研究

Connectomic analysis of Alzheimer’s disease
using percolation theory

Parker Kotlarz1

, Juan C. Nino1*

, and Marcelo Febo2*

1Department of Materials Science and Engineering, University of Florida, Gainesville, FL, 美国
2Department of Psychiatry, University of Florida, Gainesville, FL, 美国
*J. Nino and M. Febo are co-senior authors.

关键词: 阿尔茨海默氏病, Connectomics, Percolation theory, Biomarker, 功能磁共振成像, Graph theory

开放访问

杂志

抽象的

阿尔茨海默氏病 (广告) is a severe neurodegenerative disorder that affects a growing worldwide
elderly population. Identification of brain functional biomarkers is expected to help determine
preclinical stages for targeted mechanistic studies and development of therapeutic interventions to
deter disease progression. Connectomic analysis, a graph theory–based methodology used in the
analysis of brain-derived connectivity matrices was used in conjunction with percolation theory
targeted attack model to investigate the network effects of AD-related amyloid deposition. We used
matrices derived from resting-state functional magnetic resonance imaging collected on mice
with extracellular amyloidosis (TgCRND8 mice, n = 17) and control littermates (n = 17). 全球的,
nodal, 空间的, and percolation-based analysis was performed comparing AD and control mice.
These data indicate a short-term compensatory response to neurodegeneration in the AD brain via a
strongly connected core network with highly vulnerable or disconnected hubs. Targeted attacks
demonstrated a greater vulnerability of AD brains to all types of attacks and identified progression
models to mimic AD brain functional connectivity through betweenness centrality and collective
influence metrics. 此外, both spatial analysis and percolation theory identified a key
disconnect between the anterior brain of the AD mice to the rest of the brain network.

作者总结

Accurate biomarkers of Alzheimer’s disease (广告) are needed for early diagnosis and
treatments. Connectomic analysis, a graph theory approach, coupled with percolation theory,
a network attack approach, were applied here to analyze neuroimaging through a quantitative
lens. We report a marker of AD vulnerability, which highlighted a core network disconnected
from key hubs, notably within the anterior portion of the brain disconnected. 此外,
preliminary models using targeted attacks provide potential pathways of neurodegeneration
from the control state to the diseased state. These findings show key differences in brain
connectivity due to AD and provide a potential methodology for identifying biomarkers.

介绍

阿尔茨海默氏病 (广告) is a neurodegenerative disorder that accounts for 60%–80% of cases
of dementia with typical symptoms involving memory loss, confusion, changes in personality,
social withdrawal, and language difficulties (2020 Alzheimer’s Disease Facts and Figures,

引文: Kotlarz, P。, Nino, J. C。, & Febo,
中号. (2022). Connectomic analysis of
Alzheimer’s disease using percolation
理论. 网络神经科学, 6(1),
213–233. https://doi.org/10.1162/netn_a
_00221

DOI:
https://doi.org/10.1162/netn_a_00221

支持信息:
https://doi.org/10.1162/netn_a_00221

已收到: 15 九月 2021
公认: 8 十二月 2021

利益争夺: 作者有
声明不存在竞争利益
存在.

通讯作者:
Parker Kotlarz
kotlarz.parker@ufl.edu

处理编辑器:
奥拉夫·斯波恩斯

版权: © 2021
麻省理工学院
在知识共享下发布
归因 4.0 国际的
(抄送 4.0) 执照

麻省理工学院出版社

我

D
哦
w
n
哦
A
d
e
d

F
r
哦
米
H

t
t

p

:
/
/

d
我
r
e
C
t
.

米

我
t
.

/

/

t

e
d
你
n
e
n
A
r
t
我
C
e
–
p
d

我

F
/

/

/

/

/

6
1
2
1
3
2
0
0
2
4
2
8
n
e
n
_
A
_
0
0
2
2
1
p
d

t

.

F

乙
y
G
你
e
s
t

t

哦
n
0
7
S
e
p
e
米
乙
e
r
2
0
2
3

Connectomic analysis of Alzheimer’s disease using percolation theory

2020). Sporadic nonfamilial forms of AD affect 5.8 million people in the United States aged
65 years or older, and this population is estimated to rise to about 13.8 百万 2050
(Hebert et al., 2013). Major risk factors for familial AD include genetics (Bertram et al.,
2010; Farrer et al., 1997) and previous family history (Mayeux et al., 1991; Yi et al., 2018),
while age and apolipoprotein-E status are risk factors for sporadic late-onset AD that accounts
超过 95% of all cases (Hebert et al., 2013; Koffie et al., 2012; Launer et al., 1999). Due to
AD’s progressive nature, different stages of AD show variations in the severity of symptoms.
例如, preclinical AD entails measurable brain functional changes with few or no symp-
toms, mild cognitive impairment (MCI) with more pronounced brain alterations and mild
symptoms, and AD with dementia with significant symptomology and brain structural changes
(Sperling et al., 2011). Through this progression model, identification of features that distin-
guish preclinical AD from other stages is important for timely therapeutic intervention and
the targeting of stage-specific biological factors that may delay the progression of AD and
its symptoms (Bakker et al., 2015; Crous-Bou et al., 2017). Identifying biomarkers in patients
who are likely to develop AD through cerebrospinal fluid (CSF) tests and radioligand-based
neuroimaging techniques are serving as a major clinical resource to understand and treat
AD before it progresses significantly (Frisoni et al., 2017). 然而, CSF tests are invasive
for patients, have the possibility of introducing infection into the central nervous system,
and cannot always be performed. 此外, positron emission tomography neuroimaging
techniques can serve as a more clinically applicable approach for identifying biomarkers,
but these are limited by the amount of exposure to radiolabeled compounds. 反过来, mag-
netic resonance (MRI)-based biomarkers, particularly using approaches that interrogate the
brain’s white matter and functional connectomic patterns, are highly valuable due to their
安全的, noninvasive nature, and because there are several national and international data repos-
itories that can be used to investigate lead biomarkers that have clinical importance.

One encouraging approach at identifying potential biomarkers in AD is through the field
of functional connectomics. Major advancements in brain mapping techniques, 例如
functional MRI (功能磁共振成像), allow for comprehensive and quantitative assessments of functional
connectivity in the human brain (Milano et al., 2019). Functional connectivity measures the
co-activation between the activity of different brain regions (弗里斯顿, 1994). Functional con-
nectomics uses data derived from imaging modalities to create adjacency matrices (网络
of nodes and edges), or connectomes, that are then analyzed with broadly applicable math-
ematical principles of graph theory (鲁比诺夫 & 斯波恩斯, 2010). Through network analysis, A
growing range of quantifiers can be explored to understand local and global brain connectivity
图案. Connectomic analysis can also be applied to compare differences between brains
through statistical (Shehzad et al., 2014), quantifier-based (Pompilus et al., 2020), 和
machine learning techniques (Sarwar et al., 2021). Previous functional connectomic analysis
in rodent models have found anatomical motifs (Díaz-Parra et al., 2017), rich-club organiza-
的 (Liang et al., 2018), and contextual changes in network topology (Pompilus et al., 2020).
此外, connectomics has yielded promising results in understanding and identifying
biomarkers in AD with an increasing focus on utilizing functional connectivity (Alderson
等人。, 2018; Brier et al., 2012; Damoiseaux et al., 2012; Filippi et al., 2020; Khazaee et al.,
2015; Ren et al., 2020; Ye et al., 2019).

In the present study we used a network analysis approach based on percolation theory, A
subbranch of graph theory that involves removing (or adding) nodes or edges to assess their
importance or influence on overall network integrity (阿尔伯特 & 巴拉巴斯, 2002). Percolation
theory has been proposed as a model to determine network resilience and possibly inform
on the stages of neurodegenerative progression of diseases such as AD (Fornito et al., 2015;

Connectomics:
Graph theory–based methodology
that involves deconstructing the
brain into mathematical matrices.

Functional connectivity:
Measure of the coactivation of
different brain regions.

Graph theory:
Mathematical approach to studying
relationships between structures
(节点) through their connections
(边缘).

Quantifier:
Mathematical descriptor based on a
relationship in the network.

Percolation theory:
Subbranch of graph theory that
analyzes the removal of nodes/edges
of a network.

网络神经科学

214

我

D
哦
w
n
哦
A
d
e
d

F
r
哦
米
H

t
t

p

:
/
/

d
我
r
e
C
t
.

米

我
t
.

/

/

t

e
d
你
n
e
n
A
r
t
我
C
e
–
p
d

我

F
/

/

/

/

/

6
1
2
1
3
2
0
0
2
4
2
8
n
e
n
_
A
_
0
0
2
2
1
p
d

.

t

F

乙
y
G
你
e
s
t

t

哦
n
0
7
S
e
p
e
米
乙
e
r
2
0
2
3

Connectomic analysis of Alzheimer’s disease using percolation theory

Lo et al., 2015). Percolations model either random network failure via indiscriminate deletions
of individual nodes or edges, or it can use a planned or targeted attack strategy in which node
removal is guided by quantifiers that rank node prominence within the network. Through these
random and targeted attacks, the resilience of the network can be measured through quanti-
fiers reflecting network integrity (largest cluster size) (Albert et al., 2000) and communication
efficiency (path length) (Achard et al., 2006; Kaiser et al., 2007). Given evidence of disrupted
synaptic communication in amyloid mouse models and functional connectivity in the pres-
ence of high amyloid load in AD (Myers et al., 2014), information on network resilience
through the use of percolation theory may provide a robust biomarker for early detection
and progression in AD. Such models of network resilience are currently underdeveloped in
广告 (Mrdjen et al., 2019), but their optimization and testing may lead to the discovery of
key network epicenters as identified in AD propagation studies (Zhou et al., 2012). In the pres-
ent proof-of-concept study, we applied graph theory to analyze functional connectivity net-
works derived from the TgCRND8 mouse model of amyloidosis and control mice of the same
background strain (Colon-Perez et al., 2019) (数字 1). In addition to providing a spatial neu-
roanatomical analysis of the distribution of network quantifiers, we used percolation theory to
investigate network resilience as a function of amyloid status.

我

D
哦
w
n
哦
A
d
e
d

F
r
哦
米
H

t
t

p

:
/
/

d
我
r
e
C
t
.

米

我
t
.

方法

Description of Node-Based Functional Connectivity Data

The functional connectivity adjacency matrices analyzed in the present work were part of a
larger study originally published by Colon-Perez et al. (2019). 还, the methods used for
image acquisition and image processing, the brain regions included in the present analysis,
and the generation of the adjacency matrices were published in the original study (Colon-
Perez et al., 2019). 所以, no new data were collected for the present study, 其中重点
on novel analyses of resting-state fMRI data collected previously. Briefly, in the prior original
学习, TgCRND8 mice were bred via transgenic (Tg) males (carrying amyloid precursor

t

/

/

e
d
你
n
e
n
A
r
t
我
C
e
–
p
d

我

F
/

/

/

/

/

6
1
2
1
3
2
0
0
2
4
2
8
n
e
n
_
A
_
0
0
2
2
1
p
d

.

t

F

乙
y
G
你
e
s
t

t

哦
n
0
7
S
e
p
e
米
乙
e
r
2
0
2
3

数字 1. Overview of connectomic analysis.

