Introduction

Functional Magnetic Resonance Imaging (fMRI) has been recently become more popular in brain function studies. During the fMRI examination, the low-frequency fluctuations called Blood Oxygen Level Dependent (BOLD) signal that shows the oxygen consumption of the brain regions, has been recorded [ 1 ]. In brain research, there are three types of brain connectivity called structural, functional, and effective. The temporal correlation of fMRI signals shows the functional connectivity in the brain that could be among all voxels (that is very time-consuming) or Regions of Interest (ROI) [ 2 ]. Several functional connectivity studies based on fMRI signals show that different pathological or physiological conditions affect the brain functional connectivity [ 3 - 5 ]. There are several methods to calculate the correlation between time-series, including Pearson Correlation Coefficient (PCC), Kendall, and Spearman. All the methods are popular in literature but the PCC is the most common method used in fMRI functional connectivity analysis [ 6 ].

Alzheimer’s Disease (AD) that is the most common type of dementia, is a neurodegenerative illness, disrupting the performance of the brain and the normal life of the patient in the final stages of the disease. Official deaths authentications recorded 122,019 deaths from AD in 2018, making Alzheimer’s the 6^th and 5^th main reason for death in the United States and among Americans age 65 and older, respectively [ 7 ]. Accordingly, using fMRI signals to study AD is very popular and also helpful for all the people involved in this issue directly or indirectly [ 8 ].

Studies on AD shows that the functional connectivity of the brain and especially main brain networks such as Default Mode Network (DMN) has decreased [ 9 , 10 ]. Classification AD patients from the healthy individuals is another popular topic that has been performed using different features and dimension reduction algorithms, and a wide range of classifiers, including K-Nearest Neighbors, Artificial Neural Networks (ANN) and Support Vector Machine (SVM) [ 11 - 13 ]. There are also several studies on the early stage of the disease called Mild Cognitive Impairment (MCI) [ 14 , 15 ]. Besides, using additional information such as MRI, structural images has been investigated [ 16 ]. In functional connectivity analysis, non-linear methods such as mutual information have been used as well [ 17 ]. The study of the functional connectivity using coherence analysis [ 18 ] or comparing the effect of AD and normal aging in the functional connectivity was done before [ 19 ]. Moreover, some studies especially focused on white matter functional connectivity [ 20 ] or some brain networks or ROIs [ 21 ].

As mentioned above the functional connectivity analysis is very common and popular among researchers. Although there are many ways to compute the functional connectivity, the most common method for analyzing functional connectivity is Pearson Correlation Coefficient (PCC). PCC is conducted using the linear correlation; however, in non-linear relationships, this method is weak. Besides, there a not enough studies that compare the result of the different correlation methods to PCC. In this study, functional connectivity matrices are generated using different correlation methods, including PCC, Spearman, and Kendall, to explore the performance of these methods in brain functional connectivity analysis in AD subjects.

In the materials and methods section, the database is introduced. Then the preprocessing step is explained and different correlation methods and their formulas are presented. After that, graph theory and feature extraction are proposed. In the result section, the statistical outcomes and different analysis findings are presented. Finally, the results are going to discuss in the last section. This study aims to investigate the different correlation methods in functional connectivity analysis.

Material and Methods

In this analytical research, the data and the tools used in this study are presented and explained completely. The flowchart of the study is shown in Figure 1.

Figure 1. The flowchart of the study.

Database

The fMRI data has been collected from the Alzheimer’s Disease Neuroimaging Initiative (ADNI) phase 2 [ 22 , 23 ]. The data consists of 28 individuals for the AD group and 34 individuals for the control group. All the scans, including structural and functional images have been done by a 3 Tesla Philips MRI machine. The Repetition Time (TR) and Echo Time (TE) are 3000 msec and 30 msec, respectively. The flip angle was 80 and 3.3125 mm was the thickness of each slice [ 24 ]. The demographic information is depicted in Table 1.

Preprocessing

The preprocessing was done using the Data Processing Assistant for fMRI (DPARSF) toolbox in Matlab software [ 25 ]. The preprocessing consists of realignment that performed by a six parameter rigid body transformation. BY the last slice, the slice timings were corrected. Then the Montreal Neurological Institute (MNI) atlas has been used for data normalization. Data were passed through a bandpass filter (0.01-0.08 Hz) and smoothed by a Gaussian filter (FWHM=4 mm). Finally, to obtain the time-series, the Automated Anatomical Labeling (AAL) atlas, reliable in this field, has been employed. Based on AAL atlas, the brain parcellates into 116 distinct regions [ 26 ].

