Abstract
INTRODUCTION
It remains unclear whether the local amyloid‐beta (Aβ) burden in key regions within the default mode network (DMN) affects network and cognitive functions.
METHODS
Participants included 1002 individuals from the Chinese Preclinical Alzheimer's Disease Study cohort who underwent 18F‐florbetapir positron emission tomography resting‐state functional magnetic resonance imaging scanning and neuropsychological tests. The correlations between precuneus (PRC) Aβ burden, DMN function, and cognitive function were investigated.
RESULTS
In individuals with high PRC Aβ burden, there is a bidirectional relationship between DMN local function or functional connectivity and PRC Aβ deposition across various cognitive states, which is also linked to cognitive function. Even below the PRC Aβ threshold, DMN function remains related to PRC Aβ deposition and cognitive performance.
DISCUSSION
The findings reveal the critical role of PRC Aβ deposition in disrupting neural networks associated with cognitive decline and the necessity of early detection and monitoring of PRC Aβ deposition.
Highlights
Precuneus (PRC) Aβ burden impacts DMN function in different cognitive stages.
High PRC Aβ burden is linked to early neural compensation and subsequent dysfunction.
Low PRC Aβ burden correlates with neural changes before significant Aβ accumulation.
Changes in DMN function and connectivity provide insights into AD progression.
Early detection of regional Aβ burden can help monitor the risk of cognitive decline.
Keywords: Alzheimer's disease, amyloid‐beta, cognitive decline, default mode network, mild cognitive impairment, precuneus, subjective cognitive decline
1. BACKGROUND
The progression of Alzheimer's disease (AD) follows a continuum, starting from normal cognition (NC) and gradually advancing to dementia. 1 , 2 Within this trajectory, individuals without detectable objective cognitive impairment are considered to be in the preclinical stage, typically including those with NC and those with subjective cognitive decline (SCD) who have cognitive complaints but normal objective cognitive function. 3 , 4 Individuals with detectable mild objective cognitive impairment, but who do not meet the criteria for dementia, are classified as having mild cognitive impairment (MCI), 5 considered the prodromal stage of AD.
Amyloid‐beta (Aβ) is a crucial pathological biomarker of AD and is a necessary condition for the diagnosis of preclinical and prodromal AD. 2 , 6 , 7 Positron emission computed tomography (PET) is an effective, noninvasive method for detecting Aβ deposition in the brain. Using Aβ‐PET, researchers have found that Aβ deposition in the brain shows a staged progression, particularly in the early stages of the disease. 8 , 9 , 10 Notably, local Aβ deposition in key regions is associated with downstream pathological damage and cognitive impairment. 11 The precuneus (PRC) is a key region for the staged deposition of Aβ and has been identified in some studies as the initial site of Aβ accumulation in the pathological progression of AD trajectory. 9 , 10 , 12
The default mode network (DMN) is a network of brain regions that are active when an individual is at rest and not focused on the external environment. It includes key areas such as the medial prefrontal cortex, posterior cingulate cortex/PRC, and lateral parietal cortex. 13 , 14 The DMN is involved in various functions, including self‐referential thought, memory consolidation, language and semantic memory, and future planning. 15 In AD, alterations in the DMN have been consistently observed. These changes include reduced connectivity and activity within the DMN, which correlate with cognitive decline and the progression of AD pathology. 14 , 16 The PRC, a central hub in the DMN, plays a crucial role in integrating information and supporting cognitive functions. Pathological damage to the PRC significantly disrupts DMN function, contributing to the progression of neurodegenerative diseases. 17
Despite these insights, the understanding of how Aβ burden in key regions specifically affects DMN function across different stages of cognitive impairment remains insufficient. Previous studies have often focused on global Aβ deposition, whereas the nuanced changes in local brain function and network connectivity with varying levels of Aβ burden in key regions need further elucidation. Given the pivotal role of the DMN and the PRC in AD, our study aims to explore the association between regional Aβ burden and local function and connectivity within the DMN across different stages of cognitive impairment. We hypothesize that a higher Aβ burden in the PRC will correlate with significant alterations in local brain function and connectivity, which may vary across individuals with NC, SCD, MCI, and dementia. By examining these relationships, we aim to elucidate the neural mechanisms underlying cognitive decline and identify potential biomarkers for early diagnosis, monitoring, and intervention in AD.
2. METHODS
2.1. Participants
The study comprised 1002 participants from the Chinese Preclinical Alzheimer's Disease Study (C‐PAS) 18 cohort, recruited between May 2019 and April 2024. Participants were recruited from both the community and the Cognitive Disorder Clinic at Shanghai Sixth People's Hospital. Specifically, most NC and SCD participants were community volunteers, primarily recruited through Cognitive Disorder Friendly Communities, with some recruited via social media campaigns. Another portion of MCI participants and most dementia participants were recruited from the Cognitive Disorder Clinic. Eligibility was determined through neuropsychological assessments, medical history reviews, and physical examinations. The inclusion criteria comprised individuals who were native Chinese speakers, had no severe hearing or visual impairments, and were capable of undertaking neuropsychological testing. Exclusion criteria encompassed individuals with a history of alcohol or drug abuse, psychiatric disorders, epilepsy, head trauma, stroke, and other severe neurological conditions. Additionally, those with non‐AD‐related cognitive impairments (eg, Parkinson's disease, dementia with Lewy bodies, frontotemporal lobe dementia), significant thyroid function abnormalities, or syphilis serological abnormalities were excluded. All participants underwent Aβ‐PET scans and magnetic resonance imaging (MRI) scans, along with neuropsychological testing. The sample size and group distributions in this study were determined primarily by the availability of participants and their distribution across diagnostic groups.
2.2. Neuropsychological testing
Participants underwent a comprehensive battery of neuropsychological tests, which included the Montreal Cognitive Assessment‐basic (MoCA‐B), 19 Addenbrooke's Cognitive Examination III (ACE III), 20 Subjective Cognitive Decline Interview (SCD‐I), 21 Everyday Cognition (ECog), Functional Activities Questionnaire (FAQ), and Activities of Daily Living (ADL) as general cognition and function assessments; the Auditory Verbal Learning Test (AVLT) 22 and Brief Visuospatial Memory Test (BVMT) 23 for memory function assessment; the Verbal Fluency Test (VFT) and Boston Naming Test (BNT) for language function assessment; the Shape Trail Test (STT)‐A and B, 24 Stroop Word‐Color Interference Task (SCWT), Category Switching Test (CaST), 25 and Digit Span Test (DST) 26 for attention and executive function assessment; and the Silhouettes Test (ST) 27 and Judgement of Line Orientation (JLO) for spatial function assessment.
