ON THE FOUNDATIONS OF CANCER MODELLING: SELECTED TOPICS, SPECULATIONS, AND PERSPECTIVES (Q3521624)

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English	ON THE FOUNDATIONS OF CANCER MODELLING: SELECTED TOPICS, SPECULATIONS, AND PERSPECTIVES	scientific article

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title

ON THE FOUNDATIONS OF CANCER MODELLING: SELECTED TOPICS, SPECULATIONS, AND PERSPECTIVES (English)

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26 August 2008

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zbMATH Keywords

multiscale modelling

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complexity in biology

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living systems

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population dynamics

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kinetic theory

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cellular tissue models

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discrete models

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macroscopic tissue models

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continuum models

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mechanical models

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moving boundary models

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describes a project that uses

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A simplified mathematical model of tumor growth

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A mathematical model of tumor growth. II. Effects of geometry and spatial nonuniformity on stability

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A mathematical model of tumor growth. III. Comparison with experiment

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Mathematical models of tumor growth. IV: Effects of a necrotic core

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A Multiple Scale Model for Tumor Growth

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Multiscale modelling of tumour growth and therapy: the influence of vessel normalisation on chemotherapy

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On the mechanics of a growing tumor

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ON THE CLOSURE OF MASS BALANCE MODELS FOR TUMOR GROWTH

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A hybrid mathematical model of solid tumour invasion: the importance of cell adhesion

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Continuous and discrete mathematical models of tumor-induced angiogenesis

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From a class of kinetic models to the macroscopic equations for multicellular systems in biology

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On the onset of non-linearity for diffusion models of binary mixtures of biological materials by asymptotic analysis

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MATHEMATICAL TOPICS ON THE MODELLING COMPLEX MULTICELLULAR SYSTEMS AND TUMOR IMMUNE CELLS COMPETITION

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From microscopic to macroscopic description of multicellular systems and biological growing tissues

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MULTICELLULAR BIOLOGICAL GROWING SYSTEMS: HYPERBOLIC LIMITS TOWARDS MACROSCOPIC DESCRIPTION

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Multiscale Modeling and Mathematical Problems Related to Tumor Evolution and Medical Therapy

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Dynamics of tumor interaction with the host immune system

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LOOKING FOR NEW PARADIGMS TOWARDS A BIOLOGICAL-MATHEMATICAL THEORY OF COMPLEX MULTICELLULAR SYSTEMS

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PREFACE — CHALLENGING MATHEMATICAL PROBLEMS IN CANCER MODELLING

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MATHEMATICAL METHODS AND TOOLS OF KINETIC THEORY TOWARDS MODELLING COMPLEX BIOLOGICAL SYSTEMS

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Q5493430

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A Free Boundary Problem with Unilateral Constraints Describing the Evolution of a Tumor Cord Under the Influence of Cell Killing Agents

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A MATHEMATICAL MODEL FOR TUMOR CORDS INCORPORATING THE FLOW OF INTERSTITIAL FLUID

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EXACT SOLUTIONS AND DYNAMICS OF GLOBALLY COUPLED OSCILLATORS

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HIGH-FIELD LIMIT OF THE VLASOV–POISSON–FOKKER–PLANCK SYSTEM: A COMPARISON OF DIFFERENT PERTURBATION METHODS

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The role of cell-cell interactions in a two-phase model for avascular tumour growth

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FROM THE PHYSICAL LAWS OF TUMOR GROWTH TO MODELLING CANCER PROCESSES

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A two-phase model of solid tumour growth

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MODELLING THE RESPONSE OF VASCULAR TUMOURS TO CHEMOTHERAPY: A MULTISCALE APPROACH

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Modelling solid tumour growth using the theory of mixtures

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HYBRID TWO SCALES MATHEMATICAL TOOLS FOR ACTIVE PARTICLES MODELLING COMPLEX SYSTEMS WITH LEARNING HIDING DYNAMICS

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Avascular growth, angiogenesis and vascular growth in solid tumours: The mathematical modelling of the stages of tumour development

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Mathematical modelling of the loss of tissue compression responsiveness and its role in solid tumour development

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Kinetic models for chemotaxis and their drift-diffusion limits

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MODEL HIERARCHIES FOR CELL AGGREGATION BY CHEMOTAXIS

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Nonlinear simulation of tumor growth

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QUALITATIVE ANALYSIS OF A MEAN FIELD MODEL OF TUMOR-IMMUNE SYSTEM COMPETITION

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Mathematical models of therapeutical actions related to tumour and immune system competition

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ANALYSIS OF A NEW MODEL FOR TUMOR-IMMUNE SYSTEM COMPETITION INCLUDING LONG-TIME SCALE EFFECTS

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Spatial tumor-immune modeling

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Kinetic models for chemotaxis: Hydrodynamic limits and spatio-temporal mechanisms

