Noninvasive modulation of human corticostriatal activity

Significance

We aimed to demonstrate that corticostriatal activity could be noninvasively modulated in humans. We used transcranial static magnetic field stimulation (tSMS) for noninvasive brain stimulation and resting-state functional MRI (fMRI) to assess changes in corticostriatal activity. Standard measures of functional connectivity cannot disambiguate changes in corticostriatal activity from local changes in cortical activity. To solve this ambiguity, we developed the ISAAC analysis framework, which allowed us to demonstrate that tSMS induced changes of both local activity within and shared activity between the stimulated cortex and the connected striatum. These results provide the least ambiguous evidence so far that corticostriatal activity can be targeted, monitored, and modulated noninvasively in humans, which may foster the development of new treatments for brain disorders.

Abstract

Corticostriatal activity is an appealing target for nonpharmacological treatments of brain disorders. In humans, corticostriatal activity may be modulated with noninvasive brain stimulation (NIBS). However, a NIBS protocol with a sound neuroimaging measure demonstrating a change in corticostriatal activity is currently lacking. Here, we combine transcranial static magnetic field stimulation (tSMS) with resting-state functional MRI (fMRI). We first present and validate the ISAAC analysis, a well-principled framework that disambiguates functional connectivity between regions from local activity within regions. All measures of the framework suggested that the region along the medial cortex displaying greater functional connectivity with the striatum is the supplementary motor area (SMA), where we applied tSMS. We then use a data-driven version of the framework to show that tSMS of the SMA modulates the local activity in the SMA proper, in the adjacent sensorimotor cortex, and in the motor striatum. We finally use a model-driven version of the framework to clarify that the tSMS-induced modulation of striatal activity can be primarily explained by a change in the shared activity between the modulated motor cortical areas and the motor striatum. These results suggest that corticostriatal activity can be targeted, monitored, and modulated noninvasively in humans.

The striatum is the main input of the basal ganglia from the cortex. Human corticostriatal projections are organized with an elegant topographic arrangement of parallel circuits for motor, associative, and limbic domains (1, 2). Accordingly, alteration of corticostriatal activity in these domains is associated with neurodevelopmental, neuropsychiatric, and movement disorders, such as autism, obsessive-compulsive disorder, schizophrenia, major depression, Huntington’s disease, and Parkinson’s disease (3–7). Targeting corticostriatal activity is thus appealing for developing nonpharmacological treatments for brain disorders (8–11).

At least in principle, corticostriatal activity of a specific domain could be modulated in humans with noninvasive brain stimulation (NIBS) of the corresponding cortical area, for example, by applying repetitive transcranial magnetic stimulation (rTMS) or transcranial direct current stimulation (tDCS). Several studies partly support this possibility. On the one hand, rTMS of the motor cortex or the prefrontal cortex can increase dopamine release in the corresponding striatal region, as measured by (11)C-raclopride positron emission tomography (PET) (12–14). These results are compelling, but dopamine release is only an indirect measure of corticostriatal activity, and PET remains a powerful but logistically inconvenient neuroimaging technique. On the other hand, both rTMS and tDCS can modulate corticostriatal functional connectivity, as assessed with resting-state functional MRI (fMRI) (15, 16). Resting-state fMRI is indeed a widely accessible neuroimaging technique, and functional connectivity is a common and informative measure for studying brain networks (17). However, functional connectivity is normally assessed by temporal correlation of activity between two regions, and it is now widely recognized that inference based on correlation is limited due to its ambiguity about several aspects of between-region interactions (18). More specifically, standard correlation cannot be readily employed to measure the distant effects of a local perturbation (e.g., by NIBS) because a change in variance within a region necessarily affects the correlation between regions, even without any actual change in coupling (19–23). Therefore, the combination of a NIBS technique with a sound neuroimaging measure that directly demonstrates a change in corticostriatal activity in humans is still lacking. The objective of the present work is to bridge this gap.

Transcranial static magnetic field stimulation (tSMS) is possibly the simplest NIBS technique currently available (24, 25), which makes it particularly attractive for delivering long-term treatments at home (26, 27). Previous studies showed that tSMS can reduce cortical excitability (24, 28–35) and modulate local as well as distant cortical activity (36–39), but the effects of tSMS over subcortical structures remain unexplored. Here, we combine tSMS with resting-state fMRI in order to investigate the modulation of corticostriatal activity. We first develop the ISAAC analysis, a framework including a data-driven version and a model-driven version, which overcomes the limitations of standard correlation by disambiguating the interaction of functional connectivity between regions with the local activity within regions. We then use the framework to map the functional connectivity between the medial cortex and the striatum along the fronto-posterior direction, showing maximal corticostriatal connectivity in the supplementary motor area (SMA), namely between the motor striatum and the SMA proper. Subsequently, we use the data-driven version of the framework to show that tSMS applied for 30 min over the SMA specifically modulates the local activity of both SMA proper and sensorimotor cortex and the motor striatum. We finally use the model-driven version of the framework to clarify that the tSMS-induced modulation of striatal activity can be primarily explained as a change in the shared signal between the motor striatum and the modulated motor cortical areas. Overall, our data show that tSMS can modulate human corticostriatal activity.

Results

The ISAAC Analysis Framework.

The goal of this study was to assess the ability of tSMS to modulate corticostriatal activity, which would normally be characterized in resting-state fMRI by functional connectivity measured as temporal correlation between the average BOLD signals of two regions (cortical and striatal) (Fig. 1A). Correlation alone, however, is known to be ambiguous, because changes in correlation cannot distinguish changes in shared activity between from changes in local activity within regions (19–21). This ambiguity, albeit always present in the study of functional connectivity, is especially relevant in the context of tSMS (and NIBS in general), where local perturbations are expected to occur. The same ambiguity applies to the estimation of functional connectivity in event-related fMRI, e.g., through psycho-physiological interactions (PPI) (40, 41) (SI Appendix, Figs. S1 and S2), although here we focus on resting-state fMRI. In short, the ambiguity arises from the dependency of functional connectivity on the intraregion structure, amplitude, and asymmetric covariation (ISAAC) of BOLD activity within and between regions. We therefore designed the ISAAC analysis framework to disambiguate functional connectivity by integrating local and shared activity between pairs of regions. The ISAAC framework includes two complementary approaches: one descriptive or data-driven and another one inferential or model-driven.

Fig. 1.

