the development of cancer cells from healthy somatic cell. We discuss the impact of stem cells and stem cell mutations pre-puberty on breast development and present support for the hypothesis that fields of mutations can be the reason why breast cancer is such an often seen phenomenon in women. Through clonal formation of the breast, mutations in stem cells are inherited by their daughter cells, and the resulting high number of cells susceptible to further mutative hits may prove crucial. With our model we can simulate successively, the development, growth and invasion of a solid tumour within the breast, focussing on single cell dynamics as well as tumour-tissue interactions. Subsequently the application of mathematical models to predict the efficacy of different treatment strategies in providing tumour control becomes feasible. In particular we will combine our model of tumour development with the established linear-quadratic model of irradiation response in order to examine the effect of conventional radiotherapy as well as novel treatment protocols.
|
| Friedman, Avner |
| Multiscale models of tumours |
|
View Abstract
Hide Abstract
|
At the restriction point of its first growth phase G1, the cell must decide whether to go into the S phase, apoptosis, or the quiescent phase G0. A similar decision is made just before the cell is ready to go into mitosis. The above decisions are affected by the cell's environmental conditions, e.g., hypoxic neighborhood, overpopulation, etc. When some genes are mutated, the decision to go into S may be made in spite of unfavorable conditions, such hypoxic conditions, and this leads to tumour proliferation.
The multiscale model we shall discuss deals with the effects of gene mutation during the time a cell spends in each phase, as well as during the absolute time. After formulating the general model, I shall deal with much simpler situations whereby the cells are divided into only three different populations: proliferating, quiescent, and dead cells. In the even simpler case when we have only proliferating cells, I shall describe mathematical results such as global existence and bifurcation for PDE free boundary problems. It will be very challenging to extend these results to models which include several classes of cells.
|
| Gatenby, Robert A |
| The roles of microenvironmental hypoxia and acidosis in carcinogenesis, from mathematical models to clinical observations |
|
View Abstract
Hide Abstract
|
|
<p>Conceptual models of carcinogenesis typically depict a sequence of heritable changes in genes that control cellular proliferation, apoptosis, and senescence. We hypothesize (Gatenby and Gillies, Nature Rev. Cancer, 2004) these steps, while necessary, are not sufficient to produce an invasive cancer and that critical components of the malignant phenotype emerge as adaptations to regional hypoxia and acidosis in premalignant lesions. This is a direct consequence of the anatomy of mucosal surfaces which enforces separation of evolving tumor populations from their blood supply by an intact basement membrane. The diffusion-reaction kinetics for substrate and metabolites results in regional hypoxia and acidosis as tumor proliferation carries cells away from the basement membrane. These environmental selection forces promote adaptations including constitutive upregulation of glycolysis and resistance to acid-induced toxicity. We hypothesize that this phenotype has adaptive advantages essential for formation of invasive cancers because it creates an acidic environment through aerobic glycolysis which: 1. is toxic to its competitors but less so to itself and 2. promotes extracellular matrix degradation, increasing invasiveness. Because evolutionary dynamics cannot be directly observed <em>in-vivo</em>, we examine the microenvironmental properties and cellular adaptations in premalignant lesions using mathematical models and <em>in-vitro</em> experiments with multicellular spheroids that mimic the anatomy and physiology of <em>in-situ</em> tumors. The mathematical models predict that populations with fixed upregulation of glycolysis and resistance to acid-mediated toxicity will emerge in premalignant lesions. Their adaptive advantage allows these phenotypes to invade and replace the other populations. The sequence of these changes dictates morphologic features within the premalignant lesions. Empirical observations of cellular evolution in spheroids and clinical specimens are consistent with the model predictions.</p>
|
| Gerisch, Alf |
| Taxis-driven instability in a model of cancer cell invasion of tissue |
|
View Abstract
Hide Abstract
|
|
During the avascular growth phase of solid tumours the insidious process of cancer cell invasion of peritumoural tissue takes place. A key enzymatic system in this invasion process is the urokinase plasminogen activator system. When activated by the tumour cells, an enzymatic cascade leads to the formation of the matrix degrading protein plasmin. Numerical simulations of a recent model of this enzymatic system coupled to cancel cells via chemotaxis and haptotaxis generate highly heterogeneous spatio-temporal solutions. Using a linear stability analysis we can show that this heterogeneity is due to a taxis-driven instability of the underlying spatially homogeneous steady state of the reaction system. Some implications for tissue invasion are discussed.
