Abnormal Connectional Fingerprint in Schizophrenia: A Novel Network Analysis of Diffusion Tensor Imaging Data

The graph theoretical analysis of structural magnetic resonance imaging (MRI) data has received a great deal of interest in recent years to characterize the organizational principles of brain networks and their alterations in psychiatric disorders, such as schizophrenia. However, the characterization of networks in clinical populations can be challenging, since the comparison of connectivity between groups is influenced by several factors, such as the overall number of connections and the structural abnormalities of the seed regions. To overcome these limitations, the current study employed the whole-brain analysis of connectional fingerprints in diffusion tensor imaging data obtained at 3 T of chronic schizophrenia patients (n = 16) and healthy, age-matched control participants (n = 17). Probabilistic tractography was performed to quantify the connectivity of 110 brain areas. The connectional fingerprint of a brain area represents the set of relative connection probabilities to all its target areas and is, hence, less affected by overall white and gray matter changes than absolute connectivity measures. After detecting brain regions with abnormal connectional fingerprints through similarity measures, we tested each of its relative connection probability between groups. We found altered connectional fingerprints in schizophrenia patients consistent with a dysconnectivity syndrome. While the medial frontal gyrus showed only reduced connectivity, the connectional fingerprints of the inferior frontal gyrus and the putamen mainly contained relatively increased connection probabilities to areas in the frontal, limbic, and subcortical areas. These findings are in line with previous studies that reported abnormalities in striatal–frontal circuits in the pathophysiology of schizophrenia, highlighting the potential utility of connectional fingerprints for the analysis of anatomical networks in the disorder.

Thus, the connectional fingerprint obtained from probabilistic tractography is asymmetric.
Since DTI itself cannot assess the directionality of fibres, previous studies including Gong et al.
(2009) symmetrized the connection probability ( ij S ) between two nodes i and j through averaging as follows: where i j w is the connection probability between i and j in the projection pattern of node i, and j i w is the connection probability between i and j in the connectional fingerprint of node j. Gong et al. (2009) justified this procedure by pointing out that the correlation between i j w and j i w was high in their dataset. In agreement with this data, the correlation between i j w and j i w for all participants in the current study was similarly high (r=0.82  0.0121). However, since two connection probabilities i j w and j i w are conditional probabilities derived from a unique connection distribution of the node i and the node j in order, they cannot be averaged as shown above. Thus, we suggest that the connectional fingerprints should not be symmetrized as proposed by Gong et al. (2009).
In contrast, 'absolute connectivity' can be symmetrized. The 'absolute connectivity' from node i to node j ( i j a ) is defined by the number of samples propagated from node i, that reached node j: ii j jq q ac = å where i jq c represents the number of fibre samples from a voxel q of the node i to the target node j using the nomenclature of the main text. Although i j a is slightly different from j i a due to the tractography algorithm, their correlation was very high (r=0.930.0131), and significantly higher than the correlation between i j w and j i w (paired t-test; t=-41.16, p<0.001). Following Gong et al (2009), the higher correlation may strengthen our assumption that absolute connectivity is more suitable to be symmetrized than the connection probabilities provided in the connectional fingerprints.

