Functional connectomes incorporating phase synchronization for the characterization and prediction of individual differences

Abstract

Background:

Functional connectomes have been proven to be able to predict an individual’s traits, acting as a fingerprint. A majority of studies use the amplitude information of fMRI signals to construct the connectivity but it remains unknown whether phase synchronization can be incorporated for improved prediction of individual cognitive behaviors.

Methods:

In this paper, we address the issue by extracting phase information from the fMRI time series with a phase locking approach, followed by the construction of functional connectomes.

Results:

We first examine the identification and prediction performance using phase-based profiles in comparison with amplitude-based connectomes. We then combine both phase-based and amplitude-based connectivity to extract subject-specific information enabled by the phase synchronization. Results show that high individual identification rates (from 82.7% to 92.6%) can be achieved by phase-based connectomes. Phase-based connectivity offers unique information complementary to amplitude-based signals. Intra-network phase-locking appears more informative for individual prediction. In addition, phase synchronization can be used to predict cognitive behaviors.

Comparison with existing method:

The amplitude-based connectivity cannot capture the subject-specific information due to neural synchronization. The comparison with other phase-based methods has been involved in the discussion session.

Conclusions:

Our findings suggest that neural synchronization carries subject-specific information, which can be captured by phase locking value. The incorporation of phase information into connectomes presents a promising approach to understand each individual brain’s uniqueness.

I. INTRODUCTION

The human brain is a complicated system which we are still trying to understand. As a non-invasive interrogation technique, functional magnetic resonance imaging (fMRI) based on the blood-oxygenation-level-dependent-signal (BOLD signal) has provided a promising means to unveil connections within the brain [1], [2], [3]. A large number of studies have linked brain connections with various mental disorders and developmental stages [4], [5], [6], [7]. For instance, Du et al. revealed the difference in brain connections among patients diagnosed with bipolar disorder with psychosis (BPP), schizoaffective disorder (SAD), and schizophrenia (SZ) [8]. Allen et al. demonstrated that connections among intrinsic connectivity networks (ICNs) change with age [9]. Simultaneously, reoccurring connectivity patterns have been detected through dynamic analysis, which provide additional information about the brain [10], [11], [12], [13], [14], [15], [16], [17], [17], [18].

Each brain has unique connectivity patterns [19]. As a result, functional connectomes can serve as a neural fingerprint to identify an individual from the population. Finn et al. pointed out that connectivity profiles can identify individuals among adult participants across rest/task paradigms. They also indicated that individual discriminative subnetworks contributed a lot to the cognitive profile [20]. Rosenberg et al. showed that whole-brain functional network connectivity served as a reliable neuromarker for predicting individual differences in sustained attention [21]. Kaufmann et al. reported that reduced mental health induced a delay and an overall reduction of individual wiring functional patterns during adolescence [22]. Prior research has shown that unique connectivity patterns are stable across months and even years [23], [24].

Recently, there are some attempts to further study the differences in individuals’ profiles. Liu et al. leveraged the time-varying information to do the individual identification [25]. Cai et al. removed the population-wise contributions to enhance the predictability of neural fingerprint[26]. Most of the studies mentioned above constructed functional connectomes from the correlations between brain regions. Other than this amplitude-based connectivity, neural synchronization has been proposed to describe individual patterns and represent the behavioral traits [27]. Furthermore, Zhang et al. demonstrated that phase-based profiles could be used to discriminate the individual from participants [28], [29]. It offers an alternative way to characterize dynamic functional connectivity organization and provide different individual specific information relative to the commonly used amplitude-based methods. Inspired by this finding, we conduct the following studies. First, we validate whether phase-based functional connectomes can be used to effectively predict individual cognitive behaviors. Second, we investigate the difference in obtaining subject-wise information between amplitude-based and phase-based profiles.

The remainder of this paper is organized as follows. In Section II, we first describe the dataset used in this work. Then, we introduce our proposed pipeline for extracting individual functional connectomes, followed by a series of validation experiments. Specifically, we examine whether phase-based profiles can distinguish each individual from a population and predict high-level cognitive behaviors. Results are presented in Section III. Some discussion and concluding remarks are given in Section IV and V, respectively

II. MATERIALS AND METHODS

A. Data acquisition

1). Experimental dataset:

The publicly available S1200 Data Release of the Human Connectome Project (HCP) was used as the experimental dataset in this study [30]. 889 out of 1200 healthy young adult participants have complete data for all four 3T MRI paradigms in the HCP protocol: structural images (T1w and T2w), resting-state fMRI (rsfMRI), task fMRI (tfMRI), and high angular resolution diffusion imaging (dfMRI). A written informed consent was obtained for each participant. The fMRI data was acquired using a whole-brain multiband gradient-echo (GE) echoplanar (EPI) sequence with the following parameters: TR/TE =720/33.1ms, flip angle = 90°, FOV = 208 × 180mm, matrix = 104 × 90 (RO × PE), multiband factor = 8, echo spacing = 0.58ms, slice thickness = 2mm. The resulting normal voxel size was 2.0 × 2.0 × 2.0mm.

