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Background: The time to maximum of the residue function (TMax) has been employed to identify the penumbra in acute ischemic stroke. Cognitive impairment in patients with Carotid Artery Stenosis (CAS) has been attributed to chronic cerebral hypoperfusion. The study aimed to examine whether cognitive impairment can be detected based on a preliminary TMax cutoff in patients with unilateral CAS. Methods: Fifty unilateral CAS patients underwent dynamic susceptibility contrast MR perfusion. The preliminary TMax cutoff (3 seconds) was derived on the basis of the upper limit of 95% confidence interval of TMax in the Middle Cerebral Artery (MCA) contralateral to the CAS side. All patients were allocated to the Right-delayed group (n=18), Left-delayed group (n=12), and Nondelayed group (n=20) by the cutoff. Cognitive assessment was also administered on all patients and 22 healthy volunteers. Results: No significant interhemispheric mean TMax differences of the Non-delayed group were noted (p=0.75), but the mean TMax of ipsilateral MCA was significantly longer than that of the contralateral MCA of the Left- and Right-delayed groups (ps&<0.001), respectively. Compared to healthy volunteers, the Right-delayed group performed significantly worse on most of the visuospatial tests (ps&<0.04), while the Left-delayed group performed significantly worse on most of the verbal tests (ps&<0.05). The performance of the Non-delayed group on all cognitive domains was similar to that of healthy volunteers (ps>0.07). Conclusion: TMax can be used to differentiate the chronic hypoperfusion state in unilateral CAS patients. Prolonged TMax in the MCA of either hemisphere may lead to lateralized impairment in cognition functions in patients with unilateral CAS.