|
| Gerlee, Philip |
| Stability analysis of a hybrid cellular automaton model of solid tumour growth |
|
View Abstract
Hide Abstract
|
|
Solid tumours have been shown to exhibit complex branched growth patterns under nutrient limited growth conditions. In order to investigate this phenomenon we present a simple hybrid cellular automaton model of solid tumour growth. In the model the growth of the colony is limited by a nutrient that is consumed by the cells and which inhibits cell division if it falls below a certain threshold. We found that for high nutrient levels the colony takes on a Eden-like morphology, while for low concentration rates the morphology of the colony is branched with a fractal geometry. By observing that the local growth of the colony is proportional to the flux of the nutrient we derive an approximate dispersion relation for the growth of the colony interface. This dispersion relation shows that the stability of the growth depends on how far the nutrient penetrates into the colony. For high concentrations the penetration distance is large, which stabilises the growth, while for low concentrations the penetration distance is small, which leads to unstable branched growth. The dispersion relation was verified by measuring how the average branch width depends on the nutrient concentration and shows good agreement between theory and simulations.
|
| Hillen, Thomas |
| Mathematical modelling of cell movement in fibre tissues |
|
View Abstract
Hide Abstract
|
|
In current studies on cell movement in tissues, Friedl et al. have observed single metastatic cancer cells as they move through collagen network tissue. This form of cell movement is termed “mesenchymal motion”. Based on these observations, I will derive mathematical models for mesenchymal motion. On a mesoscopic level, I will formulate transport equations. To obtain macroscopic models in the form of advection-diffusion equations, I will use hyperboplic and parabolic scaling techniques. Numerical simulations of these models show interesting pattern formation in form of networks. I will discuss specific applications and present new results on steady states.
|
| Kevrekidis, Yannis |
| Equation-free modelling for complex systems |
|
View Abstract
Hide Abstract
|
|
In current modelling practice for complex systems, and in biologically inspired models in particular, the best available descriptions of a system often come at a fine level (atomistic, stochastic, microscopic, individual-based) while the questions asked and the tasks required by the modeller (prediction, parametric analysis, optimization and control) are at a much coarser, averaged, macroscopic level. <p>Traditional modelling approaches start by first deriving macroscopic evolution equations from the microscopic models, and then bringing our arsenal of mathematical and algorithmic tools to bear on these macroscopic descriptions.</p><p>Over the last few years, and with several collaborators, we have developed and validated a mathematically inspired, computational enabling technology that allows the modeler to perform macroscopic tasks acting on the microscopic models directly. We call this the “equation-free” approach, since it circumvents the step of obtaining accurate macroscopic descriptions. </p><p>We will argue that the backbone of this approach is the design of (computational) experiments. In traditional numerical analysis, the main code “pings” a subroutine containing the model, and uses the returned information (time derivatives, function evaluations, functional derivatives) to perform computer-assisted analysis. In our approach the same main code “pings” a subroutine that sets up a short ensemble of appropriately initialized computational experiments from which the same quantities are estimated (rather than evaluated). Traditional continuum numerical algorithms can thus be viewed as protocols for experimental design (where “experiment” means a computational experiment set up and performed with a model at a different level of description).</p><p>Ultimately, what makes it all possible is the ability to initialize computational experiments at will. Short bursts of appropriately initialized computational experimentation through matrix-free numerical analysis and systems theory tools like variance reduction and estimation- bridges microscopic simulation with macroscopic modelling.</p><p>I will also discuss some recent developments in data mining algorithms, exploring large complex data sets to find good "reduction coordinates".</p>
|
| Lachowicz, Miroslaw A |
| Modelling of cancer invasion at the microscopic scale |
|
View Abstract
Hide Abstract
|
|
The mathematical theory for modelling of cancer invasion of tissues is proposed at the microscopic scale of description. The mathematical relationships with the models on the macroscopic scale are given.