网络神经科学

215

Connectomic analysis of Alzheimer’s disease using percolation theory

蛋白质) with C57B6/C3H F1 females (Envigo) (Janus et al., 2000). 此外, mice were
subject to intracerebroventricular adeno-associated viral vector interleukin-6 (IL6) injections
at P0, which led to brain expression of murine IL6 or enhanced green fluorescent protein as
described in Chakrabarty et al. (2010). In this original study by Colon-Perez et al. (2019), 功能磁共振成像
images were collected through a single-shot spin-echo echo planar imaging sequence (=
15 多发性硬化症, TR = 2 s, 180 repetitions, 15 × 11 mm in plane, 14 slices with 0.9-mm thickness per
slice, data matrix = 64 × 48) using a 11.1 T MRI scanner. fMRI image processing included (1)
removal of time series spikes, (2) slice timing correction, (3) motion and linear drift correction,
(4) subject-to-atlas registration, (5) regression of white matter and CSF (ventricle) signals, (6)
bandpass filtering (0.01–0.1 Hz), 和 (7) spatial blurring (0.3 mm FWHM). 最后, average
BOLD signals were extracted based on their atlas location, 创造 4,005 pairwise Pearson
correlation coefficients.

We used a subset of data collected on mice with extracellular amyloidosis (TgCRND8
老鼠, n = 17, male = 6, female = 11) and control littermates (n = 17, male = 9, female = 8).
For clarity of data presentation, we refer to the TgCRND8 mouse as ‘AD mice’ and nontrans-
genic mice as ‘control mice’ throughout the manuscript. As described in the original study,
TgCRND8 mice have early-onset expression of human mutant APP (Swedish APP
KM670/671NL and Indiana APP V717F), which increases human APP five times above endog-
enous murine APP. These mice have cognitive impairment, Aβ plaque deposits, and increased
inflammation at 3–4 months of age, synaptic deficits, and some synaptic and neuronal loss in
the hippocampus by 6 月. (Chishti et al., 2001). The mice were 8 months old at the time of
成像. Subsets of mice had additional experimental manipulations such as viral vector
administration into the brain at postnatal day 0 and increased brain expression of the cytokine,
IL6. 然而, we focus on the distinction between the two main groups to investigate the
ability of network quantifiers to discern differences as a function of amyloid status.

Matrix Manipulation and Processing

To address subject-specific differences in the location of nodes with strong and weak connec-
tions across matrices, which can impact results even after controlling for graph density, we first
assessed general characteristics of the targeted attack approach in group-averaged matrices
and then conducted separate statistical comparisons on quantifiers drawn from individually
prethresholded matrices. For group-averaged comparisons, weighted matrices were first aver-
aged within each group and then normalized and thresholded at 10% graph density. 这
threshold removed weak and negative edges and kept small-world characteristics during
group comparisons. A 10% graph density was chosen, as thresholds below 10% produced
networks that were too fragmented to differentiate and upper graph densities (>10%) 显示
similar trends as 10% but with differences less apparent. This group-averaged approach high-
lighted stable and strong connections that were generally consistent with connections in
individual-level analyses and thus served as a representative model for each group. 尽管
group-averaged comparisons have been utilized in previous studies, (Brown et al., 2012;
哈格曼等人。, 2008; Perry et al., 2015; 史密斯等人。, 2013), it is important to note that
individual-specific weak connections will unavoidably be omitted from analyses (Amico &
戈尼, 2018; Gordon et al., 2017; Roberts et al., 2017).

Network Quantifier and Statistical Analysis

Weighted global and nodal quantifiers were applied to both the individual and group-
averaged matrices. Global quantifiers examine aspects of the network as a whole. Largest clus-
ter size and graph density were calculated to understand network composition. Measures of

Graph density:
Measure of how many overall
connections are present out of
possible connections in a network.

Group-averaged:
Method of averaging matrices
together to eliminate weak edges
while keeping core network
特征.

Small-world:
Organized network whereby any
node can reach another node in a
short sequence of edges.

网络神经科学

216

我

D
哦
w
n
哦
A
d
e
d

F
r
哦
米
H

t
t

p

:
/
/

d
我
r
e
C
t
.

米

我
t
.

/

/

t

e
d
你
n
e
n
A
r
t
我
C
e
–
p
d

我

F
/

/

/

/

/

6
1
2
1
3
2
0
0
2
4
2
8
n
e
n
_
A
_
0
0
2
2
1
p
d

t

.

F

乙
y
G
你
e
s
t

t

哦
n
0
7
S
e
p
e
米
乙
e
r
2
0
2
3

Connectomic analysis of Alzheimer’s disease using percolation theory

Betweenness centrality:
Quantifies how often a node lies
within a shortest path of the network.

Collective influence:
Optimal percolation method through
targeting region connecting nodes.

integration that analyze how network information flows efficiently include characteristic path
length (CPL) (Watts & Strogatz, 1998), network radius, network diameter, and global efficiency
(Latora & Marchiori, 2001). CPL is characterized by the average shortest path, or the number of
边缘, between all the nodes in the network (Watts & Strogatz, 1998). This quantifier details
possible routes of transmission of information of data in the network by measuring functional
integration of the network, with smaller CPLs indicating a more integrated network. 全球的
efficiency (Latora & Marchiori, 2001), the inverse of CPL, also measures integration and
may be more valuable in disconnected networks, like those observed in the present study,
due to the ability of this quantifier to account for disconnected nodes (鲁比诺夫 & 斯波恩斯,
2010). For CPL, global efficiency, network radius, and network diameter, diagonal and infinite
distances were omitted to prevent infinite values since thresholding and attacking the networks
create network fragments. Measures of segregation that examine how the network is separated
into different functional modules or groups include maximized modularity (纽曼, 2006)
and transitivity (纽曼, 2003). Assortativity (Leung & Chau, 2007; 纽曼, 2002), a mea-
sure of resilience, was also calculated. Nodal quantifiers examine individual nodes and their
role in the network. Quantifiers that measure nodal characteristics include degree centrality
(直流) measuring the number of connections and strength (英石) which measures the total sum of
edge weights connected to a node. Nodal measures of segregation examine how individual
nodes function within groups include clustering coefficient (CC) (Onnela et al., 2005; Watts &
Strogatz, 1998) and local efficiency (LE) (Latora & Marchiori, 2001). Measures of centrality
which explore how nodes interact with the rest of the brain include eigenvector centrality
(EC) (纽曼, 2016), participation coefficient (PC) (Guimerà & Amaral, 2005), 和之间-
ness centrality (BC) (弗里曼, 1978). The quantifiers above were calculated using MATLAB’s
Brain Connectivity Toolbox (MATLAB. Version 9.7.0.1319299, R2019b; 鲁比诺夫 & 斯波恩斯,
2010), and a detailed list of equations and derived information from the associated measures
above can be found extensively detailed from Rubinov and Sporns (2010). In addition to the
previously stated quantifiers, collective influence and small worldness were also calculated.
Collective influence (CI), a novel quantifier that ranks nodes by using an optimized percola-
tion method designed to break up major network components (Morone et al., 2016; Morone &
Makse, 2015), was calculated using ComplexCi in C++ (F. 朱, 2018) and transferred to
MATLAB for further analysis. 此外, small worldness (汉弗莱斯 & Gurney, 2008), A
global measure that identifies high clustering with a short CPL compared to a random network,
was also calculated using MATLAB.

Statistical analysis was conducted to compare control and AD mouse networks. Global and
nodal quantifiers were examined across groups. Using JMP ( JMP, Version Macintosh; SAS Insti-
tute Inc., Cary, NC, 1989–2019), the normality of the data was examined. Since different quan-
tifiers displayed different degrees of normality, especially in the nodal group quantifiers, 这
Wilcoxon rank-sum test was used to test for statistical significance since it is a more conser-
vative approach that does not require the assumption of normality. 此外, using non-
parametric tests such as the Wilcoxon rank-sum test is shown to be more appropriate for
smaller studies (Fagerland, 2012). This test does not require normality and is also resistant
to outliers. Effect sizes (r), calculated by dividing the test statistic by the square root of the
number of samples, are also reported for significant values.

Spatial Analysis Using Brain Net Viewer

Nodal quantifiers were compared regionally using nodes generated using a mouse brain par-
cellation and template (Moore et al., 2016). Spatial analysis through BrainNet Viewer (Xia
等人。, 2013), a graphical tool that overlays network nodes and connections on 3D brain

网络神经科学

217

我

D
哦
w
n
哦
A
d
e
d

F
r
哦
米
H

t
t

p

:
/
/

d
我
r
e
C
t
.

米

我
t
.

/

/

t

e
d
你
n
e
n
A
r
t
我
C
e
–
p
d

我

F
/

/

/

/

/

6
1
2
1
3
2
0
0
2
4
2
8
n
e
n
_
A
_
0
0
2
2
1
p
d

t

.

F

乙
y
G
你
e
s
t

t

哦
n
0
7
S
e
p
e
米
乙
e
r
2
0
2
3

Connectomic analysis of Alzheimer’s disease using percolation theory

型号, was used to visualize the group-average control and AD mouse brains. To analyze
shared connections, the weighted averaged matrices were binarized and then subtracted to
create a matrix to input into BrainNet Viewer. Through BrainNet Viewer, between-region
and within-region brain connectivity were analyzed and specific modules, 节点, 和骗局-
nections were highlighted.

Network Targeted Attacks and Progression Analysis

The control and AD mouse networks were subsequently analyzed using targeted node
removal involving selectively removing nodes from the connectivity matrix by changing all
connections for that node to zero based on a specific nodal quantifier until the network
was completely degraded. After each attack, global and nodal network quantifiers were cal-
culated for the new network to analyze for progressive change. There were two categories of
attack methods: basis and iterative. Basis attacks used the initially calculated quantifier of the
unaltered matrix to remove nodes. Iterative attacks continually recalculated the quantifier on
the new network after each node removal. Strength, degree centrality, betweenness centrality,
eigenvector centrality, clustering coefficient, local efficiency, and participation coefficient
were included using both basis and iterative attack schemes. Collective influence was utilized
only as a basis attack scheme due to its high computational cost. 此外, a random attack
scheme was also conducted that removed nodes at random. A limitation to both the random
and basis attack schemes involves removing nodes that already are disconnected. Since these
attack schemes do not continually update like the iterative attack schemes, they have the pos-
sibility of removing a node that has already previously been disconnected. This limitation did
not appear to have a significant effect on our results. The response to different attack schemes
was compared between control and AD mice. 此外, attack schemes in healthy mice
were compared to initial quantifiers in AD mice to examine if any attack schemes model dis-
ease development.

结果

Global Network Characteristics

Global network measures were determined for both individual and group-averaged matrices.
桌子 1 summarizes the global network quantifiers for control and AD mice. No differences
between these groups were observed in either individual or group-averaged network quanti-
fiers (IE。, quantifiers from group-averaged matrices were within bounds of quantifiers analyzed
across individual subjects; 见表 1). This result provided evidence of consistency between
individual and group-wise analyses and suggested that the latter accurately represents network
特性. A difference in betweenness centrality was observed between the networks of indi-
vidual AD mice (113.72) and the group-average brain of the same group (44.18). This differ-
ence most likely stems from an emphasis on stronger and consistent stable connections across
subjects (a ‘core’ network) by preaveraging individual matrices prior to calculating network
量词. Within groups, there were also no significant differences between male and female
functional networks.

There were significant differences in CPL ( p = 0.0138, r = 0.419), efficiency ( p = 0.0138,
r = 0.419), diameter ( p = 0.0045, r = 0.484), and average strength ( p = 0.0167, r = 0.408)
between control and AD mice. In the group-average groups, there were notable differences
in the same quantifiers and also in largest cluster size, assortativity, and average betweenness
centrality. For all groups, the average degree was 8.911 with a graph density of 0.1001 作为一个
result of the 10% graph density thresholding method. Both group average and individuals as a

网络神经科学

218

我

D
哦
w
n
哦
A
d
e
d

F
r
哦
米
H

t
t

p

:
/
/

d
我
r
e
C
t
.

