Nuclear Magnetic Resonance

Question 1

What is MRI used for and why?

Answer 1

To clinically detect:
* tumours and other abnormalities
* regions of stroke
* bleeding in the brain
* brain injuries

due to its good soft tissue contrast and high spatial resolution

Question 2

Where does MRI signal come from?

Answer 2

Primarily from protons in water: hydrogen which is highly abundant in the body

Question 3

What is put in the walls of MRI scanner rooms?

Answer 3

Iron plates

Question 4

What does NMR focus on and what is used?

Answer 4

NMR focuses on the properties of atomic nuclei

For MRI, our favourite nucleus is 1H (a proton)

Nuclei possess an intrinsic quantum mechanical property called spin

Question 5

What is the angular momentum of a point object of mass m?

Answer 5

L = mv x r

v = linear momentum
r = radius

Question 6

What do elementary particles with angular momentum have and what is the equation for it?

Answer 6

Spin:

S = ħ √ (I (I +1))

I = spin quantum number (either zero, integer or half integer)
ħ = reduced Planck’s constant (h/2π)

Question 7

When will a nucleus have non-zero spin?

Answer 7

If its number of protons and/or neutrons is odd and it will exhibit NMR

Question 8

What are examples of nuclei with non-zero spin?

Answer 8

1H: I = 1/2
2H: I = 1 (odd number of protons and neutrons)
3H: I = 1/2 (odd atomic number)
4He: I = 0 (spins cancel as even)

Question 9

What happens in the absence of an external magnetic field, according to quantum theory?

Answer 9

Knowledge of the magnitude but no knowledge of the direction of the vector at the same time

Question 10

When a magnetic field is applied in z direction, how is the projection of S quantised?

Answer 10

S_z = m_z ħ

m_z = spin projection or magnetic quantum number = 2I + 1

Question 11

What are the possible spin angular momentum projection states for protons?

Answer 11

As I = 1/2 so m_z = (2(1/2) +1) = 2, only 2 possible states: -1/2 ħ (spin down) and 1/2 ħ (spin up)

Question 12

Which spin is less energetically favourable?

Answer 12

spin down as it requires more energy

Question 13

What does a magnetic moment experience?

Answer 13

A magnetic moment in an applied magnetic field experiences a rotating force “torque”:

τ = m x B

also happens when a current loop I enclosing an area

Question 14

What is the magnetic moment of a rotating sphere?

Answer 14

A rotating sphere with uniformly distributed charge and mass will have a magnetic moment given by:
μ = q/2m L

L = angular momentum

Question 15

What is the gyromagnetic ratio γ?

Answer 15

How rotation relates to magnetism for given nucleus (known constant for each nuclear species)

γ = q/2m

Question 16

What is the magnetic moment associated with spin?

Answer 16

μ = γS = γħ √(I(I+1))

(gives size of magnet)

Question 17

What is the projection of μ in the direction z?

Answer 17

μ_z = γS_z = γ m_z ħ

Question 18

What is the direction of the field and what do the other two axis form?

Answer 18

Z axis (magnetic field moves up and down)

Transverse plane: Y and X axis (magnetic field moves side to side)

Question 19

What happens when an external field is applied to a magnetic moment?

Answer 19

A torque is produced:

dμ / dt = μ x γ B

Question 20

What is the solution to the torque produced when an external field is applied to a magnetic moment?

Answer 20

Precession frequency: ω = γ B

Angular frequency which defines MR system

Question 21

What is the energy of a magnetic moment in a static magnetic field of strength B?

Answer 21

E = - μ . B

Along the axis:
E = - μ _z . B = - γ S_z B

Question 22

What do transitions between the two energy levels involve?

Answer 22

The release of a photon at frequency of ΔE = γ ħ B = hf

Question 23

What happens as B increases?

Answer 23

ΔE increases and spin up becomes more preferable as it is at a lower energy level and moves in direction of field (unlike spin down)

Question 24

What is the energy of spin up and spin down in a static field?

Answer 24

Spin down: E = 1/2 γ ħ B

Spin up: E = - 1/2 γ ħ B

Question 25

What is the frequency (equation) that will cause transitions between two energy levels?

Answer 25

f = γB / 2π or (Lamor) angular frequency: ω = γ B (ω = 2π f)

Question 26

What causes transitions between energy levels?

Answer 26

Radio frequency (body is transparent at this frequency)

Question 27

How are the units of gyromagnetic ratios converted?

Answer 27

(γ / 2π = MHz/T) MHz/T divided by 2π = MHz

Question 28

What happens in the absence of an external field to nuclear magnetic moments?

Answer 28

They are aligned randomly and their vector sum is zero

Question 29

How do nuclear magnetic moments get aligned or anti-aligned?

Answer 29

With an external field B Alignment with B is less energy-costly than anti-alignment More nuclei will align parallel with B than anti-parallel

Question 30

What is macroscopic magnetisation?

Answer 30

Once nuclei are aligned with B, a magnetisation is parallel to B this leads to bulk magnetisation which leads to individual spins getting cancelled out (including x and y components)

Question 31

What describes

Answer 31

The distribution of nuclei between energy states in thermal equilibrium N_u / N_d = e^(ΔE/kT) N_u = Number of spin up nuclei N_d = Number of spin down nuclei T = temperature (K)

Question 32

Are there more spin up nuclei or spin down nuclei? What does this lead to?

Answer 32

There is a small excess of N_u spins as they require less energy to align with field This leads to a net macroscopic magnetisation which is the source of the MRI signal

Question 33

What happens to the population energy levels, N_u and N_d when B is increased?

Answer 33

Difference in population increases and the net magnetisation signal increases

Question 34

Why does MRI require large magnetic fields?

Answer 34

To get large population difference and increase net magnetisation

Question 35

How can a response be excited?

Answer 35

If energy is put in at a resonant frequency into the oscillating system

Question 36

What are radio frequency (RF) coils used for?

Answer 36

To transmit signals at the Larmor frequency in the transverse plane

Question 37

How can magnetisation be detected at thermal equilibrium?

Answer 37

Magnetisation can only be detected in transverse (xy) plane, (perp to B_0)

Question 38

Are magnetic moments aligned in the z-direction?

Answer 38

No, they are precessing in the xy plane at the Lamor frequency

Question 39

What does a rotating frame do?

Answer 39

xy plane are continually rotating so net magnetization will appear static and magnetic moment doesn't appear to rotate about z axis

Question 40

After radio frequency is applied, what happens to the rotating frame?

Answer 40

RF magnetic field, B1 is produces which appears static in rotating y direction and the net magnetic field also still appears static in z direction

Question 41

How is the motion of a net magnetic field M in the presence of an applied magnet field described?

Answer 41

By Bloch equations" dM/dt = M x γB With time, the net magnetic field M will drop towards x -axis due to perpendicular force imposed