Presentation and validation of the ISAAC framework. (A–D) Schematic representation of the framework. (A) Classical functional connectivity (FC) between two regions, each comprised by several voxels, computed as the correlation between their spatial mean signals. (B) ISAAC descriptive approach, to measure a local activity within regions (variance and homogeneity) and coupling between regions (distant correlation). (C) ISAAC model and inferential approach, which estimates the variances of homogeneous signals (equally distributed across a region), divided in the shared signal (present in all the voxels of both regions) and the independent signals, and of unstructured signals that are specific for each voxel. (D) Summary table of how the variance (or variance changes) of the different ISAC components affect the descriptive metrics. An increase in a specific component can induce an increase (+) a decrease (−) or no effect in each metric. (E) Schematic representation of the Monte Carlo validation of the inferential part of the framework. In each iteration the dataset was generated according to the ISAAC model with randomized variances and Bx and the parameters of the model were later estimated with the variance decomposition equations. (F) Results from the Monte Carlo validation, comparing the estimated variance with the simulated one for each component. The identity (y = x) and least-squares (y = ax + b) linear fits are shown. The R-squared is from the least-squares fit.

The ISAAC descriptive approach (Fig. 1B) simply consists of considering functional connectivity between two regions X and Y as the compound canvas of five measures: homogeneity within regions (Hom) for the intraregion structure, variance within regions (Var) for amplitude, and distant correlation between regions (DCorr) for covariation:

$$Hom\left(X\right)={\langle corr\left({\mathit{x}}_i,{\mathit{x}}_j\right)\rangle }_{\left(i\ne j\right)},$$ [1]

$$Hom\left(Y\right)={\langle corr\left({\mathit{y}}_i,{\mathit{y}}_j\right)\rangle }_{\left(i\ne j\right)},$$ [2]

$$Var\left(X\right)=\langle Var\left({\mathit{x}}_i\right)\rangle ,$$ [3]

$$Var\left(Y\right)=\langle Var\left({\mathit{y}}_{\mathit{j}}\right)\rangle ,$$ [4]

$$DCorr\left(X,Y\right)=\langle corr\left({\mathit{x}}_i,{\mathit{y}}_j\right)\rangle ,$$ [5]

where $\langle \cdots \rangle$ indicates averaging across voxels. Note that DCorr is the mean correlation between pairs of voxels in two regions, whereas classical functional connectivity is the correlation between the mean signals of the two regions. DCorr thus corresponds to classical functional connectivity (and Var corresponds to the variance of the mean signal) in two limit cases: i) when $Hom\left(X\right)=Hom\left(Y\right)=1$ and ii) when there is only one voxel per region. Importantly, the expected values of DCorr, Var, and Hom are independent of the number of voxels, whereas classical functional connectivity (and the variance of the mean signal) always depends on the number of voxels (see SI Appendix, Supporting Methods for details). The ISAAC descriptive measures provide the simplest disambiguation, integrating within the same mathematical formulation the metrics that affect the measured functional connectivity so that they can be jointly taken into account when interpreting the results. Compared to classical correlation, the ISAAC descriptive approach offers a less ambiguous, albeit somewhat indirect, interpretation of possible changes in coupling between the two regions.

The ISAAC inferential approach (Fig. 1C) extends this perspective by providing direct estimators of the amount of activity in each region that contributes (or not) to the homogeneity within regions and to the coupling between regions. This approach is based on a linear model of BOLD activity, the ISAAC model, with which we account for intraregion structure and asymmetric covariation. With the ISAAC model, for our two regions X and Y we describe the activity of an arbitrary voxel as:

$$\begin{array}{c}{\mathit{x}}_{\mathit{i}}={\mathit{h}}_{\mathit{x}}+{\mathit{u}}_{\mathit{x}\mathit{i}}+{\mathit{\in }}_{\mathit{x}\mathit{i}}={\mathit{s}}_{\mathit{x}\stackrel{\sim }{\mathit{y}}}+B_x{\mathit{s}}_{\mathit{x}\mathit{y}}+{\mathit{u}}_{\mathit{x}\mathit{i}}+{\mathit{e}}_{\mathit{x}\mathit{i}}\mathbf{,}\hfill \end{array}$$ [6]

$$\begin{array}{c}{\mathit{y}}_{\mathit{j}}={\mathit{h}}_{\mathit{y}}+{\mathit{u}}_{\mathit{y}\mathit{j}}+{\mathit{\in }}_{\mathit{y}\mathit{j}}={\mathit{s}}_{\mathit{y}\stackrel{\sim }{\mathit{x}}}\pm \left(1-B_x\right){\mathit{s}}_{\mathit{x}\mathit{y}}+{\mathit{u}}_{\mathit{y}\mathit{j}}+{\mathit{e}}_{\mathit{y}\mathit{j}}\mathbf{,}\hfill \end{array}$$ [7]

where $\mathit{h}$ represents perfectly homogeneous intraregion activity (i.e., common to all voxels), $\mathit{u}$ represents unstructured intraregion activity (i.e., independent across voxels), and $\mathit{e}$ represents the (unstructured) noise. The rationale of introducing $\mathit{u}$ and $\mathit{e}$ as separated terms is to conceptually acknowledge the possible presence of both biological and nonbiological unstructured activity. The coupling between regions is accounted for by further decomposing the homogeneous activity within each region ( ${\mathit{h}}_{\mathit{x}}$ or ${\mathit{h}}_{\mathit{y}}$ ) into two mutually independent terms: the component that is shared between X and Y ( ${\mathit{s}}_{\mathit{x}\mathit{y}}$ ) and the component that is not ( ${\mathit{s}}_{\mathit{x}\stackrel{\sim }{\mathit{y}}}$ or ${\mathit{s}}_{\mathit{y}\stackrel{\sim }{\mathit{x}}}$ ). The balance coefficient $B_x$ , constrained to the (0,1) interval, accounts for asymmetric covariation, i.e., the possibility that the shared component is distributed asymmetrically between the two regions (see Supporting Methods for more detailed definitions). In the context of resting-state fMRI, $\mathit{h}$ represents the component of the BOLD signal that is common to all voxels in a region, $\mathit{u}$ represents the biological component of the BOLD signal that is unique to individual voxels, and $\mathit{e}$ is the nonbiological noise that is unique to individual voxels. These terms are local in the sense that they are fully defined for individual regions. When pairs of regions are considered, the homogeneous BOLD signals $\mathit{h}$ is intuitively the sum of shared activity and independent activity between regions. The shared activity ${\mathit{s}}_{\mathit{x}\mathit{y}}$ is specifically the activity of interest for obtaining a nonambiguous measure of functional connectivity.