The resting-state runs (R1 and R2) were acquired in separate sessions on two different days. Task runs included the following: working memory (Wm), motor (Mt), language (Lg) and emotion (Em). The working memory task and motor task were acquired on the first day, while the language and emotion tasks were obtained on the second day. To maintain consistency with the validation dataset, only resting-state (R1), working memory and emotion task fMRI sessions were included in this work. Note that not all subjects have both the working memory and emotion fMRI data. Hence, we filtered out participants lacking one or two paradigms of the fMRI scanning sessions. Finally, a cohort of 862 participants (aged 22–35 years, 409 male and 453 female) was retained in our analysis. Within each session, oblique axial acquisitions alternated between phase encoding in a right-to-left (RL) direction in one run and phase encoding in a left-to-right direction in another run. Here, we applied only the left-to-right encoding runs to avoid potential effects of different phase encoding directions on our findings. More details about S1200 Data Release of the HCP can be found in the reference manual [31].

Our study used the fMRI dataset from HCP with minimal preprocessing pipeline, which included gradient distortion correction, head motion correction, image distortion correction, spatial normalization to standard Montreal Neurological Institute (MNI) and intensity normalization [32]. Further, we used the standard preprocessing procedures to reduce biophysical and other noise sources in the minimally processed fMRI data. These procedures included the removal of linear components related to the 12 motion parameters (original motion parameters and their first-order deviations), removing linear trend and performing band-pass filtering (0.01–0.1Hz). Note that Finn et al. has pointed out that the smoothing level had essentially no effect on identification accuracy [20]. Hence, spatial smoothing was not included in the preprocessing steps.

To facilitate the understanding of human behaviors associated with different brain regions, we applied a 268-node functional atlas provided by Finn et al.[20], which was defined by a groupwise spectral clustering algorithm [33]. More specifically, we extracted the time series of each node by averaging the time courses of all voxels within the region denoted by that node. Then, we assigned these nodes into 8 functional networks, including medial frontal (Med F), frontoparietal (FP), default mode (DMN), subcortical-cerebellum (Sub-Cer), motor (Mt), visual I (Vis I), visual II (Vis II) and visual association (Vis Assn) regions. Axial, sagittal and coronal views of these functional networks are displayed in Fig. 1.

Fig. 1.

Axial, sagittal and coronal views (from left to right) of 8 functional networks provided by Finn et al. 1. Med F: Medial Frontal; 2. FP: Frontoparietal; 3. DMN: Default Mode; 4. Sur-Cer: Subcortical-cerebellum; 5. Mt: Motor; 6. Vis I: Visual I; 7. Vis II: Visual II; 8. Vis Assn: Visual Association.

2). Validation dataset:

To validate the findings from the experimental data, an independent dataset, the PNC (Philadelphia Neurodevelopmental Cohort) dataset was applied in this work. The PNC is a large-scale collaborative project between the Brain Behavior Laboratory at the University of Pennsylvania and the Children’s Hospital of Philadelphia [34]. BOLD fMRI was acquired using a whole-brain, single-shot, multi-slice, gradient-echo (GE) echoplanar (EPI) sequence of 124 volumes with the following parameters: TR/TE = 3000/32ms, flip = 90°, FOV = 192 × 192mm, matrix = 64 × 64, slice thickness/gap = 3mm/0mm. The resulting voxel size was 3.0 × 3.0 × 3.0mm.

In the PNC dataset, three paradigms of fMRI sessions including resting-state, working memory and emotion were collected. By selecting the participants who have all these three fMRI paradigms, 623 subjects (aged 8–22 years, 280 male and 343 female) were included. Functional images were preprocessed using the same standard pipeline mentioned above. Note that all paradigms of fMRI were preprocessed following the same strategy.

B. Amplitude-based and phase-based functional connectivity (FC) construction

We implemented three different methods to determine the functional connectomes: amplitude-based FC, phase-based FC, and FC containing both the amplitude and phase information. For the amplitude-based FC (aFC), the Pearson correlation coefficient was calculated with the time series between every pair of nodes for each participant. Then, we obtained a 268 × 268 symmetric correlation matrix. The correlation values were Fisher z-transformed, resulting in one aFC for each fMRI scanning session per subject.

