Functional Connectome Fingerprint Gradients in Young Adults

We have used the fMRI data from the HCP-YA 1200 subjects release [49][1]. The fMRI resting-state data (HCP-YA filenames: rfMRI_REST1 and rfMRI_REST2) were acquired in separate sessions on two different days, with two different phase acquisitions (left to right or LR and right to left or RL) per day [49][1][7]. The seven fMRI tasks are the following: gambling (tfMRI_GAMBLING), relational (tfMRI_RELATIONAL), social (tfMRI_SOCIAL), working memory (tfMRI_working memory), motor (tfMRI_MOTOR), language (tfMRI_LANGUAGE, including both a story-listening and arithmetic task), and emotion (tfMRI_EMOTION). Two runs (LR and RL) were acquired for each task. Working memory, gambling, and motor task were acquired on the first day, and the other tasks on the second day [7][50]. Table 2 summarizes the run time and number of frames per condition:

The following is a brief description of each fMRI condition. More extensive information may be found in the HCP S1200 Release Reference Manual.

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  REST: Resting state fMRI (rs-fMRI) data was acquired in four runs of approximately 15 minutes each, two runs in each session. The subjects were instructed to keep their eyes open with relaxed fixation on a projected bright cross-hair on a dark background presented in a darkened room. 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 (LR) direction in the other run. 1200 frames were obtained per run at 720 ms TR.

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  EMOTION: This task was adapted from the one developed by Hariri et al. [51]. Subjects are shown blocks of trials that either ask them to decide which of two faces on the bottom of the screen match the face at the top, or which of two shapes at the bottom match the shape at the top of the screen. The faces have either an angry or fearful expression. Trials are presented in blocks of 6 trials of the same task (face or shape), with the stimulus presented for 2000 ms and a 1000 ms ITI. Each block is preceded by a 3000 ms task cue (“shape” or “face”). Each of the two runs includes three face blocks and three shape blocks, with 8 seconds of fixation at the end of each run. In total, the emotion processing task fMRI had a run duration of 2:16 minutes per run, with 176 frames per run.

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  GAMBLING: This task has been adapted from the one developed by Delgado and Fiez [52]. Subjects are asked to play a card guessing game wherein they are asked to guess the number on a mystery card in order to win or lose money. Subjects are told that potential card numbers are between 1 and 9 and to indicate whether they think the mystery card number is more or less than 5 by a button press. Feedback to the subject is the actual number on the card and either a green arrow up with ”$1” for reward or red arrow down with ”-$0.5” for loss. If the mystery number is equal to 5, the trial is considered neutral and a grey double headed arrow is shown. The subjects have 1500 ms to respond with button press, followed by 1000 ms of feedback. If the subject responds before the 1500 ms is over, a fixation cross is displayed. The task is presented in blocks of 8 trials that are either mostly reward or mostly loss. In each of the two runs, there are 2 mostly reward and 2 mostly loss blocks, interleaved with 4 fixation blocks (15 seconds each). In total, the gambling task fMRI had a run duration of 3:12 minutes per run, with 253 frames per run.

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  LANGUAGE: This task was developed by Binder el al. [53] and uses the E-prime scripts provided by them. The task consists of two runs that each interleave four blocks of a story task and four blocks of a math task. The lengths of the blocks vary (average of approximately 30 seconds), but the task was designed so that the math task blocks match the length of the story task blocks, with some additional math trials at the end of the task to complete the 3.8 minute run as needed. The story blocks present participants with brief auditory stories (5-9 sentences) adapted from Aesop’s fables, followed by a 2-alternative forced choice question that asks participants about the topic of the story. The math task also presents trials aurally and requires subjects to complete addition and subtraction problems. Participants push a button to select either the first or the second answer from the options presented. The math task is adaptive to try to maintain a similar level of difficulty across participants. In total, the language task fMRI had a run duration of 3:57 minutes per run, with 316 frames per run.

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  MOTOR: This task was adapted from the one developed by Yeo et al., 2011 [23]. In this task, subjects are shown visual cues asking them to either tap their left or right fingers, or squeeze their left or right toes, or move their tongue to map different motor areas in the brain. There are total 10 movements and each movement type lasted 12 seconds, preceded by a 3 second cue. In each of the two runs, there are 13 blocks, with two of tongue movements, four of hand movements (2 right and 2 left), and four of foot movements (2 right and 2 left). In addition, there are three 15-second fixation blocks per run. In total, the motor task fMRI had a run duration of 3:34 minutes per run, with 284 frames per run.

