1 / 74

MR Imaging: k-Space formalism

MR Imaging: k-Space formalism. A. Tannús – 11/2006 IFSC - USP. Nobel prizes: NMR as a source of insight. 1942 (1930): Physics: I. Rabbi: Resonant method for measuring magnetic properties of atomic nuclei. 1952 (1946): Physics : F. Bloch & E. Purcell:

yvonne
Télécharger la présentation

MR Imaging: k-Space formalism

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. MR Imaging:k-Space formalism A. Tannús – 11/2006 IFSC - USP

  2. Nobel prizes: NMR as a source of insight • 1942 (1930): Physics: I. Rabbi: • Resonant method for measuring • magnetic properties of atomic nuclei. 1952 (1946): Physics : F. Bloch & E. Purcell: Precision measurement of Nuclear Magnetism

  3. Nobel prizes in MR 1992 (1966): Chemistry: R. Ernst: High Resolution Pulsed Magnetic Resonance - Spectroscopy. 2003 (1973): Medicine: P. Mansfield & P. C. Lauterbur Magnetic Resonance Imaging.

  4. MRI temporal and spatial resolution Improve Improve

  5. NMR Phenomena • Quantum Mechanical approach: • Easy for spin ½; • Gets complex when dealing with different nuclear species in a system. • Classical Approach. • Explain almost completely the development of Imaging methodologies. To QM..

  6. Classical Approach Fundamental properties of nuclei Evolution described by an equation of a precessing rotor

  7. Spinning Top in a gravitational field:a very bad example… “Spinning nucleus” B0 “Spinning Top” Reaction from base m = magnetic moment L=angular momentum L=angular momentum t = magnetically induced torque = - mxB0 Weight force • = torque produced by the binary forces: Weight and reaction at contact point

  8. Macroscopic Magnetization Relaxation T1 and T2 are determined based on experimental results! (Phenomenology)

  9. Bloch Phenomenological Equations:

  10. z a) B e.m.f o y x M V(t) Excitation/Detection Scheme e.m.f B1

  11. Detected signal Induced e.m.f. FID t

  12. Imaging Scanner Overview:Hardware Fully digital, multichannel now! Work in progress at our group Gradient Controller Master Controller X Y Z RF Controller RF Amplifier DAC Receiver Gradient Coil RF coil preamp Magnet

  13. Magnet: superconducting,axial access.

  14. Other Magnet Types Permanent magnets, e.g. light weight rare earth magnets, <0.3T “H” type, transverse access “C” type, transverse access (open systems)

  15. Other Magnet Types “H” and “C” mixed type, transverse access (open systems)

  16. Other Magnet Types Electromagnet <0.3T

  17. RF Coils Remember: Brf (B1) must be orthogonal toB0 !! Saddle coil allows axial access. Efficiency is low, and homogeneity is poor Field is aligned to subject; Other designs than solenoidal must be used.

  18. z z z y y y x x x Gz Gx Gy Imaging basic principles: encoding Now that we have an NMR signal, how to get an image? By mapping the spins according to their position. How?Using their frequency/position correspondence(r) =B0(r)

  19. A bit of history… P. C. Lauterbur - (1973) State University - New York First 2D NMR image: came from an annoyance for spectroscopists!!! Projection/Reconstructionmethod(same as in CT)

  20. 10 years later…

  21. Encoding inmore than one dimension:solving the projection paradox. Magnetic field gradients add as vectors, giving a newly oriented gradient!!

  22. Magnetic Field Gradients Now, gradients are time dependent!!

  23. Spatially encoded frequency and phase:more than one dimension?

  24. Generalizing the definition of k(t)

  25. The 3D Image Equation!! 3D Signal 3D Image

  26. K-Space properties

  27. B0 z RF Gz x Gz y e.m.f. Steps to NMR Imaging Selective excitation • Absorption line broadening • Narrow bandwidth RF pulses Only spins inside this band are excited

  28. Gy B0 z Gz Gy x y e.m.f Principles of NMR Imaging Phase encoding Selective excitation • Absorption line broadening • Narrow bandwidth RF pulses Encoding in this dimension is done through the initial phase.

  29. z B0 Gx x Gz y e.m.f Gy Gx Principles of NMR Imaging Frequency encoding Phase encoding Selective excitation • Absorption line broadening • Narrow bandwidth RF pulses Encoding in this dimension is done through the spatially dependent frequency.

  30. Gz Gy Gx Principles of NMR Imaging Phase encoding Frequency encoding Selective excitation • Absorption line broadening • Narrow bandwidth RF pulses

  31. ky p p/2 RF Gz p Gy A’’ A A’ Gx kX 0 FID ECO Gz B Signal Gy C t @ 0 Gx B’ C’ 2t tC tB tA @ B’’ C’’ Acquisition Preparation Principles of NMR Imaging Acquisition sequences and image formation : • Spin Echo ( SE ) • Spin Echo ( SE ) • Echo Planar Imaging ( EPI ) • Gradient Recalled Echo ( GRE )

  32. k-space • k-space is the raw data space before Fourier transformation into the image • 2D image will be represented by a 2D array of data points spread throughout k-space (it could be 3D!!) • Changing the k-space trajectory will alter image contrast

  33. k-space • k-space must be sampled in equally spaced intervals in order to allow 2D FFT. • As a consequence the image is also presented in equally spaced sampled values. • All concepts of discrete Fourier formalism applies.

  34. Image vs. k-space data (r) S(k) k(t)= /2G(t)dt

  35. Image vs. k-space data (r) S(k) k(t)= /2G(t)dt

  36. Image vs. k-space data (r) S(k) k(t)= /2G(t)dt

  37. Image vs. k-space data (r) S(k) k(t)= /2G(t)dt

  38. Image vs. k-space data FFT (r) S(k) k(t)= /2G(t)dt

  39. GE k-space trajectory RF G S G R G P S(t) (r) S(k) k(t)= /2G(t)dt

  40. GE k-space trajectory RF G S G R G P S(t) -kr +kr (r) S(k) k(t)= /2G(t)dt

  41. GE k-space trajectory RF G S G R G P S(t) -kr +kr (r) S(k) k(t)= /2G(t)dt

  42. GE k-space trajectory +kp RF G S G R G P S(t) -kp -kr +kr (r) S(k) k(t)= /2G(t)dt

  43. GE k-space trajectory +kp RF G S G R G P S(t) -kp -kr +kr (r) S(k) k(t)= /2G(t)dt

  44. GE k-space trajectory +kp RF G S G R G P S(t) -kp -kr +kr (r) S(k) k(t)= /2G(t)dt

  45. GE k-space trajectory +kp RF G S G R G P S(t) -kp -kr +kr (r) S(k) k(t)= /2G(t)dt

  46. GE k-space trajectory +kp RF G S G R G P S(t) -kp -kr +kr (r) S(k) k(t)= /2G(t)dt

  47. GE k-space trajectory +kp RF G S G R G P S(t) -kp -kr +kr (r) S(k) k(t)= /2G(t)dt

  48. GE k-space trajectory +kp RF G S G R G P S(t) -kp -kr +kr (r) S(k) k(t)= /2G(t)dt

  49. GE k-space trajectory +kp RF G S G R G P S(t) -kp -kr +kr (r) S(k) k(t)= /2G(t)dt

More Related