Magnetic Resonance Imaging II

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Magnetic Resonance Imaging II

• K-space data acquisition and image
  reconstruction

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K-space matrix

• MR data are initially stored in the k-space
  matrix, the frequency domain repository
• The axes have units of cycles/unit distance
• Each axis is symmetric about the center of
  k-space, ranging from fmax to fmax
• Low-frequency signals are mapped around the
  origin of k-space and high-frequency signals are
  mapped further from the origin in the periphery

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K-space matrix (cont.)

• Frequency domain data are encoded in the kx
  direction by the frequency encode gradient (FEG),
  and in the ky direction by the phase encode
  gradient (PEG) in most image sequences
• Lowest spatial frequency increment is the
  bandwidth across each pixel

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Two-dimensional data acquisition

• MR data acquired as a complex, composite
  frequency waveform
• With methodical variations of the PEG during each
  acquisition, the k-space matrix is filled to
  produce the desired variations across the
  frequency and phase encode directions

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• Narrow band RF excitation pulse applied
  simultaneously with the slice select gradient
  (SSG)
• Energy absorption dependent on amplitude and
  duration of the RF pulse at resonance
• Longitudinal magnetization converted to
  transverse magnetization, extent of which depends
  on saturation of spins and angle of excitation
• 90-degree flip angle produces maximal transverse
  magnetization

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• Phase encode gradient (PEG) applied for a brief
  duration to create phase difference among spins
  along the phase encode direction
• Produces several views of the data along the ky
  axis, corresponding to the strength of the PEG
• Refocusing 180-degree pulse delivered after
  selectable delay time, TE/2
• Inverts direction of individual spins and
  reestablishes phase coherence of transverse
  magnetization with formation of echo at time TE

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• During echo formation and subsequent decay,
  frequency encode gradient (FEG) applied
  orthogonal to both slice select and phase encode
  gradient directions
• Encodes precessional frequencies spatially along
  the readout gradient

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• Simultaneous to application of FEG and echo
  formation, computer acquires the time-domain
  signal using an analog-to-digital converter (ADC)
• Sampling rate determined by excitation bandwidth
• One-dimensional Fourier transform converts the
  digital data into discrete frequency values and
  corresponding amplitudes
• Proton precessional frequencies determine
  position along the kx (readout) direction

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• Data deposited in k-space matrix in a row,
  specifically determined by the PEG strength
  applied during excitation
• Incremental variation of the PEG throughout the
  acquisition fills the matrix one row at a time
• Possible to acquire the phase encode data in
  nonsequential order to fill portions of k-space
  more pertinent to the requirements of the exam
  (e.g., in low-frequency, central area of k-space)
• After matrix is filled, columns contain
  positionally dependent phase change variations
  along the ky (phase encode) direction

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• Two-dimensional inverse Fourier transform decodes
  the frequency domain information piecewise along
  the rows and then along the columns of k-space
• Final image is a spatial representation of the
  proton density, T1, T2, and flow characteristics
  of the tissue using a gray-scale range
• Each pixel represents a voxel thickness
  determined by slice select gradient strength and
  RF frequency bandwidth

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K-space segmentation

• Central area of k-space (lower spatial
  frequencies) represents the bulk of the
  anatomical information
• Information near the center of k-space provides
  the large area contrast in the image
• Outer areas in k-space contribute to the
  resolution and detail

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2D multiplanar acquisition

• Direct axial, coronal, sagittal, or oblique
  planes can be obtained by energizing the
  appropriate gradient coils during image
  acquisition
• The slice select gradient determines the
  orientation of the slices
• Axial uses the z-axis coils
• Coronal uses the y-axis coils
• Sagittal uses the x-axis coils
• Oblique plane acquisition depends on a
  combination of two or more coils energized
  simultaneously

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Acquisition time

• Time required to acquire an image is equal to
• Spin echo sequence for a 256 x 192 image matrix
  and two averages per phase encode step with TR
  600 msec yields an imaging time of 3.84 minutes
• Where nonsquare pixels are used, the phase encode
  direction is typically placed along the small
  dimension of the image matrix

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Multislice data acquisition

• Average time per slice significantly reduced
  using multiple slice acquisition methods
• Several slices within the tissue volume
  selectively excited during a TR interval to fully
  utilize the (dead) time waiting for longitudinal
  recovery in a specific slice
• This requires cycling all of the gradients and
  tuning the RF excitation pulse many times during
  the TR interval

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Multislice data acquisition (cont.)

• Total number of slices is a function of TR, TE,
  and machine limitations
• C is a constant dependent on MR equipment
  capabilities (computer speed, gradient
  capabilities, RF cycling, etc.)
• Long TR acquisitions such as proton density and
  T2-weighted sequences provide greater number of
  slices than T1-weighted sequences with short TR

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Data synthesis

• Data synthesis takes advantage of the symmetry
  and redundant characteristics of the frequency
  domain signals in k-space
• Acquisition of as little as one-half the data
  plus one row of k-space allows the mirroring of
  complex conjugate data to fill the remainder of
  the matrix
• Reduces the acquisition time by nearly one-half
• Penalty is a reduction in the SNR and potential
  for artifacts

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Fast spin echo acquisition

• FSE technique uses multiple phase encode steps in
  conjunction with multiple 180-degree refocusing
  RF pulses per TR interval to produce a train of
  up to 16 echoes
• Each echo experiences differing amounts of phase
  encoding that correspond to different lines in
  k-space
• Points near the center of k-space acquired from
  first echoes for best SNR

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Inversion recovery acquisition

• Phase and frequency encoding occur similarly to
  the spin echo pulse sequence
• Since TR is typically long, several slices can be
  acquired within the volume of interest
• STIR (short tau inversion recovery) and FLAIR
  (fluid attenuated inversion recovery) pulse
  sequences are commonly used

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Gradient recalled echo acquisition

• Similar to standard spin echo sequence with a
  readout gradient reversal substituting for the
  180-degree pulse
• With small flip angles and gradient reversals,
  considerable reduction in TR and TE is possible
  for fast image acquisition ability to acquire
  multiple slices is compromised
• PEG rewinder pulse of opposite polarity applied
  to maintain phase relationship from pulse to pulse

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GRE acquisition (cont.)

• Gradient echo image acquisition time given by
  same expression as for spin echo technique
• Gradient-echo sequence for a 256 x 192 image
  matrix, two averages, and TR 30 msec, imaging
  time is approximately 15.5 seconds
• Compromises include SNR losses, magnetic
  susceptibility artifacts, and less immunity from
  magnetic field inhomogeneities

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Echo planar image acquisition

• EPI acquisition provides extremely fast imaging
  time
• For single-shot EPI, image acquisition typically
  begins with a standard 90-degree flip, then a
  PEG/FEG gradient application to initiate
  acquisition of data in periphery of k-space,
  followed by a 180-degree echo-producing pulse
• Immediately after, an oscillating readout
  gradient and phase encode gradient blips are
  continuously applied to stimulate echo formation
  and rapidly fill k-space in a stepped pattern

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EPI acquisition (cont.)

• Echo planar images typically have poor SNR, low
  resolution, and many artifacts
• Technique offers real-time snapshot image
  capability with 50 msec or less total acquisition
  time
• Emerging as a clinical tool for studying
  time-dependent physiologic processes and
  functional imaging

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My brain hurts

• With apologies to Monty Python

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