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HST.583 Functional Magnetic Resonance Imaging: Data Acquisition and Analysis
Fall 2006
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HST.583: Functional Magnetic Resonance Imaging: Data Acquisition and Analysis, Fall 2006
Harvard-MIT Division of Health Sciences and Technology
Course Director: Dr. Randy Gollub.
Basics of Magnetic Resonance Imaging
Images removed due to copyright restrictions.
See van Bruggen, N., et al. "The application of magnetic resonance
imaging to the study of experimental cerebral ischaemia."
Cerebrovasc. Brain Metab. Rev. 6 no. 2 (1994): 180-210.
Two images of a rat brain 1.5 hours after occlusion of the middle
cerebral artery. In the diffusion-weighted image (left), ischaemic tissue
in the region supplied by the middle cerebral artery is highlighted; while
it is not detected in the T2-weighted image (right).
Cite as: Karl Helmer, HST.583 Functional Magnetic Resonance Imaging: Data Acquisition and Analysis, Fall 2006. (Massachusetts Institute
of Technology: MIT OpenCourseWare), http://ocw.mit.edu (Accessed MM DD, YYYY). License: Creative Commons BY-NC-SA.
Angular Momentum
Orbital Angular Momentum
G G
L = mr × v
Axis
La
v
r
m
Object with mass m orbiting around an axis at a radius r and with velocity v
has an angular momentum La.
Figure by MIT OpenCourseWare.
Cite as: Karl Helmer, HST.583 Functional Magnetic Resonance Imaging: Data Acquisition and Analysis, Fall 2006. (Massachusetts Institute
of Technology: MIT OpenCourseWare), http://ocw.mit.edu (Accessed MM DD, YYYY). License: Creative Commons BY-NC-SA.
Angular Momentum
Spin Angular Momentum
Spin is an intrinsic property
of the nucleons (protons
and neutrons) in a nucleus
HOWEVER –
The name doesn’t mean that
spin results from the nucleons
rotating about an axis!!!
http://svs.gsfc.nasa.gov/vis/a000000/a001300/a001319/
Cite as: Karl Helmer, HST.583 Functional Magnetic Resonance Imaging: Data Acquisition and Analysis, Fall 2006. (Massachusetts Institute
of Technology: MIT OpenCourseWare), http://ocw.mit.edu (Accessed MM DD, YYYY). License: Creative Commons BY-NC-SA.
Spin Angular Momentum
Spin is quantized – it can only take certain values
Lz = m I =
mI = I , I − 1, I − 2,... − I
Here I is the total spin quantum number of the
nucleus. The proton has I = ½. Lz is the
angular momentum due to that spin.
Cite as: Karl Helmer, HST.583 Functional Magnetic Resonance Imaging: Data Acquisition and Analysis, Fall 2006. (Massachusetts Institute
of Technology: MIT OpenCourseWare), http://ocw.mit.edu (Accessed MM DD, YYYY). License: Creative Commons BY-NC-SA.
Spin Angular Momentum
To get the total spin of a nucleus we add up
(separately) the spins of the protons and neutrons
15N
has spin ½ .
We do pairwise
addition:
7 protons
8 neutrons
Only nuclei with an odd number of protons
or neutrons will be visible to MRI
Note: 14N has spin 1.
Cite as: Karl Helmer, HST.583 Functional Magnetic Resonance Imaging: Data Acquisition and Analysis, Fall 2006. (Massachusetts Institute
of Technology: MIT OpenCourseWare), http://ocw.mit.edu (Accessed MM DD, YYYY). License: Creative Commons BY-NC-SA.
Alignment of Spins in a Magnetic Field, B0
The spin angular momentum yields
a magnetic moment
μ m = γL z
N
B0
µm
S
A magnetic vector aligns to an external magnetic field.
Figure by MIT OpenCourseWare.
Cite as: Karl Helmer, HST.583 Functional Magnetic Resonance Imaging: Data Acquisition and Analysis, Fall 2006. (Massachusetts Institute
of Technology: MIT OpenCourseWare), http://ocw.mit.edu (Accessed MM DD, YYYY). License: Creative Commons BY-NC-SA.
