The proposed network inference method requires the following inputs:

How can we decide whether voxel j of the i'th ROI connects to the k'th ROI given the fraction T_i(j, k)? The simplest approach is to examine if T_i(j, k) is larger than a given “connectivity threshold” τ (0 < τ < 1). In MANIA, τ is not a given threshold but an optimization variable, as described in the next section.

As in prior work, we assume that the i'th ROI is connected to the k'th ROI as long as at least one voxel of the former is connected to the latter (Hagmann et al., 2008; Bassett et al., 2011). This assumption is not central to MANIA however, and it can be easily replaced with a stronger connectivity constraint, depending on the size of the given ROIs and the spatial resolution at which those ROIs are specified.

For a given value of τ, we can identify the voxels of the i'th ROI that connect to every other ROI. If this process is repeated for every i, we can construct a directed network in which the i'th ROI is connected to the j'th ROI if there is at least one voxel in the former that is connected to the latter for that value of τ. This network can be represented with an adjacency matrix² G_τ, as follows:

So, the element (i, k) of this matrix is equal to one if there is a (directed) edge from the i'th ROI to the k'th ROI. The diagonal entries of G_τ are set to zero because we do not consider streamlines from a source ROI back to itself.

We define the asymmetry ϕ(G) of a directed network G as the fraction of edges that are present in only one direction, (2)ϕ(G) = ∑i=1N∑k=1NG(i,k)(1-G(k,i))∑i=1i=N∑k=1NG(i,k) The asymmetry of a network G depends on its density ρ (G), defined as the fraction of connected node-pairs, (3)ρ(G)=∑i=1N∑k=1NG(i,k)N(N-1) The more edges a directed network has, the more likely it becomes that a pair of nodes will be connected in both directions, i.e., the higher the density, the lower the asymmetry.

More formally, consider a directed network with K directed edges and N nodes. The density is ρ = K/[N(N − 1)] (0 < ρ <1). To construct such a network randomly, denoted by G_ρ, we simply connect N(N − 1)ρ randomly selected but distinct pairs of nodes with directed edges. The expected number of edges that exist in only one direction is N(N − 1)ρ (1 − ρ) and so the expected value of the asymmetry of G_ρ is: (4)ϕ¯(Gρ)=N(N-1)ρ(1-ρ)N(N-1)ρ=1-ρ To quantify the actual asymmetry of an observed network G_τ, we normalize ϕ(G_τ) by the asymmetry that is expected simply due to chance given the density of this network. So, we define the normalized asymmetry of G_τ as (5)Φ(Gτ)=ϕ(Gτ)ϕ¯(Gτ) which is well defined as long as ρ (G_τ) <1.

MANIA is based on the following premise: the inferred directed network should be as symmetric as possible. The reason is that the tractography process is unable to infer the actual direction (polarity) of the underlying neural fibers. So, if there are some fibers connecting two voxels X and Y, tractography should be able, in principle, to follow this connection in both directions, from X to Y and from Y to X. We do not claim that two connected ROIs are always attached with both afferent and efferent fibers; instead, we argue that tractography is not able to discover the polarity of those fibers and so the corresponding connection should be trace-able in both directions.

The presence of some streamlines from some voxels in ROI X to ROI Y does not necessarily mean however that the network inference method will detect an edge both from X to Y and from Y to X; this also depends on the parameter τ. Given that we aim to minimize the asymmetry of the inferred network, MANIA aims to select the value of τ that leads to the lowest possible asymmetry.

The corresponding optimization problem can be stated as follows: determine the adjacency matrix  G^ = Gτ∗, where τ^* is a value of the connectivity threshold that minimizes the normalized asymmetry of G_τ across all possible values of τ, (6)τ* = argmin0<τ<1 Φ(Gτ) So, MANIA is based on the premise that there is an ideal value (or range of values) of the connectivity threshold that can correctly classify every directed pair of ROIs as either “connection exists” or “connection does not exist.” When such a threshold exists, it will result in a completely symmetric network (because a perfectly accurate tractography-based network cannot be asymmetric). On the other hand, if such an ideal threshold does not exist (for instance, it may be that two connected ROIs are too far from each other and tractography cannot “see” their connection, or that it is impossible for streamlines to cross the White matter/Gray matter Boundary (WGB) of a certain ROI in one direction but not in the opposite), then MANIA aims to at least minimize the normalized asymmetry metric, even if the resulting network will not be completely symmetric.