|
| Litcanu, Gabriela |
| Mathematical modelling of cell-matrix interaction |
|
View Abstract
Hide Abstract
|
|
Despite the fact that normally the cell proliferation is controlled by feedback biological processes, sometimes the cell populations break away from their primary status through mutations. This invasion process involves changes in cells behaviour, in particular in motility, adhesion and production of enzymes that will modify the local environment. <p>We intend to present some aspects related to continuum mathematical models for the invasion phenomena, focusing on cell-matrix interaction. Results about the existence and qualitative behaviour of solutions of the equations involved will be presented. </p>
|
| Lowengrub, John |
| Multiscale models of solid tumor growth and angiogenesis |
|
View Abstract
Hide Abstract
|
|
We present and investigate models for solid tumor growth that incorporate features of the tumor microenvironment including tumor-induced angiogenesis. Using analysis and nonlinear simulations, we explore the effects of the interaction between the genetic characteristics of the tumor and the tumor microenvironment on the resulting tumor progression and morphology. We find that the qualitative behavior of the tumor morphologies is similar across a broad range of parameters that govern the tumor genetic characteristics. Our findings demonstrate the importance of the impact of microenvironment on tumor growth and morphology and are consistent with recent experiments. We discuss the implications for cancer therapy protocols.
|
| Macklin, Paul |
| Nonlinear Simulation of Centimeter-Scale Tumor Growth into Realistic Tissue |
|
View Abstract
Hide Abstract
|
|
In this talk, we present a new tumor growth model that accounts for viable, hypoxic (quiescent), and necrotic tumor cell populations in a tumor growing into a complex, heterogeneous tissue. We model realistic tissue structures (biomechanically soft and hard regions, bone, heterogeneous nutrient delivery) through functional relationships between a heterogeneous ECM density, a bone structure variable, and the pre-existing blood vasculature density. The growing tumor affects the microenvironment through the secretion of pro-angiogenic growth factors and ECM degradation, which, in turn, affects the mechanical properties of the tissue, nutrient delivery, and the future growth patterns of the tumor. Using newly-developed level set and ghost fluid methods, as well as a new adaptive nonlinear reaction-diffusion solver (NAGSI), we simulate an aggressive glioblastoma multiforme in a large, 1cm square region of simulated brain tissue containing white and gray matter, fluid, and bone. All the techniques we have developed are capable of running on current desktop workstations, and will provide a foundation for a new generation of realistic, large-scale cancer simulators for study by medical students, doctors, and mathematicians. Publications and multimedia downloads are available at: http://math.uci.edu/~pmacklin/research.html
|
| Maini, Philip |
| Modelling multiscale aspects of cancerous tumour growth |
|
View Abstract
Hide Abstract
|
|
The modelling of cancer provides an enormous mathematical challenge because of its inherent multiscale nature. For example, in vascular tumours, nutrient is transported by the vascular system, which operates on a tissue level. However, it affects processes occurring on a molecular level. Molecular and intracellular events, in turn, affect the vascular network and therefore the nutrient dynamics. Our modelling approach is to couple partial differential equations, ordinary differential equations, and cellular automata to address the different scales. Results of this approach are presented.
