Project Description
A variety of drugs are used to treat brain diseases such as Alzheimer's, Parkinson's Disease and brain cancers. However, due to the blood-brain barrier, drug delivery to the brain is a challenging problem as the drug may not reach its intended site of action or have other severe side effects. Pharmaceutical scientists are exploring the use of liposomes that enclose the drug and prevent it from early degradation. The liposomes are designed to release their cargo upon exposure to transcranial focused ultrasound. Mathematical modeling has long been used as a tool to understand the transport mechanisms in the brain vasculature and tissue. Together with collaborators in New Zealand and the US we have proposed a mathematical model for a single capillary in which blood carries liposomes that are in turn exposed to a time-dependent ultrasound signal. In another work we have studied mathematically capillary networks with increasingly complex topologies (jointly with SURF-supported students). We now plan to combine these hitherto unconnected strands of work. We will to focus on the delivery of L-Dopa, the standard drug used to treat the symptoms of Parkinson's Disease.
Tasks and Responsibilites
The first task is to create a model of 100-200 brain blood vessels. This includes the topology of the network and the lengths and radii of the vessels. The topology changes from tree-like near the arteries to network-like capillary beds and back to tree-like veins. Parameters such as the radii distribution will be taken from the literature. The next task is to find the flow rates through the network given the pressure drop across it. This is done using Darcy's Law (which relates the flow through a single capillary to the pressure difference) and Kirchhoff's Law (which states that the sum of the signed flows at any node needs to be zero). The third task is to implement the ordinary differential equation model from our 2016 paper to the network. It is particularly important to observe conservation laws at bifurcation and confluence points in the network. The mathematical model will be used to predict the drug delivery outcome as that depends on the timing and intensity of the ultrasound signal. Since the ultrasound heats the sensitive brain tissue, it must be delivered with caution. The input from our neuroscience collaborators in New Zealand will be critical.
Desired Qualifications
None Listed.