CS代考 BMEN90021, Lecture set 4: MRI

MRI uses the properties of nuclear spin and magnetisation to encode information in an object, that is then read out (received) and reconstructed by a detector system.
Magnetic Resonance Imaging
The same will apply for nuclear medicine and γ-rays.
The imaging modalities we have considered until now (X-ray & CT) have created image contrast from differential attenuation of X-rays.

MRI is fundamentally different.
Fourier Transform
“k-space”: to be explained later…
1 BMEN90021, Lecture set 4: MRI

Magnetic Resonance Imaging
1. Introduction to MRI
2. MR Physics
3. Signal Detection
4. Signal Localisation & Image Formation 5. MRI Sequences
6. Functional MRI
2 BMEN90021, Lecture set 4: MRI

Magnetic fields
A magnetic field is a vector field (strength & direction)
Magnetic fields arise from:
1. Permanent magnets. e.g. a bar magnet
2. Moving charges (currents) – used to create MRI scanner fields
www.reddit.com
www.boundless.com
3. The nuclear (quantum) property known as spin.
• exploited in MRI to image the internal structure of objects
3 BMEN90021, Lecture set 4: MRI

Magnetic field strength
Magnetic field strength
= magnitude of the magnetic (vector) field
Unit of magnetic field strength (actually magnetic flux density) = Tesla
Can be understood from the Lorentz force law:
A particle carrying a charge of 1 coulomb (1C) and passing through a magnetic field of 1 tesla (1T) at a speed of 1 meter per second (1m/s) experiences a force of 1 newton (1N).
What is a Tesla?
4 BMEN90021, Lecture set 4: MRI

Magnetic field strength
1 Tesla = 104 Gauss
Another common unit of magnetic field strength = Gauss
Earth’s magnetic field is about 0.3 – 0.6 Gauss
www.nasa.gov
BMEN90021, Lecture set 4: MRI

MRI fundamentals
CT scanners are described in terms of “generations”
MRI scanners are defined in terms of their field strength = strength of the superconducting magnet:
1 Tesla = 104 Gauss
Most clinical MRI scanners are 1.5T or 3T (“T” = Tesla).
1 Gauss = 10-4 Tesla
Remember, strength of Earth’s magnetic field is 0.3-0.6 Gauss = 30-60μT.
MRI machines contain STRONG MAGNETS
6 BMEN90021, Lecture set 4: MRI

NMR vs MRI
NMR = Nuclear magnetic resonance
Information about object composition,
NMR machines do not do imaging.
but information is not spatially localised.
Nobel prizes in MR
1952 Physics
Felix Bloch and Purcell
1991 Chemistry
Richard Ernst
2003 Physiology and Medicine:
and Sir Peter Mansfield
7 BMEN90021, Lecture set 4: MRI

MRI scanner
3T (Monash Biomedical Imaging) 7T (Melbourne Brain Centre Imaging Unit)
8 BMEN90021, Lecture set 4: MRI

MRI scanner diagram
Coyne 2012
9 BMEN90021, Lecture set 4: MRI

Brainstem Image
Brainstem Image
Courtesy of Z.H.Cho, Gachon Korea
Prof. Cho, Gachon Korea
The effect of field strength
10 BMEN90021, Lecture set 4: MRI

Another effect of field strength…

https://www.youtube.com/watch?v=plvIEf7JsKo https://www.youtube.com/watch?v=J2mMcDo1wo4
11 BMEN90021, Lecture set 4: MRI

MRI Safety
Must always check for metal implants, pacemakers etc before a person enters the scanner suite.
Mythbusters https://www.youtube.com/watch?v=AiE3in71YEo
What about tattoos?
Does the magnet ever ‘explode’?
• Essentially no, but the magnet can quench (rapid helium boil-off)
https://www.youtube.com/watch?v=9SOUJP5dFEg Exception — incorrect decommissioning

