# MRI and Fourier transform to form an image

1. Nov 1, 2015

I read about how MRI works briefly, by flipping the water molecules using a magnetic field to the correct state then send the radio wave to these atoms and have it bounces back to be received by receiver coils and apply Fourier Transform to figure out the imaging. My question is, how does Fourier Transform works in this case in the receiver coil to figure out the original location of the atom, is it based on the intensity of the radio wave or something else?

2. Nov 1, 2015

### Ygggdrasil

The magnetic field varies along one axis of the body, so protons in your head emit radio waves of a slightly different frequency than protons in your feet. The Fourier transform allows one to extract the different frequencies from the overall radio signal in other to figure out where each part of the signal is coming from.

3. Nov 7, 2015

So, is the signal received from the atoms like a radio wave? I understand the signal is weak because you need coils right around the body but is it possible to strengthen this signal? Stronger signal directed at the atom would have a stronger signal bounces back? I'm talking about receiving it like a radio signal, if it's possible and someone done it before.

4. Nov 7, 2015

### Ygggdrasil

In MRI the signal comes from transitions between two nuclear spin states. The difference in energy between the states is small (hence, the transition is associated with the absorption and emission of low-energy radio waves), which also means that the difference in population between the lower-energy spin state and higher-energy spin state is small. The difference between these two populations defines the strength of your signal. You cannot increase the signal by increasing the strength of the radio wave pulse because the radio wave (in most cases) already saturates the signal. The most practical way of increasing the signal would be to increase the strength of the magnetic field, which increases the energy difference between the two nuclear spin states (alternatively, one could decrease the temperature of the sample, but this is not practical for biological samples). For more discussion see: https://en.wikipedia.org/wiki/Nuclear_magnetic_resonance#Sensitivity

5. Nov 7, 2015

That makes sense. Based on this youtube video, the radio frequency is proportional to the spin of the dipole. So if it spins at higher frequency then it would emit a radio wave of higher frequency, I think.

6. Nov 8, 2015

### Ygggdrasil

Using precise terminology is important here. Spin refers to the intrinsic angular momentum of the nuclei, and the spin of the nuclei does not directly cause the radio signal. Rather, it is the precession of the magnetic moments of the nuclei around the magnetic field lines that directly generates the radio frequency signal.

7. Nov 17, 2015