Proton signal frequency

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Building an MR Image
Proton signal frequency
14,950 gauss
15,050 gauss
63.7 Mhz
64.1 Mhz
-phase
Phase of signal
phase
2
Basic MR Physics Hydrogen nuclei are protons.
Protons align along B0. Magnetization M is the
aligned along B0 (spin up) vs the aligned
against B0 (spin down). M N/N- exp - mB /
kT 5 ppm _at_ 1.5T, 10 ppm _at_ 3T.
B0
Larmor Equation
N
N
f ? / 2p B0
S
S
N
S
42.6 MHz/T E(spin up) - E(spin down) hf
B0
3
Vector model classical description Net
protons aligned together determines Net
magnetization, M.


Z


X
Y
4
Quantum mechanical description Magnetic field
defines spin quantization axis.
sp - down
se - up
sp - up
f
f128 MHz
sp - down
se - down
sp - up
1 2 3
B0 (T)
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RF pulse flips protons from Z into XY plane
T1 and T2 relaxation is the key to understanding
MR Tissue Contrast
RF excitation
Z

XY plane
T1 and T2 relaxation times descibe how fast the
proton spins can relax or realign back along
Z....
6
T1 and T2 relaxation of M occurs over time as
RF relaxation
M M0 (1-exp -TR/T1)
TR
4 sec
M M0 (exp -TE/T2)
TE
80 msec
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MR Spectrum
Water peak used for imaging.
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Each proton has a unique T1 and T2
"T1-weighted"
"T2-weighted"
Protons relax back along B0 by T1
Protons lose phase coherence by T2 or T2.
Brain
Lipid
M
M
Brain
Lipid
TR
TE
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T1 and T2 Relaxation Dominates MRI Contrast
100
TE 25
50
75
TR 150
300
600
1200
0.5 Tesla
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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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Electromagnetic Fields required for MRI
1. B0 - spin state separation 2. RF - spin
state transitions 3. Gradients - to localize
voxel
12
Current passing thro any of the 3 three gradient
coils creates magnetic fields that add and
subtract from B0 with no effect at magnet
isocenter. By changing the field, the Larmor
frequency changes...In this way, one can excite
or detect protons in any position in the
magnet...
Current in
Current out
front
back
isocenter
Adds to B0
Subtracts from B0
No change
1.500 T
1.5001 T
1.4999 T
64.1 MHZ
63.9 MHZ
63.7 MHZ
f ? / 2p (B0 z Gz)
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Looking at a set of gradient coils...
Y
Z
Current in
Current out
X
The magnetic field changes by 1
gauss/cm max.
f ? / 2p (B0 z Gz)
14
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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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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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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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
19
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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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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The RF "sinc" pulse is a shaped burst of rf energy
sinx/x sinc
response in tissue...
63.90 Mhz
"bandwidth" of the pulse 16 Khz related to
slice thickness...
frequency response...
64.06 Mhz
63.74 Mhz
22
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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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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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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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!
28
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
31
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
33
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...
35
Phase-encoding acquires 256 unique
phase-encoded views...
View 256
90 RF
180 RF
Spin-echo
FE
Frequency-encoding of each spin-echo
View 4
Phase-encoding of each frequency...
View 1
Each view differs in strength of phase-encoding
gradient. More gradient more phase change. By
changing gradient 256 times, we get 256 views of
where protons are positioned along the PE axis...
36
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...
37
180
90
No phase change here - the "center echo"
180
90
positive phase changes
38
180
90
large negative phase changes - large negative PE
gradient pulse
180
90
less negative phase change
39
The phase change for each view is a frequency. FT
of this frequency change gives projection along
PE.
FT
40
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 16-bit
  intensities.
• 6. This corresponds to a 256 X 256 image with
  32768 gray levels.

