Causal functional maps of brain rhythms in working memory

Significance

Working memory is our ability to remember useful information “online” during actions. Understanding how the human brain processes working memory is an important step toward understanding the human mind and treating people with cognitive impairments. Noninvasive neurostimulation can safely and reversibly modulate specific electric neural activity, known as oscillations, in a focal brain region. If done together with working memory testing, stimulation can probe the causality of neural processes. Here, we computationally model 28 available-to-date stimulation studies of working memory and consolidate them into one brain map. Our findings that frontal-temporal theta oscillations and occipital-parietal gamma oscillations improve memory performance give an overview of critical processes in working memory and inform future cognitive and therapeutic studies.

Abstract

Human working memory is a key cognitive process that engages multiple functional anatomical nodes across the brain. Despite a plethora of correlative neuroimaging evidence regarding the working memory architecture, our understanding of critical hubs causally controlling overall performance is incomplete. Causal interpretation requires cognitive testing following safe, temporal, and controllable neuromodulation of specific functional anatomical nodes. Such experiments became available in healthy humans with the advance of transcranial alternating current stimulation (tACS). Here, we synthesize findings of 28 placebo-controlled studies (in total, 1,057 participants) that applied frequency-specific noninvasive stimulation of neural oscillations and examined working memory performance in neurotypical adults. We use a computational meta-modeling method to simulate each intervention in realistic virtual brains and test reported behavioral outcomes against the stimulation-induced electric fields in different brain nodes. Our results show that stimulating anterior frontal and medial temporal theta oscillations and occipitoparietal gamma rhythms leads to significant dose-dependent improvement in working memory task performance. Conversely, prefrontal gamma modulation is detrimental to performance. Moreover, we found distinct spatial expression of theta subbands, where working memory changes followed orbitofrontal high-theta modulation and medial temporal low-theta modulation. Finally, all these results are driven by changes in working memory accuracy rather than processing time measures. These findings provide a fresh view of the working memory mechanisms, complementary to neuroimaging research, and propose hypothesis-driven targets for the clinical treatment of working memory deficits.

Working memory (WM) is a complex cognitive mechanism for actively holding and manipulating goal-relevant information. Several decades of brain mapping studies have associated human WM with multiple neuroanatomical hubs, including frontal, parietal, temporal, and occipital regions (1–4). Conventionally, the prefrontal cortex executes top-down control (5) and short-term maintenance and manipulation of memory engrams (6). The medial temporal cortex plays a role in WM binding, associations, and dynamic relations between working and long-term memory (3, 4, 7). Superior and inferior parietal lobules host temporal manipulation of engrams in WM tasks (8, 9) and cooperate with the occipital cortex, which also encodes visual memory items (6, 10). From a neurofunctional perspective, brain areas exhibit several patterns of macroscopic electric activity resulting in brain oscillations. Oscillations, or rhythms, arise from and reciprocally coordinate synaptic communications of neural ensembles (11–13). They exist within local circuits and distant networks as a vehicle of functional cooperation. Research studies commonly associate frontal and temporal theta rhythms (3 to 8 Hz) (14), posterior alpha (8 to 13 Hz) (15), and various gamma rhythms (30 to 100 Hz) (16) with domain-general WM processes. Furthermore, a given WM paradigm can promote stimulus or task-specific rhythms, like sensorimotor beta oscillations (13 to 30 Hz) (17).

The list of anatomical and functional components runs long due to the distributed nature of WM (4), but also the associative nature of most evidence. Classic WM research involves correlating computer task actions with neuroimaging or electrophysiological recordings in humans or nonhuman primates. Although they are fundamentally important, such studies struggle to isolate the causal bottlenecks of WM processing. Scarce but viable cognitive research in patients with brain lesions gives a more causal view on neuroanatomy. Yet, lesion impact rarely confines within a single complete anatomical unit and provides little functional information regarding specific brain oscillations.

Advances in noninvasive neuromodulation, foremost transcranial alternating current stimulation (tACS), in cognitive research provide a unique perspective on functional neuroanatomy in healthy humans (18). During tACS, an oscillatory electric current is applied at a given frequency through the scalp to the brain, creating a spatially confined electric field that can entrain frequency-specific endogenous brain oscillations in a dose-dependent manner (19, 20). Unlike neuroimaging studies, which observe an inclusive cohort of brain areas where activity markers correlate to a task course or outcome, tACS experiments can reveal a select functional area whose modulation causally changes measurable outcomes. Thus, neuromodulation complements neuroimaging to achieve a comprehensive understanding. Numerous studies tested the causal impact of stimulating brain oscillations on WM tasks, showing an improvement in performance due to entrainment of functionally relevant regions and rhythms (21–23). Alternatively, tACS at incompatible parameters can disrupt behavioral efficiency (24).

Several recent meta-analyses summarized the effects of tACS on working memory (25) or broader-defined cognitive performance (26) and found significant stimulation effects of moderate size. Moreover, previous meta-analyses show comparable effectiveness of tACS in normal adults, elderly populations, and clinical populations with cognitive deficits (26). Nevertheless, traditional meta-analyses consider experimental studies according to declared stimulation parameters, such as electrode location or total current intensity, without considering how tACS manifests in the brain across target and unavoidable off-target locations. Computational modeling can take tACS biophysics into consideration and offer novel insights (18). That is, we can virtually simulate any tACS intervention and precisely estimate the induced electric field at any point in the brain, revealing the applied “dose” per anatomical voxel (27, 28). So, we can assess the causal relationship between regional functional changes and behavioral consequences.