Correlations

After extracting fMRI signals based on AAL atlas, the correlations among time-series were computed to obtain brain functional connectivity. PCC is one of the main methods to calculate the correlation [ 27 ]. The formula of PCC is as follows:

${\rho }_{\mathrm{x.y}}=\frac{\mathrm{cov(x.y)}}{{\sigma }_x{\sigma }_y}$ (1)

Where σ_x and σ_y correspond to the standard deviation of signal x and y, respectively. The PCC computes the linear correlation and the magnitude is between -1 to 1. The sign shows the direction and the magnitude corresponds to the correlation power.

The Spearman correlation is another method, which is a nonparametric rank correlation between two variables, showing that how well the connection between two factors can be portrayed using a monotonic function [ 28 ]. For computation the Spearman correlation, the variables are firstly converted to rank variables and then the PCC formula (Equation 1) is performed.

Kendall coefficient is a non-parametric popular method for computing the correlation between two variables, quantifing the ordinal association between variables [ 29 ]. Assume that (x_i, y_i) and (x_j, y_j) are two coordintes with condition that if x_i>x_j and y_i>y_j, they are concordant and if x_i<x_j and y_i<y_j they are discordant. Accordingly, the formula of the Kendall coefficient is as follows:

$\tau =\frac{n_c-n_d}{\frac{n\mathrm{(n-1)}}{2}}$ (2)

Where n_c and n_d correspond to the number of concordant and number of discordant pairs, respectively. Besides, n is the number of pairs.

Brain Networks and Graph Theory

In functional connectivity analysis, the brain is modeled as an undirected graph. In this graph, the brain ROIs correspond to the graph nodes and the functional connectivities between nodes were modeled as network edges. The edges of the graph demonstrates the functional connectivity (correlation) [ 30 ]. In mathematics, G=(V, E) is a graph that E is the representatives of links and V corresponds to vertices. Besides, some studies sparsed the graphs by thresholding to remove weak links and noises. As this paper aims to compare the effect of different correlation methods, sparsification is not obliged. As this study focused on functional connectivity, the absolute value of negative correlations was considered for further analysis [ 31 ]. After generating weighted undirected graphs based on different correlation methods, graph global features were computed. The formula of graph measures is shown in Table 2.

In Table 2, n and d_G(x.y) show the number of nodes and the distance between the x and y, respectively. The G^Ideal is the representative of a fully connected network. The l is the number of links and A_x.y shows the connectivity matrix. δ_x.y is 0 if the x and y are from the same community. C_r and L_r correspond to an equivalent random graph. The average efficiency formula is $\mathrm{(G)}=\frac{1}{\mathrm{n(n-1)}}{\sum }_{\mathrm{x\ne y\in G}}\frac{1}{\mathrm{p(x.y)}}$, where p(x.y) corresponds to the shortest path length between x and y.

Some measures are computed over a single node. These types of features demonstrate the performance of a single node in the network specifically. Betweenness measures the centrality in a network based on the shortest paths, and is the ratio of the shortest path (that crosses through a hub to the total number of shortest paths). Closeness is the inverse of the path length of a hub [ 33 ]. Participation estimates the connection between the number of edges associating a hub outside its locale and all of its outnumber of edges. The participation formula is:

$P_i=1-{\sum }_s{\left(\frac{K_{s_i}}{K_i}\right)}^2$ (3)

where s_i and K_i are the all outnumber of links of vertice i and K_si is the number of edges associating the vertice i inside Module (neighborhood).

Results

After generating weighted undirected functional brain networks and extracting graph features, statistical analysis was performed. Since there is no assumption about the distribution of the data, the non-parametric permutation test was implemented. The results of the statistical test are shown in Table 3 in terms of P-values. The bold numbers in Table 3 correspond to the P-values<0.05.

According to Table 3, the Pearson correlation shows significant changes in strength, characteristic path length, global efficiency, local efficiency, clustering, and transitivity features. In addition to the mentioned features, Spearman and Kendall correlations show significant changes in the modularity feature as well. Regardless of the features that show significant differences, generally, the P-values obtained from Kendall and Spearman were smaller in comparison to the Pearson method. It can be concluded that Kendall and Spearman are more powerful in the discrimination of Alzheimer’s disease from the control group in terms of functional connectivity and graph measures.

The diameter and radius were computed based on the eccentricity feature, capturing the maximal distance between two nodes. Moreover, they did not show any significant changes. It can be interpreted that although Alzheimer’s affects the brain function, the paths between ROIs that flowing information still exists. Accordingly, none of the brain ROIs is isolated from the rest of the brain. The small worldness architecture of the brain remains in this database. Since there was no sparsification step, it was expected that the degree feature indicates no significant differences.

