Abnormal Functional Brain Networks in Mild Cognitive Impairment and Alzheimer’s Disease: A Minimum Spanning Tree Analysis

Abstract

Alzheimer’s disease (AD) disrupts the topological architecture of whole-brain connectivity. Minimum spanning tree (MST), which captures the most important connections in a network, has been considered an unbiased method for brain network analysis. However, the alterations in the MST of functional brain networks during the progression of AD remain unclear. Here, we performed an MST analysis to examine the alterations in functional networks among normal controls (NCs), mild cognitive impairment (MCI) patients, and AD patients. We identified substantial differences in the connections among the three groups. The maximum betweenness centrality, leaf number, and tree hierarchy of the MSTs showed significant group differences, indicating a more star-like topology in the MCI patients and a more line-like topology in the NCs and AD patients. These findings may correspond to changes in the core of the functional brain networks. For nodal properties (degree and betweenness centrality), we determined that brain regions around the cingulate gyrus, occipital lobes, subcortex, and inferior temporal gyrus showed significant differences among the three groups and contributed to the global topological alterations. The leaf number and tree hierarchy, as well as the nodal properties, were significantly correlated with clinical features in the MCI and AD patients, which demonstrated that more star-to-line topology changes were associated with worse cognitive performance in these patients. These findings indicated that MST properties could capture slight alterations in network topology, particularly for the differences between NCs and MCI patients, and may be applicable as neuroimaging markers of the early stage of AD.

Keywords

Alzheimer’s disease brain networks functional magnetic resonance imaging mild cognitive impairment minimum spanning tree

INTRODUCTION

Alzheimer’s disease (AD) is a neurodegenerative disorder characterized by dementia and cognitive decline [1]. Mild cognitive impairment (MCI) is an intermediate disease stage that occurs at the onset of early AD, and subjects with MCI are at a high risk of developing AD [2, 3]. Various studies have described AD as a disconnection syndrome as a result of the observed alterations in the functional and structural connectivity of brain regions [4, 5], and it has been demonstrated that patients with MCI and AD have altered functional and whole-brain connectivities [6, 7].

The brain has been structurally and functionally conceived as a complex network. By means of graph theory, topological analyses of human brain networks have confirmed that brain networks in healthy subjects have topological attributes, such as small-worldness, hubness, and rich clubs [8, 9]. Recent studies have indicated abnormal functional brain networks in AD patients, with a loss of small-world features, disturbed community structure, and selective hub vulnerability in both structural and functional network studies [10 –12]. For example, using resting-state functional magnetic resonance imaging (rs-fMRI), Liu et al. showed that both MCI and AD patients exhibited a loss of small-world attributes, as indicated by longer path lengths and larger clustering coefficients, and the properties of the whole-brain networks in the MCI patients ranged between those of normal subjects and AD patients [11]. Christos et al. also reported that amnestic MCI and mild dementia patients showed reduced global network properties (small-worldness and mean clustering coefficient) compared with those of healthy controls [12]. Yao et al. determined that the clustering coefficient and the path length of the cortical network in subjects with MCI exhibited median values between the values of normal controls (NCs) and AD patients over a wide range of sparse threshold values. However, no significant difference in the two measurements was identified between the NC and MCI populations or the MCI and AD populations over the entire range of sparse threshold values [13]. An 18 F-deoxyglucose positron emission tomography (FDG-PET) study reported the opposite result, in which the clustering coefficient was lower in both MCI and AD patients than NCs; moreover, MCI patients showed more severe alterations in the clustering coefficient than AD patients, rather than being intermediate between the NC and AD subjects [14]. These studies suggest that brain networks may be disrupted in a disease-specific manner; however, the reported directions of the disruptions are inconsistent, which might reflect biases introduced by network construction.

Although conventional brain network analyses are widely employed and have resulted in substantial achievements, these analyses suffer from methodological problems in comparing network parameters across different groups and conditions [15, 16]. Conventionally, after constructing a weighted connectivity matrix of functional correlation or synchronization, a threshold (or a range of thresholds) is used to generate a binary matrix (connections exist or do not exist). The corresponding network topology of the binary matrix may subsequently be characterized by calculating the network properties of interest. Importantly, most network characteristics depend on the number of connections in the network, and the estimated network topology is therefore biased by the choice of the threshold. This limitation hinders meaningful comparisons of network topology between individuals or groups [13, 14]. It has been proposed that threshold problems may be avoided by normalizing the network parameters by comparison with network parameters of surrogate networks with a matched number of nodes and number of edges; however, this normalization strategy does not eliminate the issues of bias [16]. The use of the original weighted networks leads to similar problems because differences in average weights influence the values of network parameters and cause biased group comparisons [15, 16].

