A study on modified Szabo's wave equation modeling of frequency-dependent dissipation in ultrasonic medical imaging

The modified Szabo's wave equation, in which the positive fractional derivative has first been used, is a new model to describe the frequency-dependent dissipative ultrasonic wave propagation through human tissues. To our best knowledge, the verification of this model, however, has not been reported in literature. Based on the frequency-dependent dissipation characterization of tumor and surrounding normal tissues, clinical amplitude velocity reconstruction imaging (CARI) is a recent ultrasonography for effectively detecting early breast tumors. This study makes the first attempt to numerically test the modified Szabo's model to the CARI clinical technique. The finite difference method is employed to solve the modified Szabo's wave equation. It is observed from our experimental results that the reflecting line of ultrasound pressure of the model is enhanced in the region of tumor against surrounding normal tissues. This finding agrees well with clinical observations and shows that the model can well describe the ultrasonic frequency-dependent dissipation. We also note that the numerical solution of positive fractional derivative modified Szabo's wave equation is as expensive as that of the standard fractional derivative equations.