Mathematical modeling of the heterogeneous distributions of nanomedicines in solid tumors

Abstract

The distribution of nanomedicines inside solid tumors is often restricted to perivascular areas, leaving most distal tumor cells out of reach. This partly explains modest patient benefit of many nanomedicines compared to their free-form counterparts. The objective for this study is to develop a mathematical model to quantitatively analyze this phenomenon and the influencing factors to such perivascular distribution and seek for effective strategies to alleviate this. A spatial tumor distribution model was firstly constructed to mimic the geometrical structure of tumor vessels and the surrounding tumor cells. This tumor model was further integrated with a systemic pharmacokinetics model for nanoparticles. A variety of factors on the tumor spatial distributions of nanomedicines were considered in the model. With the model, we quantified the effect of these influencing factors on tumor delivery efficacy (ID %), the magnitude of heterogeneous distribution (H index), and the effect of enhanced permeability and retention (EPR). In particularly, we compared the spatial distributions of the nanoparticles and the free payloads insides tumors. The model predicted high degrees of distributional heterogeneity for both nanoparticles and free payloads. The degree of heterogeneity and the influencing factors for free payloads were markedly different from those for nanoparticles. We found that nanoparticle diffusion coefficient was the most effective factor in reducing the nanoparticle H index but exerted moderate influence on the free payloads H index. The most effective factor in reducing the H index of free payload was payload diffusion coefficient. The factors that improved free payload distribution were closely associated with higher drug efficacy. In contrast, the factors that improved nanoparticle spatial distributions did not always confer improved anti-tumor efficacy of the delivered drug. These findings highlight the importance of assessing the heterogeneous free payload distribution in tumors for the development of effective nanomedicines.

Keywords: Heterogeneous distribution; Mathematical modeling; Nanoparticles; Solid tumors.