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The Worst Page of Math

How many excess protons are there in a single voxel at 1.5T?

  • Assume a voxel is 2 x 2 x 5 mm = .02 ml

  • Avagadro's Number says that there are 6.02x1023 molecules per mole

  • .1 mole of water weighs 18 grams (O16 + 2H1) has 2 moles of hydrogen and fills 18 ml, so.....

  • 1 voxel of water has
    2 x 6.02 x1023 x 0.02 / 18 = 1.338 x 1021 total protons.

  • The total number of excess protons =

    Or.... 6 million billion

You do not have to know how to do this derivation, nor the exact result. The important lesson here is that even though a spinning proton is a very poor magnet, the number of excess protons that align with the field is so very large that we can pretty much ignore quantum mechanics and focus on the classical mechanics description.

Question: Why does a high field MRI scanner have a higher signal to noise ratio than a low field scanner?

Answer: Because there are more excess protons available to make the MRI signal.

The # of excess protons is so large that we can ignore quantum mechanics and focus just on classical mechanics.

The total magnetic field of the excess protons is called Mø

The Last Quantum
Physics Page

Energy is proportional to frequency..

MRI is able to make such great pictures not because of the high energy involved but because of the large number of protons found in the body, primarily in water and fat.
h is Planck's constant
v is the symbol that is normally used with Planck's constant to denote frequency.

This is the only place that we will use v. (Go ahead and forget it.) The energy levels used in X-ray and CT are on the order of a trillion times larger than those used in MRI! No ionizing radiation is used with MRI (which is why I went into MRI as a profession!)

X rays are a trillion times more energetic (and potentially damaging) than radio waves.



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