For the phase-based FC, a phase locking value (PLV) approach was adopted to measure the phase synchrony between the time courses of paired nodes [35]. For each subject, we have $c_i(t)$, $i=1,2,\dots ,268$ time series. The Hilbert analytic signal can be estimated as follows:

$$\begin{gathered} z_i(t)=c_i(t)+j{\tilde{c}}_i(t)=a_i(t)e^{j{\theta }_i(t)} \\ {\tilde{c}}_i(t)=\frac{1}{\pi }P{\int }_{-\mathrm{\infty }}^{\mathrm{\infty }} \frac{c_i(t)}{t-\tau }d\tau \\ {a}_i(t)=\sqrt{c_i^2(t)+{\tilde{c}}_i^2(t)} \\ {\theta }_i(t)=\mathrm{a}\mathrm{r}\mathrm{c}\mathrm{t}\mathrm{a}\mathrm{n}\left({\tilde{c}}_i(t)/c_i(t)\right) \end{gathered}$$ (1)

where ${\tilde{c}}_i(t)$ represents the Hilbert transform of $c_i(t)$, the symbol $P$ denotes the Cauchy principle value, $a_p(t)$ indicates the envelope of the instantaneous amplitude and ${\theta }_i(t)$ is the instantaneous phase. Given two time series for ROIs $b_1$, $b_2(c_{b_1}(t)$ and $c_{b_2}(t)$), ${\theta }_{b_1}(t)$ and ${\theta }_{b_2}(t)$ are their corresponding instantaneous phases. Then, the PLV can be used to describe the phase synchrony.

$$PL{V}_{b_1,b_2}=|e^{-j({\theta }_{b_1}(t)-{\theta }_{b_2}(t))}|$$ (2)

In the fully synchronized time courses, the phase difference is a constant and the $PLV=1$. If the time series are unsynchronized, the phase difference follows the uniform distribution and $PLV=0$. The normalized Hilbert analytic signal can be used to determine the value of PLV. According to Eq.1, the normalized Hilbert analytic signal of $c_{b_1}(t)$ can be described as:

$${\tilde{z}}_{b_1}(t)=\frac{z_{b_1}(t)}{\left|z_{b_1}(t)\right|}=e^{j{\theta }_{b_1}(t)}$$ (3)

Thus, the PLV can be estimated as:

$$PL{V}_{b1,b2}=|{\tilde{z}}_{b_1}(t)\cdot {\tilde{z}}_{b_2}{\left(t\right)}^{\mathrm{*}}|=|{\tilde{\mathbf{Z}}}_{b_1}\cdot {\tilde{\mathbf{Z}}}_{b_2}^T|$$ (4)

where the symbol ${(\cdot )}^{\mathrm{*}}$ denotes complex conjugate, $\tilde{\mathbf{Z}}$ is the vector format of $\tilde{z}$ and ${\tilde{\mathbf{Z}}}^T$ is the conjugate transpose of $\tilde{\mathbf{Z}}$. The estimation of the aFC and PLV-FC can be found in Step 1 of Fig. 2. In addition, in the following experiments, we also concatenated the aFC and PLV-FC so we can investigate whether the combination of both the amplitude and phase-based FC can help with individual identification and cognitive behavior prediction.

Fig. 2.

The framework of functional connectivity construction for the identification of an individual. Step 1: FC matrices estimated by the amplitude and phase information separately. Step 2: Applying the sparse dictionary learning (SDL) model to reduce the group-wise contribution to individual identification. Step 3: Identification of an individual by applying maximal similarity value derived from Pearson correlation between target and database matrices.

C. Improved individual identifiability through sparse dictionary learning

We have pointed out that reducing the group-wise contribution benefits individual identification [26]. Hence, in this work, we also implemented the same framework on aFC, PLV-FC, and combined (aFC + PLV-FC) to enhance the inter-subject variability. More specifically, let us assume that we have $n\in \mathbb{N}$ subjects, and $n_t$ time points and $p$ ROIs ($n_t,p\in \mathbb{N}$) from a fMRI BOLD time series for each participant. We first calculate a correlation matrix, $C_i\in {\mathbb{R}}^{p\times p}(i\in 1,2,\dots ,n)$, for each subject. $C_i\left(b_1,b_2\right)$ denotes the correlation between ROIs $b_1$ and $b_2$ across the time courses. Due to the symmetric characteristic of the correlation matrix, the lower triangular section of $C_i$ is retained as the $vec\left(C_i\right)$. In this way, we have the edge weight vector $e_i=vec\left(C_i\right)\in {\mathbb{R}}^{p(p-1)/2}$ for each participant. Then, we concatenate edge weight vectors from all subjects to form $Y=\left[e_1,e_2,\dots ,e_n\right]$ with the size of $m\times n$, where $m=p(p-1)/2$, $n=1,2,....$ The shared representation of the functional connectomes across subjects $\left(Y\right)$ can be modeled as a sparse dictionary learning (SDL) problem. We can approximate the given data $\mathrm{Y}$ by solving the following equation:

