Modeling the effects of transcranial magnetic stimulation on spatial attention

Thirty healthy volunteers (15 female, mean age 30.80 ± 5.31 years) were recruited for the fMRI experiment. All participants had normal or corrected to normal vision, and no psychiatric or neurological disorders, or contraindications against TMS or MRI. All participants were right-handed, with a mean laterality index of 90.77 (standard deviation, SD = 10.06) according to the Edinburgh Handedness Inventory (Oldfield 1971). Written informed consent was obtained from each participant prior to the experiment. The study was approved by the local ethics committee of Leipzig University (ethics number: 371/19-ek). We re-invited seventeen participants (8 female, age 30.12 ± 5.84 years, laterality index 91.24 ± 9.46) to participate in the TMS experiment. Selection criteria were based on fMRI results, with participants being required to show significant activation in the predefined rIPL ROI and a mean error rate in the Posner task below 30%.

We used an adapted version of Posner's location-cueing task (Rushworth et al 2001, Thiel et al 2004, Numssen et al 2021a) to trigger orienting and reorienting of spatial attention. The fMRI version of the task contained three trial types: valid, invalid, and neutral, to target different attentional processes (figure 1). The contrast between invalid and valid trials isolates attentional reorienting processes, and the contrast between valid and neutral trials defines attentional orienting processes/attentional benefits (Grosbras and Paus 2002, Peelen et al 2004). During the task, each trial started with the presentation of two rectangular boxes (each size 2.6° of visual angle, with the center situated 8.3° left or right, positioned horizontally) and a fixation cross (size 0.88°) at the center of the screen. To avoid expectancy effects, the duration of fixation (interstimulus interval, ISI) was randomly set to either 2, 3, 4, or 5 s. Subsequently, an arrow was displayed for 250 or 350 ms which served as a cue for the upcoming target location. For valid cues (60%), the arrow pointed at the side where the target appeared. Participants were trained to orient their attention towards the indicated target position while keeping their fixation at the central fixation cross. For invalid cues (20%), the arrow pointed to the opposite side of the target, which required participants to reorient their attention to the target side. Neutral cues (20%) did not contain any information about the target's location. Finally, a target was presented either at the left or right side (equally distributed) for 2 s. Participants were instructed to identify the positions of the targets by pressing the right/left button using their index and middle fingers as fast and accurately as possible.

We included a total number of 250 trials in the fMRI experiment and 500 in the TMS experiment. The fMRI scan lasted 25 min with 150 valid trials, 50 invalid trials, and 50 neutral trials. Participants had a 30 s break in the middle of the task to prevent fatigue (figure 1(a)). Before the MRI experiment, participants performed 10 trials as training outside the scanner. In the TMS experiment we specifically focused on attentional reorienting and, thus, only presented valid (75%) and invalid (25%) trial types. The ISI was shortened to 3–4 s (figure 1(b)). The stimulation lasted approximately 60 min with a short break after every 100 trials. The order of trial types was randomized across participants. Stimuli were administered with Presentation software (v20.1, Neurobehavioral Systems, Berkeley, CA).

Both functional and structural MRI data were collected using a 3 Tesla Siemens Skyra fit scanner with a 32-channel head coil. To segment the main tissues of the head (scalp, skull, gray matter (GM), white matter (WM), cerebrospinal fluid (CSF), and ventricle) for further calculation of the E-field, T1-weighted, and T2* images were acquired with following parameters: T1 MPRAGE sequence with 176 sagittal slices, matrix size = 256 × 240, voxel size = 1 × 1 × 1 mm³, flip angle 9°, TR/TE/TI = 2300/2.98/900 ms; T2* with 192 sagittal slices, matrix size = 512 × 512, voxel size = 0.488 × 0.488 × 1 mm³, flip angle 120°, TR/TE = 5000/394 ms. The T1-weighted image was also used for neuronavigation during TMS. Diffusion MRI with 88 axial slices, matrix size = 128 × 128, voxel size = 1.719 × 1.719 × 1.7 mm³, TR/TE = 80/6000 ms, flip angle 90°, 67 diffusion directions, b-value 1000 s/mm³ was acquired for the estimation of the conductivity anisotropy in the WM.