Energy Levels of Spins and B0
Energy Level
B=0
B0
Energy diagram for spin = 1/2 nucleus. Without a magnetic field (B = 0), energy levels of the
nuclear spin states are equal. Applying a magnetic field creates different energies for the two
spin states through Zeeman splitting.
Figure by MIT OpenCourseWare.
Cite as: Karl Helmer, HST.583 Functional Magnetic Resonance Imaging: Data Acquisition and Analysis, Fall 2006. (Massachusetts Institute
of Technology: MIT OpenCourseWare), http://ocw.mit.edu (Accessed MM DD, YYYY). License: Creative Commons BY-NC-SA.
Energy Levels and Spin
E1 = μB0
E2 = -μB0
ΔE = E1 - E2 = 2 μB0
= γ(h/2π) B0 for spin-1/2 particles
B0 is the main magnetic field
Cite as: Karl Helmer, HST.583 Functional Magnetic Resonance Imaging: Data Acquisition and Analysis, Fall 2006. (Massachusetts Institute
of Technology: MIT OpenCourseWare), http://ocw.mit.edu (Accessed MM DD, YYYY). License: Creative Commons BY-NC-SA.
Energy Level Population and Field Strength
2,000,000
B0 = 0
Δn = 0
999,999
999,995
1,000,002
1,000,005
B0 = 0.5T
Δn = 3
B0 = 1.5T
Δn = 10
999,987
1,000,014
B0 = 4.0T
Δn = 27
Spins are distributed according to the Boltzmann distribution
( N upper / N lower ) = e − ΔE / kT
Cite as: Karl Helmer, HST.583 Functional Magnetic Resonance Imaging: Data Acquisition and Analysis, Fall 2006. (Massachusetts Institute
of Technology: MIT OpenCourseWare), http://ocw.mit.edu (Accessed MM DD, YYYY). License: Creative Commons BY-NC-SA.
Larmor Frequency
ω = γB0
B in Z direction
M
1/2 dipole moments
mmxy
mmz
mm
-1/2 dipole moments
A small net magnetization vector M produced by precessing protons aligns parallel
to the axis of the applied magnetic field. The random distribution of individual spins
around the Z axis leads to a net magnetization vector of zero in the XY plane.
Figure by MIT OpenCourseWare.
Cite as: Karl Helmer, HST.583 Functional Magnetic Resonance Imaging: Data Acquisition and Analysis, Fall 2006. (Massachusetts Institute
of Technology: MIT OpenCourseWare), http://ocw.mit.edu (Accessed MM DD, YYYY). License: Creative Commons BY-NC-SA.
Excitation Energy and Frames of Reference
B0
Beff
B0 = main magnetic field
B1 = applied field (pulse)
Beff = vector sum B0+B1
B1
z′
z
μ
μ
y′
y
x
lab frame
x′
rotating frame
Cite as: Karl Helmer, HST.583 Functional Magnetic Resonance Imaging: Data Acquisition and Analysis, Fall 2006. (Massachusetts Institute
of Technology: MIT OpenCourseWare), http://ocw.mit.edu (Accessed MM DD, YYYY). License: Creative Commons BY-NC-SA.
Net Magnetization, M, and the
Rotating Frame
While B1 ≠ 0, M
precesses around B1
z′
z′
M
M
y′
y′
B1
x′
x′
B0 ≠ 0
B1 = 0
B0 ≠ 0
B1 ≠ 0
Cite as: Karl Helmer, HST.583 Functional Magnetic Resonance Imaging: Data Acquisition and Analysis, Fall 2006. (Massachusetts Institute
of Technology: MIT OpenCourseWare), http://ocw.mit.edu (Accessed MM DD, YYYY). License: Creative Commons BY-NC-SA.
Net Magnetization, M, and the
Rotating Frame
We turn B1 “on” by a applying radiofrequency (RF) to the
sample at the Larmor frequency. This is a resonant
absorption of energy.
If we leave B1 on just long enough for M to rotate into the x′
- y′ plane, then we have applied a “90° pulse”. In this case,
Nupper = Nlower.
If we leave B1 on just long enough for M to rotate along the
-z′ axis, then we have applied a “180° pulse” (inversion).
In this case, Nupper = Nlower + M.
