An analytical model to calculate the primary and secondary acoustic forces acting on microbubbles due to a short pulsed laser excitation

Abstract

This work presents a comprehensive analytical approach to describe photoacoustic waves resulting from a pulsed laser excitation. The spatial part of the laser is modeled by a zeroth-order Bessel function of the first kind, which has a wide range of applications in optics and medical physics, such as optical trapping and nonlinear effects resulting from the interaction of a pulsed laser with tissue in photoacoustic imaging. The temporal part of the laser is described by a Gaussian function, which is a pretty realistic approximation since the interaction of the laser with the medium is instantaneous. The photoacoustic wave equation is solved analytically using the Fourier transform and the Greens’ function methods. The solution of the photoacoustic wave equation depends explicitly on position, time, pulse duration, and beam-width of the pulsed laser. The effects of these dependencies on the photoacoustic wave are investigated. Later, the primary and secondary radiation forces acting on microbubbles Albunex and Quantison are calculated using the magnitude of the photoacoustic pressure wave. The primary and secondary radiation forces decrease considerably with the distance from the photoacoustic absorber. These forces increase as the beam-width increases while they decrease as the pulse duration gets longer. The primary radiation forces on the microbubbles are on the order of nanonewtons. The force at this scale can be used to manipulate microbubbles. The secondary radiation force between identical microbubbles is in the range of piconewtons. Hence, this force can be used to determine the viscoelastic properties of microbubbles even though it is very small compared to the primary radiation force. The radiation forces determined by this work are also compared with those calculated by another study describing the laser’s spatial profile with a Gaussian function. The forces obtained by this work are larger than the forces determined by the Gaussian function approximation at the positions near the source. The forces obtained by the two approaches show similar behaviors, and they decrease remarkably with the distance from the source. Thus, the model presented in this work can be used to study the nonlinear mechanism in photoacoustics, such as enhancing image contrast and determining the tissue temperature. It can also be helpful for the applications of microbubbles in medical imaging and drug delivery as carriers.