Here, we synthesize causal functional maps of domain-general WM using a meta-modeling of tACS studies. A meta-modeling leverages large-scale computational simulations of published experiments to establish the populational relationship between WM performance and oscillatory modulation of brain regions. We identified 28 placebo-controlled tACS studies in anatomically normal adults assessing WM, which reported 64 intervention types including a variety of anatomical targets, stimulation intensities, and oscillation frequencies. We simulated each intervention in 100 neurotypical adult brains for a total of 6,400 computational models, projected them into a common brain space per a frequency band, and analyzed induced electric fields against reported behavioral consequences, such as WM accuracy and processing time. These functional maps identify the most sensitive neuroanatomical regions per oscillation rhythm for modulating domain-general WM.

Results

The available data features a total of 39 different stimulation electrode positions (21–23, 29–53), each resulting in a unique combination of anatomical target and off-target brain areas. The frontal cortex was targeted most frequently, as was indicated by the largest average induced electric field across studies (Fig. 1A). The smallest average electric field was in the occipital regions (46.3% of the average maximum), which were least targeted across all studies. Together, studies reported 64 intervention types or substudies, commonly with several outcome measures per intervention type. Such outcome measures include WM accuracy and processing time per one or several WM tasks and difficulty levels. Out of a total of 298 outcome measures, 58.4% characterized modulation of theta oscillations (3 to 8 Hz), and 35.2% — gamma oscillations (30 to 100 Hz) (Fig. 1B), whereas in the remaining 6.4% of the studies other frequencies were targeted. The outcome measures cover a variety of WM modalities. The WM stimuli were presented visually (82.8%), acoustically (14.3%), or as a combination of both (2.9%). The cognitive tasks measured phonological verbal (letter or word), phonological numeric, spatial, object, and color memory domains (Fig. 1C). An overview of all experiments and stimulation parameters is in SI Appendix, Table S1. Overall, available data covers the anatomical brain space well, enabling our causal mapping. We focus subsequent frequency analyses on theta and gamma bands, as the most studied to date, and WM analysis on domain-general features, by averaging over various available task domains.

Fig. 1.

Overview of the available studies in WM. (A) Average weighted electric field on the neocortical surface across all unique stimulation montages. Warm colors indicate regions where on average electric fields were strong, whereas cold colors indicate regions where electric fields on average were weak. Stronger electric fields also indicate more commonly sampled areas across the studies. (B) Summary of the original experimental papers. The Left diagram depicts the proportion of stimulation frequencies (one frequency per condition), excluding 6.4% of outcome variables related to neither theta nor gamma frequencies. The Right diagram depicts explored WM modalities (visual, auditory, audio-visual) and domains [color, phonetic (word, letter), spatial, numeric, object]. (C) Summary of the tACS effects on WM for the primary target stimulation conditions and control stimulation conditions, including control frequencies and locations, across all studies and separately for theta and gamma stimulations (in Hedges’ g). See SI Appendix for the effect sizes of all 298 individual outcome measures.

The included outcome measures reflected both “target” conditions, typically the main intervention, and a variety of control conditions, such as off-target stimulation locations, frequencies, and intensities. When considering only target conditions, tACS has a beneficial effect on WM performance (median Hedges’ g = 0.54; Fig. 1C). Control conditions did not alter WM performance. These nonsignificant conditions are crucial for the meta-modeling approach because they provide variance at each location of the brain map for our statistical analysis and information on nonsignificant loci of brain oscillations. A distribution of all 298 outcome variables individually is shown in SI Appendix, Fig. S1.

Functional Maps of Theta and Gamma Oscillations in WM.

To map the causality of theta and gamma oscillations in domain-general WM, we analyzed the relation between tACS-induced electric field strength in the brain and behavioral effect sizes per spatial node, per outcome measure, and across our virtual population of neurotypical adults (N = 100). This performance-to-electric field index (PEI) represents the likelihood of a given brain loci being causally involved in memory processing and the strength of its involvement. The resulting population-average maps consist of positive and negative PEI values corresponding to improved or reduced WM performance due to frequency-specific brain stimulation, respectively. For subanalyses, the maps are parcellated at the anatomical level on 44 regions (54) and at the cytoarchitectural level on 360 subregions of HCP-MMP atlas (55).