The individual activation map of attentional processing was measured by an event-related fMRI design based on the gradient echo planar (GE-EPI) sequence (60 axial slices, matrix size = 102 × 102, voxel size = 2 × 2 × 2.26 mm³, flip angle 80°, TR/TE = 2000/24 ms, 775 volumes). Participants were instructed to perform the Posner task that required spatially congruent button presses in response to visual target stimuli.

2.4.1. Preprocessing

2.4.2. Activation analysis

Seventeen of the thirty fMRI participants underwent an online TMS experiment while performing the Posner-like task (figure 1(b)). TMS pulses were applied with coil positions over the larger rIPL area using a MagPro X100 stimulator (MagVenture, firmware version 7.1.1) and an MCF-B65 figure-of-eight coil. Coil positioning was guided by a neuronavigation system (TMS Navigator, Localite, Germany, Sankt Augustin; camera: Polaris Spectra, NDI, Canada, Waterloo). The electromyographic (EMG) signal was amplified with a patient amplifier system (D-360, DigitimerLtd., UK, Welwyn Garden City; bandpass filtered from 10 Hz to 2 kHz) and recorded with an acquisition interface (Power1401 MK-II, CED Ltd, UK, Cambridge, 4 kHz sampling rate) and Signal (CED Ltd, version 4.11).

To determine the optimal stimulation intensity, we manually measured the resting motor threshold (rMT) of the participants' right index fingers with one surface electrode positioned over the first dorsal interosseous (FDI) muscle belly and one at the proximal interphalangeal joint (PIP). During the rMT measurement, we first positioned the TMS coil over the left-hand knob, which was identified based on established anatomical landmarks (e.g. Diekhoff et al 2011). The coil was initially placed at 45° to the midline, and then moved around until the optimal coil location and orientation were identified based on the MEP response. The rMT was defined as the minimum stimulator intensity to induce an MEP larger than 50 μV in at least 5 of 10 consecutive trials (Beynel et al 2019).

500 bursts of rTMS with 5 pulses at 10 Hz each were applied at 100% rMT (Rushworth et al 2001) during the 500 Posner-like task trials, comprising 375 valid trials (75%) and 125 invalid trials (25%). The bursts were initiated 20 ms after the target presentation to disrupt attentional processing transiently (figure 1(b)). After every 100 trials, a short break of ∼2 min was advised to avoid fatigue. We restricted the area over which the coil centers were located to a circular zone of 3 cm radius around the individual fMRI-derived activation peak (invalid > valid trials) in the rIPL. Stimulation area centers were moved 2 cm anterior/superior in 4 subjects because their activation peaks were close to the occipital or temporal lobe. Coil positions and orientations were randomly selected within the defined circular zone for each burst, to increase electric field variability by minimizing cross-correlations between induced electric fields (Numssen et al 2021b). The range of coil orientations was limited to 60° (±30° from the traditional 45° orientation) due to hardware constraints such as the spatial restriction of the navigation system and the obstruction of the coil handle and cable. Note that eleven participants were sampled with a 'quadrant mode': we randomly sampled 100 stimulations for each quadrant of the stimulation area, resulting in 400 trials. The final 100 trials were arbitrarily attributed across the whole stimulation area. To diminish possible sequential effects, we used a 'random mode' for the remaining six participants: all 500 trials were randomly sampled throughout the experimental session. Coil positions and corresponding behavioral responses, i.e. reaction time and accuracy, were recorded for each trial.

2.6.1. Numerical simulations of the induced electric field

2.6.2. Regression analysis

The regression approach used in this study is based on a recently developed modeling framework in the motor cortex (Weise et al 2020, Numssen et al 2021b, Weise et al 2023). The principal idea of the regression approach is to combine the outcome of multiple stimulation experiments with the induced E-fields of different coil positions and orientations, assuming that, at the effective site, the relationship between E-field and behavioral performance is stable, i.e. the same electric field strength always evokes the same behavioral output. In particular, the method leverages more information by simultaneously varying both coil positions and orientations exploiting electric field variability to avoid bias towards locations with high E-field magnitudes, such as the gyral crown.

