A mathematical model of doxorubicin penetration through multicellular layers.

Inadequate drug delivery to tumours is now recognised as a key factor that limits the efficacy of anticancer drugs. Extravasation and penetration of therapeutic agents through avascular tissue are critically important processes if sufficient drug is to be delivered to be therapeutic. The purpose of this study is to develop an in silico model that will simulate the transport of the clinically used cytotoxic drug doxorubicin across multicell layers (MCLs) in vitro. Three cell lines were employed: DLD1 (human colon carcinoma), MCF7 (human breast carcinoma) and NCI/ADR-Res (doxorubicin resistant and P-glycoprotein [Pgp] overexpressing ovarian cell line). Cells were cultured on transwell culture inserts to various thicknesses and doxorubicin at various concentrations (100 or 50 microM) was added to the top chamber. The concentration of drug appearing in the bottom chamber was determined as a function of time by HPLC-MS/MS. The rate of drug penetration was inversely proportional to the thickness of the MCL. The rate and extent of doxorubicin penetration was no different in the presence of NCI/ADR-Res cells expressing Pgp compared to MCF7 cells. A mathematical model based upon the premise that the transport of doxorubicin across cell membrane bilayers occurs by a passive "flip-flop" mechanism of the drug between two membrane leaflets was constructed. The mathematical model treats the transwell apparatus as a series of compartments and the MCL is treated as a series of cell layers, separated by small intercellular spaces. This model demonstrates good agreement between predicted and actual drug penetration in vitro and may be applied to the prediction of drug transport in vivo, potentially becoming a useful tool in the study of optimal chemotherapy regimes.