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Review Hydrogen nuclei are protons spinning
charges. Spinning protons align along the
constant field B0. Magnetization is determined
by the aligning. Spinning rate is the
precessional rate. Determined by the B0 as
described by the LARMOR equation.
B0
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Review
42.6 MHz per Tesla is the relation in the Larmor
equation. RF excitation flips protons away from
B0 - all protons experience this - they are in
phase coherence during RF Relaxation or
realignment back along B0 occurs by T1 and
T2 -
B0
S
3
Review of T2 T2s are on the order of 10-1000
milliseconds. Full dephasing occurs after 5 x
T2. T2 does not change with B0 (T1 increases
with B0). T2 is affected by interactions of
protons with other protons. Spin-spin relaxation
processes are important. More macromolecules
large of stationary protons shorter
T2. More water large mobile protons
less interaction longer T2.
time
4
Review of T1 T1s are on the order of
seconds. Full relaxation occurs after 5 x T1. T1
increases with B0 - faster precession, easier to
align along B0 than against B0 more align
along B0 more protons greater
magnetization... T1 is affected by interactions
of protons with the lattice or the
microenvironment... More macromolecules greater
proton interaction shorter T1. Lipids
long C-H chains greater interaction
shorter T1.
time
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Recipe for MR The Magnet
1. Stable field - superconducting,
LHe-cooled 2. Homogeneous - 0.1 ppm
homogeneity 3. Precise field strength - 1.5
Tesla 15,000 gauss
6
Recipe for MR The RF Coil
1. Pulses RF energy at any given frequency. 2.
Vary power to control the proton excitation. 3.
Detects B0 fluctuations as signals ... 4. Wide
variety of RF coil sizes and shapes...
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Raw MR Spectrum - Brain
Mostly water !
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Fields required for localized MRS
1. B0 - spin state separation 2. RF - spin
state transitions 3. Gradients - to localize
voxel
Available in all commercial imaging systems at
1.0T and above.
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Recipe for MR The Gradient Coils
1. Changes B0 linearly by 1 gauss/cm from
center. 2. Creates linear distribution of
magnetic fields. 3. Links space with frequency -
"Larmor Equation"
F 42.8 (B0)
Change B0 over length Each cm. 1 gauss Each
cm. 4 kHz
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Fundamentals II Building Blocks of an MR Image
Gradient pulses in a sequence encode signal
frequencies and signal phases to map proton
positions in the magnet...
Proton signal frequency
14,950 gauss
15,050 gauss
63.7 Mhz
64.1 Mhz
-phase
Phase of signal
phase
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The MRI "sequence"uses changes in the magnetic
field to map frequency and phase of the
protons. "Gradient coils" do this...
X gradient
Z gradient
Y gradient
Z gradient
Readout Echo "Frequency- Encode"
Slice 90 RF
Phase Encode
Slice 180 RF
256
Frequency- encoding along Y
Y
Phase Encode along X
1
256
X
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Magnetic Field Gradients Summary
"Gradients"
1. They change the static field when turned
on... (off until pulsed on) by max. 1
gauss/cm. 2. This change is small 50 parts in
15,000. 3. We have gradients in all 3
directions.
Y
15,050 gauss
14,950 gauss
Field
Z
X
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Gradient coils are built to create a magnetic
field gradient (G/cm) Along the x, y, and z axes
to correspond to 3-D space... The image
orientation depends on which gradient is used for
slice selection...
Y
Z
X
Y
AXIAL
Y
SAGITTAL
CORONAL
X
Z
X
Z
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Y
AXIAL
X
Y
SAGITTAL
CORONAL
Z
X
Z
Z
Y
X
Slice Read Phase
Y
Z
Z
X
X
Y
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Magnetic Field Gradients Summary
"Gradients"
1. The changes in the static field (115,000)
changes the resonating frequency of the
protons. 2. We can now frequency encode the
proton signals (the spin-echo) from the
magnet front to the back (or top to bottom).
15,050 gauss
14,950 gauss
Z
63.7 Mhz
64.1 Mhz
lower frequencies
higher frequencies
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Slice Selection

• 1. Done by slice-selection gradient.
• 2. Changes the excitation frequency of
  protons along direction of the slice selection
  gradient.
• 3. Broadcasting over an excitation bandwidth
  excites only spins within a slice.
• 4. The bandwidth or slice selection strength
  changes slice thickness.
• 5. Slice offset is determined by broadcast
  frequency.

