Pressure wave transmission across the lamina cribrosa #

Peter Stewart, Ifeanyi Sunday Onah, David MacTaggart

14:50 Monday in 4Q56.

Part of the Mathematical and computational ophthalmology session.

Abstract #

Retinal haemorrhage (RH) is the abnormal bleeding of the blood vessels in the retinal circulation of the eye, often linked with traumatic brain injury. We test a clinical hypothesis for the mechanism of RH, where a rise in intracranial pressure in the brain (e.g. following an injury) leads to an increase in cerebrospinal fluid pressure around the optic nerve; this increase is then transmitted into the central retinal vessels as they cross through the nerve sheath, triggering an increase in venous pressure in the retinal circulation which can lead to bursting of one or more retinal veins. Here we consider transmission of the pressure increase along the retinal veins (against the flow), with particular focus on the influence of the abrupt change in environment surrounding the blood vessel as it crosses the lamina cribrosa into the eye. To this end, we consider a one-dimensional model of flow and nonlinear wave propagation along a deformable blood vessel with an abrupt discontinuity in elastic stiffness, formulating a nonlinear Riemann problem local to the discontinuity. As expected, the generic response is for the discontinuous initial condition to break up into left- and right-moving waves separated by a stationary wave across the point of discontinuity. However, we show that for a range of parameters a rarefaction wave can become transcritical, resonating with the stationary wave and generating an additional shock wave which is either zero speed or propagating away from the transcritical rarefaction. These additional shock waves introduce a number of interesting new possibilities as they propagate into the retinal circulation, including resonance as the waves spread through the network and are partially reflected at junctions.