$$\begin{array}{c}\underset{D,X}{\mathrm{m}\mathrm{i}\mathrm{n}} \Vert Y-DX{\Vert }_F^2\\ \text{subject}\text{to}{‖x_i‖}_0\le L,i=1,2,\dots ,K.\\ {‖d_i‖}_2\le 1,i=1,2,\dots ,K.\end{array}$$ (5)

where $L$ is a non-negative model parameter to control the sparsity level of the representations. $D=\left[d_1,d_2,\dots ,d_K\right]\in {\mathbb{R}}^{m\times K}$ represents the dictionaries, and $K$ is the size of dictionaries. $X=\left[x_1,x_2,\dots ,x_n\right]\in {\mathbb{R}}^{K\times n}$ is the representation matrix, and $\Vert \cdot {\Vert }_0$, $\Vert \cdot {\Vert }_F$ denote the ${\ell }_0$ and Frobenius norms, respectively. More details can be found in our previous work[26].

After that, the group-wise contribution can be excluded from each correlation matrix $C_i$. The obtained functional connectivity can be represented as follows:

$${\hat{C}}_i=C_i-mat\left(D{x}_i\right)$$ (6)

where $mat\left(D{x}_i\right)\in {\mathbb{R}}^{p\times p}$ denotes the correlation matrix reconstructed from the lower triangular vector $D{x}_i$. The procedure of refined FC extracted is illustrated in Step 2 of Fig. 2. Note that the SDL model is implemented on each subject from different fMRI paradigms, respectively.

D. Individual identification analysis

1). Whole brain and subnetwork-wise analysis:

To investigate the predictability of three kinds of FCs as fingerprints, we used the same pipeline proposed by Finn et al. [20]. Identification was performed across pairs of scans consisting of one target and one session from the database. For the target session with a given subject (e.g., resting-state or Rest), we would like to identify that the connectivity from the session in the database (e.g., working memory or Wm) belonged to the same participant. To accomplish that, we calculated the similarity between the target session and each of all other sessions. Then, we found the predicted identity by detecting the matrix with the maximal similarity score. Here, the similarity scores were simply determined using the Pearson correlation coefficient. Then, we performed 10,000 nonparametric permutation tests (two-sided) to assess the significance level of the observed identification accuracy. For each permutation, the identities of the participants in both sessions were randomly shuffled. Next, we repeated the identification experiment described above and recorded the results. A significance level of p = 0.05 was applied as the threshold for the 10,000 permutation tests.

To evaluate each functional network’s contribution, connections that corresponded to a single network were used for the identification. More details about the functional networks can be found in the section of data acquisition. Note that if we define the set of nodes coming from network $\mathrm{j}$ as $V_j=\left\{v_{jk}\right.,\left.k=1,2,\dots ,K_j\right\}$, where $K_j$ is the total number of nodes in network $\mathrm{j}$, only connections within the selected network are included. In addition, we compared the difference between the amplitude based and PLV connectomes.

2). Edgewise contribution to identification:

To investigate which edge contributes most to the identification, we investigated the modified differential power (DP) proposed by Liu et al. [25]. Similarly, the combined connectomes were not involved in this section. Besides, only the resting-state fMRI signals were applied. The modified differential power was described as follows:

$$\begin{array}{l}DP\left(i,j\right)=1-\sum _l P_l\left(i,j\right),\\ P_l(i,j)=\frac{\left|{\varphi }_{lk}(i,j)>{\varphi }_{ll}(i,j)\right|+\left|{\varphi }_{kl}(i,j)>{\varphi }_{ll}(i,j)\right|}{2\left(n-1\right),}\end{array}$$ (7)

where $P_l(i,j)$ denotes the empirical probability to quantify the differential power of an edge for the identification; $l$ and $k(l\ne k)$ represent the labels of two different subjects; $i$ and $j(i\ne j)$ are two different ROIs within the connectivity; $n$ is the total number of subjects. $\left|{\varphi }_{lk}(i,j)>{\varphi }_{ll}(i,j)\right|$ indicates the probability that $\left|{\varphi }_{lk}\right|$ between two different subjects is higher than $\left|{\varphi }_{ll}\right|$ of the same participant. Given two sets of connectivity matrices $\left[X_l^{R1}(i,j)\right],\left[X_k^{R2}(i,j)\right]$ obtained from the rsfMRI sessions after z-score normalization, the corresponding edgewise product vector ${\varphi }_{lk}(i,j)$ can be calculated as follows:

