A history of the study of solid tumour growth: the contribution of mathematical modelling
From MaRDI portal
Publication:253611
DOI10.1016/j.bulm.2003.11.002zbMath1334.92187OpenAlexW2111663010WikidataQ35856186 ScholiaQ35856186MaRDI QIDQ253611
R. P. Araujo, D. L. Sean McElwain
Publication date: 8 March 2016
Published in: Bulletin of Mathematical Biology (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1016/j.bulm.2003.11.002
Related Items
Existence of weak solutions to multiphase Cahn–Hilliard–Darcy and Cahn–Hilliard–Brinkman models for stratified tumor growth with chemotaxis and general source terms, Numerical simulation of a thermodynamically consistent four-species tumor growth model, ROLE OF CYTOTOXIC T-LYMPHOCYTES IN TUMOR STABILITY: A PREY-PREDATOR MODELING APPROACH, On the avascular ellipsoidal tumour growth model within a nutritive environment, Multiphase modelling of desmoplastic tumour growth, Loss- and gain-of-function mutations in cancer: mass-action, spatial and hierarchical models, The influence of time delay in a chaotic cancer model, Optimal therapy protocols in the mathematical model of acute leukemia with several phase constraints, On the global stability of the axial equilibrium for the \(n\)-dimensional Gompertz system, Galerkin finite element method for cancer invasion mathematical model, Analysis of a free boundary problem for solid avascular tumor growth with a time delay in regulatory apoptosis, Tumor growth dynamics with nutrient limitation and cell proliferation time delay, Mathematical and computational modeling for tumor virotherapy with mediated immunity, A phenotype-structured model to reproduce the avascular growth of a tumor and its interaction with the surrounding environment, An optimal control problem of immuno-chemotherapy in presence of gene therapy, Analysis of a diffuse interface model of multispecies tumor growth, Mathematical modeling and optimal control problems in brain tumor targeted drug delivery strategies, Tumor evolution models of phase-field type with nonlocal effects and angiogenesis, Influence of non-local diffusion in avascular tumour growth, A numerical method based on the moving mesh for the solving of a mathematical model of the avascular tumor growth, Analysis of a free boundary problem modeling the growth of spherically symmetric tumors with angiogenesis, On a diffuse interface model of tumour growth, A multi-scale analysis of drug transport and response for a multi-phase tumour model, Vacuum effects over the closing of enterocutaneous fistulae: a mathematical modeling approach, Qualitative analysis of a free boundary problem for tumor growth under the action of periodic external inhibitors, Interactions between the immune system and cancer: A brief review of non-spatial mathematical models, Simulating complex tumor dynamics from avascular to vascular growth using a general level-set method, Bifurcations and Chaotic Dynamics in a Tumour-Immune-Virus System, Parameter non-identifiability of the Gyllenberg-Webb ODE model, Minimal morphoelastic models of solid tumour spheroids: a tutorial, Solution of the feedback control problem in the mathematical model of leukaemia therapy, A displacement-based approach to geometric instabilities of a film on a substrate, A two-fluid model for tissue growth within a dynamic flow environment, STOCHASTIC MODELING OF LOSS- AND GAIN-OF-FUNCTION MUTATIONS IN CANCER, A HYBRID MODEL FOR TUMOR SPHEROID GROWTH IN VITRO I: THEORETICAL DEVELOPMENT AND EARLY RESULTS, Optimal Control Problem for Cancer Invasion Reaction–Diffusion System, Analysis of tumour-immune evasion with chemo-immuno therapeutic treatment with quadratic optimal control, Critical fitness collapse in three-dimensional spatial population genetics, Mathematical modelling of tumour growth and treatment, AN IN VITRO CELL POPULATION DYNAMICS MODEL INCORPORATING CELL SIZE, QUIESCENCE, AND CONTACT INHIBITION, GENERAL DIFFUSE-INTERFACE THEORIES AND AN APPROACH TO PREDICTIVE TUMOR GROWTH MODELING, MATHEMATICAL MODELLING OF CANCER CELL INVASION OF TISSUE: THE ROLE OF THE UROKINASE PLASMINOGEN ACTIVATION SYSTEM, Complex dynamics of a tumor-immune system with antigenicity, Optimal control problem for cancer invasion parabolic system with nonlinear diffusion, Modelling the formation of necrotic regions in avascular tumours, Optimal chemotherapy in cancer treatment: state dependent Riccati equation control and extended Kalman filter, On the stability of an ellipsoidal tumour, Cancer stem