If there is more than one value of τ that results in the same minimum of the normalized asymmetry (potentially zero), MANIA reports the network with the largest density. The rationale behind this tie-breaker is to avoid trivial solutions that include only a subset of the actual network edges. The previous optimization problem can be solved numerically by scanning the range of τ values with a given resolution³. The density of the resulting network is denoted by (7)ρ* = ρ(Gτ*) As an illustration of the previous method, Figure 2 shows how the network asymmetry (both ϕ and Φ) varies with the density ρ as well as the relation between ρ and τ for the dataset that corresponds to one of the subjects in our case-study.

A common network inference method is to rely on a given connectivity threshold τ, as shown in Equation (1). This threshold is sometimes chosen to achieve a certain network density or to ensure that the network is connected (Li et al., 2009).

Given that tractography cannot detect the direction of inferred edges, the resulting network is often “post-symmetrized” (Azadbakht et al., 2015; Donahue et al., 2016). Consider two network nodes i and j and suppose that the fraction of streamlines from i to j is denoted by T_{i, j}. Supose that T_{i, j} > τ but T_{j, i} < τ, where τ is a given threshold (not necessarily the threshold chosen by MANIA). We can resolve this conflicting evidence between the two directions of the edge by comparing the ratio (T_{i, j} − τ)/(1 − τ), which reflects our confidence that the edge from i to j exists, with the ratio (τ − T_{j, i})/τ that reflects our confidence that the edge from j to i does not exist. The two nodes are connected with an (undirected) edge only if the former ratio is larger.

If MANIA cannot find a threshold value that gives a completely symmetric network, the aforementioned post-symmetrization method is applied on the network that results from MANIA.

MANIA can be viewed as a binary classifier: each possible directed edge is classified as present or absent. We evaluate MANIA based on the following standard metrics for binary classification: the false positive rate (or false alarm) p_f, and the false negative rate (or miss detection) p_m. The former is defined as the fraction of absent edges that are incorrectly classified as present, while the latter is defined as the fraction of present edges that are incorrectly classified as absent.

Also, the Jaccard similarity between the sets of edges E(G) and E(Ĝ) of the actual network G and the MANIA network Ĝ, respectively, is defined as (8)J(G,Ĝ)=|E(G)∩E(Ĝ)||E(G)∪E(Ĝ)| and it varies between zero (no common edges) and one (identical networks).

We can also compare the network that results from MANIA with the network that would result if we knew the optimal value τ^opt of the connectivity threshold, i.e., the value of τ that maximizes the Jaccard similarity between the inferred network G_τ and the ground truth network G: (9)τopt=argmax0<τ<1 J(Gτ,G) Even though it is not possible to know this optimal threshold value when analyzing real tractography data, we can easily compute its value (or range of values) in experiments with synthetically generated networks, where the ground-truth network G is known.

The output of MANIA is an unweighted directed network. We can quantify the level of confidence we have in each edge with the following edge ranking scheme.

Let ρ_α be the minimum network density at which edge α is present. If the edge α is from a source X to a target Y, the lower ρ_α is, the higher the fraction of streamlines from X to Y. Consequently, we can rank edges so that we are more confident in the presence of edge α than of edge β if ρ_α < ρ_β (see Figure 3).

We define a confidence metric for an edge α that is present in the MANIA network (i.e., ρα<ρ*) as follows (10)C(α)=ρ*-ραρ*

C (α) varies from 0 (the edge is only marginally present) to 1 (highest confidence that the edge is present). Similarly, if edge α is absent from the MANIA network (i.e., ρα>ρ*), its confidence metric is defined as (11)C(α)=ρ*-ρα1-ρ* and C (α) varies from 0 (the edge is only marginally absent) to −1 (highest confidence that the edge is absent).

We also define a confidence metric for a pair of nodes (X,Y), as the arithmetic mean of the confidence metric of the two directed edges between X and Y, (12)C(X,Y)=C(X→Y)+C(Y→X)2 Note that one of the two edges may be present while the other may be absent. In that case, the confidence of the corresponding node-pair will be less than the confidence of the present edge.

Note that this edge confidence metric is not related to connection “strength” or “quality,” and the resulting network is still meant to be interpreted as an unweighted graph.

