1. MRI Physics: Spatial Encoding Anna Beaumont FRCR Part I Physics

2. Introduction MRI extremely flexible spatial localisation – Orientation easily altered Spatial encoding relies on successively applying field gradients – A slice selection gradient selects the anatomical volume of interest (GSS) Position then encoded vertically & horizontally by use of: – Phase encoding gradient (GPE) – Frequency encoding gradient (GFE) Signal is reconstructed with 2D or 3D Fourier Transformation

3. Spin Echo Sequence RF GzGz GyGy GxGx Signal TE 90° 180° Slice Selection Phase Encoding Frequency Encoding An axial image..

4. Gradients Recall that the resonant frequency is proportional to field strength Magnetic gradient changes B 0 field strength over distance In MRI a linear gradient changes the resonant frequency in a given direction

5. Slice Selection isocentre B0B0 00 B0+BB0+BB0-BB0-B  0+  0+   0-  0-  Gradient in z-direction G z y x z B0B0

6. Slice Selection

7. Gradient used to change resonant frequency in slice direction Excite spins using 90° RF pulse containing a bandwidth (range) of frequencies Only a particular section of spins are excited into transverse plane Signal has been discriminated in one dimension Can change orientation, slice thickness and position

8. Slice Selection: Slice thickness A & B: Steepness of gradient kept same, bandwidth changed C & D: Steepness changed, bandwidth kept the same.

9. Slice Thickness Thickness can be varied by adjusting bandwidth of selective pulse & amplitude of the slice selection gradient Fixed amplitude gradient – Wider bandwidth → greater no. of photons excited; thicker slice Fixed Bandwidth – Stronger gradient → greater variation of precession frequency in space; thinner slice Thinner slices gives better anatomical detail, but takes longer to excite

10. Frequency Encoding Need to discriminate signal in-plane Another gradient is used to produce changes in resonant frequency This gradient is applied when the signal is received

11. Phase Encoding Need to still encode signal in remaining direction (y) – Use changes of phase When a gradient is applied the spins will precess with varying frequencies. Once the gradient is removed the spins will return to spinning with the same frequency, but they will now be at different phases. This is the role of the phase encoding gradient

12. Initially, all spins have same frequency

13. Apply phase encoding gradient slower unchanged faster

14. After PE Gradient turned off All spins have same frequency again, but different phase

15. Apply Frequency Encoding Gradient Faster unchanged slower

16. Phase Encoding G phase ω =  B 0 time → Y-direction→ GyGy

17. Phase Encoding ω =  (B 0 +yG y ) time → Y-direction→ G phase GyGy z

18. Phase Encoding time → Y-direction→ ω =  B 0 G phase GyGy

19. Phase Encoding Each pixel is assigned a unique phase and frequency FT decodes unique frequency but only measures summation of phase Individual phase contributions cannot be detected Need multiple increments of PE gradient to provide enough information about phase changes By comparing the pattern of increasing phase angles it is possible to decipher the separate signals Number of PE increments depends on image matrix

20. Phase Encoding From Picture to Proton: McRobbie et al.

21. Spin Echo Sequence RF GzGz GyGy GxGx TE 90° 180° GzGz Resonance condition ω =  (B 0 + zG z ) z

22. Spin Echo Sequence RF GzGz GyGy GxGx TE 90° 180° GyGy z increment gradient after RF pulse and before read-out

23. Spin Echo Sequence RF GzGz GyGy GxGx Signal TE 90° 180° GxGx z Apply gradient during read-out

24. Scan Time Frequency encoding done at time of echo Phase encoding done over many TRs Scan time is given by N PE  TR  NEX (NEX = No. of excitations, improves signal to noise ratio, but increases scan time)

25. Summary Selecting the slice plane and spatial encoding involves the use of magnetic field gradients. The different gradients used to perform spatial localisation have identical properties but are applied at distinct moments and in different directions. Slice selection gradient applied simultaneously to all RF pulses Phase encoding gradient differentiates the rows (in k space, more on that later) PE is regularly incremented, for as many rows as there are.

26. Fourier Transform ( FT ) Time signal can be decomposed into sum of sinusoids of different frequencies, phases and amplitudes Fourier series may be represented by frequency spectrum Time and frequency domain data can be thought of as FT pairs s(t) = a 0 + a 1 sin(  1 t +  1 ) + a 2 sin(  2 t +  2 ) + …

27. Fourier Transform ( FT ) S1 has amplitude a and frequency f S2 has a/2 and 3f S3 = S1 + S2 S3 is two sine waves of different frequency and amplitude The FT is shown A f

28. FT Pairs FT Time Frequency Sinusoid Sinc Delta ‘Top Hat’