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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 signal-to-noise ratio of a nuclear magnetization measurement scale with the filling-factor? 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 signal-to-noise ratio is proportional to the filling-factor. 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 filling-factor, and hence the signal-to-noise ratio, decreases. Problem 2: (5 points) In order to maximize the signal-to-noise 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 fill-factor, and correspond- ingly, the signal-to-noise 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