12 BMEN90021, Lecture set 4: MRI

Components of an MRI scanner The main cylindrical
superconducting magnet
Electronics and computers
Static field
Gradient coils
RF coil(s)
Varies the static field linearly
x, y and z direction gradients Used to select ‘slices’ and image
Produces the excitation (B1) field Receives signal from object
• Control, data acquisition & reconstruction
13 BMEN90021, Lecture set 4: MRI

Inside the gradient coil
14 BMEN90021, Lecture set 4: MRI
Coyne 2012

Clinical vs pre-clinical scanners
“Clinical” scanners
Human-sized, 60-90cm bore diameter Made primarily by Siemens, GE, Philips Some other companies like Toshiba
“Pre-clinical” scanners
Animal-sized, eg. 10-30cm bore diameter
Made by Bruker, MRSolutions
Until fairly recently, also Agilent (originally Varian)
Field strengths higher than clinical systems
University of Melbourne 7T
Easier to create homogeneous magnetic fields across
a smaller area.
15 BMEN90021, Lecture set 4: MRI
Ex-Florey 4.7T

Making an MRI scanner
• MRI scanners cost $millions
• Installation of UoM 7T in mid-2014:
16 BMEN90021, Lecture set 4: MRI

Types of MRI (all from same scanner)
Structural
Functional
Angiography
BMEN90021, Lecture set 4: MRI
The Age, 12 April 2015
“They were lying inside the functional MRI machine when they watched the video game
while their brain was being scanned.”

Magnetic Resonance Imaging
2. MR Physics
1. Introduction to MRI
3. Signal Detection
4. Signal Localisation & Image Formation 5. MRI Sequences
6. Functional MRI
18 BMEN90021, Lecture set 4: MRI

Magnetic moment
Therefore spin is atomic number dependent.
Table 4.1 Spin values of several nuclei of biomedical interest.
A given nucleus is characterized by a unique spin value (the values are explained on p. 66). Note that the
Figure4.2 If particle with a
momentumJ⃗
magnetic mom
MR physics: spin
= vector sum of electron, proton & neutron spins. Chapter 4: Magnetic resonance imag
The spin of an atomic nucleus
Spins of charged particles result in magnetic moments.
which are abundant in the human body.
suspended wit
biomedically important nuclei 12C and 16O have noMRI is primarily concerned with H = protons,
6 8 spin and thus no NMR sensitivity [18].
friction in an e magnetic field
v0 m=gJ 2π ur
Nucleus Spin γ (MHz/T) 1 1 H 12 42.57
2H1 6.54 1
13C 1 10.71 62
14N 1 3.08 x 7
precession abo occurs. The an frequency ω0 o precession is proportional to positive γ , the precession is c
The protons are in constant random tumbling motion
−4.31 −5.77
in an external magnetic field. Throughout this t direction of the external magnetic field B is defi
31P 1 17.23 15 2
33S 3 3.27 16 2 19
43Ca 7 −2.86
the z -axis of the coordinate system: B = (0, 0, B
BMEN90021, Lecture set 4: MRI
Let J⃗be a spin angular momentum and μ⃗ it

Magnetic moment
nce imaging
MR physics: magnetic moment
68 hus no NMR sensitivity [18].
⃗ magnetic fieldB, a⃗
γ (MHz/T) 2π
precession aboutB occurs. The angular frequency ω0 of this precession is proportional to B 0. For positive γ , the precession is clockwise.
The magnetic moment
The proton spins rapidly around its own axis, but also precesses around a static
external magnetic field.
Like a spinning top precesses.
Spin values of several nuclei of biomedical
cleus is characterized by a unique spin value s are explained on p. 66). Note that the lly important nuclei 12C and 16O have no
Figure4.2 Ifa particle with angular
1 3.08 x f 12
10.71 −4.31
BMEN90021, Lecture set 4: MRI
Chapter 4: Magnetic resona
momentumJ⃗and magnetic moment μ⃗ is suspended without friction in an external

