1

Magnetic Resonance Imaging

Pål Erik Goa Associate Professor in Medical Imaging

Dept. of Physics pal.e.goa@ntnu.no

2

Why MRI?

•  X-ray/CT: –  Great for bone structures and high spatial resolution –  Not so great for soft tissue.

•  Ultrasound: –  Great for real-time imaging, quick and easily available. –  Not so great in terms of spatial resolution, and for imaging behind

bones/air. •  Magnetic Resonance Imaging:

–  Great for soft tissue, in particular brain! –  Not so great for bones and close to metal implants –  Spatial resolution ~1 mm.

3

MRI: Main components

•  Requires a large magnet to put the patient in (expensive and potentially dangerous).

•  The signal is coming from the hydrogen nucleus (proton) -> water (fat).

•  Radio frequency antennas (coils) are used for transmitting and receiving the signal.

•  Additional coils for generating gradients in the magnetic field needed for spatial localization/coding.

•  Signal is acquired in Fourier-space.

4

The Magnet

5

A closer look

•  Magnet coils: –  Superconducting wire at 4.2 K creating a strong magnetic field

(typically 1.5-3.0 T) •  Shim coils:

–  Fine adjustment of magnetic field •  Gradient coils:

–  Resistive wire creating linear gradients in the magnetic field –  used for spatial encoding

•  RF-coils: –  Signal transmission and reception –  Individually designed for different body regions

6

Rf-coils

7

Operator room

8

Technical room

Cooling pump Gradient amplifiers

Control electronics

9

Rf shielding

•  To avoid artefacts in images, the magnet-room must be shielded from all electromagnetic radiation.

•  Walls, floor and roof is covered by copper plates.

10

MRI = Contrast Versatility

•  Image contrast can be controlled and changed depending on acquisition parameters.

•  Basic Image contrasts: –  Relaxation times (T1, T2, T2*) –  Water content (proton density)

•  Image contrast can also be made sensitive to: –  Diffusion, temperature, flow, oxygen content

11

MR-physics: Warning

•  MRI is based on the precession of the magnetic moment in protons (usually called spin).

•  Is often explained using a combination of quantum physics and classical equations of motion.

•  A simplified quantum picture is used to explain: –  Thermal equilibrium distribution –  Resonance condition

•  Classical equations of motion are used to explain the rest. •  Beware that the simplified quantum picture is insufficient to describe

MRI, because it does not deal with the phase of the magnetic moments.

12

Proton spin

•  Atomic nuclei with odd number of nuclear particles have a physical property called spin.

•  Since nuclei also have electric charge, the spin gives rise to a magnetic moment.

•  The simplest atomic nucleus is the hydrogen proton.

•  Hydrogen is everywhere in the body through water.

•  All ordinary MRI is based on the hydrogen nucleus (proton) H+ in the water molecule.

•  All the properties described in the following relate to the proton spins.

S

H+

N

13

Magnetic Moment

•  Each spin is like a small compass needle: •  The strength of this needle is called the magnetic

moment and is determined by the gyromagnetic ratio γ .

•  γ is a physical constant and is different for different nuclei.

•  Proton: γ = 2.68 108 rad/s/Tesla (γ = 42.58 MHz/Tesla)

S

H+

N

14

Energy Levels

•  If we put the spin in a magnetic field B0, two possible energy states exists (quantization):

1.  Up. 2.  Down.

•  More energy is needed for the Down state compared to the Up state.

•  Energy difference involved is given by the socalled Larmor frequency ω0:

B0

E

ΔE !E = hf = !!0!0 = "B0

15

Resonance

•  Whenever a spin moves between the two energy states, energy is absorbed or released:

•  The energy is released as an electromagnetic wave at the

Larmor frequency:

•  @1.5 T: 63.87 MHz

E

ΔE ΔE

!E = hf0 = !!0!0 = "B0

16

Boltzmann distribution •  Gives the probability of finding an individual spin in

one of the two possible energy states, given the thermal energy available:

•  P+ = Probability of Spin Up. •  P- = Probability of Spin Down. •  ΔE = hf. •  k = Boltzmanns constant ( 1.381 10-23 J/K) •  T = Temperature (Kelvin).

P+ P! = exp "E kT( )

17

Equilibrium state •  The Boltzmann-distribution describes the equilibrium state:

–  If left to itself, nature will relax towards this state. •  Example:

–  B0 = 3.0 Tesla. –  T = 37 oCelcius. –  P+/P- = 1.0000198. –  If you have 200000 spins, 100001 will be in the Up state,

99999 in the Down state! –  But: Water contains 6.7 1022 protons per ml

(67000000000000000000000). •  The fraction is low, but the total number is high.