Theta entrainment in the frontal and temporal regions led to significant positive PEI values (PEI_MAX = 0.260, P < 0.001; Figs. 2 and 3). In particular, the causal improvement was strong in the right and left orbitofrontal regions (right: PEI = 0.214, P = 0.005; left: PEI = 0.150, P = 0.049), right medial prefrontal cortex (PEI = 0.179, P = 0.018), right medial temporal cortex (PEI = 0.166, P = 0.029), and right insular region (PEI = 0.175, P = 0.021). These effects are moderately biased to the right hemisphere. Together, these regions formed a continuous significant cluster (p_cluster = 0.031, SI Appendix, Fig. S3). Subsequent analysis reveals significant PEI in 50 subregions (10 and 40 in the left and right hemisphere, respectively) of the Glasser atlas (PEI range: 0.149 to 0.236, P = 0.049 to 0.002; Fig. 3), spanning Brodmann areas 10 (frontopolar cortex), 11 (anterior orbitofrontal cortex), 13 (posterior orbitofrontal cortex), 35 (perirhinal cortex), 36 (ectorhinal cortex), and 38 (temporal pole). Theta entrainment led to no significant negative relationships (PEI_MIN = −0.054, P > 0.4; no identified clusters, SI Appendix, Fig. S3). Together, these results suggest that theta oscillations in the ventral prefrontal area causally improve WM performance.

Fig. 2.

Causal functional maps of brain oscillations in WM. Theta entrainment (3 to 8 Hz) in prefrontal and anterior temporal regions improved WM performance (warmer colors), whereas gamma entrainment (30 to 100 Hz) in the same regions decreased it (colder colors). In contrast, entrainment of gamma oscillations in occipital and parietal areas supported WM improvement.

Fig. 3.

Parcellated functional maps. Inflated brains display significant subregions according to the HCP-MMP atlas for theta and gamma entrainment in both hemispheres. Additionally, averaged PEI values per head model (N = 100) are shown for each complete cortical region according to Huang et al. (54). Significant positive subregions and whole regions are highlighted with orange color. Significant negative subregions are depicted in blue color (no complete cortical region showed significant negative PEI). A spatial representation of significant cortical regions is provided in SI Appendix, Fig. S2.

For gamma entrainment, significant effects occurred in bilateral occipital, parietal, and frontal areas (PEI_MAX = 0.259, P < 0.001; Figs. 2 and 3). Positive PEI emerged in the right posterior and occipital cortical divisions, specifically early visual regions (PEI = 0.235, P = 0.021), dorsal visual stream (PEI = 0.234, P = 0.016), ventral visual stream (PEI = 0.213, P = 0.029), lateral occipital complex (PEI = 0.235, P = 0.016), temporal-parietal-occipital junction (PEI = 0.219, P = 0.025), posterior cingulate cortex (PEI = 0.206, P = 0.035), and inferior (PEI = 0.207, P = 0.034) and superior parietal cortex (PEI = 0.216, P = 0.027). Furthermore, we found positive PEI in bilateral primary visual area V1 (left: PEI = 0.195, P = 0.046; right: PEI = 0.237, P = 0.015). Together, these regions formed a significant positive cluster (p_cluster = 0.044, SI Appendix, Fig. S3). Subregion analysis showed significant PEI in 84 subparcels (20 and 64 in the left and right hemisphere, respectively; PEI range: −0.240 to 0.241, P = 0.049 to 0.013; Fig. 3), spanning Brodmann areas 7 (superior parietal sulcus), 31 (dorsal posterior cingulate cortex), 39 (temporo-parietal junction), and 40 (intraparietal sulcus). Importantly, significant negative relationships between the gamma modulation and WM were found in the orbitofrontal and dorsolateral prefrontal cortex, across the parcels within the Brodmann areas 9 and 10 (PEI = −0.240 to −0.195, P = 0.013 to 0.046). Indeed, this negative relationship in prefrontal regions was confirmed by the cluster-based analysis (p_cluster = 0.001, SI Appendix, Fig. S3). Thus, entrainment of gamma oscillations in occipitoparietal regions improved WM performance, whereas in entrainment in frontopolar areas decreased it.

Distinct Role of Low and High Theta Oscillations.

Given possibly different roles of low and high theta oscillations in the brain (23, 56), we investigated the causal spatial map of low vs. high theta oscillations in domain-general WM. For low-frequency theta oscillations (3.5 to 6 Hz), positive associations emerged in the orbitofrontal area (PEI = 0.247, P = 0.006), anterior cingulate cortex (PEI = 0.199, P = 0.029), medial temporal cortex (PEI = 0.217, P = 0.017), lateral temporal cortex (PEI = 0.204, P = 0.025, and insula (PEI = 0.208, P = 0.022; Fig. 4), forming a significant cluster (p_cluster = 0.023, SI Appendix, Fig. S3). These effects occurred in the right hemisphere and no negative relations were observed. For high-frequency theta entrainment (6 to 8 Hz), a positive association with WM performance arose in the left inferior frontal cortex (PEI = 0.326, P = 0.017), left orbitofrontal cortex (PEI = 0.305, P = 0.026), and left dorsolateral prefrontal cortex (PEI = 0.272, P = 0.049). Conversely, high theta entrainment showed a trend toward worsened WM performance in select visual and parietal cortical subregions. While no complete anatomical region reached significance (P > 0.05), a significant posterior spatial cluster was identified (p_cluster = 0.016, SI Appendix, Fig. S3).

Fig. 4.

Causal functional maps of low and high frequency theta entrainment. The Top row displays the brain from the top (dorsal) view and the bottom row shows the brain from the bottom (ventral) view. For each view and metric, the Left brain image depicts the PEI (effect size) and the Right brain image depicts the significance thresholds.

