The effectiveness of anticancer treatments is often hampered by the serious side effects owing to toxicity of anticancer drugs and their undesirable uptake by healthy cells in vivo. Thermosensitive liposome-mediated drug delivery has been developed as part of research efforts aimed at improving therapeutic efficacy while reducing the associated side effect. Since multiple steps are involved in the transport of drug-loaded liposomes, drug release, and its uptake, mathematical models become an indispensible tool to analyse the transport processes and predict the outcome of anticancer treatment. In this study, a computational model is developed which incorporates the key physical and biochemical processes involved in drug delivery and cellular uptake. The model has been applied to idealized tumour geometry, and comparisons are made between continuous infusion of doxorubicin and thermosensitive liposome-mediated delivery. Results show that thermosensitive liposome-mediated delivery performs better in reducing drug concentration in normal tissues, which may help lower the risk of associated side effects. Compared with direct infusion over a 2-hour period, thermosensitive liposome delivery leads to a much higher peak intracellular concentration of doxorubicin, which may increase cell killing in tumour thereby enhancing the therapeutic effect of the drug.

Results obtained in this study can be used to guide the design and optimisation of CED treatment regimens.

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Although convection-enhanced delivery (CED) can successfully facilitate a bypass of the blood brain barrier, its treatment efficacy remains highly limited in clinic. This can be partially attributed to the brain anisotropic characteristics that lead to the difficulties in controlling the drug spatial distribution. Here, the responses of six different drugs to the tissue anisotropy are examined through a parametric study performed using a multiphysics model, which considers interstitial fluid flow, tissue deformation and interlinked drug transport processes in CED. The delivery outcomes are evaluated in terms of the penetration depth and delivery volume for effective therapy. Simulation results demonstrate that the effective penetration depth in a given direction can be improved with the increase of the corresponding component of anisotropic characteristics. The anisotropic tissue permeability could only reshape the drug distribution in space but has limited contribution to the total effective delivery volume. On the other hand, drugs respond in different ways to the anisotropic diffusivity. The large delivery volumes of fluorouracil, carmustine, cisplatin and doxorubicin could be achieved in relatively isotropic tissue, while paclitaxel and methotrexate are able to cover enlarged regions into anisotropic tissues. Results obtained from this study serve as a guide for the design of CED treatments.

Drug delivery to solid tumour involves multiple physiological, biochemical and biophysical processes taking place across a wide range of length and time scales. The therapeutic efficacy of anticancer drugs is influenced by the complex interplays among the intrinsic properties of tumours, biophysical aspects of drug transport and cellular uptake. Mathematical and computational modelling allows for a well-controlled study on the individual and combined effects of a wide range of parameters on drug transport and therapeutic efficacy, which would not be possible or economically viable through experimental means. A wide spectrum of mathematical models has been developed for the simulation of drug transport and delivery in solid tumours, including PK/PD-based compartmental models, microscopic and macroscopic transport models, and molecular dynamics drug loading and release models. These models have been used as a tool to identify the limiting factors and for optimal design of efficient drug delivery systems. This article gives an overview of the currently available computational models for drug transport in solid tumours, together with their applications to novel drug delivery systems, such as nanoparticle-mediated drug delivery and convection-enhanced delivery.

Drug transport and its uptake by tumour cells are strongly dependent on tumour properties, which vary in different types of solid tumours. By simulating the key physical and biochemical processes, a numerical study has been carried out to investigate the transport of anti-cancer drugs in 3-D tumour models of different sizes. The therapeutic efficacy for each tumour is evaluated by using a pharmacodynamics model based on the predicted intracellular drug concentration. Simulation results demonstrate that interstitial fluid pressure and interstitial fluid loss vary non-linearly with tumour size. Transvascular drug exchange, driven by the concentration gradient of unbound drug between blood and interstitial fluid, is more efficient in small tumours, owing to the low spatial-mean interstitial fluid pressure and dense microvasculature. However, this has a detrimental effect on therapeutic efficacy over longer periods as a result of enhanced reverse diffusion of drug to the blood circulation after the cessation of drug infusion, causing more rapid loss of drug in small tumours.

9Most of the computational models of drug transport in vascular tumours assume a uniform distribution of 10 blood vessels through which anti-cancer drugs are delivered. However, it is well known that solid 11 tumours are characterised by dilated microvasculature with non-uniform diameters and irregular 12 branching patterns. In this study, the effect of heterogeneous vasculature on drug transport and uptake is 13 investigated by means of mathematical modelling of the key physical and biochemical processes in drug 14delivery. An anatomically realistic tumour model accounting for heterogeneous distribution of blood 15 vessels is reconstructed based on magnetic resonance images of a liver tumour.