18

Magnetization at equilibrium •  The net magnetic moment from all

the individual spins is called the magnetization M.

•  Zero magnetic field: –  Arbitrary orientation of spins and

no net magnetization.

•  With magnetic field: –  A small majority of spins will align

with the magnetic field and create an additional field M0.

M = 0

B0

M > 0

M

M 0 =

!0"2!2

4kTB0

19

•  So far with quantum physics… •  In the following we deal with classical equations of motion •  This is possible because the QM expectation value for the

magnetic moment of individual spins follows the classical equations of motion.

•  When, in the following we use the term “spin”, we don’t necessarily mean individual spins, but larger collection of spins in a coherent state.

20

Precession •  When put in a magnetic field:

–  Spin will rotate around the applied field –  Identical to the interaction between the angular moment of a

spinning top and the gravitational field. –  Precession frequency (Larmor frequency) will depend on

the applied field and the magnetic moment of the nucleus:

!0 = " B0

21

Magnetization vector •  The magnetization vector describes the

sum of all individual magnetic moments •  Equilibrium: M is directed along the z-

axes, magnitude given by the thermal equilibrium value (M0).

•  The precession of spins will NOT create a net rotating M in the x-y plane, due to random phases of the individual magnetic moments. x

y

z

B0

M

22

Application of rf field

•  In addition to the static B0, we now apply a rotating magnetic field B1 (ω0).

•  Magnetization vector will start to precess around the total magnetic field.

•  Results in a spiraling motion of M if viewed in the laboratory frame of reference:

x

y

z

B0

M

B1

23

Rotating frame of reference

•  Used to simplify the visualization of M. •  Rotates at the Larmor frequency.

•  Only precession around rf-field B1 (which now appears static) is visible.

24

Effect of rf-field •  Excitation by radio frequency

radiation will bring the system away from its equilibrium state.

•  This excitation can be described as a rotation of the magnetization vector away from the z-axis.

•  The angle with which M rotates is called the flip angle and can be controlled (often 90 deg).

•  The result after the rf-pulse is a net magnetization in the x’-y’ plane

x'

y'

z

B0

M

rf

90º

M

25

MR-signal

•  If we jump back to the laboratory reference frame, the magnetization vector will now rotate in the x-y plane at the Larmor-frequency.

•  This rotating magnetic field can be detected as rf-radiation -> MR signal.

26

MR-signal

x

y

z

B0

M

x

time

27

Relaxation (T1) •  After the rf-pulse, the spin magnetization

vector will relax back towards its equilibrium value, which is along the z-axis.

•  This effect is called T1-relaxation, longitudinal relaxation or spin-lattice relaxation.

•  When the x-y component of M has dissappeared completely, the MR signal is lost.

x'

y'

z

B0

M

Free Induction Decay

28

Relaxation (T2) •  In most cases the x-y component of the magnetization vector

disappears faster than expected from the T1-relaxation process, meaning that we loose the MRI signal faster than expected.

•  This effect is called dephasing,T2-relaxation, transversal relaxation or spin-spin relaxation.

x'

y'

z

B0

M

Free induction decay

29

Relaxation (T2) •  We can understand this effect by introducing phase.

+

=

In phase:

+

=

Out of phase:

30

Origin of dephasing •  B0 is not identical all over the sample at all times, it varies slightly.

•  This means rotation speed of different spins vary slightly, leading to dephasing.

•  After a while, different spins are at different points along the circle.

•  Eventually the spins will spread out to cover the whole circle, and the signal is lost.

Mx

x

x

y

31

Rotating frame of reference •  Dephasing is better visualized in the rotating frame of

reference. •  Here dephasing corresponds to a fanning out of the phases of

the individual spins

z

x’

y’

32

T1 versus T2 relaxation

•  T1-relaxation: –  the regrowth of the z-magnetization (longitudinal magn.). –  Usually in the range of seconds.

•  T2-relaxation: –  the loss of x’y’- magnetization (transverse magn.) –  Usually in the range of 100 ms.

•  The two processes are usually considered independent of each other, although T2≤T1.

33

Summary

•  Magnetic field B0. –  Resonance frequency. –  Strength of equilibrium magnetization M0

•  Magnetization vector. –  The net magnetic field created by all the spins.

•  RF-pulse. –  Radio frequency radiation which rotates M away from z-axis.