Cite as: Karl Helmer, HST.583 Functional Magnetic Resonance Imaging: Data Acquisition and Analysis, Fall 2006. (Massachusetts Institute
of Technology: MIT OpenCourseWare), http://ocw.mit.edu (Accessed MM DD, YYYY). License: Creative Commons BY-NC-SA.
Free Induction Decay
What is the effect of applying a 90 ° pulse?
π/2
RF
time
Cite as: Karl Helmer, HST.583 Functional Magnetic Resonance Imaging: Data Acquisition and Analysis, Fall 2006. (Massachusetts Institute
of Technology: MIT OpenCourseWare), http://ocw.mit.edu (Accessed MM DD, YYYY). License: Creative Commons BY-NC-SA.
Free Induction Decay
The effect of a 90° pulse is to rotate M into the x′ - y′
(transverse) plane. If we place a detection coil (a loop of wire)
perpendicular to the transverse place, we will detect an induced
current in the loop as M precesses by (in the lab frame).
z′
Y
Minitial
B1
x′
Mx
Mxy
My
y′
Mx
X
Time
Mfinal
Induced voltage in a coil aligned with Y axis, plotted as a function of time.
Figure by MIT OpenCourseWare.
Cite as: Karl Helmer, HST.583 Functional Magnetic Resonance Imaging: Data Acquisition and Analysis, Fall 2006. (Massachusetts Institute
of Technology: MIT OpenCourseWare), http://ocw.mit.edu (Accessed MM DD, YYYY). License: Creative Commons BY-NC-SA.
Signal Processing of Free Induction Decay
Y
Mx
Mxy
My
Mx
X
Time
Induced voltage in a coil aligned with Y axis, plotted as a function of time.
Figure by MIT OpenCourseWare.
We can characterize the signal by its:
ƒAmplitude
ƒPhase
Fourier Transform
ƒFrequency
Cite as: Karl Helmer, HST.583 Functional Magnetic Resonance Imaging: Data Acquisition and Analysis, Fall 2006. (Massachusetts Institute
of Technology: MIT OpenCourseWare), http://ocw.mit.edu (Accessed MM DD, YYYY). License: Creative Commons BY-NC-SA.
Signal Processing of Free Induction Decay
We see that after a 90° pulse, we get a cosinusoidal signal.
To quantitatively describe the signal we
calculate its Fourier transform.
(think: Larmor frequency)
Time
(A)
Frequency
(B)
A wave can be expressed as a function of time (A) or of frequency (B). (A) Represents
a waveform that goes on forever
Figure by MIT OpenCourseWare.
Cite as: Karl Helmer, HST.583 Functional Magnetic Resonance Imaging: Data Acquisition and Analysis, Fall 2006. (Massachusetts Institute
of Technology: MIT OpenCourseWare), http://ocw.mit.edu (Accessed MM DD, YYYY). License: Creative Commons BY-NC-SA.
Fourier Transform of Time Domain Data
http://www.med.harvard.edu/JPNM/physics/didactics/improc/intro/fourier3.html
Courtesy of Harvard Medical School Joint Program in Nuclear Medicine. Used with permission.
Cite as: Karl Helmer, HST.583 Functional Magnetic Resonance Imaging: Data Acquisition and Analysis, Fall 2006. (Massachusetts Institute
of Technology: MIT OpenCourseWare), http://ocw.mit.edu (Accessed MM DD, YYYY). License: Creative Commons BY-NC-SA.
Image Contrast (I)
We can detect the signal from water molecules in the
body.
Can we make an image?
Will it be a useful image?
Tissue
Water content (%)
Skeletal muscle
79
Myocardium
Liver
80
71
Kidney
81
Brain white matter
84
Brain gray matter
72
Nerve
56
Femur cortex
12
Teeth
10
Water Content of fat-free normal human tissue
Figure by MIT OpenCourseWare.
Cite as: Karl Helmer, HST.583 Functional Magnetic Resonance Imaging: Data Acquisition and Analysis, Fall 2006. (Massachusetts Institute
of Technology: MIT OpenCourseWare), http://ocw.mit.edu (Accessed MM DD, YYYY). License: Creative Commons BY-NC-SA.
Relaxation Processes
Fortunately for us, the signal we get from water molecules
in the body depends on their local environment.
Spins can interact by exchanging or losing energy (or both).
