1. How MRI Works
By Wesley Eastridge, adapted from and with illustrations from The Basics of MRI by Joseph P. Hornak, Ph.D.

2. From Protons to Pixels
Images from NHS

3. Magnetic Resonance Imaging makes a picture of the inside of the body… …by reading radio waves emitted by protons in a strong magnet.

4. Say what?

5. Yes, most molecules in the body contain hydrogen atoms, whose nuclei are single protons. And protons have a characteristic called ‘spin’ which causes them to line up with or against a magnetic field.

6. How MRI Works A strong magnet aligns protons
Protons absorb and then emit radio waves
Computer processing of the signals generates an image

7. What Resonance Means…
Repeated pushing has an amplified effect when timed with the object's intrinsic frequency.

8. How MRI Works
1. MRI Physics 2. Decoding the Radio Signals 3. Special Techniques

9. 1. MRI Physics
Specifically, magnetic resonance imaging makes a picture of the inside of the body by reading radio waves emitted by precessing protons in a strong magnet.

10. Protons have properties called spin which causes them to tend to line up within a magnetic field

11. Moreover, protons precess in a magnetic field just as spinning tops and the spinning Earth precess in gravitational fields…

12. Protons precess whether they are lined up with or against the magnetic field

13. Importantly, the frequency of their precession is proportional to the strength of the magnetic field. In a strong magnet as we use in MRI, that frequency is in the radio wave range (MHz).

14. As long as the protons are out of phase with each other the sum of their magnetic fields is just a non- rotating vector pointing in the direction of the field they are in (B).

15. But if we can synchronize them, their sum vector rotates with their precession frequency.

16. Now a rotating magnet generates electromagnetic (radio) waves…
…and so do the precessing protons when synchronized.

17. Radio waves are alternating magnetic fields perpendicular to alternating electric fields

18. Our task is to differentiate radio waves from different parts of the body so we can make an image.

19. We’ll do that by applying pulses of radio waves and various magnetic gradients…

20. …Then protons will emit their own radio waves in slightly different frequencies and phases according to their location.

21. First we will select a single slice in the z-axis, the direction of the main magnetic field.

22. We do that with a magnetic gradient so that only one slice of the body is precessing at the desired frequency:

23. Then we apply a synchronizing pulse of radio waves (i. e
Then we apply a synchronizing pulse of radio waves (i.e. oscillating magnetic fields).

24. Once synchronized that slice emits radio waves briefly until it gets out of sync again.

25. At this point all the areas in the slice have the same frequency and phase.

26. Second, we differentiate locations along the x-axis by adjusting the phase of oscillations
Phase Shift

27. Applying Phase Shift
A temporary orthogonal magnetic gradient in the x-axis makes protons precess a little faster or slower than the others while the gradient is on, getting out of phase with each other…

28. Applying Phase Shift
… after which they have the same frequency but different phases along the x-axis.

29. Finally we differentiate areas along the y-axis by adjusting their frequencies

30. Applying frequencies
An orthogonal magnetic field gradient in the y- direction is left on while we detect the protons' signals, making their frequency dependent on location along the y-axis

31. Le Voila!
After a synchronizing pulse during a gradient in the z axis (slice selection)
..followed by a temporary gradient in the x-direction (phase gradient)
..we record the signal during a gradient in the y- direction (frequency gradient)

32. Le Voila!
Now we have protons precessing in the body with phases and frequencies according to their location in the x,y and z axes!
We can generate an image by assessing how strong the signals are from those various areas.

33. 2. Decoding the Radio Signals

34. Fourier Transform

35. Fourier Transform
For example in in real time analysis of sound waves it shows shows signal strength by frequency.

36. Fourier Transform
Bottom line: FT takes a wave function and creates a function of how much of each frequency made up that wave.
Since proton frequency varies along the magnetic gradient, the FT is a function of distance along that axis.

37. Localization in the frequency axis (y)
A simple Fourier transform of the signal shows signal strength along the frequency-axis.

38. Localization along the phase axis (x)
But a single Fourier transform doesn’t reflect the phase shifts, so another level of trickery is required:

39. We repeat the pulse sequences with varying strengths of phase gradients
Note the changing height of phase gradient (Gø) in 256 or so rapid pulse sequences.

40. Decoding the waveforms
Requires two applications of Fourier transform, one in the frequency, one in the phase direction.
See for more

41. Another look at phase shifts
Left collection of 9 sequential raw wave signals shows phase shift through one cycle
Right Fourier transform of 12 sequential signals shows phase shift through > 3 cycles

42. All repetitions agree with the frequency locating the red pixel’s x-location in the first Fourier transform, but with varying peaks. The frequency with which the peaks cycle through up and down directions in the phase encoding direction determines the pixel’s location in the y axis in the second Fourier transform.
See for more

43. 3. Special Techniques
(quick overview)

44. Signal strength relates to the density of protons in various parts of the body, but also to other factors that affect how the protons react to the radio pulse sequences.

45. Physiology
T1-weighted vs T2-weighted images

46. Spin-echo sequence
Produces a T1 or T2-weighted image, depending on timing

47. T1 vs T2 weighted images
T1 on the left, T2 on the right

48. Physiology Metabolic activity Gadolinium
FLAIR (fluid attenuated inversion recovery)
Etc...
Gadolinium, gadolinium, t2
FLAIR, axial gradient

49. In Summary…
Magnetic resonance imaging makes a picture of the inside of the body,
By reading radio waves emitted by precessing protons in a strong magnet,
After manipulating their frequencies and phases with repeated sequences of radio pulses and magnetic gradients,
So that their spacial location is identifiable by computer processing.