Comparison of fractional wave equations for power law attenuation in ultrasound and elastography.
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.
['Holm|Sverre|S|', 'Näsholm|Sven Peter|SP|']
D000465:Algorithms D000818:Animals D003198:Computer Simulation D055119:Elastic Modulus D054459:Elasticity Imaging Techniques D004735:Energy Transfer D006801:Humans D007090:Image Interpretation, Computer-Assisted D008954:Models, Biological D012542:Scattering, Radiation D033081:Shear Strength D013016:Sound D013314:Stress, Mechanical
Power law Ultrasound Elastography Constitutive equations Absorption Fractional derivative Lossy wave equation Viscoelastic