HST.583 MRI Physics - Problem Set #4 Due 10/30/02Problem 1: Advantages of high field MR systemsa) If B0=7.0 Tesla, and the nuclei of interest are protons, what is the ratio of parallel to anti-parallel spins at room temperature? How does this compare to 1.5 Tesla and 3.0 Tesla systems? How do these answers change if the nucleus of interest is carbon 13?b) Say you just don't think that this is enough of a difference in the spin states, so you set out to explore two possibilities: lower temperatures, or raise field strength. For protons, at what temperature can you get a 2-1 ratio of low to high energyspins at 7.0 Tesla? And for carbon 13?For protons, what field strength would you need to achieve this population ratio at room temperature? And for carbon 13?Problem 2: Ernst anglea) Assume that a series of identical short RF pulses (flip angle ) are applied to a sample with relaxation times T1 and T2 . Assume that the time interval between consecutive RF pulses is kept constant and is given by the repetition time TR >> T2 . Further, assume that steady state has beenreached.Demonstrate that under these assumptions the flip angle (also known as the Ernst angle) that maximizes the MR signal measured after each RF pulse is given by: cos = exp - TR T1Hint: Find an expression for the transverse magnetization using the conditions of dynamic equilibrium, the effect of an RF pulse, and the relaxation of the magnetization between consecutive RF pulses. Once you have the transverse magnetization, take the first derivate with respect to and make it zero to find the condition that gives a maximum.b) Assume that you will run a functional MRI experiment where a series of RF pulses are applied and the signal after each RF pulse is used to generate an image for your time series analysis. Imagine that the TR of your experiment is fixed by conditions in your paradigm. What T1 would you consider in order to maximize your functional MRI sensitivity?Problem 3You are evaluating an EPI acquisition protocol for an experiment testing a hypothesis regarding orbito-frontal cortex and hippocampus and you are worried about image distortion because these regions are closed to air-filled spaces in the head. The in-plane field-of-view is set to 256mm on a 64x64 grid. The width of the head is approximately 130mm. How can the 'extra' field-of-view be utilized to reduce the amount of EPI distortion without changing the resolution? Is signal-to-noise affected?Problem 4: Playing with T1 and T2 contrastUsing the table of tissue parameters below, we will investigate the pulse sequence parameters forT1- and T2-weighted pulse sequences. We will make use the relationship: S = (1 – exp -TR/T1 ) exp -TE/T2, where S is the MR signal strength, is the spin density, TR the repetition time and TE the echo time.Tissue T1 T2 Gray matter 1.2 s 70 ms .98White matter 800 ms 45 ms .80a) If you want a T1-weighted pulse sequence, what would be a suitable choice for TE? Think of a choice that will minimize T2-weighting. Using your choice of TE and Matlab (or by hand),plot (or sketch) the signal strength S vs. TR for a range of TRs from 0 to 2000 ms. Put gray and white matter on the same plot (in different colors).b) In another figure, plot the signal difference between white matter and gray matter. At what TR is this difference maximized? How does this relate the tissue T1 s? c) For a T2-weighted pulse sequence, what would be your choice of TR to remove all T1 weighting. Use your choice of TR to plot the signal strength, S, vs. TE for a range of TE s from 0 to 150 ms. Put gray and white matter on the same plot (in different colors).d) In another figure, plot the signal difference between white matter and gray matter. At what TE is this difference maximized? [Optional: Set =1 for both and determine the optimal TE. How does this relate the tissue T2
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