Efficacy of functional connectome fingerprinting using tangent-space brain networks

Abstract

Functional connectomes (FCs) are estimations of brain region interaction derived from brain activity, often obtained from functional magnetic resonance imaging recordings. Quantifying the distance between FCs is important for understanding the relation between behavior, disorders, disease, and changes in connectivity. Recently, tangent space projections, which account for the curvature of the mathematical space of FCs, have been proposed for calculating FC distances. We compare the efficacy of this approach relative to the traditional method in the context of subject identification using the Midnight Scan Club dataset in order to study resting-state and task-based subject discriminability. The tangent space method is found to universally outperform the traditional method. We also focus on the subject identification efficacy of subnetworks. Certain subnetworks are found to outperform others, a dichotomy that largely follows the "control" and "processing" categorization of resting-state networks, and relates subnetwork flexibility with subject discriminability. Identification efficacy is also modulated by tasks, though certain subnetworks appear task independent. The uniquely long recordings of the dataset also allow for explorations of resource requirements for effective subject identification. The tangent space method is found to universally require less data, making it well suited when only short recordings are available.

Keywords: Fingerprinting; Functional connectomes; Resting-state networks.

Figure 1.

(a) Functional connectivity (FC) matrix for a single resting state recording. Rows and columns have been grouped according to which resting-state network the regions belongs to in the Gordon 333 atlas. Each resting-state network is highlighted by the thicker lines. (b) Pictorial demonstration of TS projection. The FC matrices P₁, P₂ belong to a curved manifold of positive definite matrices, S, and thus distances between any of the matrices are non-Euclidean. Choosing C_ref as a reference point, the TS, T, is a new linear vector space tangent to S at the point C_ref. The FC matrices P_1,2 in S are projected onto the TS T where they are labeled as Q_1,2, for which the distances are Euclidean. (c) TS representation of the FC shown in (a) using the logarithmic mean over all resting state recordings as C_ref (see Equation 4).

Figure 2.

(a) Pairwise correlation distance matrix between TS projected FCs (left) and non-TS FCs (right) for the nine subjects (S1–S9) and their 10 resting-state sessions. The I, J-th block denotes the set of pairwise distances between recordings of subjects I and J. Distances are indicated by the color bar, which is the same for both panels. (b) CDF of intrasubject distances (solid) and intersubject (dashed) distances for the tangent space projected FCs (blue) and regular FCs (red). (c) Classifier accuracy as a function of the classification threshold θ for both the TS method (blue) and non-TS method (orange). The dashed-blue line denotes the accuracy of random assignment. Black line at accuracy of one is provided for visual aid. (d) ROC curve for classifying intra- versus intersubject distances using the TS, non-TS, and geodesic methods. Inset: The PR curve for the same classification. (e) Average distance from the first recording of each patient for both the TS (blue) and non-TS (red) methods. Both curves have been shifted down to be centered around zero to allow for comparison (originally at 0.61 for TS, 0.25 for non-TS), but the variance of the curves around zero has not been changed. Error bars denote the standard deviation across the nine subjects.

Figure 3.

(a) Distance matricies for the three tasks and rest using the non-TS method. Within each block are the correlation distances between each pair of FCs. (b) The ROC curve for each of the cases shown in panel a. The corresponding AUC_S is also provided. (c) The distance matricies for TS method. Rows represent which category the recordings to be fingerprinted belong to. Columns represent which category the recordings that make up the tangent space reference C_ref. belong to. Within each block are the correlation distances between the tangent space projected FCs, using the indicated reference. For each block, AUC = 1. (d) The degree of separability as measured by Δ (Equation 9) corresponding to each case as ordered in panel c.

Figure 4.

(a) The AUC of the ROC curve for different resting-state networks in the context of rest conditions and different task conditions obtained using the non-TS method. The dotted horizontal line shows the AUC for the whole brain analysis for reference. Lines are used as visual guide. (b) Same as panel a but for the TS method.

Figure 5.

The mean AUC-ROC values for different recording durations, averaged over all bootstrap samples. Across all three panels, solid markers denote the TS method, with hollow markers for non-TS. Lines shown for visual aid. The following cases are considered: (a) Resting-state recordings across nine subjects and 10 sessions. (b) Task-based recordings. The resting-state non-TS method (blue) is included for comparison. (c) The SMH resting-state network during motor task (square markers) for the TS and non-TS methods. The whole-brain motor task using the non-TS method is included for reference (circle). Error bars denote one standard deviation across all bootstrapped samples. To avoid oversampling, the number of samples is inversely related to the recording length, which results in smaller error bars for the larger recording lengths.