2.3. Diagnostic criteria for cognitive impairment
The recruitment of SCD participants followed the SCD‐initiative (SCD‐I) framework. 28 Participants were classified as SCD if they met the following criteria: self‐reported SCD (perceived as worse than peers) with associated concerns, onset of SCD within 5 years before the interview, and neuropsychological test scores within 1.5 standard deviations of the normative mean after controlling for age, sex, and education. Notably, SCD participants do not exhibit significant objective cognitive impairment, as their neuropsychological test results do not meet the criteria for MCI.
The diagnostic criteria for MCI follow the Petersen criteria, 29 encompassing the following: (1) self‐reported cognitive decline noted by the individual, family members, or an informant; (2) cognitive assessment scores at least 1.5 standard deviations below the mean for their age and educational level (using the MoCA‐B assessment in this research); (3) predominantly intact cognitive function; (4) unaltered performance in daily activities; and (5) exclusion of dementia or any physical or mental conditions that could impact cognitive function.
The diagnosis of dementia follows the 2011 National Institute on Aging–Alzheimer's Association (NIA‐AA) criteria for probable AD dementia. 30
RESEARCH IN CONTEXT
Systematic review: We conducted a comprehensive literature review using sources such as PubMed and Google Scholar, focusing on studies examining the relationship between regional amyloid‐beta (Aβ) deposition, local brain function, and connectivity within the default mode network (DMN) across cognitive impairment stages. While the roles of Aβ pathologies in Alzheimer's disease (AD) progression are well‐studied, the detailed changes in local brain function and connectivity associated with varying levels of Aβ burden in key regions like the precuneus (PRC) remain less understood.
Interpretation: Our findings show that higher PRC Aβ burden correlates with significant changes in local brain function and connectivity, which vary across cognitive impairment stages. These changes indicate early neural network disruptions due to PRC Aβ deposition, even before substantial cognitive impairment is detectable. Furthermore, PRC Aβ burden‐related DMN functions are also associated with cognitive performance, showing both compensatory mechanisms and impairment. Even low PRC Aβ burden is linked to significant neural alterations, suggesting potential biomarkers for early AD diagnosis.
Future directions: Future research should replicate these findings in larger, diverse cohorts and conduct longitudinal studies to establish the temporal sequence of the impact of Aβ deposition on brain function and connectivity. Exploring other brain networks beyond the DMN could provide deeper insights into AD progression. Integrating multimodal imaging approaches is also recommended.
2.4. DMN definition
We utilized a region of interest (ROI)‐based approach to define the DMN. Based on previous research, 31 the DMN was defined using the following 10 ROIs: the anterior medial prefrontal cortex (amPFC), the PRC, the left and right intraparietal cortex (lIPC and rIPC), the ventromedial prefrontal cortex (vmPFC), the dorsomedial prefrontal cortex (dmPFC), left and right lateral temporal cortex (lLTC and rLTC), and left and right parahippocampal formation (lPHF and rPHF). Each ROI was identified by delineating a sphere with an 8‐mm radius centered on the designated coordinate. Of these, the PRC was used as the ROI for evaluating localized Aβ deposition because the PRC is the central hub within the DMN, playing a critical role in brain organization. 32 , 33
2.5. Aβ‐PET image acquisition and processing
Cerebral Aβ deposition was visualized by utilizing 18F‐florbetapir PET. The PET imaging was conducted at the Siemens Biograph mCT FlowMotion PET/CT system situated at the PET Center of Huashan Hospital, Fudan University. Standardized uptake value ratios (SUVRs) for the 18F‐florbetapir tracer were calculated using the whole cerebellum as the reference area. The SUVR of the PRC (the overall ROI formed by bilateral PRC) was extracted for further research. Given the absence of established SUVR thresholds specific to the PRC and the higher proportion of cognitively normal or mildly impaired participants in our cohort, we employed a median‐based dichotomy to split the study population into high and low Aβ deposition groups. 34 , 35 , 36 , 37 In the NC group, the median method was utilized to establish the SUVR of the PRC as a threshold. Subsequently, individuals with varying cognitive functional statuses were categorized into groups labeled as “high PRC SUVR” and “low PRC SUVR” according to this threshold. Details of the 18F‐florbetapir PET scanning and image processing methods are described in the eMethods section in the Supplementary Material.
2.6. Resting‐state functional MRI image acquisition and processing
Resting‐state functional MRI (fMRI) data were acquired using a 3.0‐Tesla scanner (SIEMENS MAGNETOM Prisma 3.0 T, Siemens, Erlangen, Germany) at the Shanghai Sixth People's Hospital Affiliated to Shanghai Jiao Tong University School of Medicine. Participants were instructed to keep their eyes closed, remain relaxed without falling asleep, and minimize movements during the scans. The image acquisition was performed utilizing an echo planar imaging (EPI) sequence, transverse plane. The specific parameters were as follows: repetition time = 800 ms, echo time = 37 ms, flip angle = 52°, matrix size = 104 × 104, field of view = 208 mm × 208 mm, slice number = 72 slices, slice thickness = 2 mm, and voxel size = 2 mm × 2 mm × 2 mm. The imaging procedure produced 488 slices. The data were preprocessed with SPM12 (http://fil.ion.ucl.ac.uk/spm/) and RESTplus (http://restfmri.net/forum/restplus).
This study calculated the fractional amplitude of low‐frequency fluctuation (fALFF), regional homogeneity (ReHo), and degree centrality (DC) of 10 DMN nodes as local function metrics and computed the connectivity strength between nodes within the DMN. See the eMethods section in the Supplementary Material for the preprocessing procedure; specific calculations are also described in the eMethods section in the Supplementary Material.
