{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,23]],"date-time":"2026-03-23T13:57:39Z","timestamp":1774274259058,"version":"3.50.1"},"reference-count":70,"publisher":"Wiley","issue":"1","license":[{"start":{"date-parts":[[2025,11,4]],"date-time":"2025-11-04T00:00:00Z","timestamp":1762214400000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0\/"},{"start":{"date-parts":[[2025,11,4]],"date-time":"2025-11-04T00:00:00Z","timestamp":1762214400000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/doi.wiley.com\/10.1002\/tdm_license_1.1"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["32171085"],"award-info":[{"award-number":["32171085"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["12405062"],"award-info":[{"award-number":["12405062"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["advanced.onlinelibrary.wiley.com"],"crossmark-restriction":true},"short-container-title":["Advanced Science"],"published-print":{"date-parts":[[2026,1]]},"abstract":"<jats:title>Abstract<\/jats:title>\n                  <jats:p>\n                    Current Alzheimer's disease (AD) diagnostics rely on late\u2010stage cognitive assessments or invasive biomarkers. Neuroimaging offers non\u2010invasive alternatives, but single\u2010modality approaches (structural atrophy or functional connectivity) face limitations in sensitivity and specificity for early detection. Entropy and temperature, novel structure\u2010function coupling (SFC) biomarkers based on gray matter eigenmodes, are introduced to quantify cortical disorganization in early AD. Using multimodal MRI and amyloid\u2010PET data from two cohorts (BABRI: N = 135; ADNI: N = 275), including cognitively normal (CN), mild cognitive impairment (MCI), and AD individuals, entropy is computed by projecting fMRI onto structural eigenmodes and temperature via eigenmode\u2010based functional connectivity reconstruction. These indices are tested for diagnostic classification, A\u03b2 prediction, and MCI subtype stratification (reversed\/stable\/progressed). Entropy is significantly higher in AD than CN and MCI (\u0394 = 8\u201321%,\n                    <jats:italic>p<\/jats:italic>\n                    &lt; 0.001) in both cohorts. Left\u2010hemisphere entropy yielded optimal diagnostic accuracy (AUC = 0.901 for CN vs MCI), while right\/global entropy predicted A\u03b2 burden (error reduction: 38.7\u201342.1%,\n                    <jats:italic>p<\/jats:italic>\n                    &lt; 0.01). Entropy also distinguished MCI subtypes and captured biphasic changes in progressors. Temperature indices showed no significant group differences. Entropy from gray matter eigenmodes is a sensitive, non\u2010invasive biomarker for AD diagnosis and pathology prediction, revealing hemispheric asymmetries and nonlinear progression in MCI.\n                  <\/jats:p>","DOI":"10.1002\/advs.202511614","type":"journal-article","created":{"date-parts":[[2025,11,4]],"date-time":"2025-11-04T18:15:42Z","timestamp":1762280142000},"update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Shannon Entropy of Gray Matter Eigenmodes: A Novel Biomarker for Alzheimer's Disease and Heterogeneous MCI Trajectories"],"prefix":"10.1002","volume":"13","author":[{"ORCID":"https:\/\/orcid.org\/0009-0008-3107-3778","authenticated-orcid":false,"given":"Yumeng","family":"Li","sequence":"first","affiliation":[{"name":"Beijing Aging Brain Rejuvenation Initiative (BABRI) Centre Beijing Normal University  Beijing 100875 China"},{"name":"State Key Laboratory of Cognitive Neuroscience and Learning Beijing Normal University  Beijing 100875 China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0270-762X","authenticated-orcid":false,"given":"Gaoping","family":"Long","sequence":"additional","affiliation":[{"name":"College of Physics &amp; Optoelectronic Engineering Jinan University  Guangzhou 510632 China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xinyue","family":"Zhang","sequence":"additional","affiliation":[{"name":"Beijing Aging Brain Rejuvenation Initiative (BABRI) Centre Beijing Normal University  Beijing 100875 China"},{"name":"State Key Laboratory of Cognitive Neuroscience and Learning Beijing Normal University  Beijing 100875 China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Kewei","family":"Chen","sequence":"additional","affiliation":[{"name":"Banner Alzheimer's