cell, niche and EGFR decide tumor development and treatment response: a bio-computational simulation study, Delay differential model for tumour-immune response with chemoimmunotherapy and optimal control, Distributed parameters deterministic model for treatment of brain tumors using Galerkin finite element method, The dynamics of war between benign cells, malignant cells, and killer agents, Biomechanical and Nutrient Controls in the Growth of Mammalian Cell Populations, Modelling of Cancer Growth, Evolution and Invasion: Bridging Scales and Models, ATP Production and Necrosis Formation in a Tumour Spheroid Model, Unnamed Item, Bifurcation for a free boundary problem modeling tumor growth with inhibitors, On the complete classification of nullcline stable competitive three-dimensional Gompertz models, Mesoscopic and continuum modelling of angiogenesis, Hopf bifurcation, cascade of period-doubling, chaos, and the possibility of cure in a 3D cancer model, An element-free Galerkin meshless method for simulating the behavior of cancer cell invasion of surrounding tissue, Analysis of a nonlinear age-structured tumor cell population model, A Nonlinear Mathematical Model of Virus-Tumor-Immune System Interaction: Deterministic and Stochastic Analysis, Bridging the gap between individual-based and continuum models of growing cell populations, Mix and match: phenotypic coexistence as a key facilitator of cancer invasion, Close encounters of the cell kind: the impact of contact inhibition on tumour growth and cancer models, Mathematics + Cancer: An Undergraduate "Bridge" Course in Applied Mathematics, Dynamics of tumor growth: chemotherapy and integrative oncology, Chaotic dynamics of a delayed tumor–immune interaction model, Local and nonlocal phase-field models of tumor growth and invasion due to ECM degradation, On the unsteady Darcy–Forchheimer–Brinkman equation in local and nonlocal tumor growth models, Exploring dynamical complexity in a time-delayed tumor-immune model, The Steady State of Multicellular Tumour Spheroids: A Modelling Challenge, Complex far-field geometries determine the stability of solid tumor growth with chemotaxis, Computational modelling of multiscale, multiphase fluid mixtures with application to tumour growth, FROM THE PHYSICAL LAWS OF TUMOR GROWTH TO MODELLING CANCER PROCESSES, MODELLING THE RESPONSE OF VASCULAR TUMOURS TO CHEMOTHERAPY: A MULTISCALE APPROACH, An Evolutionary Model of Tumor Cell Kinetics and the Emergence of Molecular Heterogeneity Driving Gompertzian Growth, Mathematical analysis of hydrodynamics and tissue deformation inside an isolated solid tumor, Analysis of a tumor-model free boundary problem with a nonlinear boundary condition, A MULTIPHASE MODEL OF TUMOR AND TISSUE GROWTH INCLUDING CELL ADHESION AND PLASTIC REORGANIZATION, Derivation and Application of Effective Interface Conditions for Continuum Mechanical Models of Cell Invasion through Thin Membranes, Dynamical Behaviors of the Tumor-Immune System in a Stochastic Environment, Effects of delayed immune-activation in the dynamics of tumor-immune interactions, Boundedness of solutions of a non-local reaction–diffusion model for adhesion in cell aggregation and cancer invasion, Optimal control and pattern formation for a haptotaxis model of solid tumor invasion, On a 2D model of avascular tumor with weak Allee effect, Synthesis of optimal control in a mathematical model of tumour–immune dynamics, Predicting drug pharmacokinetics and effect in vascularized tumors using computer simulation, Modelling cell migration strategies in the extracellular matrix, Microenvironment driven invasion: a multiscale multimodel investigation, Multiphase modelling of tumour growth and extracellular matrix interaction: mathematical tools and applications, Individual-based and continuum models of growing cell populations: a comparison, Nonlinear simulations of solid tumor growth using a mixture model: invasion and branching, Multiscale modelling and nonlinear simulation of vascular tumour growth, A cellular automata model of chemotherapy effects on tumour growth: targeting cancer and immune cells, Discrete and Continuum Models for the Evolutionary and Spatial Dynamics of Cancer: A Very Short Introduction Through Two Case Studies, MODELING THE EVOLUTION OF A TUMORAL MULTICELLULAR SPHEROID AS A TWO-FLUID BINGHAM-LIKE SYSTEM, Existence and uniqueness results on biphasic mixture model for an in-vivo tumor, Optimal control oriented to therapy for a free-boundary