A Unified Mathematical Model for Nano-Liposomal Drug Delivery to Solid Tumors

Nanoparticles, such as liposomes, allow more targeted drug delivery for improved efficacy and/or reduced toxicity in both passive (e.g., Doxil) or active [e.g., thermo-sensitive liposomes (TSL)] release forms compared with unencapsulated drugs (i.e., conventional chemotherapy). Optimization and evaluation of these different drug delivery systems are experimentally challenging because of varying tissue parameters as well as limited avaiability of experimental data. Here, we present a novel unified mathematical model that can simulate various liposomal drug delivery systems and unencapsulated drugs with a single set of equations. We use this model to evaluate the chemotherapy performance of free Doxorubicin (as drug), as well as various liposomal drug delivery systems: 1) passive liposomes (Doxil) and 2) active-triggered TSL with either intravascular (TSLi) or extravascular (TSLe)-triggered release. Furthermore, we implemented a more accurate expression to consider incomplete liposomal drug release. The proposed model matches experimental in vivo results in terms of maximum drug concentration in tumor. The simulations predict better overall performance for all liposomal delivery systems than free Dox. TSLe is shown to be more efficient for less permeable and perfused tumors than other systems. The optimal release rate is lower for TSLe and Doxil than TSLi. The performance of free DOX changes a little for varying tumor characteristics such as perfusion and permeability.