|
| Mamontov, Eugen |
| Oncogenic hyperplasia caused by combination of various factors: A decision-support software for radionuclide therapy (Authors: E. Mamontov, K. Psiuk-Maksymowicz, A. Koptioug) |
|
View Abstract
Hide Abstract
|
|
The present work deals with the software based on the PhasTraM model [1] for oncogenic hyperplasia, the first stage of formation of any solid tumor. The work generalizes the related results of [2]-[6] and discusses application of the software for decision support in radionuclide therapy. The software capabilities to allow for combinations of various causes of oncogeny are emphasized. The causes comprise inflammation, immune dysfunction, and chronic psychological stress. The immune dysfunction is represented with hypogammaglobulenimia expressed in terms of the concentration of the immunoglobulin-G molecules. The level of chronic pychological stress is described with the concentration of the interleukin-6 molecules. The work considers how application of the software can support decisions on the specific radionuclide-therapy setting depending on the tissue-, organ-, and patient-specific data. This is illustrated by a number of numerical-simulation results, also the ones which include the effects of common and fractionation-based radionuclide-therapy modalities. A proper attention is paid to how specifically the input data can be prepared by prospective users of the software, i.e. the specialists who apply radionuclide therapy. The work also formulates a few directions for future research in connection with the features of the everyday work of the prospective users. <p>REFERENCES<br />[1] E. Mamontov, K. Psiuk-Maksymowicz, A. Koptioug, 2006, Stochastic mechanics in the context of the properties of living systems, Mathl Comput. Modelling, 44(7-8) 595-607. </p><p>[2] E. Mamontov, A. V. Koptioug, K. Psiuk-Maksymowicz, 2006, The minimal, phase-transition model for the cell-number maintenance by the hyperplasia-extended homeorhesis, Acta Biotheoretica, 54(2) 61-101. </p><p>[3] K. Psiuk-Maksymowicz and E. Mamontov, 2006, The homeorhesis-based modelling and fast numerical analysis for oncogenic hyperplasia under radiotherapy, Mathl Comput. Modelling, Special Issue </p>
|
| Marciniak-Czochra, Anna |
| Multiscale modelling of early lung cancer progression |
|
View Abstract
Hide Abstract
|
|
There exists evidence that early-stage precancerous lesions progress along linear, tubular, or irregular surface structures. This seems to be the case for the atypical adenomatous hyperplasia (AAH), a likely precursor of adenocarcinoma of the lung. Recent evidence indicates also that early stages of carcinogenesis require cooperation (mutualism) of proliferating cells cells of different types. A specific mechanism proposed is that cells of type 1 produce growth factor for cells type 2 and vice versa. We propose a model that includes this mechanism. The model shows that early structures have a potential towards spontaneous invasive growth following a latency phase. The transition is facilitated by diffusion of a growth factor and nonlinear cell cycle regulation in cancer cells. We study the impact of the mutualism on the dynamics of the cancer progression and investigate how the population of cells which cannot exist without each other can trive under different values of parameters and with different initial conditions.
|
| McDougall, Steven |
| Simulating chemotherapy treatment efficacy: the impact of adaptive vascular architecture |
|
View Abstract
Hide Abstract
|
|
<p>In this paper, we present a theoretical investigation of the influence of adaptive vascular architecture upon simulations of chemotherapeutic drug perfusion through tumour-induced capillary beds. Results from earlier rigid tube models are compared with those emerging from a more sophisticated dynamically adaptive approach, whereby capillaries dilate and constrict both spatially and temporally in response to blood perfusion. A number of different therapeutic targets are discussed and results clearly demonstrate that the combined effects of network architecture and vessel compliance should ideally be included in models of angiogenesis. The paper concludes by highlighting several limitations of the current modelling approach and identifies additional biological parameters that should be incorporated if therapy protocols and treatment efficacy are to be adequately simulated in future.</p>
|
| Othmer, Hans G |
| A hybrid model for tumour growth |
|
View Abstract
Hide Abstract
|
|
Existing mathematical models of tumour development are either discrete (cell-based) models or continuum models. Both have advantages and disadvantages; the former allows for incorporation of significant cell-level information but is computationally expensive when growth and mechanics are incorporated, whereas the latter is easy to formulate and computationally straightforward, but to date it has been difficult to accurately translate cell-level information into the continuum description. In this talk we introduce a hybrid model that retains the advantages of both the discrete and the continuum models. In this model the surface layers of a growing multicellular spheroid are described by a cell-based model, whereas the interior quiescent and necrotic zones (when present) are described by a continuum model, as is the extracellular matrix. We will discuss the theoretical foundation of the model and the computational algorithms developed to analyze it, and present illustrative numerical results for growing tumours.
