Elastic jumps on networks: Quantifying patterns of retinal haemorrhage

Non-accidental head injury in infants has far-reaching medical and legal implications. The symptoms typically involve a `triad' including subdural haemorrhage (bleeding in the region between the skull and the brain), retinal haemorrhage (bleeding of the retina at the back of the eye) and brain swelling. However legal investigation is difficult as the cause and effect of the injury are not always easy to distinguish. This project will use mathematical modelling to elucidate the origin(s) of one of these symptoms, retinal haemorrhage, constructing a novel new mechanical framework capable of predicting the onset and severity of retinal bleeding following a traumatic brain injury, in an attempt to correlate the pattern of bleeding to the injury sustained and thus aid clinical decision making.

Such a traumatic brain injury will create a steep pressure wave (like a tsunami) which will propagate through the blood vessels in the retina, causing some of them to burst and hence bleeding (haemorrhage). This project will examine the mathematical properties of such a pressure wave as it spreads across blood vessel junctions and hence across an entire networks of arteries and veins. This project will be to examine and quantify how the final pattern of blood vessel bursting (ie bleeding) correlates to the type of injury sustained. Such a correlation will be of enormous value to doctors and legal practitioners making difficult decisions about the origin of injuries in infants.

Severe head trauma in infants is an unpleasant but crucially important subject. Retinal haemorrhage (bleeding of the retina at the back of the eye) is one of the three clinically used indicators of such trauma, but the cause and effect of injury can be difficult to decipher.

The primary impact of this research will be to deliver a mathematical framework capable of rational prediction of retinal haemorrhage, correlating the pattern of vessel rupture (bleeding) to the severity and magnitude of trauma sustained. This framework will impact healthcare professionals, developed through extensive collaboration with clinical partners and disseminated through publications in top international medical journals and talks at leading clinical conferences, including events run by the International Brain Mechanics Trauma Laboratory. The research will also impact healthcare professionals through networking activities, such as a two day `Dialogue with Clinicians' event to be held toward the end of the grant period, to improve understanding and dialogue, present our current results and to identify relevant clinical targets and next steps for the research.

The results of this research will have significant implications for improving quality of life for sufferers of traumatic injuries, aiding clinicians in devising improved treatment protocols to improve patient outcome and prolong life. It will also provide guidance in clinical decision making in cases of suspected non-accidental head injury in infants.

The proposed project will result in significant new scientific advances through development of a novel methodology for predicting the propagation of steep pressure waves through a network, which will benefit a wide range of academic beneficiaries, including biologists, clinical scientists and modellers interested in blood flow through the circulatory system or traumatic brain injury. The mathematical framework will also benefit engineers and mathematicians interested in the propagation and interaction of shock waves. To ensure that these groups can benefit from the outcomes of this research, we will disseminate our methodology and results in the top scientific journals and present at leading national and international conferences.

This project will also develop new techniques including a novel new suite of sophisticated numerical methods for solving networks of coupled PDEs with explicit shock capture. This research will provide new (lower-order) network models derived using analytical approximations. Novel aspects of the computational work will be disseminated in specialist journal articles (J. Computat. Phys.) and selected data and numerical methods from the project will be made publicly available through GU's Research Data Management service.

This research project will provide training of a PDRA, offering the opportunity to be involved in a multi-disciplinary project, engage in high-impact research in a stimulating environment in collaboration with clinicians and with the new EPSRC centre SofTMech.

Finally, the work in this project will play a role in motivating the next generation of mathematicians and scientists through dissemination at public engagement events, including outreach talks in local secondary schools demonstrating the usefulness of mathematics in solving real world problems.