1. Magnetic Resonance Imaging
Part 1

2. Magnetic Resonance Imaging
A great multidisciplinary application of physics and other sciences. And example of a “pure science” discovery given a practical application
Based on NMR – Nuclear Magnetic Resonance – discovered in the 1940s

3. Torque
Torque occurs when a force is applied with a moment arm, meaning that it is applied at a point away from the axis of rotation, and with a component in a direction not pointed toward or away from the axis of rotation.
Torque causes angular acceleration, which results in rotation.

4. Angular Momentum
When an object is rotating around any axis, it has angular momentum. This is a conserved quantity, so in the absence of external torques it will not change.

5. Precession
When an object rotates on an axis and there is a torque applied that will rotate its axis, it will introduce a new rotation in an attempt to conserve angular momentum. This is called precession. You have seen this in the spinning of a top or a gyroscope.

6. Precession
Retrieved July 14, 2016, from

7. Precession
Precession (2016). . In Wikipedia. Retrieved from Public Domain

8. Proton Spin
Spin is a quantum measure of the angular momentum carried by elementary particles.
You can imagine the proton as a tiny sphere spinning on an axis for this discussion (classical view), but quantum physics doesn’t really behave like classical physics.

9. Protons and rotation
Because protons have spin. They are also magnetic.
If exposed to a large external magnetic field, the proton spin axes will almost align themselves with the field. Since they are spinning, their axes will precess around that direction.
Fig2spins.gif. (2007, October 5). Retrieved July 14, 2016, from
Creative Commons Attribution/Share-Alike License
Precess.gif Retrieved July 14, 2016, from

10. Precession frequency
The precession frequency – the number of precession rotations per second – is directly proportional to the strength of the external magnetic field and certain magnetic properties of the atom. This is called the Larmor frequency. (discovered in 1897)
ω = γB
Where γ is the gyromagnetic ratio, a property of the atom, and B is the magnetic field strength

11. Precession frequency
In hydrogen, the Larmor frequency of a proton is MHz per Tesla.
In an MRI machine with a 1.5 T magnetic field, the Larmor frequency is 63.9 MHz
In an MRI machine with a 3.0 T magnetic field, the Larmor frequency is MHz
(hydrogen is good to use since it is everywhere in the body – particularly prevalent in fluids and fats and tissue)

12. Resonance Resonance is a wave oscillation phenomenon.
Resonance occurs when energy is added to a system periodically at nearly or exactly the natural frequency that the object oscillates (called its resonance frequency).
When this happens, the energy is absorbed very, very efficiently.
Example: pushing a child on a swing
Example: breaking glass with sound

13. Resonance
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14. Resonance
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15. Resonance
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16. NMR (Nuclear Magnetic Resonance)
Put this together...
Hydrogen protons in an external magnetic field will precess at a certain frequency (defined earlier as the Larmor frequency)
If energy is given to an oscillating object at its natural frequency then it is absorbed efficiently and has a significant effect (resonance).
Conclusion - Hydrogen protons in an external magnetic field will absorb energy at a specific resonance frequency. This is the basis of Nuclear Magnetic Resonance (NMR). Its discovery (1938), measurement and applications (1946) resulted in three Nobel Prizes in Physics.

17. NMR (Nuclear Magnetic Resonance)
Earlier it was said that the Larmor frequency of hydrogen protons in a 1.5 T field was 63.9 MHz. This is in the radio part of the EM spectrum.
To excite the hydrogen protons precessing in an external magnetic field you need to expose them to radio frequency (RF) waves at their resonance frequency (Larmor frequency).
The excited protons will emit a weak, but detectable signal

18. How is NMR used in medicine?
First use in medicine was in the 1970s, earning another two Nobel Prizes in Chemistry and one Nobel Prize in Medicine along the way for its development.
In the early 1980s the name of the procedure was changed from NMR to MRI because the word "nuclear" made people fearful of radiation. (Three Mile Island happened in 1979)
MRI uses no harmful or ionizing radiation. It is extremely safe – more so than traditional x-rays or CT scans.
MRI machines are expensive. To create a T field requires a superconducting magnet, which must be kept at a temperature near absolute zero using liquid helium at 4.2 Kelvin.

19. How is NMR used in medicine?
Observing that hydrogen protons absorb energy at a certain frequency and then emit a weak signal is interesting, but how is that useful?
To be useful, the device must be able to detect the absorption and resulting signal from specific areas in the body and distinguish them from other areas in the body.
This is the trick that earned another Nobel Prize and made this medically useful...

20. Precession frequency
Since the precession frequency varies with magnetic field strength (Larmor frequency ω = γB), if the field strength changes then the precession frequency changes.
The MRI machine introduces a gradient field. This means that the magnetic field strength changes linearly over the length of the MRI machine, from head to feet.

21. Precession frequency
The protons in hydrogen precess at a frequency based on the magnetic field strength at their location.
This means that the precession frequency of hydrogen protons will be different depending where in the body they are.
Retrieved July 14, 2016, from
Public Domain

22. Slice Selection
If you expose the hydrogen protons to RF energy at a specific frequency, it will only be absorbed by protons that are precessing at exactly that frequency.
Since the precession frequency varies from head to feet in the person, the energy will only be absorbed at a specific location along the length of the person. This is called slice selection.
If you change the RF frequency, you change which hydrogen protons will absorb the energy, and therefore select a different slice of the body to analyze.

23. Slice Selection
Applying magnetic field gradients in three dimensions (x, y, z) allows the device to analyze specific locations within the body.
After we have done magnetism, we will revisit this and discuss exactly how the image is formed from the absorbed and emitted RF energy.
MRI: A guided tour - MagLab. (2015, January 8). Retrieved July 14, 2016, from

24. Question The Larmor frequency for hydrogen protons is 43.6 MHz/Tesla.
Your MRI scanner can create a field gradient of 0.1 Tesla/meter. You want your device to have a spatial resolution such that it can create a slice of 0.1 mm.
Your receiver antenna must be able to distinguish between frequencies of _____ Hz.

25. Solution
If your slices are to be separated by 0.1 mm, that is meter
The gradient is 0.1 Tesla/meter.
0.1 T/m x m = Tesla
So, two adjacent 0.1 mm slices will have magnetic fields that differ by Tesla.
Since the Larmor frequency is 43.6 MHz/T,
43.6 MHz/T x T = MHz = 436 Hz