An alternative approach is to construct and compare the minimum spanning trees (MSTs) of the original weighted graphs [17]. An MST, which connects all nodes in the original weighted network without forming cycles, is a simplified representation of the core network with a minimized connection cost. Therefore, each MST has the same number of nodes and connections, which enables the direct comparison of network properties between groups and avoids the previously described methodological biases [15, 18]. MSTs are insensitive to scaling effects because their topology depends only on the ordering of the weights in the original network and not on the absolute values or the distribution of these weights [17]. Importantly, changes in the topology of MSTs strongly correlate with changes in the topology of the underlying network. For alterations on the scale of regular to random networks, the MST diameter and leaf number change similarly to the path length for the underlying network. The MST diameter is positively correlated with the path length, and the MST leaf number is negatively correlated with the path length [18]. Previous brain network studies using MSTs have shown that MST analysis provided a sensitive and practical tool for tracking developmental network changes and identifying abnormal brain network topology in epilepsy, multiple sclerosis, child development, aging, and Parkinson’s disease [19 –23]. An fMRI study showed that the MST of the default mode network was disrupted in AD patients compared with the MSTs of young and elderly controls [24]. A recent EEG study confirmed a parietal and occipital loss of MST organization in AD patients compared to subjects with subjective cognitive decline [25]. However, the alterations in the MST of functional brain networks measured via rs-fMRI in MCI and AD remain largely unclear.

In this study, to examine the alterations in functional networks among NCs, MCI patients, and AD patients, we analyzed the nodal strength and the global and nodal properties of MSTs. In addition, we evaluated the relationship between MST properties and clinical cognitive deterioration.

MATERIALS AND METHODS

Subjects

This study included 29 NCs, 62 MCI subjects, and 27 AD subjects (Table 1). Data used in the preparation of this article were obtained from the Alzheimer’s Disease Neuroimaging Initiative (ADNI) database (http://adni.loni.usc.edu). The ADNI was launched in 2003 as a public-private partnership, led by Principal Investigator Michael W. Weiner, MD. The study subjects provided written informed consent at the time of enrollment for imaging and completed questionnaires approved by the institutional review board (IRB) of each participating site, including Albany Medical College and Banner Alzheimer’s Institute.

Table 1

Demographics and neuropsychological characteristics

	NC	MCI	AD	ANOVA
Gender (M/F)	11/18	35/27	10/17	0.12 a
Age	74.0±6.1	71.9±7.2	72.1±7.4	0.35^b
Education	16.8±2.0	16±2.4	16±2.7	0.41 b
MMSE	28.9±1.6	27.3±2.3	21.0±3.3	< 0.0001 b
CDR	0.1±0.2	0.9±0.3	0.5±0.1	< 0.0001 b
FAQ	4.8±3.6	2.9±3.2	0.7±1.3	< 0.0001 b

Data are represented as the mean±standard deviation (SD); MMSE, Mini-Mental State Examination; CDR, Clinical Dementia Rating; FAQ, Functional Activities Questionnaire.

The p values were obtained by an independent Pearson chi-square test;

The p values were obtained by one-way ANOVA.

The fMRI data were collected using a 3.0-Tesla Philips MRI scanner. The rs-fMRI data of each subject consisted of 140 functional volumes. The rs-fMRI scans were acquired using a single-shot echo-planar imaging (EPI) pulse sequence with pixel size 3.3 mm×3.3 mm; flip angle 80.0°; TE = 30 ms; TR = 3000 ms; matrix = 64×64; and 48 slices. Structural T1-weighted images were obtained using a sagittal 3D magnetization-prepared rapid acquisition with a gradient echo MP-RAGE sequence with pixel size 1 mm×1 mm×1.2 mm; flip angle ∼9°; TE ∼4 ms; TR ∼7 ms; matrix = 256×256; and 170 slices.

Image processing

The preprocessing of the rs-fMRI data was performed using the Data Processing Assistant for Resting-State fMRI (DPARSF) toolbox [26] and the SPM8 package (http://www.fil.ion.ucl.ac.uk/spm). Briefly, the preprocessing steps were as follows: the first 10 volumes of the functional images during the participant’s adaptation to the circumstances were discarded; slice-timing correction was performed; the images were realigned for head movement compensation using a six-parameter rigid-body spatial transformation; the images were normalized to the Montreal Neurological Institute (MNI) space; the signal drift was removed using a linear model; and the images were further spatially smoothed with a 6-mm full-width at half-maximum (FWHM) Gaussian kernel. Finally, temporal filtering (0.01 Hz < f < 0.1 Hz) was applied to the time series of each voxel.

