High amplitude elastic jump propagation through blood vessel junctions #

Tamsin A Spelman, Ifeanyi S Onah, David MacTaggart, Peter S Stewart

15:10 Monday in 4Q56.

Part of the Mathematical and computational ophthalmology session.

Abstract #

Traumatic brain injury can cause large amplitude waves to form in retinal blood vessels. The waves steepen to form an elastic jump, and then propagate through blood vessel junctions deeper into the retinal blood vessel network. This is dangerous and can cause blood vessel rupture, in the form of retinal haemorrhage. Small amplitude perturbations passing through junctions are well explained with linear theory. Here, we extend this to examine large amplitude perturbations moving through a single junction with one parent and two daughter vessels. We use a finite volume scheme in each vessel coupled using junction boundary conditions, and validate this method against a novel Riemann solver. The incoming pressure wave splits into three at the junction, transmitting a nonlinear wave along each daughter vessel and a reflective wave back up the parent vessel. For relatively low driving the system generates a reflected rarefaction wave in the parent and elastic jumps in each of the daughters. The flow speed of the reflected rarefaction wave increases with the driving pressure and the reflected amplitude increases up to a local maxima before decreasing. However, above a threshold driving we see a change in behaviour with the reflected rarefaction resonating with a stationary wave at the junction. These new resonant states exhibit two additional zero speed shocks, one each side while one edge of the rarefaction remains pinned to the junction. This behaviour is robust to changes in base flow speed and direction and has interesting consequences for shock wave propagation through a network.