4 Putting Everything Together (ExamType Question): It's All In Your Head (3 pts). Your head is in an MRI machine, with the z axis straight up, the z: axis through your nose, and the y-axis through your left ear. There is a 1.5 Tesla mag- z netic eld Bo directed along the zaxis. a. In lecture 5d (MRI) we introduced the idea of an alternating magnetic eld B1. Why must the di- rection of the pulse B1 be alternated? At what frequency must this oscillation occur? Does this frequency depend on B1? b. You wish to apply a 90\" pulse to the protons in a horizontal plane located 10cm below the my plane [i.e. about at the level of your neck). You ap- ply a magnetic eld gradient along the z direc- tion so that the eld is given by the expression: B; = Bo +G'z, where the gradient G is 10\"1 T/cm. Find the angular frequency of the pulse that you should apply, and determine the desired duration of the pulse. (Assume the applied pulse has a strength of Bl = 10-4 T.) X c. If some protons in this slice of your neck have a T1 of 1.0 seconds, how long will it take for the z- magnetization Ma to return to 98% of its equilibrium value? d. Suppose you are starting to develop a thyroid goiter, which can be characterized by a particular T1 value. You measure the magnetization with a magnetic gradient in the y direction: 3; = Bo + Gy, where the gradient G is 10'4 T/cm. If the goiter is 1 cm to the left of the origin (i.e. along the positive y axis), what will be the angular frequency of the signal recorded from the protons in the goiter? If the goiter were instead 1 cm to the right, what would be the angular frequency of the signal? Explain how these kinds of measurements can tell doctors where a particular organ or unusual mass is located inside the body. e. Listed below are typical ranges for T1 and T2 for various types of tissue found in the head and neck. Below that are two MRI images, A and B. Image A was taken in a mode that highlights contrast based on different values of T1; Image B focused instead on contrast based on T2. Briey explain how you can determine that Image A highlights T1 contrast and Image B highlights T2 contrast given the table and gures below