Use of a composite nonlinear model including microbubbles and tissue to examine effects for ultrasonic propagation and backscatter in complex tissues: nonlinear ultrasonic waves in composite tissues

Several numerical modeling studies have examined nonlinear propagation of ultrasound in tissue (KZK equation). Similarly, other investigations have studied nonlinear backscatter characteristics from ultrasound contrast microbubbles (RP equation). However, very few reports on combined tissue-bubble models are available, especially in the area of nonlinear contribution of microbubbles to ultrasonic propagation and backscatter in complex tissue where both blood vessels and surrounding soft tissue are incorporated. Results from such studies should contribute further to the continuing optimization of harmonic imaging techniques. In this study, the well-known KZK equation is adapted to include tissue and blood vessels with microbubbles. A composite approach utilizing the equivalent nonlinearity and attenuation parameters for the blood vessel with varying amount of contrast (volume fraction of bubbles to blood: 10^-8 to 10^-6) provides the resultant equation which is then solved using a time-domain finite difference technique. Harmonic analysis of tissue propagation shows that the microbubbles induce significant nonlinearity in the propagating wave, which influences both harmonic generation and waveform distortion by causing spatial shifts of the harmonic focal points (2^nd and 3^rd harmonics) and production of higher amplitude harmonic wave components. Wave-diffraction patterns of the multi-harmonic components varied mainly as a function of bubble concentration within the local blood vessel. These results provide a means for understanding harmonic effects in a realistic composite tissue-blood vessel model and should provide pathways to improve signal-to-noise ratio in harmonic imaging.