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Edited by: Feng Shi, Amazon, United States

Reviewed by: Jingyun Chen, New York University, United States; Ying Han, Capital Medical University, China

†These authors have contributed equally to this work and share first authorship

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Alzheimer's disease (AD) is a neurodegenerative disease that commonly affects the elderly; early diagnosis and timely treatment are very important to delay the course of the disease. In the past, most brain regions related to AD were identified based on imaging methods, and only some atrophic brain regions could be identified. In this work, the authors used mathematical models to identify the potential brain regions related to AD. In this study, 20 patients with AD and 13 healthy controls (non-AD) were recruited by the neurology outpatient department or the neurology ward of Peking University First Hospital from September 2017 to March 2019. First, diffusion tensor imaging (DTI) was used to construct the brain structural network. Next, the authors set a new local feature index 2hop-connectivity to measure the correlation between different regions. Compared with the traditional graph theory index, 2hop-connectivity exploits the higher-order information of the graph structure. And for this purpose, the authors proposed a novel algorithm called 2hopRWR to measure 2hop-connectivity. Then, a new index global feature score (GFS) based on a global feature was proposed by combing five local features, namely degree centrality, betweenness centrality, closeness centrality, the number of maximal cliques, and 2hop-connectivity, to judge which brain regions are related to AD. As a result, the top ten brain regions identified using the GFS scoring difference between the AD and the non-AD groups were associated to AD by literature verification. The results of the literature validation comparing GFS with the local features showed that GFS was superior to individual local features. Finally, the results of the canonical correlation analysis showed that the GFS was significantly correlated with the scores of the Mini-Mental State Examination (MMSE) scale and the Montreal Cognitive Assessment (MoCA) scale. Therefore, the authors believe the GFS can also be used as a new biomarker to assist in diagnosis and objective monitoring of disease progression. Besides, the method proposed in this paper can be used as a differential network analysis method for network analysis in other domains.

Alzheimer's disease (AD) is a neurodegenerative disease that commonly affects the elderly. It is a continuous process, from the pre-clinical stage to mild cognitive impairment (MCI) to dementia. Effective intervention in the pre-dementia or MCI stage can slow down or reverse the disease process. Therefore, early identification of patients with AD in the pre-dementia or MCI stage, as well as early and timely intervention, are of great importance to the prognosis of patients. With the development of imaging technology, the detection of AD is no longer limited to the phenomenon of abnormal protein deposition. Analysis of structural brain network information, such as brain connectome analysis, may be an effective method for early diagnosis and monitoring of disease progression (Fan et al.,

Previous studies (Liu et al.,

In this work, 20 patients with AD and 13 patients in the pre-dementia stages (non-AD) were recruited. The authors collected demographic data and clinical data and completed neuropsychological scale assessments and DTI scans. After preprocessing, the brain structural network was constructed based on the number of fibers between different brain regions. The data from the AD and the non-AD groups were analyzed to obtain the local topological features of the brain structural network. Meanwhile, the authors designed an algorithm called 2hopRWR to get the local feature index 2hop-connectivity, and then a new index global feature score (GFS) was proposed by combing four classical local features and 2hop-connectivity. As a result, the authors predicted and analyzed the top 10 brain regions based on the difference of the GFS scores between the AD and the non-AD groups. Then, the authors analyzed the correlation between the GFS and the cognitive scale scores by performing canonical correlation analysis (CCA). Finally, the strengths and limitations of the work presented in this paper and its prospects are discussed.

A case–control study design was adopted in this study. Patients with AD who were admitted to the neurology outpatient department or the neurology ward of Peking University First Hospital from September 2017 to March 2019 were recruited in the study. Normal controls were recruited at the same time. The inclusion criteria for the AD group were as follows: (1) Han nationality, over 18 years old, who were right-handed and agreed to participate in this study; (2) patients diagnosed as probable AD clinically according to the 2011 National Institute on Aging and the Alzheimer's Disease Society (NIA-AA) diagnostic criteria (McKhann et al.,

This study was approved by the Clinical Research Ethics Committee of Peking University First Hospital. All participants or their family members signed the informed consent.

