title: Comparison of fractional wave equations for power law attenuation in ultrasound and elastography.
abstract: A set of wave equations with fractional loss operators in time and space are analyzed. The fractional Szabo equation, the power law wave equation and the causal fractional Laplacian wave equation are all found to be low-frequency approximations of the fractional Kelvin-Voigt wave equation and the more general fractional Zener wave equation. The latter two equations are based on fractional constitutive equations, whereas the former wave equations have been derived from the desire to model power law attenuation in applications like medical ultrasound. This has consequences for use in modeling and simulation, especially for applications that do not satisfy the low-frequency approximation, such as shear wave elastography. In such applications, the wave equations based on constitutive equations are the viable ones.
authors.affiliation: Department of Informatics, University of Oslo, Oslo, Norway. Electronic address: sverre@ifi.uio.no.
authors.forename: Sverre
authors.initials: S
authors.lastname: Holm
authors.affiliation: Norsar, Kjeller, Norway.
authors.forename: Sven Peter
authors.initials: SP
authors.lastname: Näsholm
mesh_terms: D000465:Algorithms; D000818:Animals; D003198:Computer Simulation; D055119:Elastic Modulus / Q000502:physiology; D054459:Elasticity Imaging Techniques / Q000379:methods*; D004735:Energy Transfer / Q000502:physiology*; D006801:Humans; D007090:Image Interpretation, Computer-Assisted / Q000379:methods*; D008954:Models, Biological; D012542:Scattering, Radiation; D033081:Shear Strength / Q000502:physiology; D013016:Sound; D013314:Stress, Mechanical
keywords: Absorption; Constitutive equations; Elastography; Fractional derivative; Lossy wave equation; Power law; Ultrasound; Viscoelastic