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![Page 1: Medical Imaging Systems: MRI Image Formation Instructor: Walter F. Block, PhD 1-3 Notes: Walter Block and Frank R Korosec, PhD 2-3 Departments of Biomedical.](https://reader033.fdocuments.in/reader033/viewer/2022051401/56649e2e5503460f94b1eb72/html5/thumbnails/1.jpg)
Medical Imaging Systems:MRI Image Formation
Instructor: Walter F. Block, PhD 1-3
Notes: Walter Block and Frank R Korosec, PhD 2-3
Departments of Biomedical Engineering 1,Radiology 2 and Medical Physics 3
University of Wisconsin - Madison
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MRI Physics: So far...
What we can do so far:
1) Excite spins using RF field at o2) Record time signal (Known as FID)3) Mxy decays, Mz grows4) Repeat.
But so far RF coils only integrate signal from entire body. We have no way of forming an image. That brings us to the last of the three magnetic fields in MRI.
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Image Formation Overview
• Gradient fundamentals• Slice Selection
• Limit excitation to a slice or slab• Can be in any orientation
• Gradient echo in-plane spatial encoding• Radial imaging ( like CT)• Frequency encoding• Phase encoding
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3nd Magnetic Field • Static High Field
• Termed B0
• Creates or polarizes signal• 1000 Gauss to 100,000 Gauss
• Earth’s field is 0.5 G
• Radiofrequency Field (RF)• Termed B1
• Excites or perturbs signal into a measurable form• O.1 G but in resonant with signal
• Gradient Fields • 1 -4 G/cm• Used to determine spatial position of signal• MR signal not based directly on geometry
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Gradient Coils
Fig. Nishimura, MRI Principles
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X Gradient Example: Gx
Magnetic field all along z, but magnetic strength can varies spatially with x. Stronger at right, no change in middle, weaker at left.
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Gradient Coil Fundamentals
• Gradient strength directly proportional to current in coil• On the order of 100 amps peak
• Performance• Power needed proportional to radius5
• Tight bore for patient• Strength – G/cm or mT/m
• 4 G/cm is near peak now for clinical scanners• Higher strength with localized gradients (research only)
• Slew rate• Need high voltages to change current quickly• 100- 200 T/m/s is high performance
• Rise to 1 G in .1 ms at 100 T/m/s• Limited by peripheral nerve stimulation
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Magnetic Field Gradient Timing Diagrams
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B0
Larmor Equation
PrecessionalFrequency
Static Magnetic Field
tB0 + Gx(t)x)
Before, only B0
Now with Gx
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Gx, Gy, Gz: One for each spatial dimension
Magnetic field all along z, but magnetic strength can vary spatially with x, y, and/or z.
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Two Object Example of Spatial Encoding
x
m(x)
t
sr(t)
Receiver Signal: No gradient
Gx On: Beat Frequency Demodulated Signal
Water
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Gz Gradient Example
The effects of the main magnetic field and the applied slice gradient. In this example, the local magnetic field changes in one-Gauss increments accompanied by a change in the precessional frequency from chin to the top of the head.
Image, caption: copyright Proruk & Sawyer, GE Medical Systems Applications Guide, Fig. 11
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Selective RF Excitation
Build RF pulse from sum of narrow frequency range
Recall frequency of RF excitation has to be equal
or in resonance with spins
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Slice Selection- Consider a pulse B1(t) that is multiplied by cos(ot). This is called
modulation .
B1(t) is called the RF excitation.
o is the carrier frequency = B0. Mixer
cos(ot)
B1(t) cos(ot)
A(t)
o f
Frequency profile of modulated RF pulse
o = 2fo
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Frequency Encoding
Spin Frequency (x)
Image each voxel along x as a piano key that has a different pitch. MR coil sums the “keys” like your ear.
