I have a biomedical imaging exam tomorrow and I'm struggling quite a bit with this question below (from b-d). I was hoping someone could help answer these questions or at. I'll describe my approach to each question and hopefully someone can give me some direction on if and where I have gone wrong.

Qb) the total response should just be the sum of the individual responses. Thus the total signal is a sinc of magnitude 1mV and frequency approximately $π/5\cdot10^3$ rad/sec (since it appears as though there are 5 peaks in the echo within 50ms corresponding to a period of 10 ms). Thus the magnitude-frequency plot should just be a rect

Qc) the intensity of an MRI signal is: $I=k [H^+] (1-e^{-TR/T_1}) e^{-TE/T_2}$
No intensity is given but is it possible to use the voltage given each material? if TR is long then $1-e^{-TR/T_1)}$ should be approximately=1. Therefore $I=k [H^+]e^{-TE/T_2}$.

A simple substitution of $0.4\cdot10^{-3}=e^{-TE/T_2}$ for material 1 then gives T2=12.8 ms. T2 for material 2 would be 13.5 ms. But is it justified to substitute voltage into $\frac{I}{k[H^+]}$?

Qd) I'm really not sure. It seems like the question is asking about the magnitude-frequency when T2 weighted (long TR and long TE) and so material 1 would appear slightly brighter than material 2. But not sure where to go from that.

MRI example question


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