2.7. Statistics
Statistical analyses were performed using R version 4.4.1. Data were presented as mean ± standard deviation for continuous variables and as percentages for categorical variables. Descriptive statistics were calculated for demographics, 18F‐florbetapir deposition level, cognitive functioning characteristics, and DMN functioning indicators, and comparisons across groups were conducted using analysis of variance (ANOVA) for continuous variables and chi‐square tests for categorical variables. Correlations between PRC Aβ SUVR, local brain function, and connectivity within the DMN were analyzed using a general linear model, with adjustments for age and sex. Correlations between functional metrics and cognitive function were also analyzed using a general linear model, with adjustments for age, sex, and education level. Significance levels were set at p < 0.05. Our study employed multiple correlation analyses to explore the associations between PRC Aβ burden, local brain function, and connectivity; therefore, we provided false discovery rate (FDR) (Benjamini–Hochberg)‐corrected p‐values for multiple comparisons. However, given the exploratory nature of this study, we primarily presented and interpreted the results before correction. 38
3. RESULTS
3.1. Demographic and cognitive function characteristics
The study included 190 participants in the NC group, 213 in the SCD group, 410 in the MCI group, and 189 in the Dementia group. The demographic characteristics, Aβ deposition, and cognitive function scores for these groups are summarized in Table 1. The sex distribution was similar across groups, with no significant differences (p = 0.632). However, significant differences were observed in age, with NC averaging 64.46 ± 8.53 years, SCD 63.35 ± 7.77 years, MCI 66.5 ± 7.04 years, and Dementia 67.5 ± 8.45 years (p < 0.001). Education years also varied significantly among the groups, with NC averaging 12.62 ± 3.29 years, SCD 12.51 ± 3.09 years, MCI 11.34 ± 3.37 years, and Dementia 9.2 ± 4.11 years (p < 0.001).
TABLE 1.
Demographics, Aβ deposition, and cognitive function information.
| NC | SCD | MCI | Dementia | |||
|---|---|---|---|---|---|---|
| (n = 190) | (n = 213) | (n = 410) | (n = 189) | Statistic | p | |
| Demographic | ||||||
| Age | 64.46 ± 8.53 | 63.35 ± 7.77 | 66.50 ± 7.04 | 67.50 ± 8.45 | 12.93 | <0.001 |
| Sex (male%) | 40.5% | 35.2% | 39.3% | 40.7% | 1.72 | 0.632 |
| Education years | 12.62 ± 3.29 | 12.51 ± 3.09 | 11.34 ± 3.37 | 9.20 ± 4.11 | 40.95 | <0.001 |
| Aβ deposition | ||||||
| Global Aβ SUVR | 1.12 ± 0.17 | 1.11 ± 0.13 | 1.14 ± 0.18 | 1.30 ± 0.27 | 42.75 | <0.001 |
| PRC Aβ SUVR | 1.13 ± 0.33 | 1.11 ± 0.21 | 1.20 ± 0.33 | 1.53 ± 0.48 | 61.22 | <0.001 |
| General cognition and function | ||||||
| ECog | 16.93 ± 5.98 | 18.52 ± 5.59 | 19.13 ± 7.77 | 30.62 ± 10.62 | 123.30 | <0.001 |
| MoCA‐B | 26.32 ± 2.11 | 25.59 ± 2.82 | 22.02 ± 3.77 | 12.65 ± 4.33 | 617.87 | <0.001 |
| ACE‐III | 83.50 ± 7.33 | 81.66 ± 7.46 | 72.58 ± 9.21 | 48.47 ± 13.44 | 530.02 | <0.001 |
| ADL | 20.15 ± 0.77 | 20.28 ± 1.57 | 20.64 ± 3.48 | 24.22 ± 7.00 | 48.53 | <0.001 |
| FAQ | 0.29 ± 0.93 | 1.00 ± 3.35 | 1.13 ± 2.87 | 6.74 ± 6.75 | 117.74 | <0.001 |
| Memory function | ||||||
| AVLT short delay recall | 6.34 ± 2.04 | 6.08 ± 2.08 | 3.06 ± 2.09 | 0.79 ± 1.29 | 244.67 | <0.001 |
| AVLT long delay recall | 6.14 ± 2.05 | 5.76 ± 2.26 | 2.34 ± 1.95 | 0.49 ± 0.91 | 305.43 | <0.001 |
| AVLT recognition | 22.17 ± 1.43 | 21.91 ± 1.64 | 18.97 ± 3.08 | 15.50 ± 4.68 | 167.17 | <0.001 |
| BVMT short delay recall | 9.51 ± 2.64 | 9.16 ± 2.77 | 6.78 ± 3.48 | 1.75 ± 2.41 | 139.32 | <0.001 |
| BVMT long delay recall | 9.51 ± 2.66 | 9.24 ± 2.82 | 6.70 ± 3.66 | 1.77 ± 2.54 | 126.25 | <0.001 |
| BVMT recognition | 11.83 ± 0.54 | 11.62 ± 0.97 | 10.79 ± 1.98 | 8.11 ± 2.72 | 101.30 | <0.001 |
| Language function | ||||||
| VFT | 18.37 ± 4.23 | 17.58 ± 4.32 | 13.93 ± 4.14 | 9.96 ± 4.57 | 156.24 | <0.001 |
| BNT | 24.90 ± 2.61 | 24.65 ± 2.89 | 22.01 ± 4.10 | 18.95 ± 4.64 | 74.78 | <0.001 |
| Executive function | ||||||
| STT‐A (s) | 46.95 ± 17.17 | 46.71 ± 15.23 | 56.79 ± 23.00 | 85.93 ± 40.77 | 67.70 | <0.001 |
| STT‐B (s) | 122.69 ± 36.80 | 123.01 ± 35.95 | 157.35 ± 54.96 | 212.46 ± 62.57 | 82.99 | <0.001 |
| SCWT | 23.47 ± 1.18 | 23.21 ± 1.68 | 22.36 ± 3.35 | 20.20 ± 4.10 | 26.60 | <0.001 |
| SCWT time (s) | 33.84 ± 10.82 | 34.27 ± 9.69 | 41.33 ± 17.45 | 56.20 ± 21.85 | 45.37 | <0.001 |
| CaST | 16.52 ± 4.83 | 15.33 ± 4.54 | 12.78 ± 4.40 | 9.14 ± 4.95 | 55.78 | <0.001 |
| DST | 12.79 ± 2.21 | 12.46 ± 2.36 | 11.80 ± 2.42 | 10.79 ± 2.17 | 17.22 | <0.001 |
| Spatial function | ||||||
| ST | 10.11 ± 2.62 | 9.90 ± 2.72 | 8.72 ± 2.77 | 6.68 ± 3.00 | 36.77 | <0.001 |
| JLO | 21.74 ± 4.65 | 21.22 ± 3.85 | 19.63 ± 4.82 | 17.03 ± 5.60 | 22.80 | <0.001 |
Abbreviations: Aβ, amyloid‐beta; ACE‐III, Addenbrooke's Cognitive Examination III; ADL, Activities of Daily Living; AVLT, Auditory Verbal Learning Test; BNT, Boston Naming Test; BVMT, Brief Visuospatial Memory Test; CaST, Category Switching Test; DST, Digit Span Test; ECog, Everyday Cognition; FAQ, Functional Activities Questionnaire; JLO, Judgement of Line Orientation; MCI, mild cognitive impairment; MoCA‐B, Montreal Cognitive Assessment‐basic; NC, normal cognition; PRC, precuneus; SCD, subjective cognitive decline; SCWT, Stroop Word‐Color Interference Task; ST, Silhouettes Test; STT, Shape Trail Test; SUVR, standardized uptake value ratio; VFT, Verbal Fluency Test.