$${\varphi }_{lk}(i,j)=X_l^{R1}(i,j)\mathrm{*}{X}_k^{R2}(i,j),l,k=1,2,\dots ,n$$ (8)

and $\left|{\varphi }_{ll}\right|$ can be observed in the same way. DP describes the ability of a specific connection to distinguish each individual from others. More specifically, a higher DP value indicates a more significant contribution to the identification and vice versa. We estimated the DP for all edges across the whole brain and only retained values within the 99.9% percentile.

E. Individual prediction of cognitive behaviors

To explore the predictability of different connectomes (amplitude, PLV, and combined connectivity) in inferring cognitive behaviors, we tested from two aspects: regression and classification analysis for continuous and discrete targets, respectively. For the HCP dataset, fluid intelligence (Mean±SD: 17.04±4.71, Range: 4.00–24.00), cognitive flexibility/executive (Mean±SD: 102.54±9.89, Range: 57.79–122.65), inhibition/executive function (Mean±SD: 102.05±9.94, Range: 72.81–123.56) and language/vocabulary comprehension (Mean±SD: 109.44±15.07, Range: 68.68–153.09) were used. As to the validation dataset (PNC), only the corresponding fluid intelligence score was included (Mean±SD: 102.38±15.80, Range: 70.00–145.00). After that, the connectomes calculated from the rsfMRI data were used as features to define the cognitive behavior score.

1). Regression analysis:

To compare the performance of various connectomes in depicting the cognitive behavior, we used the leave-one-subject-out cross-validation (LOOCV) strategy to describe the prediction accuracy [26]. Taking fluid intelligence as an example, in each LOOCV fold, one subject was set as the test sample and the remaining $n-1$ participants were applied as the training set. We first concatenated all the edges within the connectomes to generate a feature vector for each participant. Then, we performed the feature selection based on the correlation between the features and the corresponding fluid intelligence scores. Here, the Pearson correlation was applied. If the correlation is of statistical significance (p-value < 0.001), the corresponding feature is retained and vice versa. A predictive model was then built using a simple linear regression model to fit the selected features to the fluid intelligence scores in the training set. At the end, the generated model was used to predict the score using the testing data. During this procedure, each participant was used for testing once. When all the LOOCV experiments were finished, we estimated the prediction ability via the correlation coefficient between the predicted and observed scores.

We then conducted nonparametric permutation testing (10,000 times) to reveal the observed cognitive behavior scores’ significance level. During each permutation testing, the observed scores were randomly shuffled before regression analysis. In this way, the likelihood that a prediction occurred by chance can be examined..

2). Classification analysis:

We also conducted the classification of low and high cognitive behavior scores to examine the predictability of FC profiles. Specifically, we first selected participants whose score were in the lowest and highest $\theta$-percentile of the distribution for the cognitive assessments. Here, cases of $(\delta \in \{10,20,30\left\}\right)$ were considered. That is, only subjects with the lowest or highest $\delta \%$ were included in the analysis. We also investigated the feature selection step discussed above on the selected participants (the significant level p = 0.001). A support vector machine (SVM) with a Gaussian Kernel was used to perform the classification.

We had a relatively small number of participants within each subset based on various $\delta$ values. For the HCP dataset, we have 172 subjects for $\delta =10,344$ subjects for $\delta =20$ and 516 subjects for $\delta =30$. Thus, we repeated the experiment 100 times for each $\delta$ case. For each run, we divided participants into a training set (75%) and a testing set (25%). An SVM function built in Matlab with a Gaussian kernel was employed, and a grid search was used to optimize parameters within the SVM model (e.g., the radius of Gaussian kernel, the weight of the soft margin cost function).

