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Planar Gradient Diffusion System to Investigate Chemotaxis in a 3D Collagen Matrix
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Pattern formation in multiphase models of chemotactic cell aggregation.

J E F Green1, J P Whiteley2, J M Oliver3

  • 1School of Mathematical Sciences, University of Adelaide, Adelaide, SA, Australia.

Mathematical Medicine and Biology : a Journal of the IMA
|May 19, 2017
PubMed
Summary
This summary is machine-generated.

We developed a continuum model for cell aggregation, revealing conditions for pattern formation. Simplified models offer qualitative insights, while complex ones provide quantitative accuracy for cell culture dynamics.

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Area of Science:

  • Continuum mechanics
  • Biophysics
  • Mathematical modeling

Background:

  • Cell aggregation in culture wells is crucial for biological studies.
  • Understanding cell-medium interactions and pattern formation is key.
  • Existing models may lack detail in capturing complex dynamics.

Purpose of the Study:

  • To develop a continuum model for cell aggregation in a nutrient medium.
  • To investigate pattern formation from homogeneous cell distributions.
  • To compare simplified model reductions with a full model.

Main Methods:

  • A two-phase continuum mechanics approach treating cells and medium as fluids.
  • Development of coupled nonlinear partial differential equations.
  • Analytical and numerical investigation of 1D and thin-film extensional flow reductions.

Main Results:

  • Identified conditions for pattern formation from homogeneous steady states.
  • 1D and thin-film models show similar qualitative behavior in linear/weakly nonlinear regimes.
  • Significant quantitative differences observed in full simulations away from marginal stability.

Conclusions:

  • Simplified 1D models are useful for qualitative understanding of cell aggregation.
  • Thin-film extensional flow models offer better quantitative predictions.
  • Model choice depends on the desired level of accuracy for cell culture dynamics research.