A Mathematical Relationship for Hydromorphone Loading into Liposomes with Trans-Membrane Ammonium Sulfate Gradients

We have studied the loading of the opioid hydromorphone into liposomes using ammonium sulfate gradients. Unlike other drugs loaded with this technique, hydromorphone is freely soluble as the sulfate salt, and, consequently, does not precipitate in the liposomes after loading. We have derived a mathematical relationship that can predict the extent of loading based on the ammonium ion content of the liposomes and the amount of drug added for loading. We have adapted and used the Berthelot indophenol assay to measure the amount of ammonium ions in the liposomes. Plots of the inverse of the fraction of hydromorphone loaded versus the amount of hydromorphone added are linear, and the slope should be the inverse of the amount of ammonium ions present in the liposomes. The inverse of the slopes obtained closely correspond to the amount of ammonium ions in the liposomes measured with the Berthelot indophenol assay. We also show that loading can be less than optimal under conditions where osmotically driven loss of ammonium ions or leakage of drug after loading may occur.