米

我
t
.

/

t

/

e
d
你
n
e
n
A
r
t
我
C
e
–
p
d

我

F
/

/

/

/

/

6
1
2
1
3
2
0
0
2
4
2
8
n
e
n
_
A
_
0
0
2
2
1
p
d

.

t

F

乙
y
G
你
e
s
t

t

哦
n
0
7
S
e
p
e
米
乙
e
r
2
0
2
3

0.361

0.151

62.0

7.19

0.164

1.07

16.5

−0.0146

0.120

2.62

44.2

0.642

0.185

0.514

0.0138*

0.0138*

0.0943

0.0045**

0.438

0.134

0.0167*

0.301

0.459

0.0820

0.931

我

D
哦
w
n
哦
A
d
e
d

F
r
哦
米
H

t
t

p

:
/
/

d
我
r
e
C
t
.

米

我
t
.

/

/

t

e
d
你
n
e
n
A
r
t
我
C
e
–
p
d

我

F
/

/

/

/

/

6
1
2
1
3
2
0
0
2
4
2
8
n
e
n
_
A
_
0
0
2
2
1
p
d

.

t

Connectomic analysis of Alzheimer’s disease using percolation theory

Quantifier
Small worldness

控制 (Ind.)
1.81 ± 0.0844 (0.348)

控制 (Avg.)
1.43

Alzheimer (Ind.)
1.76 ± 0.111 (0.457)

Alzheimer (Avg.)
2.07

P value
0.877

桌子 1. Global network quantifiers across groups

模块化

Transitivity

0.374 ± 0.0208 (0.0856)

0.381

0.356 ± 0.0255 (0.105)

0.113 ± 0.0159 (0.0654)

0.0684

0.163 ± 0.0275 (0.113)

Largest cluster size

83.8 ± 2.916 (12.0)

CPL

11.7 ± 0.889 (3.66)

81.0

20.4

80.8 ± 3.29 (13.6)

8.40 ± 0.753 (3.12)

Global efficiency

0.117 ± 0.0123 (0.0509)

0.0667

0.167 ± 0.0197 (0.0811)

Radius

Diameter

13.1 ± 2.03 (8.35)

26.4 ± 1.71 (7.06)

2.89

64.8

9.22 ± 1.68 (6.92)

19.3 ± 1.72 (7.08)

Assortativity

0.221 ± 0.0334 (0.138)

0.246

0.195 ± 0.0367 (0.151)

Avg. CC

Avg. 英石

Avg. BC

Avg. EC

Avg. LE

Avg. PC

0.0875 ± 0.0107 (0.0441)

0.0560

0.116 ± 0.0154 (0.0635)

2.23 ± 0.179 (0.737)

1.42

3.05 ± 0.266 (1.10)

127 ± 9.55 (39.4)

151

113 ± 9.97 (41.1)

0.0683 ± 0.00232 (0.00958)

0.0669

0.0728 ± 0.00329 (0.0136)

0.0718

0.117 ± 0.0124 (0.0509)

0.0753

0.152 ± 0.0161 (0.0663)

0.357 ± 0.0270 (0.111)

0.306

0.362 ± 0.0334 (0.138)

