# Figuring out how an RF pulse affects the MRI spins

So, I understand how the slice selection gradients work in MRI. So, the frequency offset introduced by the slice selection gradient at a location $z$ relative to the MRI isocenter is given by:

$$\Delta f = \gamma z G_z$$

Putting some numbers to it, for a gradient of 5 mT/m and a slice thickness of 3 mm, we introduce an offset of $639.7$ Hz per slice.

Now, say I have an RF pulse which has a bandwidth of 2000 Hz and a center frequency of 10 kHz. Given the location of the spin along the slice direction, I want to know whether this spin will be excited by the RF pulse or not.

• Is it possible to figure that out from this information?

I have a feeling it should be possible from the relation above but I am not sure how the bandwidth parameter will come into play here.

• Is it a simple matter of checking that if the resonant frequency experienced by the spin falls in the RF center frequency $\pm$ bandwidth / 2.0?

Is it possible that you accidentally mixed up angular frequency and normal frequency? I am asking, because your frequency spread and RF bandwidth would excite $\frac{2000\,\textrm{Hz}}{639.7\,\frac{\textrm{Hz}}{\textrm{slice}}} \approx 3.12\,\textrm{slices}$, if I am not mistaken, and... when it comes to frequencies and a ratio is so close to $\pi$, and there is a "/2.0" in the original question, there could be something going on with wrong frequency units.
• Ya, the issue is that the 5mT/m gradient strength was really picked put of thin air. With those parameters, it should be more like: $(2000)/(42.57 * 3 * 1000)$ which is more like 15 mT/m. Thank you for pointing that out to me.