RAD229: Midterm Exam 2015/2016 October 19, Minutes. Please do not proceed to the next page until the exam begins.

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1 RAD229: Midterm Exam 2015/2016 October 19, Minutes Name: Student ID: General Instructions: 1. Write your name legibly on this page. 2. You may use notes including lectures, homework, solutions or Matlab script text on the course website. 3. You may not use Matlab or the Internet. 4. Please answer questions on the exam, and show your final answer clearly. 5. Show your reasoning and work, as this will often earn you partial points. 6. You may request more paper if needed. Please do not proceed to the next page until the exam begins. The following formula from the class notes may be useful. RAD 229 Midterm 2015/2016 1

2 Short Answer Questions (25% of Points) 1. [5pts] Starting at equilibrium [m x m y m z ] T = [0 0 1] T what is a sequence with the minimum number of RF pulses and gradients (each dephasing +1 cycle over a voxel) that results in non-zero values of the EPG coefficients F - 2 (or equivalently F + -2)and Z 2? Draw the sequence. 2. [5pts] An RF pulse rotates magnetization by an angle α, about an axis in the transverse plane that makes an angle β with the M x axis. Express the 3x3 rotation matrix for this pulse as a function of rotations R x (θ) and R z (θ), which rotate an angle θ about the M x and M z axes respectively. Don t worry about the sign of α or β here. 3. [5pts] Assuming standard 2D sampling what is the effect on the image of: a. Dividing the amplitude of the odd k y lines of data by 2. b. Setting the sample at k x =k y =0 to 0. RAD 229 Midterm 2015/2016 2

3 4. [5pts] Given the Fourier transform m(r) from a standard MR acquisition M(k) with complex Gaussian k-space noise, describe qualitatively the pixel probability distribution function if: a. the noise-free image phase φ(r) in radians is perfectly known, and the final image value is calculated as m a =Re{m(r) exp[-i φ(r)]}, where Re{} denotes the real part of a complex number. b. the signal value in the pixel is zero, and the magnitude m(r) is used as the image. 5. [5pts] In a gradient-echo sequence with flip angle α, and assuming transverse magnetization dies out over TR, explain three reasons you might see image shading in MRI, even if the object is a uniform material (same density, T 1 and T 2 at all locations)? RAD 229 Midterm 2015/2016 3

4 Long Answer (75% of Points) 6. [25pts] If a constant RF pulse of amplitude 5µT is on for 0.5ms, with a constant, rectangular gradient of 1.0mT/m along z, use the small-tip angle approximation to write an expression for the transverse magnetization m xy = m x +im y at the end of the pulse as a function of position (z), and draw the excited profile magnitude and phase. Use γ/2π = 50MHz/T for this question! RAD 229 Midterm 2015/2016 4

5 7. [25pts] Consider the sequence shown below, where each RF tips the magnetization about -y by an angle α, and the gradient polarity in each TR is flipped as shown. a. Draw an EPG coherence pathway diagram for the first 4 TRs from equilibrium, labeling any potentially non-zero transverse states and showing transverse transitions with solid lines, and longitudinal transitions with dashed lines. b. Give an expression for the observed m xy signal immediately before the 3 rd RF pulse. You may neglect relaxation here. c. Give an expression for the observed m xy signal immediately following the 3 rd RF pulse. You may neglect relaxation here. (Continued on next page) RAD 229 Midterm 2015/2016 5

6 d. If the first pulse is 90 -y º and the remaining pulses are 180º x repeat part (a), and explain what happens to observed m xy signal in parts (b) and (c). RAD 229 Midterm 2015/2016 6

7 8. [25pts] Consider a sequence 180º - T a 180º - T b 90 -y º, with magnetization starting at equilibrium, as shown below. The goal of this sequence is to simultaneously null the signal from two different T 1 times. The sequence parameters T a and T b must be greater than 0. (note a 90º -y from equilibrium gives m x = 1). a. Write an expression for m x immediately after the 90º pulse, as a function of T a, T b, and T 1. b. Explain intuitively, including a diagram if you would like, why there is always some value of T 1 at which the signal (m x ) immediately after the 90º pulse is positive. c. Draw m z curves for T a = T b that show plausible cases where immediately prior to the 2 nd 180º pulse the value of m z is (i) positive, (ii) negative and (iii) zero. Explain, in terms of T a, what T 1 values will be nulled by the sequence if T b is very close to zero? (Continued on next page) RAD 229 Midterm 2015/2016 7

8 d. If T a = 5T b, draw two distinct plausible m z curves where after the 90º pulse m x = 0. RAD 229 Midterm 2015/2016 8

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