Modified szaboʹs wave equation for arbitrarily frequency-dependent viscous dissipation in soft matter with applications to 3D ultrasonic imaging

Soft matters are observed anomalous viscosity behaviors often characterized by a power law frequency-dependent attenuation in acoustic wave propagation. Recent decades have witnessed a fast growing research on developing various models for such anomalous viscosity behaviors, among which one of the present authors proposed the modified Szaboʹs wave equation via the positive fractional derivative. The purpose of this study is to apply the modified Szaboʹs wave equation to simulate a recent ultrasonic imaging technique called the clinical amplitudevelocity reconstruction imaging (CARI) of breast tumors which are of typical soft tissue matters. Investigations have been made on the effects of the size and position of tumors on the quality of ultrasonic medical imaging. It is observed from numerical results that the sound pressure along the reflecting line, which indicates the detection results, varies obviously with sizes and lateral positions of tumors, but remains almost the same for different axial positions.