Functional network construction

As shown in Fig. 1, the fMRI data were segmented into 90 regions (45 for each hemisphere, Supplementary Table 1) using an automated anatomical labeling template [27]. The time series of each individual region was obtained by averaging the fMRI time series over all voxels in this region. An interregional correlation matrix (90 * 90) was subsequently obtained by calculating the Pearson correlation coefficients of the time series for each pair of regions. Currently, all self-connections or negative connections (for elusive function in negative correlations) must be removed from the networks prior to analysis [28].

Fig. 1

Schematic overview of the image processing pipeline for each subject. The weighted MST was generated from the functional network with the weights of Pearson correlation coefficients.

MST properties

An MST is defined as a weighted, undirected subset of network nodes with the least total weight of all connections among all possible spanning trees that connects all nodes and contains no cycles [17]. As the functional connections with stronger strengths are more important in the network, the strengths of connection were inversed, and the MST method was subsequently applied based on the Kruskal algorithm [29]. Using this method, an MST of a functional network that contains 90 nodes and 89 connections is generated for each individual (Fig. 1). The MST was simplified; however, the impact of the larger connections on the network performance was retained. Finally, the connections of MST were weighted as the original strengths of the functional connection.

After constructing the MST, the nodal strength may be calculated for each node as the sum of the correlation coefficients of all connections coupled to a node. To characterize the topology of the MSTs, all connection weights were assigned to 1, and binary MSTs were used. We initially characterized the topology of the MSTs using MST overlap, defined as the percent of the MST connection (the number of existing connections in one group divided by the total number of subjects). We then further calculated three nodal MST properties, including the degree, betweenness centrality (BC), and eccentricity of each node, and six global MST properties, including the maximum degree, maximum BC, eccentricity, diameter, leaf number, and tree hierarchy [19]. We provided the definitions and brief interpretations of the MST properties in Supplementary Table 2.

Statistical analysis

The statistical analysis was performed with SPSS (version 19, IBM SPSS Statistics, Chicago, IL). Group differences were evaluated using one-way analysis of variance (ANOVA) with age, gender and education as covariates. Tukey’s post hoc pairwise test for multiple comparisons was performed for significant group differences (F(2,115) > 3.05, p < 0.05). We investigated the relationship between MST properties and behavior using a partial correlation analysis, with age, gender and education as covariates.

RESULTS

Connectivity and strength of MST

As shown in Fig. 2A, the variability in the connections was obtained as the percentage of subjects in each group. Connections with a large percentage were likely to show a stable core of tree topology across subjects, whereas connections with a smaller percentage showed more subject-specific variations. We also identified several connections with a significant difference in percentage among the three groups mainly around frontal and parietal lobes (Fig. 2B). The multiple comparisons showed that these connections of MCI had smaller percentages than those of NC and AD. There was small number of connections showed differences in percentage (Fig. 2C). We further identified significant changes in the nodal strength in several nodes (all: F≥3.15, p < 0.05, Fig. 3). For example, the posterior cingulate gyrus, left amygdala, and inferior temporal gyrus showed higher strengths in the NC than MCI and AD (p < 0.05, corrected). Compared with the NCs and MCI patients, the AD patients had a lower strength in the right calcarine and a higher strength in the right putamen. The strength of the left middle frontal gyrus was lower in the MCI patients than the NCs.

Fig. 2

Connection overlap of MST. A) The matrix shows the percent of subjects that share each connection. The color range scales the tree connections from 0.01 (blue; connection owned by one subject) to 100% (light blue; connection shared by all subjects). B) The matrix shows the connections that were significantly different among the three groups (p < 0.01); the color indicates the significance. C) The connections with significant differences in pairwise comparisons (p < 0.01). The former versus the latter; the blue indicates negative, and the red indicates positive. The p values were obtained by an independent Fisher’s chi-square test.

Fig. 3

Network nodal strengths of the NC (left), MCI (middle) and AD (right) subjects. Significant differences in pairwise comparisons are indicated, ^*p≤0.05; ^**p≤0.01.

