Abstract #3296: A mathematical tool to predict the efficacy of nanoparticles for cancer treatment and imaging

The purpose of the study is the development of a mathematical model to predict over time the distribution of nanoparticles within the tumor vasculature and the concentration of drug molecules released by the nanoparticles towards the tumor mass. Within the framework of Isogeometric Analysis, the proposed mathematical model analyzes (i) the transport of nanoparticles in the highly permeable and tortuous cancerous microvasculature; (ii) the firm specific and non-specific adhesion of nanoparticles to the vessel walls and (iii) the long term release of drug molecules from the adhered nanoparticles towards the cancerous microenvironment. The transport of nanoparticles is analyzed considering a \#8216;single phase flow\#8217; governed by an advection-diffusion equation, where nanoparticles are treated as passive scalars transported in a Non-Newtonian fluid. At the vessel walls, the Starling law is imposed to account for the vessel permeability and a first order kinetic reaction law is used to predict the rate of nanoparticles adhesion. The adhesive boundary conditions are formulated as a function of the particle characteristic features (size, shape; surface ligand density; surface physico-chemical properties) and of the vascular physiology (wall shear stress; surface density and type of receptors; vascular architecture), following the recent models developed by Decuzzi and Ferrari (2006,2008). The concentration of adhered nanoparticles along the vascular surface is also estimated. The vascular geometry can be directly derived from CT scans of the patient or Intravital Microscopy images of the animal under analysis. The extravascular diffusion of drug molecules released from the adhered nanoparticles is analyzed employing an advection-diffusion equation accounting for the variation of the diffusion coefficient within the tissue and for the contribution of the vessel permeability. The proposed mathematical model is anticipated to constitute an ideal tool for predicting the behavior of nanoparticles and select their optimal formulation (size, shape and surface properties) before injection and, more importantly, as a function of the patient-specific vascular features. Citation Information: In: Proc Am Assoc Cancer Res; 2009 Apr 18-22; Denver, CO. Philadelphia (PA): AACR; 2009. Abstract nr 3296.