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A phase-field model for viscoelastic compressible tumor growth
Arxiv
|July 10, 2026
Summary
Tumor growth is complex, influenced by mechanical stress and nutrient availability. Our model reveals how mechanical instabilities and nutrient gradients drive tumor shape changes and potential invasion.
Area of Science:
- Computational biology
- Biophysics
- Mathematical modeling
Background:
- Growing tumors create mechanical stress in their microenvironment.
- Mechanotransduction and biochemical signaling intricately regulate tumor growth patterns.
Purpose of the Study:
- To develop a phase-field model simulating tumor growth dynamics.
- To investigate the influence of mechanical properties and nutrient diffusion on tumor progression.
Main Methods:
- Utilized a phase-field model for tumor simulation.
- Coupled continuum modeling of viscoelastic mechanics with nutrient concentration.
- Analyzed tumor behavior in 2D and 3D, considering elastic and viscous properties.
Main Results:
- Demonstrated model convergence to sharp interface models.
- Observed symmetry-breaking instabilities in stationary tumors.
- Identified nutrient gradients and apoptosis-related loss as key drivers of instability.
Conclusions:
- The phase-field model robustly simulates tumor growth and mechanics.
- Mechanical instabilities and nutrient signaling significantly impact tumor progression and invasiveness.
- Tissue fluidity and compressibility alter tumor topology and dynamics.
