Complex Far-Field Geometries Determine the Stability of Solid Tumor Growth with Chemotaxis

Min Jhe Lu, Chun Liu, John Lowengrub, Shuwang Li

Research output: Contribution to journalArticlepeer-review

7 Scopus citations


In this paper, we develop a sharp interface tumor growth model to study the effect of the tumor microenvironment using a complex far-field geometry that mimics a heterogeneous distribution of vasculature. Together with different nutrient uptake rates inside and outside the tumor, this introduces variability in spatial diffusion gradients. Linear stability analysis suggests that the uptake rate in the tumor microenvironment, together with chemotaxis, may induce unstable growth, especially when the nutrient gradients are large. We investigate the fully nonlinear dynamics using a spectrally accurate boundary integral method. Our nonlinear simulations reveal that vascular heterogeneity plays an important role in the development of morphological instabilities that range from fingering and chain-like morphologies to compact, plate-like shapes in two dimensions.

Original languageEnglish (US)
Article number39
JournalBulletin of Mathematical Biology
Issue number3
StatePublished - Mar 1 2020

All Science Journal Classification (ASJC) codes

  • General Neuroscience
  • Immunology
  • General Mathematics
  • General Biochemistry, Genetics and Molecular Biology
  • General Environmental Science
  • Pharmacology
  • General Agricultural and Biological Sciences
  • Computational Theory and Mathematics


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