Because the activity components of the ISAAC model are coindependent, the overall regional variance (Var(X) and Var(Y)) is the sum of their variances. Therefore, for each region, the overall variance can be decomposed at two levels, a local one in terms of homogeneous/unstructured activity and an additional one by further decomposing the homogeneous activity in terms of shared/independent activity between the two regions:

$$Var\left(X\right)=Var\left({\mathit{h}}_{\mathbf{x}}\right)+〈Var\left({\mathit{u}}_{\mathbf{x}\mathbf{i}}+{\mathit{e}}_{\mathbf{x}\mathbf{i}}\right)〉,$$ [8]

$$\begin{array}{c}Var\left({\mathit{h}}_{\mathit{x}}\right)=Var\left({\mathit{s}}_{\mathit{x}\stackrel{\sim }{\mathit{y}}}\right)+{B_x}^2·Var\left({\mathit{s}}_{\mathit{x}\mathit{y}}\right),\hfill \end{array}$$ [9]

$$Var\left(Y\right)=Var\left({\mathit{h}}_{\mathbf{y}}\right)+〈Var\left({\mathit{u}}_{\mathbf{y}\mathbf{j}}+{\mathit{e}}_{\mathbf{y}\mathbf{j}}\right)〉,$$ [10]

$$\begin{array}{c}Var\left({\mathit{h}}_y\right)=Var\left({\mathit{s}}_{\mathit{y}\stackrel{\sim }{\mathit{x}}}\right)+{\left(1-B_x\right)}^2·Var\left({\mathit{s}}_{\mathit{x}\mathit{y}}\right).\hfill \end{array}$$ [11]

From this variance decomposition based on the ISAAC model, we thus define our inferential approach to functional connectivity as a set of seven measures that estimate the homogeneous and unstructured variance (HVar and UVar, respectively) in each region, as well as the component of the homogeneous variance within regions that is shared (SVar) or independent (IVar) between regions:

$$HVar\left(X\right)=Var\left({\mathit{h}}_{\mathbf{x}}\right)\cong \langle Cov\left({\mathit{x}}_{\mathbf{i}},{\mathit{x}}_{\mathbf{j}}\right){\rangle }_{i\ne j},$$ [12]

$$HVar\left(Y\right)=Var\left({\mathit{h}}_{\mathbf{y}}\right)\cong \langle Cov\left({\mathit{y}}_{\mathbf{i}},{\mathit{y}}_{\mathbf{j}}\right){\rangle }_{i\ne j},$$ [13]

$$UVar\left(X\right)=\langle Var\left({\mathit{u}}_{\mathit{x}\mathit{i}}+{\mathit{e}}_{\mathit{x}\mathit{i}}\right)\rangle \cong \langle Cov\left({\mathit{x}}_{\mathit{i}},{\mathit{x}}_{\mathit{i}}\right)\rangle -HVar\left(X\right),$$ [14]

$$UVar\left(Y\right)=\langle Var\left({\mathit{u}}_{\mathit{y}\mathit{i}}+{\mathit{e}}_{\mathit{y}\mathit{i}}\right)\rangle \cong \langle Cov\left({\mathit{y}}_{\mathit{i}},{\mathit{y}}_{\mathit{i}}\right)\rangle -HVar\left(Y\right),$$ [15]

$$SVar\left(X,Y\right)=Var\left({\mathit{s}}_{\mathit{x}\mathit{y}}\right)\cong \frac{\left|\langle Cov\left({\mathit{x}}_{\mathit{i}},{\mathit{y}}_{\mathit{j}}\right)\rangle \right|}{B_x\left(1-B_x\right)},$$ [16]

$$\begin{array}{c}IVar\left(X,Y\right){\left.\right|}_{inX}=Var\left({\mathit{s}}_{\mathit{x}\tilde{\mathit{y}}}\right)\cong Var\left({\mathit{h}}_x\right)-B_x^{2}Var\left({\mathit{s}}_{\mathit{x}\mathit{y}}\right),\hfill \end{array}$$ [17]

$$IVar\left(X,Y\right){|}_{inY}=Var\left({\mathit{s}}_{\mathbf{y}\stackrel{\mathbf{~}}{\mathbf{x}}}\right)\cong \left({\mathit{h}}_{\mathbf{y}}\right)-{\left(1-B_x\right)}^{2}Var\left({\mathit{s}}_{\mathbf{x}\mathbf{y}}\right),$$ [18]

where the balance coefficient $B_x$ can be estimated from the data (see SI Appendix, Supporting Methods for derivations, assumptions, and details). Even though the ISAAC model conceptually separates unstructured biological activity $\mathit{u}$ from unstructured nonbiological noise $\mathit{e}$ , the two components cannot be separated in the variance decomposition, and both contribute to UVar.

Note that each of the components in the ISAAC inferential approach has a different spatial distribution, thus contributing differently to homogeneity, variance, and distant correlation of the descriptive approach (Fig. 1D). The ISAAC model thus makes explicit the ambiguity of correlation for estimating changes in coupling, in terms of both false positives and false negatives. On the one hand, not only a genuine increment in shared variance, but also a decrement in any other component (or a more complex combination of changes) can all induce an increase of distant correlation (and of the correlation between mean signals employed in classical functional connectivity). On the other hand, a genuine increment in shared variance can be masked by changes in other components and induce no measurable changes in distant correlation. Thus, while the joint estimation of local and shared properties with the ISAAC descriptive metrics allows for a deeper but indirect understanding of functional connectivity (compared to correlation alone), the ISAAC inferential metrics allow for a direct estimation of actual changes in coupling between regions.

To validate the ISAAC inferential approach, we used Monte Carlo simulations (Fig. 1 E and F). We generated 500 datasets with two regions X and Y (Y being smaller than X), for which the components of the ISAAC model were generated with randomized variances and $B_x$ and mixed into the time course of each voxel. These time courses were then used to estimate the variance of each component with the equations, and the estimates were compared to their known true values. The estimation of homogeneous and unstructured variance within regions was extremely precise and unbiased (R² > 0.99), with a negligible effect of region size (differences in R² of around 0.002). The estimation of the balance coefficient and of the shared and independent variances between regions was also extremely precise (R² > 0.95). The estimation of the balance coefficient displayed only a small bias towards 0.5, which resulted in a negligible underestimation of the shared variance and, consequently, of the contribution of the shared variance to the variance of each region. Conversely, the independent variances were slightly overestimated. Nevertheless, these estimations were still highly accurate in the full range (within 2% of the true values). Note that these small systematic errors are conservative upper bounds and will be mitigated when computing differences, e.g., evaluating changes between conditions or sessions. Overall, the values estimated from the equations are precise and accurate, with negligible deviations from the true values, proving appropriate for the estimation of corticostriatal activity in the response to local perturbations.

Mapping Corticostriatal Connectivity.