We first discarded TMS trials with RT < 100 ms or RT > 1000 ms, and those with a coil distance $\geqslant$ 5 mm from the skin surface. After applying these exclusion criteria, the average number of trials remaining for analysis was 115 (out of 125) for the invalid condition, and 365 (out of 375) for the valid condition. Subsequently, the valid trials were randomly downsampled to match the number of invalid trials to guard against potential sample-size-dependent effects. In addition, any linear trends of RT over time were removed to mitigate potential learning or fatigue effects.

After data cleaning, we performed Linear regression analysis to identify the neural populations that are causally involved in attentional processing for every element within the ROI (Weise et al 2020). The linear relationship between E-field magnitude ${x}_{i,j}$ of TMS trial $i$ ($1\leqslant i\leqslant {N}_{{TMS}}$) at the cortical element $j$ ($1\leqslant j\leqslant {N}_{{elms}}$) and the estimated RT ${\hat{y}}_{i,j}$ is calculated:

$$\begin{eqnarray*}&&{\hat{y}}_{i,j}={\alpha }_{j}+{\beta }_{j}{x}_{i,j}\end{eqnarray*}$$

Here, $\alpha$ is the intercept and $\beta$ is the slope. We set the constraint of $\alpha$ and $\beta$ to (−3000, 3000) and (−1000, 1000), respectively.

The site of effective stimulation can be quantified by the goodness-of-fit (GOF), which would be highest at the cortical site that houses the relevant neuronal populations (Numssen et al 2021b). We assessed the element-wise GOF by the coefficient of determination ${R}^{2}:$

$$\begin{eqnarray*}&&{R}_{j}^{2}=1-\frac{{VAR}(y-{\hat{y}}_{j})}{{VAR}(y)}\end{eqnarray*}$$

where $y$ is the measured RT, and ${\hat{y}}_{j}$ is the estimated RT. The ${R}^{2}$ value measures how well the regression model explains the observed data, with higher ${R}^{2}$ denoting better fitting results. Note that ${R}^{2}$ values can range from negative infinity to 1, where negative values indicate that the chosen model does not follow the trend of the data. Negative ${R}^{2}$ values occur when the variance of the residual is greater than the variance of the data, i.e. $\frac{{VAR}(y-{\hat{y}}_{j})}{{VAR}(y)}\gt 1.$

The regression analysis was applied separately to invalid and valid trials and yielded one ${R}^{2}$ score each for valid and invalid conditions per ROI element. We replaced all negative ${R}^{2}$ values with 0, as these denote areas of poor fitting and are very small.

To assess the significance of the observed ${R}^{2}$ values and determine if they could be explained by chance alone, we carried out a permutation test for each element. This was combined with the FDR analysis to correct for multiple comparisons across different elements. Our permutation test involved randomly shuffling the RT values 1000 times. For each permutation, we calculated the linear regression between the magnitudes of E-field and the shuffled RT values. This process was repeated 1000 times to obtain a distribution of ${R}^{2}$ values from chance. We then compared the real ${R}^{2}$ value with the 1000 shuffled ${R}^{2}$ values. Only real ${R}^{2}$ values that exceeded the 95th percentile of the shuffled data were deemed statistically significant. To control the probability of false positives within the ROI, the FDR was employed to keep the false positives rate below 5% for all permutation tests (q < 0.05).

We then multiplied the raw ${R}^{2}$ value with the slope's sign to include not only the goodness of fit (${R}^{2}$) but also the direction of the TMS effect in one metric:

$$\begin{eqnarray*}&&{\tilde{R}}_{j}^{2}={R}_{j}^{2}\cdot {\rm{sign}}{(\beta }_{j})\end{eqnarray*}$$

This allowed us to visually differentiate cortical areas of inhibitory TMS effects (positive slope areas) from areas of facilitatory TMS effects (negative slope areas). We assumed that high-frequency rTMS on rIPL will selectively impair performance on invalid trials, resulting in higher ${\widetilde{R}}_{j}^{2}$ values compared to valid trials.