tumor growth model, Analysis of a radial free boundary tumor model with time-dependent absorption efficiency, Tumor boundary instability induced by nutrient consumption and supply, Optimal control of an Allen-Cahn model for tumor growth through supply of cytotoxic drugs, EXISTENCE AND OPTIMAL CONTROL ANALYSIS OF ACID-MEDIATED TUMOR INVASION, Could mathematics be the key to unlocking the mysteries of multiple sclerosis?, Predicting radiotherapy patient outcomes with real-time clinical data using mathematical modelling, Formation and growth of co-culture tumour spheroids: new compartment-based mathematical models and experiments, Spatial stochastic models for cancer initiation and progression, Analytical solutions of the Fokker-Planck equation for generalized Morse and Hulthén potentials, Phase transitions in tumor growth. III: Vascular and metastasis behavior, Understanding the antiangiogenic effect of metronomic chemotherapy through a simple mathematical model, Bifurcation analysis for a free-boundary tumor model with angiogenesis and inhibitor, Analysis of a free boundary problem for tumor growth in a periodic external environment, Necrotic core in EMT6/Ro tumour spheroids: is it caused by an ATP deficit?, On eigenvalues of the linearization of a free boundary problem modeling two-phase tumor growth, Modeling and analysis of a nonlinear age-structured model for tumor cell populations with quiescence, Stability and bifurcation analysis of delay induced tumor immune interaction model, Nonlinear simulation of vascular tumor growth with chemotaxis and the control of necrosis, Stationary solutions of a free boundary problem modeling growth of angiogenesis tumor with inhibitor, Analysis of a tumor model as a multicomponent deformable porous medium, Phase transitions in tumor growth. VI: Epithelial-mesenchymal transition, A time delay model of tumour-immune system interactions: global dynamics, parameter estimation, sensitivity analysis, Analysis of a time-delayed mathematical model for solid avascular tumor growth under the action of external inhibitors, The evolution of tumour composition during fractionated radiotherapy: implications for outcome, Combining mechanisms of growth arrest in solid tumours: a mathematical investigation, Nonlinear optimization for a tumor invasion PDE model, A direct RBF-PU method for simulating the infiltration of cytotoxic T-lymphocytes into the tumor microenvironment, Optimal multitherapy strategy in mathematical model of dynamics of the number of nonuniform tumor cells, Mechanistic model for cancer growth and response to chemotherapy, Incompressible limit of a continuum model of tissue growth for two cell populations, Stochastic bifurcation for a tumor-immune system with symmetric Lévy noise, Phase transition in tumor growth: I avascular development, Global dynamics of Nicholson-type delay systems with applications, New insights into vascular collapse and growth dynamics in solid tumors, A new ghost cell/level set method for moving boundary problems: application to tumor growth, Stability of Hahnfeldt angiogenesis models with time lags, Are tumor cell lineages solely shaped by mechanical forces?, Multiphase modeling of tumor growth with matrix remodeling and fibrosis, Nutrient limitations as an explanation of Gompertzian tumor growth, Analysis of a solid avascular tumor growth model with time delays in proliferation process, From individual-based mechanical models of multicellular systems to free-boundary problems, The role of mechanical host-tumour interactions in the collapse of tumour blood vessels and tumour growth dynamics, A cellular automata model of tumor-immune system interactions, A mathematical model for the effects of HER2 over-expression on cell cycle progression in breast cancer, Multi-stability and multi-instability phenomena in a mathematical model of tumor-immune-virus interactions, Global stability of solutions to a free boundary problem of ductal carcinoma in situ, Periodic solutions of angiogenesis models with time lags, A convection-diffusion-shape model for aberrant colonic crypt morphogenesis, On strategies on a mathematical model for leukemia therapy, Incorporating energy metabolism into a growth model of multicellular tumor spheroids, Analysis of a free boundary problem for avascular tumor growth with a periodic supply of nutrients, Model of vascular desmoplastic multispecies tumor growth, What mathematical models can or cannot do in glioma description and understanding, Composite