MRI Basics

Question 1

How are the different energy levels needed to make a signal created in an MRI scanner?

Answer 1

Conventional MRI looks at H nuclei (protons)
When the protons are placed in a magnetic field, the interaction between the applied field and the nuclear dipole moment creates the different energy levels

Question 2

What is the gyromagnetic ratio for a proton?

Answer 2

g=2.6752x10^8 rad/s/T

Question 3

What is the equation for the energy difference between the two quantum levels in a proton in a magnetic field?

Answer 3

dE = (ghB)/2*pi

g = gyromagnetic ratio
h = plank's contant
B = applied magnetic field

Question 4

Briefly explain how a signal is created in an MRI scanner in terms of the quantum energy levels

Answer 4

Patient placed in magnetic field.
Protons in the patient either align with (stable, low energy state) or against (unstable high energy state) the magnetic field and occupy different energy levels.
RF wave, with energy equal to energy difference in levels, emitted by the scanner into the patient.
Lower energy protons absorb RF waves and transition to high energy level.
Protons in higher energy level eventually decay back to lower energy level, emitting same frequency RF that was absorbed.

Question 5

Briefly explain how a signal is created in an MRI scanner in terms of the net magnetisation vector.

Answer 5

B0 field aligns protons to the z-axis.
B1 field *supplied by magnetic component of RF wave at Larmor frequency) causes net magnetisation to precess about z-axis, and tilts it into x-y plane.
Rotation magnetisation induces a current in a suitably placed coil.
Generates MR signal.

Question 6

What is free induction decay (FID)?

Answer 6

The loss of signal due to relaxation of the net magnetisation vector in the x-y plane.

Question 7

Spin-Spin relaxation is characterised by which time constraint?

Answer 7

T2

Question 8

Spin-Lattice relaxation is characterised by which time constraint?

Answer 8

T1

Question 9

What is the cause of T2 (spin-spin) decay?

Answer 9

T2 decay is caused by the incoherent exchange of energy between nuclei

Question 10

What is the equation for spin-spin decay?

Answer 10

M(t) = M(0)exp(-t/T2)

Where M is the component of the magnetisation in the x-y plane

Question 11

What is the cause of T1 (spin-lattice) decay?

Answer 11

T1 decay is caused by the loss of energy from the nuclei to their surroundings.

Question 12

For a 90 degree pulse, what is the equation for T1 decay?

Answer 12

M(t) = M(0)[1-exp(-t/T1)]

Where M is the component of the magnetisation in the z-axis.

Question 13

For a 180 degree pulse, what is the equation for T1 decay?

Answer 13

M(t) = M(0)[1-2exp(-t/T1)]

Where M is the component of the magnetisation in the z-axis.

Question 14

Which time constant is shortest? T1 orT2?

Answer 14

T2 is shorter than T1.

Question 15

Describe the energy levels of the hydrogen nucleus in terms of the gyromagnetic nucleus, and the magnetic field strength? What is the energy of a radiowave of frequency ω?

Answer 15

The lower energy level is –γhB0/(4π) and the higher energy level is + γhB0/(4π) . The difference between the two energy levels is therefore γhB0/(2π).

Ew=hw/2π

Question 16

How would on-resonance magnetisation that has been rotated into the transverse plane appear in the rotating frame?

Answer 16

It would appear to be a stationary vector (the frame rotates at the resonant frequency)

Question 17

Briefly describe the two principal types of relaxation that can occur after spin excitation

Answer 17

They are T2 relaxation (spin-spin or transverse relaxation) and T1 relaxation (spin-lattice or longitudinal relaxation).

T2 relaxation occurs because of incoherent exchange of energy between nuclei, whereas T1 relaxation occurs due to loss of energy from the nuclei to their surroundings.

Question 18

For a spin with a T1 relaxation time of 2000ms, what is the longitudinal magnetisation after 500ms following a 180 degree pulse? What about after 10000ms (10s)?

Answer 18

Mz(500ms)/M0 = 1-(2 * exp(-500/2000)) = 1 – (20.779) = -0.56Mz(10s)/M0 = 1 – (2 exp(-10000/2000)) = 1 – (2* 0.007) = 0.987 (i.e. nearly fully relaxed).

Question 19

Describe what happens to the net magnetisation when an r.f. pulse is applied at the Larmor frequency.

Answer 19

The net magnetisation precesses around B1 with the result that for a pulse of appropriate length and duration, the net magnetisation will be tipped into the transverse plane.