A mathematical model of drug release from liposomes by low frequency ultrasound

Administration of drugs using small (<100 nm) unilamellar liposomes enables effective targeting of tumors and inflamed tissue. Therapeutic efficacy may be enhanced by triggering liposomal drug release in the desired organ in a controlled manner using a noninvasive external signal. Previous studies have demonstrated that low frequency ultrasound (LFUS) can be used to control the release of drugs from liposomes. LFUS irradiation has a twofold effect: (1) it causes the impermeable liposome membrane to become permeable and (2) it induces liposome disintegration. Immediately upon cessation of LFUS irradiation the membrane resumes its impermeable state and liposome disintegration stops. The mathematical model presented here is aimed at providing a better quantitative and qualitative understanding of LFUS-induced liposomal drug release, which is essential for safe and effective implementation of this technique. The time-dependent release patterns are determined by the liposome disintegration patterns and by two key parameters: (a) the average permeability of the membrane to the drug and (b) the ratio between the volume of the entire dispersion and the initial volume of all the liposomes in the dispersion. The present model implies that LFUS irradiation triggers two liposomal drug-release mechanisms: the predominant one is diffusion through the LFUS-compromised liposome membrane, and the less significant one is liposome disintegration.