•  Flip Angle. –  Angle which the magnetization is rotated away from z-direction.

•  FID (free induction decay). –  The decaying MR-signal as the system relaxes back to equilibrium.

•  T1-relaxation. –  Regrowth of longitudinal magnetization.

•  T2-relaxation. –  Loss of transverse magnetization.

f = !B0

34

Weighting: motivation for T1/T2 •  To adjust acquisition parameters to obtain different types of contrast

in an MR image is called weighting.

•  In a proton-weighted image the contrast is due to the spin density ρ0.

•  In a T1-weighted image the contrast is due to variation in the T1 values an so on….

•  T1 and T2-weighted images are important because ρ0 alone does not vary much in biological tissue. However there are big variations in T1 and T2.

•  In addition will pathology affect T1 and T2.

•  It is important to understand how we can get T1 and T2 weighted images.

35

T1-relaxation one more time…

•  The relaxation of longitudinal magnetization is described by the Bloch-equation which simply stats:

–  The time derivative of the z-magnetization is proportional to the distance from the equilibrium value:

•  When you solve this equation you get the following expression for the z-magnetization as a function of time t (after applying a 90º-rf-pulse)

Mz = M 0 1! e! t T1"# $%

dMzdt

=1T1

M 0 ! Mz"# $%

36

T1-relaxation curve

t (sec)

Mz T1 = 4 sec

T1 = 1 sec

37

T2-relaxation

•  The dephasing-process can similarly be described by the following Bloch-equation:

•  Again we get an exponential solution (with FA = 90o):

Mxy =M0 !e"t/T 2

dMxydt

= !1T 2

Mxy

38

T2 Relaxation curve

t (sec)

Mxy

T2 = 0.4 sec

T2 = 0.1 sec

39

The MR sequence •  An MR-experiment consists of repeated blochs of rf-

excitation pulses and signal acquisition:

40

TR and TE

•  TR = Repetition time –  Time between successive rf-excitation pulses. –  Controls T1-weighting

•  TE = Echo Time –  Time between rf-excitation and signal acquisition. –  Controls T2-weighting

41

A basic signal equation

•  By varying TR we control sensitivity to tissue variations in T1.

•  By varying TE we control sensitivity to tissue variations in T2.

S ! "0 i 1# e#TR /T1$% &'e

#TE /T 2

42

Short TR, short TE:

•  T1-weighted

S ! "0 i 1# e#TR /T1$% &'e

#TE /T 2

43

T1-weighting

•  Maximize T1-effects: Short TR •  Minimize T2-effects: Short TE

TR (sec)

Mz

TE

Mxy

44

Long TR, long TE:

•  T2-weighted

S ! "0 i 1# e#TR /T1$% &'e

#TE /T 2

45

T2-weighting

•  Minimize T1-effects: Long TR •  Maximize T2-effects: Long TE

TR (sec)

Mz

TE

Mxy

46

Long TR, short TE:

•  Proton weighted

S ! "0 i 1# e#TR /T1$% &'e

#TE /T 2

47

Proton-weighting

•  Minimize T1-effects: Long TR •  Minimize T2-effects: Short TE

TR (sec)

Mz

TE

Mxy

48

There is more…

•  The signal decay due to dephasing happens through two separate processes: –  Dynamic dephasing (T2) –  Static dephasing (T2’)

•  The standard FID experiment is sensitive to both processes through T2*:

1T 2 *

=1T 2

+1T 2 '

49

Dynamic versus Static Dephasing

•  Dynamic dephasing is the result of B0 variations in time. –  Spins move around and affect each others local field. –  Irreversible process. –  All MR-sequences are sensitive to this.

•  Static dephasing is the result of spatial BUT time constant B0 variations. –  Due to imperfect magnetic field. –  Reversible process. –  FID sequence sensitive to this. –  The spin echo is not (next slides)

50

Spin-echo. •  In stead of measuring the FID signal it is

possible to create an echo at a chosen time after the 90º excitation pulse.

•  Is achieved by an 180º refocusing pulse •  Can be understood with the help of the rotating

coordinate system:

z z 180º

Ekko

51

Spin-Echo

52

Spin echo versus FID 90 180 180

53

Signal acquisition

•  The transverse magnetization vector is a complex quantity (Magnitude and phase).

•  Both signals are aquired. •  Usually only the magnitude image is used. •  The phase image contains mostly information about B0.

54

Magnitude image Phase image

55

So how to get an image?

•  So far we only discussed a single MR-signal from the whole object •  How to spatially code the signal will be the topic of the next

presentation.