MR physics: quantum model The quantum mechanical model is of spin states
having quanta of energy: m = ±1⁄2 = “eigenstates”
Fat molecules are large and surrounded by many elec-
difference normalized to the Larmor frequency of a reference element ((CH3)4Si), expressed in parts per million (ppm), is called the chemical shift. Hence, the chemical shift between fat and water is about 3.5 ppm.
Dynamic equilibrium: the net
magnetization vector of matter
In imaging, each volume element (voxel) is still large
enough to contain a huge amount of protons, each
( m _21 )
Figure 4.3 The Zeeman effect for particles with spin j = 1/2. In
the presence of a time-independent external magnetic fieldB⃗of magnitude B 0, the particle can occupy two different energy states,
“spin up” (↑) and “spin down” (↓). The energy difference between the two states is proportional to B 0.
possible energy levels. Referring to Figure 4.2, in the
spin-up state the magnetic moments point upwards,
that is, μz (t ) > 0, whereas in the spin-down state, the
magnetic moments point downward (i.e., μ (t ) < 0). z The correct description of this dynamic equilib- rium must in principle be obtained from statistical Comparing Eq. (4.13) with Eq. (4.6) shows that the Larmor angular frequency is exactly the angular quantum mechanics. Fortunately, it can be shown that the expected behavior of a large number of spins is Chapter 4: Magnetic resonance imaging “Spin-up” state is the lower energy state. E 12g B0 trons, which reduce the effective external field. This lower at 1 T (220 Hz at 1.5 T) than that of water. This upon measurement. “Spin-down” state requires excitation; netic moment. In each voxel, a dynamic equilibrium it is a higher energy state. exists in which the spins are distributed over the two BMEN90021, Lecture set 4: MRI ( m _1 ) 2 E E gB0 E 1 g B 20 proton having its own spin with its associated mag- MR physics: bulk magnetisation In the absence of an external magnetic field, the spinning protons do not align, and therefore create no bulk magnetisation: We do not observe the individual spins, but rather the collection of ensembles of spins. 22 BMEN90021, Lecture set 4: MRI ~3 in 1,000,000 unpaired MR physics: bulk magnetisation parallel (“spin-up”) are the basis of the MR signal: M > 0. Note: This is a classical model, not
quantum physics.
In the presence of a static external magnetic field, B0, the spins align:
anti-parallel (“spin-down”) •
Most are paired, except for a very few, that
23 BMEN90021, Lecture set 4: MRI

θ (4.6 the value
constants μ x
he componen
t) and μ (0 xy
ponent can t
MR physics: Larmor relationship
r 4: Magnetic resonance imaging
The LARMOR RELATIONSHIP states that:
The frequency by which the protons precess around the static external magnetic field is directly proportional to the strength of the magnetic field.
ith he(0),μ(0),andμ(0)ares
ω=γB.) 0 0
The angular frequency
(units: rads/sec) of this
ttsatt=0.Letμ(t)=+ xy
precession is ω0.
μ ( ) = μ (0) + iμ (0). The transverse y xy
omhenbewrittenas
Protons precess out of phase. Therefore while there is a net bulk magnetisation, M, in the direction of the magnetic field, B0, the bulk
magnetisation does not precess.
24 −iω t BMEN90021, Lecture set 4: MRI μ (t) = μ (0)e 0 . (4.7)

agnetic resonance imaging
MR physics: Gyromagnetic ratio
Table 4.1 Spin values of several nuclei of biomedical
The constant, γ, is calledA gthiven ngucyleruos ims chargacnteerizteidcbyrautniioqu.e spin value
(the values are explained on p. 66). Note that the
The correct
It has a specific value forbioemaedcichallyniumpcolretauntsnuwcleiithCnaondn-Ozeharvoe nsopin value:
68 spin and thus no NMR sensitivity [18].
and subatom
v0 γ mechanics.
ω =γB . (4.6)
(0), μ (0), and μ (0) are the values
Nucleus Spin
2π (MHz/T) 42.57
Quantum mec
6C 2 10.71
nts at t = 0. Let μ (t) = μ (t) + xy 7 x
0) = μ (0) + iμ (0). The transverse
14N 1 3.08 x
Motion equation
Quantum me
then be written as
(t) = μ xy
17O 5 −5.77
8 2 inanexte
31 1 15P 2
33S 3 16 2
of the compo
3.27 the z-axis −2.86 Let J⃗
(0)e . (4.7)
However, to explain certain experimental facts
ciated m the same
Eq. (4.6) and
43Ca 7 21 2
as a classical
25 BMEN90021, Lecture set 4: MRI
observed in atomic spectra, Uhlenbeck and Goudsmit

