Magnetic Resonance Imaging

FRCR Physics Lectures

Anna Beaumont

Basic MR Physics

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

How large a field?Tesla - unit of magnetic field strengthGauss - unit of magnetic field strength1G = 0.0001 T

Earth’s magnetic field ~ 0.5G or 50μT

MRI scanners ~ 1 – 3T or 10-30kG

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.

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.

No external magnetic field

Random orientation

no net magnetisation

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

B0

Net Magnetisation

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)

0BE

E

NN exp

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

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

00 B

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

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.

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

www.olympusmicro.com

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˚

B1

B0

Relaxation Mechanisms I

B1 pulse is then removed

Spins begin to dephase

This is called transverse relaxation or decay

B0

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.

(1) without relaxation, signal is sinusoidal

(2) real signal is attenuated (sinc function) due to relaxation (FID)

z

y

x

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*

Magnitude signal measured in coil

Decay envelope due to T2*

T2* DecaySignal 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

'

11

*

1

222 TTT T2* T2

T2 Decay (Spin-Spin)

0

0.2

0.4

0.6

0.8

1

0 100 200 300 400 500TE (ms)

Mxy

(a

.u.)

20

Tt

xy eMM

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

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

Relaxation Mechanisms II Spins return to equilibrium

– Spin-Lattice relaxation

This is called T1 relaxation or recovery

This requires a loss of energy

B0

T1 Recovery (Spin-Lattice)

0

0.2

0.4

0.6

0.8

1

0 100 200 300 400 500

TR (ms)

Mz

(a.u

.)

)1( 10

Tt

z eMM

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

Causes of Spin-Lattice RelaxationLarge, 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

Typical Relaxation TimesMaterial T1 (ms) T2 (ms)

Fat 250 80

Liver 400 40

White Matter 650 90

Grey Matter 800 100

CSF 2000 150

Water 3000 3000

Bone, Teeth Very long Very short

*Abnormal tissue has higher PD, T1 & T2 than normal tissue, due to increased water content or vascularity

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

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

Ref: From Picture to Proton, McRobbie et al

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

Spin-Echo SequenceT2 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

Spin-Echo

1. Spins dephase: fast and slow

2. Apply 180° at t = TE/2

3. Echo at t = TE

T2* FID

T2 decay

FID refocused to giveSpin-Echo

Time 0 TE/2 TE

RF 90° 180°

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)

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)

Fat-Water: T2 Contrast T2-weighting is

controlled by TE Water appears

brighter than Fat

TE

time

Mxy

Fat-Water: T1 Contrast

TR

time

Mz

T1-weighting is controlled by TR

Water appears darker than Fat

The Opposing Effects of T1 & T2T1 & 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

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

Example in Brain

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

Example in Prostate

PD-weightedT2-weighted

Summary: important pointsMRI 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

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.

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.