Full wave modeling of therapeutic ultrasound: efficient time-domain implementation of the frequency power-law attenuation.
For the simulation of therapeutic ultrasound applications, a method including frequency-dependent attenuation effects directly in the time domain is highly desirable. This paper describes an efficient numerical time-domain implementation of the power-law attenuation model presented by Szabo [Szabo, J. Acoust. Soc. Am. 96, 491-500 (1994)]. Simulations of therapeutic ultrasound applications are feasible in conjunction with a previously presented finite differences time-domain (FDTD) algorithm for nonlinear ultrasound propagation [Ginter et al., J. Acoust. Soc. Am. 111, 2049-2059 (2002)]. Szabo implemented the empirical frequency power-law attenuation using a causal convolutional operator directly in the time-domain equation. Though a variety of time-domain models has been published in recent years, no efficient numerical implementation has been presented so far for frequency power-law attenuation models. Solving a convolutional integral with standard time-domain techniques requires enormous computational effort and therefore often limits the application of such models to 1D problems. In contrast, the presented method is based on a recursive algorithm and requires only three time levels and a few auxiliary data to approximate the convolutional integral with high accuracy. The simulation results are validated by comparison with analytical solutions and measurements.
Liebler
Marko
M
Institut für Höchstfrequenztechnik und Elektronik/Akustik, Universität Karlsruhe, Kaiserstrasse 12, 76128 Karlsruhe, Germany. marko.liebler@ihe.uka.de
Ginter
Siegfried
S
Dreyer
Thomas
T
Riedlinger
Rainer E
RE
D000162:Acoustics; D000465:Algorithms; D002368:Castor Oil / Q000737:chemistry; D004853:Epoxy Resins / Q000737:chemistry; D005583:Fourier Analysis; D006801:Humans; D008954:Models, Biological; D017711:Nonlinear Dynamics; D019047:Phantoms, Imaging; D010796:Phthalic Anhydrides / Q000737:chemistry; D014464:Ultrasonic Therapy / Q000379:methods*; D014465:Ultrasonics
D004853:Epoxy Resins; D010796:Phthalic Anhydrides; C005752:araldite; D002368:Castor Oil