0.150

0.128

笔记. Data are presented as mean ± standard error. Standard deviation values are shown in parentheses. Wilcoxon’s rank-sum test used to compare control vs.
AD mice. CPL = characteristic path length; CC = clustering coefficient; ST = strength; BC = betweenness centrality; EC = eigenvector centrality; LE = local
efficiency; PC = participation coefficient. Ind, individual analysis = indicative of quantifiers calculated on individual subject matrices. Avg, group-average
analysis = indicative of quantifiers calculated after subject matrices were first averaged.
* p < 0.05. ** p < 0.01. f b y g u e s t t o n 0 7 S e p e m b e r 2 0 2 3 group of both control and AD brain networks had a heavy-tailed degree distribution with the group-averaged diseased brain containing a significantly longer tail. Brain Connectivity Characteristics Nodal network characteristics. Table 2 summarizes the anatomical locations of nodes with sig- nificant differences in nodal quantifiers between control and AD mice with nodes visualized in Figure 2. There were no significant differences between nodal quantifiers for individualized and group-averaged brains for each respective group. No nodes had significant differences in participation coefficients. Notably, both the left ventral thalamic tier and mesencephalic reticular formation nodes had significant differences in all nodal quantifiers except for betweenness centrality. Other nodes that were significantly different in multiple categories included the left retrosplenium, left rostral piriform cortex, left dorsal striatum, and right lateral tier of the thalamus. In their respective groups, the left and right sides of the brains had very few significant differences: betweenness centrality in AD cerebellar peduncle ( p = 0.0371, r = 0.354), betweenness centrality in control mouse amygdala ( p = 0.0403, r = 0.349), clustering coefficient in AD entorhinal ( p = 0.494, r = 0.334), and degree centrality in AD mouse sub- stantia nigra ( p = 0.0412, r = 0.347). Network Neuroscience 219 t N e w o r k N e u r o s c e n c e i Nodal location Control (Ind.) Control (Avg.) Alzheimer (Ind.) Alzheimer (Avg.) P value (Ind.) Effect size Table 2. Node locations with significant differences in nodal quantifiers Ventral thalamic tier L. 6.94 ± 1.12 (4.60) Retrosplenium L. 10.4 ± 1.19 (4.91) Piriform rostral L. 9.29 ± 2.12 (8.73) Mesencephalic Reticular 10.4 ± 1.85 (7.61) formation L. 4 4 12 13 Degree centrality 13.1 ± 1.79 (7.37) 6.41 ±1.33 (5.47) 13.0 ± 2.28 (9.38) 18.2 ± 2.27 (9.38) Betweenness centrality Retrosplenium L. 171.65 ± 35.14 (144.88) Prelimbic L. 125.76 ± 24.00 (98.91) Insular rostral R. 160.59 ± 38.48 (158.65) Cerebellar peduncle R. 286.24 ± 36.23 (149.39) 6 576 530 152 77.178 ± 21.017 (86.89) 56.24 ± 17.67 (72.84) 60.82 ± 15.50 (63.91) 18 2 20 37 0 0 0 172.82 ± 35.50 (146.38) 192 Eigenvector centrality 0.0093** 0.0171* 0.0431* 0.0107* 0.0375* 0.0164* 0.0305* 0.0287* Ventral thalamic tier L. 0.0421 ± 0.0122 (0.0505) 0.0213 0.126 ± 0.0190 (0.0748) 0.159 0.0036** Retrosplenium L. 0.0770 ± 0.0196 (0.0810) 0.0236 0.0430 ± 0.0164 (0.0676) 1.36E-29 Mesencephalic reticular 0.0751 ± 0.0214 (0.0882) 0.0974 0.152 ± 0.0241 (0.0992) 0.252 formation L. Amygdala R. 0.0721 ± 0.0193 (0.0794) Ventral thalamic tier R. 0.0561 ± 0.0152 (0.0628) 0.0931 0.0588 0.124 ± 0.0198 (0.0814) 0.124 ± 0.0231 (0.0953) Local efficiency Dorsal striatum L. 0.0944 ± 0.0254 (0.105) 0.0805 0.187 ± 0.0375 (0.155) Ventral thalamic tier L. 0.0818 ± 0.0212 (0.0874) 0.123 0.218 ± 0.0369 (0.152) Mesencephalic reticular 0.116 ± 0.0275 (0.114) 0.0834 0.223 ± 0.0362 (0.149) formation L. Lateral tier thalamus R. 0.0694 ± 0.0179 (0.0737) 0 0.180 ± 0.0406 (0.167) Entorhinal R. 0.162 ± 0.0234 (0.0966) 0.0982 0.243 ± 0.0308 (0.127) 2 2 0 0.196 0.183 0.178 0.234 0.177 0.240 0.202 0.0494* 0.0138* 0.0476* 0.0439* 0.0456* 0.0083** 0.0125* 0.0114* 0.496* 0.443 0.406 0.344 0.435 0.354 0.408 0.368 0.372 0.496 0.334 0.419 0.337 0.343 0.340 0.450 0.425 0.431 0.334 C o n n e c t o m i c a n a l y s i s o f A l z h e i m e r ’ s d i s e a s e u s i n g p e r c o l a t i o n t h e o r y l D o w n o a d e d f r o m h t t p : / / d i r e c t . m i t . / / t e d u n e n a r t i c e - p d l f / / / / / 6 1 2 1 3 2 0 0 2 4 2 8 n e n _ a _ 0 0 2 2 1 p d . t f b y g u e s t t o n 0 7 S e p e m b e r 2 0 2 3 Amygdala L. 2.47 ± 0.563 (2.32) Dorsal striatum L. 1.66 ± 0.448 (1.85) Globus pallidus L. 0.968 ± 0.266 (1.10) Ventral pallidus L. 0.953 ± 0.182 (0.752) Ventral thalamic tier L. 1.66 ± 0.389 (1.60) Lateral tier thalamus L. 1.19 ± 0.228 (0.941) Auditory L. 1.24 ± 0.255 (1.05) Piriform rostral L. 2.48 ± 0.754 (3.11) Mesencephalic reticular 2.78 ± 0.699 (2.88) formation L. Cerebellar peduncle L. 3.62 ± 0.426 (1.76) Dorsal striatum R. 1.78 ± 0.426 (1.76) Lateral tier thalamus R. 1.22 ± 0.207 (0.855) Ventral tegmental area R. 1.40 ± 0.211 (0.869) Strength 5.68 ± 1.32 (5.46) 4.18 ± 1.09 (4.51) 2.64 ± 0.735 (3.03) 1.69 ± 0.258 (1.06) 5.02 ± 1.16 (4.78) 2.55 ± 0.487 (2.01) 2.77 ± 0.823 (3.39) 5.07 ± 1.44 (5.93) 7.02 5.07 1.78 0.526 5.24 1.18 1.73 5.44 0.0476* 0.0093** 0.0300* 0.0341* 0.0029** 0.0201* 0.0476* 0.0287* 6.93 ± 1.38 (5.70) 10.7 0.0062** 6.11 ± 0.836 (3.45) 3.72 ± 0.942 (3.88) 2.49 ± 0.509 (2.10) 2.75 ± 0.508 (2.09) 8.53 3.67 1.44 1.52 0.0241* 0.0167* 0.0210* 0.0371* 1.37 0.708 0.114 0.131 0.574 0.487 0 1.78 1.74 3.63 0.63 0.114 0.795 Ventral thalamic tier L. 0.0575 ± 0.0149 (0.0615) Mesencephalic reticular 0.0835 ± 0.0226 (0.0933) formation L. 0.0999 0.0548 0.174 ± 0.0324 (0.134) 0.154 ± 0.0879 (0.129) 0.178 0.0850 0.0055** 0.0341* Clustering coefficient 0.337 0.443 0.369 0.360 0.508 0.396 0.337 0.372 0.467 0.384 0.408 0.393 0.355 0.473 0.360 Lateral tier thalamus R. 0.0504 ± 0.0133 (0.0549) 0 0.144 ± 0.0380 (0.157) 0.223 0.0242* 0.383 Note. Data are shown as mean ± standard error (standard deviation). Wilcoxon rank-sum test was used to compare control and AD mice. L = left; R = right. Ind., individual analysis = indicative of quantifiers calculated on individual subject matrices. Avg., group-average analysis = indicative of quantifiers calculated after subject matrices were first averaged. * p < 0.05. ** p < 0.01. t N e w o r k N e u r o s c e n c e i 2 2 1 C o n n e c t o m i c a n a l y s i s o f A l z h e i m e r ’ s d i s e a s e u s i n g p e r c o l a t i o n t h e o r y l D o w n o a d e d f r o m h t t p : / / d i r e c t . m i t . / / t e d u n e n a r t i c e - p d l f / / / / / 6 1 2 1 3 2 0 0 2 4 2 8 n e n _ a _ 0 0 2 2 1 p d . t f b y g u e s t t o n 0 7 S e p e m b e r 2 0 2 3 Connectomic analysis of Alzheimer’s disease using percolation theory Figure 2. Nodes with significant differences in nodal quantifiers between control and AD mice. Nodes are highlighted in color on represen- tative 3D mouse brains, and their existing connections to other nodes are shown (in gray). DC = degree centrality; BC = betweenness cen- trality; EC = eigenvector centrality; LE = local efficiency; ST = strength; CC = clustering coefficient; 1 = left amygdala; 3 = left dorsal striatum; 4 = left globus pallidus; 5 = left ventral pallidus; 9 = left ventral thalamic tier; 10 = left lateral tier of the thalamus; 16 = left retrosplenium; 23 = left prelimbic cortex; 24 = left auditory cortex; 28 = left rostral piriform cortex; 37 = left mesencephalic reticular formation; 43 = left cerebellar peduncle; 46 = right amygdala; 48 = right dorsal striatum; 54 = right ventral thalamic tier; 55 = right lateral tier of the thalamus; 60 = right entorhinal; 66 = right rostral insular cortex; 81 = right ventral tegmental area; 88 = right cerebellar peduncle. Connectivity hubs and patterns. Binarized group-averaged brain networks were mapped onto mouse brains in Figure 3 along with shared connections. Shared connections demonstrate a core network that is present in both brains. A notable difference between brains is the lack of connections between the prefrontal cortex and the rest of the AD mouse brain that are present in the controls. This is further demonstrated in the shared-hub brain model, which shows three sets of disconnected modules that are only connected in the control brain model: left and right retrosplenium, left and right visual cortex (in green); left and right septum, left and right infra- limbic area (in red); left and right anterior cingulate, left and right orbital cortex, left and right prelimbic area, left secondary motor cortex (M2) since right M2 is completely disconnected (in blue). In the shared network, both control and AD brains show a highly connected module in the hindbrain: left and right inferior colliculus, left and right second cerebellar lobule, left and right cerebellar simple lobule, left and right third cerebellar lobule, left and right cerebellar peduncle, left and right fifth cerebellar lobule, and left and right areas that include deep cer- ebellar nuclei (cerebellar nuclear area; in pink). Furthermore, the shared connections in the brain, excluding the highly connected posterior module, are long-range transhemispheric con- nections (in yellow). In terms of connectivity strength, both groups showed very strong intrahemispheric connec- tions between anterior nodes, including right prelimbic and right orbital nodes (both groups had a connection strength of 1 indicating the strongest connection) and left prelimbic and left orbital nodes (control: 0.7263; AD: 0.6748). Both groups also had left and right midline pos- terior thalamic tier connected to each other but separated from the rest of the brain, with a notably stronger self-connection in AD mice than in controls (control: 0.3462; AD: 0.9326). Similarly, both groups showed strong connections between the cerebellar peduncle and cer- ebellar nuclear area in their respective hemisphere with minimal difference between controls and AD networks (left control: 0.4512; left AD: 0.7695; right control: 0.6427; right AD: 0.612). Network Neuroscience 222 l D o w n o a d e d f r o m h t t p : / / d i r e c t . m i t . / / t e d u n e n a r t i c e - p d l f / / / / / 6 1 2 1 3 2 0 0 2 4 2 8 n e n _ a _ 0 0 2 2 1 p d . t f b y g u e s t t o n 0 7 S e p e m b e r 2 0 2 3 Connectomic analysis of Alzheimer’s disease using percolation theory l D o w n o a d e d f r o m h t t p : / / d i r e c t . m i t . / t / e d u n e n a r t i c e - p d l Figure 3. Binarized connectome maps of control and AD mice. Shown in the middle panel (top) are short- and long-range connections common to both groups (nodes with no connections are not shown). Also shown in the middle panel (bottom) are nodes representing hubs that are common between the two groups. In the shared-length brain, yellow connections represent long-range con- nections while blue connections indicate close-range connections. L = left; R = right. f / / / / / 6 1 2 1 3 2 0 0 2 4 2 8 n e n _ a _ 0 0 2 2 1 p d . t f b y g u e s t t o n 0 7 S e p e m b e r 2 0 2 3 Targeted Attack of Brain Networks Brain resilience against attack schemes. The group-averaged brain networks of control and AD mice responded different to the various targeted attack schemes (Figure 4). On average, iter- ative attacks degraded both brain networks at a faster rate than basis attacks. Iterative between- ness centrality and collective influence attacks degraded the network at the quickest rate in both groups. Within the first 20% of nodes removed, both brains were reduced to only 40% of the original cluster size. When examining the largest cluster size of a network, the control group had a wider variety of degradation as opposed to the AD group in which all attacks degraded the network at a significantly faster rate than random attacks. This variety of degra- dation was also seen in examining attacks compared to the average clustering coefficient (data not shown). Similarly, this pattern of greater resilience to degradation was also recognizable in examining attacks compared to betweenness centrality, average degree, number of edges remaining, average local efficiency, and average strength to a lesser degree. Notably, the clus- tering coefficient was affected at a rate comparable to random in iterative betweenness cen- trality and collective influence, even at the quick degradation rate in the largest cluster size of the control group. Iterative and basis attacks based on clustering coefficient, local efficiency, and participation coefficient were also explored but showed results consistent with a reduced efficiency at degrading the network compared to the shown attack schemes. Network Neuroscience 223 Connectomic analysis of Alzheimer’s disease using percolation theory l D o w n o a d e d f r o m h t t p : / / d i r e c t . m i t . t / / e d u n e n a r t i c e - p d l f / Figure 4. The graphs above show the reactions of control and AD brain networks in response to targeted attacks. The axes are normalized for comparison. “Basis” indicates attack schemes that use quantifiers calculated with the unaltered network while “Iter” indicates attack schemes that iteratively calculate the attack quantifier after each attack. DC = degree centrality; BC = betweenness centrality; EC = eigenvector cen- trality; ST = strength; CI = collective influence. / / / / 6 1 2 1 3 2 0 0 2 4 2 8 n e n _ a _ 0 0 2 2 1 p d t . f b y g u e s t t o n 0 7 S e p e m b e r 2 0 2 3 Control brain networks compared to AD baseline. To examine the progression of the degradation effects of node attacks on AD functional networks, quantifiers examined during attacks to the group-averaged control brains were compared to quantifiers of the unaltered group-averaged AD brain (Figure 5). Iterative betweenness centrality and collective influence attacks reached the largest cluster size baseline in between attacks five and six. When examining these attack schemes compared to the average betweenness centrality, which had a large difference in global measures (Table 1), the control brain reached the level of betweenness centrality of the diseased brain in only six attacks for iterative betweenness centrality and seven attacks for collective influence. In contrast, it takes other attack schemes 16 to 38 attacks to reach the level of betweenness centralized of the diseased baseline. Since the goal is to identify bio- markers, early network degradation is prioritized. Regarding characteristic path length, both betweenness centrality attack schemes and collective influence are the only attack schemes to progressively move closer to the AD baseline without regressing further away. For both tran- sitivity and network diameter, collective influence was the only measure that progressively moved close to matching the diseased brain baseline, while iterative betweenness centrality stays at the healthy baseline and then quickly reached the diseased baseline. Similarities were found when exploring the iterative betweenness centrality and collective influence attack schemes more closely. Since both attacks reached the largest cluster size in Network Neuroscience 224 Connectomic analysis of Alzheimer’s disease using percolation theory l D o w n o a d e d f r o m h t t p : / / d i r e c t . m i t . t / / e d u n e n a r t i c e - p d l f / / / / / 6 1 2 1 3 2 0 0 2 4 2 8 n e n _ a _ 0 0 2 2 1 p d . t f b y g u e s t t o n 0 7 S e p e m b e r 2 0 2 3 Figure 5. The graphs above show the progression of the control network compared to the AD baseline (diseased quantifier at baseline – healthy quantifier after each attack). The number of attacks axis shortened to 50 rather than extended to removing the full 90 nodes since, after a certain number of attacks, quantifiers become unstable due to the small and disconnected set of networks in the brains. “Basis” indicates attack schemes that use quantifiers calculated with the unaltered network, while “Iter” indicates attack schemes that iteratively calculate the attack quantifier after each attack. DC = degree centrality; BC = betweenness centrality; EC = eigenvector centrality; ST = strength; CI = collective influence. between five and six attacks, the first six attacks were mapped onto mice brains in Figure 6. The context of the attacks reaching the AD baseline of betweenness centrality diseased base- line in very few attacks (six for iterative betweenness centrality and seven for collective influ- ence) is also important. In the first six attacks, iterative betweenness centrality and collective influence shared four nodes: right rostral piriform cortex, right amygdala, right rostral insular cortex, and right accumbens. In collective influence’s seventh attack, the attack at which it reached diseased baseline betweenness centrality, the right periaqueductal gray node is shared with iterative betweenness centrality’s fifth attack. Both attack schemes also fractured the network significantly, separating key nodes from the main network. After only two iterative betweenness centrality attacks or six collective influ- ence attacks, key anterior nodes were completely disconnected from the rest of the brain: left and right orbital cortex, left and right prelimbic area, left and right primary somatosensory cor- tex, and left secondary motor region. For iterative betweenness centrality after two attacks, other key anterior nodes were disconnected: right primary motor cortex, right secondary motor cortex, and left and right anterior cingulate cortex. These nodes, excluding the left anterior Network Neuroscience 225 Connectomic analysis of Alzheimer’s disease using percolation theory l D o w n o a d e d f r o m h t t p : / / d i r e c t . m i t . t / / e d u n e n a r t i c e - p d l f / / / / / 6 1 2 1 3 2 0 0 2 4 2 8 n e n _ a _ 0 0 2 2 1 p d . t f b y g u e s t t o n 0 7 S e p e m b e r 2 0 2 3 Figure 6. The brains above show the healthy group-averaged brain progression through the iter- ative betweenness centrality and collective influence attack schemes. The red node and accompa- nying connections highlighted is the node that will be removed next. After two attacks in the BC scheme, the anterior portion of the control brain networks was disconnected. After six attacks in the CI scheme, the anterior portion of the control brain was disconnected; the side view of the brain was tilted to better illustrate this. BC = betweenness centrality, CI = collective influence; IPN = interpeduncular nucleus; INSr = rostral insular cortex; PirRos = rostral piriform cortex; AMYG = amygdala; PAG = periaqueductal gray; NAC = accumbens; SUB = subiculum; ACC = anterior cin- gulate cortex; L = left; LT = left tilt; R = right. cingulate cortex, which was removed in the fifth collective influence attack, are still connected in the collective influence scheme by a single connection of the right anterior cingulate cortex to the left interpeduncular nucleus. After six iterative betweenness centrality attacks, the left and right infralimbic, left and right septum, and right dorsal striatum were fully disconnected. These nodes remained connected in the collective influence attack scheme after six attacks but were subsequently disconnected following the seventh attack through the removal of the right periaqueductal gray node. Network Neuroscience 226 Connectomic analysis of Alzheimer’s disease using percolation theory DISCUSSION The observed global network differences between control and amyloid mice are possibly due to Aβ’s pathological effect on synaptic transmission, which in turn may impact brain-wide functional connectivity. Both individual and group-averaged networks of control mice had sig- nificantly higher characteristic path length and lower global efficiency than AD mice (Table 1). While some functional connectome studies have reported opposite findings (Stam et al., 2007; J. Wang et al., 2013; R. Wang et al., 2014) or no significant differences, such as a similar mouse model study (Brier et al., 2014; Kesler et al., 2018; Seo et al., 2013; Supekar et al., 2008), other studies have found similar results (Palesi et al., 2016; Sanz-Arigita et al., 2010). This variation in results most likely stems from a difference in MR image acquisition and signal processing approaches, which can impact network topology and graph sparsity. Relatedly, compared to AD mice, both individual and group-averaged controls had a larger network diameter, which measures the longest possible path between nodes in the network. These differences in CPL, global efficiency, and diameter may be associated with the observed reductions in functional connectivity of rostral regions of the brain to caudal areas in AD mice. While shown in the group-averaged control mice having a higher largest cluster size and as shown through the more connected hubs in Figure 3, these findings also indicate a similar pattern of a core network with many disconnected nodes found in individual control and AD brain networks. For instance, in human AD, differences in connectivity between anterior portions or posteromedial regions of the default mode network have been associated with mood disorders such as depression, amyloid deposition, and cognitive impairment (Andrews-Hanna et al., 2010; Coutinho et al., 2016; Mormino et al., 2011; X. Zhu et al., 2012). This rostral-caudal imbalance in connectivity patterns might be an important marker of an underlying AD pathology. Even with comparable largest cluster sizes when looking at individual subjects, the differences in these quantifiers point toward a more centralized con- nectivity scheme in AD mice as opposed to the more distant connectivity pattern formed as a result of stronger connections to distant hubs in control mice. This is further supported by the lower average strength in both control mice and higher BC in the group-averaged AD mice, indicating overall weaker connections between distant hubs of a core network. Additional quantifier analysis of a compensatory response, neuroanatomical localization of functional changes, and diaschisis can be found in the Supporting Information. Examining similarities and differences in brain resilience in response to targeted attacks can further elucidate critical changes in the AD brain. Targeted attacks degrading both brain networks at a faster rate than random is consistent with findings due to the brains having heavy-tailed distributions (Albert et al., 2000) (Figure 4). Since the AD brain heavy-tailed dis- tribution was extended, this may explain the higher susceptibility of the diseased brain to all attacks demonstrated by all attacks performing significantly better than random attacks. The extended heavy-tailed distribution may be a result of the brain compensating to AD by relying more heavily on high-strength nodes to minimize wiring cost to hubs (Crossley et al., 2014). Similarly, the negative assortativity (Table 1) of the group-averaged AD brain also indicates a low-resilience network with vulnerable high-degree hubs (Newman, 2002). The effectiveness of the collective influence and iterative BC further support the degradation of high-strength connecting hub nodes since these measures specifically examine hub-to-hub connectivity. AD brains having lower resilience to targeted attacks is supported by earlier studies showing AD-affected areas are more vulnerable (Klupp et al., 2014; Myers et al., 2014). This increased vulnerability demonstrates the possibility of the compensatory response only effectively delaying cognitive function degradation in the short-term and may be a factor in the transition from MCI to AD. Network Neuroscience 227 l D o w n o a d e d f r o m h t t p : / / d i r e c t . m i t . / t / e d u n e n a r t i c e - p d l f / / / / / 6 1 2 1 3 2 0 0 2 4 2 8 n e n _ a _ 0 0 2 2 1 p d t . f b y g u e s t t o n 0 7 S e p e m b e r 2 0 2 3 Connectomic analysis of Alzheimer’s disease using percolation theory Part of the effectiveness of a biomarker may be determined by how early it can detect path- ological signs before severe disease progression, exploring the earliest stages of degradation in unaffected brains compared to AD brains has a high potential to be identifiable before the onset of AD. Collective influence and iterative BC attacks were found to be the most likely AD progression model by comparing these attacks to an AD baseline (Figure 5). As demon- strated by quantifier, spatial, and targeted attack analyses, the AD brains showed a markedly different hub connectivity pattern in their greater reliance on high-strength connecting hub nodes, long-range connectivity patterns, and increased connectivity in the core network. This hub-pattern weakness in AD brains is also shown by the decreased BC in the group-averaged AD brain (Table 1). Other studies have also found a significant decrease in BC in AD brains (Cai et al., 2019; D. Wang et al., 2020) and thereby provide a potential explanation for the feeder-hub connectivity differences. This relationship is also supported by classification schemes identifying BC as an important difference between AD and healthy brains (Jalili, 2017; Sheng et al., 2019). Since collective influence is optimized to separate hubs, it is also similarly related to BC and the hub-connectivity pattern shown in AD. Through these quantifiers, two progression models were mapped onto mouse brains (Figure 6). Eight nodes that were removed were identified using these progression models that were present early in network degradation: left interpeduncular nucleus, right insular cortex, right piriform cortex, right amygdala, right periqueductal gray, right accumbens, left subiculum, and left anterior cingulate cortex. The right amygdala and right rostral insula were also identi- fied when analyzing differences between individual brains through BC and eigenvector centrality, respectively (Figure 2). While the removal of these nodes may model disease progres- sion, it is equally important to look at the nodes disconnected from the brain through these targeted attacks. Both attack schemes (six BC attacks, seven CI attacks) disconnected the fol- lowing nodes from the core network: left and right orbital, left and right prelimbic, left and right primary somatosensory cortex, left secondary motor region, the left and right infralimbic cortex, left and right septal nucleus, and right dorsal striatum. After two BC attacks the right primary and secondary motor regions and the anterior cingulate were also disconnected from the main net- work. These nodes are still connected in the CI attack scheme through a single connection of the right anterior cingulate with the left interpeduncular nucleus. The left prelimbic and right dorsal striatum were also identified when analyzing differences between individual brains through BC and node strength, respectively (Figure 2). Most notably, many of these nodes were found in disconnected hubs in Figure 3. These include the left and right septum, left and right infralimbic cortex, left and right anterior cingulate cortex (BC only), left and right orbital, left and right prelimbic, left m2, and right m2 (BC only). Both the BC and CI attack schemes quickly disconnect the anterior portion of the brain with the rest of the brain while maintaining within- region connectivity. Previous evidence of anterior-to-posterior disconnections in AD has been found in both graph theory and biological studies (Dauwan et al., 2016; Delbeuck et al., 2003; Kocagoncu et al., 2020; Liu et al., 2014). Since connections between anterior nodes were some of the strongest in the network, the anterior-to-posterior disconnect could explain cognitive def- icits in AD patients rather than degradation in the anterior brain. Namely, communication between anterior regions playing important roles in active behavioral outputs and processes such as decision-making and cognitive flexibility and posterior regions involved in long-term memory retrieval may be adversely affected in AD, according to our present results. Further- more, these regions identified both by spatial analysis and percolation theory could act as potential biomarker regions to track early onset of AD pathway degradation. Additionally, the importance of the two related measures of betweenness centrality and collective influence underscore the effect AD has on disconnecting key hubs from the core network. Network Neuroscience 228 l D o w n o a d e d f r o m h t t p : / / d i r e c t . m i t . / / t e d u n e n a r t i c e - p d l f / / / / / 6 1 2 1 3 2 0 0 2 4 2 8 n e n _ a _ 0 0 2 2 1 p d t . f b y g u e s t t o n 0 7 S e p e m b e r 2 0 2 3 Connectomic analysis of Alzheimer’s disease using percolation theory This study does have some limitations. Mice were scanned while under isoflurane anesthe- sia and results may need comparisons with other sedatives, such as dexmedetomidine, in order to determine generalizability of the present results. The mouse model is highly specific for a set of mutations involved in dominant inherited AD, but the majority of cases (>95%) are sponta-
neous late-onset AD, with no clear mechanism in sight, 然而. ApoE alleles have been found to be
risk factor, but the others are age and comorbidity with cardiovascular conditions. Thresholding
在 10% graph density may also play a significant role in how the brain networks are constructed
(Roberts et al., 2017) and the effect of thresholding should be further examined. A clear limi-
tation is also the use of a threshold based on fMRI connectivity but not based on true anatomical
连接性. This is a limitation and a reason why in other cases labs use multiple thresholds to
quantify the stability/consistency of the connectomic measures across thresholds. 此外,
as mentioned in the Methods, the group-averaging method to find group-averaged healthy and
diseased brains may ignore subtle individual-level connections that are important (Amico &
戈尼, 2018; Gordon et al., 2017; Roberts et al., 2017). Individual-level connections should also
be explored. 最后, the connectomic approach in general must be scrutinized. While quanti-
fiers may characterize global estimates of connectivity and topology, the underlying neurobi-
ological drivers are not fully explained by this approach.

