1. Magnetic Resonance Imaging
FRCR Physics Lectures
Anna Beaumont

2. Basic MR Physics

3. MRI (very brief) summary
MRI imaging consists of placing the patient inside a large magnetic field.
This field causes protons in water molecules to align with/against the field.
Radiofrequency pulses are used to “excite” the protons
Energy subsequently released by these protons is measured and turned into an image

4. How large a field? Tesla - unit of magnetic field strength
Gauss - unit of magnetic field strength
1G = T
Earth’s magnetic field ~ 0.5G or 50μT
MRI scanners ~ 1 – 3T or 10-30kG

5. What types of tissue?
Fluids – cerebrospinal fluid (CSF), synovial fluid, oedema;
Water based tissue – muscle, brain, cartilage, kidney;
Fat based tissues – fat, bone marrow.
Fat based tissues have some special MR properties, which can cause artefacts.
Fluids are separated from other water based tissues because they contain very few cells and have a different appearance on images.
Pathological tissues frequently have either oedema or a proliferating blood supply, so their appearance can be a mixture of water based tissues and fluids.

6. Nuclear Spin The hydrogen nucleus consist of a proton.
Each proton has a positive charge and spins like a top.
This circulating charge is like a small loop of current.
A moving charge has an associated magnetic field.
Proton behaves like a tiny rotating magnet, represented by vectors. Tiny field that is generated is known as its magnetic moment.

7. No external magnetic field
Net Magnetisation
No external magnetic field
Random orientation
 no net magnetisation B0
Apply magnetic field
Majority of magnetic moments align with field (think of a compass needle aligning to the Earth’s magnetic field)
 net magnetisation M0

8. Energy States: the Quantum Mechanically bit
Energy levels related to magnetic field
For a proton there are two states
Spins opposing field are high energy (‘spin down’)
Spins aligned with field are low energy (‘spin up’)
Population difference exists
Slightly more dipoles point spin up than spin down (lazy protons!)
Difference is ~ 3 out of 1 million protons at 1T and S.T.P. (3ppm)

9. increase the difference in population (sensitivity)
by increasing B0 or decreasing temperature

10. Classical Physics Spin causes precession around B0
(Resonance) Larmor frequency:
At 1.5 Tesla and 1H frequency is 63.8 MHz
(Radio-frequency, RF)
At 1.0 Tesla and 1H frequency is 42.6 MHz
( γ= gyromagnetic ratio) B0

11. Tilting of spin axis splits magnetic vector, m, into two components
Longitudinal, mz
Transverse, mxy
Spins align parallel /anti-parallel with B0
Produce net longitudinal magnetisation Mz
Protons precess independently, out of phase
Mxy point in all different directions
Net transverse magnetisation Mxy=0

12. B1 Field Net magnetisation is very small, e.g. 1μT.
Cannot measure whilst lying parallel to B0
Can measure if ‘flipped’ into transverse plan perpendicular to B0
Exchange of energy between two systems at a specific frequency is called resonance.
Protons spin at the Larmor frequency. This frequency is in the Radio frequency (RF) range.
A pulse of RF at the right frequency can be absorbed by the protons and put them in a different energy state, e.g. a spin moves from the lower energy state to the higher one.
The system then relaxes back to an equilibrium state and electromagnetic energy is emitted, which can then be detected and provides a signal.
Same frequency, but fewer photon for 90 degree pulse.

13. Application of B1field (RF pulse)
B1 applied at the resonance frequency
Complicated spiral motion in stationary or laboratory frame of reference B0 B1
Transverse plane

14. Rotating Frame of Reference
Spins are ‘tipped’ into the transverse plane
‘flip angle’,α, is determined by B1 (field strength), tp (duration of pulse)
α = γB1tp
90˚ pulse: flips M0 to transverse plane
180˚ pulse: twice duration/ double strength: flips M0 through 180˚ B0 B1

15. Relaxation Mechanisms I
B1 pulse is then removed
Spins begin to dephase
This is called transverse relaxation or decay B0

16. Recording MR Signal
Receiver coil sees oscillating magnetic field which induces a varying voltage
Sinusoidal waveform without relaxation
Coil measures signal in transverse plane
Only Mxy produces an MR signal, Mz does not.
Because Mxy is produced by tipping Mz the signal produced by the 90˚ pulse depends on Mz immediately before that pulse is applied.