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TUMOR-IMMUNE SYSTEM INTERACTION: MODELING THE TUMOR-STIMULATED PROLIFERATION OF EFFECTORS AND IMMUNOTHERAPY

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Q4258102

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From Individual to Collective Behavior in Bacterial Chemotaxis

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Derivation of hyperbolic models for chemosensitive movement

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Time delays in proliferation process for solid avascular tumour

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Time delays in regulatory apoptosis for solid avascular tumour

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ANALYSIS OF A MATHEMATICAL MODEL OF TUMOR LYMPHANGIOGENESIS

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MATHEMATICAL ANALYSIS AND CHALLENGES ARISING FROM MODELS OF TUMOR GROWTH

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Cancer suppression by compression

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EVOLUTIONARY DYNAMICS IN CARCINOGENESIS

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A nonlinear structured population model of tumor growth with quiescence

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On the role of mathematics in biology

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HYPERBOLIC MODELS FOR CHEMOSENSITIVE MOVEMENT

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On the \(L^2\)-moment closure of transport equations: The Cattaneo approximation

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Global existence for chemotaxis with finite sampling radius

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LONG-RANGE PREDICTABILITY IN MODELS OF CELL POPULATIONS SUBJECTED TO PHASE-SPECIFIC DRUGS: GROWTH-RATE APPROXIMATION USING PROPERTIES OF POSITIVE COMPACT OPERATORS

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Modeling immunotherapy of the tumor -- immune interaction

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A HYBRID MODEL FOR TUMOR SPHEROID GROWTH <i>IN VITRO</i> I: THEORETICAL DEVELOPMENT AND EARLY RESULTS

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Mathematical modelling of the competition between tumors and immune system considering the role of the antibodies

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A mathematical model for single cell cancer\,--\, immune system dynamics

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Spatial stochastic models for cancer initiation and progression

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STOCHASTIC MODELING OF LOSS- AND GAIN-OF-FUNCTION MUTATIONS IN CANCER

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MICRO AND MESO SCALES OF DESCRIPTION CORRESPONDING TO A MODEL OF TISSUE INVASION BY SOLID TUMOURS

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Mathematical modeling of capillary formation and development in tumor angiogenesis: penetration into the stroma

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A mathematical model for the roles of pericytes and macrophages in the initiation of angiogenesis. I: The role of protease inhibitors in preventing angiogenesis

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Mathematical modeling of the onset of capillary formation initiating angiogenesis

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MODELING TUMOR IMMUNOLOGY

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Travelling wave solutions to a haptotaxis-dominated model of malignant invasion

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Dynamics of growth and signaling along linear and surface structures in very early tumors

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MODELLING OF EARLY LUNG CANCER PROGRESSION: INFLUENCE OF GROWTH FACTOR PRODUCTION AND COOPERATION BETWEEN PARTIALLY TRANSFORMED CELLS

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Mathematical modelling of flow through vascular networks: implications for tumour-induced angiogenesis and chemotherapy strategies

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EXISTENCE OF A SOLUTION TO THE CELL DIVISION EIGENPROBLEM

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STABILITY IN A NONLINEAR POPULATION MATURATION MODEL

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A mathematical model of cancer treatment by immunotherapy

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Models of dispersal in biological systems

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The diffusion limit of transport equations. II: Chemotaxis equations

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Mathematical tools for kinetic equations

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On the inverse problem for a size-structured population model

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A two parameter family of travelling waves with a singular barrier arising from the modelling of extracellular matrix mediated cellular invasion

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Lattice and non-lattice models of tumour angiogenesis

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Mathematical Models of Avascular Tumor Growth

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Cellular Growth Control and Travelling Waves of Cancer

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Traveling Wave Solutions of a Mathematical Model for Tumor Encapsulation

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A new mathematical model for avascular tumour growth

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The Derivation of Chemotaxis Equations as Limit Dynamics of Moderately Interacting Stochastic Many-Particle Systems

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A FREE BOUNDARY PROBLEM MODELLING CANCER RADIOVIROTHERAPY

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Nonlinear analysis of a model of vascular tumour growth and treatment

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A PARABOLIC–HYPERBOLIC FREE BOUNDARY PROBLEM MODELLING TUMOR TREATMENT WITH VIRUS

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Q4420178

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Modelling the internalization of labelled cells in tumour spheroids

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A DISCRETE MODEL OF EVOLUTION OF SMALL PARALOG FAMILIES

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Q3220397

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Nonlinear simulation of tumor necrosis, neo-vascularization and tissue invasion via an adaptive finite-element/level-set method

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full work available at URL

https://doi.org/10.1142/s0218202508002796

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published in

M\(^3\)AS. Mathematical Models \& Methods in Applied Sciences

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Identifiers

zbMATH Open document ID

1151.92014

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DOI

10.1142/S0218202508002796

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Mathematics Subject Classification ID

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Sitelinks

Mathematics(1 entry)

mardi Publication:3521624