As in all spectroscopy methods, we put energy into the
system and we then detect the emitted energy to learn
about the composition of the sample.
We then use some variables to characterize the emission of
energy which (indirectly) tell us about the environment of
the spins.
Image Contrast!
Cite as: Karl Helmer, HST.583 Functional Magnetic Resonance Imaging: Data Acquisition and Analysis, Fall 2006. (Massachusetts Institute
of Technology: MIT OpenCourseWare), http://ocw.mit.edu (Accessed MM DD, YYYY). License: Creative Commons BY-NC-SA.
Relaxation Processes (T2)
1. Spin-spin relaxation time (T2): when spins interact
With each others magnetic field, they can exchange
energy (perform a spin flip). They can lose phase
coherence, however. Only affects Mxy.
Mxy = signal intensity
tps
Signal without T2
interaction between
spins
Mxy = signal intensity
tps
Figure by MIT OpenCourseWare.
Signal including T2
interactions between
spins
T2*???
Cite as: Karl Helmer, HST.583 Functional Magnetic Resonance Imaging: Data Acquisition and Analysis, Fall 2006. (Massachusetts Institute
of Technology: MIT OpenCourseWare), http://ocw.mit.edu (Accessed MM DD, YYYY). License: Creative Commons BY-NC-SA.
T2* and T2
T2 is an intrinsic property of the sample. This is what
we are interested in to use for contrast generation.
T2* is the time constant of the decay of the free
induction decay. It is related to the intrinsic T2 in the
following way:
1
1
1
1
= + inhomogeneity + susceptibility
*
T2 T2 T2
T2
sample
only
depends upon the local
magnetic field
Cite as: Karl Helmer, HST.583 Functional Magnetic Resonance Imaging: Data Acquisition and Analysis, Fall 2006. (Massachusetts Institute
of Technology: MIT OpenCourseWare), http://ocw.mit.edu (Accessed MM DD, YYYY). License: Creative Commons BY-NC-SA.
T2* and T2
1
1
1
1
= + inhomogeneity + susceptibility
*
T2 T2 T2
T2
random
process
Not a random
process
Inhomogeneity term - dephasing due to magnet (B0)
imperfections depends upon position
Susceptibility term - dephasing due to the interaction of
different sample regions with B0
(depends upon position)
Cite as: Karl Helmer, HST.583 Functional Magnetic Resonance Imaging: Data Acquisition and Analysis, Fall 2006. (Massachusetts Institute
of Technology: MIT OpenCourseWare), http://ocw.mit.edu (Accessed MM DD, YYYY). License: Creative Commons BY-NC-SA.
Relaxation Processes (T2)
π/2 pulse
τ (delay)
Cite as: Karl Helmer, HST.583 Functional Magnetic Resonance Imaging: Data Acquisition and Analysis, Fall 2006. (Massachusetts Institute
of Technology: MIT OpenCourseWare), http://ocw.mit.edu (Accessed MM DD, YYYY). License: Creative Commons BY-NC-SA.
Effect of Spin Coherence on Signal
z
y
Mxy = signal intensity
tps
x
z
Mxy = signal intensity
tps
y
Figure by MIT OpenCourseWare.
x
Cite as: Karl Helmer, HST.583 Functional Magnetic Resonance Imaging: Data Acquisition and Analysis, Fall 2006. (Massachusetts Institute
of Technology: MIT OpenCourseWare), http://ocw.mit.edu (Accessed MM DD, YYYY). License: Creative Commons BY-NC-SA.
Irreversible versus Reversible
http://www.cchem.berkeley.edu/demolab/images/HahnEchoSpinRes.htm
Sequence of 12 lab photos removed due to copyright restrictions.
Cite as: Karl Helmer, HST.583 Functional Magnetic Resonance Imaging: Data Acquisition and Analysis, Fall 2006. (Massachusetts Institute
of Technology: MIT OpenCourseWare), http://ocw.mit.edu (Accessed MM DD, YYYY). License: Creative Commons BY-NC-SA.
Hahn Spin Echo Pulse Sequence
http://www.esr.ethz.ch/intro/spinecho.html
t=0
a
t=τ-
b
t=τ+
c
Figure by MIT OpenCourseWare.