Theta and Gamma Oscillations in WM Accuracy vs. Processing Time.

Finally, we investigated whether theta and gamma entrainment differentially affect the WM accuracy (e.g., percentage of correct responses, number of errors, sensitivity) and processing time (e.g., reaction time, completion time). The accuracy was positively associated with theta entrainment (cluster-based permutation analysis p_cluster = 0.035, SI Appendix, Fig. S3), specifically in the right orbitofrontal cortex (PEI = 0.218, P = 0.012; Fig. 5), anterior cingulate cortex (PEI = 0.184, P = 0.034), medial temporal cortex (PEI = 0.187, P = 0.031), and insula (PEI = 0.187, P = 0.031), with no negative relationships. The WM accuracy improvements related to gamma entrainment in the posterior cingulate cortex (PEI = 0.286, P = 0.027), superior (PEI = 0.305, P = 0.018) and inferior parietal region (PEI = 0.305, P = 0.018), temporal-parietal-occipital junction (PEI = 0.322, P = 0.012), as well as all occipital cortical divisions (P < 0.05), forming a significant cluster (p_cluster = 0.031). Some subregions in the orbitofrontal cortex, specifically Brodmann areas 10 and lateral 11 (PEI = −0.341 to −0.260, P = 0.007 to 0.045), showed a negative association between the gamma rhythms and WM accuracy. While no individual complete cortical region reached significance (P > 0.05) a significant posterior cluster was identified (p_cluster = 0.004, SI Appendix, Fig. S3). For the processing time, no significant clusters were identified (p_cluster > 0.05) and no complete cortical divisions reached significance (P > 0.05) neither for theta nor gamma entrainment (SI Appendix, Fig. S3). However, eight prefrontal subregions (within Brodmann Areas 9 and 10, left and right) showed a positive association between the theta rhythms and processing time (PEI = 0.368 to 0.310, P = 0.018 to 0.049).

Fig. 5.

WM accuracy and processing time. Causal functional maps and significance maps of theta and gamma oscillations in WM separately for accuracy and processing time outcomes. The Top row displays the brain from the top (dorsal) view and the Bottom row shows the brain from the bottom (ventral) view. For each view and metric, the Left brain image depicts the PEI (effect size) and the Right brain image depicts the significance thresholds.

Control Analyses.

First, we ruled out possible sampling bias in anatomical targets between the theta and gamma tACS studies. For that, we separately calculated the average induced electric field across substudies that targeted theta oscillations and gamma oscillations. A comparison of the two averages shows high intermap correlation (r = 0.96) and a minor absolute difference (<15%) in stimulation strength in the brain regions with significant effects, such as prefrontal, temporal, parietal, and occipital cortices (SI Appendix, Fig. S4).

Second, we performed a leave-one-out analysis at the study level to identify whether a single experimental study disproportionally drives our meta-modeling findings. The causal maps were recalculated 28 times, leaving out one study each time. The variability between the recalculated maps is low (<10%, as shown in SI Appendix, Fig. S5), and their average is not different from the main results, indicating that our findings are reasonably robust.

Third, we investigated whether putative outliers in the WM effect sizes could bias our findings. We reestimated the relationship between electric fields and Hedges’ g using nonparametric rank-order statistics (non-parametric PEI). The nonparametric maps are well comparable to the original PEI maps (inter-map correlation r = 0.91 for theta and r = 0.95 for gamma maps; SI Appendix, Fig. S6), leading to identical interpretations.

Finally, we tested possible bias in our findings due to unequal sample sizes. We again recalculated the relation between electric fields and Hedges’ g, this time weighted by study recruitment numbers (weighted PEI). Weighted to unweighted intermap correlations of r = 0.97 for theta and r = 0.99 for gamma maps show that sample sizes of individual studies do not affect our conclusions (SI Appendix, Fig. S6). Similarly, we controlled for inequality in the number of outcomes between accuracy and performance time (PT). We estimated alternative weighted PEI using a proportion of outcomes as a weighting factor. The resulting maps are shown in SI Appendix, Fig. S7, indicating little-to-no difference from the original results (linear correlation r = 0.98 for theta and r = 0.99 for gamma maps).

Exploratory Analyses.

To calculate the spatial overlap between the causal WM maps derived here from the neuromodulation studies and functional maps known from the functional MRI (fMRI) studies, we calculate the Dice similarity coefficient (57) between them. The neuroimaging map was generated from meta-analytic NeuroSynth base (58). It represents an association test significance map (p_FDR ≤ 0.01) displaying areas reported more often in fMRI articles that mention “working memory” (1,091 articles) relative to other fMRI articles. The spatial overlaps for theta, negative gamma, and positive gamma clusters separately with the neuroimaging statistical map are small but significant according to the permutation test (theta Dice coefficient: 0.136, P < 0.001; gamma negative Dice coefficient: 0.119, P < 0.001; and gamma positive Dice coefficient: 0.155, P < 0.001). The overlapping regions are depicted in SI Appendix, Fig. S8. Thus, neuromodulation and neuroimaging provide a complementary picture of WM processes.