Global MST properties

The global MST properties showed significant differences among the NCs, MCI patients, and AD patients, including the maximum BC (F = 3.06, p = 0.05), leaf number (F = 4.73, p = 0.01) and tree hierarchy (F = 6.55, p = 0.002, Fig. 4). In addition, the multiple comparisons showed that compared with the NC subjects, the MCI patients had a lower maximum BC (p = 0.04) and a higher leaf number (p = 0.03) and tree hierarchy (p = 0.01) (Fig. 4). Furthermore, the leaf number and tree hierarchy of the MCI patients were less than those of the AD patients (p < 0.01). No significant differences were identified in the six global properties between the NCs and AD subjects. The MST properties were further normalized by dividing by the MST properties from 1000 random networks and were significantly different from 1 (p < 0.01, Supplementary Figure 1). The normalized leaf number and tree hierarchy of the MCI patients were larger than those of the NCs and AD patients (p < 0.01), which indicates that the MCI network was closer to a random network.

Fig. 4

Distribution of MST global properties among the NC, MCI, and AD subjects. Horizontal line: mean value of properties; the significant differences among the NC, MCI, and AD subjects are shown by pairwise comparisons, ^*p < 0.05; ^**p < 0.01.

Nodal MST properties

As shown in Table 2, ANOVAs indicated differences across the three groups in nodal properties that were mainly concentrated in the medial and posterior cingulate gyrus, putamen, calcarine, and supplementary motor area. Tukey’s test for multiple comparisons was applied for nodal properties with significant differences according to ANOVA. The BC of the left middle cingulate and the bilateral posterior cingulate, as well as the degrees of the right pallidum and inferior temporal gyrus, were lower in the MCI and AD patients than those in the NC subjects (p < 0.05). The AD patients also had a smaller degree in the right calcarine than the MCI patients and NCs (p < 0.05). Compared with the MCI patients and NCs, the AD patients had higher BC and degree values in the right putamen (p < 0.05). In addition, the right cuneus and calcarine showed a higher degree in the MCI patients than in the AD patients and NCs (p < 0.05). We did not identify a difference in the eccentricity of nodes.

Table 2

Brain nodes with significant differences (p < 0.05) among the NCs, MCI patients, and AD patients

	Mean value			ANOVA
	NC	MCI	AD	F (2,115)	p value
BC
DCG.L	0.12 (0.02)	0.05 (0.02)	0.03 (0.02)	3.92	0.02 a , b
PCG.L	0.09 (0.02)	0.03 (0.01)	0.03 (0.02)	6.22	0.003 a , b
PCG.R	0.07 (0.02)	0.02 (0.01)	0.03 (0.02)	3.68	0.03 a , b
PUT.R	0.02 (0.02)	0.03 (0.01)	0.09 (0.02)	6,83	0.002 b , c
Degree
MFG.L	2.5 (0.20)	1.9 (0.14)	2.3 (0.21)	3.15	0.05 a
SMA.R	1.4 (0.16)	1.9 (0.11)	1.8 (0.17)	3.31	0.04 a
CAL.R	1.87 (0.15)	1.98 (0.19)	1.48 (0.15)	4.53	0.01 c
CUN.R	1.8 (0.16)	2.15 (0.11)	1.6 (0.17)	3.52	0.03 c
PUT.R	1.51 (0.16)	1.56 (0.11)	2.07 (0.16)	3.77	0.03 b
PAL.R	1.91 (0.15)	1.48 (0.11)	1.39 (0.16)	3.35	0.04 b
ITG.L	3.28 (0.27)	2.47 (0.19)	2.36 (0.29)	3.56	0.03 a

The NC and MCI groups showed significant differences (p < 0.05);

The NC and AD groups showed significant differences (p < 0.05);

The MCI and AD groups showed significant differences (p < 0.05). NC, normal control; MCI, mild cognitive impairment; AD, Alzheimer’s disease; BC, betweenness centrality; DCG, median cingulate & paracingulate gyri; PCG, posterior cingulate gyrus; PUT, putamen; MFG, middle frontal gyrus; SMA, supplementary motor area; CAL, calcarine; CUN, cuneus; PAL, pallidum; ITG, inferior temporal gyrus; L, left; R, right.

To further clarify the alteration in degrees from NC to AD via MCI, we analyzed the degree distribution of each node as the percentage of subjects in each group (Fig. 5). We identified significant differences in the degree distribution among the three groups. The NC group showed a higher percentage at degrees of 3 in the left amygdala, superior parietal gyrus, and right supplementary motor area than MCI and AD patients (p < 0.05). The right supplementary motor area exhibited an opposite pattern of change for the degree of 4. Moreover, the AD patients showed higher percentages at degrees of two in the left parahippocampal gyrus and left lingual gyrus than the NC and MCI (p < 0.01). The percentages became smaller at degree 1, particularly for the left lingual gyrus (p < 0.001).