Courtesy of Françoise Sauriol. Used with permission.
Courtesy of EPR Research Group - ETH Zürich.
Used with permission.
http://www.chem.queensu.ca/FACILITIES/NMR/nmr/webcourse/t2.htm
Cite as: Karl Helmer, HST.583 Functional Magnetic Resonance Imaging: Data Acquisition and Analysis, Fall 2006. (Massachusetts Institute
of Technology: MIT OpenCourseWare), http://ocw.mit.edu (Accessed MM DD, YYYY). License: Creative Commons BY-NC-SA.
Hahn Spin Echo and T2
We can calculate T2 by changing the echo
spacing, τ, and recording the signal at 2τ.
Courtesy of Michael Richmond. Used with permission.
http://spiff.rit.edu/classes/phys273/exponential/exponential.html
S (2τ ) = e
−2τ / T2
Signal
Echo spacing , τ
Cite as: Karl Helmer, HST.583 Functional Magnetic Resonance Imaging: Data Acquisition and Analysis, Fall 2006. (Massachusetts Institute
of Technology: MIT OpenCourseWare), http://ocw.mit.edu (Accessed MM DD, YYYY). License: Creative Commons BY-NC-SA.
Spin-Lattice Relaxation, T1
To look at the behavior of the longitudinal
component of M (Mz), we start by putting M along
the -z axis and then read it out with a 90° pulse.
M z = M 0 (1 − 2e
−TI / T1
)
Cite as: Karl Helmer, HST.583 Functional Magnetic Resonance Imaging: Data Acquisition and Analysis, Fall 2006. (Massachusetts Institute
of Technology: MIT OpenCourseWare), http://ocw.mit.edu (Accessed MM DD, YYYY). License: Creative Commons BY-NC-SA.
Spin-Lattice Relaxation, T1
Energy levels and Inversion
Equilibrium
Net
Magnetization:
=
After Inversion
=
Cite as: Karl Helmer, HST.583 Functional Magnetic Resonance Imaging: Data Acquisition and Analysis, Fall 2006. (Massachusetts Institute
of Technology: MIT OpenCourseWare), http://ocw.mit.edu (Accessed MM DD, YYYY). License: Creative Commons BY-NC-SA.
Relaxation Processes (T1)
π pulse
short TI
long TI
π/2 pulse
π/2 pulse
Cite as: Karl Helmer, HST.583 Functional Magnetic Resonance Imaging: Data Acquisition and Analysis, Fall 2006. (Massachusetts Institute
of Technology: MIT OpenCourseWare), http://ocw.mit.edu (Accessed MM DD, YYYY). License: Creative Commons BY-NC-SA.
Image Contrast and T1
Courtesy of Stuart Clare, PhD. Used with permission.
In (a) the TI is chosen to null the signal from
curve [ii], while the TI in (b) nulls out [i]
http://www.fmrib.ox.ac.uk/~stuart/thesis/chapter_2/section2_4.html
Cite as: Karl Helmer, HST.583 Functional Magnetic Resonance Imaging: Data Acquisition and Analysis, Fall 2006. (Massachusetts Institute
of Technology: MIT OpenCourseWare), http://ocw.mit.edu (Accessed MM DD, YYYY). License: Creative Commons BY-NC-SA.
Now Can We Make A Useful Image?
Tissue
Water content (%)
The spin-lattice relaxation time (T1) and spin-spin relaxation time (T2) of
various biological tissues at 0.2 tesla
Skeletal muscle
79
Tissue
Myocardium
Liver
80
71
Fat
240
20
60
10
Kidney
81
Muscle
400
40
50
10
Gray matter
495
85
100
10
Brain white matter
84
White matter
390
70
90
20
Brain gray matter
72
Lung
460
90
80
30
Nerve
56
Kidney
670
60
50
10
Femur cortex
12
Liver
380
20
40
20
Teeth
10
Liver metastases
570
190
40
10
Lung carcinoma
940
460
20
10
Water Content of fat-free normal human tissue
Figure by MIT OpenCourseWare.
T1, msec
T2, msec
Source: Morgan and Hendee, 1984.
Figure by MIT OpenCourseWare.
