ArticleComputer methods in applied mechanics and engineering2018
A monolithic multiphase porous medium framework for (a-)vascular tumor growth.
Article in Computer methods in applied mechanics and engineering, 2018. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Cited by 11 papers.
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Who cites it
11 citing papers in PubMed, 24 citations in OpenAlex.
- 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
- An in silico model of the capturing of magnetic nanoparticles in tumour spheroids in the presence of flow.Biomedical microdevices · 2023Article
- Article
- A PDE Model of Breast Tumor Progression in MMTV-PyMT Mice.Journal of personalized medicine · 2022Article
- A continuum mechanical framework for modeling tumor growth and treatment in two- and three-phase systems.Archive of applied mechanics = Ingenieur-Archiv · 2022Article
- Foundations for Soft, Smart Matter by Active Mechanical Metamaterials.Advanced science (Weinheim, Baden-Wurttemberg, Germany) · 2020Review
- Drug delivery: Experiments, mathematical modelling and machine learning.Computers in biology and medicine · 2020Article
- Extension of a multiphase tumour growth model to study nanoparticle delivery to solid tumours.PloS one · 2020Article
- Coupling tumor growth and bio distribution models.Biomedical microdevices · 2019Article
- New formulation of the Gompertz equation to describe the kinetics of untreated tumors.PloS one · 2019Article
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Authors and funding
5 authors at 2 institutions in 2 countries.
Funding
Abstract
We present a dynamic vascular tumor model combining a multiphase porous medium framework for avascular tumor growth in a consistent Arbitrary Lagrangian Eulerian formulation and a novel approach to incorporate angiogenesis. The multiphase model is based on Thermodynamically Constrained Averaging Theory and comprises the extracellular matrix as a porous solid phase and three fluid phases: (living and necrotic) tumor cells, host cells and the interstitial fluid. Angiogenesis is modeled by treating the neovasculature as a proper additional phase with volume fraction or blood vessel density. This allows us to define consistent inter-phase exchange terms between the neovasculature and the interstitial fluid. As a consequence, transcapillary leakage and lymphatic drainage can be modeled. By including these important processes we are able to reproduce the increased interstitial pressure in tumors which is a crucial factor in drug delivery and, thus, therapeutic outcome. Different coupling schemes to solve the resulting five-phase problem are realized and compared with respect to robustness and computational efficiency. We find that a fully monolithic approach is superior to both the standard partitioned and a hybrid monolithic-partitioned scheme for a wide range of parameters. The flexible implementation of the novel model makes further extensions (e.g., inclusion of additional phases and species) straightforward.
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