If the objective is to create a single “average network” based on data from several subjects, the question is how to best aggregate the tractography data from the given group. One approach is to average the diffusion MRI data, after transforming them in a standard space. Another approach is to average the fraction of streamlines from a given seed voxel to a given target ROI, across all subjects. The previous approaches can be sensitive to outliers, variations in the diffusion MRI process across subjects, tractography errors and mapping/warping into a standard space. A recently proposed method is to construct a group-level network based on the consistency of the edge weights across subjects (Roberts et al., 2016); this approach preserves edges that appear consistently strong for their length, rather than penalizing long-distance connections. This approach may not be applicable however when the group size is small.

Another method is to construct an individual network for each subject, perhaps using MANIA, and then form an aggregate network by only keeping those edges that appear in a large fraction of subjects. This approach requires a group-level threshold for the minimum fraction of subjects that should have a connection. For instance, de Reus et al. have proposed a statistically rigorous method to compute such a threshold (de Reus and van den Heuvel, 2013a).

Here we propose a different group analysis method, referred to as group-MANIA, that is based on the aggregation of edge-rankings across subjects. The rank-based nature of this method makes it robust to outliers.

As in the previous section, the edges of a subject can be ranked based on the minimum network density at which an edge first appears. We are more confident in the presence of edge α than of edge β if ρ_α < ρ_β (see Figure 3).

Suppose that we compute an edge rank vector R_m for each subject m, so that the lowest rank R_m(1) corresponds to the edge for which we are most confident. The number of possible (not necessarily present) directed edges is the same for all subjects: N (N − 1) where N is the number of network nodes.

Given a group of size M, we have M distinct rank vectors R_m, m = 1⋯M. The computational problem of rank aggregation (Schalekamp and van Zuylen, 2009) is to compute an optimal permutation R^ of the N (N − 1) possible edges that captures as well as possible the ordering relations in the M input rank vectors. Specifically, the Kemeny distance between two rank vectors R₁ and R₂ is defined as

where δ_{i, j}(R₁, R₂) = 1 if R₁ and R₂ disagree in the relative position of elements i and j, and zero otherwise. Rank aggregation aims to compute a vector R^ that minimizes the cumulative Kemeny distance between R^ and all input rank vectors R_m. It is an NP-hard problem, and so it is typically solved heuristically. We use the Quicksort algorithm (Ailon et al., 2008) since it is has been shown to provide a good approximation of the optimum solution. QuickSort selects a random edge as pivot at each recursive step, while the remaining edges are separated in a left and right list. The left list includes edges that have a lower rank than the pivot in the majority of the subjects; similarly for the right list. The algorithm proceeds recursively in the left and right lists until all edges are ordered.

After computing the optimal aggregate rank vector, we apply MANIA on R^ to compute the network with the minimum normalized asymmetry (as in the case of a single subject). Note however that the input to MANIA in this case is an ordered list of edges R^ rather than the set of connectivity matrices T (see the MANIA Inputs section). Group-MANIA forms a network with the first K = N(N − 1)ρ edges in R^, and it computes the normalized asymmetry of that network. It then repeats this step, for all values of K, to identify the network with the minimum value of Φ. We refer to the resulting network as the rank-aggregated network.

We utilize the publicly available FiberCup dataset (Poupon et al., 2008, 2010; Fillard et al., 2011) as one of the benchmarks to evaluate MANIA's accuracy. We use a FiberCup acquisition in which the b-value is 1500. FiberCup resembles a human brain coronal section with 18 ROIs and seven fiber bundles—see Figure 2 of Neher et al. (2014). These fiber bundles are constructed to include sharp turns as well as crossing, kissing and branching points, making it a challenging benchmark for any tractography algorithm. Due to the practical difficulties of generating a realistic phantom, FiberCup does not contain any complex 3D fiber structures.

We apply probtrackx and MANIA on the FiberCup phantom to infer the network of the seven underlying connections. The FDT probabilistic tractography parameters are set to their default values (number of streamlines = 5000, maximum number of steps = 2000, loop check: set, curvature threshold = 0.2, step length = 0.5 mm, no distance bias correction). Probtrackx is seeded at the WGB of the ROIs that are connected to fiber terminals.

To evaluate the accuracy and sensitivity of MANIA in a reliable manner we need to rely on synthetic networks rather than actual DTI and tractography data. The benefit of these computational experiments is that we can test MANIA under a wide range of noise conditions and for arbitrary network densities. Unfortunately there are no good statistical models for the noise in the output of tractography data (Jbabdi and Johansen-Berg, 2011). We evaluate MANIA based on a simple noise model that is based on the theory of maximum entropy distributions, as described next.

