KSpace

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K-Space

• Contemporary Topics in Imaging
• Stephanie Powell
• October 5, 2004

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MRI Basics
Magnetic Resonance Precession of protons in a
magnetic field.
Proton spin (?) at a certain location will be
equal to the magnetic field B?.
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Radiofrequency Slice Encoding
A RF pulse is sent in at a specific frequency to
excite protons at a specific slice along one
axis.
RF signal received after the pulse would be
energy release from the protons at this slice
only.
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Phase Encoding
The magnetic gradient application along one axis
of the transverse plane (the XY plane) is
referred to as phase encoding. The location
along the y-axis will determine the gradient
intensity.
This encoding results in a position
differentiation along the y-axis.
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Frequency Encoding
The magnetic gradient application along one axis
of the transverse plane (the XY plane) is
referred to as frequency encoding. The location
along the x-axis will determine the magnitude of
the magnetic field.
This encoding results in a position
differentiation along the x-axis.
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Fourier Transformation
An FID signal is received by the RF coils. Any
wave signal is composed of many smaller wave
components.
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Fourier Transformation
Fourier information is encoded into grayscale.
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2D Fourier Transform
One point in the Fourier domain corresponds to a
single wave at the specified frequency and
amplitude in the spatial domain.
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K-Space
Slice Encoding
Freq. Encoding
Phase Encoding
FFT
K-Space Spatial Frequency Image Information
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Low/High Frequency K Space Information
K-Space contains high and low frequency spatial
information.
K-space must be complete in order for a complete
spatial domain image.
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K-space Acquisition
K-space is conventionally collected
rectilinearly, also known as spin-warp, where
each line of k-space corresponds to one phase
gradient.
The k-space line also contains frequency and
amplitude corresponding to the x-position and the
number of protons precessing at a certain
location.
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Fourier Reconstruction
Since k-space is the spatial frequency domain of
an image, a simple 2DFT can be performed to
transform the image into spatial domain.
The Fourier transform is computed first in the x
direction (u direction) and then in the y
direction (v direction) or vice-a-versa.
The result is the image in the spatial domain.
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Radon Reconstruction
Originally, k-space collection was in projection
format similar to CT imaging.
Radon reconstruction is used to transform
projection information into 2-dimensional k-space.
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Partial K-space Acquisition
New research is being done to decrease total scan
time.
Partial K-space acquisition is performed with the
assumption of symmetry of high frequency Fourier
space.
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Real Time Changes
Decreased scan times has pushed MRI imaging into
real-time imaging.
Real-time imaging to require the beating heart is
completed with projection k-space acquisition.
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K-space trajectory path collection
K-space can be collected in paths different from
the conventional rectilinear trajectory.
These methods require interpolation which results
in image blurring, but the scan time is decreased.
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fMRI
A latest development in imaging is functional MRI.
fMRI relies on BOLD, or blood oxygen level
dependent signal
In fMRI, the subject is stimulated followed by
the brain being imaged.
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Conclusion

• Understanding K-space is the key to improving MRI
  and increasing MRI application in the future.
• As K-space acquisition time decreases, MRI will
  be sufficient in imaging real-time movement, such
  as a beating heart.
• This opens the door for new possibilities for the
  high resolution MRI.

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Any Questions?