III. RESULTS

A. Whole brain based individual identification

As a first pass, we evaluated the individual identification accuracy based on the whole brain connectivity (268 ROIs) and compared three different connectomes (aFC, PLV-FC and aFC + PLV-FC). The identification rates generated by the HCP dataset are depicted in Fig. 3. Among the various fMRI session pairs, all three connectomes can provide a high identification rate (from 82.7% to 95.7%). Relative to the amplitude-based connectomes, phase-based connectomes performed similarly in individual identification. That is, phase information estimated from the fMRI time series can also differentiate each participant from the population. The rates extracted by the combined connectivity were higher than the accuracies estimated by the amplitude-based connectomes under all scenarios (90.8% vs. 88.9% for rest-emotion pair, 87.5% vs. 84.5% for emotion-rest pair, 95.7% vs. 94.2% for rest-wm pair, 93.1% vs. 90.7% for wm-rest pair, 94.1% vs. 92.8% for emotion-wm pair and 93.4% vs. 92.7% for wm-emotion pair). Hence, we believe that PLV connectivity contains supplementary subject-specific information that amplitude-based connectomes cannot posses. To test this hypothesis, we repeated the same experiments on the PNC dataset and found consistent results. More details can be viewed in Fig.S1 of the supplementary materials. Given that identification trails were not independent of each other, we investigated 10,000 nonparametric permutation tests (two-sided) to assess the level of significance in these results. Across 10,000 iterations, the p-value for each pair of sessions is below 0.0001. It indicates that the rates of identifications are significantly above chance.

Fig. 3.

Identification accuracy across session pairs using the whole brain connectivity. Rest: resting-state fMRI, Emotion: emotion task fMRI, WM: Working Memory task fMRI. Here, * means p-value < 10⁻⁵ for two-tailed t-test for various combinations (aFC-PLV, aFC-Combined and PLV-Combined).

B. Subnetwork-wise individual identification

We examined the identification rates based on each functional network to further explore subject-specific information captured by the aFC and PLV-FC individually. The subnetworks were defined by Finn et al. [20] and described in Fig. 1. We found many consistent results for both the aFC and PLV-FC. The medial frontal network (network 1) and the frontoparietal network (network 2) contributed substantially to individual discrimination, which comprised the higher-order association cortices in the frontal, parietal and temporal lobes. By comparison, the subnetworks related to the visual system had little effect on the identification accuracy. Among the rest-task combinations, the motor network (network 5) benefited the identification rates. The subcortical-cerebellum system (network 4) carried the subject-specific information for the pairs of resting and working memory sessions. Meanwhile, the PLV connectivity provided some individual features which were not be obtained by the amplitude-based connectomes. As shown in Fig. 4, the subcortical-cerebellum network helped the individual identification with the PLV connectivity in each fMRI session combination. However, it only benefited the accuracy for the pair of rest-WM when applying the amplitude-based connectomes. Moreover, we observed that the DMN network (network 3) performed much better with the PLV-based connectomes than amplitude-based connectivity. These findings indicate that the phase information can provide unique features that improve the discrimination of individuals.

Fig. 4.

Identification accuracy across session pairs for each subnetwork. Rest: resting-state fMRI, Emotion: emotion task fMRI, WM: Working Memory task fMRI.

C. Edgewise contributions to identification

By calculating the modified differential power (DP), we investigated which connections contribute most to individual identification. Next, we explained the difference of features extracted from the aFC and PLV-FC. Here, the modified DP represented the ability of edgewise connections to differentiate each participant from the population. A connection with high DP tended to have a similar value within an individual across fMRI sessions, but had different degrees across individuals regardless of the fMRI paradigms.

In this experiment, the modified DP was calculated for both the aFC and PLV-FC. Note that the analysis was restricted to the resting-state fMRI session. As shown in Fig. 5, we detected the connections with the highest 99.9% DP values across all the links. Similarly, we achieved some matching results for both the amplitude and PLV connectivity. First, we found that most edges with high DP are related to the frontal, parietal, and temporal lobes. Furthermore, a large proportion of high DP connections were involved in the frontoparietal and medial frontal networks. For instance, the medial frontal network, frontoparietal network, and the interaction between them included 47.9% of high DP connections when using the amplitude-based connectivity (As to the PLV based connectomes, this value increased to 62.7%). It shows that medial frontal and frontoparietal networks play a significant role in individual identification. By checking the results displayed in Fig. 5, we found that connections within each subnetwork were more beneficial to individual discrimination with the PLV connectivity than the amplitude-based connectomes. Furthermore, the interactions between various functional networks carried less subject-specific information for the PLV matrices. We believe that phase-based features were mainly represented by the activities within each functional network.

Fig. 5.

Edgewise contributions to individual identification for both the aFC and PLV-FC. (a) Connections that possess the highest DP scores in individual connectivity profiles (top, circle plot). Axial, sagittal and coronal views of these links are also provided (bottom, from left to right). Note that connections with the highest 1% DP values are displayed here. In the circle plots (top), the 268 nodes (the inner circle) are organized into a lobe scheme (the outer circle) roughly reflecting brain anatomy from anterior (top of the circle) to posterior (bottom of the circle) and split into left and right hemisphere. Lines indicate edges or connections. (b) The percentage of connections within and between each pair of networks (8 functional networks defined Fig. 1) using the same data as (a). The color depth of the grid in the matrix indicates the fraction of DP edges for each pair of networks.

