Mathematical modelling of avascular-tumour growth.

No abstract is available for this paper.

• Publication year

  1997

• Venue

  IMA journal of mathematics applied in medicine and biology

• Publication date

  1997-03-01

• Fields of study

  Mathematics, Medicine

• Identifiers
  DOI 10.1093/IMAMMB/14.1.39PMID 9080687
• External record

  Open on Semantic Scholar

• Source metadata

  Semantic Scholar, PubMed

• No claims are published for this paper.

• No concepts are published for this paper.

• Growth of necrotic tumors in the presence and absence of inhibitors.

  1996cited by this paper
• Growth of nonnecrotic tumors in the presence and absence of inhibitors.

  1995cited by this paper
• Nonlinear diffusion of a growth inhibitory factor in multicell spheroids.

  1994cited by this paper
• Mathematical model of prevascular growth of a spherical carcinoma-part II

  1993cited by this paper
• Cell migration in multicell spheroids: swimming against the tide.

  1993cited by this paper
• On the concentration profile of a growth inhibitory factor in multicell spheroids.

  1993cited by this paper
• Variations in tumor cell growth rates and metabolism with oxygen concentration, glucose concentration, and extracellular pH

  1992cited by this paper
• Effects of non-uniform inhibitor production on the growth of cancer cell cultures

  1992cited by this paper
• Mathematical modelling of microenvironment and growth in EMT6/Ro multicellular tumour spheroids

  1992cited by this paper
• Mathematical models of tumor growth. IV. Effects of a necrotic core.

  1989cited by this paper
• Glucose diffusivity in multicellular tumor spheroids.

  1988cited by this paper
• Role of necrosis in regulating the growth saturation of multicellular spheroids.

  1988cited by this paper
• Joint oxygen‐glucose deprivation as the cause of necrosis in a tumor analog

  1988cited by this paper
• A mathematical model of tumor growth. III. comparison with experiment

  1987cited by this paper
• Regulation of growth saturation and development of necrosis in EMT6/Ro multicellular spheroids by the glucose and oxygen supply.

  1986cited by this paper
• Influence of glucose and oxygen supply conditions on the oxygenation of multicellular spheroids.

  1986cited by this paper
• A simplified mathematical model of tumor growth

  1986cited by this paper
• Two‐Dimensional Diffusion Limited System For Cell Growth

  1985cited by this paper
• Identification of a tumor inhibitory factor in rat ascites fluid.

  1984cited by this paper
• Growth of mammalian multicellular tumor spheroids.

  1983cited by this paper
• Determination of diffusion constants for metabolites in multicell tumor spheroids.

  1983cited by this paper
• Evidence for a major role of glucose in controlling development of necrosis in EMT6/Ro multicell tumor spheroids.

  1983cited by this paper
• The role of glucose in the growth of 9l multicell tumor spheroids

  1982cited by this paper
• The glucose distribution in 9l rat brain multicell tumor spheroids and its effect on cell necrosis

  1982cited by this paper
• A model for the growth of multicellular spheroids

  1982cited by this paper
• Oxygen tensions in multicell spheroids of two cell lines.

  1982cited by this paper
• The three steps to cancer: a new concept of cancerigenesis.

  1982cited by this paper
• Shedding of mitotic cells from the surface of multicell spheroids during growth

  1981cited by this paper
• Heterogeneous oxygen partial pressure and pH distribution in C3H mouse mammary adenocarcinoma.

  1981cited by this paper
• Apoptosis as a volume loss mechanism in mathematical models of solid tumor growth

  1978cited by this paper
• Proliferation and viability in cellular spheroids of human origin.

  1978cited by this paper
• A re-examination of oxygen diffusion in a spherical cell with Michaelis-Menten oxygen uptake kinetics.

  1978cited by this paper
• Some mechanisms involved in cancer cell detachment by necrotic material

  1978cited by this paper
• A model for the growth of a solid tumor with non-uniform oxygen consumption

  1977cited by this paper
• A proliferation gradient in three‐dimensional colonies of cultured human glioma cells

  1977cited by this paper
• Cellular and geometric control of tissue growth and mitotic instability.