Fig. 5

Distribution of degree of nodes among the NC, MCI, and AD groups. The values represent the percentage of subjects at each degree level. Because relatively few subjects had a node degree larger than 4, we regarded a degree of 4 or greater as a signal level. The p values were obtained by an independent Fisher’s chi-square test. ^*p < 0.05; ^**p < 0.01; ^***p < 0.001.

Relationship between MST properties and clinical features

A partial correlation analysis with age, gender and education as covariates was performed to explore the relationship between MST properties and clinical features (Table 3). The results showed that the leaf number and tree hierarchy had significant positive correlations with the Mini-Mental State Examination (MMSE) scores and significant negative correlations with the CDR, Clinical Dementia Rating (CDR) and Functional Activities Questionnaire (FAQ) scores. In addition, the BC in the right posterior cingulate gyrus showed a significant positive correlation with the MMSE scores and a significant negative correlation with the FAQ scores. The degree in the right calcarine showed a significant negative correlation with the CDR and FAQ scores. The BC in the putamen showed a significant negative correlation with the MMSE scores.

Table 3

Partial correlation between the MST properties and MMSE scores in AD and MCI patients

	MMSE		CDR		FAQ
	r	p	r	p	r	p
Global Properties
Leaf number	0.23	0.03	−0.21	0.05	−0.23	0.04
Tree hierarchy	0.26	0.02	−0.21	0.05	−0.29	0.01
BC
PCG.L	0.294	0.006	− 0.20	0.07	−0.285	0.008
PUT.R	−0.28	0.01	0.11	0.30	− 0.04	0.70
Degree
CAL.R	− 0.21	0.06	−0.26	0.02	−0.22	0.04
ITG.L	0.13	0.24	− 0.14	0.21	−0.22	0.05

Significant correlations are indicated in bold. r, the coefficient of partial correlation; p, significance; MMSE, Mini-Mental State Examination; CDR, Clinical Dementia Rating; FAQ, Functional Activities Questionnaire; BC, betweenness centrality; PCG, posterior cingulate gyrus; PUT, putamen; CAL, calcarine; ITG, inferior temporal gyrus; L, left; R, right.

DISCUSSION

Previous studies have provided valuable insights into brain network alterations among NC, MCI, and AD subjects; however, these studies were prone to the methodological limitations inherent to classical network analytical approaches. The network characteristics depend on the number of connections and might be biased by the choice of the threshold, thus resulting in inconsistent results [13, 14], and may fail to be eliminated even by normalizing the network parameters with the surrogate networks with matched number of nodes and number of edges [16]. To overcome this bias in methodology, we used an MST approach to determine and analyze the whole-brain network topological properties of NC, MCI, and AD subjects and characterize cognitive performance-related changes in the patients. We identified significant alterations in the nodal strength and MST network properties. The MST properties with the most pronounced differences were the maximum BC, leaf number and tree hierarchy, which indicated a star-like topology in MCI patients and a line-like topology in NCs and AD patients. This star-to-line difference in topology between MCI and AD patients was clinically relevant, as it was associated with worse cognitive performance.

Alterations in the nodal strength of MST

Neuroimaging studies have suggested that brain dysfunction in AD is better explained by a disturbance of the interactions between different brain areas than by alterations in a specific brain area [5, 30]. In our study, significant differences in the nodal strength among the three groups were also identified in the left middle frontal gyrus, the left posterior cingulate gyrus, the right calcarine cortex and the right putamen (Fig. 3). These findings are consistent with the alteration in the degree of the nodes, the findings of previous studies [31 –33], and the degree in MST (Table 2). These nodes have typically been shown to overlap with regions with a high degree [31, 34] and exhibited continued brain atrophy and a decline in synaptic numbers in these regions [35, 36].

