“…Incompleteness of the Circle of Willis due to missing anterior (22%) or left posterior (46%) communicating arteries occurs in 20-30% of the population, 14 which might explain why, in our case and in the cases [10][11][12][13] cited above, flow from the left cerebral circulation was insufficient in perfusing the right side. In some of our other cases, perfusion of the left common carotid artery alone led to improvement in both left and right rSO 2 , thus increasing bilateral brain protection with only left common carotid perfusion (for better exposure) while arch repair was underway.…”