|
| Preziosi, Luigi |
| Mechanical aspects of tumour growth |
|
View Abstract
Hide Abstract
|
|
The talk will focus on the mechanical aspects of tumor growth. After describing some of the main feature of tumor growth and in particular the phenomena involving stress and deformation, the talk will focus on the use of multiphase nodels and of the concept of evolving natural configurations to describe tumor growth. Some examples are then described according to the type of constitutive equation used, specifically focusing on contact inhibition of growth, nutrient limited avascular growth and interaction with the environment.
|
| Quaranta, Vito |
| Mathematics-driven experimentation: Validating mathematical model simulations with mouse models of cancer invasion |
|
View Abstract
Hide Abstract
|
Computer simulations based on the Hybrid Discrete-Continuous (HDC) mathematical model oc cancer invasion (Anderson et al., Cell. 2006,127:905) predict that the degree of severity of the tumor microenvironment (ME) directly impacts on the emergence of invasion. More precisely, harsh ME conditions (e.g., hypoxia, discontinuous matrix, inflammation) select for dominant aggressive clones that grow into a fingering, infiltrating mass. In contrast, in mild ME conditions (normoxia, homogenous matrix) selection for dominant aggressive clones is relaxed, so that they coexist with less aggressive ones and, together, they grow into a smooth-margin, non-invasive tumor mass.
To validate these predictions in vivo, we are comparing orthotopic ("mild ME") versus subcutaneous ("harsh ME") human breast cancer xenografts in mice (in vivo VICBC group, headed by Lisa McCawley. We utilized MCF-10 variant cell lines, CA1a and CA1d, shown to have distinct and consistent tumorigenic properties through repeated passage in immunocompromised mice. We focus on the following parameters: oxygen consumption/hypoxia, tumor cell proliferation, tumor cell survival, metabolic consumption, and matrix degrading enzyme activity. Several in vivo imaging modalities are being exploited to provide quantitative analysis of cellular parameters of the same tumor over time: Magnetic Resonance Imaging (MRI) analysis to distinguish tumor volume and necrotic tumor areas (i.e. non-oxygenated states) from viable (i.e. oxygenated) tissue; positron emission topography (PET) scan imaging of 18 F-labeled-fluorodeoxyglucose(FDG) for metabolism; and Optical imaging analysis of fluorogenic probes termed "proteolytic beacons" for matrix degrading protease activity (i.e. substrate hydrolysis). Tumor specimens are also biopsied at fixed volumes (0.5, 1 and 1.5 cm diameters) for further ex vivo analyses, including histology to assess invasion, immunohistochemistry and immunofluorescence to measure cellular proliferation (BrdU incorporation), apoptosis (TUNEL) and hypoxia (hypoxiprobe).