In this research, 20 patients with AD and 13 healthy controls (non-AD) were recruited. Demographic information and the medical history of the participants were collected. Blood tests were conducted to exclude cognition impairment caused by other reasons. All the patients were assessed on a set of neuropsychological scales by the same trained neurologist to assess overall cognitive function including memory, executive function, language, and visuospatial and structural abilities of all the participants. The ability of daily living and mental and behavioral symptoms of the subjects were also evaluated (

Brain imaging examinations were performed by the Department of Imaging, Peking University First Hospital. The participants received imaging examination within 1 week before or after the completion of the scales. The images were collected by using a GE Discovery MR750 3.0Tesla MRI scanner. The acquisition sequence included the following: axial T1-weighted imaging, axial T2-weighted imaging, and high-resolution DTI sequences. Some of the sequence parameters were as follows:

Axial T1-weighted imaging: Repetition time (TR) = 2,500 ms. Echo time (TE) = 24.0 ms. Field of vision (FOV) = 24.0 cm × 24.0 cm. Layer thickness (ST) = 5 mm.

Axial T2-weighted imaging: TR = 8,400 ms. TE = 140.0 ms. FOV = 20.0 cm × 20.0 cm. ST = 3 mm.

DTI: TR = 4,600 ms. TE = 90.0 ms. FOV = 24.0 cm × 24.0 cm. ST = 4 mm. The dispersion sensitive gradient was applied in 25 directions, and 36 layers of images were scanned in each direction, b = 1,000 s/mm^{2}. Besides, there was a group of images without dispersion weighting, b = 0.

In this study, PANDA (Pipeline for Analyzing braiN Diffusion imAges) (Cui et al.,

The images of all individuals were placed in the standardized template and the eigenvalues of each dispersion were measured. The FA (fractional anisotropy) image of each individual was non-linearly loaded into the FA template (FMRIB58_FA_TEMPLATE) of the Montreal Neurological Institute (MNI) space. Through the results of transformation, the diffuse eigenvalues of each individual in the MNI space were resampled and the space was partitioned (the resolutions were 1 mm × 1 mm × 1 mm and 2 mm × 2 mm × 2 mm).

The deterministic fiber-tracking method, FACT [fiber assignment by continuous tracking [Mori and van Zijl,

Mathematically, the authors regarded 90 brain regions and their fiber connection as a weighted graph _{1}, _{2}, …, _{90}}, _{vivj}, _{i} ≠ _{j}}, _{vivj}}, where _{i} denotes the _{vivj} is the edge if there were fiber connection between brain region _{i} and _{j}, and _{vivj} is the edge weight that is the fiber number between the brain region _{i} and _{j}. The average value of the FN matrix of AD was calculated by adding the FN matrix of each patient with AD and dividing it by the number of patients with AD. Similarly, the authors took the average value of the FN matrix of all normal controls to the FN matrix of the non-AD group.

Let _{i}) denote the degree of a node _{i}, which is the number of nodes associated with _{i}. And the degree centrality of a node _{i} is defined as follows:

Betweenness centrality _{B} of a node _{i} is the sum of the fraction of the shortest paths of all pairs that pass through _{i}:

where σ(_{s}, _{t}) is the number of the shortest paths between _{s} and _{t}, and σ(_{s}, _{t}|_{i}) is the number of the shortest paths passing through the node _{i}. If _{s}, _{t}) = 1, and if _{s}, _{t}|_{i}) = 0.

In short, if the shortest path between many nodes in the network passes through a point

Closeness centrality _{c} of a node _{i} is the reciprocal of the sum of the shortest path distances from _{i} to all

where _{j}, _{i}) is the shortest path distance between _{j} and _{i}, and

Closeness centrality is the sum of the distance from a node to all other nodes. The smaller the sum, the shorter the path from this node to all other nodes is, and the closer the node is to all other nodes. It reflects the proximity between a node and other nodes.

In graph theory, the clique of graph _{MC}(_{i}) to represent the number of maximal cliques for node _{i}.

When examining the correlation between any two nodes in the network, most network analysis methods only consider whether there is an edge connection between two nodes, i.e., if there is an edge, the correlation is high, and if there is no connection, the correlation is weak. In this case, if the edges of the graph are missing due to the disturbance, the results may be highly biased. For example, for the general random walk (RW) algorithm, the state transition probability is determined by the adjacency matrix of the network. If the adjacency matrix is disturbed, its steady-state probability will change. Generally, when analyzing the correlation between network nodes, the correlation between unconnected nodes in the network will be very low, which makes it difficult to discover the potential characteristics of the network. For any two different nodes in the network, in order to describe the correlation more accurately, this work considers not only the first-order neighbors between the nodes but also the second-order neighbors between the nodes, and an algorithm called 2hopRWR is proposed. Finally, each node can get a novel local feature index 2hop-connectivity, whose numerical magnitude is represented by the local feature score _{2−hop}. The importance of a node can be judged based on _{2−hop}; the larger the _{2−hop}, the more important the node is.

