Available space and extracellular transport of macromolecules: effects of pore size and connectedness

Molecular exclusion in tumor tissues is one of the limiting factors for drug delivery to tumor cells. It can be quantified by the available volume fraction of solutes (K(AV)). We found in a previous study that K(AV) of dextran in tumor tissues decreased sharply when the molecular weight (MW) of dextran was increased from 40,000 to 70,000. Outside this range, K(AV) was less sensitive to the MW of dextran. To understand the mechanisms of the MW dependence of K(AV), we investigated K(AV) in tissue phantoms composed of tumor cells in 1% agarose gels, and performed numerical simulations of the available volume fraction in pore networks. We found that the MW dependence of K(AV) in tissue phantoms was similar to that in tumor tissues when the volume fraction of cells in the former was approximately 30%. Our numerical simulations revealed that the sharp decrease in K(AV) required two necessary conditions: (i) the existence of at least two populations of pores and (ii) the lack of connectedness of available pores in the interstitial space. Furthermore, results in this study suggest that it is important to consider not only the local structures of pores but also their connectedness in analyses of molecular transport in tissues.