Institute  Phoenix AZ 85006 USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9598-0299","authenticated-orcid":false,"given":"Xin","family":"Li","sequence":"additional","affiliation":[{"name":"Beijing Aging Brain Rejuvenation Initiative (BABRI) Centre Beijing Normal University  Beijing 100875 China"},{"name":"State Key Laboratory of Cognitive Neuroscience and Learning Beijing Normal University  Beijing 100875 China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Zhanjun","family":"Zhang","sequence":"additional","affiliation":[{"name":"Beijing Aging Brain Rejuvenation Initiative (BABRI) Centre Beijing Normal University  Beijing 100875 China"},{"name":"State Key Laboratory of Cognitive Neuroscience and Learning Beijing Normal University  Beijing 100875 China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","published-online":{"date-parts":[[2025,11,4]]},"reference":[{"key":"e_1_2_11_1_1","doi-asserted-by":"publisher","DOI":"10.1016\/S1474-4422(22)00298-8"},{"key":"e_1_2_11_2_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.cell.2023.09.023"},{"key":"e_1_2_11_3_1","doi-asserted-by":"publisher","DOI":"10.1001\/jamaneurol.2020.0387"},{"key":"e_1_2_11_4_1","first-page":"239","volume":"18","author":"Varghese T.","year":"2013","journal-title":"Neurol. Asia"},{"key":"e_1_2_11_5_1","doi-asserted-by":"publisher","DOI":"10.1212\/01.wnl.0000336925.79704.9f"},{"key":"e_1_2_11_6_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.neuroimage.2006.05.038"},{"key":"e_1_2_11_7_1","doi-asserted-by":"publisher","DOI":"10.1073\/pnas.1508831112"},{"key":"e_1_2_11_8_1","doi-asserted-by":"publisher","DOI":"10.1212\/WNL.0000000000001003"},{"key":"e_1_2_11_9_1","doi-asserted-by":"publisher","DOI":"10.1038\/s41591-023-02365-w"},{"key":"e_1_2_11_10_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.neubiorev.2015.02.008"},{"key":"e_1_2_11_11_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.pneurobio.2014.02.004"},{"key":"e_1_2_11_12_1","doi-asserted-by":"publisher","DOI":"10.1016\/S0140-6736(04)15441-X"},{"key":"e_1_2_11_13_1","doi-asserted-by":"publisher","DOI":"10.1038\/nrneurol.2009.215"},{"key":"e_1_2_11_14_1","doi-asserted-by":"publisher","DOI":"10.1002\/hbm.20744"},{"key":"e_1_2_11_15_1","doi-asserted-by":"publisher","DOI":"10.1093\/brain\/awz091"},{"key":"e_1_2_11_16_1","doi-asserted-by":"publisher","DOI":"10.1523\/JNEUROSCI.23-03-00994.2003"},{"key":"e_1_2_11_17_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.neurobiolaging.2024.09.007"},{"key":"e_1_2_11_18_1","first-page":"2789","volume":"8","author":"Xiang J.","year":"2013","journal-title":"Neural Regener. Res."},{"key":"e_1_2_11_19_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.neuroimage.2005.12.033"},{"key":"e_1_2_11_20_1","doi-asserted-by":"publisher","DOI":"10.1038\/s44220-024-00259-5"},{"key":"e_1_2_11_21_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.neuroscience.2024.05.021"},{"key":"e_1_2_11_22_1","doi-asserted-by":"publisher","DOI":"10.1038\/s41593-020-00726-z"},{"key":"e_1_2_11_23_1","doi-asserted-by":"publisher","DOI":"10.1002\/alz.14123"},{"key":"e_1_2_11_24_1","doi-asserted-by":"publisher","DOI":"10.1002\/hbm.70202"},{"key":"e_1_2_11_25_1","doi-asserted-by":"publisher","DOI":"10.3934\/mbe.2022416"},{"key":"e_1_2_11_26_1","doi-asserted-by":"publisher","DOI":"10.1038\/s41467-021-25184-4"},{"key":"e_1_2_11_27_1","doi-asserted-by":"publisher","DOI":"10.1038\/s41467-022-29770-y"},{"key":"e_1_2_11_28_1","doi-asserted-by":"publisher","DOI":"10.1038\/s41583-024-00846-6"},{"key":"e_1_2_11_29_1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.99.012313"},{"key":"e_1_2_11_30_1","doi-asserted-by":"publisher","DOI":"10.1038\/s41586-023-06098-1"},{"key":"e_1_2_11_31_1","doi-asserted-by":"publisher","DOI":"10.1212\/WNL.0000000000007133"},{"key":"e_1_2_11_32_1","doi-asserted-by":"publisher","DOI":"10.1186\/s13195-015-0132-3"},{"key":"e_1_2_11_33_1","doi-asserted-by":"publisher","DOI":"10.1186\/s40478-018-0515-3"},{"key":"e_1_2_11_34_1","doi-asserted-by":"publisher","DOI":"10.1038\/ncomms10340"},{"key":"e_1_2_11_35_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.neuroimage.2020.117364"},{"key":"e_1_2_11_36_1","doi-asserted-by":"publisher","DOI":"10.1038\/s41467-023-42053-4"},{"key":"e_1_2_11_37_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.neuroimage.2018.06.040"},{"key":"e_1_2_11_38_1","doi-asserted-by