17. z y x (1) without relaxation, signal is sinusoidal
(2) real signal is attenuated (sinc function) due
to relaxation (FID)

18. Free Induction Decay (FID)
The signal at this stage is called the FID.
Relaxation occurs due to interactions between spin-lattice and spin-spin.
FID is attenuated by characteristic relaxation time T2*
Decay envelope due to T2*
Magnitude signal measured in coil

19. T2* Decay T2*  T2 Signal loss called T2* decay
T2 (effective T2) due to inhomogeneities* in B0
T2 (natural T2) due to spin-spin interactions
(Neighbouring protons exert a tiny magnetic field which alters the rate of precession, causes dephasing)
Summation of both effects:
*Even if the magnet were perfect, the presence of the patient will always cause local inhomogeneities
T2*  T2
Dephasing occurs because some spins precess faster than others as a result of the static field inhomogeneities. 180 flips so that ones ahead are now behind and vice versa. The spins behind will catch up as they are still exposed to the same field inhomogeneities that cause the difference in the first place. The 180 pulse cannot compensate for variable field inhomogeneties that underlie spin-spin.

20. T2 Decay (Spin-Spin) Mxy is magnetisation in transverse plane
After 90° pulse it is at maximum value M0
Decays to zero as
t  
At t = T2 signal is 37% (e-1) of initial value
T2 values are unrelated to field strength
So after T2, lost 63% of its original value.

21. Causes of Spin-Spin Relaxation
Local variation of magnetic field is greatest in solids & rigid macromolecules
Dipoles in compact bone, tendons, teeth dephase quickly → very short T2
Effect is least in free water, urine, CSF. Lighter molecules in rapid thermal motion – smoothes out local field → long T2
Water bound to surface of proteins & in fat have a shorter T2 than free water

22. Relaxation Mechanisms II
Spins return to equilibrium
Spin-Lattice relaxation
This is called T1 relaxation or recovery
This requires a loss of energy B0

23. T1 Recovery (Spin-Lattice)
Mz is magnetisation in longitudinal plane
After 90° pulse it is zero
Recovers to maximum value M0 as t  
At t = T1 signal is 63% (1-e-1) of M0
T1 increases as B0 increases

24. Causes of Spin-Lattice Relaxation
Large, slow moving molecules most effective at removing energy from excited dipoles
Fat, also water bound to surface of proteins→ short T1
Small, lightweight molecules ineffective at removing energy from excited dipoles
Water, urine, CSF → long T1
Atoms in solids are relatively fixed and least effective at removing energy
Bone, teeth →very long T1

25. Typical Relaxation Times
Material
T1 (ms)
T2 (ms)
Fat
250 80
Liver
400 40
White Matter
650 90
Grey Matter
800
100
CSF
2000
150
Water
3000
Bone, Teeth
Very long
Very short
*Abnormal tissue has higher PD, T1 & T2 than normal tissue, due to increased water content or vascularity

26. Summary 90° excitation pulse B1 Spins tipped into xy plane→ in phase
B1 removed
Spins dephase (T2*)
Spins return to alignment with B0 (T1)
T2 is tissue-specific & always shorter than T1
Process repeated hundreds of times to make an image

27. Signal Characteristics
Peak signal is proportional to (and pixel brightness depends on):
Proton density (no. of protons per mm3) in the voxel.
Gyromagnetic ratio of the nucleus
Static field strength, B0

28. Ref: From Picture to Proton, McRobbie et al

29. Signal Characteristics
Only mobile protons give signals – those in large molecules or effectively immobilised in bone do not
Greater part of signal due to body water (free or bound to molecules)
Air produces no signal and is always black.
Fat has a higher PD than other soft tissues
Grey matter has a higher PD than white matter
However; tissues do not vary greatly in PD