D. Connectivity profiles predict individual cognitive scores

1). Regression analysis:

We explored the predictability of different connectomes (aFC, PLV-FC, and combined matrices) in characterizing cognitive scores. The results are presented in Fig. 6. Note that only the scatter plots for fluid intelligence are shown in Fig. 6(a). The plots for other cognitive scores are given in Fig.S2 of the supplementary materials. We observed that the PLV-based connectivity performed better than aFC in predicting all the cognitive scores. Thus, we assume that the PLV connectivity features are much more closely correlated with cognition behaviors. Besides, the performance of combining the aFC and PLV connectomes depended on the type of cognitive test. For fluid intelligence and L/V comprehension prediction, the combined connectivity obtained the highest correlation coefficient among all of the scenarios. In addition, the range of predicted scores from the combined connectomes was narrower than others. Similar outcome was obtained by the PNC dataset in Fig.S3 of the supplementary materials. As to the cognitive flexibility and inhibition, the PLV and combined connectomes held similar predicting ability. To validate the repetition of our results, we repeated 100 nonparametric permutations for each score. We observed that the prediction of cognitive scores was above chance (p-value < 0.01).

Fig. 6.

Prediction performance of aFC, PLV, and combined connectomes. (a) Scatter plots display the prediction results from a leave-one-out cross-validation (LOOCV) analysis comparing the predicted and the observed cognitive scores. Each dot represents one subject, and the area between dashed lines reflects a 95% confidence interval for the best-fit line. b Bar plots depict the correlation coefficients (R-values) between the predicted and observed cognitive scores.

2). Classification of cognitive groups:

To further analyze the prediction power of various functional connectivity, we examined whether we were able to discriminate groups of different cognitive behaviors. This was usually achieved by using functional connectomes. We show that the connectivity including both the amplitude and phase information had the best classification accuracy for all the behavior scores (e.g., for the situation of $\delta =10$ of the fluid intelligence, the classification accuracies are displayed as follows: the combined connectivity: 85.7%; the PLV connectivity: 80.3%; the amplitude-based connectivity: 82.8%). However, by involving the PLV information, the classification accuracy was improved for various behavior scores. This finding agrees with the conclusion drawn from regression analysis that the performance of combining the aFC and PLV connectomes improves and varies with the type of cognitive score used.

IV. DISCUSSION

The previous study has shown that the neural synchronization from the low-frequency resting-state fMRI BOLD signals may be a useful neural fingerprint in identifying individuals [29]. Inspired by this, we further investigated how phase-based functional connectivity can be used to identify individuals. Thus, in this study, we included three functional profiles: amplitude-based FC, phase-based FC, and the FC combining both the amplitude and phase information. As a first pass, we performed individual identification experiments with these functional connectomes. In this way, we compared PLV based connectomes’ performance with that of amplitude-based connectomes. Meanwhile, we checked whether phased based functional profiles have unique subject-specific features. Then, we applied these three connectomes to analyze whether phase synchronization signals can serve as a predictor of cognitive function.

In comparison with Zhang et al.’s project, our work possesses several significant differences [29]. First, the approach of capturing phase information from time series is different. We applied the phase-locking value technique to extract the phase information. However, amplitude envelope and instantaneous phase were used in Zhang et al.’s work. Second, in Zhang et al.’s work, they indicated that the phase information could also be used to identify individuals. By contrast, we proved that phase-based FC carries some individual information that amplitude-based FC cannot afford. Third, we pointed out that the phase-based FC could be used to predict cognitive behavior. This experiment has never been done in the previous work.

In this work, we use the intraclass correlation coefficient (ICC) introduced by Finn et al. to perform the identification analysis. [20]. The same coefficient has been applied in several related studies [20], [22], [36], [25]. By comparison, our proposed approach has two substantial differences. First, we utilize sparse dictionary learning to remove the population-wise contribution and enhance the individual difference. The raw functional connectome was used directly to perform the analysis in previous works mentioned above. In our proposed method, we increase individual differentiation by removing population-wise contribution. The performance of this approach was validated in our previous work [26]. Second, we consider the amplitude and phase information extracted from the fMRI time series. In contrast to our approach, the framework used in previous studies constructs the FC by applying the Pearson correlation only; that is, only the amplitude information is involved.

