BNG/ECE 487 FINAL (W16)

Transcription

1 BNG/ECE 487 FINAL (W16) NAME: 4 Problems for 100 pts This exam is closed-everything (no notes, books, etc.). Calculators are permitted. Possibly useful formulas and tables are provided on this page. Fourier Transform Pairs and Properties cos2 Ultrasound equations: Bandwidth for Gaussian Pulse Envelope: Depth resolution: Near-field Region: Focal width: Depth of focus: 0.5 # # MRI equations: 0 1 / BNG/ECE 487: Medical Imaging Systems Final Exam Mar 17,

2 Problem #1: General Knowledge (25 pts) (a) Ultrasound: Choose true or false for each of the following statements. If you choose false, then provide the correct statement. (i) A large fractional bandwidth means more cycles within the ultrasound pulse envelope. (ii) Imaging with higher ultrasound frequencies is always desirable, since this maximizes spatial resolution. (iii) A common transducer material is Led Zeppelin Tarantino (LZT). (b) Ultrasound: Suppose you want to image renal (kidney) blood flow, where the velocities are much lower than in cardiac imaging. Would you use continuous-wave Doppler, power Doppler, or pulsed-wave Doppler? Choose one and briefly explain why. (c) Ultrasound: Suppose an ultrasound pulse has a rect-shaped envelope (rather than Gaussian). The pulse is given by: p(t) = rect(t/)cos(2f 0 t), where = 0.8 s and f 0 = 5 MHz. Sketch p(t) and its spectrum P(f), making sure to label important features. Possibly helpful formulas are on the front page of this exam. BNG/ECE 487: Medical Imaging Systems Final Exam Mar 17,

3 (d) MRI: Suppose an MRI brain scan uses a spin echo time of TE = 70 ms and a pulse repetition time of TR = 4000 ms. What type of weighting is performed in this scan? Briefly explain why. Tissue Type Relative PD T2 (ms) T1 (ms) White matter Gray matter Cerebrospinal fluid (e) MRI: Suppose an MRI brain scan uses TE = 10 ms and TR = 800 ms. Which tissue type (from the above table) gives the strongest signal and weakest signal? Explain why. (f) MRI: Suppose an MRI pulse sequence first applies a 180 pulse (diagram a ) followed by a 90 pulse (diagram b ). On each diagram, sketch the behavior of the magnetization vector M (e.g. before and after). z z y y B180 x B90 x (a) (b) (g) Nuclear Imaging: Explain the difference in gamma ray emission by a radiotracer in planar scintigraphy (e.g. Tc-99m) compared to positron emission tomography (e.g. Fluorine-18). BNG/ECE 487: Medical Imaging Systems Final Exam Mar 17,

4 Problem #2: Ultrasound Imaging (25 pts) You are asked to design a linear array scanner to image the kidney. The desired field of view is 100 mm across and 150 mm deep. The ADC electronics operate at a 40 MHz sampling rate. The TGC electronics can produce a maximum gain of 100 db. Assume a wave speed c = 1.5 mm/s and attenuation coefficient a = 1 db/cm/mhz. (a) You must choose between transducer probes with f 0 = 1.5, 3, 5, and 7 MHz. Assuming you only need to compensate for tissue attenuation, which frequency is the best choice? Array T/R TGC A/D (b) If the desired lateral resolution is w = 1.2 mm at a depth z = 75 mm, would you use a sub-array size of 16, 32, or 64 elements? Assume the element spacing is d = 0. Show all work. (c) In order to achieve a depth resolution of 0.75 mm, what is the minimum required fractional bandwidth? Assume the ultrasound pulse has a Gaussian waveform. Hint: The front page of this exam has some useful formulas. (d) What is the total number of elements in the array? (e) What is the approximate frame rate of your imaging system? Express your answer in Hz. BNG/ECE 487: Medical Imaging Systems Final Exam Mar 17,

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6 Problem #3: Fast MRI with Spiral Scanning (25 pts) One way to achieve fast MRI acquisition is to use a single 90-pulse followed by a spiral trajectory that starts at the origin and ends at the outer edge. No spin echoes are used in this sequence. v The following assumptions can be made: B 0 = 1.5 Tesla and /2 = MHz/Tesla for all tissue. The spiral trajectory consists of segments that trace out a spiral path. For example, the sketch to the right shows 13 segments. Segment #1 starts at the origin, while segment #13 is at the very bottom. Both G x and G y are T PULSE = 50 s in duration during each segment of the spiral trajectory. Output images are 128 x 128 pixels with a pixel spacing of x = y = 1 mm. u (a) Compute G x and G y during the first segment (e.g. starting from the origin and moving to the right). Express your answer in Gauss/cm. Hint: The front page of this exam has some useful formulas. (b) Each successive segment of the spiral trajectory requires incrementing the magnitude of G x by dg x and the magnitude of G y by dg y. Compute the increments dg x and dg y (units = Gauss/cm). (c) Sketch the RF, G x, G y, and G z fields for the first 13 segments of the spiral trajectory (e.g. as shown in the above sketch). You can assume the readout starts immediately after slice selection. (d) What is the approximate total imaging time of your pulse sequence? Express your answer in ms. BNG/ECE 487: Medical Imaging Systems Final Exam Mar 17,

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8 Problem #4: MRI of Rotator Cuff Injury (25 pts) The rotator cuff is a group of muscles and tendons connecting the upper arm to the shoulder blade. A torn tendon typically results in the accumulation of fluid. Design a MRI spin echo pulse sequence that performs 2D Fourier imaging of a rotator cuff injury. MRI properties of relevant tissue types are shown in the table below. Tissue Type Relative PD T2 (ms) T1 (ms) Tendon Bone Fluid The following assumptions can be made: B 0 = 3 Tesla and /2 = MHz/Tesla for all tissue. Gx = G/cm during encode. The encode and readout times T ENCODE and T READ are the SAME. Output images are 256 x 256 pixels with a pixel spacing of 0.5 mm. (a) Suppose you want your final image to maximize the ratio of the fluid signal to the other two tissue types (bone and tendons). You must choose between spin echo times of TE = 5 and 100 ms and pulse repetition intervals of TR = 500 and 5000 ms. Which is the best combination of TE and TR? You must also explain why the other combinations are not good choices. (b) Assuming the RF pulses are 0.3 ms in duration, compute the magnitude of B 90 and B 180. Express your answer in Gauss. (c) Compute T ENCODE and dg y during phase encode. Express T ENCODE in ms and dg y in G/cm. (d) Sketch the RF, G x, G y, and G z fields for your pulse sequence. Clearly label when the 180 pulse and spin echo occurs, as well as the duration and amplitude of encode and readout gradients. What is the total imaging time for your pulse sequence? BNG/ECE 487: Medical Imaging Systems Final Exam Mar 17,

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10 (extra sheet for work) BNG/ECE 487: Medical Imaging Systems Final Exam Mar 17,