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Frequency Encoding
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GRE Pulse Sequence Timing Diagram
SliceSelect
Freq.Encode
rf
Signal
°
TE
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Frequency Encoding & Data Sampling
FrequencyEncoding
GeneratedSignal
DAQ
SampledSignal
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In-plane Encoding
• MR signal in frequency encoding (x) is Fourier transform of projection of object
• Line integrals along y
• Encoding in other direction • Vary angle of frequency encoding direction
• 1D FT along each angle and Reconstruct similar to CT
• Apply sinusoidal weightings along y direction• Spin-warp imaging or phase-encoding
• By far the most popular
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2D Projection Reconstruction MRI
kx
Gx
Gy
DAQ
Reconstruction: convolution back projection or filtered back projection
ky
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Central Section Theorem in MRI
In MR, echo gives a radial line in spatial frequency space (k-space).
x’
x’
y’
x
y
Interesting - Time signal gives spatial frequency information of m(x,y)
ky
kx
F.T.
θ
θ
Object
CT Projection
MR Signal (t)
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k-Space Acquisition (Radial Sampling)
ky
kx
Y readout
X readout
kx
ky
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In-plane Encoding
• MR signal in frequency encoding (x) is Fourier transform of projection of object
• Line integrals along y
• Encoding in other direction • Vary angle of frequency encoding direction
• 1D FT along each angle and Reconstruct similar to CT
• Apply sinusoidal weightings along y direction• Apply prior to frequency encoding• Repeat several times with different sinusoidal weightings• Spin-warp imaging or phase-encoding• By far the most popular
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Phase Encoding: Apply Gy before Freq. encoding
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GRE Pulse Sequence Timing Diagram
SliceSelect
PhaseEncode
Freq.Encode
rf
Signal
°
TE
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PhaseDirection
Frequency DirectionOne line of k-space
acquired per TR
k-Space Acquisition
PhaseEncode
DAQ
SampledSignal
kx
ky
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kx
ky
k-Space Signal
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8 x 8512 x 512
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16 x 16512 x 512
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32 x 32512 x 512
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64 x 64512 x 512
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128 x 128
512 x 512
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256 x 256
512 x 512
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512 x 32512 x 512
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Scan Duration
Scan Time = TR PE NEX
TR = Repetition TimePE = Number of phase encoding valuesNEX = Number of excitations (averages)
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GRE Pulse Sequence Timing Diagram
SliceSelect
PhaseEncode
Freq.Encode
rf
Signal
°
TE
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Images of the Knee
-weighted T2-weightedNeeds longer TE
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T2 & T2* Relaxation: Sources of Image Contrast
Mxy
Time
T2*
T2
T2*
1 =T2
1 + B0
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t
Gx(t)
6GRADECH.AVI
Effects of Local Magnetic Inhomogeneity
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Perils of Gradient Echo Imaging and T2*
TE = 8 ms TE = 24 ms
0.17 T GE Orthopedic Scanner
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Image Formation Overview
• Gradient fundamentals• Slice Selection
• Limit excitation to a slice or slab• Can be in any orientation
• Gradient echo in-plane spatial encoding• Radial imaging• Frequency encoding• Phase encoding
![Page 43: Medical Imaging Systems: MRI Image Formation Instructor: Walter F. Block, PhD 1-3 Notes: Walter Block and Frank R Korosec, PhD 2-3 Departments of Biomedical.](https://reader033.fdocuments.in/reader033/viewer/2022051401/56649e2e5503460f94b1eb72/html5/thumbnails/43.jpg)
T1-, T2-, and Density-Weighted Images
T1-weighted T2-weighted -weighted
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T2-Weighted Image of the Spine
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Images of the Knee
-weighted T2-weighted
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T1-, T2-, and Density-Weighted Images
T1-weighted T2-weighted -weighted
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Spin Echo Parameters
TR TE
T1-weighting short (400 msec) short (20 msec)
T2-weighting long (3000 msec) long (100 msec)
-weighting long (3000 msec) short (20 msec)
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Signal vs Weighting
T1-weighting long T1, small signal short T1, large signalT2-weighting long T2, large signal short T2, small signal-weighting high , large signal low , small signal
T1-weighted T2-weighted -weighted