Estimating Tumor Vascular Permeability of Nanoparticles Using an Accessible Diffusive Flux Model

Understanding the complex interplay of factors affecting nanoparticle accumulation in solid tumors is a challenge that must be surmounted to develop effective cancer nanomedicine. Among other unique microenvironment properties, tumor vascular permeability is an important feature of leaky tumor vessels which enables nanoparticles to extravasate. However, permeability has thus far been measured by intravital microscopy on optical window tumors, which has many limitations of its own. Additionally, mathematical models of particle tumor transport are often too complicated to be accessible to most researchers. Here, we present a more simplified and accessible mathematical model based on diffusive flux, which uses particle tumor accumulation and plasma pharmacokinetics to yield effective permeability, P_eff. This model, called diffusive flux modeling (DFM), allows effects from multiple parameters to be decoupled and is also the first demonstration, to the best our knowledge, of extracting P_eff values from bulk biodistribution results (e.g., routine positron emission tomography studies). The DFM equation was used to explain in vivo results of sub-20 nm nanocarriers called three-helix-micelles (3HM), particularly 3HM's selective accumulation in different tumor models. When DFM was applied to multiple published biodistribution data, a semiquantitative comparison of various tumor models, particle size, and active targeting strategies could be made. The analysis clearly pointed out the importance of balancing multiple characteristics of nanoparticles to ensure successful treatment outcome and highlights the usefulness of this simple model for initial particle design, selection, and subsequent optimization.