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Looking at a set of gradient coils...
Y
Z
Current in
Current out
X
The magnetic field changes by 2.2
gauss/cm.
f ? / 2p (B0 z Gz)
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From the Larmor equation, if the field B0
changes, then the proton excitation and detection
frequencies change as well.... This means that
gradients alter B0 allow selective excitation
....
f 42.5 (B0 z Gz)
Gradient field subtracts from B0
Gradient field adds to B0
Isocenter No change!
z Gz
- z Gz
0
63.9MHz
64.1MHz
63.7MHz
Excitation frequencies for protons located as
shown...
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Thus, to excite protons in the head, we would
need an excitation frequency of 64.1 MHz. Other
protons at other postions and frequencies, would
not be excited ( wrong frequency )
z Gz
- z Gz
0
63.9MHz
63.7MHz
64.1MHz
1.500 T
1.499 T
1.501 T
Excitation frequencies for protons located as
shown...
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Selective Sinc RF Pulses
"Sinc" rf pulse is a shaped rf pulse
of100-10000W but still contains RF frequencies
around a carrier
time
Power over a "bandwidth" of frequencies at a
carrier frequency of 63.9 MHz over 8 msec...
63.9 MHZ
100W
RF power at a center frequency over a BW
16 KHz
-16 KHz
frequency
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Slice selection uses both a RF sinc pulse
applied during a gradient pulse
magnet
RF "sinc" pulse
63.91 Mhz
Z
slice position
gradient along Z
Z gradient
4 msec
frequency
The signal arises only from the slice
SI
phase
slice position corresponding to 63.91 MHz
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Mechanics of Multi-Slice
Within TR, a series of 90-180-echoes are made,
each at different excitation frequency... the
longer the TR, the more slices possible.
63.5 MHz
63.7 MHz
63.9 MHz
64.1 MHz
echo
echo
echo
180
90
180
90
180
180
90
echo
90
TE
TR
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However, when a gradient is on during RF, the
induced signal is rapidly dephased...since
gradients dephase all protons
RF "sinc" pulse
slice selection gradient
FID rapidly dies away because of the SS
gradient...
SI
Time
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The loss of phase coherence is a loss of
signal intensity...
SI
time
Dephasing is caused by natural T2 and by gradients
1. applied magnetic field gradients applied along
x,y,z directions. 2. natural magnetic field
gradients (T2) due to susceptibility.
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Reversing a gradient will rephase was dephased...
RF "sinc" pulse
slice selection gradients
4 msec
Signal rephases to because of gradient
direction reversal....
FID
SI
Time
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Frequency Encoding

• 1. Done by readout or frequency-encoding
  gradient.
• 2. Changes Larmor frequency of protons along
• direction of the gradient during formation of
• the spin-echo.
• 3. FT of echo arranges protons according to
• their Larmor frequency.
• 4. Produces one view (!) of the image.
• 5. This view is (usually) 256 pixels wide.

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We can digitize this signal caused by the
gradient reversal... The gradient-recalled echo
is then sampled while a frequency-encoding
gradient is on...
RF "sinc" pulse
slice selection gradients
frequency encoding gradient
The Gradient-recalled-echo (GRE)
FID
Time
SI
But this will also dephase the signal!
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By dephasing and then rephasing, we can collect a
complete GRE. The frequency-encoded GRE is now
ready to digitize...
RF "sinc" pulse
slice selection gradients
frequency encoding gradient
GRE
FID
Time
SI
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A spin-echo can be collected in a similar manner
using a 180 RF pulse
90 RF "sinc" pulse
180 RF "sinc" pulse
slice selection gradients
4 msec
Spin-echo
FID
Time
SI
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Adding the frequency-encoding gradients creates a
spin-echo
90 RF "sinc" pulse
180 RF "sinc" pulse
slice selection gradients
4 msec
digitize here
frequency-selection gradients
FID
Spin-echo
Time
SI
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The Fourier Transform
SI
Frequencies
"Real World spin-echo acquired over time
SI vs. time"
Time
SI
Frequencies
"Spin-echo projection SI vs. frequency"
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Field
Higher
Lower
1.499T
1.501T
Lower frequencies
RF coil
Higher frequencies
SI
SI
FT
Time
Frequencies
MR signal from coil
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Field
Higher
Lower
1.499T
1.501T
Lower frequencies
RF coil
Higher frequencies
SI
SI
FT
Time
Frequencies
MR signal from coil
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Phase Encoding

• 1. Done by phase-encoding gradient.
• 2. Changes the PHASE of protons along direction
  of the PE
• gradient from view to view.
• 3. Amount of phase change is due to the
  POSITION of protons along the phase-encoding
  gradient.
• 4. 128 or 256 phase steps done during the total
  scan.
• 5. FT of phase-encoded views produces an image

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Phase-encoding gradients complete the sequence...
90 RF "sinc" pulse
180 RF "sinc" pulse
Time
slice selection gradients
4 msec
frequency-selection gradients
phase-encoding gradient steps
Spin-echo
FID
SI
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All "Real World signals" contain amplitude,
frequency, and phase. Every MR image has an
amplitude (signal strength) at each frequency
and at each phase of each frequency...
phase of each frequency
The MR image acquired from the RF coil is a
matrix of 256 frequencies and up to 256 phases at
each frequency. The frequency and phases used to
produce an MR image are called... "k-space".
Amplitude
frequency
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The MR Sequence Determines How k-space is
Sampled...
View 256
90 RF
180 RF
Spin-echo
FE
Frequency-encoding of each spin-echo
View 4
Phase-encoding of each frequency...
View 1
1. Typically, each spin-echo is acquired and
digitized into 256 frequency points or "view"
. The FT of a view gives a projection along FE
axis... 2. To distinguish protons along PE axis,
we alter the phase of each view by applying a
different phase-encoding gradient strength...
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Unique views from 4 different phase-encoding
steps...
90 RF
180 RF
Spin-echo
FE
Frequency-encoding of each spin-echo
Phase-encoding of each frequency...
phase change along PE axis...
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The phase change for each view is a frequency. FT
of this frequency change gives projection along
PE.
FT
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PROCESSING THE MRI IMAGE

• 1. The computer starts with 128 - 256 digitized
  spin-echoes.
• 2. Each spin-echo has a slight phase change due
  to the phase-encoding gradient.
• 3. FT each spin-echo.
• 4. FT each point in the spin-echo as a function
  of phase.
• 5. The result is a 256 X 256 grid of 8-bit
  intensities.
• 6. This corresponds to a 256 X 256 image with
  256 gray levels.

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FT
FT
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