Modeling of ultrasound propagation through contrast agents

In the past years many advances have been made in the detection of ultrasound contrast agents (UCA) by exploiting their nonlinear behavior. However, little attention has been paid to the nonlinear distortion of ultrasound (US) waves propagating through contrast media. The aim of this study is to model the nonlinear propagation of low pressure US waves through contrast media. The Burgers’ equation (approximated to the second order) is used to model the nonlinear US propagation. In addition, the results are compared to a numerical approximation of forward scattering, combining the linear-wave and modified Rayleigh-Plesset Noltingk Neppiras and Poritsky (RPNNP) equations. Measurements are performed for the model validation. Using a single element transducer, a Hanning-windowed 20 cycle US pulse was transmitted through water. An acoustically transparent tube (22 mm diameter) was positioned in the transducer focus containing different UCA concentrations up to 0.2%. All measurements were performed with an US mechanical index of 0.1 to prevent bubble collapse. The adopted frequency range was 0.5 to 3.5 MHz, which is around the UCA resonance frequency. The waves were measured by a hydrophone placed in line with the transducer. For low concentrations of UCA, the propagation of US waves can be described using the Burgers’ equation. For higher concentrations and frequencies close to the UCA resonance frequency a phase shift arises in the measurements which can be predicted by combining the modified RPNNP and the linear-wave equations.