For simplicity, each ROI of the synthetically generated networks is simply a voxel. Modeling multi-voxel ROIs in these simulation experiments would not add any new insights. Suppose that the directed network between N nodes is represented by the N × N adjacency matrix G. Let T_{i, j} be the fraction of streamlines that originate from node i and terminate at node j. Ideally, in the absence of any noise in the DTI data and without any errors in the tractography process, it should be that

So, if there is an edge between nodes i and j in either direction, the fraction of streamlines from node i to node j should be 100%; otherwise, it should be zero.

In practice, there is significant noise in DTI data and the tractography process can be error-prone, especially when the ROIs are in gray matter and/or when neural fibers cross each other, split or merge, or fan out as they approach their targets. Consequently, the tractography output may show that some streamlines do not reach from node i to node j even when the two nodes are connected, or that some streamlines get from i to j even when there is no connection between the two nodes. We model these errors probabilistically, as follows:

where Z₁ and Z₂ are two (generally different) random variables with [0, 1] support. If their probability mass is concentrated close to 0, the results of the tractography process are not significantly affected by noise. On the other hand, if these two random variables are uniformly distributed in [0, 1], the tractography results are completely random and any network inference process is hopeless.

We model the two random variables Z₁ and Z₂ with the Maximum Entropy distribution with one-degree of freedom. In this case, this distribution is the truncated exponential distribution with support [0,1],

where α > 0 is a parameter that determines the mean and variance of the distribution. Instead of controlling α, we control the intensity of noise through the mean of Z,

The two distributions Z₁ and Z₂ follow this statistical model with means μ₁ and μ₂, respectively. Figure 4 shows the previous distribution for four values of μ. Note that the distribution Z becomes almost “flat” (close to the uniform distribution) when its mean is higher than 0.3, meaning that tractography would be extremely inaccurate when the noise intensity exceeds that level. In the rest of this paper we limit the range of μ₁ and μ₂ between 0 and 0.3.

We also apply MANIA in Diffusion Tensor Imaging (DTI) data collected by an earlier study: “Brain aging in humans, chimpanzees (Pan troglodytes), and rhesus macaques (Macaca mulatta): magnetic resonance imaging studies of macro- and microstructural changes” (Chen et al., 2013). All subjects gave written informed consent, and the study was approved by the Emory University Institutional Review Board. We analyzed the data for 28 of those subjects mostly based on handedness (right-handed females, without a history of psychiatric disorder). Diffusion-weighted images were acquired using a Siemens 3T with a 12-channel parallel imaging phase-array coil. Foam cushions were used to minimize head motion. Diffusion MRI data were collected with a diffusion weighted SE-EPI sequence (Generalized Autocalibrating Partially Parallel Acquisitions [GRAPPA] factor of 2). A dual spin-echo technique combined with bipolar gradients was used to minimize eddy-current effects. The parameters used for diffusion data acquisition were as follows: diffusion-weighting gradients applied in 60 directions with a b-value of 1000 s/mm²; TR/TE of 8500/95 ms; FOV of 216 × 256 mm²; matrix size of 108 × 128; resolution of 2 × 2 × 2 mm³; and 64 slices with no gap, covering the whole brain. Averages of 2 sets of diffusion-weighted images with phase-encoding directions of opposite polarity (left–right) were acquired to correct for susceptibility distortion. For each average of diffusion-weighted images, 4 images without diffusion weighting (b = 0 s/mm²) were also acquired with matching imaging parameters. The total diffusion MRI scan time was approximately 20 min. T1-weighted images were acquired with a 3D MPRAGE sequence (GRAPPA factor of 2) for all participants. The scan protocol, optimized at 3T, used a TR/TI/TE of 2600/900/3.02 ms, flip angle of 8°, volume of view of 224 × 256 × 176 mm³, matrix of 224 × 256 × 176, and resolution of 1 × 1 × 1 mm³. Total T1 scan time was approximately 4 min.

The resulting DTI data were processed using the FMRIB's Diffusion Toolbox (FDT) provided by FSL (FMRIB 4 Software Library) (Behrens et al., 2003). The FDT probabilistic tractography parameters were set to their default values (number of streamlines = 5000, maximum number of steps = 2000, loop check: set, curvature threshold = 0.2, step length = 0.5 mm, no distance bias correction).

