The blood-brain barrier (BBB) is a strong barrier against the entrance of drugs, which has made brain cancer treatment a major challenge. We have previously shown that targeting transferrin receptors using aptamers increased brain drug delivery. To get a better understanding of this phenomenon, in the present article, a mathematical model based on the finite element method was developed accounting for the fluid flow and mass transport of the aptamer molecule inside an 8 µm capillary vessel across a 14 µm blood-brain barrier domain. The fluid flow and mass transport equations were coupled to calculate the blood velocity and aptamer concentration profiles across the BBB. It was identified that the thickness of the astrocyte and endothelial cell layers are key parameters affecting the concentration of the aptamer delivered to the last neuron dendrites in the BBB. The predicted efficacy of the drug delivery (Capt/Cin) of 10.9% to 13.8% was calculated at a porosity of 0.5 to 0.9, respectively, at a blood velocity of 0.38 mm/s, which was independent of the inlet concentration of the aptamer. This low efficacy was attributed to the mass transfer resistance across endothelial cells, astrocyte and pericyte layers, which decreased the concentration by 6.7%. It was also identified that the main mechanism of drug delivery is switched from convective mass transport in the capillary layer (with Peclet number > 50) to mixed convection mass transport (1 < Peclet number < 5) in the porous layers and to diffusion only once aptamer reached the brain parenchyma (Peclet number < 1).
Keywords: Aptamer concentration; Blood-brain barrier; Diffusion; Mathematical modelling.
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