With the aim of understanding the relevant corticostriatal connections before assessing tSMS-related changes in corticostriatal activity, we first mapped the connectivity patterns of different striatal regions with the entire cortex (Fig. 2). For these analyses, we used a relatively large (N = 100) resting-state fMRI dataset from the Human Connectome Project (HCP100 dataset). We employed a functional parcellation of the striatum into five regions corresponding to the motor, ventral attention, default mode, frontoparietal, and limbic networks (42).

Fig. 2.

Cortico-striatal functional connectivity for the medial cortex in the HCP100 dataset. A functional parcellation of the striatum was used, and spherical regions were placed along the medial cortex in two rows and in left and right hemispheres, 8 mm lateral. (A) Included striatal regions and their seed-based functional connectivity with the medial cortex. (B) Direct estimates of functional connectivity (FC), averaged between left, right, ipsilateral and contralateral (across-subjects mean and 95% CI). The color codes the striatal region, and upper and lower plots are the dorsal and ventral rows of cortical regions. From top to bottom: correlation of the mean signals (i.e., the standard estimate of FC); distant correlation (i.e., our ISAAC descriptive metric of inter-region coupling); shared variance (i.e., our ISAAC inferential metric of inter-region coupling). (C) Indirect estimates of group functional connectivity, averaged between left, right, ipsilateral and contralateral between-subjects correlation of cortical and striatal descriptive metrics of local activity (homogeneity and variance). (D) Relationship between ipsilateral and contralateral coupling estimates. All correlation-based measures where transformed by Fisher's r-to-z transform and variance was transformed by the base-10 logarithm.

We first performed a standard seed-based connectivity analysis, using the striatal regions as seeds (Fig. 2A). Since the expected rostro-caudal pattern of corticostriatal connectivity was well captured in the sagittal plane, we linearized the problem by placing spherical regions of interest (ROIs) along the entire medial cortex and performed ROI-based connectivity analysis using classical functional connectivity (correlation between mean signals) and the two estimates from the ISAAC framework (DCorr and SVar) (Fig. 2B). Despite subtle differences, all measures showed a consistent pattern of connectivity. Striatal regions that lie primarily in the putamen (i.e., the motor and ventral attention regions) showed a peak in connectivity with the posterior part of the SMA (i.e., the SMA proper). Striatal regions that lie primarily in the caudate (i.e., frontoparietal and default mode) showed a wider peak in connectivity with the anterior part of SMA (i.e., the pre-SMA) and a more defined peak with the posterior part of the precuneus (note that the limbic striatum displayed a generally lower corticostriatal connectivity, which was expected because we did not map limbic cortical areas). The motor striatum had stronger connection with the SMA proper and the paracentral lobule (PCL, which indeed corresponds to the sensorimotor cortex) than any other striatal region, especially assessed by DCorr and classical functional connectivity. As expected, absolute values of classical functional connectivity were greater than DCorr, although they reflected almost the same connectivity patterns. The patterns of SVar were also similar, despite differences in scaling (unlike correlation, SVar is not a normalized metric). Overall, there is across-metric consensus in associating caudate with pre-SMA and more frontal regions and motor striatum with SMA proper and the adjacent sensorimotor cortex, which is in line with current knowledge (42–47).

We then postulated that functionally connected regions would also show a certain degree of correlation in local activity, based on the interaction between local and shared activity that motivates the ISAAC framework. We thus computed the across-subjects correlation of a local descriptive measure (either homogeneity or variance) between each corticostriatal pair of regions (Fig. 2C). For homogeneity, putamen-predominant regions displayed relatively strong correlations with the SMA proper and sensorimotor cortex. Conversely, caudate-predominant regions displayed lower correlations with cortical regions. For variance, all striatal regions displayed a more diffuse antero-posterior gradient of correlation with cortical regions. In general, variance-based correlations were more dissociated from direct estimates of corticostriatal connectivity than homogeneity-based correlations. The joint information from all measures suggests that the maximal corticostriatal connectivity along the medial cortex occurs between the SMA-proper (extending to the sensorimotor cortex) and the motor striatum.

Finally, to assess possible differences in ipsilateral vs. contralateral corticostriatal connectivity, we compared the values of all the reported metrics (i.e., classical functional connectivity, DCorr, SVar, and across-subjects correlations of homogeneity and variance) between ipsilateral and contralateral pairs of regions (Fig. 2D). In general, ipsilateral and contralateral corticostriatal connectivity was nearly identical with little variability. Somewhat greater ipsilateral–contralateral variability was seen only for low values of SVar, corresponding to weakly connected or unconnected regions. Overall, ipsilateral and contralateral corticostriatal connectivity measures are largely equivalent along the medial cortex.

Modulation of Corticostriatal Activity with tSMS of the SMA: ISAAC Data-Driven Approach.

We then tested the ability of tSMS to modulate corticostriatal activity. In a randomized double-blind sham-controlled crossover experiment (N = 20), we acquired resting-state fMRI for 10 min at baseline and immediately after 30 min of tSMS (or sham) over the bilateral SMA (tSMS20 dataset) (39). Head movement—estimated as the mean framewise displacement (48)—was low (0.056 ± 0.020 mm, mean ± std.), and there was no evidence for a difference between conditions (repeated-measures two-way ANOVA, time x treatment: F_1,19=0.57, P = 0.46, BF_incl=0.36). Similarly, the number of volumes in the analysis was sufficient to make connectivity estimates (211.78 ± 19.89 volumes, 8.47 ± 0.80 min), with no evidence for a difference between conditions (time x treatment: F_1,19 = 2.1, P = 0.16, BF_incl = 0.95). The range of the tSMS magnetic field intensity, estimated with the finite element method (FEM), was 100 to 200 mT in the SMA, 25 to 100 mT in the adjacent cortical areas (e.g., the sensorimotor cortex), 10 to 20 mT in the caudate, and 5 to 10 mT in the putamen (Fig. 3A). We thus quantified the tSMS-induced changes in cortical and striatal activity as well as corticostriatal connectivity with the ISAAC data-driven approach.

Fig. 3.

Corticostriatal effects of SMA tSMS assessed with the ISAAC descriptive metrics. (A) Estimated distribution of the magnitude and gradient of the magnetic field in the experiment. (B) Effects on local homogeneity and variance in the medial cortex (mean and 95% CI), assessing significance by paired t test on increments (P uncorrected) (C) Effects in the local activity of the right SMA proper (Left) and paracentral lobule (PCL, i.e., sensorimotor cortex; Right). (D) Effects on the local activity in the striatum. (E) Effects on descriptive metrics of coupling between the locally-modulated regions: distant correlation and classical functional connectivity (FC). The compared regions are the left motor striatum with right SMA proper and PCL. Statistical significance was estimated with two-way repeated measures ANOVA. Significance for delta(real) vs. delta(sham) is the FDR-corrected P-value for time-treatment interaction, and significance for delta(real) and delta(sham) is the P-value of the Tukey–Kramer post-hoc test on the post-pre difference in each session.