When examining the identifiability with the whole brain, our findings suggest that similar to amplitude-based functional connectomes, functional profiles constructed by the phase information can also discriminate individuals from other participants. It demonstrates that phase signals in the BOLD time series are stable and reliable for identifying each individual. In addition, identification rates increased by combining both amplitude and phase features (combined vs aFC : 90.8% vs. 88.9% for rest-emotion pair, 87.5% vs. 84.5% for emotion-rest pair, 95.7% vs. 94.2% for rest-wm pair, 93.1% vs. 90.7% for wm-rest pair, 94.1% vs. 92.8% for emotion-wm pair and 93.4% vs. 92.7% for wm-emotion pair). We believe that phase-based profiles contain additional subject-specific information not captured by the amplitude-based correlation. Thus, the features extracted by the PLV connectomes may provide additional information describing each individual and may further elucidate our understanding of mental disorders [37]. Meanwhile, we also investigated each functional subnetwork’s contribution to individual discrimination. We found that the medial frontal and frontoparietal networks primarily contributed to individual identification. It validates the previous findings that higher-order association cortices (frontal, parietal and temporal lobes) have the most inter-subject variance. Furthermore, some subnetworks within PLV connectomes had different performance on discrimination relative to amplitude-based functional profiles. More specifically, the subcortical cerebellum with the PLV connectivity contributed a lot to the identification under all the scenarios, while the use of aFC only benefited to the recognition for the rest-WM combination. The DMN network also discriminated individuals better with the PLV functional profiles than the amplitude-based connectivity. These findings validate our hypothesis that phase information from the BOLD time courses provides subject-specific features.

We checked the edgewise contribution using the modified DP and obtained consistent results for both the aFC and PLV connectomes. First, most of the high DP edges were related to the higher-order association (frontal, parietal and temporal) lobes. Also, a larger proportion of high DP connections are involved with the frontoparietal and medial frontal networks. These are in agreement with previous studies [20], [26], [29]. It indicates that connections between frontoparietal and medial frontal networks provide similar fingerprinting information. Furthermore, some connections differ significantly from individual identification detected by PLV and aFC. To be precise, intra-network activities carried more specific information based on PLV connectomes than in inter-networks. As to the conventional aFC connectivity, the conclusion is the opposite. In addition, connections between the frontoparietal and visual association networks contribute more to fingerprinting based on the aFC relative to PLV. Hence, we assume that the individual features within the network are better distinguished by the phase rather than the amplitude. On the other hand, aFC connectivity better reveals the subject-specific patterns across functional networks.

By investigating the cognitive prediction ability with PLV connectomes, both regression and classification analysis indicate neural synchronization signals can serve as a predictor of cognitive function. Moreover, the PLV connectivity outperformed conventional connectomes in predicting cognitive scores, while this was not observed in identification experiments. Here, we believe that the subject-specific features extracted from the phase signal are more closely correlated with the cognitive processes relative to the amplitude information. Then, we increased the prediction ability by combining the aFC and PLV connectivity linking with cognitive function. For instance, combined connectomes showed the best predictive power for fluid intelligence and L/V comprehension. In contrast, the combined and PLV connectivity possessed a similar predictive ability for the cognitive flexibility and inhibition scores. This suggests that the individual features describe various cognitive processes to different extents. In this work, we put the aFC and PLV connectivity together via simple concatenation. In future work, other data integration strategies should be considered.

Several issues need further consideration. First, we estimated the correlation matrix across time series as the connectome. In this way, changes in the functional connectivity across the time are not estimated. However, recent research shows that functional connectivity has different patterns across time, which can provide complementary individual information [10], [11], [14], [17], [25], [38], [39]. Time-varying connectivity for both amplitude and phase signals may be a promising direction for individual identification. Second, functional connectivity is greatly affected by head motion artifacts that cannot be completely eliminated by motion correction. More work is needed to explore how head motion impacts phase-based connectomes in identifying individuals (such as using ICA based connectomes, which have been shown to be more robust to head motion than ROI-based approaches [40]).

V. CONCLUSION

In this study, we confirmed that phase synchronization based functional profiles can be used to identify an individual. More specifically, we found that phase-based connectomes provided subject-specific information that may not be represented by the amplitude-based connectivity. Contrary to the amplitude-based connectivity, intra-network activities carried more specific information with PLV based connectomes relative to inter-network ones. Furthermore, we found that PLV-based connectomes outperformed the amplitude-based connectivity in predicting cognitive functions. In summary, our findings indicate that neural synchronization patterns provide unique subject-specific information and offer a promising way to characterize an individual’s brain network.

Fig. 7.

Classification results between low and high cognitive group. In the feature selection step, significant edges are retained (p-value = 0.001). Then, three percentile values are considered (δ =10, 20, 30). Blue, yellow and red boxes refer to the aFC, PLV, and combined connectivity, respectively.

DATA AVAILABILITY STATEMENT

The data that support the findings of this study are openly available in dbGap at http://www.humanconnectomeproject.org/.