Thermosensitive Liposome-Mediated Drug Delivery in Chemotherapy: Mathematical Modelling for Spatio-temporal Drug Distribution and Model-Based Optimisation

Abstract

Thermosensitive liposome-mediated drug delivery has shown promising results in terms of improved therapeutic efficacy and reduced side effects compared to conventional chemotherapeutics. In order to facilitate our understanding of the transport mechanisms and their complex interplays in the drug delivery process, computational models have been developed to simulate the multiple steps involved in liposomal drug delivery to solid tumours. In this study we employ a multicompartmental model for drug-loaded thermosensitive liposomes, with an aim to identify the key transport parameters in determining therapeutic dosing and outcomes. The computational model allows us to not only examine the temporal and spatial variations of drug concentrations in the different compartments by utilising the tumour cord concept, but also assess the therapeutic efficacy and toxicity. In addition, the influences of key factors on systemic plasma concentration and intracellular concentration of the active drug are investigated; these include different chemotherapy drugs, release rate constants and heating duration. Our results show complex relationships between these factors and the predicted therapeutic outcome, making it difficult to identify the "best" parameter set. To overcome this challenge, a model-based optimisation method is proposed in an attempt to find a set of release rate constants and heating duration that can maximise intracellular drug concentration while minimising systemic drug concentration. Optimisation results reveal that under the operating conditions and ranges examined, the best outcome would be achieved with a low drug release rate at physiological temperature, combined with a moderate to high release rate at mild hyperthermia and 1 h heating after injection.

Keywords: drug delivery; mathematical model; multi-compartmental model; optimisation; thermosensitive liposome.

Figure 1

Schematic diagram of multiple compartments used in our computational model: Two compartments of “systemic plasma” and “tissues” for systemic effects of drug and the tumour compartment comprising of “tumour plasma”, “tumour extravascular extracellular space (EES)” and “tumour cells”. TSLs: Thermo-sensitive liposomes.

Figure 2

Spatio–temporal distributions of TSL and topotecan (TOP) concentrations in different compartments. (a) TSL concentrations in the systemic and tumour plasma compartments, (b) released TOP concentration in the systemic plasma, tumour plasma and extracellular space, (c) spatial profiles of TOP intracellular concentrations at different time points and (d) temporal profiles of TOP intracellular concentrations at different radial positions.

Figure 3

Simulation results for two different drugs, DOX and TOP. (a) Free drug concentrations in systemic plasma, (b) free drug concentrations in tumour plasma, (c) temporal intracellular drug concentrations in the intracellular space at r = 0 µm over the course of treatment and (d) spatial intracellular drug concentrations at t = 0.55 h.

Figure 4

Drug concentration averaged over the course of the treatment with different combinations of release rate constants kr₃₇ and kr₄₂ (a) in the systemic plasma and (b) in intracellular space.

Figure 5

Temporal concentrations of drug with different hyperthermia schedules. (a) Free drug concentration in systemic plasma, (b) drug concentration in intracellular space at r = 0 µm, (c) average and peak drug concentration in systemic plasma and (d) average and peak topotecan concentration in intracellular space at r = 0 µm.