Meeting Banner
Abstract #4184

Linear Sweeps Generate Extreme Echoes: Explanation, Generalization

Patrick H. Le Roux1, Brice Fernandez2

1Applied Science Lab, GE Healthcare, Palaiseau, France; 2Applied Science Lab, GE Healthcare, Munich, Germany

When a train of RF pulses with constant nutation is modulated in phase according to a periodic quadratic law, a refocusing for all the three components of magnetization (Extreme Echo) is generated at the end of the modulation or after two periods if the period is odd. This was first observed experimentally and also demonstrated mathematically . But that demonstration lacks any physical meaning. We propose here a simple geometrical explanation in which the symmetries of the echo to echo rotation plays an essential role. This remark leads to more general phase modulation having the same property.

Keywords

accept according adapted almost announced another anti applied axis block blocks choose circularly close collection combining complicate composed condition continuity created cycle cycles demonstration depicts deviate dispersed easy echoes eliminate equalization equidistant equivalent even example exercised explanation extreme finds form generalization generalized generally generate generates generating genesis half hence indeed index indicated integers interleaved iterating kernel kind lasting leads length linear mathematically meeting middle modulation moreover much namely natural necessary note noted nutation offset offsets painful peel perfect period periods permuting phenomenon physical position precession previous proportional proton protons pulse pulses quadratic quasi ranging receiver refocusing relies rotation rotations science scientific sees signed simple space step still striking strong suffices suite sweep sweeps swept symmetrical symmetry theory train transform uniformly units whose