Homogenization of oxygen transport in biological tissues

DOI10.1080/00036811.2015.1049600zbMath1342.35030arXiv1406.6722OpenAlexW1568981804MaRDI QIDQ2805624

Mariya Ptashnyk, Anastasios Matzavinos

Publication date: 12 May 2016

Published in: Applicable Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1406.6722

zbMATH Keywords

thin domainsperiodic homogenizationtwo-scale convergencetissue engineeringunfolding methodreconstructive surgeryarterial branching patternDIEP tissue flap

Mathematics Subject Classification ID

Reaction-diffusion equations (35K57) Effective constitutive equations in solid mechanics (74Q15) PDEs in connection with biology, chemistry and other natural sciences (35Q92) Homogenization in context of PDEs; PDEs in media with periodic structure (35B27) Homogenization and oscillations in dynamical problems of solid mechanics (74Q10)

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A MULTIPHASE MULTISCALE MODEL FOR NUTRIENT LIMITED TISSUE GROWTH ⋮ Coarse-graining and hybrid methods for efficient simulation of stochastic multi-scale models of tumour growth ⋮ Singular Limit for Reactive Diffusive Transport Through an Array of Thin Channels in case of Critical Diffusivity

Cites Work

• Mathematical modelling of flow through vascular networks: implications for tumour-induced angiogenesis and chemotherapy strategies
• A multiphase model describing vascular tumour growth
• Homogenization of a Darcy-Stokes system modeling vuggy porous media
• Diffusion, convection, adsorption, and reaction of chemicals in porous media
• Multiscale modeling of fluid transport in tumors
• Homogenization of nonstationary Navier-Stokes equations in a domain with a grained boundary
• Fluid flow through various branching tubes
• Mathematical modelling of the influence of blood rheological properties upon adaptative tu\-mour-induced angiogenesis
• The periodic unfolding method for perforated domains and Neumann sieve models
• The Periodic Unfolding Method in Domains with Holes
• Effective Transmission Conditions for Reaction-Diffusion Processes in Domains Separated by an Interface
• A two-fluid model for tissue growth within a dynamic flow environment
• Derivation of a Macroscopic Receptor-Based Model Using Homogenization Techniques
• Homogenization and Two-Scale Convergence
• A General Convergence Result for a Functional Related to the Theory of Homogenization
• AVM modelling by multi-branching tube flow: large flow rates and dual solutions
• Reactive transport through an array of cells with semi-permeable membranes
• Multi-branching flows from one mother tube to many daughters or to a network
• The Periodic Unfolding Method in Homogenization
• Homogenization Approach to Water Transport in Plant Tissues with Periodic Microstructures

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