Interaction of a high-order Bessel beam with a submerged spherical ultrasound contrast agent shell – Scattering theory

Abstract

Background and objective Acoustic scattering properties of ultrasound contrast agents are useful in extending existing or developing new techniques for biomedical imaging applications. A useful first step in this direction is to investigate the acoustic scattering of a new class of acoustic beams, known as helicoidal high-order Bessel beams, to improve the understanding of their scattering characteristics by an ultrasound contrast agent, which at present is very limited. Method The transverse acoustic scattering of a commercially available albuminoidal ultrasound contrast agent shell filled with air or a denser gas such as perfluoropropane and placed in a helicoidal Bessel beam of any order is examined numerically. The shell is assumed to possess an outer radius a = 3.5 microns and a thickness of ∼105 nm. Moduli of the total and resonance transverse acoustic scattering form functions are numerically evaluated in the bandwidth 0 < ka ⩽ 3, which corresponds to a frequency bandwidth of 0–205 MHz that covers a wide range of applications for imaging with contrast agents. Particular attention is paid to the shell’s material, the content of its interior hollow region and the fluid surrounding its exterior. The contrast agent shell is assumed to be immersed in an ideal compressible fluid so the viscous corrections are not considered. Analytical equations are derived and numerical calculations of the total and resonance form functions are performed with particular emphasis on the effect of varying the half-cone angle, the order of the helicoidal Bessel beam as well as the fluid that fills the interior hollow space. Results and conclusion It is shown that shell wave resonance modes can be excited on an encapsulated micro-bubble. The forward and backscattering vanish for a helicoidal high-order Bessel beam. Additionally, the fluid filling the inner core affects the shell’s response significantly. Moreover, there is no monopole contribution to the axial scattering of a helicoidal Bessel beam of order m ⩾ 1 so that the dynamics of contrast agents would be significantly altered. The main finding of the present theory is the suppression or enhancement for a particular resonance that may be used to advantage in imaging with ultrasound contrast agents for clinical applications.