Propagation of damage in brain tissue: coupling the mechanics of oedema and oxygen delivery.

Brain tissue swelling, or oedema, is a dangerous consequence of traumatic brain injury and stroke. In particular, a locally swollen region can cause the injury to propagate further through the brain: swelling causes mechanical compression of the vasculature in the surrounding tissue and so can cut off that tissue's oxygen supply. We use a triphasic mathematical model to investigate this propagation, and couple tissue mechanics with oxygen delivery. Starting from a fully coupled, finite elasticity, model, we show that simplifications can be made that allow us to express the volume of the propagating region of damage analytically in terms of key parameters. Our results show that performing a craniectomy, to alleviate pressure in the brain and allow the tissue to swell outwards, reduces the propagation of damage; this finding agrees with experimental observations.