The performance of different correlations methods has been analyzed through global graph measures. Since other studies [ 21 , 34 ] reported functional connectivity changes in DMN to analyze more comprehensively, the measures in DMN were investigated. Furthermore, most of the global measures can be computed for a single node. On the other hand, some features, including small worldness related to the whole graph cannot be calculated for a node. First of all, the global measures that are available in the nodal analysis were extracted for every node of the DMN network. Consequently, there were ten charts for ten ROIs of the DMN. For example, Table 4 is for frontal superior medial left ROI. The boldface P-values in Table 4 shows a statistically significant difference.

In comparison among different correlation methods, based on the number of features displaying significant changes, Pearson, Spearman, and Kendall show a significant difference in 27, 32, and 33 features, respectively out of 70 features (7 different features in 10 ROIs). These results were similar to the global measures in the whole network (Table 3) and the Spearman and Kendall were more powerful in comparison to Pearson correlation.

The eccentricity feature like the whole-brain analysis has no significant difference in neither the ROIs nor correlation methods. On the other hand, clustering, local efficiency, and path length were the features, demonstrating the most significant differences respectively. Besides, the last column of Table 4 displays the ranks of the features based on their number of significant differences in all DMN ROIs.

Among the ROIs of the DMN network, the angular area (left and right) and cingulum posterior area (left and right) seemed to be more affected by the AD because more features showed significant difference and these results are in consistent with previous studies [ 35 , 36 ]. Besides, the measures in the left hemisphere of the brain demonstrate more significant changes. Since all the subjects were right-handed, it can be concluded that the dominant hemisphere was affected more by the AD. Figure 2 exhibits the axial dorsal view of DMN ROIs, sorted based on their affection by AD.

Figure 2. Default Mode Network Regions of Interests (DMN ROIS) and their rank according to significant differences in a statistical test.(SFGmed: Frontal Superior Medial, ACG: Cingulum Anterior, PCG: Cingulum Posterior, ANG: Angular, PCUN: Precuneus)

As shown in Figure 2, it can be interpreted that the AD disrupts functional connectivity in posteriors ROI’s of DMN network more in comparison to frontal ROI’s.

Besides the global measures, there are some nodal measures computed only over a single node and do not define in the whole graph. These features were calculated in ROI’s of DMN network separately and Table 5 illustrates the P-values for frontal superior medial left ROI. The boldface P-values in Table 5 exhibits a statistically significant difference.

All three correlation methods show significant difference in 18 features out of 40 (4 nodal measures on every 10 DMN ROIs); thus, regardless of the correlation method the performances of nodal measures extracted from graphs are the same.

Among four nodal measures, the triangles and closeness feature exhibits more significant changes and the betweenness demonstrates the least significant difference. It is worthwhile to mention that the ranks of ROIs based on nodal measures were as same as global measures (Figure 2).

Discussion

This paper aims to investigate and compare the different prevalent correlation methods in generating brain functional graphs. Firstly, the fMRI data of AD patients and control groups were preprocessed and time series were extracted based on AAL atlas. Secondly, the correlation between signals of different ROIs was computed in every subject by 3 different correlation methods. Then, the graph global measures were extracted in the whole brain graph. In another analysis, the global measures were extracted in the DMN network. Moreover, nodal measures in the DMN network were also calculated. In the whole-brain analysis based on global measures, Spearman and Kendall correlations were stronger in discrimination between AD subjects and healthy ones in comparison to the Pearson correlation. Since Spearman and Kendall present more significant difference in global measures in comparison to Pearson, these methods are superior in brain functional connectivity analysis in AD.

It is worthwhile to mention that some features, including eccentricity, radius, and diameter (that calculated based on eccentricity) show no significant changes regardless of the correlation method. On the other hand, some features, showing brain functional integration and segregation such as efficiencies, characteristic path length, clustering, and transitivity show significant changes in all three different correlation methods.

In DMN network analysis employing global measures, again the Spearman and Kendall were more powerful and show more significant difference. Also, the eccentricity feature shows no significant changes in neither the correlation methods nor DMN ROIs. The most disrupted functional connectivity among DMN ROIs was the posterior, including angular, cingulum posterior, and precuneus ROIs, respectively. On the other hand, the frontal ROI’s had less functional connectivity disruption. Overall, the left hemisphere shows more significant changes. Since the individuals were right-handed, it can be concluded that the functional connectivity of the dominant hemisphere is disrupted more from AD. In the nodal analysis of DMN ROIs, the triangle and closeness features had the most better performance in distinguishing AD cases from the normal group respectively. Also, the performance of different correlation methods were the same approximately. Besides, the functional connectivity disruption in DMN ROIs based on nodal measures was similar to global measures.

