Basics of NMR

Question 1

All quantum particles and nuclei have a quantum mechanical property called spin. What is the spin quantum number and what values can it take?

Answer 1

I = 0, 1/2, 1, 1 1/2, 2 ...
I = 0 up in half integer steps

Question 2

What values of spin quantum number do nuclei need to perform MRI/NMR?

Answer 2

Spin induces a magnetic moment in the nuclei, which will interact with the applied magnetic field. Thus, only nuclei with non-zero spin can be used.

Question 3

What is the spin of H1 (proton)?

Answer 3

I = 1/2

Question 4

Quantum Mechanically, what happens when a nucleus with non-zero spin is placed in an applied magnetic field?

Answer 4

The ground state energy level splits into (2I+1) energy levels

Question 5

How many energy levels does H1 (proton) have in an applied B0 magnetic field? And What is the expression for their energies?

Answer 5

2 Energy Levels:
E1 = - gamma h B0 / (4pi)
E2= + gamma h B0/ (4pi)

Question 6

What is the difference in energy between the two H1 energy levels/ Quantum energy Gap. What are the energy levels proportional to?

Answer 6

Diff E = gamma h B0/(2pi)

The energy levels are proportional to the strength of the applied magnetic field B0

Question 7

Different numbers of nuclei will exist in the different states. What is the physical meaning of nuclei existing in either of the two states?

Answer 7

E1 is the lower energy state. Nuclei in this state have their magnetic moments aligned with B0

E2 is the higher energy state and have their magnetic moments aligned against B0

Question 8

Which state is the most stable? And which would you expect most nuclei to be in without an input of energy?

Answer 8

E1

Question 9

What does gamma stand for in the energy equations for the nuclei states?

Answer 9

Gyromagnetic ratio (Just a property of the nucleus)

Question 10

Under what condition can a nucleus transition from E1 to E2?

Answer 10

The Bohr Condition: Only if the nucleus absorbs the energy of a photon with exactly E-diff, will it excite to E2.

Question 11

What is the expression for the energy of the radiowave that we use to excite nuclei from E1 to E2

Answer 11

Ew = h.w/2pi

Question 12

Equating Ediff and Ew, what is the frequency of radiowave required to excite nuclei from E1 to E2?

Answer 12

Wo = gamma . B0

Question 13

What is the Larmor frequency physically and what is it’s expression?

Answer 13

The Larmor frequency is the frequency of the radiowave required to excite nuclei from E1 (aligned with B0) to E2 (opposed to B0). Only this exact frequency will do it due to the Bohr condition and quantisation of nuclear energy levels when nuclei are inside B0.

The expression is:
W0 = gamma . B0

Question 14

What is the magnetisation vector (M)?

Answer 14

The vector sum of all magnetic dipole moments of all nuclei. (M) Or in other words the net vector of all magnetic moments. M is basically the net difference between the number of nuclei aligned with or against B0. Normally M=0 when B=0. Otherwise when B=B0, M=M0

Question 15

In the presence of only B0, what direction dose the net magnetisation vector point?

Answer 15

Parallel to B0, in the positive z axis (defined by B0)

Question 16

At what frequency must the RF pulse be applied?

Answer 16

The Larmor frequency (gamma B0)

Question 17

What does an RF pulse of this frequency generate?

Answer 17

A magnetic field B1 perpendicular to B0, that oscillates at the larmor frequency. A component of B1 rotates around z due to the oscillation

Question 18

What effect does an oscillating B1 field have on the effective field?

Answer 18

The effective field Beff = (B0 + B1) and now is not perfectly aligned with z. It also rotates around z at the larmor frequency due to B1

Question 19

What effect does the oscillating B1 field have on the net magnetisation vector M? (Also through the effect on the effective magnetic field )

Answer 19

M is now misaligned with Beff and feels a torque, causing it to precess around the effective field. This causes M to tip downwards as it precesses around B1. This also causes M to now rotate around the z axis at the Larmor frequency (following Beff and B1 in their rotation). The resulting motion around both B0(Z) and B1 axes is a complex 3D precessional spiral.

Question 20

What is the motion of M in the rotating reference frame?

Answer 20

It is stationary in the x-y plane but rotates around B1 in the z-y plane, from z to -y.

Question 21

What happens to the axes and B0 and B1 in the rotating reference frame?

Answer 21

B0 disappears, B1 appears stationary, and the x-y axes must rotate at the larmor frequency to achieve this

Question 22

What happens if spins rotate at a lower frequency than the larmor? And what if they rotate at a higher frequency in the RRF?

Answer 22

Spins at a faster rotational frequency than w will develop an anti-clockwise angle, whilst spins at a lower frequency develop a clockwise angle.

Question 23

Can we measure the longitudinal magnetisation Mz?

Answer 23

No, B0 could be 1.5 or 3T whilst M might only be of the order ~ uT.

Question 24

What is the signal we actually measure? And what is it’s strength proportional to?

Answer 24

In the lab frame Mxy is rotating around the z axis at the larmor frequency. If this is placed inside coils then this oscillating magnetisation acts like a dynamo, inducing a voltage and current. The voltage is the NMR signal measured.

The strength is proportional to the Mxy vector

Question 25

What is the name of the signal measured?

Answer 25

The Free Induction Decay (FID)

Question 26

What are the two main relaxation mechanisms, what constants are they characterised by, and component of M do they control the decay/relaxation of?

Answer 26

Spin-Spin relaxation defined by a time constant T2. The shorter T2 the quicker the relaxation. This governs the relaxation/decay of Mxy from 1 to 0.

Spin-Lattice relaxation defined by T1. Again, the shorter T1 the quicker the relaxation occurs. This governs the relaxation/growth of Mz from 0 or -1 to 1.

Question 27

What is T2* and what causes it?

Answer 27

T2* is caused by inhomogenities (spatial) in the B0 field. They are caused by tissue structure inhomogeneities. It causes the relaxation of Mxy, and so accelerates the total T2 effect.

Question 28

What causes T2?

Answer 28

Spin-Spin relaxation is caused by molecular motion of the spins exposing and shielding each other from stronger and weaker B0 field strengths. In other words temporal inhomogenities in B0.

Question 29

Which of T1, T2, and T2* is fastest and thus which determines the decay of the FID measured?

Answer 29

T2* is faster than T2 which is always faster than T1. Thus, FID decay is determined by T2* (unless T2* is removed by Spin-Echo Imaging, in which case it’s T2)

Question 30

What general shape of T1, T2, and T2* relaxation and what is their equations?

Answer 30

They are all exponential decay functions.

T2: Mxy(t) = Mxy(0) exp(-t/T2)

T2: Mxy(t) = Mxy(0) exp(-t/T2)

T1: Mz(t) = Mz(0)[1 - exp(-t/T1)] (90 deg Flip)

T1: Mz(t) = Mz(0)[1-2exp(-t/T1)] (180 deg Flip)

Question 31

Considering we only measure the signal from Mxy, what is the simplest possible image sequence?

Answer 31

Pulse -Collect:
This involves applying an RF to apply B1 long enough to flip the spins 90 degs so that all magnetisation is in Mxy. Then we acquire the signal

Question 32

After applying B1 long enough for a 180 deg flip (twice the time for a 90 deg flip), do we measure a signal immediately?

Answer 32

No, all the magnesiation is in Mz=-M0, nothing is in Mxy immediately at t=0.