Finally, we show the applicability of synthesized causal functional maps for optimizing tACS interventions in humans. We performed a stimulation montage optimization using the SimNIBS 3 targeting framework (59) on a single exemplary subject for targeting theta cluster, positive gamma, and negative gamma clusters. The optimized electrode montages (SI Appendix, Fig. S9) generate the desired electric field at sufficient strength (≥0.3 V/m) (19) while satisfying common technical constraints (18). Future experimental work could employ similar optimization strategies for their participants or population templates using our causal functional maps as targets, which we made available online (zenodo.org/records/10651639).

Discussion

Here, we synthesize causal maps of gamma and theta oscillations in the brain underlying domain-general WM using a computational meta-modeling of neuromodulation studies. Our analysis of 298 behavioral outcomes following 64 specific types of noninvasive neuromodulation in 1,057 neurotypical adults finds that stimulated theta oscillations in the anterior prefrontal cortex and medial temporal cortex increase WM performance. Similarly, a positive relation is evident for stimulated gamma rhythms in the parietal and occipital regions. On the other hand, entrainment of frontal gamma oscillations is impairing WM performance. Other neocortical areas show no consistent causal impact on the WM tasks. We also found that these results are mainly driven by changes in task accuracy rather than processing time. Finally, we observe an overlapping but distinct spatial expression for low- and high-frequency theta oscillations. Lower theta oscillations are centered in the medial temporal and insular cortices, whereas higher theta oscillations are centered in the orbitofrontal and anterior parts of medial prefrontal and inferior frontal cortices.

Theta entrainment in orbitofrontal, medial frontal, and medial temporal regions strongly relates to WM performance. Medial frontal regions are most commonly considered the primary WM hub (27, 60, 61). This area, interconnected with the anterior cingulate and other prefrontal divisions, generates mid-frontal theta activity elevated during cognitive tasks (62). Our meta-modeling indicates that higher theta rhythms are specifically engaged in WM in the medial prefrontal cortex. We found another causal hub of prefrontal theta activity in the orbitofrontal cortex (63, 64). Canonically, orbitofrontal theta is not directly associated with WM performance but rather with motivation, reward drive, and general cognitive performance (63, 65). Stimulating theta oscillations in this area can indirectly benefit WM task performance. Consistent with our findings, these frontal theta oscillations peak around 6 Hz in the literature (62, 63, 66), higher than classic hippocampal memory-related theta rhythms (67). Interestingly, we found that modulation of both low and high theta oscillations in the orbitofrontal cortex leads to changes in WM. This can be due to specific connectivity of the orbitofrontal cortex with the deeper anterior cingulate area or because the orbitofrontal theta peak of ~6 Hz falls in between the definition of high and low theta rhythms. The hippocampal formation and the medial temporal cortex are known to generate theta oscillations, including episodic memory-related activity. Disruption of hippocampal theta using optogenetic intervention in mice abolished WM retrieval (68, 69). Furthermore, deep brain stimulation of the medial septal nucleus, the generator of hippocampal theta in mice, has shown to improve WM (70). As part of the salience network (71), the insula likely fulfills an ancillary role in highlighting important stimuli and suppressing irrelevant stimuli during working memory tasks (72–74). Here, we find independent evidence of the causal relationship between medial temporal theta and WM using noninvasive neuromodulation in neurotypical humans. Crucially, these effects emerge at lower theta rhythms, which distinguishes this hub from the medial prefrontal cortex. Both low- and high-frequency theta oscillations exist in the temporal cortex and hippocampal formation (56); however, whereas high-frequency oscillations relate to spatial navigation (56), low hippocampal theta was found to correlate with WM performance (75, 76).

Gamma activity is commonly associated with local neural spiking, including spike coding in WM (16, 77–79). Invasive recordings in nonhuman primates have demonstrated that neural spiking during WM maintenance is coupled to increased parietal local-field potentials in the gamma range (80). This relationship between parietal gamma and WM is also shown in human imaging studies (81, 82). Here, we found the causal improvement of WM performance due to the occipitoparietal stimulation. This can be a general mechanism of encoding, e.g., in the canonical fronto-parietal network (6, 83). Nevertheless, we should note that a majority of studies included in our meta-modeling used visual presentation to test WM performance. As such, the occipital hub could be more specific to visual encoding. Future studies in nonvisual paradigms will have an opportunity to explore this specialization further. The significant inverse relationship between the stimulated gamma in the frontal cortex and WM is intriguing. We may speculate that prefrontal gamma arises only in short periods during the WM task (16), and conventional neuromodulation disturbs this delicate timing. Alternatively, the prefrontal gamma activity coordinates with other concurrent processes and loses precision when modulated in isolation. One candidate mechanism is the cross-frequency coupling of gamma rhythm to theta waves (84). Neuromodulation studies that stimulated cross-frequency theta and gamma rhythms in synchrony found that only select connectivity patterns result in WM improvement (21).

Here, the causal relations between WM and functional anatomical hubs are driven mainly by task accuracy and less by task processing time. Gamma entrainment does not affect WM speed, while theta rhythms are only moderately associated with it in a small orbitofrontal region. This can be due to the relative robustness of task processing time in neurotypical adults. Although psychometric research points toward a positive association between WM capacity and processing speed, task accuracy is arguably a more direct feature of WM encoding, maintenance, and capacity, whereas processing time more broadly reflects cognitive speed (85, 86).