In terms of Aβ deposition, the global Aβ SUVR showed significant differences, with NC at 1.12 ± 0.17, SCD at 1.11 ± 0.13, MCI at 1.14 ± 0.18, and Dementia at 1.3 ± 0.27 (p < 0.001). Notably, the PRC Aβ SUVR exhibited an even more pronounced increase, with NC at 1.13 ± 0.33, SCD at 1.11 ± 0.21, MCI at 1.2 ± 0.33, and Dementia at 1.53 ± 0.48 (p < 0.001). The median PRC Aβ SUVR was 1.05, based on which the participants were divided into high PRC Aβ SUVR and low PRC Aβ SUVR groups.
Cognitive function scores showed significant differences across all groups. ECog scores were 16.93 ± 5.98 for NC, 18.52 ± 5.59 for SCD, 19.13 ± 7.77 for MCI, and 30.62 ± 10.62 for Dementia (p < 0.001). ADL scores were 20.15 ± 0.77 for NC, 20.28 ± 1.57 for SCD, 20.64 ± 3.48 for MCI, and 24.22 ± 7 for Dementia (p < 0.001). FAQ scores were higher in the Dementia group (6.74 ± 6.75) compared to NC (0.29 ± 0.93), SCD (1 ± 3.35), and MCI (1.13 ± 2.87) (p < 0.001). MoCA‐B scores decreased significantly from NC (26.32 ± 2.11) to Dementia (12.65 ± 4.33) (p < 0.001). ACE‐III scores were 83.5 ± 7.33 for NC, 81.66 ± 7.46 for SCD, 72.58 ± 9.21 for MCI, and 48.47 ± 13.44 for Dementia (p < 0.001).
Memory performance showed significant declines across groups. AVLT scores, including short delay recall, long delay recall, and recognition, progressively worsened from NC to Dementia (all p < 0.001). Similarly, BVMT scores, including short‐delay recall, long‐delay recall, and recognition, demonstrated significant declines from NC to Dementia (all p < 0.001). Language function (VFT, BNT), attention and executive function (STT‐A, STT‐B, SCWT, CaST, DST), and spatial function (ST, JLO) also demonstrated significant declines in performance from NC to Dementia (all p < 0.001). Detailed results are presented in Table 1.
3.2. Correlation of PRC SUVR with local functions and connectivities within the DMN
Selection of PRC and PRC‐adjacent ROIs, including bilateral IPC and PHF, was performed to extract local function metrics. Connectivity within the DMN was classified according to network hubs: PRC connecting the Posterior network, amPFC connecting the Anterior network, and IPC connecting the Superior network. The correlations between PRC Aβ burden and local functions, as well as connectivities within the DMN, varied across groups with high and low PRC Aβ burden (Table 2, Figures 1 and 2).
TABLE 2.
Correlation of PRC SUVR with local functions and connectivities within DMN.
| Group | Local function | r | p (corrected) | Connectivity | r | p (corrected) | |
|---|---|---|---|---|---|---|---|
| High PRC SUVR | |||||||
| NC (n = 95) | ReHo‐lPHF | 0.22 | 0.038(0.094) | ||||
| ReHo‐rPHF | 0.29 | 0.005(0.023) | |||||
| SCD (n = 121) | fALFF‐PRC | −0.22 | 0.017(0.086) | Anterior | amPFC‐lLTC | 0.18 | 0.047(0.378) |
| ReHo‐PRC | −0.19 | 0.035(0.175) | Posterior | PRC‐lLTC | 0.27 | 0.003(0.025) | |
| Posterior | PRC‐rLTC | 0.25 | 0.005(0.025) | ||||
| Posterior | PRC‐lPHF | −0.18 | 0.045(0.134) | ||||
| Superior | lIPC‐rLTC | 0.20 | 0.032(0.208) | ||||
| Superior | rIPC‐rLTC | 0.22 | 0.015(0.195) | ||||
| MCI (n = 251) | ReHo‐lPHF | 0.17 | 0.008(0.042) | Superior | lIPC‐rLTC | −0.15 | 0.021(0.141) |
| ReHo‐rPHF | 0.14 | 0.029(0.072) | Superior | lIPC‐lPHF | −0.15 | 0.022(0.141) | |
| DC‐lPHF | 0.13 | 0.040(0.198) | |||||
| Dementia (n = 157) | fALFF‐rIPC | −0.20 | 0.012(0.060) | Anterior | amPFC‐lPHF | −0.22 | 0.005(0.040) |
| ReHo‐rIPC | −0.20 | 0.012(0.062) | Posterior | PRC‐rIPC | −0.18 | 0.026(0.136) | |
| DC‐rIPC | −0.20 | 0.014(0.068) | Posterior | PRC‐lPHF | −0.17 | 0.030(0.136) | |
| Superior | lIPC‐lPHF | −0.21 | 0.010(0.125) | ||||
| Superior | rIPC‐lPHF | −0.18 | 0.024(0.155) | ||||
| Low PRC SUVR | |||||||
| SCD (n = 92) | fALFF‐lPHF | −0.28 | 0.008(0.042) | ||||
| ReHo‐lIPC | 0.23 | 0.032(0.080) | |||||
| ReHo‐lPHF | −0.25 | 0.017(0.080) | |||||
| DC‐PRC | −0.23 | 0.031(0.154) | |||||
| Dementia (n = 32) | Anterior | amPFC‐lPHF | 0.46 | 0.010(0.079) | |||
| Posterior | PRC‐lPHF | 0.41 | 0.023(0.208) | ||||
Note: Adjusted for age and sex.
