# HW6_solutions - ECE 380 Biomedical Imaging Spring 2010...

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1 ECE 380 Biomedical Imaging Spring 2010 Homework 6 Solutions _____________________________________________________ Problem 1 : (20 points) a) What is the precession frequency of protons in a main magnetic field Bo=3 T? (10 points) Using equation (4.6) from your book i.e. 00 wB and the value of / 2 42.57 / MHz T  from Table 4.1, the precession frequency is 0 0 0 6 0 2 (42.57 10 ) (3) 2 127.71 w B fB B f f MHz  b) A 2 mm slice perpendicular to the z-axis at position z = 0.1 m is excited with a radiofrequency pulse at frequency f. Assume Bo=1.5 T Gz=10 mT/m. What is the frequency f (in Hz) of the RF pulse to excite this slice? And what is the bandwidth? (10 points) Using equation (4.33) from the book, 0 0 63 0 ( ) ( ) 2 ( ) () (42.57 10 ) (1.5 (10 10 )(0.1)) 2 63.89 z z z w z G z B f B G z B G z f f MHz  Bandwidth Using equation (4.35) from the book

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2 3 3 6 2 2 (2 10 )(10 10 )(42.57 10 ) 851.4 zz z f z GG zG f f f Hz        Problem 2 : NMR (30 points) a) Suppose a sample has a T 1 value of 0.6 seconds. The net magnetization from the sample is set equal to zero. This sample is then allowed to recover towards its
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HW6_solutions - ECE 380 Biomedical Imaging Spring 2010...

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