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  RELATIONAL: This task has been adapted from the work done by Smith et al. [54]. The stimuli are six different shapes filled with one out of six different textures. Subjects are presented with 2 pairs of objects, one at the top of the screen and the other at the bottom. They have to first decide whether shape or texture differs across the top pair and then they have to decide whether the bottom pair also has the same difference. In the control matching condition, participants are shown two objects at the top of the screen and one at the bottom, and a word in the middle of the screen (either “shape” or “texture”). They are told to decide whether the bottom object matches either of the top two objects on that dimension (e.g., if the word is “shape”, is the bottom object the same shape as either of the top two objects. For both conditions, the subject responds with a button press. For the relational condition, the stimuli are presented for 3500 ms, with a 500 ms inter-task interval, with four trials per block. In the matching condition, stimuli are presented for 2800 ms, with a 400 ms inter-task interval, and there are 5 trials per block. Each type of block (relational or matching) lasts a total of 18 seconds. In each of the two runs of this task, there are three relational blocks, three matching blocks, and three 16-second fixation blocks. In total, the relational processing task fMRI had a run duration of 2:56 minutes per run, with 232 frames per run.

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  SOCIAL: Subjects were shown 20 second video clips of objects (squares, circles, triangles) that either interacted in some way, or moved randomly on the screen. These videos were developed by either Castelli et al. [55][56] or Martin et al. [57][58]. After each video clip, subjects were asked to judge whether the objects had a mental interaction (an interaction that appears as if the shapes are taking into account each other’s feelings and thoughts), Not Sure, or No interaction (i.e., there is no obvious interaction between the shapes and the movement appears random). Each of the two task runs has 5 video blocks (2 Mental and 3 Random in one run, 3 Mental and 2 Random in the other run) and 5 fixation blocks (15 seconds each). In total, the social cognition task fMRI had a run duration of 3:27 minutes per run, with 274 frames per run.

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  WORKING MEMORY: The working memory task has been adapted from the one developed by Drobyshevsky et al., 2006 [59] and Caceres et al., 2009 [60]. Category specific representation task [61][62][63][64] and working memory (working memory) task [61][64][65][62] were combined into a single task paradigm. Subjects were presented with blocks of trials consisting of pictures of places, tools, faces, and non-mutilated body parts. Within each run, the four different stimulus types were presented in separate blocks. Also, within each run, half of the blocks use a 2-back working memory task and the other half use a 0-back working memory task (as a working memory comparison). A 2.5 second cue indicates the task type (and target for 0-back) at the start of the block. Each of the two runs contains 8 task blocks (10 trials of 2.5 seconds each, for 25 seconds) and 4 fixation blocks (15 seconds). On each trial, the stimulus is presented for 2 seconds, followed by a 500 ms inter-task interval (ITI). In total, the working memory task fMRI had a run duration of 5:01 minutes per run, with 405 frames per run.

Our starting point to process the HCP-YA data is the denominated minimally processed dataset, as provided by HCP [7]. The pipeline includes artifact removal, motion correction, and registration to standard space. The main steps of this pipeline are spatial (minimal) preprocessing, in standard volumetric and combined volume and surface spaces. By taking care of the necessary spatial preprocessing once in a standardized fashion, rather than expecting each user to repeat this processing, the minimal preprocessing pipeline avoids duplicate effort and ensures a minimum standard of data quality. The main steps of this minimal processing functional pipeline [66][7][66] are described in this section.

In total, there are six minimal preprocessing pipelines included in the HCP, three structural (PreFreeSurfer, FreeSurfer, and PostFreeSurfer), two functional (fMRIVolume and fMRISurface), and a Diffusion Preprocessing (not covered in this work) pipeline. Following is a brief description of the structural pipelines:

1. 1.

   PreFreeSurfer: This produces an undistorted ”native” structural volume space for each subjects, aligns the T1w and T2w images, performs a bias field correction, and registers the subject’s native structural volume space to MNI space.

2. 2.

   FreeSurfer: This pipeline is based on FreeSurfer version 5.2. It segments the volume into predefined structures, reconstructs white and pial cortical surfaces, and performs FreeSurfer’s standard folding-based surface registration to their surface atlas (fsaverage).

3. 3.

   PostFreeSurfer: This pipeline produces all of the NIFTI volume and GIFTI surface files necessary for viewing the data in Connectome Workbench, applies the surface registration to the Conte69 surface template [67], downsamples registered surfaces for connectivity analysis, and creates the final brain mask and myelin maps.