Abbreviations: amPFC, anterior medial prefrontal cortex; DC, degree centrality; DMN, default mode network; fALFF, fractional amplitude of low‐frequency fluctuation; IPC, intraparietal cortex; l, left; LTC, lateral temporal cortex; MCI, mild cognitive impairment; NC, normal cognition; PHF, parahippocampal formation; PRC, precuneus; ReHo, regional homogeneity; r, right; SCD, subjective cognitive decline; SUVR, standardized uptake value ratio.
FIGURE 1.

Correlation between PRC Aβ burden and local function of nodes within the DMN. (A) NC group with high PRC Aβ burden. (B) SCD group with high PRC Aβ burden. (C) MCI group with high PRC Aβ burden. (D) Dementia group with high PRC Aβ burden. (E) SCD group with low PRC Aβ burden. Aβ, amyloid‐beta; DC, degree centrality; DMN, default mode network; fALFF, fractional amplitude of low‐frequency fluctuation; lLTC, left lateral temporal cortex; lPHF, left parahippocampal formation; MCI, mild cognitive impairment; NC, normal cognition; PRC, precuneus; ReHo, regional homogeneity; rLTC, right lateral temporal cortex; rPHF, right parahippocampal formation; SCD, subjective cognitive decline; SUVR, standardized uptake value ratio.
FIGURE 2.

Correlation between PRC Aβ burden and local function of nodes within the DMN. (A) Connectivity within the DMN under different cognitive states and PRC Aβ burdens. (B) Correlation between PRC Aβ burden and functional connectivity between nodes within the default mode network. Aβ, amyloid‐beta; amPFC, anterior medial prefrontal cortex; DMN, default mode network; dmPFC, dorsomedial prefrontal cortex; lIPC, left intraparietal cortex; lLTC, left lateral temporal cortex; lPHF, left parahippocampal formation; MCI, mild cognitive impairment; NC, normal cognition; PRC, precuneus; rIPC, right intraparietal cortex; rLTC, right lateral temporal cortex; rPHF, right parahippocampal formation; SCD, subjective cognitive decline; SUVR, standardized uptake value ratio; vmPFC, ventromedial prefrontal cortex.
3.3. High PRC SUVR subgroups
For individuals with high PRC Aβ burden, correlations were observed in the NC group (n = 95) between PRC Aβ burden and local functions, including positive correlations with ReHo in lPHF (r = 0.22, p = 0.038) and rPHF (r = 0.29, p = 0.005). After applying FDR correction, the correlation with ReHo in rPHF remained statistically significant (p = 0.023).
In the SCD group (n = 121), correlations were observed for local functions and connectivities with PRC Aβ burden. Local functions included fALFF in PRC (r = −0.22, p = 0.017) and ReHo in PRC (r = −0.19, p = 0.035). Connectivities included amPFC with lLTC (r = 0.18, p = 0.047), PRC with lLTC (r = 0.27, p = 0.003) and rLTC (r = 0.25, p = 0.005), PRC with lPHF (r = −0.18, p = 0.045), lIPC with rLTC (r = 0.20, p = 0.032), and rIPC with rLTC (r = 0.22, p = 0.015). After applying FDR correction, the connectivities between PRC and both lLTC and rLTC remained statistically significant, with p‐values of 0.025 for both in relation to PRC SUVR.
For the MCI group (n = 251), observed correlations with PRC Aβ burden included ReHo in lPHF (r = 0.17, p = 0.008) and rPHF (r = 0.14, p = 0.029), and DC in lPHF (r = 0.13, p = 0.040). After FDR correction, the correlation with ReHo in lPHF remained significant (p = 0.042). Negative correlations were observed for connectivities such as lIPC with rLTC (r = −0.15, p = 0.021) and lPHF with lIPC (r = −0.15, p = 0.022).
In the Dementia group (n = 157), negative correlations with PRC Aβ burden were found for fALFF in rIPC (r = −0.20, p = 0.012), ReHo in rIPC (r = −0.20, p = 0.012), and DC in rIPC (r = −0.20, p = 0.014). Connectivity correlations with PRC Aβ burden were observed for amPFC with lPHF (r = −0.22, p = 0.005), PRC with rIPC (r = −0.18, p = 0.026) and lPHF (r = −0.17, p = 0.030), lIPC with lPHF (r = −0.21, p = 0.010), and rIPC with lPHF (r = −0.18, p = 0.024). After applying FDR correction, the connectivity between amPFC and lPHF remained significantly correlated with PRC Aβ burden, with a p‐value of 0.040.
3.4. Low PRC SUVR subgroups
For individuals with low PRC Aβ burden, correlations were observed in the SCD group (n = 92) between PRC Aβ burden and local functions such as fALFF in lPHF (r = −0.28, p = 0.008), ReHo in lIPC (r = 0.23, p = 0.032), ReHo in lPHF (r = −0.25, p = 0.017), and DC in PRC (DC‐PRC) (r = −0.23, p = 0.031). After FDR correction, the correlation with fALFF in lPHF remained significant (p = 0.042).
In the Dementia group (n = 32) with low PRC Aβ burden, correlations with PRC Aβ burden were found in connectivities between amPFC and lPHF (r = 0.46, p = 0.010) and between PRC and lPHF (r = 0.41, p = 0.023).
These results indicate varying relationships between PRC Aβ burden and both local function and connectivity within the DMN across different stages of cognitive impairment. Detailed results are presented in Table 2, and Figures 1 and 2. Comparisons of local function and connectivity between groups are presented in Tables S1 and S2. The complete correlations between PRC SUVR and local functions and connectivities are detailed in Tables S3–S6.
3.5. Correlation between local function and connectivity strength within the DMN
In Figure 3, the correlation matrix within the DMN illustrates the relationship between local function and connectivity strength across different groups and levels of PRC SUVR. Here, we analyzed the local function of all ROIs within the DMN as well as their interconnections.
FIGURE 3.

Integration of DMN local function and connectivity under different cognitive states and PRC Aβ burdens. The horizontal axis represents the local function metrics of nodes, and the vertical axis represents functional connectivity between nodes. Aβ, amyloid‐beta; amPFC, anterior medial prefrontal cortex; DC, degree centrality; DMN, default mode network; dmPFC, dorsomedial prefrontal cortex; fALFF, fractional amplitude of low‐frequency fluctuation; lIPC, left intraparietal cortex; lLTC, left lateral temporal cortex; lPHF, left parahippocampal formation; MCI, mild cognitive impairment; NC, normal cognition; PRC, precuneus; ReHo, regional homogeneity; rIPC, right intraparietal cortex; rLTC, right lateral temporal cortex; rPHF, right parahippocampal formation; SCD, subjective cognitive decline; SUVR, standardized uptake value ratio; vmPFC, ventromedial prefrontal cortex.
