Functional Connectivity-Based Modelling Simulates Subject-Specific Network Spreading Effects of Focal Brain Stimulation

Participants

Data for an additional set of 93 PD patients with resting-state fMRI were obtained from the Parkinson’s Progression Markers Initiative (PPMI) database. Three cases were excluded due to severe head motion using the same exclusion criteria. All data were fully anonymized as required by HIPAA regulations and participating sites received local Institutional Review Board approval for acquisition of the contributed data. Detailed information about the PPMI patients is available at www.ppmi-info.org.

MRI Datasets

All local participants were scanned with a standard 12-channel head coil on a Siemens Tim Trio 3.0 T scanner (Erlangen, Germany) at the Institute of Neuroscience, Chinese Academy of Sciences. Each participant was instructed to lie supine in the scanner wearing earplugs with the head snugly fixed by tight but comfortable foam pads. Real-time electrocardiogram and heart rate were continuously monitored throughout the scan (Erlangen, Germany). High-resolution T1-weighted images were acquired using a 3D magnetization-prepared rapid gradient-echo sequence (TR/TE = 2300/3 ms, TI = 1000 ms, flip angle = 9°, FOV = 256 × 256 mm², voxel size = 1 × 1 × 1 mm³, 176 consecutive sagittal slices). Resting-state fMRI images from patients were acquired for 300 volumes using a multiband echo-planar imaging sequence (TR/TE = 2000/30 ms, flip angle = 62°, in-plane resolution = 3 × 3 mm², slice thickness = 3 mm, 56 axial slices, multiband acceleration factor = 2). Note that the local PD patients received their medication at the time of the scan. In the HCs, resting-state fMRI images were acquired for 300 volumes with a single-shot echo-planar imaging sequence (TR/TE = 3000/30 ms, flip angle = 90°, in-plane resolution = 2 × 2 mm², 3 mm slice thickness, 47 axial slices). During the resting-state scan, participants were instructed to lie still with their eyes closed, remain awake, and not think of anything in particular (adherence was confirmed by participants immediately after the scan).

Anatomical and resting-state fMRI data from the public PPMI dataset were acquired on Siemens Tim Trio 3.0 T scanners. Structural images were recorded using a protocol similar to that described above. Resting-state fMRI images were acquired for 210 volumes using an echo-planar imaging sequence (TR/TE = 2400/25 ms, flip angle = 80°, in-plane resolution = 3.3 × 3.3 mm², slice thickness = 3.3 mm, 40 axial slices). Further technical details can be found in the MRI operation manual available at http://www.ppmi-info.org/.

Network Construction

Construction of a 1024-Region Template

We also constructed a brain template with 1024 regions to cross-validate whether our results were biased by the parcellation scheme. In doing so, 1024 seeds were randomly distributed into 92 brain regions of the AAL atlas with a probability proportional to the size of the regional volume. Two additional constraints were set during the distribution of seeds: each region had at least one seed and all seeds were equally allocated between the two hemispheres. This seeding procedure determined how many sub-regions had to be further generated for each original AAL-based brain region. Then, a k-means method was applied to assign the voxels within the original region into k sub-regions based on their spatial locations.

Whole-Brain Network Model of Neurostimulation

We first simulated the network effects of neurostimulation by considering the constructed connectome F as the resultant network of information spread or diffusion over a direct network D for individual patients. The rationale here was that the local effect is the action of stimulation imposed on the direct network D, and the globally distributed effect is the propagated result of the local effect on the direct network. As such, we used a network deconvolution algorithm [41] to derive a direct network D from the observed network F, and used the corresponding transformation rule, transitive closure, to simulate the global effects of local stimulation on a large-scale neuronal network (a detailed description of the modeling is provided below). We then denoted a hypothetical neurostimulation event as a regulation operator P, which was imposed on the direct network D (i.e., \( {\mathbf{D}}^{'} = {\mathbf{D}} \odot {\mathbf{P}} \), where ⊙ is the element-wise product of two matrices). If neurostimulation targets one pair of bilateral loci, most P entries have a value of one, with the exception of the two columns and two rows that are directly connected to the locus. For simplicity, the same value that represents the neurostimulation strength is applied to the remaining entries in P: a value > 1 signifies up-regulation, whereas a value < 1 indicates down-regulation (e.g., 1.5 represents a 50% up-regulation, 0.7 represents 30% down-regulation). Finally, the neurostimulation-tuned direct network \( {\mathbf{D^{\prime}}} \) is convolved with transitive closure to obtain the post-neurostimulation connectivity matrix \( {\mathbf{F^{\prime}}} \) (Fig. 1A).

