1 Department of Psychiatry, Yale University School of Medicine, New Haven, Connecticut, USA, 06510.
2 Multimodal Functional Imaging Lab, Biomedical Engineering Department, McGill University, Montréal, QC, Canada H3A 2B4.
3 Multimodal Functional Imaging Lab, Department of Physics, Concordia University, Montréal, QC, Canada H4B 2A7.
4 Concordia School of Health / PERFORM Centre, Concordia University, Montréal, QC, Canada H4B 1R6.
5 Institute for Medical Imaging Technology, Ruijin Hospital, Shanghai Jiao Tong University School of Medicine, Shanghai, China 200025.
6 Department of Radiology, Ruijin Hospital, Shanghai Jiao Tong University School of Medicine, Shanghai, China 200025.
7 Sleep, Cognition and Neuroimaging Lab, Department of Health, Kinesiology and Applied Physiology & Center for Studies in Behavioral Neurobiology, Concordia University, Montréal, QC, Canada H4B 1R6.
8 Centre de Recherche de l'Institut Universitaire de Gériatrie de Montréal, CIUSSS Centre-Sud-de-l'Ile-de-Montréal, Montréal, QC, Canada H3W 1W5.
9 School of Psychology and Clinical Language Sciences, University of Reading, Reading, United Kingdom, RG6 6ET.
10 Neurology and Neurosurgery Department, Montreal Neurological Institute, McGill University, Montréal, QC, Canada H3A 1A1.
11 Analytical Neurophysiology Lab, Montreal Neurological Institute and Hospital, McGill University, Montréal, QC, Canada H3A 2B4.
12 Interdepartmental Neuroscience Program, Yale University School of Medicine, New Haven, Connecticut, USA, 06510.
13 Department of Psychology, Yale University School of Medicine, New Haven, Connecticut, USA, 06510.
14 Analytical Neurophysiology Lab, Department of Neurology, Duke University Medical Center, Durham, NC, USA.
15 Biomedical Imaging and Healthy Aging Laboratory, Department of Electrical and Computer Engineering, Concordia University, Montréal, Québec, Canada H3G 1S6.
16 Centre De Recherches En Mathématiques, Montréal, Québec, Canada H3C 3J7.

Decrease in cognitive performance after sleep deprivation followed by recovery after sleep suggests its key role, and especially non-rapid eye movement (NREM) sleep, in the maintenance of cognition. It remains unknown whether brain network reorganization in NREM sleep stages N2 and N3 can uniquely be mapped onto individual differences in cognitive performance after a recovery nap following sleep deprivation. Using resting state functional magnetic resonance imaging (fMRI), we quantified the integration and segregation of brain networks during NREM sleep stages N2 and N3 while participants took a 1-hour nap following 24-hour sleep deprivation, compared to well-rested wakefulness. Here, we advance a new analytic framework called the hierarchical segregation index (HSI) to quantify network segregation across spatial scales, from whole-brain to the voxel level, by identifying spatio-temporally overlapping large-scale networks and the corresponding voxel-to-region hierarchy. Our results show that network segregation increased in the default mode, dorsal attention and somatomotor networks during NREM sleep compared to wakefulness. Segregation within the visual, limbic, and executive control networks exhibited N2 versus N3 sleep-specific voxel-level patterns. More segregation during N3 was associated with worse recovery of working memory, executive attention, and psychomotor vigilance after the nap. The level of spatial resolution of network segregation varied among brain regions and was associated with the recovery of performance in distinct cognitive tasks. We demonstrated the sensitivity and reliability of voxel-level HSI to provide key insights into within-region variation, suggesting a mechanistic understanding of how NREM sleep replenishes cognition after sleep deprivation.