Modelling Perfusion and Temperature Effects of Ischaemic Stroke using Expanded Discrete Cerebral Vasculature in a Vascular-Porous Model*

Modelling of the effects of ischaemic stroke requires vasculature of a resolution that is unobtainable from conventional cerebral-vasculature imaging techniques. We have developed a technique to generate additional vasculature to complement the obtainable vasculature and together form a hybrid 1D vasculature. This is then combined with our existing Vascular-Porous (VaPor) model to fully simulate the cerebral geometry, crucially including the ischaemic region. In the VaPor model, the hybrid 1D vasculature is embedded into a 3D porous tissue. The additional 1D vasculature is created using an algorithm that has been developed to procedurally generate new nodes based on the main arterial territories and tissue type. A variety of severities of ischaemic stroke can be simulated by obstructing any given vessel segment in the arterial tree. The resulting occlusion geometry, perfusion, and thermal effects are then calculated by solving mass, momentum, and energy equations. Our results show discrete vessels are important in modelling cerebral temperature and perfusion, and particularly the effects of stroke. Visual agreement can be seen between 3D perfusion maps obtained from VaPor and those from in-vivo cerebral imaging of stroke, including the presence of potentially salvageable penumbral tissue. The presence of additional vasculature in our model leads to greater homogeneity in the resulting temperature profiles. Using our model, a temperature rise of the order of 0.5 °C can be observed in the affected region following ischaemic stroke. Further, our model shows that direct brain cooling via the scalp may be more effective at reducing cerebral temperatures than previously thought.