Cerebral venous steal equation for intracranial segmental perfusion pressure predicts and quantifies reversible intracranial to extracranial flow diversion

Abstract

Cerebral perfusion is determined by segmental perfusion pressure for the intracranial compartment (SPP), which is lower than cerebral perfusion pressure (CPP) because of extracranial stenosis. We used the Thevenin model of Starling resistors to represent the intra-extra-cranial compartments, with outflow pressures ICP and Pe, to express SPP = Pd–ICP = FFR*CPP–Ge(1 − FFR)(ICP–Pe). Here Pd is intracranial inflow pressure in the circle of Willis, ICP—intracranial pressure; FFR = Pd/Pa is fractional flow reserve (Pd scaled to the systemic pressure Pa), Ge—relative extracranial conductance. The second term (cerebral venous steal) decreases SPP when FFR < 1 and ICP > Pe. We verified the SPP equation in a bench of fluid flow through the collapsible tubes. We estimated Pd, measuring pressure in the intra-extracranial collateral (supraorbital artery) in a volunteer. To manipulate extracranial outflow pressure Pe, we inflated the infraorbital cuff, which led to the Pd increase and directional Doppler flow signal reversal in the supraorbital artery. SPP equation accounts for the hemodynamic effect of inflow stenosis and intra-extracranial flow diversion, and is a more precise perfusion pressure target than CPP for the intracranial compartment. Manipulation of intra-extracranial pressure gradient ICP–Pe can augment intracranial inflow pressure (Pd) and reverse intra-extracranial steal.