  1976cited by this paper
• Cellular and geometric control of tissue growth and mitotic instability.

  1976cited by this paper
• Oxygen diffusion in a spherical cell with nonlinear oxygen uptake kinetics.

  1976cited by this paper
• Model for the growth of a solid in vitro tumor.

  1975cited by this paper
• Model for the growth of a solid in vitro tumor.

  1975cited by this paper
• SELF-REGULATION OF GROWTH IN THREE DIMENSIONS

  1973cited by this paper
• Instability and Mitotic Patterns in Tissue Growth

  1973cited by this paper
• The effect of hypoxia on the generation time of mammalian cells.

  1973cited by this paper
• Models for the Growth of a Solid Tumor by Diffusion

  1972cited by this paper
• Tumor angiogenesis: therapeutic implications.

  1971cited by this paper
• Growth of nodular carcinomas in rodents compared with multi-cell spheroids in tissue culture.

  1970cited by this paper
• Rate of growth of solid tumours as a problem of diffusion.

  1966cited by this paper
• The Histological Structure of Some Human Lung Cancers and the Possible Implications for Radiotherapy

  1955cited by this paper
• On the solution of nonlinear hyperbolic differential equations by finite differences

  1952cited by this paper

• The Impact of Oxygen Distribution on the Tumor Necrotic Region: A Two-phase Model

  2026cites this paper
• The application of experimental models for the drug discovery for digestive tumors.

  2026cites this paper
• Modeling localized thermal therapy through coupled heat transfer and metabolic dynamics.

  2026cites this paper
• Modeling Tumor Microenvironment Complexity In Vitro: Spheroids as Physiologically Relevant Tumor Models and Strategies for Their Analysis

  2025cites this paper
• Parameter identification for the stochastic ductal carcinoma in situ model with free boundary conditions

  2025cites this paper
• Computational Modeling of Tumor Dynamics Incorporating Drug Resistance and Immune Response for Optimized Cancer Treatment

  2025cites this paper
• SSRCA: A Novel Machine Learning Pipeline to Perform Sensitivity Analysis for Agent-Based Models

  2025cites this paper
• Spatio-Temporal Dynamics of M1 and M2 Macrophages in a Multiphase Model of Tumor Growth

  2025cites this paper
• Control of the Fisher-Stefan system

  2025cites this paper
• Higher-order compact finite difference method for a free boundary problem of ductal carcinoma in situ

  2024cites this paper
• A mathematical study of the interaction between oxygen and lactate in an in vivo and in vitro tumor

  2024cites this paper
• Insights from a multiscale framework on metabolic rate variation driving glioblastoma multiforme growth and invasion

  2024cites this paper
• A Population-Based Tumor-Volume Model for Head-and-Neck Cancer During Radiotherapy with a Dynamic Oxygenated Compartment.

  2024cites this paper
• Modelling adaptive therapy for tumor using reaction-diffusion equation

  2024cites this paper
• Dynamics of an age-structured tumor cell population model with nutrition

  2024cites this paper
• The development of drug resistance in metastatic tumours under chemotherapy: An evolutionary perspective.

  2024cites this paper
• Making Predictions Using Poorly Identified Mathematical Models

  2024cites this paper
• Studying a cylindrical moving boundary problem in ductal carcinoma in situ

  2024cites this paper
• Computational model of the cancer necrotic core formation in a tumor-on-a-chip device.

  2024cites this paper
• High-density sampling reveals volume growth in human tumours

  2024cites this paper
• Selected aspects of avascular tumor growth reproduced by a hybrid model of cell dynamics and chemical kinetics.

  2024cites this paper
• A large deformation theory for coupled swelling and growth with application to growing tumors and bacterial biofilms

  2023cites this paper
• Tumor Microenvironment

  2023cites this paper
• How do cell crowding and starvation affect avascular tumor growth of the EMT6/Ro tumor?

