Accurately predicting brain tissue perfusion and infarct volume after an acute ischaemic stroke requires the two-way coupling of perfusion models on multiple scales. We present a method for such two-way coupling of a one-dimensional arterial blood flow model and a three-dimensional tissue perfusion model. The two-way coupling occurs through the pial surface, where the pressure drop between the models is captured using a coupling resistance. The two-way coupled model is used to simulate arterial blood flow and tissue perfusion during an acute ischaemic stroke. Infarct volume is estimated by setting a threshold on the perfusion change. By two-way coupling these two models, the effect of retrograde flow and its effect on tissue perfusion and infarct volume can be captured.