Initial results from these analyses reveal advantages and limits of in vivo parameterization and validation. The main advantage is that relevant variables and parameters for tumor invasion can only be truly identified in a living organism, at least until convincing in vitro surrogates are developed. The limits reflect largely the fact that conventional experimental biology has been seldom used for model validation, so that tools and approaches must be refined and adapted. These broad issues as well as intitial specific data will be discussed.
|
| Ramis Conde, Ignacio |
| Influence of E-Cadherin - beta - Catenin pathway in cancer invasion and tissue architecture: A mathematical multi-scale approach |
|
View Abstract
Hide Abstract
|
|
E-cadherins bind to beta-catenin in a complex which interacts with the closest neigh- bour cell to form bonds, and with the cytoskeleton forming part of the structural system of the cell. When one of the cells decides to detach from the other, the beta -catenin is released into the cytoplasm, targeted for degradation in the proteasome and down- regulated. In this process there are multiple protein complexes which are involved and interact with beta -catenin and E-cadherin. Within the complexity of this biological scenario, we show in this paper how a simple part of it can regulate cell adhesion in an efficient manner and how is related with cell migration and epithelial-mesenchymal transition.
|
| Ribba, Benjamin |
| Towards the development of a numerical platform for tumour growth simulation |
|
View Abstract
Hide Abstract
|
We have developed and integrated multi-scale mathematical models of tumour growth in a numerical platform. Up to now, discrete genetic network and cell cycle regulation models have been coupled to a macroscopic description of tumour growth. The platform that is being developed is highly modular which allows us to efficiently integrate additional biological phenomena.
The integrated models are being specifically designed to study the multi-scale features of tumour growth, from gene to tissue, allowing biomathematical researchers to perform theoretical studies on the complex intricacies of cancer growth processes. Moreover, theoretical investigations have already been carried out on the efficacy and toxicity of different therapeutic strategies.
We are presently integrating the details of several molecular pathways and the process of blood vessels formation (angiogenesis).
As for the educational point of view, we recently received the support of the Faculty of Medicine Lyon-Sud and the University of Lyon to integrate the use of the platform in the educational program of medical students specializing in oncology.
In this talk, I'll present the technical characteristics of the numerical platform and will summarize the theoretical results we have obtained on the efficacy of radiotherapy and anti-invasive therapies on avascular tumours.
|
| Sherratt, Jonathan |
| Modelling cell adhesion in cancer |
|
View Abstract
Hide Abstract
|
|
Changes in cell-cell and cell-matrix adhesion play key roles in the development of many solid tumours. However, they are difficult to incorporate into mathematical models and are often neglected. I will present a new continuum modelling approach for cellular adhesion, using integrodifferential equations, and will show that it is able to reproduce a range of standard in vitro experiments on cell aggregation. I will then discuss the implications of the model for solid tumour growth. This work is collaborative with Nicola Armstrong and Kevin Painter (both at Heriot-Watt University).
|
| Stevens, Angela |
| Alignment and orientational aggregation |
|
View Abstract
Hide Abstract
|
|
Alignment and orientational aggregation play an important role in structure forming processes, where cellular interaction with fibers or interaction of fibers themselves are involved. This is the case in in vivo and in vitro tissues. Since many mathematical models in this context are highly sensitive on the inital data with respect to the pattern forming process, we first analyzed just fibre alignment for itself, in order to understand which mechanisms do allow for robust patterns and which of them do not. These concern e.g. the specific types of interactions between the filamentous bundles. Rigorous results can be given, on how many bundles finally form and how they are oriented. In the future these models should be coupled with cellular interaction. (joint work with K. Kang, B. Perthame, and J.J.L. Velazquez)<br />
|
| Wang, Zhian |
| Pattern formation for a volume filling chemotaxis model |
|
View Abstract
Hide Abstract
|
|
We establish the global existence of the classical solution to a generalized chemotaxis model which includes the volume filling effect. We generalize earlier results by Wrzosek (2004) allowing more general kinetic terms and a nonlinear transitional probability function that better describes the elastic properties of cells. We derive necessary and sufficient conditions for spatial pattern formation and analyze the underlying bifurcations. In numerical simulations, we show the dynamics of merging and emerging patterns. We conclude that the emerging process of pattern formation is due to cell growth. This is a joint work with Thomas Hillen.
|
Mathematical Modelling and Analysis of Cancer Invasion of Tissues