It is essential to distinguish between our neuromodulatory WM maps and the neuroimaging findings. Neuromodulation, such as tACS, probes the causality of brain oscillations and provides a map of processing “bottlenecks” in the brain. However, a region or process could theoretically play a role in WM performance without having a measurable impact on the overall behavior following its facilitation or inhibition. For example, this can be due to a bottleneck further down the processing chain, an overwhelming robustness and performance overhead of the target process, or effective parallel routes of computations. Prime example, the dorsolateral prefrontal cortex (DLPFC), a canonical hub of WM (61, 87), is not significantly associated with any modulation in our meta-modeling. This is not to say that the DLPFC is irrelevant for WM. Persistent activity in the DLPFC arises during the active maintenance and manipulation of memory items (60). Its lesions result in detriments of information manipulation (87). However, our meta-modeling suggests that the DLPFC involvement in WM is either weakly dependent on a specific brain oscillation and governed by other neural mechanisms, such as fast neuroplasticity, or does not present a WM bottleneck. Overall, our exploratory analysis indicates a small but significant overlap between the classic WM hubs seen in functional neuroimaging literature and novel neuromodulatory causal maps. Interestingly, the causal theta map coincides with the most anterior hubs of the fMRI network, while causal positive gamma cluster overlaps with posterior regions. Thus, the causal mapping we provide here and previously identified WM networks in the neuroimaging observational studies paint a complementary landscape of WM in the brain.

Our meta-modeling represents a computational approach to the synthesis of neuromodulation studies (27). Rather than grouping the experimental studies by a few arbitrary characteristics (e.g., those that aimed at the prefrontal vs. parietal cortices) and ignoring all other parameters (e.g., collateral or “off-target” brain areas), we computationally simulate each neuromodulatory intervention in all available detail using finite element method head modeling (28, 88, 89). This gives us a neuromodulatory dose (that is, the strength of the induced electric field) in every brain voxel during every intervention, which we then statistically test against known behavioral outcomes. Our simulations are performed in head models representing a population of neurotypical adults before grand-averaging individual maps into a common brain space. As a result, the findings are generalizable and reasonably robust against the individual differences of brain anatomy and uncertainties of real-life experiments. Furthermore, our key statistical index (performance-to-electric field index, PEI) is a relative measure, which makes it resilient against putative sources of variability in absolute values of the induced electric fields (18, 27, 90). Overall, the present methodology is an advanced and reliable framework for synthesizing rather than describing brain stimulation findings.

We evaluated the functional anatomical maps across all neocortical areas and gamma and theta oscillations. These brain oscillations have been the focal point within WM research for a long time (14, 15). Accordingly, cognitive neuromodulation studies mostly targeted theta and gamma frequencies. More recently, other brain rhythms such as delta, alpha, and beta, as well as cross-frequency connectivity patterns, were also postulated as important for domain-general WM (1). Although some recent neuromodulation research is exploring these processes, the number of published placebo-controlled reports is low for now. Future investigations in the brain stimulation field will clarify the causal role of these oscillations. Anatomically, our data reasonably covered all neocortical locations, with a moderate bias toward the frontal cortex. Noteworthy, the most focused region in the neuromodulation literature — the dorsolateral prefrontal cortex, showed no significant causality for any condition. Thus, the moderate anatomical representation bias within the neocortex has a minimal impact on our conclusions. Causal involvement in WM of deep subcortical regions remains an open question. Here, we consider studies that use tACS, which can be done in healthy adults and is a noninvasive method with the main effect in the neocortex. Although most established hypotheses of WM postulate its primary anatomical origin within the neocortex (4), recent findings in patients with epilepsy or Parkinson’s disease using deep brain stimulation suggest that deep subcortical regions may play a causal role in WM too (91). Advances in tACS research with computationally optimized montages and high doses (18) will improve tACS of brain oscillations in the deeper brain areas.

The functional maps can be interpreted as relevant for domain-general WM processes. We should note that ~80% of studies analyzed here presented memory tasks visually, reflecting the imbalance in the investigation of different sensory systems seen across cognitive science and, thus, impacting our knowledge about WM. Nevertheless, we synthesized causal maps from WM studies that used various tasks in phonological verbal, phonological numeric, spatial, object, and color memory domains. Thus, our findings reasonably represent the “common denominator” of neuromodulatory WM research. It is most likely that specific memory types are associated with additional domain-specific functional brain hubs. Growing number of cognitive neuromodulation studies will enable more detailed meta-analyses in the future. Furthermore, it will be interesting to explore various subprocesses of WM, such as encoding and retrieval phases. This will require new neurostimulation paradigms that specifically apply stimulation during a select subprocess, which is rarely done today. Finally, several pioneering tACS studies costimulated multiple brain areas to explore interregional connectivity (22, 24, 92, 93) or cross-frequency interactions (21, 22). However, the number of studied neuromodulatory paradigms is currently insufficient for meta-modeling, and the effects of connectivity modulation will remain for future research.

