Macromolecule Transport in Tumours: Mathematical Modelling and Experimental Studies

Abstract

The delivery of immunoreactive macromolecules to tumour cells in solid, heterogeneously perfused tumours is a major problem in the effectiveness of immunotherapy. To help optimize the new experimental treatment method, a published mathematical model of macromolecule transport (Baxter & Jain 1989,1990,199la) was appraised and verified experimentally. Computational and analytical tools were developed to predict the interstitial plasma fluid pressure and velocity distributions in well perfused spherical tumours. Their published analytical solutions of the formulation were found to have some errors and were corrected in this work. To check the validity of the formulation, a series of animal experiments was performed to quantify the total vascular volume, and plasma fluid extravasation rate in SKOV3ipl human ovarian tumour xenografts in nude mice. The results compared well with the theoretically predicted total plasma fluid extravasation rate. Computer codes were also developed to predict the spatial and temporal distributions of intact IgG and its F(ab')₂ and Fab/Fab' fragments in well perfused spherical tumours using the formulation proposed by Baxter & Jain (1989,1990,1991a). The cases of non-binding and binding macromolecules were treated separately. The codes for both the interstitial pressure and macromolecule distributions were written to include a radially variable vessel surface area for transcapillary exchange per unit volume of tumour tissue (SN). The sensitivity of the overall tumour perfusion to variation of (a) the macromolecule m.w., binding affinity, and metabolism, (b) SN, tumour radius, and (c) microvascular permeability were investigated. Comparison of the theoretical predictions with available experimental data leads to the realization of a number of shortcomings in the previously proposed formulations. Finally, a computational method for deriving the effective spherically symmetric spatial distributions for the vascular volume density, and SN from tumour serial sections was developed. This bridges the gap between the actual topology of vascular distributions in tumours and the format of current formulations.