To generate the group ${\widetilde{R}}^{2}$ map, all individual ${\widetilde{R}}^{2}$ maps were first mapped to the group-averaged brain template, then voxel-wise ${\widetilde{R}}^{2}$ values were averaged across subjects.

Behavioral results from the fMRI experiment showed a reliable difference of RT between conditions (F_2,87 = 5.38, p < 0.01; invalid_fMRI: 403 $\pm$ 69 ms; valid_fMRI: 345 $\pm$ 70 ms; neutral_fMRI: 384 $\pm$ 72 ms). Post-hoc t-tests confirmed a reorienting effect, that is, slower RTs for invalid compared to valid targets (t₂₉ = 15.25, p < 0.01). There was no significant difference between neutral and valid or invalid trials (figure 2(a)). No significant differences were found in accuracy (F_2,87 = 0.92, p = 0.40; invalid_fMRI: 0.95 $\pm$ 0.08, valid_fMRI: 0.97 $\pm$ 0.06, neutral_fMRI: 0.95 $\pm$ 0.06).

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In the TMS experiment, we again found a significantly slower response speed for invalid relative to valid trials (t₁₆ = 12.76, p < 0.01; invalid_TMS: 357 $\pm$ 62 ms; valid_TMS: 286 $\pm$ 61 ms). In line with our hypothesis, task accuracy was also significantly decreased in the invalid condition (t₁₆ = 4.16, p < 0.01; invalid_TMS: 0.93 $\pm$ 0.06; valid_TMS: 0.99 $\pm$ 0.02) (figure 2(b)).

Note that subjects had generally faster RTs in the TMS experiment compared to the fMRI session. These behavioral differences between sessions inside and outside of the MRI scanner might be driven by unspecific distracting factors inside the scanner, such as the supine position and the noise, which could slow down motor execution times and decrease attentional focus inside the MRI scanner (Koch et al 2003, Jamadar et al 2010, van Maanen et al 2016)

The fMRI results revealed distributed bilateral brain regions from different networks for the reorienting of attention (figure 3(a)). These include the ventral attention network (IPL, MFG), the dorsal attention network (SPL, FEF), and the salience network (Insula; anterior cingulate cortex, ACC). In contrast, the default mode network (DMN) (posterior cingulate cortex, PCC; medial prefrontal cortex, mPFC) was deactivated for invalid relative to valid trials. These findings go beyond the classic view of a ventral, right-lateralized reorientation system. Relative to the neutral condition, attentional orienting showed deactivation of both IPS and SPL, but increased activation of mPFC (figure 3(b)). All activations are reported at the level of q < 0.05 after FDR correction.

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To elucidate the structure–function relationships in spatial attention, we correlated the magnitudes of the E-field with behavioral performance in the Posner task. Figure 4 displays correlation maps (i.e. ${\widetilde{R}}^{2}$ maps) obtained from the TMS mapping experiment, alongside corresponding fMRI activation maps, for all seventeen participants. Warm colors in the ${\widetilde{R}}^{2}$ maps indicate positive correlations between E-field and reaction time, while cold colors signify negative correlations. The green background indicates the group-averaged results, while the pink and cyan backgrounds represent the 'quadrant sampling mode' and 'random sampling mode', respectively.

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In figure 5, we present results of a representative subject with moderate fitting results, showcasing the linear regression maps from prominent locations. As shown at three elements (one with the highest GOF of negative linear trend, one on the activation peak, and one with the highest GOF of positive linear trend), the correlation between measured RTs and the computed E-fields did not show a clear S-shaped curve, as MEP data did (Weise et al 2020, Numssen et al 2021b).

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At the subject level, most participants showed significant correlations between E-fields and reaction time within the rIPL ROI after permutation test (p < 0.05), especially in the invalid condition (figure 4). The significant brain regions are marked by black contours in figure 4. After FDR correction, only five subjects (sub-05, sub-06, sub-12, sub-13, and sub-15) retain their significance for the invalid condition. Surviving brain regions are highlighted by light green contours. No significant results were found in the valid condition, implying that TMS selectively modulated attentional reorientation. Notably, the locations of these surviving regions are subject-specific. For instance, in sub-05, the significant region is situated in the angular gyrus, whereas sub-12 shows significant results in the supramarginal gyrus.