The simulated outcome of neurostimulation was evaluated by quantitatively measuring the similarity between a group-averaged healthy matrix obtained from HCs and an individual or group-averaged post-neurostimulation matrix from PD patients. Connectomic similarity was quantified as the Pearson correlation coefficient between two vectorized (concatenated by rows) upper triangles of the connectivity matrix. This index was appropriate to characterize the discriminant difference between HCs and PD patients, as shown in Fig. 2. In order to compare the outcomes across brain regions, individuals, and groups, we standardized all outcome similarities using relative change, defined as follows:

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$$ relative\,change = \frac{{CC\left( {poststim, healthy} \right) - CC\left( {prestim,healthy} \right)}}{{CC\left( {prestim, healthy} \right)}} \times 100\%. $$

Relative change was used as a quantitative measure to represent the percentage improvement in connectomic similarity towards a healthy regime that was achieved by neurostimulation. The higher the connectomic similarity to the matrix of the HC group, the better was the simulated therapeutic effect. At each targeted brain region, the magnitude of up- or down-regulation that resulted in the highest relative change was deemed to be the best strength. All target regions were then ranked according to their relative change at the optimal neurostimulation strength. Higher ranks indicated desirable stimulation candidates with better therapeutic effects. All simulations were made at both single patient and patient group levels, as illustrated in Fig. 1B.

Derivation of a Transformation Rule for Local-Global Network Effects

Although the neurobiological and therapeutic mechanisms underlying a variety of brain stimulation approaches are not fully understood [8, 42, 43, 44], the network effects of focal neurostimulation can be roughly categorized into two types: local and distributed brain alterations [1, 44, 45]. The local effect that is generated by direct physical stimulation is believed to elevate excitation or inhibition in the target area [4, 8]. The distributed network effect, considered a global change, is assumed to account for all reverberating effects of the target loci and other connected regions. The challenge of computational modeling of stimulation lies in the lack of effective rules to estimate complex distributed network effects at the whole-brain scale [1, 6, 17, 23, 45, 46]. Given the existence of neuronal dynamics and parallel circuits (direct and indirect pathways), we hypothesized that the functional connectivity matrix F measured for individuals in the spontaneous state intrinsically contains a myriad of direct and indirect interactions among distant brain regions. As network size increases, particularly in whole-brain computational modeling, a considerable amount of indirect edges (connections between regions) may reflect second-, third- or even higher-order interactions between nodes (regions). It is therefore expected that the functional connectivity matrix F constructed for each individual in the spontaneous state contains direct and additional indirect relationships among distant regions, particularly considering the existence of neuronal dynamics and parallel circuits (pathways) [47]. Hypothetically, the functional brain connectome F is a resultant network of information spread or diffusion from a direct network D. Therefore, a network deconvolution algorithm was originally proposed to identify direct effects and weights from an observed correlation matrix in which both direct and indirect dependencies exist [41]. The corresponding transform, referred to as transitive closure, is the reverse process which derives the indirect effects from direct effects [41]. Two transforms were used to model the local-global network effect transformation of neurostimulation.

Note that the direct network D is not sparse, such that it contains all core neural circuits or pathways and the corresponding probabilistic weights of individual edges representing direct interactions.

Evidently, transitive closure (TC) and network deconvolution (ND) are inverse operators, i.e., \( {\mathbf{F}} = TC { \left( {ND \left( {\mathbf{F}} \right)} \right)} \) and \( {\mathbf{D}} = ND \left( {TC \left( {\mathbf{D}} \right)} \right) \). The potential benefits of this analytically reversible procedure are many-fold. First, key driving sources of a measured connectome and their associated weights can be deduced (i.e., relative contributions). Second, the location and strength of focal manipulation applied to the direct network can be assessed to predict whether or not a desired network can be achieved. Third, the transformation rule is empirically derived from the functional connectivity matrix recorded from each individual, which is not theoretically hypothesized and uniformly applied to a group of individuals. Last, it has enabled the study of network functions and properties in the core domain of direct interactions, rather than in the originally measured network plagued by complicated indirect interactions. Investigation in this direct network may help to unveil fundamental topological and dynamic properties of a network, and to improve prediction performance (e.g., the area under the precision-recall curve and the area under the receiver operating characteristic curve) [41]. In short, network deconvolution provides a succinct analytical solution to estimate a participant-specific, local-global transformation rule of information flow propagating over a network, which may approximately account for complex processes over the whole brain triggered by focal stimulation.