This study utilizes connectomics to analyze differences in control and AD mouse brains.
Through quantifier, 空间的, and targeted attack analyses, a short-term compensatory response
was found in the core of the AD brain through a vulnerable high-strength hub connector reli-
ant network. 此外, a significant disconnect between hubs and the core network was
present in the AD brain. This was notably reinforced using the collective influence and
betweenness centrality progression models showing an anterior-to-posterior disconnect that
may explain cognitive deficits through a disconnection syndrome lens. These preliminary pro-
gression models also identified key nodes that can potentially serve as biomarkers to identify
early connectivity changes in patients with a risk of developing AD. 一起, these results
point toward a progression model identifying key brain regions that serve as anterior-to-
posterior connecting nodes that may explain AD symptomology and act as a biomarker for
early intervention.

SUPPORTING INFORMATION

Supporting information for this article is available at https://www.doi.org/10.1162/netn_a
_00221.

作者贡献

Parker Kotlarz: 概念化; 数据管理; 形式分析; 调查; Methodol-
奥吉; 软件; 验证; 可视化; Writing – original draft; 写作——复习 & 编辑.
Juan C. Nino: 概念化; 资金获取; 项目管理; 资源;
监督; 写作——复习 & 编辑. Marcelo Febo: 概念化; 数据管理;
资金获取; 项目管理; 资源; 监督; Writing – original draft;
写作——复习 & 编辑.

资金信息

Parker Kotlarz, University of Florida AI2020 Catalyst Grant, 奖项ID: AWD09459. 马塞洛
Febo, Foundation for the National Institutes of Health (https://dx.doi.org/10.13039
/100000009), 奖项ID: AG065819. Marcelo Febo, National Science Foundation (https://dx
.doi.org/10.13039/501100008982), 奖项ID: DMR-1644779.

网络神经科学

229

我

D
哦
w
n
哦
A
d
e
d

F
r
哦
米
H

t
t

p

:
/
/

d
我
r
e
C
t
.