There are two volume spaces and three surface spaces in the HCP-YA data. The volume spaces are the subject’s undistorted native volume space and the standard MNI space, which is useful for comparisons across subjects and studies. The surface spaces are the native surface mesh for each individual ( 136k vertices, most accurate for volume to surface mapping), the high resolution Conte69 registered standard mesh ( 164k vertices, appropriate for cross-subject analysis of high resolution data like myelin maps), and the low resolution Conte69 registered standard mesh ( 32k vertices, appropriate for cross-subject analysis of low resolution data like fMRI or diffusion). The 91,282 standard grayordinate (CIFTI) space is made up of a standard subcortical segmentation in 2 mm MNI space and the 32k Conte69 mesh of both hemispheres. The functional and diffusion pipelines can be run after completing the structural pipelines described above. Following is a brief description of the two functional pipelines:

1. 1.

   fMRIVolume: This pipeline removes the spatial distortions, carries out motion correction by realigning volumes, reduces the bias field, normalizes the 4-dimensional image to a global mean, and masks the data with the final brain mask. There is no overt volume smoothing in this pipeline as the output of this pipeline is in the volume space and can be used for volume-based fMRI analysis.

2. 2.

   fMRISurface: In this pipeline, the volume-based time series is brought into the CIFTI grayordinate standard space. The voxels within the cortical gray matter ribbon are mapped onto the native cortical surface. This transforms the voxels according to the surface registration onto the 32k Conte69 mesh and maps the set of subcortical gray matter voxels from each subcortical region in each subject to a standard set of voxels in each atlas parcel. This gives a standard set of grayordinates in every subject with 2 mm average surface vertex and subcortical volume spacing. This data is then smoothed with surface and parcel constrained smoothing of 2 mm FWHM (full width at half maximum) to regularize the mapping. This pipeline outputs a CIFTI dense time-series (denominated {TASK}_{ACQ}_Atlas_MSMAll.dtseries.nii, where {TASK} refers to the fMRI condition and {ACQ} is the acquisition, either LR or RL) that can be used for surface-based fMRI analysis.

For the resting-state data, in addition to the minimal processing pipeline described above, a 24-parameter motion regression and ICA-FIX [54][68][69] have also been applied in the data provided by HCP-YA. The 24 parameters included in the motion regression step are the 6 rigid-body parameter timeseries, their backwards-looking temporal derivatives, and all squared 12 resulting regressors. The motion regressesion and ICA-FIX step applied on resting state fMRI data has produced timeseries denominated rfMRI_REST_{ACQ}_Atlas_hp2000_clean.dtseries.nii.

We perform the following additional steps on the fMRI data (denominated {TASK}_{ACQ}_Atlas_MSMAll_ hp2000_clean.dtseries.nii for resting state and {TASK}_{ACQ}_Atlas_MSMAll.dtseries.nii for task-based fMRI in HCP-YA data):

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  Nuisance regression: This step is carried out for the task fMRI data only, where we regress out the 24-parameter motion regressors (6 rigid-body parameter timeseries, their backward-looking derivatives, and all squared resulting regressors), average time-series from the cerebro-spinal fluid (CSF), and the average time-series from the white matter. We have also provided processed data where this step is not performed.

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  Global signal regression (GSR): This step involves the removal of the global (or average) signal from the time series of each voxel using linear regression [42]. We have produced two sets of connectomes, one where GSR has been performed and one where it has not been, as there is a lack of consensus in the scientific community regarding whether it should be performed or not [43][44][45][46][47][70]. The results shown in the main text are based on connectomes where GSR has been performed as part of the preprocessing. This step was performed for all fMRI conditions (if specified).

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  Bandpass filtering: Lastly, we bandpass filter the time-series data using the following parameters:

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    Minimum frequency ($f_{min}$) = 0.009 Hz

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    Maximum frequency ($f_{max}$) = 0.08 Hz for resting state and 0.25 Hz for task-based fMRI

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    Repetition time (TR) = 0.72 s

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    Butterworth filter order = 4

  This step was always performed on all the fMRI conditions.

