BE280A, Principles of Biomedical Imaging 11/18/08 Fall Quarter 2008 BE280A Final Project Assignment Due Date: As agreed upon in class, the completed project (hard copy) will be due in my office on Tuesday, December 9, 2008 by 5 pm. In addition to the hard copy, please submit a PDF version of the report and MATLAB code (*.m file) via e-mail by 9pm on that day. For full credit, the subject line of your e-mail should read BE280A08 Final Project. The report filename should follow the following format mri_{initials of partner 1}_{initials of partner 2}.pdf – e.g. mri_lk_pb.pdf. The oral exam component of the project (10 minutes per student) will occur during the final exam period for this course (Thursday, December 11, 2008 from 8 am to 11 am). Guidelines: 1) Select a partner to work with (there are 18 registered students, so that there will be 9 groups). Your partner for the final project should not be the same as your partner for the midterm project. 2) Discussion of general ideas is encouraged between groups, however, each report submitted should reflect each group’s own understanding of the material. Figures and MATLAB code should be unique to each group. Significant discussions with other groups should be given appropriate credit (e.g. we discussed part (a) with so and so). 3) An electronic copy of the MATLAB code should be submitted with the PDF of the report. The code file should be named in a similar fashion to the *.pdf file, except with a *.m extension. 4) The MATLAB code should follow the following criteria: (a) All figures in the report can be generated just by typing the name of the *.m file (e.g. no further manipulation of the files by the instructor should be required); (b) The numbering and labeling of the Figures generated by MATLAB should exactly match what is in the report. (c) If you use functions, they should be named such that the main file can recognize them; or else, just include functions within the main file (the main program will then need to be a function). 5) Use a word-processing program to write the report, including all equations (no handwritten reports! Use an equation editor.). Neatness and clarity of exposition will play a significant role in the grading of the report. Other grading criteria include technical correctness and originality. Clearly indicate how each section of your report corresponds to each question – it’s usually best to break your report into clearly delineated sections. 6) You may use external references (print or electronic). If you do so, please cite them at the end of your report. 7) Title and label the axes on all plots and images. 8) For all problems, use ! "2#( )= 4257 Hz /G 9) In addition to answering the questions below, please be as quantitative as possible. Also provide additional details and original insights as appropriate. If you noticed something interesting or learned something new in doing this project, please comment on that.Preliminaries (5 pts.) Label your e-mail, PDF file, and MATLAB code as indicated above. (5 pts.) Make sure that your MATLAB code executes without errors. In addition, all figures should be generated simply by typing the name of the main MATLAB code provided. The number of your figure should exactly match the number in your report. Extra figures are okay, but these should be given additional figure numbers. (5 pts) Clarity. Make sure to label all sections in your report clearly. Also indicate clearly how you have addressed the questions. Description of Problem Part 1 (50 pts) Design an echoplanar imaging (EPI) pulse sequence to meet the following requirements: FOVx= 192, FOVy = 192 mm, matrix size = 64x64 (i.e., resolution in x = 3 mm; y = 3mm); maximum available gradient = 4.5 G/cm; minimum rise-time from zero gradient to full amplitude = 200 µsec (i.e. maximum slope or slew-rate = 22.5 G/cm/msec = 225 mT/m/msec). Assume that each gradient waveform duration must be an integer multiple of 4 µsec. Also assume that the ADC is only on during the readout gradient, and that the sample rate of the ADC is 250 KHz (i.e., Δt = 4 µsec). Your design should use trapezoidal and/or triangular gradients, where the maximum slope of your gradients is limited by the slew-rate specification. Your design should make full use of the gradient strengths and slew rates to cover k-space in the shortest time possible. For consistency, when there are two gradients occupying the same space, stretch the shorter gradient out when possible. That is, make the total lengths of the readout and phase encode dephasers the same; and make the total lengths of the readout ramps and the phase blips the same. For the readout ramps and phase gradient blips that occur between readout flats, round the overall time to the nearest multiple of 4 usec. Do not have the phase encode dephaser overlap with the initial positive ramp of the readout gradient. Have the dephasers move to an initial position of ! kx= "Wkx/2 and ! ky= "Wky/2. Assume that the readout gradient corresponds to the x-axis and the phase encode gradient corresponds to the y-axis. In your design, the 33rd ! kyline (phase-encode direction) should go through the ! ky= 0 origin, so that you end up with a slightly asymmetric coverage of k-space, with 32 ! ky lines below the origin and 31! ky lines above the origin. Similarly, the coverage in the readout direction is asymmetric, so that either the 33rd or 32nd ADC sample of each line (depending on odd or even line) coincides with ! kx= 0. (a) (20 pts) Determine the pulse sequence parameters that accomplish the above design parameters. Be explicit in your derivations. Use MATLAB to plot out your gradient trajectories (e.g. Gx and Gy versus time) and the corresponding k-space trajectories (e.g. kx and ky versus time). Also make a parametric plot showing the 2D k-space trajectory (e.g. Make sure to label all axes of your plots correctly). As necessary, show zoomed-in views of the critical parts of the trajectories. NOTE: Once you have a vector representation of yourgradients in MATLAB, you may want to use the cumsum function to calculate your gradient trajectories – this will provide a good check of your answer. (b) (30 pts) Write a short MATLAB program to calculate the pulse sequence parameters. Document the program clearly to explain your logic. Use the following input/output format for your program: [gxr, gxd, gyp, gyd]=
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