Propagation Failure in Excitable Media

We study a mechanism of pulse propagation failure in excitable media where stable traveling pulse solutions appear via a subcritical pitchfork bifurcation. The bifurcation plays a key role in that mechanism. Small perturbations, externally applied or from internal instabilities, may cause pulse propagation failure (wave breakup) provided the system is close enough to the bifurcation point. We derive relations showing how the pitchfork bifurcation is unfolded by weak curvature or advective field perturbations and use them to demonstrate wave breakup. We suggest that the recent observations of wave breakup in the Belousov-Zhabotinsky reaction induced either by an electric field or a transverse instability are manifestations of this mechanism.Comment: 8 pages. Aric Hagberg: http://cnls.lanl.gov/~aric; Ehud Meron:http://www.bgu.ac.il/BIDR/research/staff/meron.htm

Phase Variations in fMRI Time Series Analysis: Friend or Foe?

Functional MRI studies (fMRI) are based on the blood-oxygenation-level-dependent effect (BOLD) that arises in brain areas where neuronal activity takes place (Ogawa et al., 1990, 1993). BOLD induces changes in the local magnetic susceptibility and these can be measured by Gradient Echo (GE) Echo-Planar-Imaging (EPI). The fMRI signal thus observed consists of a complex value, which can be subdivided into a magnitude and a phase value, but in most fMRI studies the phase signal is discarded and only the magnitude changes are used to detect the activated brain areas