The general random walk on the graph is a transition process that involves moving from a given node to a randomly selected neighboring node at each step. Therefore, the set of nodes {_{1}, _{2}, …, _{n}} is considered as a set of states {_{1}, _{2}, …, _{n}} in a finite Markov chain _{j}, _{i}) = _{t+1} = _{i} | _{t} = _{j}), which implies that the _{i} at time _{j} at time _{j} of ^{|V|×|V|} of

In general, the transition probability _{j}, _{i}) is defined as follows:

Denote _{G} = _{1}, _{2}, …, _{n}} as the diagonal matrix, where

Define _{i} at step _{t+1} can be calculated iteratively by:

For the random walk with restart (RWR) algorithm (Tong et al., _{t+1} can be calculated iteratively by using the following expression:

Define initial probability

However, the RW and RWR algorithms are based on the 1-hop neighbor relations, which means that the random walk is based on the existing edges of the graph.

A schematic diagram of 1-hop and 2-hop neighbors.

The probability _{t+1} can be calculated iteratively by:

where α_{1} and α_{2} are the percentages of choosing 1-hop and 2-hop neighbors, respectively. Specifically, for each point _{i} ∈ _{1} is the ratio of the number of 1-hop neighbors to the total number of 1-hop and 2-hop neighbors, α_{2} is the ratio of the number of 2-hop neighbors to the total number of 1-hop and 2-hop neighbors. Therefore, α_{1} + α_{2} = 1.

At the beginning of the 2hopRWR, a starting node _{i} is chosen; then, it would have a probability of _{j}, it has a probability of α_{1}_{2}_{i}.

After some steps, the 2hopRWR will be stable, i.e., when _{t+1} = _{t}. The proof is given in Section Proof of Convergence. When the 2hopRWR is stable, steady-state probability between node _{i} and node _{j} is defined as the _{t} corresponding to the starting node is _{i}.

2hopRWR algorithm framework.

Here, the authors will prove that the RWR algorithm is convergent, i.e., for Equation (8) when _{t+1} = _{t}.

Define:

Thus, using (9) and (10) we get:

Define,

Then,

By (13), when t = 0, we have _{0} = (_{0}, thus:

Since

Hence,

which implies that the convergence of the algorithm is proved.

Considering higher-order structural properties of a network is not a new idea. Certain works in the literature (Salnikov et al.,

Schematic—different stochastic processes on the network.

Therefore, it is clear that the higher-order information on the network defined in the literature (Salnikov et al.,

Any two nodes can be ranked twice according to 2hopRWR. Define Π = {π_{ij}}_{|V|×|V|} as the steady-state probability matrix, where π_{ij} indicates the steady-state probability between node _{i} and node _{j}, i.e., the probability of 2hopRWR starts from node _{i} and reaches node _{j} when the process is stable. In short, the value of π_{ij} is the _{0} is 1. Therefore, the local feature score _{2−hop} for node _{i} is defined as follows:

The 2hop-connectivity exploits the higher-order information of the graph structure relative to the traditional graph theory metrics. Since there is a certain amount of noise in DTI data, a certain threshold is chosen for denoising when converting DTI data into brain networks, i.e., when the number of fibers between two brain regions is low (lower than the threshold), no fiber tracts (edges) are considered between two brain regions (nodes). However, since there are inherently fewer fiber tract connections between brain regions in patients with AD, the brain network constructed after denoising may differ significantly from the true situation. The 2hop-connectivity is insensitive to 1-hop order relations and more robust to changes in the network structure, so 2hop-connectivity is instead more effective for sparse networks (e.g., structural brain networks in patients with AD).

In this paper, the authors consider the integration of local features to obtain a new network index: global feature.

The authors normalized the component of different feature scores to [0, 1]. The normalized features are recorded as _{D}, _{B}, _{C}, _{MC}, and _{2−hop}.

Then, define global feature score _{i} as follows:

In general, let the weight α_{i} = 1/5 (

Workflow of the approach presented in this paper.

By comparing the GFS of the non-AD group with that of the AD group, the authors got the top ten brain regions in GFS scoring difference (i.e., _{non−AD} (_{i}) − _{AD} (_{i})). Then, literature verification was carried out to find out whether these brain regions were related to AD, and the results are shown in

Top 10 brain regions in GFS scoring difference between AD and non-AD groups.