Present findings build on the experimental studies conducted in neurotypical adults. One may consider if they can translate into experimental interventions in patients with WM deficit, such as mild cognitive impairment. Although their functional networks are likely altered and specific hubs, like prefrontal activity, diminished (94), one therapeutic strategy using tACS could be to promote brain activity typical for healthy adults. Thus, our causal maps could serve as the normative map for an intervention. The strategy of individual head modeling with stimulation optimization, which we showed in the exploratory results section, can compensate for moderate changes in patients’ brain anatomy to support such efforts.

In conclusion, anterior prefrontal and medial temporal theta oscillations and occipitoparietal gamma oscillations present crucial functional anatomical hubs that causally control the working memory performance in adults. Our functional mapping synthesizes more than a decade of findings in modern neuromodulatory cognitive research using placebo-controlled transcranial alternating current stimulation. These results provide a fresh viewpoint on the mechanistic understanding of working memory and offer hypothesis-driven targets for neuromodulatory treatment of working memory deficits underlying cognitive impairment disorders.

Materials and Methods

Study Sample.

After an extensive search in PubMed and Web of Science Core Collection by two experts independently, we identified and collected data from 28 studies, consisting of a total of 1,057 participants, that applied tACS and a placebo/sham protocol (placebo-controlled design) to modulate WM performance. Studies were selected if: I) they were written in English, II) they were published in a peer-reviewed journal, III) full-text was available, IV) they allowed for the extraction of mean and SD on at least one measure related to WM performance, V) there was a placebo or sham control, VI) effect sizes were reported or mean and SD could be extracted to calculate effect size. These 28 studies employed 64 active intervention types using different stimulation intensities, stimulation electrode locations, and stimulation frequencies. Each substudy investigated one or several outcomes (reaction time and/or accuracy, stimulation time courses, task difficulty levels), resulting in 298 outcome measures in total. See SI Appendix, Table S1 for details.

Effect Size Estimation.

We calculated the placebo-controlled standardized effect size expressed in Hedges’ g. To obtain this measure, first, the mean difference between sham (placebo) and active tACS was calculated. This means for each outcome measure (accuracy, RT, etc) the score during or after sham tACS was subtracted from the score during or after active tACS (score_active – score_sham). In the case that a study reported baseline measurement, performance was baseline-controlled by subtracting it from the performance during or after sham or active tACS [(score_active – score_{active_baseline}) – (score_sham – score_{sham_baseline})]. Subsequently, placebo-controlled and baseline-placebo-controlled mean scores were divided by the pooled SD, resulting in the Cohen’s d standardized effect size estimate. Hedges’ g is equivalent to Cohen’s d, but with a sample size bias correction, useful for studies with small sample sizes (n < 20) (95). In our analysis, Hedges’ g above 0 reflect improved performance, such as higher accuracy or lower reaction time, whereas values below 0 indicate worsening of performance. These effect size estimates were used for meta-modeling (described below).

To estimate the cumulative effect size, we performed random effects modeling. This cumulative effect was calculated first for all included outcomes. Then, subgroup cumulative effects were calculated for theta stimulation, low-theta (>3 and <6 Hz) stimulation, high-theta (≥6 and ≤8 Hz) stimulation, theta stimulation with performance outcomes, theta stimulation with processing time outcomes, gamma stimulation, gamma stimulation with performance outcomes, and gamma stimulation with processing time outcomes (Fig. 1B). If a substudy used variable stimulation frequency within a specific frequency band (e.g., individual theta frequency), we categorized such condition according to the reported average stimulation frequency.

Head Models and Electric Field Modeling.

We simulate induced electric fields in the brain for each intervention type in 100 healthy adults (aged 22 to 35, 50 females) to represent a typical tACS study population. The brain images (T1-weighted and T2-weighted structural magnetic resonance images; MRIs) of these adults were randomly selected from the Human Connectome Project (HCP) database. We used SimNIBS 3.2 framework (pipeline headreco) to generate individual realistic head models for computational simulations (28). The framework uses SPM12 and CAT12 to perform automatic tissue segmentations and surface reconstruction (96, 97). These reconstructions were later manually inspected by an expert in human anatomy and corrected, if needed. The resulting data are adaptively meshed using Gmsh (98) into finite element method (FEM) models consisting of ~5 to 6 million tetrahedra with 6 distinct tissue types. These are the skin, skull, cerebrospinal fluid, eyes, gray matter, and white matter with assigned conductivity representative of biological tissue. As tissue conductivities differ interindividually, we simulated this variability in our virtual population by assigning different conductivity values to each head model from a distribution that represents healthy human tissue properties (99). Specifically, scalp, skull, and gray matter conductivities were drawn from the Beta(3,3) distribution, commonly used in uncertainty modeling, while CSF, white matter, and eyes conductivities were fixed as their specific values have little impact on the generated electric field (100). Resulting conductivities are σ_skull = 0.002 to 0.03 S/m, σ_skin = 0.2 to 0.6 S/m, σ_CSF = 1.66 S/m, σ_eye = 0.5 S/m, σ_GrayMatter = 0.1 to 0.6 S/m, and σ_WhiteMatter = 0.14 S/m). The resulting mesh represents anatomically precise head anatomy in the native subject space. The stimulation electrodes were modeled and positioned on the head according to the detail in the paper (matching the shape, size, material, cable plug location, and orientation, if provided), after which tACS at a given intensity was simulated in SimNIBS to estimate the magnitude of the induced electric field in the brain. Finally, we transformed each head model into the normalized FreeSurfer Average (fsavg) space to allow for intersubject analysis. Of note, it is essential to first model tACS in individual head models and then project them into the standard brain space rather than model tACS in a standard brain atlas directly, because the brain atlases could misrepresent the head tissues outside the brain (CSF, skull, skin), which are critical for accurate modeling (101). The results were analyzed using Gmsh and MATLAB 2023a.

