Competitive bidirectional pathways of vascular tone regulation via arachidonic acid metabolites

Background and Objectives: The processes taking place in each element of a neurogliovascular unit will have repercussions in the entire unit. Astrocytes produce arachidonic acid, and its metabolites play a key role in neurogliovascular dynamics with a possibility for bidirectional control, specifically EETs and $PGE_2$ have a vasodilatory effect while 20-HETE acts as a vasoconstrictor. We develop a minimalistic model of model of neurogliovascular unit which takes into account the effect of arachidonic acid metabolites on the blood vessel radius, determining the blood flow and further activity of the elements. Materials and Methods: In order to test the model, we simulate two scenarios of model behavior, including an external influence leading to an increase in neuronal potassium, and an external influence on EETs. Results: We have proposed a mathematical model of the neurogliovascular unit, which accounts for $IP_3$-dependent calcium dynamics in the astrocyte, neuronal activity, and vascular dynamics, and relies on arachidonic acid and its metabolites as vasoactive substances. Numerical simulations have demonstrated the plausibility of such a control loop involving the elements of the neurogliovascular unit and associated with the influence of arachidonic acid metabolites on vascular tone and indirectly on synaptic activity. We conclude that the model can be used for further theoretical studies of the regulatory mechanisms pertaining to cerebral perfusion.