MRI

Question 1

What sort of nuclei possess spin angular momentum, J

Answer 1

Nuclei with odd number of protons, neutrons or both

Question 2

Magenetic moment equation,Mu

Answer 2

Mu = (gyrometric ratio)(spin angular momentum)

Question 3

Precession torque equation

Answer 3

tau = mu x B = (mu)Bsin(theta)

Question 4

Why does precession occur

Answer 4

nuclear magnetic moment in a magnetic field experiences torque

Question 5

Larmor equation

Answer 5

Frequency of precession
w= (gyrometric ratio)(Applied magnetic field - B0)

Question 6

Magnitude of spin angular momentum

Answer 6

|J| = hbar [I(I+1)]^(1/2)
Where I is spin quantum number

Question 7

How many spin states denototed by spin quantum number

Answer 7

(2I+1)

Question 8

Potential energy of magnetic moment

Answer 8

work done rotatinf magnetic moment in B-field

E = -(mu).B = -(gyrometeric ratio)(J in Z direction)(B0)

Question 9

How is spin state distributed in thermal equilibrium

Answer 9

seperated by deltaE according to Boltzman distribution

ndown/ nup = exp(-deltaE/ KbT)

Question 10

Spin state distribution in the high temperature limit

Answer 10

ndown/ nup = 1-([(hbar)(gyrometric const)(B0)]/KbT)

Question 11

Why can magnetisation within a material be detected by NMR

Answer 11

Population differences arisen by small excess of spins in the low energy state causes a net bulk magnetaisation in a material - can a;sp be increased by using a static magnetic field to polarise nuclear spins

Question 12

At what angle fo spins precess to the Z-axis at random phase

Answer 12

54degrees

Question 13

What is the bulk magnetisation in NMR

Answer 13

M = sum of spin magnetic moments

Question 14

Safety issues of static field

Answer 14

Projectile effect
Moving in spatial static fields causes the body to experience varying fields causing dizziness, metallic taste and flashing light sensation

Question 15

What is the Larmor frequency at 1T

Answer 15

42.57MHz

Question 16

How RF excitation occur in NMR (QM)?

Answer 16

• Applying RF energy spins tips spins and brings into phase Causing MO to be tipped from the longitudinal plant to the transverse plant

Question 17

What does a 90degree pulse do?

Answer 17

equalizes the population of spin states and brings spins into phase

Question 18

How RF excitation occur in NMR (CM)?

Answer 18

Apply B field oscillating at frequency ~ Larmor frequency and oriented in Bz direction

Question 19

What is the purpose of applying a magnetic field oscillating at a frequency in NMR or MRI experiments?

Answer 19

To excite the magnetization in the sample, particularly by aligning with the Larmor frequency.

Question 20

What is the total B1 field expression, and why is the anticlockwise rotating component neglected?

Answer 20

The total
B1(t) = 2B1cos(wt)i
​
cos(ωt)i, and the anticlockwise component Ba(t) is neglected due to being off-resonance.

Question 21

How does the rotating frame of reference simplify the analysis of the B1 field in NMR or MRI experiments?

Answer 21

It allows for the consideration of the B1 field as stationary for the component at
+ω1
+ω1, simplifying the analysis while the component at −ω1rotates at −ω2 and can be ignored due to being off-resonance.

Question 22

How do you relate the lab frame and kav frame

Answer 22

• z’ = z
• x’ rotating at frequency  with respect to x.
• y’ rotating at frequency  with respect to y

Question 23

What is the relationship between the rate of change of a vector in the lab frame and rotating frame?

Answer 23

The relationship is given by
dr/dt =
(w × r) +(∂r/∂t)

Question 24

How is the magnetization described in the rotating frame?

Answer 24

In the rotating frame, the magnetization is described by
dM/dt = Gyrometeric ratio(M x (B+(w/t))

Question 25

What is the effective field experienced by the magnetization in the rotating frame?