Furthermore, to better visualize the pattern differences between the TMS-based ${\widetilde{R}}^{2}$ map and the fMRI activation map, we highlighted the locations of both maximum ${\widetilde{R}}^{2}$ values (marked by green spheres) and the fMRI activation peak (marked by yellow spheres) across all subjects (figure 4). The distinct peak locations and patterns between these two maps underscore differences in BOLD-measured neuronal activity and TMS-evoked neuronal effects.

At the group level, the averaged ${\widetilde{R}}^{2}$ maps (figure 4) exhibit values close to zero for both valid and invalid conditions, indicating the absence of a clear-out group-level pattern in the TMS modulatory effect on spatial attention. We then extracted the individual maximum ${\widetilde{R}}^{2}$ scores both under the invalid and valid conditions for further comparison. Table 1 shows the maximum ${\widetilde{R}}^{2}$ scores for each condition. Given the dominance of positive ${\widetilde{R}}^{2}$ values within the group-averaged ${\widetilde{R}}^{2}$ map, we only present ${\widetilde{R}}^{2}$ scores that show a positive correlation between E-field and RT in table 1. A Wilcoxon signed rank test revealed a significant difference of the maximum ${\widetilde{R}}^{2}$ between the two conditions (Z = 2.979, p < 0.01; ${\widetilde{R}}_{{invalid}}^{2}$ = 0.064 $\pm$ 0.037, ${\widetilde{R}}_{{valid}}^{2}$ = 0.031 $\pm$ 0.022) (figure 6). This indicates that, when compared to the valid condition, the maximum ${\widetilde{R}}^{2}$ values are significantly higher in the invalid condition, identifying a stronger disruptive effect of the E-field on the response speed during attentional reorienting.

Table 1. Individual activation peaks and TMS results.

Subject ID	Activation peak	MT	Invalid ${\widetilde{R}}_{\max }^{2}$	Valid ${\widetilde{R}}_{\max }^{2}$
01	(56, −37, 34)	43%	0.055*	0.021
02	(42, −55, 50)	39%	0.031	0.024
03	(60, −41, 31)	70%	0.059*	0.007
04	(54, −33, 34)	47%	0.041*	0.024
05	(54, −61, 18)	57%	0.127*	0.079*
06	(62, −57, 34)	64%	0.084*	0.054*
07	(52, −53, 16)	46%	0.013	0.013
08	(42, −73, 40)	43%	0.030	0.048*
09	(56, −63, 25)	45%	0.039*	0.066*
10	(58, −47, 36)	45%	0.037*	0.02
11	(46, −69, 20)	42%	0.073*	0.036*
12	(69, −39, 34)	53%	0.152*	0.012
13	(52, −51, 31)	56%	0.071*	0.015
14	(54, −67, 27)	38%	0.074*	0.008
15	(42, −77, 29)	40%	0.109*	0.006
16	(56, −67, 34)	52%	0.047*	0.029*
17	(58, −47, 50)	44%	0.045*	0.058*
Group average	(51, −55, 32)	48%	0.064	0.031

The Activation peak column provides individual fMRI peak coordinates in the rIPL for the invalid-valid contrast in standard MNI space. The individual resting motor threshold (MT) is provided in the percentage of maximum stimulator output (% MSO), and the maximum ${\widetilde{R}}^{2},$ both for invalid and valid conditions with positive correlations between E-field and RT. *: ${\widetilde{R}}_{\max }^{2}$ remains significant after permutation test (p < 0.05).

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The ability to orient attention is a fundamental component of most perceptual-motor processes in everyday life (Natale et al 2009). Consequently, we took our first step in generalizing the regression method to spatial attention. Spatial orienting can be driven either endogenously, by predictive contingencies, i.e. top-down cues, or exogenously, by unexpected bottom-up signals stemming for example from visual inputs. These processes are accomplished by the interaction of several cortical regions, forming functional networks (Chica et al 2011). Our fMRI results show that large-scale brain networks were activated during attentional reorienting, including both dorsal and ventral attention networks, which reflects the neural bases of the interplay between these two attention mechanisms (Shulman et al 2009, Proskovec et al 2018). One of these regions, the rIPL, is consistently identified as a major network hub in diverse cognitive functions, from bottom-up perception to higher cognitive capacities that are unique for humans (Cabeza et al 2012, Igelström and Graziano 2017).

