Structural connectome with high angular resolution diffusion imaging MRI: assessing the impact of diffusion weighting and sampling on graph-theoretic measures

Brain connectivity and the connectome have unlocked new experimental and theoretical avenues in many areas of neuroscience. Recent advances in diffusion magnetic resonance imaging (dMRI) and functional magnetic resonance imaging (fMRI) techniques have made it possible to model the human brain as a complex network in vivo. Using graph theory, both a functional and a structural brain network can be described as a graph, i.e. a collection of nodes, each corresponding to a brain region, and connections or edges, each expressing a pathway between two nodes. On the basis of a suitable formal description, a number of graph-theoretic measures can be used to describe several properties of the network’s architecture [1].

Structural connectivity can be assessed in vivo in humans by the combination of dMRI-based white matter tractography and gray matter parcellation methods. Compared to clinical applications of dMRI, increasing the diffusion weighting and the number of diffusion gradient directions represent two simple options available to any clinician in order to increase the angular resolution of white matter tractography and therefore the robustness of graph-theoretic measures. Although the effect of b value on HARDI reconstruction for tractography has been studied before [2], here we compared for the first time the impact on the estimation of network properties in two HARDI MRI protocols, one with a low b value and a low number of direction (LBLD) and one with a high b value and a high number of directions (HBHD).

The most typical graph-theoretic metrics used in brain connectomics include the degree of clustering, the global efficiency, the modularity, and the small worldness [3]. Briefly, the degree of clustering and the strength of a given node measure the extent to which the node is connected to the rest of the network, while the centrality and the efficiency capture how many short paths between two parts of the network pass through the node. Modularity refers to the property of a network of being divided into multiple modules according to how nodes result densely interconnected with other nodes within the same module and sparsely interconnected with other nodes outside the module. A “small-world” network is characterized by a topology in which most of the nodes are not neighbors of each other but can be reached through a relatively small number of steps [4]. Some works have revealed that brain networks intrinsically possess small world properties, and some small world attributes have been proposed as clinical markers [5‐7].

To enable the calculation of these metrics and fully characterize the brain structural networks in terms of graph-theoretic measures, the diffusion tensor imaging (DTI) [8, 9] represents the most common post-processing technique for dMRI data to calculate the initial connectivity matrix, which represents the input of all graph-theoretic measures. However, HARDI acquisition techniques in combination with the Q-ball imaging (QBI) [10] have been more recently explored in the context of graph-theoretic characterizations of brain structural networks [3].

In this study, we performed a whole-brain connectomic analysis using a probabilistic QBI tractography on a cortical parcellation of 90 regions obtained from the automated anatomical label (AAL) atlas and determined the effect of the dMRI acquisition scheme on global and local graph network measures.

NBS analysis revealed a significantly higher connection probability in HBHD compared to LBLD data sets in 88 pairs of node (p = 0.0002) (Fig. 1, Table 1).

Global M and small worldness were significantly lower in HBHD, compared to LBLD data sets (M: p = 0.001; small worldness: p = 0.042). There were no significant differences in global efficiency and L.

The distribution of hubs across the whole connectome was similar between the two sequences. Hubs in common between LBLD and HBHD data sets are summarized in Table 2 (Fig. 2). Two regions corresponding to the left inferior frontal orbital gyrus and the right superior frontal orbital gyrus in the AAL were identified as hubs only in LBLD-derived matrices, and two regions corresponding to the left olfactory cortex and the left fusiform gyrus in the AAL were identified as hubs only in HBHD-derived matrices.

In terms of local measures, local efficiency was higher in HBHD in several regions (right temporal superior and medial gyri, bilateral medial cingulate cortex, right superior temporal, postcentral and anterior cingulate cortex, medial frontal gyrus, angular gyrus, and left inferior temporal gyrus) compared to LBLD data (p < 0.05, FDR corrected); local clustering coefficient was higher in HBHD in right temporal superior and medial gyrus, bilaterally medial cingulate cortex, right medial frontal and postcentral gyrus, anterior cingulate cortex, angular gyrus, left inferior temporal gyrus, and left and posterior cingulate cortex (p < 0.05, FDR corrected).

