Advantages in using multifrequency excitation of contrast microbubbles for enhancing echo particle image velocimetry techniques: initial numerical studies using rectangular and triangular waves.

Accurate measurement of velocity profiles, multiple velocity vectors and local shear stress in arteries is very important for a variety of cardiovascular diseases. We have recently developed an ultrasound based velocimetry technique, termed echo particle image velocimetry (echo PIV). This method takes advantage of the nonlinear backscatter characteristics of ultrasound contrast microbubbles when exposed to certain ultrasonic forcing conditions. Preliminary in vitro, animal and clinical studies have shown significant promise of this method for measuring multiple velocity components with good temporal (up to 2 ms) and spatial (<1 mm) resolution. However, there is still difficulty in maximizing the nonlinearity of bubble backscatter using conventional Gaussian-pulse excitation techniques because: (1) significant harmonic components may not be produced at modest pressure amplitudes; and (2) the higher incident pressure amplitudes required to induce nonlinear behavior may cause bubble destruction. We present here a potential solution to this problem through the use of multifrequency excitation, where rectangular and triangular pulses with four harmonics are used to drive the bubble. The nonlinear behavior of the microbubble, as well as fragility and backscatter, were studied through numerical modeling via a modified Rayleigh-Plesset equation. Results show that the rectangular wave is effective in improving the visibility of microbubbles, with effective scattering cross-section area significantly higher (up to 35 times) than the widely-used Gaussian waveform. However, velocity and acceleration analysis of the bubble wall shows that the rectangular wave may threaten bubble stability. Due to lower wall velocity and acceleration, the triangular wave should decrease the potential for bubble destruction yet maintain relatively high second harmonic backscatter components. The impact of higher harmonics was studied by examining backscatter differences from incident rectangular and triangular pulses with four and two harmonics. Results indicate that a two-frequency excitation (which may be easier to implement practically) may be sufficient to induce nonlinear behavior of the microbubbles at modest incident pressures. These predictions provide support for the use of multifrequency driving to enhance echo PIV applications.