Cite as: Karl Helmer, HST.583 Functional Magnetic Resonance Imaging: Data Acquisition and Analysis, Fall 2006. (Massachusetts Institute
of Technology: MIT OpenCourseWare), http://ocw.mit.edu (Accessed MM DD, YYYY). License: Creative Commons BY-NC-SA.
Magnetic Resonance Imaging
Figure removed due to copyright restrictions.
Four MRI images showing typical anatomical detail. Figure 4.1 in Gadian, D. NMR and its Applications to Living
Systems. New York, NY: Oxford University Press, 1996.
Cite as: Karl Helmer, HST.583 Functional Magnetic Resonance Imaging: Data Acquisition and Analysis, Fall 2006. (Massachusetts Institute
of Technology: MIT OpenCourseWare), http://ocw.mit.edu (Accessed MM DD, YYYY). License: Creative Commons BY-NC-SA.
Magnetic Resonance Image Formation
What do we need?
1. Ability to image thin slices
2. No projections - image slices with arbitrary orientation
3. Way to control the spatial resolution
4. Way to carry over the spectroscopic contrast mechanisms
to imaging.
Cite as: Karl Helmer, HST.583 Functional Magnetic Resonance Imaging: Data Acquisition and Analysis, Fall 2006. (Massachusetts Institute
of Technology: MIT OpenCourseWare), http://ocw.mit.edu (Accessed MM DD, YYYY). License: Creative Commons BY-NC-SA.
Magnetic Resonance Image Formation
ω = γB0
signal = A sin(ωt + φ )
Time
(A)
Frequency
(B)
A wave can be expressed as a function of time (A) or of frequency (B). (A) Represents
a waveform that goes on forever
Figure by MIT OpenCourseWare.
How can we spatially encode this signal?
Cite as: Karl Helmer, HST.583 Functional Magnetic Resonance Imaging: Data Acquisition and Analysis, Fall 2006. (Massachusetts Institute
of Technology: MIT OpenCourseWare), http://ocw.mit.edu (Accessed MM DD, YYYY). License: Creative Commons BY-NC-SA.
Magnetic Resonance Image Formation
- Slice Selection
Magnetic field gradients: B = B(position)
Beff = B0 + Gz z
ω eff = γ ( B0 + Gz z )
Gz z << B0
precessional frequency is
now a function of position
Cite as: Karl Helmer, HST.583 Functional Magnetic Resonance Imaging: Data Acquisition and Analysis, Fall 2006. (Massachusetts Institute
of Technology: MIT OpenCourseWare), http://ocw.mit.edu (Accessed MM DD, YYYY). License: Creative Commons BY-NC-SA.
Magnetic Resonance Image Formation
- Slice Selection
2π (Δν )
Δz =
γGz
Dni
n1
Δν = frequency bandwidth
Δz = slice thickness
Dni
n2
Dni
Gz
Dz
z1
Dz
z2
Dz
z3
n3
Tissue at position zi will absorbs RF energy with a center frequency ni. Each position has a unique
resonant frequency. The slice thickness Dz is determined by the amplitude of Gz, and the bandwidth
of transmitted frequencies Dn.
Figure by MIT OpenCourseWare. After Brown and Semelka.
MRI: Basic Principles and Applications - Brown, Semelka
Cite as: Karl Helmer, HST.583 Functional Magnetic Resonance Imaging: Data Acquisition and Analysis, Fall 2006. (Massachusetts Institute
of Technology: MIT OpenCourseWare), http://ocw.mit.edu (Accessed MM DD, YYYY). License: Creative Commons BY-NC-SA.
Magnetic Resonance Image Formation
- Slice Selection
How do we excite only a slice of spins?
Fourier Pairs!
sinc
rect
FT
time
frequency
Cite as: Karl Helmer, HST.583 Functional Magnetic Resonance Imaging: Data Acquisition and Analysis, Fall 2006. (Massachusetts Institute
of Technology: MIT OpenCourseWare), http://ocw.mit.edu (Accessed MM DD, YYYY). License: Creative Commons BY-NC-SA.
Magnetic Resonance Image Formation
- Phase Encoding
So far we have a slab of tissue whose spins are
excited. The next step is to place a grid over
the slab and define pixels.