There were no significant differences in betweenness centrality, node strength, and node degree after FDR correction.

Graph theoretical measures can be used to characterize network topological organization in both healthy and diseased brains and to detect structural and functional abnormalities associated with different neurological and psychiatric disorders. These measures can be broadly classified into global measures, assessing the level of network integration, and local measures, assessing the level of network segregation.

Structural brain networks have been shown to be both highly segregated (due to the presence of relatively more selective pathways between specific regions compared to other) and highly integrated, i.e. forming several small-world networks or modules [24]. Both aspects could be independently altered in brain pathology with respect to normative values. In this work, we investigated the influence of the dMRI gradient scheme on the computational measures of structural brain networks obtained with QBI tractography at different numbers of directions.

We detected an overall increase in the values of connection probability across all pairs of anatomical regions when comparing the HBHD data set to the LBLD data set. This can be due to the fact that higher b values cause stronger diffusion weightings; however, due to the lower signal-to-noise, this may also create false positive connections because of the noise. To reduce the impact of false positives on subsequent network feature estimations, we only consider as actual connections (of varying strength) those connections that were consistently present across all subjects using a non-parametric procedure based on the sign test [19].

Another difference between HBHD and LBLD data sets that might have possibly contributed to the observed increase in the connection probabilities and the number of connections is the higher density of sampled directions of the HBHD scheme. In fact, given that the number of connections depends on how much the sampled direction agrees with the orientation of the fiber, the connection probability is expected to be lower for the LBLD scheme, [25, 26] . On the other hand, with a higher number of sampled directions in the HBHD scheme, it is more probable to measure higher signal responses as more sampled directions tend to correspond better to the actual orientation of the fibers.

Using the QBI, in line with [4], we found that the small world metrics were dependent on the directional resolution of the gradient scheme, with the values of small worldness in HBHD being significantly lower than LBLD data sets. This is in agreement with our expectation since a higher number of secondary tracts in addition to the main ones (that are in common between the LBLD and HBHD schemes) likely imply that brain modules are relatively more connected to each other via secondary connections than via direct connections (that pass through the network hubs).

LBLD also showed significantly higher values for M compared to HBHD, M being the degree to which a system can be broken into multiple subnetworks. This clearly indicates that LBLD data produce more segregated and less interconnected network modules. Conversely, lower M values are indicative of stronger connections among modules, thus gathering a more integrated distribution of subnetworks or modules.

The level of clustering expresses the level of local connectedness of a network, with high levels of clustering commonly interpreted as high levels of local organization of the network in modules [23]. Averaged over the entire network, the HBHD clustering coefficient was higher than that of LBLD, suggesting a higher degree to which relatively closer nodes share local connectivity within the module. In other words, HBHD data better highlighted the presence of densely interconnected groups of regions within each module.

Despite the higher number of connections detected for HBHD, the hub structure (i.e. the approximate number and location of nodes qualified as hubs) was highly similar between LBLD and HBHD data sets. Nonetheless, the lower M values obtained for HBHD suggest that the information about the overall transmission of neural impulses among modules is better preserved by the HBDB scheme (see, e.g., [1]).

Addressing the influence of the dMRI sequence parameters on graph-theoretic measures is therefore fundamental for the interpretation of various local and global structural brain network measures. In fact, differences in structural brain network measures could be mistakenly related to markers of neurological disease whereas these might be due to a different sensitivity of the particular acquisition scheme.

For DTI [4], the average node degree has been shown to increase with the number of gradient directions (6, 12, and 32), which may result from the fact that longer streamlines are tracked and, therefore, more densely connected networks are generated, at higher directional resolution. However, even if characteristic path length increases, the mean clustering coefficient drops when the number of gradients rises from 6 to 12 [4]. Indeed, DTI can only estimate a single fiber direction per imaging voxel, thereby the partial volume effect may potentially average two or more fiber populations with different local orientations across large parts of the imaging volume. This has stimulated the investigation of different acquisition protocols in combination with alternative water diffusion models also for graph-theoretic measures.

