A Mathematical Model of Drug Release from Liposomes by Low Frequency Ultrasound GIORA ENDEN 1 and AVI SCHROEDER 2,3 1 Department of Biomedical Engineering, Ben-Gurion University of the Negev, P.O. Box 653, Beer Sheva 84105, Israel; 2 Department of Chemical Engineering, Ben-Gurion University of the Negev, P.O. Box 653, Beer Sheva 84105, Israel; and 3 The Laboratory of Liposome and Membrane Research, Department of Biochemistry, Hebrew University-Hadassah Medical School, P.O. Box 12272, Jerusalem 91120, Israel (Received 25 May 2009; accepted 19 August 2009; published online 3 September 2009) Abstract—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. Imme- diately 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 mem- brane, and the less significant one is liposome disintegration. Keywords—Low frequency ultrasound, Liposome, Controlled drug release, Mathematical model, Doxorubicin, Cisplatin, MPS, Doxil. ABBREVIATION LFUS Low frequency ultrasound INTRODUCTION Sterically stabilized liposomes <100 nm in diameter have characteristics that make them well suited to serve as a drug delivery system: a prolonged circulation time, 27 a vesicular structure that enables loading of hydrophilic or lipophilic drugs, 2 and an ability to tar- get tumors and inflamed tissue. 1,6 The problem posed by the contradictory requirements for a successful liposomal formulation—stability on the one hand and the capacity to release the drug at a sufficient rate at the target site on the other 2 —has been tackled in var- ious ways. Approaches that have been tried include introducing pH-sensitive 12,21 or light-sensitive 7 con- stituents into the membrane, and triggering drug release using an external physical signal such as hyperthermia 5,19 or low frequency ultrasound (LFUS). 15,24 The rationale for using LFUS to control liposomal drug release is based on two findings, first that such signals enhance the permeability of biological mem- branes for drug and gene delivery, 3,11,14,20,23 and sec- ond that the structure of liposome membranes and many of their physiochemical properties are similar to those of biological membranes. 13 Lin and Thomas showed that LFUS is able to release a loaded dye from sterically stabilized lipo- somes, 15 while Myhr and Moan reported that a syn- ergistic therapeutic effect occurred when LFUS was applied to tumors implanted in mice and treated with liposomal doxorubicin. 18 Recently it has been shown that LFUS irradiation induces liposomal drug release in vitro and that drug release stops upon cessation of irradiation. 24 The extent and profile of drug release have been found to be mostly dependent on the molecular constituents of the lipid bilayer, as well as on irradiation frequency and intensity. 15,24–26 Higuchi 9 performed theoretical investigations of the rate of drug release from solid matrices and dispersed ointment Address correspondence to Giora Enden, Department of Bio- medical Engineering, Ben-Gurion University of the Negev, P.O. Box 653, Beer Sheva 84105, Israel. Electronic mail: genden@bgu.ac.il The work was performed at the Department of Biomedical Engineering, Ben-Gurion University of the Negev, Beer-Sheva, Israel. Annals of Biomedical Engineering, Vol. 37, No. 12, December 2009 (Ó 2009) pp. 2640–2645 DOI: 10.1007/s10439-009-9785-z 0090-6964/09/1200-2640/0 Ó 2009 Biomedical Engineering Society 2640