Wave propagation in liposomes

Abstract

The general behavior of wave propagation in liposomes, including the effect of rotary inertia, is examined in this paper, based on a continuum cylindrical shell model. The disperse curves are obtained by solving an eigenvalue problem. The characteristics of wave propagation in liposomes are described using numerical examples. The results show that wave propagation in liposomes has a threshold critical frequency beyond which the wave speed drops dramatically and also a cut-off critical frequency below which the corresponding wave mode does not appear. The torsional wave speed is obtained for the symmetrical circumferential mode n = 0. The cut-off or threshold critical frequency decreases with the increase of liposomal radius, but the effect of radius on wave speed is not significant in the frequency region higher than the critical frequency. On the other hand, the wave number n leads to an increase in the critical frequency. For the first and second wave modes, the wave speed is insensitive to the wave number when the frequency is greater than the critical frequency. For the third wave mode in the low frequency region, the wave number leads to an increase in the wave speed. The rotary inertia has little influence on those wave modes which contain cut-off frequencies. For other wave modes, the rotary inertia results in a decrease in the wave speed in the high frequency region. This investigation may provide a useful guide in the applications of liposomes in ultrasound-based drug delivery and release.