米

我
t
.

t

/

/

e
d
你
n
e
n
A
r
t
我
C
e
–
p
d

我

F
/

/

/

/

/

6
1
2
1
3
2
0
0
2
4
2
8
n
e
n
_
A
_
0
0
2
2
1
p
d

.

t

F

乙
y
G
你
e
s
t

t

哦
n
0
7
S
e
p
e
米
乙
e
r
2
0
2
3

Connectomic analysis of Alzheimer’s disease using percolation theory

参考

2020 Alzheimer’s Disease Facts and Figures. (2020). Alzheimer’s &
Dementia, 16(3), 391–460. https://doi.org/10.1002/alz.12068,
考研: 32157811

Achard, S。, Salvador, R。, Whitcher, B., Suckling, J。, & 布莫尔, 乙.
(2006). A resilient, low-frequency, small-world human brain
functional network with highly connected association cortical
枢纽. 神经科学杂志, 26(1), 63–72. https://doi.org/10
.1523/JNEUROSCI.3874-05.2006, 考研: 16399673

阿尔伯特, R。, & 巴拉巴斯, A.-L. (2002). Statistical mechanics of com-
plex networks. Reviews of Modern Physics, 74(1), 47–97. https://
doi.org/10.1103/RevModPhys.74.47

阿尔伯特, R。, Jeong, H。, & 巴拉巴斯, A.-L. (2000). Error and attack
tolerance of complex networks. 自然, 406(6794), 378–382.
https://doi.org/10.1038/35019019, 考研: 10935628

Alderson, 时间. H。, Bokde, A. L. W., Kelso, J. A. S。, Maguire, L。, &
Coyle, D. (2018). Metastable neural dynamics in Alzheimer’s
disease are disrupted by lesions to the structural connectome.
神经影像, 183, 438–455. https://doi.org/10.1016/j
.neuroimage.2018.08.033, 考研: 30130642

Amico, E., & 戈尼, J. (2018). The quest for identifiability in human
functional connectomes. Scientific Reports, 8(1), 8254. https://
doi.org/10.1038/s41598-018-25089-1, 考研: 29844466

Andrews-Hanna, J. R。, Reidler, J. S。, 墓, J。, Poulin, R。, & 巴克纳,
右. L. (2010). Functional-anatomic fractionation of the brain’s default
网络. 神经元, 65(4), 550–562. https://doi.org/10.1016/j.neuron
.2010.02.005, 考研: 20188659

Bakker, A。, 阿尔伯特, 中号. S。, Krauss, G。, Speck, C. L。, & 加拉格尔, 中号.
(2015). Response of the medial temporal lobe network in amnes-
tic mild cognitive impairment to therapeutic intervention
assessed by fMRI and memory task performance. 神经影像:
Clinical, 7, 688–698. https://doi.org/10.1016/j.nicl.2015.02
.009, 考研: 25844322

Bertram, L。, Lill, C. M。, & Tanzi, 右. 乙. (2010). The genetics of
Alzheimer disease: Back to the future. 神经元, 68(2), 270–281.
https://doi.org/10.1016/j.neuron.2010.10.013, 考研:
20955934

Brier, 中号. R。, 托马斯, J. B., 费根, A. M。, Hassenstab, J。, Holtzman,
D. M。, Benzinger, 时间. L。, 莫里斯, J. C。, & Ances, 乙. 中号. (2014).
Functional connectivity and graph theory in preclinical Alzhei-
mer’s disease. Neurobiology of Aging, 35(4), 757–768. https://
doi.org/10.1016/j.neurobiolaging.2013.10.081, 考研:
24216223

Brier, 中号. R。, 托马斯,

J. B., 斯奈德, A. Z。, Benzinger, 时间. L。,
张, D ., Raichle, 中号. E., Holtzman, D. M。, 莫里斯, J. C。, &
Ances, 乙. 中号. (2012). Loss of intranetwork and internetwork
resting state functional connections with Alzheimer’s disease
神经科学杂志, 32(26), 8890–8899.
progression.
https://doi.org/10.1523/ JNEUROSCI.5698-11.2012, 考研:
22745490

棕色的, J. A。, Rudie, J. D ., Bandrowski, A。, Van Horn, J. D ., &
Bookheimer, S. 是. (2012). The UCLA multimodal connectivity
数据库: A web-based platform for brain connectivity matrix
sharing and analysis. 神经信息学前沿, 6. https://
doi.org/10.3389/fninf.2012.00028, 考研: 23226127

Cai, S。, 黄, K., Kang, Y。, Jiang, Y。, von Deneen, K. M。, & 黄,
L. (2019). Potential biomarkers for distinguishing people with

Alzheimer’s disease from cognitively intact elderly based on
the rich-club hierarchical structure of white matter networks.
Neuroscience Research, 144, 56–66. https://doi.org/10.1016/j
.neures.2018.07.005, 考研: 30107205

查克拉巴蒂, P。, Ceballos-Diaz, C。, Beccard, A。, Janus, C。, Dickson,
D ., Golde, 时间. E., & 这, 磷. (2010). IFN-γ promotes complement
expression and attenuates amyloid plaque deposition in amyloid
β precursor protein transgenic mice. The Journal of Immunology,
184(9), 5333–5343. https://doi.org/10.4049/jimmunol.0903382,
考研: 20368278

Chishti, 中号. A。, 哪个, D. S。, Janus, C。, Phinney, A. L。, Horne, P。,
皮尔逊, J。, Strome, R。, Zuker, N。, Loukides, J。, 法语, J。, 车工,
S。, Lozza, G。, Grilli, M。, Kunicki, S。, Morissette, C。, Paquette, J。,
Gervais, F。, Bergeron, C。, 弗雷泽, 磷. E., … Westaway, D. (2001).
Early-onset amyloid deposition and cognitive deficits in trans-
genic mice expressing a double mutant form of amyloid precur-
sor protein 695. The Journal of Biological Chemistry, 276(24),
21562–21570. https://doi.org/10.1074/jbc.M100710200,
考研: 11279122

Colon-Perez, L. M。, Ibanez, K. R。, Suarez, M。, Torroella, K., Acuna, K.,
Ofori, E., Levites, Y。, Vaillancourt, D. E., Golde, 时间. E., 查克拉巴蒂,
P。, & Febo, 中号. (2019). Neurite orientation dispersion and density
imaging reveals white matter and hippocampal microstructure
changes produced by Interleukin-6 in the TgCRND8 mouse model
of amyloidosis. 神经影像, 202, 116138. https://doi.org/10.1016
/j.neuroimage.2019.116138, 考研: 31472250

Coutinho, J. F。, Fernandesl, S. 五、, Soares, J. M。, Maia, L。, Gonçalves,
Ó. F。, & Sampaio, A. (2016). Default mode network dissociation
in depressive and anxiety states. Brain Imaging and Behavior, 10(1),
147–157. https://doi.org/10.1007/s11682-015-9375-7, 考研:
25804311

Crossley, 氮. A。, Mechelli, A。, 斯科特, J。, Carletti, F。, 狐狸, 磷. T。,
McGuire, P。, & 布莫尔, 乙. 时间. (2014). The hubs of the human
connectome are generally implicated in the anatomy of brain
disorders. Brain, 137(8), 2382–2395. https://doi.org/10.1093
/brain/awu132, 考研: 25057133

Crous-Bou, M。, Minguillón, C。, Gramunt, N。, & Molinuevo, J. L.
(2017). Alzheimer’s disease prevention: From risk factors to
early intervention. Alzheimer’s Research & Therapy, 9(1), 71.
https://doi.org/10.1186/s13195-017-0297-z, 考研:
28899416

Damoiseaux, J. S。, Prater, K. E., 磨坊主, 乙. L。, & Greicius, 中号. D. (2012).
Functional connectivity tracks clinical deterioration in Alzhei-
mer’s disease. Neurobiology of Aging, 33(4), 828.e19–828.e30.
https://doi.org/10.1016/j.neurobiolaging.2011.06.024, 考研:
21840627

Dauwan, M。, van Dellen, E., van Boxtel, L。, van Straaten, 乙. C. W.,
de Waal, H。, Lemstra, A. W., Gouw, A. A。, van der Flier, 瓦. M。,
Scheltens, P。, 索默, 我. E., & 斯塔姆, C. J. (2016). EEG-directed
connectivity from posterior brain regions is decreased in demen-
tia with Lewy bodies: A comparison with Alzheimer’s disease
and controls. Neurobiology of Aging, 41, 122–129. https://土井
.org/10.1016/j.neurobiolaging.2016.02.017, 考研:
27103525

Delbeuck, X。, Van der Linden, M。, & Collette, F. (2003). Alzheimer’
disease as a disconnection syndrome? Neuropsychology Review,

网络神经科学

230

我

D
哦
w
n
哦
A
d
e
d

F
r
哦
米
H

t
t

p

:
/
/

d
我
r
e
C
t
.

米

我
t
.

/

t

/

e
d
你
n
e
n
A
r
t
我
C
e
–
p
d

我

F
/

/

/

/

/

6
1
2
1
3
2
0
0
2
4
2
8
n
e
n
_
A
_
0
0
2
2
1
p
d

.

t

F

乙
y
G
你
e
s
t

t

哦
n
0
7
S
e
p
e
米
乙
e
r
2
0
2
3

Connectomic analysis of Alzheimer’s disease using percolation theory

13(2), 79–92. https://doi.org/10.1023/A:1023832305702,
考研: 12887040

Díaz-Parra, A。, Osborn, Z。, Canals, S。, Moratal, D ., & 斯波恩斯, 氧.
(2017). Structural and functional, empirical and modeled con-
nectivity in the cerebral cortex of the rat. 神经影像, 159,
170–184. https://doi.org/10.1016/j.neuroimage.2017.07.046,
考研: 28739119

Fagerland, 中号. 瓦. (2012). t-tests, non-parametric tests, 和大
studies—A paradox of statistical practice? BMC Medical
Research Methodology, 12(1), 78. https://doi.org/10.1186/1471
-2288-12-78, 考研: 22697476

Farrer, L. A。, Cupples, L. A。, Haines, J. L。, 海曼, B., Kukull, 瓦. A。,
Mayeux, R。, 迈尔斯, 右. H。, Pericak-Vance, 中号. A。, Risch, N。, & van
Duijn, C. 中号. (1997). Effects of age, 性别, and ethnicity on the asso-
ciation between apolipoprotein E genotype and Alzheimer dis-
舒适: A Meta-analysis. JAMA, 278(16), 1349–1356. https://土井
.org/10.1001/jama.1997.03550160069041, 考研: 9343467
Filippi, M。, Basaia, S。, Canu, E., Imperiale, F。, Magnani, G。, Falautano,
M。, Comi, G。, Falini, A。, & Agosta, F. (2020). Changes in functional
and structural brain connectome along the Alzheimer’s disease
continuum. Molecular Psychiatry, 25(1), 230–239. https://doi.org
/10.1038/s41380-018-0067-8, 考研: 29743583

假如, A。, 扎莱斯基, A。, & Breakspear, 中号. (2015). The connec-
tomics of brain disorders. 自然评论神经科学, 16(3),
159–172. https://doi.org/10.1038/nrn3901, 考研: 25697159
弗里曼, L. C. (1978). Centrality in social networks conceptual
clarification. Social Networks, 1(3), 215–239. https://doi.org/10
.1016/0378-8733(78)90021-7

Frisoni, G. B., Boccardi, M。, Barkhof, F。, Blennow, K., Cappa, S。,
Chiotis, K., Démonet, J.-F., Garibotto, 五、, Giannakopoulos, P。,
Gietl, A。, Hansson, 奥。, Herholz, K., 杰克, C. R。, Nobili, F。,
Nordberg, A。, 斯奈德, H. M。, Ten Kate, M。, Varrone, A。, Albanese,
E., … Winblad, 乙. (2017). Strategic roadmap for an early diagnosis
of Alzheimer’s disease based on biomarkers. The Lancet Neurol-
奥吉, 16(8), 661–676. https://doi.org/10.1016/S1474-4422(17)
30159-X, 考研: 28721928

弗里斯顿, K. J. (1994). Functional and effective connectivity in neuro-
成像: A synthesis. 人脑图谱, 2(1–2), 56–78.
https://doi.org/10.1002/hbm.460020107

Gordon, 乙. M。, 劳曼, 时间. 奥。, Gilmore, A. W., Newbold, D. J。,
Greene, D. J。, 伯格, J. J。, Ortega, M。, Hoyt-Drazen, C。, Gratton,
C。, Sun, H。, Hampton, J. M。, Coalson, 右. S。, 阮, A. L。,
麦克德莫特, K. B., Shimony, J. S。, 斯奈德, A. Z。, 施拉加尔,
乙. L。, 彼得森, S. E., 纳尔逊, S. M。, & Dosenbach, 氮. U. F.
(2017). Precision functional mapping of individual human
大脑. 神经元, 95(4), 791–807.e7. https://doi.org/10.1016/j
.neuron.2017.07.011, 考研: 28757305

Guimerà, R。, & Amaral, L. A. 氮. (2005). Cartography of complex
网络: Modules and universal roles. Journal of Statistical
Mechanics: Theory and Experiment, 2005(02), P02001. https://
doi.org/10.1088/1742-5468/2005/02/ P02001, 考研:
18159217

哈格曼, P。, 卡蒙, L。, 巨人, X。, 买, R。, 蜂蜜, C. J。,
威登, V. J。, & 斯波恩斯, 氧. (2008). Mapping the structural core
of human cerebral cortex. PLOS Biology, 6(7), e159. https://土井
.org/10.1371/journal.pbio.0060159, 考研: 18597554

Hebert, L. E., Weuve, J。, Scherr, 磷. A。, & 埃文斯, D. A. (2013). Alz-
heimer disease in the United States (2010–2050) estimated using

这 2010 人口普查. Neurology, 80(19), 1778–1783. https://doi.org
/10.1212/ WNL.0b013e31828726f5, 考研: 23390181

H u m p h r i e s , 中号 . D . , & G u r n e y, K .