We applied MANIA on 18 corticolimbic ROIs. All ROIs are in the left hemisphere and localized in Montreal Neurological Institute (MNI) standard space using the Automated Anatomical Labeling (AAL) (Jenkinson and Smith, 2001) of the WFU PickAtlas toolbox (Lancaster et al., 2000). The ROI acronym as well as the number of voxels in each ROI are shown in Table 1. The shape of these ROIs are not dilated and we adhere to the standard masks provided in the WFU PickAtlas toolbox. We chose these ROIs because they are known to play a significant role in various psychiatric disorders such as MDD, PTSD, OCD, anxiety and addiction (Mayberg, 1997; Seminowicz et al., 2004; Craddock et al., 2009; James et al., 2009). This sample of ROIs includes cortical, subcortical and limbic regions. Specifically, the cortical ROIs are BA6, BA9, BA10, BA40, BA46, BA47, the limbic are BA24, Th, BS, and the sub-cortical are BA11, BA25, BA32, Acb, Amg, Hp, Ht, Ins, Pc.

Figure 5A shows that the MANIA threshold results in almost the same accuracy (Jaccard similarity within 5%) as the optimal threshold (see the Optimal Threshold-based Network Inference section). However, neither MANIA nor the optimal threshold are able to perfectly reconstruct the correct network. Figure 5B shows the network inferred by MANIA. There are two asymmetric false-positive edges (shown in blue) and one false-negative edge (shown in red). However, the confidence metric (shown in Figure 5C) of the three miss-classified edges is close to zero, while the confidence metric of the true-positives and true-negatives is significantly different than zero. Further, if we also perform post-symmetrization on MANIA's output, the false positive edge from ROI-13 to ROI-17 is removed because it has negative confidence.

Figure 5D explains the root-cause of the previous miss-classified edges. Seeding Probtrackx at ROI-13, most streamlines are incorrectly directed to ROI-17 (instead of ROI-15) because of the overlap with the fiber bundle between ROI-11 and ROI-17. The probability map generated by Probtrackx makes its highly unlikely that any threshold-based network inference method would be able to discover the right connection between ROI-13 and ROI-15.

We evaluate MANIA based on computational experiments with synthetic data and random networks. The “ground-truth” networks G are constructed as follows. Suppose that G has N nodes and density ρ. We place [ρN(N-1)2] undirected edges between randomly selected but distinct pairs of nodes. Note that G is symmetric by construction because the tractography process cannot infer the true polarity of the underlying neural fibers. Given G, we then create the tractography matrix T that represents the “noisy” fraction of streamlines between any pair of nodes, as shown in Equation (15). Note that the fraction of streamlines from a node X to a node Y is typically different than the fraction of streamlines from Y to X. In the following experiments, N is set to 50 nodes, and each experiment is repeated for 1000 networks G.

We first examine the effect of post-symmetrization on the accuracy of both threshold-based network inference and MANIA. In the former, the connections are determined based on a given threshold τ₀, as discussed in the Threshold-based Network Inference with Post-Symmetrization section. We denote the Jaccard similarity between the inferred network and the ground-truth network with J_SYM when post-symmetrization is performed, and with J_NO−SYM otherwise. Figure 6 shows the difference ΔJ = J_SYM − J_NO−SYM for several choices of τ₀ as well as for MANIA. Each box-plot is generated from 1000 experiments; in each experiment we generate a random network with density between 0 and 1, while the noise parameters μ₁ and μ₂ are uniformly distributed between 0 and 0.3. The red line corresponds to the median, the box boundaries correspond to the 25 and 75th percentiles, while the dashed lines show the 10 and 90th percentiles. In all cases, ΔJ > 0 (one-sided Mann-Whitney U-test—p-values shown next to each box plot), meaning that post-symmetrization helps to improve the accuracy of network inference. This is true for both MANIA and threshold-based inference, even though the improvement is larger for the latter. Because of the positive effect of post-symmetrization, in the rest of the paper we apply it in all network inference experiments.

Figure 7 illustrates the performance of MANIA in the two-dimensional space defined by the noise parameters μ₁ and μ₂ for three values of the network density. Each square in these heat maps is the median across 1000 experiments. The false positive and false negative rates are close to 0 (less than 5%) in the lower-left half of each heat map (i.e., when μ₁ + μ₂ <0.3). For higher values of the noise intensity, the accuracy of MANIA depends on the density of the underlying network. In the case of sparse networks, MANIA also infers a sparse network and most errors are false negatives, i.e., MANIA does not detect some of the few existing edges. For dense networks, MANIA also infers a dense network and most errors are false positives, i.e., MANIA detects a few extra edges that do not actually exist. In mid-range densities, the errors are more balanced between false positives and false negatives. In all cases the maximum false positive (or negative) rate when μ₁ = μ₂ = 0.3 is less than 25%. Recall from Figure 4 that these noise intensity levels should be considered quite high in practice.

