Inverse neurovascular coupling and associated spreading depolarization models for traumatic brain injury

The paper presents the mathematical model of cortical spreading depolarisation and its effect on inverse neurovascular coupling. The paper considers the potassium ion channels present in the neuron-astrocyte blood vascular network to access the role of potassium ions during spreading depolarisation and associated inverse neurovascular coupling. Simulation of our proposed mathematical model confirms the experimental results that an increase in concentration of potassium ions beyond 20mM in the perivascular space essentially leads to vasoconstriction and hence inverse neurovascular coupling. The propagatory nature of depolarizing potassium waves has been unraveled though our proposed mathematical model.