The brain atlases used in this paper have been developed by Schaefer et al., 2018 [18]. The Schaefer parcellations are further divisions of the resting state functional networks described by Yeo et al., 2011 [23] and have different levels of granularity (100 to 1,000 brain regions, in steps of 100). We have also added the 14 subcortical regions as provided in the HCP-YA dataset (denominated Atlas_ROIs.2.nii.gz) to each of these atlases, thus making them 114, 214,…, 1,014 brain regions. All the results described in this paper correspond to the Schaefer parcellations.

The next step is to extract the functional time series corresponding to each brain region of the parcellation, z-score them, and ultimately estimate the functional connectomes. This step is conducted in Connectome Workbench (freely available at https://www.humanconnectome.org/software/connectome-workbench) with the commands cifti-reduce, cifti-math, and cifti-parcellate. The command cifti-reduce is used to compute the mean and standard deviation of time series data, while cifti-math computes the z-scored time series data using the mean and standard deviation previously computed. Lastly, cifti-parcellate parcellates the voxel-wise time series data into different brain regions as per the Schaefer parcellation, by averaging all the voxel-level time series belonging to each brain region. These parcellated time series have been made available and can be used to perform brain-region level activity and connectivity analysis.

Finally, whole-brain functional connectomes are generated by computing the Pearson’s correlation coefficients between the time series of every pair of brain regions in the parcellated time series data computed in the earlier step. These connectomes are square and symmetric matrices that have been made available and can be used to perform functional connectome analyses. Figure 1 shows a sample connectome parcellated into the Schaefer100 atlas, with 114 brain regions (100 cortical + 14 subcortical). The figure names all the subcortical regions.

In order to quantify the subject-level fingerprint from a cohort of functional connectomes, Amico and Goñi [24] proposed an object called the identifiability matrix. This is a non-symmetric correlation matrix that compares the all-to-all test-retest functional connectomes from a cohort of unrelated subjects. Thus, every entry in this matrix is the Pearson’s correlation between test and retest functional connectomes in their vector form. Typically, the x-axis of the identifiability matrix represents the test (or first run, or day 1) and y-axis the retest (or second run, or day 2). Importantly, the ordering of the subjects is kept the same in the rows and columns of this matrix (i.e., test and retest sessions), and hence the main diagonal contains the correlation values between the test and retest connectomes of the same subject. The higher the values in the main diagonal compared to the off-diagonal elements, the better the subject-level fingerprint of the dataset.

We have further expanded on this intuitive interpretation of the identifiability matrix by using the connectomes from twin pairs instead of test-retest of the same subject. In order to do so, we are extending the concept of identifiability and fingerprints beyond test/retest of the same subjects. To do so, we have computed the identifiability matrix for two different cohorts of twins, monozygotic (MZ) twins and dizygotic (DZ) twins. In this case, rows and columns of the identifiability matrix represent each of the two twins respectively, with the main diagonal values being the Pearson correlations between the FCs of the twin pair and the off-diagonal being the correlations between the FCs of unrelated subjects from the twin-cohort. Figure 2 shows the differential identifiability matrices for sample cohorts of 20 test-retest, MZ twin pairs, and DZ twin pairs.

Using the identifiability matrix, Amico and Goñi [24] have proposed a measure called differential identifiability ($I_{diff}$) to quantify the subject-level fingerprint. $I_{diff}$ quantifies the contrast between the self-similarity (main diagonal) and the similarity between different subjects (off diagonal). $I_{diff}$ can be computed as:

As discussed above, the differential identifiability score can also be calculated for a twin cohort by pairing FCs of twin subjects instead of test-retest. In this case, the main diagonal elements of the identifiability matrix will be the correlations between the FCs of twin subjects (MZ and DZ) and the off-diagonal elements will be the correlations between unrelated subjects. In this case, the twins differential identifiability can be expressed as:

This can be repeated separately for monozygotic (or identical) twins and dizygotic (or fraternal) twins. Monozygotic (MZ) twins are genetically 100% identical whereas dizygotic (DZ) twins have, on average, 50% genetic material in common [71][72].

In order to assess and compare the different Schaefer parcellations with each other in terms of their fingerprints, we have adapted the identifiability framework put forth by Amico and Goñi, 2018 [24]. They used group-level principal component analysis (PCA) to decompose functional connectomes into orthogonal principal components and then subsequently reconstructed with fewer and fewer principal components in order to find the reconstruction level where the differential identifiability score was maximum. Further developments based on the differential identifiability framework have been recently used to improve FC fingerprints across different scanning sites [48] as well as in network-derived measurements [29]. PCA is a statistical procedure that transforms a set of observations of possibly correlated variables into a set of linearly uncorrelated variables, i.e., principal components. PCA as a tool is widely used in the exploratory analysis of the underlying structure of data in pattern recognition [73][74] and denoising [75][76], among other areas.