For individuals with low PRC SUVR, the correlation between local function and connectivity strength gradually weakens from NC to Dementia. This suggests that as cognitive impairment progresses, the relationship between local brain function and its connectivity diminishes in these individuals.
In contrast, for individuals with high PRC SUVR, there is an observed increase in the correlation between local function and connectivity strength in the SCD group. This indicates that the preclinical stage exhibits a stronger relationship between local function and connectivity in individuals with high PRC SUVR. However, from the SCD stage to dementia, the correlation gradually weakens as cognitive impairment progresses to MCI and dementia. This pattern suggests that the initial strengthening of the local function‐connectivity relationship in SCD is followed by a weakening as the disease advances.
Overall, except for the SCD group, the low PRC SUVR subgroups showed lower integration between local function and connectivity compared to the high PRC SUVR subgroups, and this becomes more apparent with cognitive decline. In individuals with low PRC SUVR, the decline in correlation is consistent across the cognitive impairment statuses. In contrast, individuals with high PRC SUVR exhibit a unique pattern where the SCD stage shows an enhanced correlation, which then diminishes as cognitive impairment progresses further. These findings suggest a nuanced interplay between local brain function and connectivity within the DMN, influenced by the level of PRC Aβ burden and the stage of cognitive impairment.
3.6. Correlation of local functions and connectivities within DMN with cognitive function
The DMN function, which is correlated with PRC Aβ deposition, also shows a certain degree of correlation with cognitive function after adjustment for age, sex, and education level (Table 3 and Figure 4).
TABLE 3.
Correlation between local functions and connectivities within DMN and cognition.
| Group | Function | Domain | Indicator | r | p | |
|---|---|---|---|---|---|---|
| Local function | ||||||
| High PRC SUVR | SCD | fALFF‐PRC | Executive | CaST | 0.18 | 0.024 |
| ReHo‐PRC | Executive | CaST | 0.17 | 0.028 | ||
| MCI | ReHo‐lPHF | Executive | STT‐A | 0.12 | 0.029 | |
| Spatial | JLO | −0.15 | 0.014 | |||
| DC‐lPHF | Executive | DST | 0.16 | 0.039 | ||
| Dementia | ReHo‐rIPC | Daily Function | ADL | 0.14 | 0.040 | |
| Daily Function | FAQ | 0.16 | 0.042 | |||
| Executive | DST | −0.30 | 0.035 | |||
| Low PRC SUVR | SCD | DC‐PRC | Memory | AVLT recognition | 0.28 | 0.030 |
| Executive | CaST | 0.30 | 0.008 | |||
| Connectivity | ||||||
| High PRC SUVR | SCD | amPFC‐lLTC | Memory | AVLT recognition | −0.20 | 0.028 |
| lIPC‐rLTC | Spatial | JLO | −0.15 | 0.019 | ||
| rIPC‐rLTC | Spatial | JLO | −0.18 | 0.015 | ||
| MCI | lIPC‐lPHF | Executive | DST | 0.13 | 0.018 | |
| Dementia | amPFC‐lPHF | Executive | CaST | 0.27 | 0.038 | |
| PRC‐rIPC | Executive | SCWT‐time | 0.32 | 0.008 | ||
| PRC‐lPHF | Memory | BVMT short delay recall | 0.30 | 0.027 | ||
| PRC‐lPHF | Memory | BVMT long delay recall | 0.36 | 0.011 | ||
| Low PRC SUVR | Dementia | amPFC‐lPHF | Memory | BVMT short delay recall | 0.33 | 0.049 |
| amPFC‐lPHF | Executive | SCWT | −0.72 | 0.005 |
Note: Adjusted for age, sex, and education.
Abbreviations: ADL, Activities of Daily Living; amPFC, anterior medial prefrontal cortex; AVLT, Auditory Verbal Learning Test; BVMT, Brief Visuospatial Memory Test; CaST, Category Switching Test; DC, degree centrality; DMN, default mode network; DST, Digit Span Test; fALFF, fractional amplitude of low‐frequency fluctuation; FAQ, Functional Activities Questionnaire; IPC, intraparietal cortex; JLO, Judgement of Line Orientation; l, left; LTC, lateral temporal cortex; MCI, mild cognitive impairment; PHF, parahippocampal formation; PRC, precuneus; ReHo, regional homogeneity; r, right; SCD, subjective cognitive decline; SCWT, Stroop Word‐Color Interference Task; STT, Shape Trail Test; SUVR, standardized uptake value ratio.
FIGURE 4.

Correlation of DMN local function and connectivity with cognitive function under different cognitive states and PRC Aβ burdens. Panel A, correlation between local function and cognitive function. Panel B, correlation between connectivity and cognitive function. Aβ, amyloid‐beta; ADL, Activities of Daily Living; amPFC, anterior medial prefrontal cortex; AVLT, Auditory Verbal Learning Test; BVMT, Brief Visuospatial Memory Test; CaST, Category Switching Test; DC, degree centrality; DMN, default mode network; DST, Digit Span Test; fALFF, fractional amplitude of low‐frequency fluctuation; FAQ, Functional Activities Questionnaire; JLO, Judgement of Line Orientation; lIPC, left intraparietal cortex; lLTC, left lateral temporal cortex; lPHF, left parahippocampal formation; MCI, mild cognitive impairment; PRC, precuneus; ReHo, regional homogeneity; rIPC, right intraparietal cortex; rLTC, right lateral temporal cortex; SCD, subjective cognitive decline; SCWT, Stroop Word‐Color Interference Task; STT, Shape Trail Test; SUVR, standardized uptake value ratio.
3.7. Local function
For individuals with high PRC SUVR, correlations were found in the SCD group between fALFF in PRC and CaST (r = 0.18, p = 0.024), and between ReHo in PRC and CaST (r = 0.17, p = 0.028). In the MCI group, correlations were observed between ReHo in lPHF and STT‐A (r = 0.12, p = 0.029) and JLO (r = −0.15, p = 0.014). Additionally, DC in lPHF was correlated with DST (r = 0.16, p = 0.039). In the Dementia group, correlations included ReHo in rIPC with ADL (r = 0.14, p = 0.040), FAQ (r = 0.16, p = 0.042), and DST (r = −0.30, p = 0.035).
