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Critical Phenomena in a Heterogeneous Excitable System

Critical Phenomena in a Heterogeneous Excitable System. Marc Baghdadi Supervisor: Hugo van den Berg. Background. Muscular wall of the uterus (myometrium) only acquires ability to expel the fœtus in the final days before labour

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Critical Phenomena in a Heterogeneous Excitable System

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  1. Critical Phenomena in a Heterogeneous Excitable System Marc Baghdadi Supervisor: Hugo van den Berg

  2. Background • Muscular wall of the uterus (myometrium) only acquires ability to expel the fœtus in the final days before labour • This change is believed to be the result of a phase transition from locally excited to globally excited state • Cell synchrony is achieved by electrical conduction through gap junctions R. Smith, Parturition, N Engl J Med, 2007, 356:271-283

  3. Aim of the project • To model the changes in the muscular wall of the uterus in the days before labour • Investigate the spread of induced excitation through the system

  4. The Model Smooth muscle cells can be modelled using the Fitzhugh-Nagumo system of equations v = excitation variable w = recovery variable I = Input current

  5. The Model v

  6. Approach Taken Approach Taken Construct an (m x n) lattice of cells, each obeying Fitzhugh-Nagumo dynamics, and connected by identical resistors K

  7. Local Excitation

  8. Global Excitation

  9. Region of Excitation

  10. Removing connections at random Probability

  11. Removing connections at random

  12. Removing connections at random

  13. Percolation Points

  14. Random Connection Sizes

  15. Hexagonal Lattice

  16. Percolation Points - HL

  17. Conclusions • Minimum coupling is needed • Heterogeneity can help the transition from local excitation to global excitation

  18. Further Work • Excite several cells in a larger lattice • Introduce a pacemaker cell • Introduce time-dependence in coupling parameter

  19. Acknowledgements • Hugo van den Berg • Rachel • MOAC

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