( 2 0 0 8 ) . N e t w o r k
‘small-world-ness’: A quantitative method for determining canoni-
cal network equivalence. PLOS One, 3(4), e0002051. https://土井
.org/10.1371/journal.pone.0002051, 考研: 18446219

Jalili, 中号. (2017). Graph theoretical analysis of Alzheimer’s disease:
Discrimination of AD patients from healthy subjects. 信息
科学, 384, 145–156. https://doi.org/10.1016/j.ins.2016.08.047
Janus, C。, 皮尔逊, J。, McLaurin, J。, Mathews, 磷. M。, Jiang, Y。,
施密特, S. D ., Chishti, 中号. A。, Horne, P。, Heslin, D ., 法语, J。,
Mount, H. 时间. J。, Nixon, 右. A。, Mercken, M。, Bergeron, C。, 弗雷泽,
磷. E., St George-Hyslop, P。, & Westaway, D. (2000). Aβ peptide
immunization reduces behavioural impairment and plaques in a
model of Alzheimer’s disease. 自然, 408(6815), 979–982.
https://doi.org/10.1038/35050110, 考研: 11140685

Kaiser, M。, 马丁, R。, Andras, P。, & Young, 中号. 磷. (2007). Simulation
of robustness against lesions of cortical networks. European Jour-
nal of Neuroscience, 25(10), 3185–3192. https://doi.org/10.1111
/j.1460-9568.2007.05574.x, 考研: 17561832

Kesler, S. R。, Acton, P。, 饶, 五、, & Ray, 瓦. J. (2018). Functional
and structural connectome properties in the 5XFAD transgenic
mouse model of Alzheimer’s disease. 网络神经科学,
2(2), 241–258. https://doi.org/10.1162/netn_a_00048, 考研:
30215035

Khazaee, A。, Ebrahimzadeh, A。, & Babajani-Feremi, A. (2015).
Identifying patients with Alzheimer’s disease using resting-state
fMRI and graph theory. Clinical Neurophysiology, 126(11),
2132–2141. https://doi.org/10.1016/j.clinph.2015.02.060,
考研: 25907414

Klupp, E., Förster, S。, Grimmer, T。, Tahmasian, M。, Yakushev, 我。,
Sorg, C。, Yousefi, B., & Drzezga, A. (2014). In Alzheimer’s dis-
舒适, hypometabolism in low-amyloid brain regions may be a
functional consequence of pathologies in connected brain
地区. Brain Connectivity, 4(5), 371–383. https://doi.org/10
.1089/brain.2013.0212, 考研: 24870443

Kocagoncu, E., 奎因, A。, Firouzian, A。, 库珀, E., Greve, A。,
Gunn, R。, 绿色的, G。, 伍尔里奇, 中号. W., Henson, 右. N。,
Lovestone, S。, & 罗维, J. 乙. (2020). Tau pathology in early
Alzheimer’s disease is linked to selective disruptions in neuro-
physiological network dynamics. Neurobiology of Aging, 92,
141–152. https://doi.org/10.1016/j.neurobiolaging.2020.03.009,
考研: 32280029

Koffie, 右. M。, Hashimoto, T。, Tai, H.-C., Kay, K. R。, Serrano-Pozo,
A。, Joyner, D ., Hou, S。, Kopeikina, K. J。, Frosch, 中号. P。, 李, V. M。,
Holtzman, D. M。, 海曼, 乙. T。, & Spires-Jones, 时间. L. (2012).
Apolipoprotein E4 effects in Alzheimer’s disease are mediated
by synaptotoxic oligomeric amyloid-β. Brain: A Journal of Neu-
rology, 135(Pt 7), 2155–2168. https://doi.org/10.1093/ brain
/aws127, 考研: 22637583

Latora, 五、, & Marchiori, 中号. (2001). Efficient behavior of small-world
网络. 物理评论快报, 87(19), 198701. https://土井
.org/10.1103/PhysRevLett.87.198701, 考研: 11690461

Launer, L. J。, 安徒生, K., 杜威, 中号. E., Letenneur, L。, Ott, A。,
Amaducci, L. A。, Brayne, C。, Copeland, J. 右. M。, Dartigues, J.-F.,
Kragh-Sorensen, P。, Lobo, A。, Martinez-Lage, J. M。, Stijnen, T。,
Hofman, A。, & the EURODEM Incidence Research Group and
Work Groups. (1999). Rates and risk factors for dementia and

网络神经科学

231

我

D
哦
w
n
哦
A
d
e
d

F
r
哦
米
H

t
t

p

:
/
/

d
我
r
e
C
t
.

米

我
t
.

/

/

t

e
d
你
n
e
n
A
r
t
我
C
e
–
p
d

我

F
/

/

/

/

/

6
1
2
1
3
2
0
0
2
4
2
8
n
e
n
_
A
_
0
0
2
2
1
p
d

.

t

F

乙
y
G
你
e
s
t

t

哦
n
0
7
S
e
p
e
米
乙
e
r
2
0
2
3

Connectomic analysis of Alzheimer’s disease using percolation theory

阿尔茨海默氏病: Results from EURODEM pooled analyses.
Neurology, 52(1), 78–78. https://doi.org/10.1212/ WNL.52.1.78,
考研: 9921852

Leung, C. C。, & Chau, H. F. (2007). Weighted assortative and dis-
assortative networks model. Physica A: Statistical Mechanics and
Its Applications, 378(2), 591–602. https://doi.org/10.1016/j
.physa.2006.12.022

梁, X。, Hsu, L.-M., 鲁, H。, Sumiyoshi, A。, 他, Y。, & 哪个, 是.
(2018). The rich-club organization in rat functional brain net-
work to balance between communication cost and efficiency.
大脑皮层, 28(3), 924–935. https://doi.org/10.1093/cercor
/bhw416, 考研: 28108494

刘, Y。, 于, C。, 张, X。, 刘, J。, Duan, Y。, Alexander-Bloch, A. F。,
刘, B., Jiang, T。, & 布莫尔, 乙. (2014). Impaired long distance
functional connectivity and weighted network architecture in
阿尔茨海默氏病. 大脑皮层, 24(6), 1422–1435.
https://doi.org/10.1093/cercor/bhs410, 考研: 23314940

Lo, C.-Y. Z。, Su, T.-W., 黄, C.-C., Hung, C.-C., 陈, W.-L.,
兰, T.-H., 林, C.-P., & 布莫尔, 乙. 时间. (2015). Randomization
and resilience of brain functional networks as systems-level
endophenotypes of schizophrenia. 国家会议录
Academy of Sciences, 112(29), 9123–9128. https://doi.org/10
.1073/pnas.1502052112, 考研: 26150519

Mayeux, R。, Sano, M。, 陈, J。, Tatemichi, T。, & Stern, 是. (1991).
Risk of dementia in first-degree relatives of patients with
Alzheimer’s disease and related disorders. Archives of Neurol-
奥吉, 48(3), 269–273. https://doi.org/10.1001/archneur.1991
.00530150037014, 考研: 2001183

米兰, M。, Guzzi, 磷. H。, & Cannataro, 中号. (2019). Network build-
ing and analysis in connectomics studies: A review of algorithms,
databases and technologies. Network Modeling Analysis in
Health Informatics and Bioinformatics, 8(1), 13. https://doi.org
/10.1007/s13721-019-0192-6

摩尔, K., Madularu, D ., Iriah, S。, Yee, J. R。, 库尔卡尼, P。, Darcq, E.,
Kieffer, 乙. L。, & 费里斯, C. F. (2016). BOLD imaging in awake
wild-type and mu-opioid receptor knock-out mice reveals
on-target activation maps in response to oxycodone. Frontiers
in Neuroscience, 10. https://doi.org/10.3389/fnins.2016.00471,
考研: 27857679

Mormino, 乙. C。, Smiljic, A。, Hayenga, A. 奥。, Onami, S. H。,
Greicius, 中号. D ., Rabinovici, G. D ., Janabi, M。, 贝克, S. L。,
Yen, 我. 五、, 麦迪逊, C. M。, 磨坊主, 乙. L。, & Jagust, 瓦. J. (2011).
Relationships between β-amyloid and functional connectivity
in different components of the default mode network in aging.
大脑皮层, 21(10), 2399–2407. https://doi.org/10.1093
/cercor/bhr025, 考研: 21383234

Morone, F。, & Makse, H. A. (2015). Influence maximization in com-
plex networks through optimal percolation. 自然, 524(7563),
65–68. https://doi.org/10.1038/nature14604, 考研: 26131931
Morone, F。, 最小, B., Bo, L。, Mari, R。, & Makse, H. A. (2016).
Collective influence algorithm to find influencers via optimal per-
colation in massively large social media. Scientific Reports, 6(1),
30062. https://doi.org/10.1038/srep30062, 考研: 27455878
Mrdjen, D ., 狐狸, 乙. J。, Bukhari, S. A。, Montine, K. S。, Bendall, S. C。,
& Montine, 时间. J. (2019). The basis of cellular and regional vulner-
ability in Alzheimer’s disease. Acta Neuropathologica, 138(5),
729–749. https://doi.org/10.1007/s00401-019-02054-4,
考研: 31392412

迈尔斯, N。, Pasquini, L。, Göttler, J。, Grimmer, T。, 科赫, K., Ortner,
M。, Neitzel, J。, Mühlau, M。, Förster, S。, Kurz, A。, Förstl, H。,
Zimmer, C。, Wohlschläger, A. M。, Riedl, 五、, Drzezga, A。, & Sorg,
C. (2014). Within-patient correspondence of amyloid-β and
intrinsic network connectivity in Alzheimer’s disease. Brain,
137(7), 2052–2064. https://doi.org/10.1093/ brain/awu103,
考研: 24771519

纽曼, 中号. 乙. J. (2002). Assortative mixing in networks. Physical
Review Letters, 89(20), 208701. https://doi.org/10.1103
/PhysRevLett.89.208701, 考研: 12443515

纽曼, 中号. 乙. J. (2003). The structure and function of complex
网络. SIAM Review, 45(2), 167–256. https://doi.org/10
.1137/S003614450342480