  2023influential citation
• A computational model of cell viability and proliferation of extrusion-based 3D-bioprinted constructs during tissue maturation process

  2023cites this paper
• Unsung versatility of elastin-like polypeptide inspired spheroid fabrication: A review.

  2023cites this paper
• Multiscale modeling of the dynamic growth of cancerous tumors under the influence of chemotherapy drugs

  2023cites this paper
• Analysis of a radial free boundary tumor model with time-dependent absorption efficiency

  2023cites this paper
• 3D cell aggregates amplify diffusion signals

  2023cites this paper
• A mathematical model for nutrient-limited uniaxial growth of a compressible tissue.

  2023cites this paper
• On impact of oxygen distribution on tumor necrotic region: A Multiphase Model

  2023cites this paper
• Survival, extinction, and interface stability in a two–phase moving boundary model of biological invasion

  2023cites this paper
• Modeling and analysis of a multilayer solid tumour with cell physiological age and resource limitations

  2023cites this paper
• Evaluation of innate and adaptive immune system interactions in the tumor microenvironment via a 3D continuum model.

  2022cites this paper
• Minimal Morphoelastic Models of Solid Tumour Spheroids: A Tutorial

  2022cites this paper
• Τhe Study of Square Periodic Perturbations as an Immunotherapy Process on a Tumor Growth Chaotic Model

  2022cites this paper
• Pattern formation and travelling waves in a multiphase moving boundary model of tumour growth

  2022cites this paper
• Individual-based and continuum models of phenotypically heterogeneous growing cell populations

  2022cites this paper
• A second dynamic population invasion study from reactive telegraph equation and boundary element formulation – a numerical assay about tumour growth in vitro

  2022cites this paper
• Evolution of the Solid Human Tumor Cells Properties in Various Experimental Systems in Vitro

  2022cites this paper
• The effect of geometry on survival and extinction in a moving-boundary problem motivated by the Fisher–KPP equation

  2022cites this paper
• TOWARDS A MINIMAL ADMISSIBLE MODEL OF SOLID TUMOUR SPHEROID GROWTH

  2022cites this paper
• Biparametric identification for a free boundary of ductal carcinoma in situ

  2022cites this paper
• State-dependent evolutionary models reveal modes of solid tumour growth

  2022cites this paper
• Geometric analysis enables biological insight from complex non-identifiable models using simple surrogates

  2022influential citation
• Intra-tumor heterogeneity and its impact on cytotoxic therapy in a two-dimensional vascular tumor growth model

  2022cites this paper
• Two-phase model of compressive stress induced on a surrounding hyperelastic medium by an expanding tumour

  2022cites this paper
• Asymmetric Growth of Tumor Spheroids in a Symmetric Environment

  2022cites this paper
• A three-dimensional angiogenesis model with time-delay

  2022cites this paper
• The global existence and numerical method for the free boundary problem of ductal carcinoma in situ

  2022cites this paper
• Designing and interpreting 4D tumour spheroid experiments

  2022cites this paper
• A two-dimensional mathematical model of tumor angiogenesis with CD147

  2022cites this paper
• Macrophage Anti-inflammatory Behaviour in a Multiphase Model of Atherosclerotic Plaque Development

  2022cites this paper
• Concentration-Dependent Domain Evolution in Reaction–Diffusion Systems

  2022cites this paper
• Nonlocal Reaction–Diffusion Equations in Biomedical Applications

  2022cites this paper
• Pattern formation and front stability for a moving-boundary model of biological invasion and recession

  2022cites this paper
• Ion-Induced Volume Transition in Gels and Its Role in Biology

  2021cites this paper
• Kinetics of Nanomedicine in Tumor Spheroid as an In Vitro Model System for Efficient Tumor-Targeted Drug Delivery With Insights From Mathematical Models

  2021cites this paper
• A mathematical investigation into the uptake kinetics of nanoparticles in vitro

  2021influential citation
• In-Silico Modeling of Tumor Spheroid Formation and Growth

  2021cites this paper
• Linear stability for a periodic tumor angiogenesis model with free boundary

  2021cites this paper
• Numerical simulations and analysis for mathematical model of avascular tumor growth using Gompertz growth rate function

  2021cites this paper
• A phenotype-structured model to reproduce the avascular growth of a tumor and its interaction with the surrounding environment.

