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Fingering in Stochastic Growth Models.

Andreas C Aristotelous1, Richard Durrett1

  • 1Department of Mathematics, Duke U., Box 90320, Durham, NC 27708-0320.

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|October 3, 2015
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Summary
This summary is machine-generated.

This study explores two cancer growth models using cellular automata and oxygen. A phase transition from solid growth to fingering was observed in the first model, while the second model consistently showed fingering.

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Area of Science:

  • Computational Biology
  • Mathematical Biology
  • Biophysics

Background:

  • Hybrid-discrete cellular automata are widely used for cancer modeling.
  • Oxygen availability significantly influences tumor growth and morphology.

Purpose of the Study:

  • To investigate two distinct cellular automata models for cancer growth incorporating oxygen.
  • To analyze the impact of oxygen concentration on tumor morphology and growth dynamics.

Main Methods:

  • Development of two 2D lattice-based cellular automata models.
  • Model 1: Oxygen concentration calculated based on geometry.
  • Model 2: Oxygen concentration governed by a reaction-diffusion equation.
  • Cellular birth and death rates depend on oxygen thresholds.

Main Results:

  • Model 1 exhibited a phase transition between solid blob growth and "fingering" at a threshold θ = 0.5.
  • Model 2 consistently displayed "fingering" morphology, irrespective of the threshold (θ = 0).

Conclusions:

  • The geometric calculation of oxygen in Model 1 leads to distinct growth patterns.
  • Reaction-diffusion dynamics of oxygen in Model 2 promote invasive "fingering" growth.
  • These models provide insights into oxygen-driven cancer morphology.