Mathematical modelling of liposomal drug release to tumour.

The primary aim of liposomal drug delivery is to wisely modulate the drug delivery system in order to target diseased tissues. Temperature-sensitive liposomes function as a prospective weapon to combat toxic side effects corresponding to direct infusion of anticancer drugs. The main objective of the present study is to model liposomal drug release, subsequent drug transport in solid tumour along with integrated actions of tumour cell surface and endosomal events. Generalized mathematical model for liposomal drug delivery is proposed in which vital physical phenomena, such as kinetics of liposome-encapsulated drug, free drug release from liposomes, transport of both liposomal drug and free drug into the tumour compartment, plasma clearance, protein-drug interactions, drug-tumour cell receptor interactions, internalization of drug through endocytosis along with corresponding endosomal events. The model is expressed through a system of coupled partial differential equations along with appropriate set of initial, interface and boundary conditions which is solved numerically. Simulated results are compared with respective existing experimental data to demonstrate the potency and reliability of the proposed model. Graphical representations of time variant concentration profiles are illustrated to understand the underlying phenomena in details. Moreover, the model speaks for the sensitivity of important drug kinetic parameters, such as advection coefficients, drug release coefficient, plasma clearance rate and internalization parameters through graphical portrayals. The proposed model and the simulated results act as a tool in designing a more effective drug delivery system for cancerous tumours.