Similar trends were observed for the diffusion spectrum imaging (DSI) approach, which uses hundreds of diffusion sensitive gradients with different amplitudes to sample directions typically along a Cartesian grid. DSI has the potential of producing biologically more meaningful mapping of the human connectome; however, it requires long acquisition times (> 35 min) [26], thereby DSI can be not feasible for clinical applications. In contrast to DSI, QBI is a model-free reconstruction scheme which allows measuring the angular structure of the diffusion spectrum with less diffusion directions and therefore shorter acquisition times (< 20 min). The QBI model estimates the orientation distribution function (ODF) over a sphere sampled at many points, allowing the identification of more than one diffusion direction in each voxel and enabling a more accurate fiber tractography in regions with multiple populations of fibers with different orientations.

Tractography studies can reveal localized network abnormalities by investigating one or more specific white matter tracts [27], but in some diseases such as epilepsy [28], Alzheimer’s disease [24] and schizophrenia [4], the abnormality does not necessarily involve specifics white matter tracts, and the exact location of the impairment remains unknown. Nonetheless, it remains possible to assess the integrity of the entire brain network using graph theory. In a previous work [25], we investigated the impact of the QBI model on the tractography of major white matter tracts using different gradient acquisition schemes and showed that clinical studies aiming to investigate WM fiber integrity may benefit from application of a QBI model to dMRI data sets acquired at high b values and high numbers of diffusion direction (HBHD scheme) compared to low b values and low number of diffusion direction (LBLD scheme), especially when analyzing fiber tracts characterized by more than one dominant fiber direction. In previous work, we proposed an HARDI acquisition scheme with a b value and number of directions resulting in an acceptable scanning time (~ 15 min) for clinical applications [29] and demonstrated that this scheme can gather good performances at reasonable scan times for studying the (generalized) fractional anisotropy of WM regions [25]. Similarly, in the present work, we have shown important effects of the dMRI scheme also on global and local network features, which in some cases could be linked to the optimal sampling of fiber bundles with more than one dominant fiber direction. This was most likely the case for the anterior part of the fronto-occipital fasciculus (right superior frontal medial and right temporal medial nodes) and the superior longitudinal fasciculus (left insula and right hippocampus nodes), which where two regions where the local network properties exhibited significant differences between the two schemes. On the other hand, apart from the acquisition protocol, network metrics for the human connectome are also affected by several post-processing parameters, such as the orientation model, the brain parcellation, the tractography algorithm, and the weight threshold [3].

Several studies have revealed important topological properties for human brain WM networks [5, 17, 30], addressing the effects of brain abnormalities on specific network properties in terms of modified weight or threshold parameters [31‐33]. For instance, in the “weighted graph” approach, a distance weight is associated with each edge linking two nodes; thus, by combining (e.g., averaging) connection matrices across multiple subjects, inconsistent or weak weights are confronted with ad hoc thresholds, and eventually removed, leading to a reduction of the connections. However, there is no standard threshold in the literature and its value is often a free choice value in the graph-theoretic analysis. Moreover, apart from the thresholds, the criterion used for cortical gray matter parcellation, the dMRI acquisition scheme, the diffusion data model, and the fiber tracking algorithm are all methodological variants that may have a substantial impact on the resulting network measures.

In conclusion, our results suggest that both local and global topological properties of human structural brain networks exhibit strong dependence on the choice of dMRI acquisition scheme, also when the Q-ball model is used for tractography. This adds up to previous similar evidence obtained on DTI schemes and may thus help the planning of future connectomic studies in specific pathological populations.

These results are potentially relevant if several pathologies are investigated, especially by comparing those mostly affecting subcortical structures (e.g., Parkinson’s disease and other movement disorders involving basal ganglia) versus those mostly affecting cortical structures (e. g., Alzheimer’s disease, frontotemporal dementia, amyotrophic lateral sclerosis, and psychiatric conditions), as supported by several recent connectomic analyses [34‐39]. In particular, a connectomic approach could reinforce current knowledge of the interplay between the cerebral cortex, the basal ganglia, and the thalamus and its role in the pathophysiology of neurological disorders involving the cortico-basal and thalamo-cortical loops and their links to the cerebellum [37, 40]. Moreover, connectomic alterations of brain circuits may have a predictive role of clinical outcome in several neurological [38, 39, 41] and psychiatric [42] conditions.