ArticleArchive of applied mechanics = Ingenieur-Archiv2022
A continuum mechanical framework for modeling tumor growth and treatment in two- and three-phase systems.
Article in Archive of applied mechanics = Ingenieur-Archiv, 2022. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Cited by 8 papers.
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Who cites it
8 citing papers in PubMed.
- Coupled mixed-dimensional multiphase porous media approach for modeling airflow, blood flow, and gas exchange in the human lungs.Biomechanics and modeling in mechanobiology · 2026Article
- Computational Modelling of Cancer Nanomedicine: Integrating Hyperthermia Treatment Into a Multiphase Porous-Media Tumour Model.International journal for numerical methods in biomedical engineering · 2025Article
- Semi-analytical solutions of passive scalar transport in generalized Newtonian fluid flow.Physics of fluids (Woodbury, N.Y. : 1994) · 2025Article
- Thermodynamically Constrained Averaging Theory: Why Bother?ARC geophysical research · 2025Article
- Modeling flow of Carreau fluids in porous media.Physical review. E · 2023Article
- Computational Modeling of Microwave Tumor Ablation.Bioengineering (Basel, Switzerland) · 2022Review
- Towards Understanding Factors Affecting Arsenic, Chromium, and Vanadium Mobility in the Subsurface.Water · 2022Article
- Generalized Newtonian fluid flow in porous media.Physical review fluids · 2021Article
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Authors and funding
3 authors.
Funding
Abstract
The growth and treatment of tumors is an important problem to society that involves the manifestation of cellular phenomena at length scales on the order of centimeters. Continuum mechanical approaches are being increasingly used to model tumors at the largest length scales of concern. The issue of how to best connect such descriptions to smaller-scale descriptions remains open. We formulate a framework to derive macroscale models of tumor behavior using the thermodynamically constrained averaging theory (TCAT), which provides a firm connection with the microscale and constraints on permissible forms of closure relations. We build on developments in the porous medium mechanics literature to formulate fundamental entropy inequality expressions for a general class of three-phase, compositional models at the macroscale. We use the general framework derived to formulate two classes of models, a two-phase model and a three-phase model. The general TCAT framework derived forms the basis for a wide range of potential models of varying sophistication, which can be derived, approximated, and applied to understand not only tumor growth but also the effectiveness of various treatment modalities.
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Registered trials
Read under generation 80e0d062 · epoch 390. Bibliography from PubMed, PubMed Central and OpenAlex; grants from NIH RePORTER; trial links from ClinicalTrials.gov; estimates, votes and beliefs from the OpenQuestion graph.