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Lattice-Gas Cellular Automaton Models for Biology: From Fluids to Cells

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Abstract

Lattice-gas cellular automaton (LGCA) and lattice Boltzmann (LB) models are promising models for studying emergent behaviour of transport and interaction processes in biological systems. In this chapter, we will emphasise the use of LGCA/LB models and the derivation and analysis of LGCA models ranging from the classical example dynamics of fluid flow to clotting phenomena in cerebral aneurysms and the invasion of tumour cells.

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References

  • Bell DN, Spain S, Goldsmith HL (1989) Adenosine diphosphate-induced aggregation of human platelets in flow through tubes. I. Measurement of concentration and size of single platelets and aggregates. Biophys J 56(5):829–843

    Article  Google Scholar 

  • Bru A, Albertos S, Subiza JL, Garcia-Asenjo JL, Bru I (2003) The universal dynamics of tumor growth. Bioph J 85:2948–2961

    Article  Google Scholar 

  • Chen S, Doolen GD (1998) Lattice Boltzmann methods for fluid flows. Annu Rev Fluid Mech 30:329

    Article  Google Scholar 

  • Chopard B, Droz M (1998) Cellular automata modeling of physical systems. Cambridge University Press, Cambridge

    Book  Google Scholar 

  • Chopard B, Ouared R, Stahl B, Rufenacht DA, Yilmaz H, Courbebaisse G (2005) Thrombosis modeling in intracranial aneurysms: a lattice Boltzmann numerical algorithm. Comput Phys Commun 179(1–3):128–131

    Google Scholar 

  • Davis PF (1995) Flow-mediated endothelial mechanotransduction. Physio Rev 75:519–560

    Google Scholar 

  • Deutsch A, Dormann S (2005) Cellular automaton modeling of biological pattern formation. Birkhauser

  • Folkman J, Hochberg M (1973) Self-regulation of growth in three dimensions. J Exp Med 138:745–753

    Article  Google Scholar 

  • Friedl P (2004) Prespecification and plasticity: shifting mechanisms of cell migration. Curr Opin Cell Biol 16(1):14–23

    Article  Google Scholar 

  • Frisch U, Hasslacher B, Pomeau Y (1986) Lattice-gas automata for the Navier-Stokes equation. Phys Rev Lett 56(14):1505–1508

    Article  Google Scholar 

  • Hanahan D, Weinberg R (2000) The hallmarks of cancer. Cell 100:57–70

    Article  Google Scholar 

  • Hardy J, Pomeau Y, de Pazzis O (1973) Time evolution of a two-dimensional classical lattice system. Phys Rev Lett 31:276–279

    Article  Google Scholar 

  • Hatzikirou H, Deutsch A (2008) Cellular automata as microscopic models of cell migration in heterogeneous environments. Curr Top Dev Biol 81:401–434

    Article  Google Scholar 

  • Hatzikirou H, Brusch L, Schaller C, Simon M, Deutsch A (2010) Prediction of traveling front behavior in a lattice-gas cellular automaton model for tumor invasion. Comput Math Appl 59(7):2326–2339

    Article  Google Scholar 

  • Hénon M (1987) Isometric collision rules for a four-dimensional fchc lattice gas. Compl Syst 1:475

    Google Scholar 

  • Hirabayashi M, Rufenacht DA, Otha M, Chopard B (2003) Characterization of flow reduction in an aneurysm due to a porous stent. Phys Rev E 68:021918

    Article  Google Scholar 

  • Humphrey JD (2001) Cardiovascular solid mechanics

  • Moroi M, Jung SM (1998) Integrin-mediated platelet adhesion. Front Biosci 3:d719–728

    Google Scholar 

  • Nasilowski R (1991) A cellular-automaton fluid model with simple rules in arbitrary many dimensions. J Stat Phys 65(2):97–138

    Article  Google Scholar 

  • Nowell PC (1976) The clonal evolution of tumor cell populations. Science 194:23–28

    Article  Google Scholar 

  • Ouared R, Chopard B (2005) Lattice Boltzmann simulations of blood flow: non-newtonian rheolgy and clotting processes. J Stat Phys 121(1-2):209–221

    Article  Google Scholar 

  • Rem PC, Somers JA (1989) Cellular automata algorithms on a transputer network. In: Monaco R (ed) Discrete kinematic theory, lattice gas dynamics and foundations of hydrodynamics. World Scientific, Singapore, pp 268–275

    Google Scholar 

  • Ruefenacht DA, Chopard B, Ouared R, Yilmaz H (2007) Lattice Boltzmann modeling of thrombosis in giant aneurysms. Int J Mod Phys C 18:712–721

    Article  Google Scholar 

  • Somers JA, Rem PC (1989) The construction of efficient collision tables for fluid flow. In: Manneville P, Boccara N, Vichniac GY, Bidaux R (eds) Cellular automata and modeling of complex physical systems. Springer, Berlin, pp 161–177

    Google Scholar 

  • Succi S (2001) The lattice Boltzmann equation: for fluid dynamics and beyond. Series Numerical Mathematics and Scientific Computation. Oxford University Press, Oxford

    Google Scholar 

  • Tektonidis M (2008) Parameter optimization in a cellular automaton model of cancer growth based on medical MRI data. Master’s thesis. TU Berlin

  • Teng MMH et al (2003) MR imaging of giant intracranial aneurysm. J Clin Neuros 10(4):460–464

    Article  Google Scholar 

  • Whittle IR, Dorsch NW, Besser M (1982) Spontaneous thrombosis in giant intracranial aneurysms. J Neurol Neurosurg Psychiat 45(11):1040–1047

    Article  Google Scholar 

  • Williams RH, Nollert MU (2004) Platelet-derived no slows thrombus growth on a collagen type iii surface. Thrombosis J 2:1–11

    Article  Google Scholar 

  • Wolf-Gladrow DA (2000) Lattice-gas cellular automata and lattice Boltzmann models: an Introduction. Springer, Berlin

    Google Scholar 

  • Wolfram S (1986) Theory and application of cellular automata. World Scientific, Singapore

    Google Scholar 

Download references

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Authors and Affiliations

  1. University of Geneva, Geneva, Switzerland

    Bastien Chopard & Rafik Ouared

  2. Center for Information Services and High Performance Computing, Technische Universität Dresden, Dresden, Germany

    Andreas Deutsch & Haralambos Hatzikirou

  3. Alfred Wegener Institute for Polar and Marine Research, Bremerhaven, Germany

    Dieter Wolf-Gladrow

Authors
  1. Bastien Chopard
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  2. Rafik Ouared
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  3. Andreas Deutsch
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  4. Haralambos Hatzikirou
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  5. Dieter Wolf-Gladrow
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Correspondence to Bastien Chopard.

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Chopard, B., Ouared, R., Deutsch, A. et al. Lattice-Gas Cellular Automaton Models for Biology: From Fluids to Cells. Acta Biotheor 58, 329–340 (2010). https://doi.org/10.1007/s10441-010-9118-5

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