The Mathematics of Drug Delivery. In: Eladdadi A, Kim P, Mallet D, editors. Mathematical Models of Tumor-Immune System Dynamics. New York: Springer; 2014. pp. 109-23. [DOI: 10.1007/978-1-4939-1793-8_5]

Signaled drug delivery and transport across the blood-brain barrier

We use a mathematical model to describe the delivery of a drug to a specific region of the brain. The drug is carried by liposomes that can release their cargo by application of focused ultrasound (US). Thereupon, the drug is absorbed through the endothelial cells that line the brain capillaries and form the physiologically important blood-brain barrier (BBB). We present a compartmental model of a capillary that is able to capture the complex binding and transport processes the drug undergoes in the blood plasma and at the BBB. We apply this model to the delivery of levodopa (L-dopa, used to treat Parkinson's disease) and doxorubicin (an anticancer agent). The goal is to optimize the delivery of drug while at the same time minimizing possible side effects of the US.