30. Spin-Echo Sequence T2 decay can be reversed in a spin-echo experiment
Initial 90° pulse
Dipoles in phase
Dipoles begin to dephase, at different speeds, some lag
180° refocusing pulse reverses the sense of the spins
Refocus to produce the echo
Signal has decayed by T2 only

31. Spin-Echo 1. Spins dephase: fast and slow 2. Apply 180° at t = TE/2
3. Echo at t = TE

32. FID refocused to give
Spin-Echo
T2 decay
T2* FID
Time TE/ TE
RF ° °

33. Contrast in MRI
MRI offers excellent soft-tissue contrast which can be manipulated.
T2 contrast can be altered by varying the echo-time (TE).
T1 contrast can be altered by varying repetition time (TR)
Time between two 90º pulses
Flip angle, α, can also be varied (Gradient echo imaging – see lecture 6)

34. Image Contrast (‘weighting’)
For T2-weighted imaging
Use a long TE and long TR
Often known as ‘pathology’ scans because collections of abnormal fluid are bright against the darker normal tissue.
For T1-weighted imaging
Use a short TR and short TE
Often known as ‘anatomy’ scans as they show most clearly the boundaries between tissues.
To minimise either the above effects
Long TR and short TE
Image signal now determined by the density of spins present i.e. Proton density weighted.
In gradient-echo sequences the ‘flip angle’ is also varied (more on that in lecture 6)
However; TE cannot be so long that it obscures the background noise.

35. Fat-Water: T2 Contrast T2-weighting is controlled by TE
Water appears brighter than Fat
Mxy
time TE

36. Fat-Water: T1 Contrast T1-weighting is controlled by TR
Water appears darker than Fat Mz
time TR

37. The Opposing Effects of T1 & T2
T1 & T2 are mutually antagonistic
Tissues with long T1 often have long T2 & vice versa.
Images cannot be weighted for T1&T2
If TE & TR not chosen correctly, tissues with different relaxation times can produce equal signal
With respect to the diagram – with a shorter TE than this, the image tends to be T1-weighted and with a longer TE it tends to be T2 weighted.

38. Choice of TR & TE for conventional SE sequence
TE is always shorter than TR
A short TR usually < 500 ms
A long TR usually >1500 ms
A short TE usually < 30ms
A long TE usually > 90ms
Choice of TR & TE for conventional SE sequence TR TE
Short (< 40ms)
Long (>75 ms)
Short (< 750ms)
T1 weighted
Not useful
Long (> 1500 ms)
PD-weighted
T2 weighted
From Picture to Proton

39. Example in Brain T2-weighted T1-weighted PD-weighted
In a PD image, grey matter (higher PD) appears brighter than white matter.
In a T2-weighted image grey matter (longer T2 and higher PD) is brighter than white matter
In a T1 weighted image, white matter is brighter than grey matter, but its shorter T1 is counteracted by its lower PD.
T2-weighted
FSE: TE/TR = 100 ms/4 s
T1-weighted
SE: TE/TR = 9/380 ms
PD-weighted
FSE: TE/TR = 19 ms/3 s

40. Example in Prostate
T2-weighted
PD-weighted

41. Summary: important points
MRI measures the hydrogen content of individual voxels in each transverse slice of the patient & represents it as a shade of grey or colour in the corresponding image pixel on the screen
The patient is placed in a strong electromagnetic field for an MRI scan
Hydrogen nuclei (protons) in the body align themselves parallel or antiparallel with the magnetic field

42. Summary: important points
For each transverse image slice, a short, powerful radiosignal is sent through the patient’s body, perpendicular to the main magnetic field.
The hydrogen nuclei, which have the same frequency as the radiowave, resonate with the RF wave.
The hydrogen atoms return to their original energy state, releasing their excitation energy as an RF signal, (the MR signal), when the input radiowave is turned off. The time this takes, relaxation time, depends on the type of tissue.

43. Summary: important points
The time and signals are computer analysed and an image is reconstructed.
Soft tissue contrast is high. The range of T1 and T2 values in soft tissue is even wider than the range of CT numbers.
Bone and air do not produce artefacts.
MRI is non-invasive, contrast media being required only for specialised techniques
Ionising radiation is not involved.