At the cortical level, a first exploratory analysis with our spherical ROIs along the medial cortex revealed local tSMS effects that were mainly focalized in the SMA proper and sensorimotor cortex, both in variance and in homogeneity, and only in the right hemisphere (Fig. 3B). We thus formally tested the effects of tSMS on the local activity of right SMA and sensorimotor cortex, using the parcellation of these two regions from the modified Automated Anatomical Labeling (AAL) atlas (43, 44, 49) (Fig. 3C). In the SMA proper, the effect in homogeneity was inconclusive (two-way ANOVA, time × treatment: F_1,19 = 3.7, P_FDR = 0.07; BF_incl = 0.864) and we found anecdotal evidence of an increase in variance after real stimulation compared to sham (two-way ANOVA, time × treatment: F_1,19 = 9.6, P_FDR < 0.01; BF_incl = 2.5). In the sensorimotor cortex, the evidence of an increase after real stimulation compared to sham was anecdotal for homogeneity (F_1,19 = 8.2, P_FDR < 0.05; BF_incl = 1.8) and moderate for variance (F_1,19 = 10.2, P_FDR < 0.01; BF_incl = 5.2). When the two regions were analyzed together (three-way ANOVA), the evidence for an effect of real stimulation compared to sham was nearly moderate for homogeneity (time × treatment: F_1,19 = 8.8, P < 0.01; BF₁₀ = 2.9) and became strong for variance (F_1,19 = 10.7, P < 0.01; BF_incl=18.4), with tSMS effects not differing between regions (time × treatment × region: F_1,19 = 2.0, P = 0.17, BF_incl = 0.306 for Hom; F_1,19 = 0.4, P = 0.54, BF_incl = 0.371 for Var).

At the striatal level, by analyzing the possible effects of tSMS on all 10 regions (five per side), we found that the tSMS-induced changes in homogeneity and variance were dissociated and spatially defined. On the one hand, there was the absence of tSMS effects on variance in all striatal regions (two-way ANOVA, time × treatment: F_1,19 < 2.4, P_FDR > 0.5; BF_incl < 0.689). On the other hand, we observed strong evidence for increased homogeneity after real stimulation compared to sham specifically in the motor region of the left striatum (F_1,19 = 11.6, P_uncorrected < 0.001, P_FDR < 0.05; BF_incl = 14.8; Fig. 3D). This increase of motor striatum homogeneity in the real session compared to sham was observed in 17/20 subjects. Similar results were obtained in the left motor striatum with standard measures of local activity, i.e., amplitude of low-frequency fluctuations (F_1,19 = 3.2, P_uncorrected = 0.088, P_FDR = 0.27; BF_incl = 0.947) (50–55) and regional homogeneity (F_1,19 = 8.8, P_uncorrected = 0.008, P_FDR = 0.076; BF_incl = 18.5) (56, 57) (SI Appendix, Fig. S3).

Despite the local changes induced by tSMS at cortical and striatal levels, there was the absence of evidence for changes in functional connectivity, as measured by either DCorr or classical functional connectivity between the modulated regions (time × treatment, F_1,19 < 3.9, P_FDR > 0.13; BF_incl < 1.4 Fig. 3E). The data-driven ISAAC approach was thus able to detect a modulation of cortical and striatal activity induced by tSMS but not the underlying change in corticostriatal coupling.

Modulation of Corticostriatal Activity with tSMS of the SMA: ISAAC Model-Driven Approach.

To directly interpret the observed changes in cortical and striatal activity in terms of their cortical, striatal, and corticostriatal components, we further studied the modulated regions with the ISAAC model-driven approach.

At the cortical level (Fig. 4A), HVar (i.e., the homogenous variance) displayed moderate evidence for an increase after real stimulation compared to sham, both in the SMA proper (two-way ANOVA, time × treatment, HVar: F_1,19 = 9.2, P_FDR < 0.01, BF_incl = 4.4) and in the sensorimotor cortex (Hvar: F_1,19 = 10.5, P_FDR < 0.01, BF₁₀ = 4.7). For UVar (i.e., the unstructured variance), the increase after real stimulation compared to sham remained anecdotal, both in the SMA proper (F_1,19 = 7.0, P_FDR < 0.05, BF_incl = 1.3) and in the sensorimotor cortex (F_1,19 = 5.9, P_FDR < 0.05, BF_incl = 1.8)

Fig. 4.

Corticostriatal effects of SMA tSMS assessed with the ISAAC inferential metrics. (A) Effects on the local activity (homogeneous and unstructured) of the right SMA (Left) proper and paracentral lobule (PCL, i.e., sensorimotor cortex; right). (B) Effects on the local activity (homogeneous and unstructured) in the left motor striatum. (C) Effects on corticostriatal activity between the modulated regions: left motor striatum with right SMA proper and PCL. From top to bottom: changes in the shared variance; changes in the striatal independent variance (not shared with the considered cortical region); changes in the cortical independent variance (not shared with the left motor striatum). Statistical significance was estimated with two-way repeated measures ANOVA. Significance for delta(real) vs. delta(sham) is the FDR-corrected p-value for time-treatment interaction, and significance for delta(real) and delta(sham) is the p-value of the Tukey–Kramer post-hoc test on the post-pre difference in each session.

At the striatal level (Fig. 4B), we observed moderate evidence for an increase of HVar after real stimulation compared to sham in the left motor striatum (F_1,19=9.4, P_uncorrected < 0.01, P_FDR = 0.064, BF_incl = 3.0), with the absence of changes in UVar (F_1,19 = 0.1, P_FDR = 0.95, BF_incl = 0.323). These results essentially confirm the changes in local cortical and striatal activity already detected with the ISAAC data-driven approach and more directly define them in terms of homogenous vs. unstructured components of the BOLD signals.

