Basics of NMR Flashcards
What do nuclei have that mean we can detect them?
What happens when we place nuclei in external magnetic field
QM and classical analogy
Nuclei have spin, QM property. If spin is non-zero the nucleus has a magnetic moment which we can detect with MR.
When you apply Bo there is an interaction between applied field and nuclear dipole moment, creating different energy levels. Number of energy levels = (2I+1), spin I is normaly 1/2 or -1/2.
Separation of energy levels is dependent on magnetic field strength. E1 = -yhBo/4pi.
QM, magnetic field has introduced splitting of energy levels due to the fact that spin can be 1/2 or -1/2. Classically, compas needles can align parallel or anti-parallel with the field, with parallell being the lower energy, more stable state.
What happens if you apply energy to nucleus in Bo?
How do you do this, what condition must be met?
eqn
Apply energy in the form of EM radio-wave, it can be absorbed and change the energy level of the nucleus.
NB// frequency, w, must exactly match the difference in energy level of the two states. (Bohr condition)
- RF, E = hw/2pi
- delta E = yhBo(2pi)
- wo = yBo LARMOUR FREQUENCY
Later, when nucles returns to low-energy state, energy is given out.
Classical picture
Bulk view of magnetisation under Bo
Under Bo, dipole moments allign parallel or anti-parallel with the field.
Because of Boltzmann distribution, there is a net magnetisationm Mo parallel to Bo.
Graphical view
What happens to Mo when you apply Bo along z-axis?
What happens when you apply RF?
What trick do we use to visualise it on paper?
Net magnetisation M alligns along z-axis.
RF generates oscilating magnetic field rotating around z-axis in x-y plane. The result is that the net B vector is no longer parallel to z, and causes M to process around B1, and rotates into x-y plane.
90 deg pulse is a RF pulse that is applied strong enough and long enough to rotate M by 90degrees into x-y plane.
Best to visualise in rotating frame of reference, spin the axis round a fL
What forms the MR signal?
What’s a FID?
Magnetisation rotating in x-y plane induces current in reciever coil (placed 90 degrees to Bo).
Signal cannot last indefinetely, decays due to relaxation, FID.
Relaxation processes
T2
T1
Alternate name for them?
What causes them?
T2 Spin-Spin (transverse) Relaxation -
- Decay of Mxy caused by incoherent echange of energy between spins.
- Exponential decay with time constant T2. Mxy(t) = Mxy(0) e-t/T2.
- Visualise this as spins getting out of phase with each other, spreading out in x-y plane, reduced net magnetisation.
T1 spin-lattice (longitudinal) relaxation
- Magnetisation vector returns to eqm state alligned along Bo, caused by loss of energy from nuclei to surrounding lattice
- Exponential process with time constant T1
T1 relaxation after a 90 deg pulse, eqn, describe
T1 relaxation after a 180 deg pulse, eqn, describe
Mxy = Mo, Mz = 0.
Mz(t) = Mo[1-e-t/T1]
Starting at zero, exponential increase as spins loose energy to lattice and allign back to lower energy state parallel to Bo.
Mxy = 0, Mz = -Mo.
Mz(t) = Mo[1-2e-t/T1]
Starting at -Mo, exponential increase through x-axis, back up to mo.
Why is FID always faster than you expect (T2*)
Which is shorter T2, or T1?
You actually decay via T2*
T2 is always shorter than T1.
Pulse collect sequence
Components,
Describe
RF, acquire after RF listen to FID.
Simplest possible sequence to record signal. Initial pulse rotates Magnetisation intro transverse plane, where the FID is detected and sampled during acquisition.
Spin-Echo Experiment
Pulse diagram
What’s going on?
How is this related to T2 & T2*
- Initial 90 deg RF pulse
- after TE/2 a second 18 deg pulse
- After TE/2 accquire signal
(0 feg pulse tips M into x-y plane, free precession. But imperction in Bo means some spins process faster or slower than the rotating reference frame. Spreading out spins in x-y plane (reduction of signal amplitude). Second RF plane flips spins/flips axis and now spins are converging again (increasing signal). Re-phasing of magnetisation vectors in x-y plane = echo.
Undo the relaxation casued by inhomogeneities in the b-field, now probing T2 nor T2*.
