B. Spin Echo Sequence in Equilibrium 1. Derive the equilibrium signal for a spin echo sequence; i.e., calculate MxyB. Assume magnetization is spoiled before each successive -pulse (MxyE=0), and that pulses have negligible duration. Hint: treat MzA as unknown and calculate MzB,MzC,MzD,MzE. Use the fact that this is a spoiled sequence! Finally, use the fact that you are in dynamic equilibrium, and so MA=ME. Solve for MzA, and use that to compute MxyB, and show that: MxyB=1+cos()eTR/T1(1+eT1TR2eT1(TR2TE))sin()M0 Note: This gives you the transverse magnetization at point B right after excitation. What you image would be the transverse magnetization a time TE/2 after the 180 pulse; this is simply given by MxyBeT2TE. Because this question is about T1 contrast we confine ourselves to the magnetization at point B (adding the T2 term is not relevant for our subsequent discussion)