Differently from the data-driven approach, the model-driven approach was indeed able to uncover and characterize changes in coupling between the modulated corticostriatal regions (Fig. 4C). Namely, we found strong evidence that, compared to sham, real stimulation increased SVar (i.e., the variance of the shared signal) between the motor striatum and the sensorimotor cortex (time x treatment: F_1,19=18.0, P_FDR < 0.001, BF_incl = 18.7). This increase in SVar was inconclusive for the SMA proper (F_1,19 = 2.54, P_FDR = 0.13, BF_incl = 1.1). When the two cortical regions were analyzed together (three-way ANOVA), the evidence for a tSMS-induced increase of SVar with the motor striatum became very strong (time × treatment: F_1,19 = 13.9; P < 0.005, BF_incl = 52.4), without a clear specificity to the sensorimotor cortex compared to SMA proper (time × treatment × region: F_1,19 = 6.5; P < 0.05, BF_incl = 1.0). Importantly, striatal IVar (i.e., the variance of the homogeneous signal in the striatum that is independent from the cortex) was not affected by tSMS (two-way ANOVA, time × treatment: F_1,19 ≤ 0.8; P_FDR > 0.60, BF_incl < 0.37). This suggests that all the change of striatal HVar was due to the change in shared signal with the cortex. Conversely, cortical IVar (i.e., the variance of the homogeneous signal in the cortex that is independent from the striatum) was anecdotically increased by tSMS compared to sham in the sensorimotor cortex (time x treatment: F_1,19 = 6.2; P_FDR < 0.05, BF_incl = 1.5). This suggests that not all the change of HVar at the cortical level may have contributed to the change in shared activity with the striatum.

Importantly, the result that tSMS increased corticostriatal SVar was based on the cortical and striatal regions that displayed significant increases in local activity, i.e., right sensorimotor cortex/SMA proper and left motor striatum. In order to test whether the increased corticostriatal SVar was truly a contralateral effect or could be more reasonably extended also to ipsilateral connectivity, we performed a new analysis of the effects of tSMS compared to sham on corticostriatal SVar with the left motor striatum (four-way ANOVA), accounting not only for cortical region (sensorimotor cortex and SMA proper) but also for laterality (ispilateral and contralateral). This analysis provided strong evidence that tSMS increased SVar compared to sham (time × treatment: F_1,19 = 6.6, P < 0.05, BF_incl = 12.4) without a clear regional specificity (time × treatment × region: F_1,19=11.4, P < 0.01, BF_incl = 1.6) and no influence of laterality (time × treatment × laterality: F_1,19 = 0.8, P = 0.38, BF_incl = 0.012; time × treatment × region × laterality: F_1,19 = 0.091, P = 0.77, BF_incl < 0.001).

Finally, we performed a seed-based connectivity analysis to assess the specificity of the observed corticostriatal effects by exploring distant cortico-cortical changes (see SI Appendix). No evidence for changes in seed-based connectivity was found when considering the pre-SMA as seed region. Conversely, we did find an effect outside the medial cortex when considering SMA-proper as the seed region, specifically a tSMS-dependent increase in connectivity with a cluster in the frontotemporal cortex, consistent with our previous work (39) (SI Appendix, Fig. S4 A and B). ISAAC analysis including this cluster revealed very strong evidence supporting an increase in shared activity between the SMA proper and the frontotemporal cluster (SI Appendix, Fig. S4C) and less clear evidence for an increase in shared activity between the frontotemporal cluster and the motor striatum (i.e., anecdotal evidence of absence with the entire dataset, anecdotal evidence for an effect when an outlier was excluded) (SI Appendix, Fig. S4D).

Overall, the model-driven ISAAC approach was able not only to detect and define tSMS-induced changes in cortical and striatal activity but also to uncover the underlying change in corticostriatal coupling. Our results combined with the known anatomical corticostriatal connectivity suggest that the observed corticostriatal effects induced by tSMS are primarily mediated directly from the SMA-sensorimotor cortex to the motor striatum.

Discussion

We combined tSMS and resting-state fMRI to noninvasively modulate corticostriatal activity in humans. We first presented and validated the ISAAC analysis, a well-principled framework to disambiguate functional connectivity between regions from local activity within regions. All measures of the framework suggested that the region along the medial cortex displaying greater functional connectivity with the striatum is the SMA, where we applied tSMS. The ISAAC data-driven descriptive metrics showed that tSMS of the SMA induces changes of local activity in the SMA proper, in the adjacent sensorimotor cortex and in the motor striatum. The ISAAC model-driven inferential metrics clarified that the tSMS-induced modulation of striatal activity arises from changes in the shared activity between the modulated cortical motor areas and the motor putamen. Extending the analyses beyond the medial cortex, distant effects induced by tSMS of SMA on the frontotemporal cortex did not convincingly contribute to the observed corticostriatal changes. Collectively, our results provide evidence of noninvasive modulation of human corticostriatal activity.

ISAAC Analysis.

In order to demonstrate genuine modulation of corticostriatal activity, our methodological challenge was to develop an analysis framework to overcome the ambiguity of classical temporal correlation in estimating functional connectivity between regions. This ambiguity extends to functional connectivity in event-related fMRI typically assessed through PPI (40, 41), as discussed in Supporting Information. Correlation is sensitive to changes in the variance of regional activity, even if such changes are not related with the coupling between the involved regions (19–21). This is especially important in the context of NIBS, since local changes are likely to occur. It is also usual in resting-state fMRI to average the BOLD activity of all the voxels within a region to obtain a single time series representing the activity of the region. The variance of this mean signal is a function not only of the variance of the activity within voxels, but also of the homogeneity of the activity across voxels. More formally, the variance of the average is equal to the average of all the possible pairwise covariances, i.e., the elements of the voxel-level autocovariance matrix. If correlation is ambiguous because of variance (19–21), we can also say that variance is ambiguous because of homogeneity. The ambiguity of classical correlation about shared vs. independent activity thus depends both on variance and homogeneity.

To overcome these ambiguities, we designed our analysis framework to dissect functional connectivity between regions by two complementary approaches: a descriptive or data-driven one to provide metrics of homogeneity, variance, and distant correlation; and an inferential or model-driven one, based on a linear model for BOLD activity that accounts for intraregion structure and asymmetric covariation (the ISAAC model), which decomposes the variance in terms of homogeneous/unstructured and shared/independent activity. The ISAAC analysis framework allowed us to formally test whether tSMS modulates corticostriatal activity.

The ISAAC Descriptive Metrics: tSMS Modulates Cortical and Striatal Activity.

Our descriptive approach integrates three aspects of BOLD activity that are widely used in the fMRI literature, rather than providing new metrics: 1) Variance is conceptually equivalent to the amplitude of low-frequency fluctuations (ALFF) (50–55) (SI Appendix); 2) homogeneity is frequently found in the literature as some averaged correlation measure between pairs of nearby voxels, such as in Regional Homogeneity (ReHo) (56, 57), integrated local correlation (ILC) (58), local correlation (LCOR) (59), or the cross-correlation of spontaneous low frequency (COSLOF) (60) (see SI Appendix for a more detailed comparison); and 3) distant correlation is closely related to classical functional connectivity and thus also suffers from the same ambiguity and interpretative limitations when used in isolation. The integration of these three aspects within the same mathematical object, and their joint interpretation in experimental data, provides a first level of disambiguation of functional connectivity by jointly taking within- and between-region activity into account, a possibility that is largely unexploited in the literature.

