A Mathematical Model of the Enhanced Permeability and Retention Effect for Liposome Transport in Solid Tumors

Shawn Stapleton,David A Jaffray,Michael Dunne,Michael Milosevic,Jinzi Zheng,Christine Allen,Ivan Yeung,Chih-Pin Chuu

doi:10.1371/journal.pone.0081157

Abstract

The discovery of the enhanced permeability and retention (EPR) effect has resulted in the development of nanomedicines, including liposome-based formulations of drugs, as cancer therapies. The use of liposomes has resulted in substantial increases in accumulation of drugs in solid tumors; yet, significant improvements in therapeutic efficacy have yet to be achieved. Imaging of the tumor accumulation of liposomes has revealed that this poor or variable performance is in part due to heterogeneous inter-subject and intra-tumoral liposome accumulation, which occurs as a result of an abnormal transport microenvironment. A mathematical model that relates liposome accumulation to the underlying transport properties in solid tumors could provide insight into inter and intra-tumoral variations in the EPR effect. In this paper, we present a theoretical framework to describe liposome transport in solid tumors. The mathematical model is based on biophysical transport equations that describe pressure driven fluid flow across blood vessels and through the tumor interstitium. The model was validated by direct comparison with computed tomography measurements of tumor accumulation of liposomes in three preclinical tumor models. The mathematical model was fit to liposome accumulation curves producing predictions of transport parameters that reflect the tumor microenvironment. Notably, all fits had a high coefficient of determination and predictions of interstitial fluid pressure agreed with previously published independent measurements made in the same tumor type. Furthermore, it was demonstrated that the model attributed inter-subject heterogeneity in liposome accumulation to variations in peak interstitial fluid pressure. These findings highlight the relationship between transvascular and interstitial flow dynamics and variations in the EPR effect. In conclusion, we have presented a theoretical framework that predicts inter-subject and intra-tumoral variations in the EPR effect based on fundamental properties of the tumor microenvironment and forms the basis for transport modeling of liposome drug delivery.

Highlights

The discovery of the enhanced permeability and retention (EPR) effect in solid tumors has led to the development of a wide range of nanomedicines, including liposomes, for cancer therapy [1]
The Intra-Tumor Transport Model’ (ITTM) was based on convective transport due to the significant molecular weight of the agent (,100 MDa) and several reports demonstrating that interstitial and transvascular diffusion is negligible compared to convection for macromolecules and liposomes [16,17,24,30,31]
The first term on the right of equation (1) represents the transvascular convective flux where LpS V is the capillary filtration coefficient (CFC), Lp is the vascular permeability to fluid flow, ðpv{piÞ is the difference between the microvascular pressure (MVP) and interstitial fluid pressure (IFP), sis the filtration reflection coefficient, and Cp is the plasma concentration of the nanoparticle

Summary

Introduction

The discovery of the enhanced permeability and retention (EPR) effect in solid tumors has led to the development of a wide range of nanomedicines, including liposomes, for cancer therapy [1]. The EPR effect describes the preferential accumulation of nanoparticles at tumor sites due to leaky vasculature (i.e. enhanced permeation) and impaired lymphatic drainage (i.e. enhanced retention), in comparison to normal tissue. Nano-sized delivery systems have been shown to result in significant increases in tumor accumulation of drugs in comparison to that achieved following administration of free drug [2]. Major limitations of liposome-based drug delivery are: (1) variability in the EPR effect and total tumor accumulation [4]; (2) limited tumor penetration [10]; and (3) slow or limited release of hydrophilic/amphiphilic drugs [11,12]. While it is clear that the poor performance has been linked to a number of factors, one of the most significant is the inability to achieve consistent inter-subject and intra-tumoral accumulation of liposomes [4,10,13,14]

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