Alteration pattern of MST properties

AD is characterized by abnormal network properties during the progression from NC to MCI and AD, which are determined by analyzing the network efficiency and small-word properties [10–12 , 38]. In the present study, we identified a new pattern of topological alterations from NC to MCI and AD. The MCI patients had a significantly lower maximum BC and higher leaf numbers and tree hierarchy than the NCs, as well as larger leaf numbers and tree hierarchy than the AD patients, which suggest a more star-like topology in the MCI patients and a more line-like topology in the NCs and AD patients [18], thus indicating the similarity of the network of MCI to random-like networks [11, 12]. The normalized MST properties also supported our findings (Supplementary Figure 1). The leaf number and tree hierarchy of the MCI patients were closer to 1 and significantly larger than those of the NCs and MCI patients. This interesting alteration pattern in the process of AD was also reported in a recent study of functional networks based on FDG-PET data. The authors reported that the clustering coefficients of the networks of MCI patients were lower than those of NC subjects and AD patients [14]. However, most studies involving fMRI [11 , 38] and EEG [12] have indicated that functional network properties varied in a gradient during the progression from NC to MCI and ultimately to AD. Moreover, other studies have not identified differences in network properties among MCI patients, AD patients, and NCs [10 , 39–41]. The MST of rs-fMRI has been proposed to have the capability to characterize the novel alteration patterns of brain networks over the AD progression.

There were two potential interpretations of the alteration patterns of MST. First, only 60 to 70% of MCI patients proceed to AD, while the remaining patients do not [42]; thus, the differences in MST between MCI patients and NCs or AD patients might be a result of this contamination of non-AD cases. Moreover, there was another potential interpretation related to the difference between MCI and AD. Although the NCs and AD patients showed similar global MST properties, the patterns of MST also reflected the development of disconnection as AD progressed. Our findings on the node strength and node properties supported this idea. MSTs mainly captured connections with larger correlation coefficients and discarded connections with weaker correlation coefficients in functional brain networks [15, 18]. We showed that the MSTs consisted of a stable core and a more variable periphery for functional brain networks (Fig. 2). We further determined that some nodes with a high degree or BC showed significant variation among the three groups (Table 2), such as the left calcarine and posterior cingulate gyrus [34]. Moreover, these nodes played a central or hub-like role in the classical network. We suggested that the alterations in these nodes might be a result of the destruction of the connections of nodes with a high degree and nodes with a low degree. Thus, to illustrate the alterations, we described a network model built from the MSTs of average functional networks (Fig. 6A-C). The model MST had eleven nodes, mainly located in the occipital lobe, to explain the alterations in MST topology among these three groups of subjects (Fig. 6). At the NC stage (Fig. 6D), the MST topology typically reflects the inherent brain networks and exhibits a line-like topology. At the MCI stage (Fig. 6E), connections among these low-degree nodes were first destroyed, such as the connection of the left calcarine and left inferior occipital gyrus; the MST reconstructed and captured new connections. Consistent with the group result, the left calcarine and left inferior occipital gyrus showed decreased degrees and BC. At the stage of AD (Fig. 6F), the connections of the whole-brain network were destroyed, particularly for the connections of high degree nodes [6, 7]. Some core connections present in NCs or MCI patients were discarded, resulting in a line-like topology and decreased degrees in the cuneus. The MST properties of these models also confirmed that MCI patients have significantly higher leaf numbers and tree hierarchy than NCs and AD patients. Although the MST of the AD patients and NCs showed a line-like topology, the connections were quite different. In the following sections, we present an additional discussion in detail.

Fig. 6

Example MSTs showing the alterations in topology among the NC, MCI, and AD subjects. These nodes of MSTs were mainly located in the occipital lobe. A-C) The functional networks of the three groups; the width of the connection reflects the correlation coefficient. D, E) The MSTs of the three groups. D) The MST of the NCs resembles a line-like topology. E) The MST of MCI resembles a star-like topology. F) The MST of AD resembles a line-like topology. LN, leaf number; BC max, maximum BC; TH, tree hierarchy.

Global properties between MCI and NC

According to the results (Fig. 4), MCI patients have a significantly lower maximum BC and higher leaf numbers and tree hierarchy than NCs, which indicates a more star-like topology of the global functional brain network in MCI patients [18]. For example, as shown in Fig. 6E, the connections between the left inferior occipital gyrus and left lingual gyrus were discarded at the MCI stage and changed to a star-like topology. This finding indicated a more star-like topology of the MST and a more random-like network topology in the MCI patients. Consistent with previous studies on functional networks, the significant loss of small-world properties in MCI patients also showed a more random-like network topology [12 , 43]. These findings indicated a more star-like MST and a more random-like network in MCI patients, as a result of the disconnections that developed during the progression of degeneration [11, 44]. MSTs might be sensitive to slight changes in brain networks, such as the differences between NCs and MCI patients. We proposed that the MST preserved the core of the brain network and could reflect the alterations of the brain network, particularly for nodal properties.

