1 / 32

Topics

Topics. spatial encoding - part 1. K-space, the path to MRI. ENTER IF YOU DARE. What is k-space?. a mathematical device not a real “space” in the patient nor in the MR scanner key to understanding spatial encoding of MR images. y. x. f(x,y). k-space and the MR Image. k y. k x.

santa
Télécharger la présentation

Topics

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Topics • spatial encoding - part 1

  2. K-space, the path to MRI. ENTER IF YOU DARE

  3. What is k-space? • a mathematical device • not a real “space” in the patient nor in the MR scanner • key to understanding spatial encoding of MR images

  4. y x f(x,y) k-space and the MR Image ky kx F(kx,ky) Image-space K-space

  5. k-space and the MR Image • each individual point in the MR image is reconstructed from every point in the k-space representation of the image • like a card shuffling trick: you must have all of the cards (k-space) to pick the single correct card from the deck • all points of k-space must be collected for a faithful reconstruction of the image

  6. 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) image-space K-space

  7. k-space and the MR Image • If the image is a 256 x 256 matrix size, then k-space is also 256 x 256 points. • The individual points in k-space represent spatial frequencies in the image. • Contrast is represented by low spatial frequencies; detail is represented by high spatial frequencies.

  8. Low Spatial Frequency

  9. Higher Spatial Frequency

  10. low spatial frequencies high spatial frequencies all frequencies

  11. Spatial Frequencies • low frequency = contrast • high frequency = detail • The most abrupt change occurs at an edge. Images of edges contain the highest spatial frequencies.

  12. Waves and Frequencies • simplest wave is a cosine wave • properties • frequency (f) • phase () • amplitude (A)

  13. Cosine Waves ofdifferent frequencies

  14. Cosine Waves ofdifferent amplitudes

  15. Cosine Waves ofdifferent phases

  16. k-space Representation of Waves image space, f=4 k-space

  17. k-space Representation of Waves image space, f=16 k-space

  18. k-space Representation of Waves image space, f=64 k-space

  19. Complex Waveform Synthesis f4 + 1/2 f16 + 1/4 f32 Complex waveforms can be synthesized by adding simple waves together.

  20. k-space Representation of Complex Waves image space k-space f4 + 1/2 f16 + 1/4 f32

  21. k-space Representation of Complex Waves image space k-space “square” wave

  22. Reconstruction of square wave from truncated k-space image space k-space reconstructed waveform truncated space (16)

  23. Reconstruction of square wave from truncated k-space image space k-space reconstructed waveform truncated space (8)

  24. Reconstruction of square wave from truncated k-space image space k-space reconstructed waveform truncated space (240)

  25. Properties of k-space • k-space is symmetrical • all of the points in k-space must be known to reconstruct the waveform faithfully • truncation of k-space results in loss of detail, particularly for edges • most important information centered around the middle of k-space • k-space is the Fourier representation of the waveform

  26. MRI and k-space • The nuclei in an MR experiment produce a radio signal (wave) that depends on the strength of the main magnet and the specific nucleus being studied (usually H+). • To reconstruct an MR image we need to determine the k-space values from the MR signal.

  27. RF signal FT A/D conversion image space k-space

  28. MRI • Spatial encoding is accomplished by superimposing gradient fields. • There are three gradient fields in the x, y, and z directions. • Gradients alter the magnetic field resulting in a change in resonance frequency or a change in phase.

  29. MRI • For most clinical MR imagers using superconducting main magnets, the main magnetic field is oriented in the z direction. • Gradient fields are located in the x, y, and z directions.

  30. MRI • The three magnetic gradients work together to encode the NMR signal with spatial information. • Remember:the resonance frequency depends on the magnetic field strength. Small alterations in the magnetic field by the gradient coils will change the resonance frequency.

  31. Gradients • Consider the example of MR imaging in the transverse (axial) plane. • Z gradient: slice select • X gradient: frequency encode (readout) • Y gradient: phase encode

  32. Slice Selection • For axial imaging, slice selection occurs along the long axis of the magnet. • Superposition of the slice selection gradient causes non-resonance of tissues that are located above and below the plane of interest.

More Related