We noticed that during the partial reconstructions of the functional connectomes using subsets of principal components, the FCs were not pure correlation matrices as some of the values in the FCs fell outside the [-1 1] range. To avoid this numerical issue, we have adapted the identifiability framework as proposed by Amico and Goñi for this study by using Fisher transform [77] as shown in Figure 3. As can be seen in the figure, we vectorize upper triangular (as the matrices are symmetrical) values in each FC (two FCs per subject for test-retest and one FC per subject for twins) before assembling them into a matrix where the columns are separate FCs and rows are the vectorized connectivity patterns. Before this vectorization, we z-transform the FCs by employing Fisher transform (MATLAB function atanh). Fisher transform has also been employed previously in several studies focusing on functional connectivity in the human brain [78][79][80][81]. The assembled matrix of Fisher transformed FCs is then decomposed using PCA into as many principal components as input FCs. In the next step, we reconstruct the FCs by incrementally adding one principal component at a time (in descending order of explained variance) and employing the inverse Fisher transform (MATLAB function tanh) in order to get back the Pearson correlation-based FCs. These FCs at each step of the reconstruction are then used to compute the identifiability matrix and, by extension, the differential identifiability score ($I_{diff}$). Through this procedure, we obtain a curve of $I_{diff}$ values for the whole range of principal components used in the reconstruction. It should also be noted that when all the principal components are used to reconstruct the FCs, we obtain the original input FCs, and thus the resulting $I_{diff}$ score corresponds to that of the original FCs.

For a given parcellation granularity and a given fMRI condition, whole-brain FCs are used to compute the differential identifiability profiles.

To facilitate meaningful comparison between the differential identifiability profiles between the Unrelated subjects, MZ twins, and DZ twins, we have run the identifiability framework on a subset of Unrelated subjects and MZ twin data so that the number of FCs in these cohorts is equal to the number of FCs in the DZ twin dataset (as DZ is the smallest dataset). This analysis was performed only for the Schaefer400 parcellation for all fMRI conditions. We have conducted the analysis for 100 bootstrap runs of 80% connectome pairs for each of the three cohorts. We hypothesize an ordinal presence of fingerprints that is highest for test-retest, lower for MZ twins, and lowest for DZ twins.

For each cohort separately, we test a null model where the rows of the identifiability matrix are shuffled before computing the identifiability score. We perform the bootstrap runs for the null models as well. This is to test whether the identifiability values we obtain from the identifiability framework applied to the three cohorts are a matter of chance.

In order to quantify the amount of fingerprint specific to a functional network, we assess the differential identifiability profiles by considering only the brain regions inside a specific functional network. For the network definitions, we use the 7 resting-state networks (RSNs) provided by Yeo et al., 2011 [23]. We should highlight that the PCA decomposition for this experiment is identical to when we explore whole-brain differential identifiability as described above, but for the differential identifiability calculation we only include the brain regions that belong to a specific RSN.

In order to test the effect of scanning length (in term of number of frames) on differential identifiability, we compute the differential identifiability profiles by gradually increasing the sequential number of fMRI volumes used in constructing the FCs. For this analysis, we have used resting-state scans as they have the longest scan duration (approx. 15 minutes) and the highest number of frames (1200). This allows us to study the effect of scanning length on differential identifiability for a wide range (50 to 1200, in steps of 50).

We first ran and assessed the differential identifiability framework on Unrelated subjects. This assessment is an extension with respect to Amico and Goñi [24] where a small cohort was evaluated (100 unrelated subjects, as opposed to 428) by using a single parcellation scheme [19]. Figure 5 shows the $I_{self}$, $I_{others}$, and $I_{diff}$ profiles for all the Schaefer parcellations for the 7 tasks and resting state included in the HCP-YA dataset.

Please note that in all the plots ($I_{self}$, $I_{others}$, and $I_{diff}$), the values for the maximum number of principal components correspond to the full reconstruction of the FCs with all the variance retained, i.e., original FCs. The number of principal components for which $I_{diff}$ is highest is considered the optimal point of reconstruction. As can be seen, the $I_{self}$ value decreases with increasing granularity for original FCs. However, as we reconstruct with fewer principal components, the $I_{self}$ values pass through a point of inflection (where $I_{self}$ values are approximately equal for all granularities) and leads to the optimal point of reconstruction where the reverse is true; i.e. $I_{self}$ increases with increasing granularity. $I_{others}$ on the other hand, is consistently lower for higher granularity across the whole range of principal components. Finally, $I_{diff}$ values for original FCs are either approximately equal (e.g.n in MOTION) or increase negligibly with increasing granularity. However, at the optimal point of reconstruction, the $I_{diff}$ score always increases with increasing granularity and the difference between the $I_{diff}$ curves is much more pronounced.

