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Acta Mechanica Solida Sinica

, Volume 25, Issue 5, pp 510–519 | Cite as

Modified Szabo’s Wave Equation for Arbitrarily Frequency-Dependent Viscous Dissipation in Soft Matter with Applications to 3D Ultrasonic Imaging

  • Xiaodi Zhang
  • Wen Chen
  • Chuanzeng Zhang
Article

Abstract

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 Szabo’s wave equation via the positive fractional derivative. The purpose of this study is to apply the modified Szabo’s wave equation to simulate a recent ultrasonic imaging technique called the clinical amplitude-velocity 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.

Key words

soft matter viscosity frequency-dependent dissipation modified Szabo’s wave equation positive fractional derivative ultrasonic imaging 

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Copyright information

© The Chinese Society of Theoretical and Applied Mechanics and Technology 2012

Authors and Affiliations

  1. 1.Institute of Soft Matter Mechanics, Department of Engineering MechanicsHohai UniversityNanjingChina
  2. 2.Department of Civil EngineeringUniversity of SiegenSiegenGermany

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