Model for Drug Uptake by Brain Tumors: Effects of Osmotic Treatment and of Diffusion in Brain

Abstract

A mathematical model describing drug uptake into brain tumors, directly from blood and indirectly from neighboring tissue, is presented. The model quantitatively describes uptake into tumor, brain surrounding tumor (BST), and normal brain and uptake following reversible osmotic blood–brain barrier (BBB) and blood–tumor barrier disruption. It employs published data on the time course for reclosure of the BBB following osmotic treatment and on the brain and tumor uptake of [¹⁴C]α-aminoisobutyric acid by Walker 256 carcinomas and C6 gliomas implanted into the rat brain. Constant infusion and bolus injection infusion schedules are considered. In untreated brain, the BST acts as a sink, reducing the integrated exposure of the adjacent tumor to the drug, whereas following osmotic treatment, tumor exposure to drug is enhanced, not only by increased delivery from blood but also by diffusion (and bulk flow) from neighboring brain. The model provides a quantitative framework for examining the efficacy of osmotic treatment to enhance chemotherapy of brain tumors.