Functional hyperaemia is an important mechanism by which increased neuronal activity is matched by a rapid and regional increase in blood supply. This mechanism is facilitated by a process known as “neurovascular coupling” – the orchestrated communication system involving the cells that comprise the neurovascular unit (neurons, astrocytes and the smooth muscle and endothelial cells lining arterioles). Blood flow regulation and neurovascular coupling are altered in several pathological states including hypertension, diabetes, Alzheimer’s disease, cortical spreading depression and stroke. By adapting and extending other models found in the literature, we create, for the first time, a mathematical model of the entire neurovascular unit that is capable of simulating two separate neurovascular coupling mechanisms: a potassium- and EET-based and a NO-based mechanism. These models successfully account for several observations seen in experiment. The potassium/EET-based mechanism can achieve arteriolar dilations similar in magnitude (3%) to those observed during a 60-second neuronal activation (modelled as a release of potassium and glutamate into the synaptic cleft). This model also successfully emulates the paradoxical experimental finding that vasoconstriction follows vasodilation when the astrocytic calcium concentration (or perivascular potassium concentration) is increased further. We suggest that the interaction of the changing smooth muscle cell membrane potential and the changing potassium-dependent resting potential of the inwardly rectifying potassium channel are responsible for this effect. Furthermore, our simulations demonstrate that the arteriolar behaviour is profoundly affected by depolarization of the astrocytic cell membrane, and by changes in the rate of perivascular potassium clearance or the volume ratio between the perivascular space and astrocyte. In the modelled NO-based neurovascular coupling mechanism, NO exerts its vasodilatory effects via neuronal and endothelial cell sources. With both sources included, the model achieves a 1% dilation due to a 60-second neuronal activation. When the endothelial contribution to NO production is omitted, the arteriole is more constricted at baseline. Without the endothelial NO contribution, the arteriolar change in diameter during neuronal activity is greater (6%). We hypothesize that NO has a dual purpose in neurovascular coupling: 1) it dixxxvi rectly mediates neurovascular coupling through release by neuronal sources, and 2) it indirectly modulates the size of the neurovascular coupling response by determining the baseline tone. Our physiological models of neurovascular coupling have allowed us to replicate, and explain, some of the phenomena seen in both neurovascular coupling-oriented and clinicallyoriented experimental research. This project highlights the fact that physiological modelling can be used as a tool to understand biological processes in a way that physical experiment cannot always do, and most importantly, can help to elucidate the cellular processes that induce or accompany our most debilitating diseases.