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Unformatted text preview: EE/BIOE 597e Problem Set 3 Solutions April 2007 Problem 1: (5 points) What is the filling factor and how does the signaltonoise ratio of a nuclear magnetization measurement scale with the fillingfactor? The filling factor is a fraction that represents the volume of the probe coil occupied by the sample. In the 1968 paper by Hill and Richards, the filling factor is defined as = sample volume B 2 1 dV all space B 2 1 dV , where B 1 is the magnetic field generated by the probe coil for a sinusoidal current at the transition frequency. From equation 1 of the same paper, the signaltonoise ratio is proportional to the fillingfactor. For this reason the probe coil should be just large enough to contain the sample. As the probe volume increases with respect to the sample volume, the fillingfactor, and hence the signaltonoise ratio, decreases. Problem 2: (5 points) In order to maximize the signaltonoise ratio of an MR image acquired over a localized area, is it better to use a volume coil or a surface coil? Justify your answer. The result from problem 1 indicates that we should employ a surface coil to maximize the fillfactor, and correspond ingly, the signaltonoise ratio. In addition, as discussed by Darrasse and Ginerfri on page 192 of their paper, using a volume coil to image a localized area has the undesirable effect of picking up sample noise, resulting from inductive and dielectric loss mechanisms, across a volume much larger than the region of interest. In contrast, the surfaceand dielectric loss mechanisms, across a volume much larger than the region of interest....
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 Spring '07
 SCHIANO

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