Title slide

Marc BaghdadiSupervisor: Hugo van den BergCritical Phenomena in a Heterogeneous Excitable System1BackgroundMuscular wall of the uterus (myometrium) only acquires ability to expel the ftus in the final days before labourThis change is believed to be the result of a phase transition from locally excited to globally excited stateCell synchrony is achieved by electrical conduction through gap junctionsR. Smith, Parturition, N Engl J Med, 2007, 356:271-283Aim of the projectTo model the changes in the muscular wall of the uterus in the days before labourInvestigate the spread of induced excitation through the systemThe ModelSmooth muscle cells can be modelled using the Fitzhugh-Nagumo system of equations

v = excitation variablew = recovery variableI = Input current

The Model

vApproach TakenConstruct an (m x n) lattice of cells, each obeying Fitzhugh-Nagumo dynamics, and connected by identical resistorsApproach TakenKLocal Excitation

Global Excitation

Region of Excitation

Removing connections at random

ProbabilityRemoving connections at random

Removing connections at randomPercolation Points

Random Connection Sizes

Hexagonal Lattice

Percolation Points - HL

ConclusionsMinimum coupling is neededHeterogeneity can help the transition from local excitation to global excitationFurther WorkExcite several cells in a larger latticeIntroduce a pacemaker cellIntroduce time-dependence in coupling parameterAcknowledgementsHugo van den Berg

Rachel

MOAC