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FT
FT
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Images and Sequences
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Tissue Contrast
Sequences
Parameters
Sequence type SE FATSAT
GRE MPGR, SPGR TR TE TI
(inversion time) View ordering
Slice thickness (ST) Matrix size (Nx,
Ny) Field-of-view (FOV) Averages (NEX) Echo
sampling (VB) Fractional views (V) Fractional
echo (FE) Slice gap (overlap)
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k-Space and MRI Physics
Frequency
Phase
FT

hi
lo
-
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128X256, 2 NEX, 12 FOV, 5mm
TR
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128X256, 2 NEX, 12 FOV, 5mm
TE
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400/20, 5 mm, 128X256, 12 FOV
NEX 2 1
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400/20, 128X256, 1 NEX, 12 FOV
ST
5 mm
3 mm
50
400/20, 5 mm, 256X256, 12 FOV, 2 NEX
Slice Gap
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Level / Window set correctly
Level / Window to noise level
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Matrix Size
400/20, 5 mm, 1 NEX, 12 FOV
Ny
Nx
128 (Ny) X 256 (Nx)
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FOV (can be square or rectangular)
Ny
Nx
24 x 12 FOV 24 cm along fe, 12 cm along pe
24 x 24 FOV 24 cm along fe and pe
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MRI IMAGE QUALITY

• Image Quality is determined by
• Spatial Resolution
• High Low Contrast
• Modulation Transfer Function
• Point Spread Function
• Contrast
• CNR
• Background signal
• Noise (statistical systematic)
• statistics - distribution-based
• bias - observer-based

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High Contrast Resolution
lp/mm 1 / 2? (mm)
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Spatial Resolution
Two images with the same field of view
(FOV) Different matrix sizes 25x25 versus
50x50 Picture element (pixel) size FOV/matrix
size Typical FOV 24 cm for brain. Typical
matrix 256x256 or 512x512
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Spatial Frequency
Ex An imaging system is to be purchased
for detecting high contrast calcifications that
are 50 microns in diameter in soft tissue. What
spatial frequency specification must this system
meet? d 50 microns 50 x 10-3 mm lp/mm
1/2d 1 / (2 x 50) x 10-3 mm
0.01 x 103 lp/mm
10 lp/mm 100 lp/cm.
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MRI has the most imaging contrast adjustments
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Intensity Resolution
Image intensity in each pixel or voxel is
represented by a value which is represented by
bits in the computer 8-bit, 16-bit, 32-bit. 8
bits 1 byte, 16 bits 2 bytes, 32 bits 4
bytes. short integers
long integers, real numbers This is the
internal binary representation of the intensity
value. 8 bits means you can represent 256 shades
of gray. Most black and white monitors show
images in 8-bit depth. 16 bits means you can
represent 32767 shades of gray. The DICOM 4
standard for medical imaging requires 16 bit
images. Heres how that works in a 4 bit
example Bit 3 2 1
0 8s 4s 2s 1s
Value 1 0 1 0
1 0 1 0 10
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Bits and Bytes
This is the internal binary representation of the
intensity value. Binary is base-2. Most
arithmetic is done in base 10. Computers use
base-2, base-8 (octal) and base-16
(hexadecimal). Heres the 4 bit example
Bit 3 2 1 0
8s 4s 2s 1s Value
1 0 1 0 1 0
1 0 10 The same example in base 10.
Place 3 2 1 0
1000s 100s 10s 1s Value
1 0 1 0 1000 0
10 0 1010
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ACR-NEMA MRI Phantom
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Distortion
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Truncation Artifact

• Discontinuities in sampling cause ringing in the
  image domain at the edges of the sampling window
• Ringing known as Gibbs artifact
• Minimized by smoothing or increased sampling.
• Caused by lack of digital resolution - of views
  in defining a sharp edge
• Occurs at interfaces of bright and dark edges
• Propagates concentrically over a short distance
• Reduced by increasing views or by smoothing.

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Gibbs Ringing
256 x 256
256 x 128
256 x 64
256 x 32
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RF Leaks
Poor shim