Figure 8 compares the MANIA-inferred network with the network that corresponds to the optimal threshold τ^opt, as discussed in the Optimal Threshold-based Network Inference section. Specifically, the heat maps of Figure 8 compare the Jaccard similarity J_MANIA between MANIA and the ground-truth network, with the Jaccard similarity Jτopt between the optimal threshold based network and the ground-truth network. The accuracy of MANIA is typically close to that of the optimal threshold method. Even under the highest noise intensity we consider (μ₁ = μ₂ = 0.3), J_MANIA is only 10% lower than Jτopt. These results suggest that MANIA selects automatically a connectivity threshold value that results in almost optimal accuracy, across all possible such threshold values.

Finally, Figure 9 compares MANIA with five given threshold values τ₀. The comparison is in terms of the Jaccard similarity difference ΔJ = J_MANIA − J_τ0. As in Figure 6, each box-plot is generated from 1000 experiments in which we vary the network density between 0 and 1, and the noise parameters μ₁ and μ₂ between 0 and 0.3. The median ΔJ is always positive and the distribution of ΔJ is skewed toward positive values (one-sided Mann-Whitney U-test—p-values shown next to each box plot), meaning that MANIA typically performs better than a fixed threshold scheme, independent of the selected threshold.

We applied MANIA in the DTI data presented in DTI Data, Tractography Parameters, and Selected ROIs, based on the 18 ROIs listed in Table 1. A single rank-aggregated network is constructed, using the group analysis method of the Group Analysis section. Using MANIA, aggregating data from 28 subjects. The rank-aggregated network is shown in the left graph of Figure 10.

Two ROIs (Pc and BA40) appear to not be directly connected with the other 16 ROIs; of course there may be indirect connections through other ROIs that have not been included here (we return to this point in the Discussion section). Every edge in the connected component of Figure 10 has been detected in both directions, i.e., MANIA identifies a completely symmetric network in this case (i.e., no post-symmetrization is needed). The density of the connected component (16 ROIs) is 19%. The color of each edge in the subfigure represents the fraction of the 28 subjects that have the corresponding edge in their individual networks (constructed by MANIA).

We measured the “centrality” of each node in the rank-aggregated network, based on four centrality metrics (degree, closeness, betweenness, PageRank) (Newman, 2010). Different centrality metrics focus on different notions of importance. For instance, the degree centrality metric associates importance with the number of direct connections a node has; BA32 (Ventral anterior cingulate) has the largest number (six) of direct connections in this network (see Table 2). This may be because BA32 is spatially adjacent to both BA10 and BA25, and those ROIs are also of high degree. The betweenness centrality of a node X, on the other hand, focuses on the number of shortest paths between any pair of nodes that go through X; BA25 (subcallosal cingulate) is the most important node from this perspective because it serves as the “unique bridge” between the 6 red nodes at its left and the 9 blue nodes at its right. BA25 is also the most central node in terms of its average distance to all other nodes (closeness centrality).

Similarly, we measured the edge centrality of all connected node pairs. In terms of edge betweenness centrality, the connection between BA25 and the Nucleus Accumbens (Acb) is by far the most central in this network. It is interesting to note that this edge includes the segment of white matter that is the target of Deep Brain Stimulation (DBS) therapies for the treatment of MDD (Mayberg et al., 2005). In fact, the DBS target is typically the point at which the fibers between (BA25-Acb), (BA25-BA32), and (BA25-BA24) intersect.

Figure 10 also shows some percentiles of the per-subject node-pair confidence metric (median, 25–75th percentiles, 10–90th percentiles, and outliers) for each node-pair that appears connected in at least one of the 28 subjects. The connections between the following node pairs appear in all subjects and have the highest confidence: Hp-Acb, Amg-Acb, BA47-Ins. On the other hand, the following connections appear only in some subjects and their confidence metric varies around zero: Th-BS, BA46-BA9, BA6-Ins. Some connections that appear in 1–2 subjects but have very low confidence are: Pc-BA24, BA11-BA24, Ins-BA25, BA40-BA6.

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