AVASCULAR TUMOUR DYNAMICS AND NECROSIS

DOI10.1142/S0218202599000294zbMath0933.92021MaRDI QIDQ4933723

G. J. Pettet, D. L. Sean McElwain, Colin P. Please

Publication date: 16 January 2000

Published in: Mathematical Models and Methods in Applied Sciences (Search for Journal in Brave)

zbMATH Keywords

multicell spheroidavascular solid tumourcell divisor

Mathematics Subject Classification ID

PDEs in connection with biology, chemistry and other natural sciences (35Q92) Medical applications (general) (92C50)

Related Items (14)

ADVECTION-DIFFUSION MODELS FOR SOLID TUMOUR EVOLUTION IN VIVO AND RELATED FREE BOUNDARY PROBLEM ⋮ MODELLING OF THE IMMUNE RESPONSE: CONCEPTUAL FRAMEWORKS AND APPLICATIONS ⋮ DISCRETE AND CONTINUOUS COMPARTMENTAL MODELS OF CELLULAR POPULATIONS ⋮ Numerical simulation of a thermodynamically consistent four-species tumor growth model ⋮ Evaluation of innate and adaptive immune system interactions in the tumor microenvironment via a 3D continuum model ⋮ A cellular automata model of tumor-immune system interactions ⋮ Three-dimensional multispecies nonlinear tumor growth. II: Tumor invasion and angiogenesis ⋮ Tumor growth in complex, evolving microenvironmental geometries: a diffuse domain approach ⋮ Simulation of the phase field Cahn-Hilliard and tumor growth models via a numerical scheme: element-free Galerkin method ⋮ Comparison between two meshless methods based on collocation technique for the numerical solution of four-species tumor growth model ⋮ Residual stress generation and necrosis formation in multi-cell tumour spheroids ⋮ Biological inferences from a mathematical model of comedo ductal carcinoma in situ of the breast ⋮ Modelling and mathematical problems related to tumor evolution and its interaction with the immune system ⋮ Critical analysis and perspectives on kinetic (cellular) theory of immune competition

Cites Work

• A new approach to modelling the formation of necrotic regions in tumours
• Cell migration in multicell spheroids: Swimming against the tide
• Modelling the growth of solid tumours and incorporating a method for their classification using nonlinear elasticity theory

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