waves for a cell population system modeling tumor growth and invasion, Chaos in a tumor growth model with delayed responses of the immune system, The avascular tumour growth in the presence of inhomogeneous physical parameters imposed from a finite spherical nutritive environment, Nonlinear simulation of the effect of microenvironment on tumor growth, Numerical solution of a two dimensional tumour growth model with moving boundary, About a generalized model of lymphoma, Cholesterol regulation in age-related macular degeneration: a framework for mathematical modelling of drusen biogenesis, In silico modelling of tumour margin diffusion and infiltration: review of current status, A 2D mechanistic model of breast ductal carcinoma \textit{in situ} (DCIS) morphology and progression, Selecting radiotherapy dose distributions by means of constrained optimization problems, Eradication-resolution dynamics with stochastic flare-ups, Three-dimensional multispecies nonlinear tumor growth. II: Tumor invasion and angiogenesis, Modeling anti-tumor Th1 and Th2 immunity in the rejection of melanoma, An immersed boundary framework for modelling the growth of individual cells: an application to the early tumour development, Estimating the variation in S phase duration from flow cytometric histograms, Mathematical modeling of cancer cell invasion of tissue: biological insight from mathematical analysis and computational simulation, High-order compact schemes for semilinear parabolic moving boundary problems, The combined effects of optimal control in cancer remission, A moving mesh study for diffusion induced effects in avascular tumour growth, An image-driven parameter estimation problem for a reaction-diffusion glioma growth model with mass effects, On a non-isothermal Cahn-Hilliard model for tumor growth, Analysis of a free boundary problem modeling the growth of multicell spheroids with angiogenesis, Optimization of additive chemotherapy combinations for an in vitro cell cycle model with constant drug exposures, Morphogenesis modelization of a fractone-based model, Optimization of the chemotherapy process on the base of the maximum principle, Temporal and spatiotemporal variations in a mathematical model of macrophage-tumor inter\-action, A biophysical model of tumor invasion, Evolution of a mathematical model of an aggressive-invasive cancer under chemotherapy, Adaptive grid modelling for cancer cells in the early stage of invasion, Mathematical modeling of tumor-immune competitive system, considering the role of time delay, A numerical algorithm for avascular tumor growth model, Response of tumor spheroids to radiation: Modeling and parameter estimation, Long-time dynamics and optimal control of a diffuse interface model for tumor growth, Some implications of scale relativity theory in avascular stages of growth of solid tumors in the presence of an immune system response, Stationary solutions of a free boundary problem modeling the growth of vascular tumors with a necrotic core, Modelling acidosis and the cell cycle in multicellular tumour spheroids, Mathematical modeling of invadopodia formation, Computational modeling of tumor-induced angiogenesis, A simple mechanistic model of sprout spacing in tumour-associated angiogenesis, Matrix adhesion and remodeling diversifies modes of cancer invasion across spatial scales, The noise and the KISS in the cancer stem cells niche, Maximum tolerated dose versus metronomic scheduling in the treatment of metastatic cancers, On interfaces between cell populations with different mobilities, Multiphase modelling of vascular tumour growth in two spatial dimensions, Three-dimensional multispecies nonlinear tumor growth. I: Model and numerical method, Choice of optimal strategy of tumor chemotherapy in Gompertz model, Global asymptotic stability of positive steady states of a solid avascular tumor growth model with time delays, A cancer model for the angiogenic switch, Explicit separation of growth and motility in a new tumor cord model, A coupled mass transport and deformation theory of multi-constituent tumor growth, Mathematical tools of the kinetic theory of active particles with some reasoning on the modelling progression and heterogeneity, The impact of time delay and angiogenesis in a tumor model, A mathematical model with aberrant growth correction in tissue homeostasis and tumor cell growth, Most probable trajectories in a two-dimensional tumor-immune system under stochastic perturbation