Conclusion

In this study, different correlation methods have been evaluated for brain functional network generation. Although there is no gold standard, the most common method is the Pearson correlation coefficient that has limitations in capturing non-linear dependencies. In the used database, the Spearman and Kendall correlation was more powerful. Accordingly, the weakness of Pearson was demonstrated. For further studies, assessing other methods, especially non linear methods such as distance correlation or mutual information, is highly recommended. Furthermore, the investigation of other databases and different types of binary graphs are suggested as well.

Authors’ Contribution

E. Fatemizadeh conceived of the presented idea and developed the theory. E. Fatemizadeh and A. Motie Nasrabadi verified the analytical methods. H. Ahmadi carried out the data analysis and wrote the draft. All authors discussed the results and contributed to the final manuscript.

Ethical Approval

The study was employed the on-line available data. According to the user’s guideline the procedure was conducted in accordance with the Declaration of Helsinki, and the protocol was approved by the Ethics Committee.

Informed consent

The study was employed the on-line available data. According to the user’s guideline the participants were informed and consent to the research.

Conflict of Interest

None

References

1. Bijsterbosch J, Smith SM, Beckmann CF. An introduction to resting state fMRI functional connectivity. Oxford University Press; 2017.
2. Rossini PM, Di Iorio R, Bentivoglio M, Bertini G, Ferreri F, Gerloff C, et al. Methods for analysis of brain connectivity: An IFCN-sponsored review. Clin Neurophysiol. 2019; 130(10):1833-58. DOI | PubMed
3. Hull JV, Dokovna LB, Jacokes ZJ, Torgerson CM, Irimia A, Van Horn JD. Resting-state functional connectivity in autism spectrum disorders: a review. Front Psychiatry. 2017; 7:205. Publisher Full Text | DOI | PubMed
4. Baggio HC, Junqué C. Functional MRI in Parkinson’s Disease Cognitive Impairment. Int Rev Neurobiol. 2019; 144:29-58. DOI | PubMed
5. Hua J, Blair NI, Paez A, Choe A, et al. Altered functional connectivity between sub-regions in the thalamus and cortex in schizophrenia patients measured by resting state BOLD fMRI at 7T. Schizophr Res. 2019; 206:370-7. Publisher Full Text | DOI | PubMed
6. Farahani FV, Karwowski W, Lighthall NR. Application of graph theory for identifying connectivity patterns in human brain networks: a systematic review. Front Neurosci. 2019; 13:585. Publisher Full Text | DOI | PubMed
7. Alzheimer’s Association. 2019 Alzheimer’s disease facts and figures. Alzheimer’s Dementia. 2019; 15(3):321-87. DOI
8. Forouzannezhad P, Abbaspour A, Fang C, et al. A survey on applications and analysis methods of functional magnetic resonance imaging for Alzheimer’s disease. J Neurosci Methods. 2019; 317:121-40. DOI | PubMed
9. Dennis EL, Thompson PM. Functional brain connectivity using fMRI in aging and Alzheimer’s disease. Neuropsychol Rev. 2014; 24(1):49-62. Publisher Full Text | DOI | PubMed
10. Gao Y, Li M, Zu Z, Rogers BP, Anderson AW, Ding Z, Gore JC. SPIE: San Diego, California, United States; 2019. DOI
11. De Vos F, Koini M, Schouten TM, Seiler S, et al. A comprehensive analysis of resting state fMRI measures to classify individual patients with Alzheimer’s disease. Neuroimage. 2018; 167:62-72. DOI | PubMed
12. Rathore S, Habes M, Iftikhar MA, Shacklett A, Davatzikos C. A review on neuroimaging-based classification studies and associated feature extraction methods for Alzheimer’s disease and its prodromal stages. Neuroimage. 2017; 155:530-48. Publisher Full Text | DOI | PubMed
13. Meszlényi RJ, Buza K, Vidnyánszky Z. Resting state fMRI functional connectivity-based classification using a convolutional neural network architecture. Front Neuroinform. 2017; 11:61. Publisher Full Text | DOI | PubMed
14. Franzmeier N, Caballero MA, Taylor AN, Simon-Vermot L, Buerger K, et al. Resting-state global functional connectivity as a biomarker of cognitive reserve in mild cognitive impairment. Brain Imaging Behav. 2017; 11(2):368-82. DOI | PubMed
