The Effective Dispersion of Nanovectors Within the Tumor Microvasculature

The effective longitudinal diffusion of nanovectors along non-permeable and permeable capillaries has been studied considering the contribution of molecular and convective diffusion based on the Taylor's theory of shear dispersion. The problem is of importance in the transport of nanovectors used for the intravascular delivery of drugs and contrast agents. It has been shown that for a given capillary size and hemodynamic conditions a critical radius $a_{\rm cr}$ exists for which the effective longitudinal diffusion along the capillary has a minimum: Nanovectors with $aa_{\rm cr}$ diffuse mainly by convection and the effective diffusion coefficient grows with $a$ . In permeable conduits, the effective diffusion reduces significantly compared to normal non-leaky vessels and it has been derived that $a_{\rm cr}$ grows almost linearly with the hydraulic permeability $L_{\rm p}$ of blood vessels. It has been shown that the blood conduits with the largest effective longitudinal diffusivity could be preferentially targeted by the circulating vectors. Based on these findings, the following strategies are proposed to increase the number of nanovectors targeting the tumor vessels: (i) The use of nanovectors with a critical radius for normal vessels, (ii) the injecting of bolus of nanovectors with different radii, and (iii) the normalization of the tumor vasculature. Finally, it has been emphasized that the size of the vector should be selected depending on the body district where the tumoral mass is developing and on the type, malignancy, and state of the tumor.