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Topics. spatial encoding - part 2. Slice Selection.  . y. 0. z. z gradient. x.  .  . . imaging plane. Slice Selection. slice thickness is determined by gradient strength. . . . . RF bandwidth. .  .  . . t 1. t 2. t 3. Slice Selection.  .

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  1. Topics • spatial encoding - part 2

  2. Slice Selection  y 0 z z gradient x    imaging plane

  3. Slice Selection slice thickness is determined by gradient strength     RF bandwidth     t1 t2 t3

  4. Slice Selection  z gradient direction Selection of an axial slice is accomplished by the z gradient.    z-axis graph of the z magnetic gradient 

  5. Slice Selection slice location is determined by the null point of the z gradient slice 1 slice 2 slice 3   RF bandwidth      

  6. Frequency Encoding • Within the imaging plane, a small gradient is applied left to right to allow for spatial encoding in the x direction. • Tissues on the left will have a slightly higher resonance frequency than tissues on the right. • The superposition of an x gradient on the patient is called frequency encoding. • Frequency encoding enables spatial localization in the L-R direction only.

  7. Frequency Encoding y higher frequency x R L z x gradient lower frequency

  8. Frequency Encoding 1 line of k-space A/D conversion, 256 points RF signal from entire slice

  9. Phase Encoding • An additional gradient is applied in the y direction to encode the image in the remaining direction. • Because the x gradient alters the frequencies in the received signal according to spatial location, the y gradient must alter the phase of the signal. • Thus, the points of k-space are revealed by recording the digitized RF signal after a phase encoding gradient application.

  10. Phase Encoding • The technique of phase encoding the second dimension in the imaging plane is sometimes referred to as spin warping. • The phase encoding gradient is “stepped” during the acquisition of image data for a single slice. Each step provides a unique phase encoding. • For a 256 x 256 square image matrix, 256 unique phase encodings must be performed for each image slice. The second 256 points in the x direction are obtained by A to D conversion of the received signal.

  11. Phase Encoding y x z y gradient, phase step #64 y gradient, phase step #192

  12. RF out RF in RF out RF in RF out RF in BEGIN Phase Encoding A/D conversion    2D k-space matrix gradient strength +128 line 128  A/D conversion     line N gradient strength N line -128  A/D conversion gradient strength -128 END

  13.       echo echo echo Spin Echo Imaging RF z gradient slice select y gradient phase x gradient readout

  14. Spin Echo Imaging k-space 256 x 256 points A/D, 256 points  row 40 row -55  view 40 row -128 view -55  • kx = frequency • ky = phase view -128

  15. MR Image Reconstruction • Acquisition of spatially encoded data as described allows for reconstruction of the MR image. • The frequency and phase data are acquired and form points in a 2D array . • Reconstruction of the image is provided by 2D inverse Fourier transform of the 2D array. • This method of spatially encoding the MR image is called 2D FT imaging.

  16. y x f(x,y) Discrete Fourier Transform F(kx,ky) is the 2D discrete Fourier transform of the image f(x,y) ky  kx F(kx,ky) MR image k-space

  17. Image Resolution and Phase Encoding • Resolution is always maximum in the frequency encoding direction because the MR signal is always digitized into 256 points. • Resolution can vary in the phase encoding direction depending on the number of phase steps used to acquire the image. • Because each phase encoding requires a separate 90 and 180 degree pulse, image acquisition time is proportional to the number of phase encode steps.

  18. Image Acquisition Time

  19. Image Acquisition Time • Example, TR 2000, 192 phase steps, 1 NEX imaging time = 6.4 minutes • At this rate, it would take 128 minutes to do an average 20 slice exam. • Because TR is typically much longer than TE, we can acquire the data for the other slices between the 90 degree RF pulses.

  20.     echo echo   echo   echo Multi-slice Imaging TR slice 1 TE slice 2 slice 3

  21. Multi-slice Imaging • The maximum number of slices that can be obtained in a single acquisition is calculated as follows:

  22. k-space Traversal • The most important phase encoding information is centered around the middle of k-space. • Typically, k-space is filled in an orderly manner, beginning with the returned echos obtained at the maximum negative y gradient strength and continuing to the maximum positive value.

  23. k-space Traversal • For images obtained with less than 256 views, the number of phase encodings is evenly divided between positive and negative values centered around zero. • Images reconstructed with less than 256 phase encodings have less detail in the phase encoding direction.

  24. ky 2 5 6 kx 256 1 2 8 256 1 2 8 256 decreased resolution

  25. Half Fourier Imaging • Because k-space is symmetrical, one half of the space can be determined from knowledge of the other half. • Imaging time can be reduced by a factor of 2 by collecting either the positive or the negative phase encodings and filling the remainder of k-space with the mirrored data.

  26. Half Fourier Imaging ky 2 5 6 kx 256 ky 1 2 8 kx 256 full resolution

  27. Half Fourier Imaging • This technique is sometimes referred to as ‘half NEX’ imaging or ‘PCS’ (phase conjugate symmetry). • Penalty: reduced signal decreases the signal to noise ratio, typically by a factor of 0.71.

  28. Half Fourier Imaging • The frequency half of k-space can also be mirrored. • This technique is called fractional echo or ‘RCS’ (read conjugate symmetry). • Decreased read time enables more slices per acquisition at the expense of reduced signal.

  29. ky ky 1 2 8 2 5 6 kx kx 256 128 read symmetry Half Fourier Imaging ky 2 5 6 kx 256 normal phase symmetry

  30. ky 1 2 8 kx 128 ky 2 5 6 kx 128 ? ky ky 1 9 2 1 2 8 kx kx 128 128

  31. 3D Acquisition • 3D is an extension of the 2D technique. • advantages: • true contiguous slices • very thin slices (< 1 mm) • no partial volume effects • volume data acquisition • disadvantages: • gradient echo imaging only • (3D FSE now available) • motion sensitive

  32. 3D Acquisition • no slice select gradient • entire volume of tissue is excited • second phase encoding gradient replaces the slice select gradient • after the intial RF pulse (), both y and z gradients are applied, followed by application of the x gradient during readout (echo)

  33. 3D Acquisition • the z gradient is changed only after all of the y gradient phase encodes have generated an echo, then the z gradient is stepped and the y gradient phase encodes are repeated

  34. 3D Imaging    RF echo echo echo z gradient slice select y gradient phase x gradient readout

  35.   3D Imaging ky z step 1 kx z step 4 2 5 6 3D k-space z step N 256

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