Global properties between MCI and AD

Interestingly, the MST metric of the AD patients showed significant decreases in leaf number and tree hierarchy compared with the MCI patients (Fig. 4). The MST networks of the AD patients were likely to have a more line-like topology (closer to a regular network topology) [18]. It is widely accepted that AD neuropathology begins in the medial temporal lobe and parietal-occipital lobe during the MCI stage and then gradually progresses to brain lesions that extend throughout the whole brain [45, 46]. We also determined that the alterations in nodes began to reduce at the MCI stage, such as the posterior cingulate gyrus, as more severe brain atrophy developed [35, 47], and AD patients showed a decrease in the degree or BC in the right cuneus and the right calcarine cortex and failed to capture this connection with the right cuneus (Fig. 6F). The line-like topology of AD reflects the disconnection of core connections and the destruction of regular core connections in NC. For example, the right cuneus and the right calcarine cortex areas with a high degree or nodal strength were decreased from MCI to AD, which is consistent with previous studies [31 , 47–50]. At the AD stage, the MST was likely to discard these connections of nodes with a high degree and nodes with a low degree, which were present at the MCI stage, thus resulting in the reformatting of the MST into a line-like topology. This finding was also supported by a recent report on the rich club of brain networks [44], in which at the MCI stage, the peripheral connections were mainly destroyed, and as AD progressed, richer club connections were destroyed. Thus, we considered that MSTs were likely to represent the degeneration in AD patients in a novel way.

Supporting the more line-like tree topology in the AD subjects, we identified significant correlations between MST properties (leaf number and tree hierarchy) and clinical features, such as positive correlations with MMSE scores and negative correlations with CDR and FAQ scores. The pathophysiological process of AD is thought to begin prior to the diagnosis of dementia [51, 52]. These results coincide with the previously described group differences in global MST properties; as dementia became more severe, the MST properties were related to clinical features.

Alterations in MST properties between NCs and AD patients

Although there were no significant differences between the AD patients and NCs in the global measures of MST topology (Fig. 4), we identified significant differences in the nodal properties between the two groups (Table 2). In previous studies, Ciftci et al. also reported consistent findings that indicated the local part of the MST network changed in AD [24]. We determined that the AD patients showed changes in strength and node properties (degree and BC) compared with the NCs. The AD patients lacked the connection of the right supplementary motor area and right paracentral lobule; however, they gained connections between the superior frontal gyrus and right orbital part of the inferior frontal gyrus (Fig. 2). Moreover, with more severe brain atrophy [35, 47], the degrees of the right calcarine, left posterior cingulate gyrus, right pallidum and left inferior temporal nodes decreased in AD. However, the left supplementary motor area showed an increased degree. As the nodal properties were different, we considered the MST topologies of the NCs and AD patients to be different.

Alterations in the nodal properties of MST

We identified decreases in the strength, BC, and degree in the posterior cingulate gyrus, right pallidum and left inferior temporal nodes from the NC to MCI and ultimately to AD (Table 2), which suggested that the network exhibited a reduced dependence on nodes with a high degree. The decrease in these nodal properties might be related to the reduced connectivity of the posterior cingulate cortex in MCI and AD patients [47 –50], as a result of the continued brain atrophy and decline in synaptic numbers in this region [35, 36]. These decreasing connections with the posterior cingulate cortex are thought to be related to dysfunctions in the encoding and retrieval of episodic memories [53]. Furthermore, we identified an increased strength, degree, and BC of the right putamen in the AD patients. Despite strongly reduced volumes of the putamen in AD patients [54, 55], the increase in the BC of the right putamen suggested that compensatory mechanisms may occur with disease progression. Similar compensatory mechanisms were observed for the left supplementary motor area, despite also being affected by AD pathology [56]. There was a higher degree in MCI and AD patients than in NCs as a result of the larger percent of degree distribution for the 4 degree level. Evidence that more subjects had connections between the supplementary motor area and the superior frontal gyrus also supported this interpretation (Fig. 2). It is widely believed that the supplementary motor area and putamen are related to motor function [56, 57]. It has been shown that older adults commonly recruit more sensorial motor regions to counteract neurobiological changes as a result of aging and the progression of AD [56, 58]. The large BC and degree in MST might reflect a greater importance of information transmission. Therefore, interventions that target the amelioration of sensory-motor deficits in AD patients may enhance patient function as AD progresses [56]. Furthermore, we determined that the centrality in the putamen was negatively correlated with the MMSE score, which also supports the important role of compensatory mechanisms in motor regions.