Here, for the ith network matrix of total n matrices, αⁱ is the upper bound determined by the largest positive eigenvalue (\( \uplambda_{ + }^{i} \)) and smallest negative eigenvalue (\( \uplambda_{ - }^{i} \)) of this matrix. Finally, all the matrices were multiplied by the determined constant α and the linearly scaled matrices were used for neurostimulation.

Study Design, Statistical Analysis, and Cross-Validation

As a proof-of-principle study, we rigorously tested the robustness and consistency of the simulated results using various cross-validation procedures. To validate whether the model is biased by the inclusion or exclusion of participant data, we randomly sampled half of the PD and HC groups 1000 times. Unblinding of between-group labels is also necessary to generate cross-validated simulation robustness. We randomly sampled half of the HC group 1000 times as the “patient group” to validate whether the present strategy for target is biased by the modeling per se. Moreover, we used the 1024-region parcellation template (described above) to determine whether the result of targets or strengths was biased by a specific brain parcellation scheme. For the results of individual patients, we assessed the statistical significance (one-sample t test) and the effect size (Cohen’s d value) of the simulated therapeutic effects for all brain regions. We assigned a rank for each region across individuals and summarized the number of occurrences of the ranks. The optimal neurostimulation strength of each region for each patient was also plotted and summarized statistically (one-sample t-test). For external validation, we repeated the same procedure using an independent public dataset (PPMI PD patients).

To reveal the extent of rectification of network topology achieved through neurostimulation, we conducted edge-wise statistical comparison between the two groups. The results of two-sample t-tests after Bonferroni correction for multiple comparisons (P < 0.05 corrected) were categorized into three types: removed abnormal connections (i.e., significant difference between the PD and HC groups before, but not after neurostimulation), newly-emerged abnormal connections, and unchanged abnormal connections. Finally, to examine the relationship between the simulated priority of regions and symptom severity, a Kendall rank correlation was calculated between each target’s rank and the UPDRS-III score for the two datasets.

Internal Validation

We began by screening all 46 bilateral brain regions as potential targets in the local PD group. The most effective neurostimulation strength for each region (resulting in the largest percentage improvement) was used to compare outcomes among all regions. At the group level, the GP was clearly identified as the best choice for neurostimulation, exhibiting the largest relative change of 2.22% (Fig. 3A). This indicates that the greatest improvement in the local PD group may be achieved by focal modulation of the GP. The STN, thalamus, and putamen evidently emerged as top-ranked targets with relative changes of 0.97%, 1.48%, and 1.17%, respectively. The hippocampus was a desirable target for which neurostimulation attained a 1.00% improvement. Importantly, these results withstood a 1000-round sub-sampling cross-validation process (Fig. 4). Using a delicate 1024-region parcellation template to repeat the analysis, we confirmed that the GP, STN, putamen, thalamus, and hippocampus remained top-ranked candidates for neurostimulation (Fig. 5). Note that the performance of different subregions within the thalamus varied widely, suggesting that specific nuclei of the thalamus may be extremely sensitive to stimulation. Furthermore, we randomly selected half of the HC sample as “patients” for target identification to demonstrate that this model would not biasedly choose any specific region as a potential target (Fig. 6). Meanwhile, neurostimulation strength, another key element of a typical stimulation protocol, was estimated for each candidate target. In the local PD group, optimal neurostimulation strengths for the top five targets (GP, STN, putamen, thalamus, and hippocampus) were determined to be 50%, 56%, 36%, 32%, and 32% down-regulation of their original connectivity strengths, respectively (Fig. 3B). Neurostimulation strengths for the remaining regions are displayed in Fig. 7.