Cite as: Karl Helmer, HST.583 Functional Magnetic Resonance Imaging: Data Acquisition and Analysis, Fall 2006. (Massachusetts Institute
of Technology: MIT OpenCourseWare), http://ocw.mit.edu (Accessed MM DD, YYYY). License: Creative Commons BY-NC-SA.
Magnetic Resonance Image Formation
- Phase Encoding
Beff = B0 + G y y
Gy
ν eff
γ
=
( B0 + G y y )
2π
νeff < ν0
νeff > ν0
Center of
magnet
Cite as: Karl Helmer, HST.583 Functional Magnetic Resonance Imaging: Data Acquisition and Analysis, Fall 2006. (Massachusetts Institute
of Technology: MIT OpenCourseWare), http://ocw.mit.edu (Accessed MM DD, YYYY). License: Creative Commons BY-NC-SA.
Magnetic Resonance Image Formation
- Phase Encoding
Apply gradient for a finite duration ⇒ φ = φ(y)
(the phase of M over each region of the sample depends
upon it’s position)
This is because the gradient makes each spin precess with
an angular frequency that depends on it’s position. For
the duration of the gradient, t, spins move faster or slower
than ω0 depending upon where they are. After the gradient
is turned off, all spins again precess at ω0.
The phase accumulated
during time, t, is:
φ = γG y yt
Cite as: Karl Helmer, HST.583 Functional Magnetic Resonance Imaging: Data Acquisition and Analysis, Fall 2006. (Massachusetts Institute
of Technology: MIT OpenCourseWare), http://ocw.mit.edu (Accessed MM DD, YYYY). License: Creative Commons BY-NC-SA.
Magnetic Resonance Image Formation
- Phase Encoding
z’
M after a 90°
pulse
y’
x’
Turn on the phase encoding gradient
z’
z’
y’
x’
Gy = 0
z’
y’
x’
Gy < 0
y’
x’
Gy > 0
Cite as: Karl Helmer, HST.583 Functional Magnetic Resonance Imaging: Data Acquisition and Analysis, Fall 2006. (Massachusetts Institute
of Technology: MIT OpenCourseWare), http://ocw.mit.edu (Accessed MM DD, YYYY). License: Creative Commons BY-NC-SA.
Magnetic Resonance Image Formation
Frequency Encoding (Readout)
Now we need to encode the x-direction...
How do we spatially encode the
frequency of the signal?
Can we turn on another gradient?
When? And for how long?
Cite as: Karl Helmer, HST.583 Functional Magnetic Resonance Imaging: Data Acquisition and Analysis, Fall 2006. (Massachusetts Institute
of Technology: MIT OpenCourseWare), http://ocw.mit.edu (Accessed MM DD, YYYY). License: Creative Commons BY-NC-SA.
Magnetic Resonance Image Formation
Frequency Encoding (Readout)
We apply a gradient while the signal is being acquired
as the spin-echo is being formed.
π/2
π
RF
Signal
Gx
time
Therefore, the precessional frequency is a function of position
Cite as: Karl Helmer, HST.583 Functional Magnetic Resonance Imaging: Data Acquisition and Analysis, Fall 2006. (Massachusetts Institute
of Technology: MIT OpenCourseWare), http://ocw.mit.edu (Accessed MM DD, YYYY). License: Creative Commons BY-NC-SA.
Magnetic Resonance Image Formation
Spin-echo Pulse Sequence
Diagram removed due to copyright restrictions.
Source: Jolesz, F. A., and I. R. Young. Interventional MR. Informa Health Care, 1998.
Cite as: Karl Helmer, HST.583 Functional Magnetic Resonance Imaging: Data Acquisition and Analysis, Fall 2006. (Massachusetts Institute
of Technology: MIT OpenCourseWare), http://ocw.mit.edu (Accessed MM DD, YYYY). License: Creative Commons BY-NC-SA.
Gy
(1)
Mxy
Each acquisition
is separately encoded
with a different phase.
The sum total of the N
acquisitions is called
the ‘k-space’ data.
Signal
x
y
1
Phase Encoding:
Gx
2
j
3
2j
4
3j
5
4j
6
5j
7
6j
8
7j
9
8j
10
9j
11
10j
= f (x)
j = f (y)
N
Nth Phase
Encoding Gradient
Nth Frequency
Encoding Gradient
Nth
Signal
Figure by MIT OpenCourseWare.
