Selected aspects of avascular tumor growth reproduced by a hybrid model of cell dynamics and chemical kinetics
From MaRDI portal
Publication:6550777
DOI10.1016/j.mbs.2024.109168zbMath1537.92032MaRDI QIDQ6550777
Publication date: 5 June 2024
Published in: Mathematical Biosciences (Search for Journal in Brave)
PDEs in connection with biology, chemistry and other natural sciences (35Q92) Cell movement (chemotaxis, etc.) (92C17) Pathology, pathophysiology (92C32)
Cites Work
- A history of the study of solid tumour growth: the contribution of mathematical modelling
- Lattice and non-lattice models of tumour angiogenesis
- Nonlinear simulation of tumor necrosis, neo-vascularization and tissue invasion via an adaptive finite-element/level-set method
- A deterministic model of growth factor-induced angiogenesis
- On the mechanics of a growing tumor
- A single-cell approach in modeling the dynamics of tumor microregions
- The migration of cells in multicell tumor spheroids
- Mathematical modeling of capillary formation and development in tumor angiogenesis: penetration into the stroma
- A computational study of the development of epithelial acini. I: Sufficient conditions for the formation of a hollow structure
- A computational study of the development of epithelial acini. II: Necessary conditions for structure and lumen stability
- Asymptotic behavior of solutions of a free boundary problem modelling the growth of tumors with Stokes equations
- Modeling the motion of a cell population in the extracellular matrix
- A new approach to modelling the formation of necrotic regions in tumours
- Continuous and discrete mathematical models of tumor-induced angiogenesis
- Analysis of a mathematical model for the growth of tumors
- Mathematical models for tumour angiogenesis: Numerical simulations and nonlinear wave solutions
- Spatio-temporal pattern formation on spherical surfaces: numerical simulation and application to solid tumour growth
- Complex dynamics of tumors: modeling an emerging brain tumor system with coupled reaction-diffusion equations
- Nonlinear simulation of tumor growth
- A hierarchy of cancer models and their mathematical challenges
- A two-phase model of solid tumour growth
- Individual-based approaches to birth and death in avascular tumors
- Modelling and mathematical problems related to tumor evolution and its interaction with the immune system
- Residual stress generation and necrosis formation in multi-cell tumour spheroids
- Modelling the early growth of ductal carcinoma in situ of the breast
- Growth of nonnecrotic tumors in the presence and absence of inhibitors
- Avascular growth, angiogenesis and vascular growth in solid tumours: The mathematical modelling of the stages of tumour development
- Hypoxic cell waves around necrotic cores in glioblastoma: a biomathematical model and its therapeutic implications
- An immersed boundary framework for modelling the growth of individual cells: an application to the early tumour development
- Microenvironment driven invasion: a multiscale multimodel investigation
- A single cell-based model of the ductal tumour microarchitecture
- 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
- Modeling cell movement in anisotropic and heterogeneous network tissues
- Travelling wave solutions to a haptotaxis-dominated model of malignant invasion
- ATP Production and Necrosis Formation in a Tumour Spheroid Model
- Analysis of a Population Model Structured by the Cells Molecular Content
- 'Go or Grow': the key to the emergence of invasion in tumour progression?
- Single-Cell-Based Models in Biology and Medicine
- Multiscale Computational Modelling and Analysis of Cancer Invasion
- Mathematical modelling of the loss of tissue compression responsiveness and its role in solid tumour development
- ON THE FOUNDATIONS OF CANCER MODELLING: SELECTED TOPICS, SPECULATIONS, AND PERSPECTIVES
- Multi-scale models of cell and tissue dynamics
- Modelling Physiological and Pharmacological Control on Cell Proliferation to Optimise Cancer Treatments
- Free Boundary Problems Associated with Multiscale Tumor Models
- Free boundary value problems associated with the growth and development of multicellular spheroids
- A free boundary problem for a singular system of differential equations: An application to a model of tumor growth
- CELLULAR AUTOMATON MODELS OF TUMOR DEVELOPMENT: A CRITICAL REVIEW
- A reinforced random walk model of tumour angiogenesis and anti-angiogenic strategies
- Interactions between a uniformly proliferating tumour and its surroundings: uniform material properties
- Mathematical Modelling of Tumour Invasion and Metastasis
- A linear-elastic model of anisotropic tumour growth
- Modelling solid tumour growth using the theory of mixtures
- AVASCULAR TUMOUR DYNAMICS AND NECROSIS
- Traveling Wave Solutions of a Mathematical Model for Tumor Encapsulation
- A Mixture Theory for the Genesis of Residual Stresses in Growing Tissues I: A General Formulation
- MATHEMATICAL ANALYSIS AND CHALLENGES ARISING FROM MODELS OF TUMOR GROWTH
- A HYBRID MODEL FOR TUMOR SPHEROID GROWTH IN VITRO I: THEORETICAL DEVELOPMENT AND EARLY RESULTS
- A Mixture Theory for the Genesis of Residual Stresses in Growing Tissues II: Solutions to the Biphasic Equations for a Multicell Spheroid
- Multiscale Angiogenesis Modeling Using Mixed Finite Element Methods
- Models for the Growth of a Solid Tumor by Diffusion
- Nonlinear modelling of cancer: bridging the gap between cells and tumours
- Mathematical modeling of the onset of capillary formation initiating angiogenesis
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
This page was built for publication: Selected aspects of avascular tumor growth reproduced by a hybrid model of cell dynamics and chemical kinetics