  2021cites this paper
• Improving cancer treatments via dynamical biophysical models.

  2021cites this paper
• Travelling wave analysis of cellular invasion into surrounding tissues

  2021cites this paper
• Rules of Engagement: A Guide to Developing Agent-Based Models.

  2021cites this paper
• Two Numerical Solutions for Solving a Mathematical Model of the Avascular Tumor Growth

  2021cites this paper
• Spezielle Primärkulturen

  2021cites this paper
• Antimonotonicity, Crisis, and Route to Chaos in a Tumor Growth Model

  2021cites this paper
• Characterization and quantification of necrotic tissues and morphology in multicellular ovarian cancer tumor spheroids using optical coherence tomography.

  2021cites this paper
• Towards a Mechanical Model for anisotropic Glioma Spread using Darcy’s law

  2021cites this paper
• Spezielle zellbiologische Methoden in der Zellkultur

  2021cites this paper
• Quantitative analysis of tumour spheroid structure

  2021cites this paper
• Designing and interpreting 4D tumour spheroid experiments

  2021cites this paper
• A stochastic mathematical model of 4D tumour spheroids with real-time fluorescent cell cycle labelling

  2021cites this paper
• Non-vanishing sharp-fronted travelling wave solutions of the Fisher-Kolmogorov model.

  2021cites this paper
• The existence and numerical method for a free boundary problem modeling the ductal carcinoma in situ

  2021cites this paper
• Multi-cellular aggregates, a model for living matter

  2021cites this paper
• Modeling the Emergence of Phenotypic Heterogeneity in Vascularized Tumors

  2021cites this paper
• Simulation of 3D centimeter-scale continuum tumor growth at sub-millimeter resolution via distributed computing

  2021cites this paper
• Another way of solving a free boundary problem related to DCIS model

  2020cites this paper
• Analysis of a nonautonomous free boundary tumor model with infinite time delays

  2020cites this paper
• Colorectal cancer triple co-culture spheroid model to assess the biocompatibility and anticancer properties of polymeric nanoparticles.

  2020cites this paper
• A free boundary tumor model with time dependent nutritional supply

  2020cites this paper
• A numerical method based on the moving mesh for the solving of a mathematical model of the avascular tumor growth

  2020cites this paper
• Mechanistic Modeling of Longitudinal Shape Changes: Equations of Motion and Inverse Problems

  2020cites this paper
• Avascular tumour growth models based on anomalous diffusion

  2020cites this paper
• An on-lattice agent-based Monte Carlo model simulating the growth kinetics of multicellular tumor spheroids.

  2020cites this paper
• University of Dundee From Individual-based Mechanical Models of Multicellular Systems to Free-boundary Problems

  2020cites this paper
• Models of Bone Cancers - Part I. Mathematical Models of Cancers. An Introduction

  2020cites this paper
• Modeling the autophagic effect in tumor growth: a cross diffusion model and its free boundary limit

  2020cites this paper
• Numerical Solution of a Two Dimensional Tumour Growth Model with Moving Boundary

  2020cites this paper
• Modeling neoplastic disease with spheroids and organoids

  2020cites this paper
• Mathematical modelling reveals cellular dynamics within tumour spheroids

  2020cites this paper
• A three phase model to investigate the effects of dead material on the growth of avascular tumours

  2020cites this paper
• A quantitative cellular automaton model of multicellular spheroid tumour growth

  2020cites this paper
• Mathematical Model of Tumour Spheroid Experiments with Real-Time Cell Cycle Imaging

  2020cites this paper
• Mathematical Modeling Shows That the Response of a Solid Tumor to Antiangiogenic Therapy Depends on the Type of Growth

  2020cites this paper
• The importance of dead material within a tumour on the dynamics in response to radiotherapy

  2020cites this paper
• A tumor growth model with autophagy: The reaction-(cross-)diffusion system and its free boundary limit

  2020cites this paper