Wave scattering from encapsulated microbubbles subject to high-frequency ultrasound: contribution of higher-order scattering modes

Abstract

The theoretical understanding of encapsulated microbubble response to high-frequency ultrasound (HFUS) excitation is still limited although some novel experimental HFUS contrast imaging techniques have been well developed. In this paper, the higher-order modal (HOM) contributions to the scattered field are studied for such microbubbles driven by 1-100 MHz ultrasound. An exact solution of all small-amplitude vibrational modes of a single encapsulated microbubble in water is given by the wave scattering theory (WST) method and compared to results obtained from Church's Rayleigh-Plesset-like model for the small-amplitude radial oscillation of a microbubble in an incompressible fluid. From numerical results, we show that the HOM field contribution is significant for scattering properties from individual Nycomed microbubbles with normalized frequency > or = 0.2. It is also shown that the multiple scattering is strengthened for monodispersed Definity microbubbles of 3 microm radius at frequencies >40 MHz. However, comparisons between the authors' analyses and known experimental data for polydispersed Definity microbubbles indicate that the HOM contributions are insignificant in attenuation estimation at frequencies <50 MHz. In conclusion, the WST model analysis suggests that HOM scattering is an important consideration for single bubbles but may be less critical in the modeling of polydispersed Definity bubbles at high frequencies.

Figure 1

Schematic sketch of the model.

Figure 2

Contribution of first three modes of WST model as a function of driving frequency. The Albunex^® bubble is 2 μm in radius.

Figure 3

Reduced scattering cross sections of Albunex^® bubbles with radius (a) 1 μm and (b) 2 μm.

Figure 4

Attenuation coefficients A in Definity^® microbubble suspensions. The bubbles are identical in radii of (a) 1 μm and (b) 3 μm. The bubble concentrations are (a) 2×10⁶ and (b) 5×10⁵ bubbles∕ml.

Figure 5

Attenuation coefficients A from models and measurements;

Figure 6

Primary acoustic radiation forces on the Albunex^® bubble in water as a function of radius under a driving ultrasound pulse wave with peak negative pressure p_a=100 kPa and central frequencies of (a) f=3.5 MHz and (b) f=50 MHz.

Figure 7

Reduced scattering cross sections of single Albunex^® bubble as a function of driving frequency. The polytropic exponents are (a) 1.0 (left), (b) 1.1 (center), and (c) 1.4 (right).

Figure 8

Scattering cross sections of single Nycomed bubble as a function of normalized frequency.

Figure 9

Contour plot of normalized frequency.