Limitations and future work

Our study has several limitations. First, the MST is sensitive to alterations in the connection strength. We determined that the MST consisted of a stable core and a more variable periphery for functional brain networks, and the MCI patents showed significant differences compared with the NC and AD patients. The present study identified more significant differences between the NCs and MCI patients than conventional small-world analyses [59]. However, we failed to identify differences between the NCs and AD patients, which were identified in previous studies [13, 60]. The MST properties showed a nongradient descent trend, which might limit the application to clinical measures. Moreover, the MST might be sensitive to slight changes in brain networks, such as the differences between NCs and MCI patients. We proposed that the MST preserved the core of the brain network and could reflect the alterations of the brain network, particularly for nodal properties, may be applicable to measures of alterations during the early stage of AD. In future work, we will improve the MST by adding the density of the connections. We also consider it important to quantify the role of the stable core connection in the brain networks of AD patients. Second, the sample size of the NC and AD groups (less than 30) was somewhat limited compared with that of the MCI group (more than 60). The weak statistical threshold may be associated with the small sample size. With a larger sample of subjects, these differences in the connections of the variable periphery will become more stable and significant, which is important for clarifying the changes in network topology from NCs to AD via MCI.

Conclusion

In this analysis of functional brain networks, we used MSTs to demonstrate alterations in network topology during the progression from normal cognition to MCI and ultimately AD. MST network analyses are not biased by commonly encountered methodological issues, such as the use of arbitrary thresholds, and are sensitive to characterizing functional network changes among NCs, MCI patients and AD patients. The differences among the MST properties were most pronounced for the maximum BC, leaf number and tree hierarchy, thus indicating a more star-like topology in MCI patients and a more line-like topology in NCs and AD patients, which may reflect changes in the core connections of the brain networks. For nodal MST properties, we determined that the cingulate, putamen and cuneus showed significant differences among the three groups, which might contribute to network topological alterations. The leaf number and tree hierarchy were significantly positively correlated with clinical features in the MCI and AD patients, which demonstrated that the star-to-line topology changes were associated with worse cognitive performance in these patients. These findings indicated that MST properties could capture the core connections of brain networks and reflect the alterations in network topology from NCs to MCI and AD patients. Specifically, the differences between NCs and MCI patients suggested a potential application as neuroimaging markers of the early stage of AD.

Footnotes

ACKNOWLEDGMENTS

This project was supported by the National Natural Science Foundation of China (61503272, 61305142, and 61373101), the Natural Science Foundation of Shanxi (2015021090), a project funded by the China Postdoctoral Science Foundation (2016M601287), and the Scientific Research Foundation for Returned Overseas Chinese Scholars (2016-037).

Data collection and sharing for this project was funded by the Alzheimer’s Disease Neuroimaging Initiative (ADNI) (National Institutes of Health Grant U01 AG024904) and DOD ADNI (Department of Defense award number W81XWH-12-2-0012). ADNI is funded by the National Institute on Aging, the National Institute of Biomedical Imaging and Bioengineering, and through generous contributions from the following: AbbVie, Alzheimer’s Association; Alzheimer’s Drug Discovery Foundation; Araclon Biotech; BioClinica, Inc.; Biogen; Bristol-Myers Squibb Company; CereSpir, Inc.; Cogstate; Eisai Inc.; Elan Pharmaceuticals, Inc.; Eli Lilly and Company; EuroImmun; F. Hoffmann-La Roche Ltd and its affiliated company Genentech, Inc.; Fujirebio; GE Healthcare; IXICO Ltd.; Janssen Alzheimer Immunotherapy Research & Development, LLC.; Johnson & Johnson Pharmaceutical Research & Development LLC.; Lumosity; Lundbeck; Merck & Co., Inc.; Meso Scale Diagnostics, LLC.; NeuroRx Research; Neurotrack Technologies; Novartis Pharmaceuticals Corporation; Pfizer Inc.; Piramal Imaging; Servier; Takeda Pharmaceutical Company; and Transition Therapeutics. The Canadian Institutes of Health Research is providing funds to support ADNI clinical sites in Canada. Private sector contributions are facilitated by the Foundation for the National Institutes of Health (). The grantee organization is the Northern California Institute for Research and Education, and the study is coordinated by the Alzheimer’s Therapeutic Research Institute at the University of Southern California. ADNI data are disseminated by the Laboratory for Neuro Imaging at the University of Southern California.

Authors’ disclosures available online ().

The supplementary material is available in the electronic version of this article: .

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