Answers to Problem Set #1
  1. The flip angle produced by an RF pulse depends on its duration and intensity. If the frequency is off, that will affect the flip angle as well. The phase is irrelevant because only the z-magnetization of the sample will be affected.
  2. The MR signal arises from the protons of atoms.
  3. Hydrogen is the nucleus used because i) it has a nonzero spin, ii) it is a common atom, and iii) it has a large Larmor constant. With regards to the other answers, all nuclei are small, and there are 6.255e23 of anything per mole.
  4. Absent a magnetic field, hydrogen nuclei are not oriented in a preferred direction.
  5. The purpose of the magnet is to orient the protons in a preferred direction.
  6. B0 refers to the strength of the static magnetic field.
  7. With application of B0, nuclei precess about the B0, flip from spin up to down, and reach an equilibrium that depends on temperature. The precession is not necessarily orthogonal. There was no phase coherence to start with. Since there is no phase coherence, there is no signal.
  8. The net difference between parallel and anti-parallel is small.
  9. F = gamma * B0
  10. Once nuclei are aligned with the main magnetic field, an RF pulse at 90 degrees to the static magnetic field is used to change the orientation of the protons.
  11. T2* is the signal decay rate due to field inhomogeneity.
  12. tr=400, te=10

SIgray = k(1-exp(400/600))*exp(10/80) Å .4294 (Ignoring k)

Siwhite = k(1-exp(400/500))*exp(10/70) Å .4774

SIgray/SIwhite = 0.8995

tr=3000, te=90

SIgray = k(1-exp(3000/600))*exp(70/80) Å .3225

Siwhite = k(1-exp(3000/500))*exp(70/70) Å .2758

SIgray/SIwhite = 1.169