纽曼, 中号. 乙. J. (2006). Modularity and community structure in
网络. 美国国家科学院院刊, 103
(23), 8577–8582. https://doi.org/10.1073/pnas.0601602103,
考研: 16723398

纽曼, 中号. 乙. J. (2016). Mathematics of networks. In The new
Palgrave dictionary of economics (PP. 1–8). 伦敦, 英国: Palgrave
Macmillan UK. https://doi.org/10.1057/978-1-349-95121-5
_2565-1

Onnela, J.-P., Saramäki, J。, Kertész, J。, & Kaski, K. (2005). Intensity
and coherence of motifs in weighted complex networks. Physical
Review E, 71(6), 065103. https://doi.org/10.1103/PhysRevE.71
.065103, 考研: 16089800

Palesi, F。, Castellazzi, G。, Casiraghi, L。, Sinforiani, E., Vitali, P。,
Gandini Wheeler-Kingshott, C. A. M。, & D’Angelo, 乙. (2016).
Exploring patterns of alteration in Alzheimer’s disease brain net-
作品: A combined structural and functional connectomics anal-
分析. Frontiers in Neuroscience, 10. https://doi.org/10.3389/fnins
.2016.00380, 考研: 27656119

Perry, A。, Wen, W., Lord, A。, Thalamuthu, A。, 罗伯茨, G。, 米切尔,
磷. B., Sachdev, 磷. S。, & Breakspear, 中号. (2015). The organisation of
the elderly connectome. 神经影像, 114, 414–426. https://土井
.org/10.1016/j.neuroimage.2015.04.009, 考研: 25869857
Pompilus, M。, Colon-Perez, L. M。, Grudny, 中号. M。, & Febo, 中号.
(2020). Contextual experience modifies functional connectome
indices of topological strength and efficiency. Scientific Reports,
10(1), 19843. https://doi.org/10.1038/s41598-020-76935-0,
考研: 33199790

Ren, H。, 朱, J。, Su, X。, 陈, S。, 曾, S。, 兰, X。, Zou, L.-Y.,
Sughrue, 中号. E., & Guo, 是. (2020). Application of structural and
functional connectome mismatch for classification and individu-
alized therapy in Alzheimer disease. Frontiers in Public Health,
8. https://doi.org/10.3389/fpubh.2020.584430, 考研:
33330326

罗伯茨, J. A。, Perry, A。, 罗伯茨, G。, 米切尔, 磷. B., & Breakspear,
中号. (2017). Consistency-based thresholding of the human con-
nectome. 神经影像, 145, 118–129. https://doi.org/10.1016/j
.neuroimage.2016.09.053, 考研: 27666386

鲁比诺夫, M。, & 斯波恩斯, 氧. (2010). 复杂的网络措施
大脑连接: 用途和解释. 神经影像, 52(3),
1059–1069. https://doi.org/10.1016/j.neuroimage.2009.10.003,
考研: 19819337

Sanz-Arigita, 乙. J。, Schoonheim, 中号. M。, Damoiseaux, J. S。,
Rombouts, S. A. 右. B., 马里斯, E., Barkhof, F。, Scheltens, P。, &
斯塔姆, C. J. (2010). Loss of ‘small-world’ networks in Alzheimer’s
疾病: Graph analysis of fMRI resting-state functional

网络神经科学

232

我

D
哦
w
n
哦
A
d
e
d

F
r
哦
米
H

t
t

p

:
/
/

d
我
r
e
C
t
.

米

我
t
.

/

t

/

e
d
你
n
e
n
A
r
t
我
C
e
–
p
d

我

F
/

/

/

/

/

6
1
2
1
3
2
0
0
2
4
2
8
n
e
n
_
A
_
0
0
2
2
1
p
d

.

t

F

乙
y
G
你
e
s
t

t

哦
n
0
7
S
e
p
e
米
乙
e
r
2
0
2
3

Connectomic analysis of Alzheimer’s disease using percolation theory

连接性. PLOS One, 5(11), e13788. https://doi.org/10.1371
/journal.pone.0013788, 考研: 21072180

萨瓦尔, T。, Tian, Y。, 杨, 乙. 时间. T。, 你的兄弟, K., & 扎莱斯基, A.
(2021). Structure-function coupling in the human connectome: A
machine learning approach. 神经影像, 226, 117609. https://
doi.org/10.1016/j.neuroimage.2020.117609, 考研:
33271268

Seo, 乙. H。, 李, D. Y。, 李, J.-M。, 公园, J.-S., Sohn, 乙. K., 李, D. S。,
Choe, 是. M。, & Woo, J. 我. (2013). Whole-brain functional net-
works in cognitively normal, mild cognitive impairment, 和
阿尔茨海默氏病. PLOS One, 8(1), e53922. https://doi.org
/10.1371/journal.pone.0053922, 考研: 23335980

Shehzad, Z。, 凯莉, C。, Reiss, 磷. T。, Cameron Craddock, R。, Emerson,
J. W., 麦克马洪, K., Copland, D. A。, Xavier Castellanos, F。, &
Milham, 中号. 磷. (2014). A multivariate distance-based analytic
framework for connectome-wide association studies. Neuro-
图像, 93, 74–94. https://doi.org/10.1016/j.neuroimage.2014
.02.024, 考研: 24583255

盛, J。, 王, B., 张, Q., 刘, Q., Ma, Y。, 刘, W., Shao, M。, &
陈, 乙. (2019). A novel joint HCPMMP method for automati-
cally classifying Alzheimer’s and different stage MCI patients.
Behavioural Brain Research, 365, 210–221. https://doi.org/10
.1016/j.bbr.2019.03.004, 考研: 30836158

史密斯, S. M。, Vidaurre, D ., 贝克曼, C. F。, Glasser, 中号. F。,
詹金森, M。, 磨坊主, K. L。, Nichols, 时间. E., 罗宾逊, 乙. C。,
Salimi-Khorshidi, G。, 伍尔里奇, 中号. W., Barch, D. M。, Uğurbil, K.,
& Van Essen, D. C. (2013). Functional connectomics from
resting-state fMRI. 认知科学的趋势, 17(12), 666–682.
https://doi.org/10.1016/j.tics.2013.09.016, 考研: 24238796
Sperling, 右. A。, Aisen, 磷. S。, 贝克特, L. A。, Bennett, D. A。, Craft, S。,
费根, A. M。, Iwatsubo, T。, 杰克, C. R。, Kaye, J。, Montine, 时间. J。,
公园, D. C。, Reiman, 乙. M。, 罗维, C. C。, Siemers, E., Stern, Y。,
Yaffe, K., Carrillo, 中号. C。, Thies, B., Morrison-Bogorad, M。, ……
Phelps, C. H. (2011). Toward defining the preclinical stages of
阿尔茨海默氏病: Recommendations from the National Insti-
tute on Aging-Alzheimer’s Association workgroups on diagnostic
guidelines for Alzheimer’s disease. Alzheimer’s & Dementia, 7(3),
280–292. https://doi.org/10.1016/j.jalz.2011.03.003, 考研:
21514248

斯塔姆, C。, 琼斯, B., 诺尔特, G。, Breakspear, M。, & Scheltens, 磷.
(2007). Small-world networks and functional connectivity in
阿尔茨海默氏病. 大脑皮层, 17(1), 92–99. https://土井
.org/10.1093/cercor/bhj127, 考研: 16452642

Supekar, K., Menon, 五、, 鲁宾, D ., Musen, M。, & Greicius, 中号. D.
(2008). Network analysis of intrinsic functional brain connectiv-
ity in Alzheimer’s disease. PLOS Computational Biology, 4(6),
e1000100. https://doi.org/10.1371/journal.pcbi.1000100,
考研: 18584043

王, D ., Belden, A。, Hanser, S. B., Geddes, 中号. R。, & Loui, 磷.
(2020). Resting-state connectivity of auditory and reward systems
in Alzheimer’s disease and mild cognitive impairment. Frontiers
in Human Neuroscience, 14. https://doi.org/10.3389/fnhum
.2020.00280, 考研: 32765244

王, J。, Zuo, X。, Dai, Z。, Xia, M。, 赵, Z。, 赵, X。, Jia, J。, Han,
Y。, & 他, 是. (2013). Disrupted functional brain connectome in
individuals at risk for Alzheimer’s disease. Biological Psychiatry,
73(5), 472–481. https://doi.org/10.1016/j.biopsych.2012.03.026,
考研: 22537793

王, R。, 王, J。, 于, H。, Wei, X。, 哪个, C。, & Deng, 乙. (2014).
Decreased coherence and functional connectivity of electroen-
cephalograph in Alzheimer’s disease. Chaos: An Interdisciplinary
Journal of Nonlinear Science, 24(3), 033136. https://doi.org/10
.1063/1.4896095, 考研: 25273216

Watts, D. J。, & Strogatz, S. H. (1998). Collective dynamics of
‘small-world’ networks. 自然, 393(6684), 440–442. https://土井
.org/10.1038/30918, 考研: 9623998

Xia, M。, 王, J。, & 他, 是. (2013). BrainNet Viewer: A network
visualization tool for human brain connectomics. PLOS One, 8(7),
e68910. https://doi.org/10.1371/journal.pone.0068910, 考研:
23861951

叶, C。, 森, S。, Chan, P。, & Ma, 时间. (2019). Connectome-wide net-
work analysis of white matter connectivity in Alzheimer’s dis-
舒适. 神经影像: Clinical, 22, 101690. https://doi.org/10.1016
/j.nicl.2019.101690, 考研: 30825712

Yi, D ., 李, Y。, Byun, 中号. S。, 李, J. H。, Ko, K., Sohn, 乙. K., Choe,
是. M。, Choi, H. J。, Baek, H。, Sohn, C.-H., Kim, 是. K., 李, D. Y。, &
for the KBASE Research Group. (2018). Synergistic interaction
between APOE and family history of Alzheimer’s disease on
cerebral amyloid deposition and glucose metabolism. Alzhei-
mer’s Research & Therapy, 10(1), 84. https://doi.org/10.1186
/s13195-018-0411-x, 考研: 30134963

周, J。, Gennatas, 乙. D ., 克莱默, J. H。, 磨坊主, 乙. L。, & Seeley,
瓦. 瓦. (2012). Predicting regional neurodegeneration from
the healthy brain functional connectome. 神经元, 73(6),
1216–1227. https://doi.org/10.1016/j.neuron.2012.03.004,
考研: 22445348

朱, F. (2018). Improved collective influence of finding most influ-
ential nodes based on disjoint-set reinsertion. Scientific Reports,
8(1), 14503. https://doi.org/10.1038/s41598-018-32874-5,
考研: 30266910

朱, X。, 王, X。, Xiao, J。, Liao, J。, Zhong, M。, 王, W., & Yao, S.
(2012). Evidence of a dissociation pattern in resting-state default
mode network connectivity in first-episode, treatment-naive
major depression patients. Biological Psychiatry, 71(7), 611–617.
https://doi.org/10.1016/j.biopsych.2011.10.035, 考研:
22177602

网络神经科学

233

我

D
哦
w
n
哦
A
d
e
d

F
r
哦
米
H

t
t

p

:
/
/

d
我
r
e
C
t
.

米

我
t
.

/

t

/

e
d
你
n
e
n
A
r
t
我
C
e
–
p
d

我

F
/

/

/

/

/

6
1
2
1
3
2
0
0
2
4
2
8
n
e
n
_
A
_
0
0
2
2
1
p
d

t

.

F

乙
y
G
你
e
s
t

t

哦
n
0
7
S
e
p
e
米
乙
e
r
2
0
2
3

下载pdf