Cite as: Karl Helmer, HST.583 Functional Magnetic Resonance Imaging: Data Acquisition and Analysis, Fall 2006. (Massachusetts Institute
of Technology: MIT OpenCourseWare), http://ocw.mit.edu (Accessed MM DD, YYYY). License: Creative Commons BY-NC-SA.
The Effect of Frequency Encoding on the
Signal (dephasing gradient)
(2)
TE/2
O
180
TE/2
RF
90
O
180
O
TE
Gslice
Dephaser
Gfreaquency encode
Read
Phase
Receiver
Echo
(a)
(b)
(a) Frequency encoding gradient is played along one of the two principal axes with the selected slice. "Dephaser"
of the pulse avoids severe dephasing of the echo due to the read gradient. (b) A useful depiction is a phase plot
along an axis running from -180 degrees to +180 degrees.
Figure by MIT OpenCourseWare. After Brown and Semelka.
Cite as: Karl Helmer, HST.583 Functional Magnetic Resonance Imaging: Data Acquisition and Analysis, Fall 2006. (Massachusetts Institute
of Technology: MIT OpenCourseWare), http://ocw.mit.edu (Accessed MM DD, YYYY). License: Creative Commons BY-NC-SA.
(3)
z
y
Slice-select
refocusing
gradient
x
The effect of having the gradient on during the time that
the magnetization is moving from the z-axis to the y-axis is
to curve the path. In general, one needs to apply a slice
refocussing gradient of opposite magnitude after the RF
pulse so that the spins are in phase at the end of the pulse.
The area of the negative gradient must be one half the area
of the slice selection gradient pulse.
Cite as: Karl Helmer, HST.583 Functional Magnetic Resonance Imaging: Data Acquisition and Analysis, Fall 2006. (Massachusetts Institute
of Technology: MIT OpenCourseWare), http://ocw.mit.edu (Accessed MM DD, YYYY). License: Creative Commons BY-NC-SA.
Structure of MRI Data: k-space
A/D, 256 points
view -128
k-space 256 x 256 points
view -55
view 40
Row 40
Row -55
Row -128
kx = frequency
ky = phase
Figure by MIT OpenCourseWare.
Cite as: Karl Helmer, HST.583 Functional Magnetic Resonance Imaging: Data Acquisition and Analysis, Fall 2006. (Massachusetts Institute
of Technology: MIT OpenCourseWare), http://ocw.mit.edu (Accessed MM DD, YYYY). License: Creative Commons BY-NC-SA.
Structure of MRI Data: k-space
What is k-space?
The time-domain signal that we collect from each
spatially encoded spin echo gets put in a matrix.
This data is called k-space data and is a space of
spatial frequencies in an image.
To get from spatial frequencies to image space
we perform a 2-D Fourier Transform of the
k-space data.
General intensity level is represented by low spatial
frequencies; detail is represented by high spatial freq’s.
Cite as: Karl Helmer, HST.583 Functional Magnetic Resonance Imaging: Data Acquisition and Analysis, Fall 2006. (Massachusetts Institute
of Technology: MIT OpenCourseWare), http://ocw.mit.edu (Accessed MM DD, YYYY). License: Creative Commons BY-NC-SA.
Images removed due to copyright restrictions.
Three MRI photos originally found at: http://www.indyrad.iupui.edu/public/lectures/mri/iu_lectures/mri_homepage.htm
Cite as: Karl Helmer, HST.583 Functional Magnetic Resonance Imaging: Data Acquisition and Analysis, Fall 2006. (Massachusetts Institute
of Technology: MIT OpenCourseWare), http://ocw.mit.edu (Accessed MM DD, YYYY). License: Creative Commons BY-NC-SA.
Structure of MRI Data: k-space
Pair of diagrams removed due to copyright restrictions.
See http://www.jsdi.or.jp/~fumipon/mri/K-space.htm
Cite as: Karl Helmer, HST.583 Functional Magnetic Resonance Imaging: Data Acquisition and Analysis, Fall 2006. (Massachusetts Institute
of Technology: MIT OpenCourseWare), http://ocw.mit.edu (Accessed MM DD, YYYY). License: Creative Commons BY-NC-SA.