The Suppression of Selected Acoustic Noise Frequencies in MRI by XINGXIAN SHOU Submitted in partial fulfillment of the requirements For the degree of Doctor of Philosophy Dissertation Adviser: Robert W. Brown, Ph.D. Department of Physics CASE WESTERN RESERVE UNIVERSITY January, 2011 CASE WESTERN RESERVE UNIVERSITY SCHOOL OF GRADUATE STUDIES We hereby approve the thesis/dissertation of ______________________________________________________XINGXIAN SHOU candidate for the ________________________________degreePh.D. *. (signed)_______________________________________________Robert W. Brown (chair of the committee) ________________________________________________Jeffrey Duerk ________________________________________________David Farrell ________________________________________________Harsh Mathur ________________________________________________Shmaryu Shvartsman ________________________________________________ (date) _______________________July 26, 2010 *We also certify that written approval has been obtained for any proprietary material contained therein. To my parents Jun Shou, Huiqin Bian and my fiancée Shuofen Li ii Table of Contents Chapter 1 An Overview of Magnetic Resonance Imaging ....................................................... 1 1.1 What Is MRI? .................................................................................................................. 1 1.2 Principles of Magnetic Resonance Imaging .................................................................... 2 1.2.1 Spin Precession and Larmor Frequency ................................................................... 2 1.2.2 Rotating Reference Frame and the Bloch Equation ................................................. 7 1.2.3 Signal Detection ..................................................................................................... 14 1.2.4 Phase Encoding and Fourier Transform ................................................................. 19 1.3 MRI Systems ................................................................................................................. 25 1.3.1 Main Magnet........................................................................................................... 26 1.3.2 Gradient Coil System.............................................................................................. 28 1.3.3 Radiofrequency Coil ............................................................................................... 30 Chapter 2 Acoustic Noise and Its Reduction in Magnetic Resonance Imaging ..................... 35 2.1 Acoustic Noise Characterization ................................................................................... 36 2.1.1 Noise Source ........................................................................................................... 37 2.1.2 Noise Pathways ...................................................................................................... 38 2.2 Reduction of Acoustic Noise in MRI ............................................................................ 39 2.2.1 Reduction of Acoustic Noise via its Source ........................................................... 39 2.2.2 Reduction of Acoustic Noise via Transmission ..................................................... 44 2.2.3 Reduction of Acoustic Noise at Human Ear ........................................................... 46 iii 2.2.4 Reduction of Acoustic Noise Using New Sequences ............................................. 47 Chapter 3 String Model of the Acoustic Noise Vibration ....................................................... 56 3.1 Background ................................................................................................................... 56 3.2 String Model: Equations and Solutions ......................................................................... 59 3.3 Solution for Gradients ................................................................................................... 61 3.3.1 Boxcars ................................................................................................................... 61 3.3.2 Trapezoidal Gradient Solution ................................................................................ 67 3.3.3 Follow-up Pulses for Additional Frequency Cancellation ..................................... 71 3.3.4 General Rules for General Pulses ........................................................................... 76 3.3.5 Repeated Pulse: Pulse Trains .................................................................................. 78 Chapter 4 String Simulation.................................................................................................... 83 4.1 String Simulation........................................................................................................... 83 4.1.1 Boxcars ................................................................................................................... 83 4.1.2 Single and Double Trapezoids ................................................................................ 87 4.1.3 Simulation with Damping Effect ............................................................................ 90 4.1.4 Longitudinal and Transverse Gradient Pulse .......................................................... 93 4.1.5 Enhancement of Multiple Pulses ............................................................................ 95 Chapter 5 Experimental Design and Results .......................................................................... 98 5.1 Experimental Design ..................................................................................................... 98 5.1.1 Experiment Setup ................................................................................................... 98 5.2 Experimental Results................................................................................................... 100 iv 5.2.1 Cancellation as A Function of Pulse Timings ...................................................... 100 5.2.2 Cancellations in the Frequency Spectrum ............................................................ 108 5.3 Frequency Response Function .................................................................................... 123 5.4 Experiment with a Vacuum System ............................................................................ 129 Chapter 6 Discussion and Conclusion .................................................................................. 134 6.1 Summary of Results .................................................................................................... 134 6.2 Discussion ................................................................................................................... 136 6.3 Conclusion ................................................................................................................... 142 v List of Tables Table 1.1 List of selected nuclear species with their spins (in units of where the proton has spin ½), their associated magnetic moments in units of a nuclear magnetonmn , gyromagnetic ratios g (in units of MHz/T), and their relative body abundances. .......................................... 4 Table 3.1 Convolution results of boxcars ............................................................................... 78 vi List of Figures Figure 1.1 Clockwise precession of a proton’s spin along an external magnetic field through a negative differential df . ........................................................................................................ 5 p Figure 1.2 An on-resonance spin flip, as viewed in the (a) laboratory frame and (b) 2 rotating frame, ww= 0 and ww10= 0.05 . In MR applications, the frequency w1 would be much smaller in relation to the RF frequency, but the spiraling would then be much too dense to illustrate. ............................................................................................................................. 10 Figure 1.3 An overview of MRI system. The main magnet, the gradient system, and the RF coil system all have their own shielding, which is not indicated in the figure. ...................... 26 Figure 2.1 (A) The sketch shows the Lorentz forces applied on a loop segments carrying current at an external magnetic field B along the z-direction, which is perpendicular to the plane of the loop. (B) The sketch shows an arc-loop setup for x-gradient with balanced Lorentz force over the whole loop. Given the radii of a and c of the arcs, the separation 2b is adjusted to obtain the desired gradient field strength and linearity. ....................................... 41 Figure 3.1 A boxcar gradient pulse with duration t1 . ............................................................. 62 Figure 3.2 (a) The top plot shows a 2-ms duration boxcar gradient killing the string vibration with 500 Hz for t > t = 2 ms . (b) The bottom plot shows a 1 ms top boxcar gradient 1 maximally enhancing the 500 Hz string vibration for t > t = 1 ms . In both plots, the thick 1 vii curve is the vibration induced by the positive Q impulse, the thin curve is the vibration induced by the negative Q impulse, while the dashed curve is the superposition of the two.66 Figure 3.3 A trapezoidal gradient pulse with ramp time (up and down) tr and flat-top time ttop . .......................................................................................................................................... 68 Figure 3.4 A double-trapezoid gradient pulse with ramp time tr , flat-top