SI Text 2. Evaluating permutation testing of similarity for connectional fingerprints with synthetic data
We tested the suggested approach over synthetic data to evaluate its performance. First, since connection probabilities of a connectional fingerprint sums up to one, the basis connectional fingerprint is necessary, which represents a healthy subject. For simplicity, it has 100 connection probabilities and thus 0.01 for each connection probabilities. Second, we added a small contrast to a randomly selected connection probability with a magnitude of 10% of the selected connection probability (i.e. 0.001) which representing a patient. Third, we replicated the synthetic healthy subjects and patients 50 times each, and added a zero-mean Gaussian noise which forms inter-subject variability. When its standard deviation is σ, the contrast-to-noise ratio (CNR) is simply 0.001/ σ.
After adding the noise, we re-normalized each connectional fingerprint to make the summation of its connection probabilities one. Afterwards, we performed statistical tests: 1) the suggested approach, and 2) permutation testing of each connection probabilities between groups with the false discovery rate (FDR) procedure (Benjamini and Hochberg 1995) for the multiple comparison correction; the second simple test is significant when any connection probability showed a significant difference after the FDR procedure. Next, we repeated the last two steps 100 times to construct receiver operating characteristic (ROC) curves and compute area-under-curves (AUC). The ROC curve plots the true positive rate (TPR) against the false positive rate (FPR), capturing the sensitivity and (1-specificity) in order. If the curve approaches the top-left corner, the test has very good sensitivity and specificity.
Similarly, as the AUC value is larger, the performance of the test is better.
There are two possible conditions that lead to significant differences in the connectional fingerprints between groups with the suggested approach: a) few connection probabilities that differ between groups by a large magnitude and b) many connectional probabilities that differ by a small magnitude. In our study, the connection probabilities of Puta.l differ by a large magnitude between groups, while the MFG.R show many connection probabilities with small differences between schizophrenia patients and controls. So, we repeated the evaluation above for various numbers of contrasts. We tested the condition that 1, 3, 5, 7, and 10 connectional probabilities have contrasts along with three CNR conditions: 0.5, 1, and 1.5. When the number of contrast is small and CNR is high, it is the case of a), while it is the case of b) when the number of contrast is large and CNR is low since low CNR means small magnitude of contrasts. We collected AUC values for all cases (Table S2, Figure S1) and visualized the ROC curve in the range of the false positive rate (FPR) between 0.001 and 0.1 since FPR represents α-level of the test ( Figure S2).
When the number of contrasts is one and CNR is high ( Figure S2), the permutation test with the FDR procedure performs better than the suggested approach. However, the purpose of this study is not to detect a single very significant connection probability but to detect overall differences in the connectional fingerprint. Our approach is especially sensitive in the condition of low CNR ( Figure   S2); it helps to detect the overall difference in the connectional fingerprint. Moreover, since the AUC values were quite similar between two tests ( Figure S1, Table S2), our suggested approach showed comparable performance with the permutation tests with the FDR procedure when there is a large peak in the connectional fingerprint while it showed excellent performance otherwise.
Another advantage of the suggested approach is that it provides the smaller p-values than the other approach. To perform the whole brain analysis of the connectional fingerprints, the multiple comparison correction over brain regions is also required. Thus, the smaller p-value of each brain region will ease the multiple comparison correction over brain regions. However, p-values from the permutation test with the FDR procedure are already inflated. For examples, where the number of contrasts equals to one and CNR equals to 1.5, though the AUC values is slightly higher in the permutation test with the FDR procedure, the mean p-value over 100 runs was smaller in the suggested approach (suggested approach: 0.0002 vs. the permutation test with FDR: 0.0066).   Table S2. In our proposed approach, the definition of the similarity measure was crucial. We computed the sum of absolute difference between the connection probabilities of the corresponding connectional fingerprint and transformed it to a similarity measure using a simple monotonically decreasing exponential function. We tested two alternative similarity measures: a cosine similarity and a simple Pearson correlation. The cosine similarity, assesses the angle between two vectors in the 109-dimensional space, which represent the connectional fingerprints. The Pearson correlation between two vectors assesses how strongly they vary together.
Compared to what we suggested in the manuscript, these similarity measures were less sensitive to identify the local changes in the connectional fingerprint. Using the cosine similarity, only the connectional fingerprint of the medial frontal gyrus (MFG.r) was different between groups. The Pearson correlation approach identified both inferior frontal gyrus, pars opercularis (IFG.po.r and IFG.po.l). These alternative similarity measures show lower sensitivity, because they capture the overall difference in general. The cosine similarity evaluates the overall difference in terms of the angle between two vectors in the high dimensional space, which could be too small to be sensed since the vectors resided in the very high dimensional space. Similarly, the Pearson correlation captures the overall degree that two vectors co-vary. The similarity measure we used in the manuscript regarding the sum of all absolute errors of each connectional probability captures also the local differences. In addition, we noted that the shape of the exponential function might help to detect even small differences. Figure S3. Abnormal connection probabilities from the right medial frontal gyrus (MFG.r). Blue bars represent the controls and red bars represent the patients, where asterisks showed the significantly different connection probability. We showed the connection probabilities whose mean values in the healthy controls equal to or are above 0.001. The abbreviation of regions can be found in Table S1 Figure S4. Abnormal connection probabilities from the right inferior frontal gyrus, pars opercularis (IFG.po.r). Blue bars represent the controls and red bars represent the patients, where asterisks showed the significantly different connection probability. We showed the connection probabilities whose mean values in the healthy controls equal to or are above 0.001. The abbreviation of regions can be found in Table S1 Figure S5. Abnormal connection probabilities from the left inferior frontal gyrus, pars opercularis (IFG.po.l). Blue bars represent the controls and red bars represent the patients, where asterisks showed the significantly different connection probability. We showed the connection probabilities whose mean values in the healthy controls equal to or are above 0.001. The abbreviation of regions can be found in Table S1 Figure S6. Abnormal connection probabilities from the left putamen. Blue bars represent the controls and red bars represent the patients, where asterisks showed the significantly different connection probability. We showed the connection probabilities whose mean values in the healthy controls equal to or are above 0.001. The abbreviation of regions can be found in Table S1.