MRI convention is that the z-axis is in the direction of the B0 field = along the bore of the scanner.
The bulk magnetisation component:
in the x-y plane is known as transverse magnetisation, along the z-axis is known as longitudinal magnetisation.
MR physics: Vectors & axes
That is, they have a magnitude and a
It is important to remember that magnetic fields and bulk magnetisation are vector quantities.
direction.
26 BMEN90021, Lecture set 4: MRI

Bulk magnetisation
Bulk magnetisation is a vector quantity:
24 Mx(t) 35 M(t) = My(t) Mz (t)
• WewillsometimesrefertoMxy(t),whichisthe magnitude of the transverse magnetisation.
This is the transverse magnetisation in the ‘rotating frame of reference’.
27 BMEN90021, Lecture set 4: MRI

The Bloch equation
The Bloch equation (1946) describes how the bulk magnetisation in an object reacts to an external magnetic field.
dMx(t) = (M(t) ⇥ Bext(t))x Mx(t) dt T2
dMy(t) = (M(t) ⇥ Bext(t))y My(t) dt T2
dMz(t) = (M(t) ⇥ Bext(t))z Mz(t) M0 dt T1
28 BMEN90021, Lecture set 4: MRI

Equilibrium conditions
• In the presence of only a static magnetic field, B0, the bulk magnetisation does not change.
The system is at equilibrium, with bulk magnetisation M0, pointing in the z-direction.
Can work through the algebra in the Bloch equation to show that:
Bext(t) = B0, =) dM(t) = 0 dt
30 BMEN90021, Lecture set 4: MRI

Equilibrium conditions
• The B0 field is ALWAYS ON. House MD shoots a corpse.
• This is done by application of the “B1” excitation field.
We need to perturb the bulk magnetisation in order to create time-varying magnetisation.
Also called the “RF” field, due to ~RF frequencies.
31 BMEN90021, Lecture set 4: MRI

Bext(t) = B0 + B1(t)
B1(t) = B1ej0t
Application of B1 (RF) field
The external B-field is now the sum of a static and a dynamic component:
Importantly, the B1 field is constructed to oscillate (rotate) at ω0, the resonance frequency, as given by the Larmor relationship:
In order to perturb the bulk magnetisation away from equilibrium, a second magnetic field is applied, this one oscillating in the x-y plane.
32 BMEN90021, Lecture set 4: MRI

B1 spiral trajectory
• If the B1 field is applied for a short time (much shorter than tissue time constants T1 and T2), then bulk magnetisation follows a spiral trajectory:
BMEN90021, Lecture set 4: MRI

B1 spiral trajectory
34 BMEN90021, Lecture set 4: MRI

Often α = 90°. This is referred to as a “90° pulse”.
Flip Angle
The “flip angle”, α, is the angle that M makes with the z-axis
when the B1 field is switched off after time τ.
The Bloch equation predicts with very good approximation that:
= ⇥B1⇤ BMEN90021, Lecture set 4: MRI
Q. Why is a magnetic field called a “pulse”?
A. Because of its short duration.

Control of B1 and the Flip Angle
The Bloch equation predicts with very good approximation that:
Q: Which terms in the equation are controllable? That is, which are set at the scanner by the user?
BMEN90021, Lecture set 4: MRI
Extension challenge: Under what assumptions does the Bloch equation predict this Flip Angle relationship?