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We then moved on to target and strength identification for individual patients. For each brain region, we plotted the relative change in individual patients (Fig. 8A, left panel). In the local cohort, the top-five regions (GP, STN, thalamus, putamen, and hippocampus) consistently demonstrated significant improvement (Fig. 8A, left panel), with rather large effect sizes (Fig. 8A, right panel). We subsequently plotted the complete rank of all regions as potential candidates for each patient in the local cohort (Fig. 8B, left panel) and counted their occurrence frequencies as the best or top-five choice (Fig. 8B, right panel). Evidently, the GP was the best choice for 11 (25.6%) and a top-five choice for 33 (76.7%) patients, and the STN was the best choice for 11 (25.6%) and a top-five choice for 36 (83.7%) patients (pie plot in Fig. 8B, right panel). Meanwhile, the caudate, thalamus and hippocampus were the best targets for 9 (20.9%), 6 (14.0%), and 4 (9.3%) patients, and a top-five choice for 22 (51.2%), 28 (65.1%), and 25 (58.1%) patients, respectively. In sum, the nuclei of the basal ganglia circuit were identified as the best choices for 86.1% and as a top-five choice for 97.7% of the local cohort, in striking agreement with previous clinical results [48]. Intriguingly, we found a significant relationship between the rank of the STN in this cohort and the severity of symptoms as indexed by the UPDRS-III (P < 0.05, Kendall rank correlation), but no other top sites. Moreover, we performed personalized identification of optimal strengths for each region in individual patients of the local cohort (Fig. 9, left panel). Regardless of the marked variability between individuals, consistent down-regulation (Fig. 9, right panel) of basal ganglia- and hippocampus-related functional connectivity substantially contributed to the rectification of dysfunctional networks.

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External Validation

As a robust test of generalizability, we applied the present modeling analysis to a completely independent validation dataset from the public PPMI database, which provides resting-state fMRI data for 90 patients with PD (Fig. 10). We found that nuclei of the basal ganglia circuit and hippocampus stood out as prioritized selections, in agreement with results from the local PD cohort (Fig. 10A). Correspondingly, we found that the optimal neurostimulation strengths for the GP, STN, caudate, putamen, and hippocampus were almost identical to those in the local group (58%, 82%, 84%, 40%, and 52% down-regulation, respectively; Fig. 10B). At the single patient level, the top-five targets selected for each patient in the public cohort were also consistent with those of the local group. Stimulation of the GP, STN, thalamus, putamen, hippocampus, and amygdala showed significant percentages of improvement (Fig. 10C, left panel) in this group with large effect sizes (Cohen’s d > 1.3, Fig. 10C, right panel). The GP was the best target for 17 (18.9%) and a top-five choice for 77 (85.6%) patients, and the STN was the best target for 15 (16.7%), and a top-five choice for 67 (74.4%) patients (Fig. 10D). The caudate, thalamus, hippocampus, and amygdala were the best choices for 45 (50.0%), 2 (2.2%), 8 (8.9%), and 1 (1.1%) individual patients, and a top-five choice for 66 (73.3%), 50 (55.6%), 75 (83.3%), and 24 (26.7%) patients (Fig. 10D), respectively. We therefore summarize the nuclei of the basal ganglia circuits as prioritized targets for 87.8% and as top-five choices for 100% of this public group. Note that we did not find a significant relationship between the ranks of any top-five sites and the severity of motor symptoms in the public cohort (P > 0.05, Kendall rank correlation). Meanwhile, personalized identifications of the optimal strength for each region are shown for the public cohort in Fig. 10E; they manifested consistent down-regulation.

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Reconfiguration of Network Topology by Neurostimulation

We investigated whether and how focal stimulation of the GP or STN resulted in topological reconfiguration of the functional brain connectome in the local (Fig. 11) and public cohorts (Fig. 12). Neurostimulation remarkably resulted in the removal of a large number of abnormal connections between the target regions and widespread areas in the temporal, parietal, frontal, and limbic regions. Considerable abnormal connections in the basal ganglia circuits that bypass the GP (Fig. 12A, B) or STN (Fig. 12E, F) were eliminated in both the local and the public cohort, although a substantial number of connections emerged from the simulated intervention process for the public PD cohort. Taken together, these results demonstrate that focal stimulation leads to remarkable topological reconfiguration toward healthy bifurcation of the functional connectomes as measured in controls, suggesting potential therapeutic mechanisms for the alleviation of symptoms.

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