The rIPL is a large region that comprises two major gyri: SMG and AG, separated by the intermediate sulcus of Jensen (Segal and Petrides 2012). Previous studies suggested that both SMG and AG are critical for attention shifts between visual stimuli (Chambers et al 2004). A behavioral and functional connectivity-based meta-analysis study further defined the functional topography of rIPL (Wang et al 2016). This study revealed that the SMG primarily participates in attention, execution, and action inhibition, while the AG is involved in social and spatial cognition. In line with our group activation results, both SMG and AG exhibited significant activation during attentional reorientation, supporting their involvement in basic attention and spatial cognition.

It is worth noting that we found bilateral IPL and VFC activated when participants attempted to process the target at an unexpected location, which challenges the traditional view that the VAN is lateralized to the right hemisphere (Lunven and Bartolomeo 2017). The comparison of attentional orientation and neutral trials (valid-neutral) allowed us to separate attentional benefits from visual, motor, or other basic cognitive tasks (i.e. valid-baseline), and to explore the influence of cue predictiveness on spatial attention. Previous studies could not provide conclusive explanations for this effect of top-down predictions. Some researchers observed significant activation for valid minus neutral trials in either DAN or VAN (Peelen et al 2004, Natale et al 2009), while others found a significant deactivation of the rIPL when participants are orienting their attention to the predictive cues (Doricchi et al 2010). Our results demonstrate that, when attention was focused on the valid side, bilateral IPS and SPL were suppressed, potentially to prevent reorienting to distracting events. Specifically, activation of medial PFC as a part of DMN may indicate an endogenous focus. These findings provide new insight into the functional contribution of the brain regions involved in spatial attention.

We performed state-of-the-art FEM-based E-field simulations to allow for realistic quantifications of the effect of cortical stimulation on attentional processes. The analysis revealed significant correlations between E-fields and behavioral outcomes in the majority of subjects after the permutation test. However, only five out of seventeen subjects maintained their significance under the invalid condition after FDR correction. This implies that the modulatory effect of TMS on attentional reorientation is weak, exhibiting significant variability across subjects.

Supporting evidence for the specificity of the TMS effect is shown in the significantly stronger relationships observed between E-field exposure and behavioral modulation during attentional reorientation compared to attentional orientation (figure 6). However, in general, the TMS-induced effect, as measured by the coefficient of determination ${\widetilde{R}}^{2}$, was much lower for attention as compared to the motor domain where the TMS regression approach was previously established (Weise et al 2020, Numssen et al 2021b). Lower ${\widetilde{R}}^{2}$ values likely reflect the more restricted impact of the E-field on reaction time compared to its effect on muscle recruitment when stimulating the primary motor cortex.

In fact, TMS studies with cognitive paradigms often show high inter-individual variability and results are not always conclusive (Bergmann and Hartwigsen 2021). Moreover, some cognitive paradigms suffer from relatively low test-retest reliability which may contribute to the strong variability of behavioral results (Hedge et al 2018). The key problem is that the underlying neural basis of cognitive functions is much more complex and variable than that of eliciting hand muscle twitches (Fetsch 2016). In our study, in spite of this high variability, we were still able to distill out the TMS effect on attentional reorienting. However, the large amount of residual variance indicates that taking into account additional variables and more complex models (e.g. multivariate regression) is likely to improve accuracy and reliability.

We paralleled the fMRI-based activation maps with TMS-based cortical mapping to explore the gains of regression-based functional TMS mappings in the domain of spatial attention. The comparison between BOLD-measured neuronal activity obtained from fMRI and neuronal stimulation effects evoked by TMS revealed notable discrepancies. This incongruence highlights the principal distinction between neural activity being correlated with or potentially caused by particular paradigms and the activity of neural populations that exert a direct causal influence the behavioral outcomes. While fMRI provides information about overall neural responses associated with spatial attention, TMS offers insights into the specific and causal effects of targeted neural modulation.