Frames of Reference
• Axes are labelled {x,y,z}.
We define a “Rotating frame of reference” to be the coordinate system oscillating in the xy-plane at the Larmor frequency.
• Axes are labelled {x’,y’,z}.
• Q1: Why z and not z’?
• Q2: What does an RF excitation spiral look like in the rotating frame of reference?
The “Laboratory frame of reference” is observing the bulk magnetisation from a fixed point in space.
37 BMEN90021, Lecture set 4: MRI

90 and 180 degree pulses
Chapter 4: Magnetic resonance imaging
Figure4.4 (a)M⃗precessesaboutB⃗ andisrotatedawayfromthez-axistothey′-axis.Theangleαbetweenthez-axisandM⃗iscalledtheflip
angle. (b) α = 90 , which is obtained by a 90 RF-pulse. (c) α = 180 , which is obtained by a 180 RF-pulse, also called an inversion pulse.
reference frame, whereas in the rotating reference frame, it stands still.
• The 180◦ or inversion pulse This RF pulse rotates M⃗ to the negative z-axis (Figure 4.4(c)):
by a first-order model. The time constant of the exponential decay is called the spin–spin relaxation time T2:
38 BMEN90021, Lecture set 4: MRI Mtr (t ) = M 0 sin α e− t /T2 . (4.25)

Result of the B1 (RF) field
What happens next?…
The B1 field causes the bulk magnetisation to flip out of the equilibrium position to another point on the Bloch sphere.
39 BMEN90021, Lecture set 4: MRI

Figure 2.14: Relaxation curves after a π/2 pulse.
Free Induction Decay • When the B1 field is switched off, the
Bloch equation predicts that the bulk magnetisation moves back to equilibrium, known as the Free Induction Decay (FID):
This is known as “spin-spin
Exponential decay of the transverse magnetisation, Mxy, in the x-y plane (dephasing)
interaction”.
This is known as “spin-lattice
Exponential recovery of the longitudinal magnetisation, Mz, along the z-axis (recovery of energy equilibrium).
interaction”.
B.Tahayori
2.8 MR Signal Generation
2.8.2 Longitudinal Relaxation
40 BMEN90021, Lecture set 4: MRI

Transverse Magnetization after a π/2 pulse
FID Signal
Free Induction Decay
Transverse (xy) magnetisation decays much quicker
The return of bulk magnetisation to equilibrium does not occur along the same spiral path as the excitation
than longitudinal magnetisation recovers.
41 BMEN90021, Lecture set 4: MRI

T2= 2000 ms 37%
T2= 100 ms
T1= 200 ms
T1= 3000 ms
Chapter 4: Magnetic resonance imaging
• T1andT2areintrinsicpropertiesofthetissue.
Figure 4.5 Dephasing of the transverse component of the net magnetization vector with time. (a) At t = 0, all spins are in phase (phase coherence). (b) At t = T2, dephasing results in a decrease of the transverse component to 37‰ of its initial value. (c) Ultimately, the spins are isotropically distributed and no net magnetization is left.
These diagrams are in the rotating frame of reference.
100 80 60 40 20
Figure 4.6 The spin–spin relaxation process for CSF and fat (for α = 90 ◦ ). At t = T2 , the transverse magnetization has decreased to 37‰ of its value at t = 0. At t = 5T2 , only 0.67‰ of the initial value remains. (b) The spin–lattice relaxation process for water and fat at 1.5 T. At t = T1 , the longitudinal magnetization has reached 63‰ of its equilibrium value. At t = 5T1, it has reached 99.3‰.
100 80 60 40 20
t = T2 (b)
Spin–spin relaxation
Spin–lattice relaxation
1500 2000 Time (ms)
macromolecules). The spin–lattice relaxation is an energy phenomenon. The energy transferred to the
42 Spin–lattice relaxation BMEN90021, Lecture set 4: MRI 100
Transverse magn. (%)
Longitudinal magn. (%)

!Tissues have a range of T1 and T2 values”MR contrast
! White matter ! Grey matter ! CSF
T1= 510ms T1= 760ms T1= 2650ms
T2 = 67ms T2 = 77ms T2 = 280ms
The basis of contrast in MR

程序代写 CS代考加微信: powcoder QQ: 1823890830 Email: powcoder@163.com

Related Posts