Modelling biological cell attachment and growth on adherent surfaces

Greg Lemon, Ylva Gustafsson, Johannes C. Haag, Mei L. Lim, Sebastian Sjoqvist, Fatemeh Ajalloueian, Philipp Jungebluth, Paolo Macchiarini

Research output: Contribution to journalJournal articleResearchpeer-review

Abstract

A mathematical model, in the form of an integro-partial differential equation, is presented to describe the dynamics of cells being deposited, attaching and growing in the form of a monolayer across an adherent surface. The model takes into account that the cells suspended in the media used for the seeding have a distribution of sizes, and that the attachment of cells restricts further deposition by fragmenting the parts of the domain unoccupied by cells. Once attached the cells are assumed to be able to grow and proliferate over the domain by a process of infilling of the interstitial gaps; it is shown that without cell proliferation there is a slow build up of the monolayer but if the surface is conducive to cell spreading and proliferation then complete coverage of the domain by the monolayer can be achieved more rapidly. Analytical solutions of the model equations are obtained for special cases, and numerical solutions are presented for parameter values derived from experiments of rat mesenchymal stromal cells seeded onto thin layers of collagen-coated polyethylene terephthalate electrospun fibers. The model represents a new approach to describing the deposition, attachment and growth of cells over adherent surfaces, and should prove useful for studying the dynamics of the seeding of biomaterials.
Original languageEnglish
JournalJournal of Mathematical Biology
Volume68
Issue number4
Pages (from-to)785-813
ISSN0303-6812
DOIs
Publication statusPublished - 2014
Externally publishedYes

Keywords

  • Agricultural and Biological Sciences (miscellaneous)
  • Applied Mathematics
  • Modeling and Simulation
  • Biomaterials
  • Cell culture
  • Integro-partial differential equations
  • Mathematical modelling
  • Tissue engineering
  • Animals
  • Cell Adhesion
  • Cell Proliferation
  • Mesenchymal Stromal Cells
  • Models, Biological
  • Numerical Analysis, Computer-Assisted
  • Rats
  • biomaterial
  • cell growth
  • cell proliferation
  • collagen-coated polyethylene terephthalate electrospun fiber
  • 02502, Cytology - General
  • 04500, Mathematical biology and statistical methods
  • 10511, Biophysics - Bioengineering
  • 10515, Biophysics - Biocybernetics
  • Computational Biology
  • biological cell attachment modelling mathematical and computer techniques
  • one-dimensional model mathematical and computer techniques
  • tissue engineering laboratory techniques, culturing techniques
  • Cell Biology
  • Models and Simulations
  • BIOLOGY
  • MATHEMATICAL
  • MESENCHYMAL STEM-CELLS
  • IN-VITRO
  • MATHEMATICAL-MODEL
  • EXTRACELLULAR-MATRIX
  • POROUS SCAFFOLDS
  • BONE-MARROW
  • ADHESION
  • PROLIFERATION
  • TISSUE
  • KINETICS
  • MATHEMATICAL models
  • HASH(0x42d6340)
  • 92B05
  • 45K05

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