Physics in Medicine and Biology ; DOI:10.1109/TUFFC.2012.2372
A k-space method for moderately nonlinear wave propagation in absorptive media is presented. The Westervelt equation is first transferred into k-space via Fourier transformation, and is solved by a modified wave-vector time-domain scheme. The present approach is not limited to forward propagation or parabolic approximation. One- and two-dimensional problems are investigated to verify the method by comparing results to analytic solutions and finite-difference time-domain (FDTD) method. It is found that to obtain accurate results in homogeneous media, the grid size can be as little as two points per wavelength, and for a moderately nonlinear problem, the Courant–Friedrichs–Lewy number can be as large as 0.4. Through comparisons with the conventional FDTD method, the k-space method for nonlinear wave propagation is shown here to be computationally more efficient and accurate. The k-space method is then employed to study three-dimensional nonlinear wave propagation through the skull, which shows that a relatively accurate focusing can be achieved in the brain at a high frequency by sending a low frequency from the transducer. Finally, implementations of the k-space method using a single graphics processing unit shows that it required about one-seventh the computation time of a single-core CPU calculation.
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Clinic Ultrasound Laboratory (クレメント超音波研究室)
Cleveland Clinic (クリーブランド・クリニック),
Lerner Research Institute
Case Western Reserve University
© 2014
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Clement GT, Nomura H, Adachi H, Kamakura T, Feasibility of non-contact ultrasound for medical imaging, Physics in Medicine and Biology 2014; 58: 6263-6278
Tang SC, Jolesz FA, Clement GT. A Wireless Batteryless Implantable Ultrasonic Pulser-Receiver. IEEE Trans Ultrason Ferroelectr Freq Control 2011;58:1211-21.
Paltiel HJ, Padua HM, Gargollo PC, Cannon GM Jr, Alomari AI, Yu R, Clement GT. Volumetric ultrasound imaging of tissue perfusion: preliminary results in a rabbit model... Phys Med Biol 2011;56:2183-97.
McDannold N, Clement GT, Black P, Jolesz F, Hynynen K. Focused ultrasound surgery of brain tumors: Initial findings in three patients. Neurosurgery 2010;66:323-32; discussion 332.
Clement GT, Hynynen K. A non-invasive method for focusing ultrasound through the human skull. Phys Med Biol 2002;47(8):1219-36.