Answer 25

The effective field Beff is given by Beff = (B0 - wRADIOFREQ/ gyrometric ratio)+B1

Question 26

What does the effective field represent in the rotating frame?

Answer 26

In the rotating frame, the magnetization precesses around the effective field B eff

Question 27

What does 'on resonance' mean? What does this cayse

Answer 27

RF field is applied at Larmor frequency of spins Effective field in rotating frame of Beff is aligned w x' axis

Question 28

What does 180 pulses do

Answer 28

Flips magnetisation to -z Called inverted Pulse can refocus magnitisation

Question 29

What do 90 degree pulses do?

Answer 29

Flips magnetisation to xy plane called excited or saturated After 90 degree, Mz=0 and Mxy = M0

Question 30

What does a tip/flup angle pulse (Alpha) acting on equilibrium magnetisation do?

Answer 30

Reduces Mz from M0 to M0cos(alpha) Increases Mxy to M0sin(alpha)

Question 31

What are the safety issues of radiofrequencies?

Answer 31

- Tissue heating - More dangerous in poorly perfused organs -Pt to be kept in low humidity - skin burns

Question 32

Steps of signal detection

Answer 32

90degree pulse tips magnetisation into x-y plane (phase coherence) RF pulse is switched off Transverse xy magnetisation caused by pulse, processes about B0 at larmor freq Rotating magnetisation causes oscillating emf Causes pick up coil in receiver to be tuned to RF freq

Question 33

What is Phase sensitive detection?

Answer 33

PSD is a technique used to compare the signal from precessing spins with a reference frequency, allowing for the digitization and storage of only the frequency difference, typically in the audio range.

Question 34

Why is the oscillator frequency (ω0) generally set to be approximately equal to the mean Larmor frequency (ωL) of the sample? in PSD

Answer 34

Setting (ω0) close to (ωL) simplifies the detection and analysis of the signal by focusing on the difference between these frequencies, which is critical for imaging encoding and spectroscopy.

Question 34

What does the exponential decay rate T2∗ indicate in the context of FID?

Answer 34

T2∗ represents the rate at which the signal decays due to inhomogeneities in the magnetic field and interactions within the sample, with the signal typically decaying to nothing in a time equal to 5T2∗

Question 34

What is the purpose of Quadrature Phase Sensitive Detection in NMR?

Answer 34

Quadrature Phase Sensitive Detection allows for the distinction between positive and negative frequency differences relative to a reference, enhancing the analysis of NMR signals.

Question 35

How does Quadrature Detection work?

Answer 35

It employs two PSDs with a 90-degree phase shift between reference signals, enabling the separate detection of real and imaginary components of the signal, which correspond to the cosine and sine of the frequency difference, respectively.

Question 35

What is Free Induction Decay (FID) in NMR?

Answer 35

FID is the signal detected in NMR that oscillates at the difference between the Larmor and oscillator frequencies (ωL−ω0)and decays exponentially with a characteristic time T2∗

Question 36

3 Steps of a MRI scanner

Answer 36

1 - Production of RF pulses 2- Signal Detection 3- Gradient

Question 37

How do MRI produce signals

Answer 37

Computer send pulse to waveform controller. Frequency synthesiser produces RF freq (usually set at Larmor freq) Multiplied by RF pulse envelope in mixer giving RF pulse consisting of an RF carrier frequency modulated at audio-frequencieS pulse is then passed to an RF amplifier before being sent to the RF coil

Question 37

How do MRI detect signals?

Answer 37

Reference signal from synthesiser is passed through quadrature splitter producing two reference signals at 90 degrees out of pjse Signal detected by RF coil sends pre amp- so SNR is dominated by coil and sample not electronics mixed with ref signals in two quadrature phase sensitive detectors - demodulated signals to audio frequencies Sent to two analogue digital converters and sent to computer to be processed and stored

Question 37

What are gradients in MRI?

Answer 37

Gradients encode image information Waveform controller produces analogue gradent waveforms amplified by gradient amplifiers,