For individuals with low PRC SUVR, correlations in the SCD group included DC in PRC with AVLT recognition (r = 0.28, p = 0.030) and CaST (r = 0.30, p = 0.008).
3.8. Connectivity
For individuals with high PRC SUVR in the SCD group, correlations were found between amPFC‐lLTC connectivity and AVLT recognition (r = −0.20, p = 0.028), lIPC‐rLTC connectivity and JLO (r = −0.15, p = 0.019), and rIPC‐rLTC connectivity and JLO (r = −0.18, p = 0.015). In the MCI group, lIPC‐lPHF connectivity was correlated with DST (r = 0.13, p = 0.018). In the Dementia group, correlations were observed between amPFC‐lPHF connectivity and CaST (r = 0.27, p = 0.038), PRC‐rIPC connectivity and SCWT‐time (r = 0.32, p = 0.008), PRC‐lPHF connectivity and BVMT short delay recall (r = 0.30, p = 0.027), and PRC‐lPHF connectivity and BVMT long delay recall (r = 0.36, p = 0.011).
For individuals with low PRC SUVR in the Dementia group, correlations included amPFC‐lPHF connectivity with BVMT short delay recall (r = 0.33, p = 0.049) and SCWT (r = −0.72, p = 0.005).
3.9. Functional changes across cognitive statuses under different PRC Aβ burdens
Figure 5 summarizes the different patterns related to PRC Aβ burden exhibited by NC and SCD, and their association with mild or subtle cognitive impairment.
FIGURE 5.

Patterns related to PRC Aβ burden exhibited by NC and SCD and their associations with cognition. Aβ, amyloid‐beta; NC, normal cognition; MCI, mild cognitive impairment; PRC, precuneus; SCD, subjective cognitive decline.
In NC individuals with high PRC Aβ burden, there are noticeable local functional changes associated with PRC Aβ burden. For SCD individuals under high PRC Aβ burden, changes in functional connectivity associated with PRC Aβ burden become evident. These alterations overlap to some extent with the local functional and connectivity changes seen in MCI individuals with high PRC Aβ burden. However, the local functional changes in NC and SCD individuals with high PRC Aβ burden are not consistent with each other. Additionally, SCD individuals with high PRC Aβ burden exhibit a disorder in the integration of local function and connectivity. These findings suggest that both NC and SCD individuals with high PRC Aβ burden are intrinsically linked to further objective cognitive impairment. However, the neural mechanisms underlying these changes differ, indicating that NC and SCD might not represent sequential stages but rather coexisting heterogeneous preclinical AD states.
Notably, SCD individuals with low PRC Aβ burden also display local functional changes associated with PRC Aβ burden, despite their objective cognitive function remaining within normal ranges. These local functional changes are correlated with subthreshold cognitive impairment.
4. DISCUSSION
Global Aβ deposition in the brain has been suggested to be associated with decreased connectivity and functional decline in the DMN, 39 , 40 , 41 , 42 but the role of Aβ deposition in key regions within the DMN remains unclear. Previous studies emphasized the role of regional tau deposition in AD progression as a marker of disease advancement. 43 , 44 However, some studies have also identified the regional characteristics of Aβ deposition and its role in AD progression. 8 , 9 , 10 , 45 , 46 The PRC is considered a central hub in the brain's neural network, integral for information integration and self‐referential processing. 47 , 48 In the AD continuum, the PRC is one of the regions most affected by Aβ and tau pathologies, which are linked to neural network disruptions and cognitive decline. 49 , 50 , 51 The PRC's connectivity suggests it plays a key role in understanding AD progression and potential therapeutic interventions. 48 , 52 , 53
Our study suggests PRC Aβ deposition increases more than global Aβ as cognitive impairment progresses, indicating its potential as a sensitive marker for monitoring disease progression. Even in NC individuals with high PRC Aβ burden, Aβ deposition in the PRC is associated with changes in local brain activity. Furthermore, correlations between PRC Aβ with local function and connectivity are biphasic. In the SCD stage, the PRC Aβ burden is negatively correlated with local functions, indicating early impairment of local brain function in the PRC. However, positive correlations between PRC Aβ burden and connectivities in regions such as lLTC and rLTC suggest that enhanced DMN functional connectivity might be a response to Aβ deposition and local functional loss. In the MCI stage, the positive correlations of ReHo and DC in the PHF with PRC Aβ burden suggest that early Aβ accumulation in the PRC may lead to neural damage, triggering compensatory mechanisms. These responses may involve enhanced coordination between adjacent neural regions, as observed in the NC group, or increased communication with other brain areas, in an effort to preserve cognitive function. However, the negative correlations between PRC Aβ burden and the superior DMN connectivities indicate a disruption in network integration as cognitive impairment progresses.
The directional differences in the relationships between local neural function, functional connectivity, and PRC Aβ accumulation in SCD and MCI may reflect distinct neural responses to Aβ accumulation during the preclinical and prodromal stages. Researchers have noted the bidirectional changes in brain function associated with increased Aβ burden, which may be related to the brain's antagonistic pleiotropy. 54 , 55 , 56 Our study confirms that the variability in the direction of these functional changes is also related to regional Aβ deposition and cognitive stage.
Functional changes related to PRC Aβ deposition observed during cognitive stages before dementia align with findings from previous studies. These include local function changes in the PHF during MCI, and connectivity changes between amPFC‐LTC, PRC‐LTC, PRC‐PHF, and IPC‐LTC during SCD, as well as connectivity involving the IPC during MCI. Studies in SCD populations have confirmed functional changes in the PRC, 57 hyperconnectivity in DMN network seeds, 58 but reduced connectivity between PRC and hippocampal formation, 59 consistent with our findings. Intervention studies suggest that connectivity involving amPFC, LTC, hippocampal formation, and PRC may improve through cognitive training, making these areas potential targets for enhancing cognitive function. 60 , 61 The parahippocampal formation, significantly affected by AD pathology, 62 shows functional changes that differentiate between converting and nonconverting MCI. 63 Some research links functional enhancement in this region to maintaining executive function under Aβ pathology, 64 though others suggest it may drive further Aβ and tau pathology. 65 While Aβ deposits later in the parietal lobe, 9 , 10 our results show PRC Aβ affects related DMN superior connectivity as early as SCD and MCI stages. Overall, the Aβ burden has complex effects on DMN function, which warrants further exploration of its mechanisms and intervention targets.