In our experimental conditions, tSMS applied over the SMA increased both the local variance and the homogeneity of BOLD fluctuations at the cortical level (in SMA proper and in the adjacent sensorimotor cortex), while it increased only the homogeneity at the striatal level (motor striatum). This dissociation between variance and homogeneity may be relevant to understand the effects of tSMS on corticostriatal activity. Variance and homogeneity are interrelated measures, both reflecting brain metabolism (52, 61–63). On the one hand, variance is directly related to the amplitude of the BOLD signal, which is sensitive to changes in both neural activity (55) and nonneural hemodynamic activity (64–66). On the other hand, homogeneity is invariant to amplitude scaling, so the neurovascular changes affecting variance do not necessarily entail homogeneity changes, unless there is an actual change in the local structure of the fluctuations. Our results thus suggest that variance and homogeneity might reflect different aspects of local and distant tSMS-induced plasticity. Since the intensity of the magnetic field—and its corresponding gradient—applied with tSMS was obviously largest in the targeted SMA (100 to 200 mT), intermediate in the adjacent sensorimotor cortex (25 to 100 mT), and considerably lower in the distant putamen (5 to 10 mT), it is tempting to propose that the increased variance might reflect, at least in part, the local effects directly induced by tSMS, whereas the increased homogeneity might reflect the effects propagated through the connected network. In any case, the distant increase of homogeneity in the motor striatum is evidence per se that tSMS was able to alter corticostriatal activity.

Importantly, the ISAAC descriptive metrics collectively solve some crucial aspects of mathematical ambiguity of functional connectivity, which is necessary for reducing the physiological ambiguity but admittedly does not completely solve the problem of physiological interpretation. Still, a cautious interpretation can be attempted by considering BOLD fluctuations as the neuroimaging counterpart of infraslow fluctuations of neuronal (and nonneuronal) activity (67, 68), which can be observed in the firing of neurons (69, 70), in DC-coupled EEG signals (71, 72), and in the envelope of local field potential/EEG oscillations at higher frequencies (70, 73). Importantly, the infraslow fluctuations in the amplitude of local field potential/EEG oscillations typically correlate with their power (74). An increase in BOLD variance, homogeneity, and distant correlation thus suggests, respectively, an increase in power, local synchronization, and distant synchronization of underlying neuronal oscillations.

Two negative findings deserve consideration. First, tSMS did not induce changes of local activity in the pre-SMA and its connected striatal regions. This is somewhat surprising since the intensity (and the gradient) of the magnetic field applied with tSMS was similar in SMA-proper and pre-SMA. One possible explanation for the greater responsiveness of SMA proper compared to pre-SMA to tSMS may be sought in the different patterns of BOLD activity at baseline, with cortically deeper—and thus possibly more difficult to modulate—peaks of corticostriatal connectivity in pre-SMA. Second, more strikingly, tSMS did not seem to induce any change in distant correlation (or classical functional connectivity) between locally affected cortical and striatal motor regions. How could we alter cortical and striatal activity without modulating corticostriatal functional connectivity? This paradoxical situation offers an illustrative example of the ambiguity of classical functional connectivity (19–21), but in a “false negative” sense that is not often appreciated: The absence of change in classical functional connectivity does not necessarily imply that an actual change in connectivity did not occur. To uncover the underlying change in corticostriatal connectivity, we needed to recur to the ISAAC inferential approach.

The ISAAC Inferential Metrics: tSMS Modulates Corticostriatal Connectivity.

The ISAAC inferential approach expresses functional connectivity in terms of shared and unshared activity between two regions. This can also be achieved, to some extent, by substituting classical correlation with covariance, which is insensitive to unshared activity (20). However, interpreting covariance changes directly as changes in shared activity is equivalent to our ISAAC-based variance decomposition, but forcing the shared component to be symmetrically distributed (i.e., $B_x=0.5$ ). This implicitly allows for a negative variance of the unshared component (which is especially prone to occur in the case of strongly coupled regions with unbalanced variances) and thus is an inconsistent model to support inferences. Of note, thanks to the inclusion of intraregion homogeneous vs. nonhomogenous activity in the model, the ISAAC model-driven metrics can detect not only additive signal changes (ASC) (21) but also some nonadditive signal changes. For example, nonadditive local synchronizations that induce no change in overall variance can manifest as an increase of the homogeneous variance in a region, just as we observed in the motor striatum. Overall, the ISAAC inferential metrics allowed us to disentangle the local effects and distant effects of tSMS on corticostriatal activity.

We found that tSMS increased the homogenous variance both at the cortical level (SMA proper and sensorimotor cortex) and in the motor striatum, with no consistent changes in unstructured variance. Under the assumption that the homogenous activity is homogeneously distributed within regions, which seems reasonable in our ROIs, the unstructured variance describes activity that in principle is not correlated with other brain regions. Conversely, the homogeneous variance describes the activity that is most likely correlated with other regions (e.g., forming the typical resting-state networks). The ISAAC inferential metrics explicitly clarify to what extent the increased homogeneous variance is shared (SVar) or independent (IVar) between regions, providing the following picture (Fig. 5): i) Not all of the increased homogeneous variance in the cortex seems to be shared with the striatum, which is consistent with the tSMS-induced changes in cortico-cortical connectivity we previously reported (39); ii) virtually all of the increased homogeneous variance in the striatum is shared with the modulated cortex. The result that tSMS increases the shared variance between motor cortex and striatum is possibly the least ambiguous evidence obtained so far that corticostriatal activity can be targeted, monitored, and modulated noninvasively in humans.

Fig. 5.

Summary of corticostriatal changes induced by tSMS of the SMA. With the ISAAC perspective, we observe changes in the amplitude of fluctuations in the SMA proper and in the paracentral lobe (PCL, i.e., sensorimotor cortex), as well as an enhancement of local structure in the PCL and the putamen. The effect on the SMA is most likely exerted directly by the magnetic field, and then propagated through existing physiological connections to the PCL and the motor putamen. While we cannot discard some direct effect of the magnetic field over the PCL, the putamen is too far away from the magnet’s direct influence. The main observed shared effect (SVar) occurs between the SMA/PCL and the motor putamen.