Monozygotic (or identical) twins share 100% of their genetic material [72][71]. The differences between the MZ twins thus arise from their having different environments.

Both $I_{twins}$ and $I_{others}$ for MZ twins decrease with increasing granularity for the original FCs. $I_{diff}$ scores are approximately equal across all granularities for original FCs. However, similarly as in Unrelated subjects, $I_{diff}$ score increases with increasing granularity and the difference between the $I_{diff}$ profiles for MZ twins is prominent at the optimal reconstruction.

Dizygotic (or fraternal) twins are, on average, share 50% of their genetic material [72][71]. Thus, genetically speaking, they are siblings, but often their environment is more similar than that of non-twin siblings as they are born at the same time [82].

Similar to the results of MZ twins, both $I_{twins}$ and $I_{others}$ for DZ twins also decrease with increasing granularity for the original FCs. $I_{diff}$ scores are approximately equal across all granularities for original FCs and, similar to Unrelated subjects and MZ twins, $I_{diff}$ score increases with increasing granularity at the optimal point of reconstruction. However, the difference between the $I_{diff}$ profiles for DZ twins is not as prominent as that for Unrelated subjects or MZ twins, but is still noticeable.

In order to facilitate a meaningful comparison across the three cohorts (Unrelated subjects, MZ twins, and DZ twins), we chose a random subset of Unrelated subjects and a separate random subset of MZ twins so that their numbers match the sample size of DZ twins (DZ twins cohort has the smallest sample size out of the three cohorts). In Figure 8, we have plotted the $I_{diff}$ profiles for Unrelated subjects, MZ twins, and DZ twins cohorts for all tasks and resting state for the Schaefer400 parcellation.

As can be seen in Figure 8, the $I_{diff}$ scores are the highest for Unrelated subjects across all the fMRI conditions for the entire range of principal components. These are then followed by the $I_{diff}$ scores for MZ twins and DZ twins, respectively. The three curves at the bottom of the figures are results for the null models. As can be seen, the $I_{diff}$ scores for these null models are approximately zero for the entire range of the principal components (two of the curves are mostly hidden behind the third).

In order to assess the level of fingerprint in specific functional networks of the brain, we have computed the $I_{diff}$ profiles of each of the 7 resting-state networks, as proposed by Yeo et al. [23]. Figure 9 shows the differential identifiability profiles for the 7 RSNs using resting-state FCs for all Schaefer parcellations. Please note that the decomposition/reconstruction based on PCA is carried out on whole-brain FCs and not on isolated functional networks. In other words, results presented in this section belong to the same decomposition/reconstruction procedure as the ones shown in Figure 5.

When assessing $I_{diff}$ in an isolated fashion on each RSN, it can be observed that granularity of the parcellations increases $I_{diff}$ at any level of reconstruction. Notice that some RSNs present higher levels of fingerprints than others for all granularities. For any RSN (with the only exception of VISUAL), at the optimal level of reconstruction the $I_{diff}$ scores for any given Schaefer parcellation are higher than that achieved when computing the $I_{diff}$ scores using whole-brain FCs (see Figure 5).

For the next analysis, we assessed the effect of different lengths of acquisition time on the differential identifiability of functional connectomes. In order to do so, we subsampled different lengths of time series from the resting state fMRI acquisition and applied the identifiability framework on the resulting connectomes. We repeated this experiment for all the Schaefer parcellations. Figure 10 shows the original and optimal differential identifiability for different number of time points and for all Schaefer parcellations, along with the difference between them. Also observe that the difference between original and optimal $I_{diff}$ increases with the granularity of the brain atlas. From the plot showing the difference between the original and optimal $I_{diff}$ scores, we can also note that, for every parcellation and scanning length combination, the differential identifiability is always higher. The different levels of granularity are more distinguishable from each other in terms of their $I_{diff}$ scores for shorter scanning lengths ($>$150 timepoints) at the optimal reconstruction as compared to the original FCs ($>$300 timepoints).