1 | 40 | ParaHippocampal_R | van Hoesen et al., |

2 | 3 | Frontal_Sup_L | Perri et al., |

3 | 37 | Hippocampus_L | Du et al., |

4 | 42 | Amygdala_R | Tsuchiya and Kosaka, |

5 | 22 | Olfactory_R | Wilson et al., |

6 | 78 | Thalamus_R | Ryan et al., |

7 | 15 | Frontal_Inf_Orb_L | Liu et al., |

8 | 9 | Frontal_Mid_Orb_L | Li et al., |

9 | 68 | Precuneus_R | Karas et al., |

10 | 38 | Hippocampus_R | Du et al., |

For the brain structure network of the AD and non-AD groups, visualization results (Manning et al.,

Brain structural network of the AD group.

Brain structural network of the non-AD group.

More importantly, the authors compared the respective predictive effects of all local features. As can be learned from

Comparison of the proportion of verified AD-related brain regions for top 10, 20, 30, and 40% ranked by different measures.

Top 10 | ||||||

Top 20 | 88.89 | 94.44 | 94.44 | 83.33 | 83.33 | |

Top 30 | 85.19 | 92.59 | 88.89 | 85.19 | 70.37 | |

Top 40 | 80.56 | 80.56 | 80.56 | 75.00 |

In this section, the authors analyze whether GFS in the top ten brain regions correlates with the results of MMSE and MoCA. It allows for the analysis of whether there is a correlation between two sets of variables. Since some people were illiterate, so they could not complete the MoCA test; the authors took all the people who completed two scales, which were 29 in total (19 AD and 10 non-AD). At this point, canonical correlation analysis can be used. The basic principle is that to grasp the correlation between the two groups of variables as a whole, two composite variables U and V (linear combination of the two groups of variables) are extracted from the two groups of variables, respectively, and the correlation between the two composite variables is used to reflect the overall correlation between the two groups of variables.

The results of the canonical correlation analysis showed that the correlation coefficient between the typical variable pair 1 is 0.7136, which means that there is a very strong correlation between GFS and MMSE/MoCA scale information.

In this paper, a new local feature index 2hop-connectivity was set up to measure the correlation between different regions. 2hop-connectivity is a node importance metric, just like graph-theoretic metrics such as degree centrality. Since most biological networks are relatively sparse, 2hop-connectivity may work better for node importance metrics of sparse networks. And for this purpose, a novel random walk algorithm 2hopRWR is proposed, which can calculate the local feature index 2hop-connectivity. Also, the proof of convergence is given. Next, the idea of combining five local features to obtain the GFS was used in this paper, which is more convincing than using a single network parameter to describe the importance of network nodes. Then, the results of literature verification and canonical correlation analysis also verify the rationality and the validity of the proposed method. Thus, GFS can be used to distinguish DTI images of the AD and the non-AD groups. Finally, the top 10 brain regions in the GFS scoring difference predicted in this paper have been validated in the literature. Literature validation results comparing GFS with local features showed that GFS outperforms individual local features. However, the brain network constructed in this paper is a structural network, and the structure and function should be combined in the future. For example, more results may be obtained upon combining the available fMRI data and analyzing the differences of different brain regions in different tasks. For the importance evaluation of network nodes, there is no perfect standard measurement at present, and it is difficult to evaluate the advantages and disadvantages of the node importance algorithm. Another important problem is the need to design evaluation indicators to measure the importance of nodes.

In brief, GFS is expected to be an important and useful index for identifying the difference between network nodes and detecting the changes in information transmission between brain regions in patients with AD. Moreover, it may provide useful insights into the underlying mechanisms of AD. Many elder test subjects are illiterate and are not able to perform the MMSE and MoCA scales properly, so the GFS can be used as a diagnostic aid to infer whether a subject may be a patient with AD from DTI imaging data alone, which can greatly reduce the workload of medical practitioners. Finally, GFS can be used as a differential network analysis method (Lichtblau et al.,

The raw data supporting the conclusions of this article will be made available by the authors, without undue reservation.

QW designed the work, developed the computing method, wrote the code, analyzed the result, and wrote the manuscript. SC collected clinical data, analyzed the statistics, and polished the manuscript. HW and LC contributed to the imaging work and the statistical analysis. YS designed the work, collected clinical data, and contributed with theoretical support. GY designed the work, analyzed the result, and revised the manuscript. All authors contributed to the article and approved the submitted version.

The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

We thank Prof. Ang Li, Institute of Biophysics, Chinese Academy of Sciences, for his suggestions for the results section. We would also like to thank the two reviewers for their comments on improving this manuscript.

The Supplementary Material for this article can be found online at:

MMSE & MoCA data.

DTI data overview.

Results of literature validation for GFS and local features.