15. Cai S, Chong T, Peng Y, Shen W, Li J, Von Deneen KM, Huang L. Altered functional brain networks in amnestic mild cognitive impairment: a resting-state fMRI study. Brain Imaging Behav. 2017; 11(3):619-31. DOI | PubMed
16. Dai Z, Lin Q, Li T, Wang X, Yuan H, et al. Disrupted structural and functional brain networks in Alzheimer’s disease. Neurobiol Aging. 2019; 75:71-82. DOI | PubMed
17. Hlinka J, Paluš M, Vejmelka M, Mantini D, Corbetta M. Functional connectivity in resting-state fMRI: is linear correlation sufficient?. Neuroimage. 2011; 54(3):2218-25. Publisher Full Text | DOI | PubMed
18. Bowyer SM. Coherence a measure of the brain networks: past and present. Neuropsychiatric Electrophysiology. 2016; 2(1):1-2. DOI
19. Chirles TJ, Reiter K, Weiss LR, Alfini AJ, et al. Exercise training and functional connectivity changes in mild cognitive impairment and healthy elders. J Alzheimers Dis. 2017; 57(3):845-56. Publisher Full Text | DOI | PubMed
20. Zhao J, Ding X, Du Y, Wang X, Men G. Functional connectivity between white matter and gray matter based on fMRI for Alzheimer’s disease classification. Brain Behav. 2019; 9(10):e01407. Publisher Full Text | DOI | PubMed
21. Yamashita KI, Uehara T, Prawiroharjo P, et al. Functional connectivity change between posterior cingulate cortex and ventral attention network relates to the impairment of orientation for time in Alzheimer’s disease patients. Brain Imaging Behav. 2019; 13(1):154-61. DOI | PubMed
22. Mueller SG, Weiner MW, Thal LJ, et al. The Alzheimer’s disease neuroimaging initiative. Neuroimaging Clin N Am. 2005; 15(4):869-77. Publisher Full Text | DOI | PubMed
23. Petersen RC, Aisen PS, Beckett LA, et al. Alzheimer’s disease neuroimaging initiative (ADNI): clinical characterization. Neurology. 2010; 74(3):201-9. Publisher Full Text | DOI | PubMed
24. Jack Jr CR, Bernstein MA, Fox NC, et al. The Alzheimer’s disease neuroimaging initiative (ADNI): MRI methods. J Magn Reson Imaging. 2008; 27(4):685-91. Publisher Full Text | DOI | PubMed
25. Yan C, Zang Y. DPARSF: a MATLAB toolbox for” pipeline” data analysis of resting-state fMRI. Front Syst Neurosci. 2010; 4:13. Publisher Full Text | DOI | PubMed
26. Tzourio-Mazoyer N, Landeau B, Papathanassiou D, et al. Automated anatomical labeling of activations in SPM using a macroscopic anatomical parcellation of the MNI MRI single-subject brain. Neuroimage. 2002; 15(1):273-89. DOI | PubMed
27. Benesty J, Chen J, Huang Y, Cohen I. Springer Topics in Signal Processing: Berlin, Heidelberg; 2009.
28. Myers L, Sirois MJ. Spearman correlation coefficients, differences between. Encyclopedia of Statistical Sciences. 2004. DOI
29. Akoglu H. User’s guide to correlation coefficients. Turk J Emerg Med. 2018; 18(3):91-3. Publisher Full Text | DOI | PubMed
30. Ehtemami A, Scott R, Bernadin S. IEEE: USA; 2018.
31. Bullmore E, Sporns O. Complex brain networks: graph theoretical analysis of structural and functional systems. Nat Rev Neurosci. 2009; 10(3):186-98. DOI | PubMed
32. Rubinov M, Sporns O. Complex network measures of brain connectivity: uses and interpretations. Neuroimage. 2010; 52(3):1059-69. DOI | PubMed
33. Meghanathan N. Assortativity Analysis of Real-World Network Graphs based on Centrality Metrics. Computer and Information Science. 2016; 9(3):7-25. DOI
34. Qian W, Fischer C, Churchill N, Kumar S, et al. Decreased Default Mode Network Functional Connectivity in Alzheimer’s Disease Patients with Delusions. Am J Geriatr Psychiatry. 2019; 27(10):1060-8. DOI | PubMed
35. Filippi M, Basaia S, Canu E, Galantucci S, et al. Structural and functional brain connectome architecture in Alzheimer’s disease and amnesic mild cognitive impairment patients (P4. 091). J Neurology. 2017; 88(16 Supplement):P4.091.
36. Liang Y, Chen Y, Li H, Zhao T, et al. Disrupted functional connectivity related to differential degeneration of the cingulum bundle in mild cognitive impairment patients. Curr Alzheimer Res. 2015; 12(3):255-65. DOI | PubMed