MRI: From Signal to Image

Transcription

1 MRI: From Signal to Image Johannes Koch physics / 27

2 Tomography Magnetic Resonance Tomography Tomography: tomos: section graphein: to write Signal measured as function of space 2 / 27

3 Tomography Signal Receiver coils placed with their normal direction perpendicular to z-axis Precessing transversal magnetic moment m T induces signal into receiver coils Flux Φ proportional to m T 3 / 27

4 Tomography Signal Magnetic moments precess with Larmor frequency ω 0 = γb Received signal is caused by all precessing moments in the sample Problem: No spatial differentiation of the signals Solution Spatial encoding using magnetic gradient fields 4 / 27

5 Slice Selection Frequency Encoding Phase Encoding Slice Selection Apply gradient in z-direction during the HF pulse Larmor frequency: ω 0 (z) = γ(b 0 + G ss z) 5 / 27

6 Slice Selection Frequency Encoding Phase Encoding Applying HF pulse with desired spectrum results in transversal magnetization in selected slice Usually slice with sharp transition is desired Envelope function of pulse approximates the sinc function 6 / 27

7 Slice Selection Frequency Encoding Phase Encoding Along the slice m T gets dephased Reverse gradient after excitation for half the excitation time rephasing 7 / 27

8 Slice Selection Frequency Encoding Phase Encoding Frequency Encoding Applying gradient (e.g. in x direction) during readout Larmor frequency: ω 0 (x) = γ(b 0 + G fe x) Amplitude of measured signal per frequency is projection of single slice 8 / 27

9 Slice Selection Frequency Encoding Phase Encoding 9 / 27

10 Slice Selection Frequency Encoding Phase Encoding Works only in one spatial dimension Multiple gradients lead to ambiguous results Another mechanism must be used to encode second dimension: Phase encoding 10 / 27

11 Slice Selection Frequency Encoding Phase Encoding Phase Encoding Gradient (e.g. in y direction) is applied for a fixed time T y, before readout Results in phase angle φ p = γg pe yt y 11 / 27

12 Slice Selection Frequency Encoding Phase Encoding 12 / 27

13 Slice Selection Frequency Encoding Phase Encoding Start with gradient that turns the transversal magnetization by 360 Double the gradient with each measurement, until neighboring pointers face in opposite direction Same procedure for negative gradients Results in a frequency comb, scanning through all needed spatial frequencies 13 / 27

14 Slice Selection Frequency Encoding Phase Encoding Unlike frequency encoding, phase encoding can be done in multiple dimensions As many measurements as scanned rows needed Basically frequency encoding in pseudo time 14 / 27

15 is spanned by k x = γg fe t and k y = γg pe T y Every measurement is positioned in k-space Measured signal in k-space S (k x, k y ) = dxdy M T (x, y) exp ( ik x x ik y y) Measurement in k-space is the 2D Fourier transform of transverse magnetization! 15 / 27

16 To reconstruct image, k-space needs to be adequately sampled Every traversal to fill k-space is equal (e.g. Cartesian, spiral) 16 / 27

17 Cartesian Sampling Example 17 / 27

18 Pixel in k-space is a frequency information Pixels close to the center represent low spatial frequencies, far away from the center high spatial frequencies Selective sampling of k-space can be used to reduce measuring time z = ω hf γg ss y = π γg max pe T y x = π γg fe T x 18 / 27

19 19 / 27

20 20 / 27

21 Low-Pass Filtering 21 / 27

22 High-Pass Filtering 22 / 27

23 Noise 23 / 27

24 Many individual measurement on different slices Mainly used for thick slices Faster, but worse signal-to-noise ratio compared to three dimension k-space scanning Three dimensional k-space scanning Add third gradient using phase encoding S (k x, k y, k z ) = dxdydz M T (x, y, z) exp ( i(k x x + k y y + k z z)) 24 / 27

25 Thank you for your attention! 25 / 27

26 O. Dössel: Bildgebende Verfahren in der Medizin, Springer-Verlag Berlin Heidelberg, H. Morneburg: Bildgebende Systeme für die medizinische Diagnostik, 3rd edition, Publicis MCD Verlag, Erlangen, D. W. McRobbie, E. A. Moore, M. J. Graves, M. R. Prince: MRI: From Picture to Proton, 2nd edition, Cambridge University Press, Cambridge, / 27

27 Sources of Figures Slide 2: Adaption from [3], page 56. Slide 3: From [3], page 13. Slide 5: Adaption from [3], page 115. Slide 6: Adaption from [3], page 114. Slide 7: Adaption from [3], page 122, adaption from [3], page 109. Slide 8: Adaption from [3], page 124. Slide 9: Adaption from [3], page 126. Slide 11: Adaption from [3], page / 27

28 Sources of Figures Slide 12: From [3], page 121. Slide 14: Adatption from [3], page 124. Slide 16: From [3], page 129. Slide 17: Adaption from Physics of magnetic resonance imaging, Wikipedia, retrieved April 27, 2013, from http: //en.wikipedia.org/w/index.php?title=physics_of_ magnetic_resonance_imaging&oldid= / 27