":"publisher","DOI":"10.1007\/s11064-019-02926-x"},{"key":"e_1_2_11_39_1","doi-asserted-by":"publisher","DOI":"10.1186\/s13195-022-00999-5"},{"key":"e_1_2_11_40_1","doi-asserted-by":"publisher","DOI":"10.1186\/s13024-024-00740-w"},{"key":"e_1_2_11_41_1","doi-asserted-by":"publisher","DOI":"10.1212\/01.wnl.0000240127.89601.83"},{"key":"e_1_2_11_42_1","doi-asserted-by":"publisher","DOI":"10.1073\/pnas.2109889118"},{"key":"e_1_2_11_43_1","doi-asserted-by":"publisher","DOI":"10.3389\/fnagi.2017.00378"},{"key":"e_1_2_11_44_1","doi-asserted-by":"publisher","DOI":"10.1186\/s40035-023-00394-6"},{"key":"e_1_2_11_45_1","doi-asserted-by":"publisher","DOI":"10.1093\/brain\/awz150"},{"key":"e_1_2_11_46_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.jneumeth.2013.03.018"},{"key":"e_1_2_11_47_1","doi-asserted-by":"publisher","DOI":"10.3389\/fnagi.2017.00378"},{"key":"e_1_2_11_48_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.neurobiolaging.2014.04.007"},{"key":"e_1_2_11_49_1","doi-asserted-by":"publisher","DOI":"10.1038\/mp.2011.81"},{"key":"e_1_2_11_50_1","doi-asserted-by":"publisher","DOI":"10.1162\/089976698300017052"},{"key":"e_1_2_11_51_1","unstructured":"Q.Jiang J.Shi presented at36th Ann. Int. Conf. the IEEE Eng. Med. Biol. Soc. Chicago IL USA August 2014."},{"key":"e_1_2_11_52_1","doi-asserted-by":"publisher","DOI":"10.1142\/S0218348X24500993"},{"key":"e_1_2_11_53_1","doi-asserted-by":"publisher","DOI":"10.1002\/alz.13789"},{"key":"e_1_2_11_54_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.bosn.2025.02.002"},{"key":"e_1_2_11_55_1","doi-asserted-by":"publisher","DOI":"10.4103\/1673-5374.156954"},{"key":"e_1_2_11_56_1","doi-asserted-by":"publisher","DOI":"10.1007\/s10072-025-08268-7"},{"key":"e_1_2_11_57_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.expneurol.2022.114205"},{"key":"e_1_2_11_58_1","doi-asserted-by":"publisher","DOI":"10.3390\/ijms21103435"},{"key":"e_1_2_11_59_1","doi-asserted-by":"publisher","DOI":"10.1038\/s41593-024-01737-w"},{"key":"e_1_2_11_60_1","doi-asserted-by":"publisher","DOI":"10.1002\/alz.12326"},{"key":"e_1_2_11_61_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.jalz.2010.03.006"},{"key":"e_1_2_11_62_1","doi-asserted-by":"publisher","DOI":"10.1111\/j.1365-2796.2004.01388.x"},{"key":"e_1_2_11_63_1","doi-asserted-by":"publisher","DOI":"10.1212\/WNL.34.7.939"},{"key":"e_1_2_11_64_1","doi-asserted-by":"publisher","DOI":"10.1016\/S1474-4422(10)70223-4"},{"key":"e_1_2_11_65_1","doi-asserted-by":"publisher","DOI":"10.1002\/jmri.21049"},{"key":"e_1_2_11_66_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.jalz.2010.03.004"},{"key":"e_1_2_11_67_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.neuroimage.2012.01.021"},{"key":"e_1_2_11_68_1","doi-asserted-by":"publisher","DOI":"10.1038\/s41592-018-0235-4"},{"key":"e_1_2_11_69_1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevD.110.064017"},{"key":"e_1_2_11_70_1","doi-asserted-by":"publisher","DOI":"10.1093\/cercor\/bhx179"}],"container-title":["Advanced Science"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/advanced.onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/advs.202511614","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/advanced.onlinelibrary.wiley.com\/doi\/full-xml\/10.1002\/advs.202511614","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/advanced.onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/advs.202511614","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,3,23]],"date-time":"2026-03-23T13:01:48Z","timestamp":1774270908000},"score":1,"resource":{"primary":{"URL":"https:\/\/advanced.onlinelibrary.wiley.com\/doi\/10.1002\/advs.202511614"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,11,4]]},"references-count":70,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2026,1]]}},"alternative-id":["10.1002\/advs.202511614"],"URL":"https:\/\/doi.org\/10.1002\/advs.202511614","archive":["Portico"],"relation":{},"ISSN":["2198-3844","2198-3844"],"issn-type":[{"value":"2198-3844","type":"print"},{"value":"2198-3844","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,11,4]]},"assertion":[{"value":"2025-06-23","order":0,"name":"received","label":"Received","group":{"name":"publication_history","label":"Publication History"}},{"value":"2025-11-04","order":3,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}],"article-number":"e11614"}}