Physiological Implications for Future Clinical Applications.

The possibility to noninvasively modulate corticostriatal activity is attractive for future clinical applications. In order to delineate a rational path toward clinical trials, it is important to carefully consider the physiological implications and boundaries of our findings, particularly regarding i) experimental limitations, ii) functional asymmetries, and iii) inferences about changes in neuronal activity.

First, the effects of 30-min tSMS on cortical excitability were previously estimated to last at least 30 min when the stimulation was applied to the motor cortex (33), but the design of the present study does not allow us to estimate the duration of the effects on corticostriatal activity beyond the 10 to 15 min duration of the resting-state fMRI protocol plus the time needed for the subject to enter the scanner. We also have no information about what happens during the stimulation, since bringing the tSMS magnet into the scanner is currently unfeasible, nor about the behavioral correlates of the observed changes in corticostriatal activity, which may differ in normal vs. clinical populations. These issues should be considered and addressed in future replication experiments in larger samples.

Second, bilateral SMA stimulation seemed to induce lateralized effects on brain activity, primarily affecting the right cortex and the left striatum. From an experimental viewpoint, we cannot fully exclude possible hemispheric asymmetries of static magnetic field exposure during tSMS, even though in our protocol the variability of tSMS positioning is greater in the sagittal than in the coronal plane (39). From a physiological viewpoint, lateralized effects may be partly counterintuitive but are not an unexpected finding because SMA activity is already lateralized in basal conditions (39, 75, 76). This baseline imbalance between hemispheres, combined with the strong homotopic anatomical (77) and functional (78) connectivity within the motor network through transcallosal projections (79), likely leads to asymmetric interhemispheric interactions (80) that could explain the lateralized effects. These interactions may also explicate the predominance of contralateral corticostriatal changes, although our analyses are compatible with a modulation of both ipsilateral and contralateral corticostriatal projections from cortical motor areas (81, 82). Importantly, our metrics—similarly to classical correlation—are neutral to directness (monosynaptic/polysynaptic) and direction (afferent/efferent) of the connectivity (18). These properties could be inferred with other methodologies such as partialization (17, 18) and dynamic causal modeling (18, 83). We therefore infer the likely corticostriatal directness and direction of the tSMS-induced changes not from the data but from prior anatomical knowledge.

Third, all our metrics showing tSMS-dependent changes of local/shared corticostriatal activity were increased by the stimulation, which at first glance may appear to contrast with the well-known inhibitory effects of tSMS (24, 28–35, 84). Increases in BOLD-related measures are commonly observed also with other inhibitory NIBS techniques such as cathodal tDCS (85–88) or low-frequency rTMS (89, 90). Importantly, increases in BOLD-related measures (and in the underlying neuronal oscillations) do not necessarily reflect an increase of neuronal firing activity. In fact, recent causal experiments in animals suggest that chemogenetically increasing neuronal firing activity actually decreases BOLD-related measures (91). Our results are thus compatible with a tSMS-induced reduction of cortical excitability (24, 28–35, 84), increase in resting oscillations (36, 37), and overall reduction of corticostriatal neuronal activity.

The possibility to noninvasively modulate corticostriatal activity is particularly relevant for brain disorders related with striatal dysfunction. At the empirical level, for example, diminished putaminal homogeneity has been consistently reported in Parkinson’s disease (92, 93). Even though the mechanisms of this alteration are not fully understood, the tSMS-induced increase of putaminal homogeneity reported here may help reinstating a more normal function in the striatal network. At a mechanistic level, an excess of corticostriatal glutamatergic activity has been proposed as a neurodegenerative factor in both Parkinson’s disease (10) and Huntington’s disease (94). A putative decrease of glutamatergic corticostriatal activity by tSMS could be used as a modulatory technique to further understand the disease or investigated as a potential symptomatic or even disease-modifying therapeutical option. More in general, neuromodulation of corticostriatal activity could be explored to treat several neurodevelopmental, neuropsychiatric, and movement disorders (3–11) by delivering tSMS at cortical regions targeting motor, associated, or limbic domains (1, 2). Overall, even though the path toward clinical applications is a long one ahead, a NIBS protocol with a sound neuroimaging measure is now available.

In conclusion, by combining tSMS with resting-state fMRI and presenting an analysis framework that disambiguates the interactions of functional connectivity between regions with the local activity within regions, we provide solid evidence that corticostriatal activity can be modulated noninvasively in humans.

Materials and Methods

In this study, we used two resting-state fMRI datasets. Corticostriatal connectivity was characterized in a relatively large (N = 100 subjects), public dataset from the Wu-Minn Human Connectome Project (95–98) (HCP100). This dataset comprised several sessions of high-quality preprocessed resting-state fMRI from 100 subjects, which were used for a reliable characterization of corticostriatal activity. tSMS effects on corticostriatal activity were assessed in a dataset of a previous neuromodulation study (39) (tSMS20). This dataset comprised resting-state fMRI sessions from 20 subjects who participated in a randomized, longitudinal, cross-over, sham-controlled experiment involving transcranial static magnetic field stimulation (tSMS). In each session, real or sham tSMS was applied over the supplementary motor area (SMA) for 30 min, with pre and post acquisitions of resting-state fMRI (10 min). The magnetic field generated by the magnet across the brain was estimated by the finite element method in standard MNI space. The effect of tSMS on cortical, striatal, and corticostriatal activity was assessed by two-way ANOVA (Bayesian and frequentist, time x treatment interaction). Cortical, striatal, and corticostriatal activity were assessed by ISAAC analysis, as well as with classical functional connectivity (i.e., temporal correlation of the mean signals) of cortical and striatal regions. ISAAC analysis was derived analytically and validated via Monte Carlo simulation. Cortical regions were defined according to the Automated Anatomical Labeling atlas (49) modified so that the SMA is divided in its anterior and posterior parts, the pre-SMA and SMA proper (43, 44), and striatal regions were defined according to a functional parcellation (42). Further details on the materials and methods, as well as the full justification, mathematical derivation, and validation of ISAAC analysis, including additional simulations (SI Appendix, Figs. S5 and S6), can be found in SI Appendix.

Supplementary Material

Appendix 01 (PDF)

Data, Materials, and Software Availability

The anonymized, preprocessed fMRI data from the tSMS experiment used in this study, together with the list of subjects included in the HCP100 dataset have been made accessible in Zenodo (https://doi.org/10.5281/zenodo.7752283) (99), and HCP data is available from the Human Connectome Project (100). A toolbox to perform ISAAC analysis has also been made accessible as a GitHub repository (https://github.com/upsidedownbrain/isaac_analysis) (101).