Diffusivity and distribution of vinblastine in three-dimensional tumour tissue: Experimental and mathematical modelling

The distribution of chemotherapeutics in solid tumours is poorly understood and the contribution it makes to treatment failure is unknown. Novel approaches are required to understand how the three-dimensional organisation of cancer cells in solid tumours affects drug availability. Since convective drug transport is limited by increased interstitial pressure in poorly vascularised cancers, the aim of this study was to measure the diffusive hindrance exerted by solid tumour tissue. Multicell layer tumour models comprising DLD1 colon cancer cells were characterised and fluxes were determined for [3H]-vinblastine and [14C]-sucrose. The mathematical models provided the diffusion coefficients for both compounds and predicted higher exposure of cells in the vicinity of vessels. The diffusion of vinblastine was three times slower than that of sucrose. Although slow diffusion delays vinblastine penetration into the avascular regions of tumours, the proliferating cells are generally in the marginal area of tumours. The mathematical model that we have developed enabled accurate quantification of drug pharmacokinetic behaviour, in particular, the diffusivity of vinblastine within solid tissue. This mathematical model may be adapted readily to incorporate the influence of factors mediating pharmacokinetic drug resistance.