Transcript No Slide Title

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
MRI Physics: So far...
What we can do so far:
1) Excite spins using RF field at o
2) Record time signal (Known as FID)
3) Mxy decays, Mz grows
4) 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.
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
• Frequency encoding
• Phase encoding
• Spin echo formation
• SNR
• Generalized encoding
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
Gradient Coils
Fig. Nishimura, MRI Principles
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.
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
Magnetic Field Gradient Timing Diagrams
Larmor Equation
Before, only B0
Precessional
Frequency
Now with Gx
B0
Static Magnetic Field
(t)(B0 + Gx(t)x)
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.
Two Object Example of Spatial Encoding
Receiver Signal: No gradient
m(x)
Water
x
Demodulated Signal
Gx On: Beat Frequency
sr(t)
t
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
Selective RF Excitation
Recall frequency of RF excitation has to be equal
or in resonance with spins
Build RF pulse from sum of narrow frequency range
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
B1(t) cos(ot)
A(t)
cos(ot)
Frequency profile of modulated RF pulse
o
f
o = 2fo
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.
Frequency Encoding
GRE Pulse Sequence Timing Diagram
a°
rf
Slice
Select
Freq.
Encode
Signal
TE
Frequency Encoding & Data Sampling
Frequency
Encoding
Generated
Signal
DAQ
Sampled
Signal
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
2D Projection Reconstruction MRI
ky

kx
Gx
Gy
DAQ
Reconstruction: convolution back projection or filtered back projection
Central Section Theorem in MRI
Object
y
x
θ
In MR, echo gives a radial line
in spatial frequency space (kspace).
ky
θ
kx
F.T.
MR Signal (t)
Interesting - Time signal gives spatial frequency information of m(x,y)
k-Space Acquisition (Radial Sampling)
Y readout
X readout
kx
kx
ky
ky
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
Phase Encoding: Apply Gy before Freq. encoding
GRE Pulse Sequence Timing Diagram
a°
rf
Slice
Select
Phase
Encode
Freq.
Encode
Signal
TE
k-Space Acquisition
Phase
Encode
Sampled
Signal
DAQ
ky
Phase
Direction
kx
One line of k-space
acquired per TR
Frequency Direction
k-Space Signal
ky
kx
512 x 512
8x8
512 x 512
16 x 16
512 x 512
32 x 32
512 x 512
64 x 64
512 x 512
128 x 128
512 x 512
256 x 256
512 x 512
512 x 32
Scan Duration
Scan Time = TR  PE  NEX
TR = Repetition Time
PE = Number of phase encoding values
NEX = Number of excitations (averages)