Finally, in the dementia group with high PRC Aβ burden, fALFF, ReHo, and DC in the rIPC were negatively correlated with Aβ burden, indicating that the parietal lobe, which is affected later by Aβ accumulation, 9 , 10 also exhibits multiscale functional impairment. Furthermore, the extensive disruption of DMN network connectivity further emphasizes the severe impact of Aβ burden in the late stages of cognitive decline.
The cognitive performance further illustrates the significance of these changes. In the SCD group, lower PRC local function is associated with poorer executive function, indicating that increased local Aβ burden in the PRC impairs executive function by disrupting local brain activity. Negative correlations between anterior and superior DMN connectivity with memory and spatial functions indicate that early network integration is linked to cognitive decline. This suggests that increased PRC Aβ burden causes distinct changes in both local function and connectivity, contributing to subthreshold cognitive decline. In the MCI population, the enhancement of local function is associated with compensation for attention and executive function. However, connectivity generally weakens and is linked to impaired executive function.
Interestingly, our study found that in individuals with low PRC Aβ burden, correlations were observed in the SCD group between PRC Aβ burden and DMN functions. This indicates that even subthreshold increases in Aβ at early stages can disrupt neural function. The correlation analysis with cognitive function shows that impaired function associated with low levels of Aβ increase is related to relatively poorer memory and executive function. Additionally, in the Dementia group, enhanced anterior and posterior local functional connectivity associated with low levels of Aβ burden was also observed, further suggesting that subthreshold Aβ deposition may have some physiological or pathological significance. Research shows that even low Aβ levels affect brain function, and early Aβ deposition is linked to cognitive decline and may signal the onset of neurodegeneration. 66 , 67 , 68
Additionally, our study found that from NC and SCD to MCI, changes in local function differ from those in functional connectivity. The distinction between local function and connectivity changes may suggest two different Aβ‐related pathways to cognitive impairment. These distinct mechanisms may be linked to the decoupling of local metabolism and functional connectivity under Aβ burden. 69 Such decoupling of local function and connectivity within the DMN may be a key feature of AD pathophysiology. 65 The correlation between local function and network connectivity is significant as it reflects the integrity and efficiency of neural networks. 70 Our findings suggest that under a low PRC Aβ burden, neural coupling deteriorates more uniformly, whereas a high PRC Aβ burden initially triggers compensatory mechanisms that eventually fail, leading to neural coupling breakdown. This result helps us understand the disruption pattern of PRC Aβ deposition on the coupling between local function and connectivity strength within the DMN.
An important finding in our study is that in the NC group, local functional changes associated with high PRC Aβ burden overlap with those in MCI‐affected regions. In contrast, the SCD group shows connectivity changes in the superior DMN that overlap with MCI, but in the opposite direction. This suggests that functional connectivity changes might be a key neural mechanism in the transition from SCD to MCI, differing from NC. Therefore, in preclinical AD individuals with high Aβ burden, SCD and NC may represent heterogeneous states, implying different pathways to MCI conversion.
Our findings highlight the importance of early detection and monitoring of Aβ deposition in key regions such as the PRC and elucidate its potential neural mechanisms through which it affects cognitive function via the DMN. If confirmed by longitudinal studies, these results could inform early intervention strategies aimed at preserving brain network function. With recent evidence suggesting that cognitive activities can modulate the DMN, 60 and the availability of amyloid‐targeting therapies, 71 , 72 there is potential to combine pharmacological and non‐pharmacological interventions to slow cognitive decline and maintain neural connectivity.
4.1. Limitations
This study has several limitations. The cross‐sectional design limits causal inferences between Aβ burden and cognitive decline, highlighting the need for longitudinal studies to establish the temporal sequence of Aβ deposition and its effects on brain function and connectivity. There are some confounding factors in this study. Although we adjusted for key demographic variables such as age, education, and sex, these and other unmeasured confounding factors may still influence the results. Future research with more diverse cohorts and multimodal imaging (eg, tau deposition, neuroinflammation) will help address these limitations and improve generalizability. The median‐based cutoff for high/low Aβ groups introduces potential limitations in interpretability; future studies should explore more refined amyloid, tau, and neurodegeneration (ATN) biomarkers for the PRC. Furthermore, focusing solely on the DMN and PRC may overlook other relevant brain networks. Lastly, multiple comparisons increase the risk of false positives, and uncorrected results should be interpreted with caution. Larger studies with more focused hypotheses are needed to confirm these findings and reduce the impact of multiple comparisons.
5. CONCLUSION
This study shows that the PRC Aβ burden is associated with changes in neural function and connectivity within the DMN. In the early stages, increased PRC Aβ deposition leads to bidirectional changes in local function and connectivity, eventually causing DMN collapse in later stages. Even subthreshold PRC Aβ increases are linked to brain function changes. PRC Aβ deposition has potential as a biomarker for both early detection and continuous monitoring of AD.
CONFLICT OF INTEREST STATEMENT
The authors declare that they have no conflicts of interest. Author disclosures are available in the supporting information
CONSENT STATEMENT
The study was reviewed and approved by the Ethics Committee of Shanghai Sixth People's Hospital (approval number 2019‐041). It was performed in accordance with the principles of the Declaration of Helsinki. All participants provided written informed consent to participate in the study.
Supporting information
Supporting Information
Supporting Information
ACKNOWLEDGMENTS
We would like to thank Jie‐Hua Zhu, Xian‐Qing Xie, and Yun Yang for their help with neuropsychological tests. This study was funded by the National Natural Science Foundation of China (82171198, 62303295), the Shanghai Municipal Science and Technology Major Project (2018SHZDZX01), and the Shanghai Municipal Health Commission (202140042).
Cui L, Zhang Z, Tu Y‐Y, et al. Association of precuneus Aβ burden with default mode network function. Alzheimer's Dement. 2025;21:e14380. 10.1002/alz.14380
Liang Cui and Zhen Zhang contributed equally to this work.
Contributor Information
Yue‐Hua Li, Email: liyuehua312@163.com.
Fang Xie, Email: fangxie@fudan.edu.cn.
Qi‐Hao Guo, Email: qhguo@sjtu.edu.cn.
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