The TMS regression approach integrates information from multiple stimulation patterns to map structure–function relationships based on the causal effect of the induced electric field. The main metric to separate cortical locations is the explained variance of the behavioral modulation (${\widetilde{R}}^{2}$). However, when applied to attentional processes, the explained variance is relatively low. In comparison to the motor domain, where up to 80% of the variance can be explained at the single subject level (Numssen et al 2021b), only 10% of the individual variance could be explained in the attention domain in the present study. These comparatively low ${\widetilde{R}}^{2}$ values for attentional processes probably stem from various sources.

As a first potential explanation for the observed discrepancy between the motor and attention domains, behavioral responses to cognitive tasks intrinsically exert higher variance due to complex processing demands (Hedge et al 2018) that give rise to confounding factors, such as fatigue or differences in the mental state. Additionally, the organization of the rIPL is challenging to study due to the complex anatomy and highly divergent functional segregation of this cortical region (Krall et al 2016, Williams et al 2022).

Another potential factor that may affect the explained variance is the spread of attentional task processing across the cortex. In contrast to the focal representations within the motor system, a multitude of cortical locations may interact with the stimulation effect during attentional processing. The TMS trials with different coil positions/orientations may differentially target cortical sites that have various functions. Some of the varying targets can accumulate and thus exert inhibitory or excitatory effects, others might neutralize the TMS effect. Previous studies confirmed that compared to single-node TMS, concurrent frontal-parietal network TMS showed a reduction of the reorienting effect in the right hemifield (Gallotto et al 2022). Therefore, network effects should be considered in future studies. One possibility would be the multivariate regression schemes.

Several limitations may have contributed to the limited explained variance. Firstly, we did not adjust the stimulation strength to account for the differences of the cortical depths between the primary motor cortex, where the rMT was assessed, and IPL, where the regression localization approach was performed. Instead, we used the same intensity of 100% rMT as in previous studies (Rushworth et al 2001) to modulate spatial attention. Ignoring potential individual differences between brain regions may have contributed to the observed variability of the current study. To elaborate on this potential shortcoming, we further computed E-field ratios between the rIPL and the M1 hotspot for all participants. This revealed that the E-field exposure in the rIPL was consistently lower (maximum ratio = 0.95, minimum ratio = 0.25, median ratio = 0.73 across subjects). Subsequently, we conducted Spearman correlation analyses to explore the relationship between the E-field ratio and the maximum ${\widetilde{R}}^{2}$ value across participants to further explore if stronger stimulation yielded better functional localization. However, the results did not reach statistical significance (${\rho }_{{invalid}}$ = 0.18, p = 0.48).

Secondly, the current study employed the 5/10 methods to determine the rMT, which is defined as the minimum stimulus intensity required to elicit a peak-to-peak MEP amplitude greater than 50 μV in 5 out of 10 consecutive trials. This rMT determination method has been reported as relatively less reliable than the 10/20 method, which requires eliciting an MEP amplitude greater than 50 μV in 10 out of 20 consecutive trials (Awiszus 2012). Therefore, the utilization of the 5/10 method could potentially contribute to additional sources of variance. Another limitation of our study is the absence of a sham TMS condition. Consequently, the left part of the input/output line, representing the linear regression between magnitudes of E-field and behavioral outcomes, is missing. This missing information could provide valuable insights into the baseline excitability of the motor cortex. In addition, while we attempted to maximize the range of coil orientations to minimize potential cross-correlations between electric fields, hardware limitations, such as the visible range of positions in the navigation system and coil handle obstruction, limited the true orientation range to 60°.

Finally, it should be noted that the interaction between internal factors such as the current brain state, fatigue, baseline performance level, and external stimulation parameters such as intensity, frequency, and duration is not well understood (Hartwigsen and Silvanto 2022). Such interactions may induce strong inter-individual variability in response to TMS in studies of cognition. Nonetheless, transferring the TMS regression approach to cognitive domains is promising and will ultimately help to optimize TMS protocols for a wide range of applications. Future work should explore network effects of different TMS protocols, dosing, and individual differences in response to TMS.