Displaying Results using HCP-MMP Atlas.

We used the Human Connectome Project multimodal parcellation atlas (HCP-MMP) to obtain averaged results for different brain regions (55, 102). The HCP-MMP parcellates the brain into 180 regions per hemisphere (360 subregions in total). We use the terminology “subparcels” or “subregions” when discussing these. A more general categorization of the HCP-MMP into 22 broader areas per hemisphere was also used (54). To these we refer as “cortical divisions” or “regions.” Electric field values and performance-electric field indices (explained below) were averaged per subregion and weighted by node areas. That is, differences in the exact size elements in the model were taken into account when averaging regional data.

Averaged Electric Fields across Studies.

We identified 64 intervention types (substudies) that targeted a variety of prefrontal, parietal, and temporal neocortical regions. To explore possible regional bias, we calculated the average electric field values across nodes per region, which were weighted by the node area to account for the variable element sizes in FEM models., This results in a map showing which regions were targeted the most and which the least across all studies (Fig. 1A).

WM PEI.

To identify brain regions where tACS electric fields causally relate to altered WM performance, we estimated the PEI, as suggested and validated before (27, 103). At each surface node (or triangular region) of the head models the electric field values are correlated with the corresponding Hedges’ g values for the outcome measure of interest. In the main analysis, the number of nodes corresponds to the FreeSurfer average (fsavg) brain space (327,684 nodes). Given 298 outcome measures, this resulted in one 327,648 × 298 matrix of E-field values per head model. Then, we estimated a linear Pearson correlation between the selection of columns in the matrix above related to a specific condition (e.g., theta stimulation) and corresponding outcome (Hedges’ g) values. This procedure results in a vector of 327,648 PEI values in the fsavg space. For some control analyses, nonparametric Spearman or linear weighted Pearson correlations were estimated instead (Control Statistical Analyses). For a subset of analyses, we looked at the HCP-MMP parcellations (180 parcels per hemisphere) (55) and cortical divisions (22 regions per hemisphere) (54). PEI maps were generated for each head model (100 subjects) and combined into a single brain space by averaging the PEI values across the models. Here, we treat all WM outcome measures as independent from each other, whether they were estimated in the same empirical study or different, because, in the absence of the single subject data in most empirical studies, it is not possible to evaluate a degree of putative association between the outcomes. A PEI value below 0 reflects a negative association between the electric field and Hedges’ g, i.e., tACS over this region relates to reduced WM performance. A PEI value above 0 reflects a positive associated between the electric field and hedges g, i.e., tACS over this region relates to increased WM performance. In the results, we report the PEI values averaged for cortical divisions and subregions weighted by the node area, as well as the corresponding two-sided P-value from the nonparametric permutation tests. Note, the causal interpretation of tACS-induced effects on WM performance arises from the experimental study designs, whereas the performance is measured after the tACS onset.

Statistical Analysis and Functional Mapping.

Analyses were performed for different frequencies, and types of outcome measure. Specifically, separate PEI maps were generated for studies that applied theta tACS (3 to 8 Hz; N = 174) and gamma tACS (>30 Hz, N = 105). Other frequency bands were not explored as the sample size for them was too small. Then, we generated separate PEI maps for low (>3 and <6 Hz, N = 121) and high (≥6 and ≤8 Hz; N = 53) theta tACS. This analysis was rooted in recent studies providing evidence for differential effects of slow and fast theta oscillation in WM performance (23, 30). In these first two analyses, all outcome measures (accuracy and speed) were included. Next, we performed separate analyses for outcome measures of performance speed, such as reaction time and completion time (theta N = 41, gamma N = 45), versus outcome measures of accuracy, such as percentage correct and d prime (theta N = 133, gamma N = 41).

After calculation of PEI, additional permutation testing was performed to provide an indication of significance. For this, a null model was generated by performing 1,000 permutations where PEI values were randomized per element. This null-model reflects a distribution of spurious PEI values. The actual PEI values were then compared to the distribution (approximately Gaussian) of the null-model permutations, which results in a P-value. Two-sided P-values were reported in separate p-value maps. For illustration of significant PEI and P-values at different subregions, we utilized the ggseg library available for R (version 4.3), which allows for displaying HCP-MMP subregions on an inflated brain surface.

We performed a nonparametric cluster-based permutation test (104) to control for the multiple comparisons problem on identified functional maps. After estimating the PEI and corresponding significance (P-value) at every spatial node, we defined clusters as spatially continuous groups of significant nodes (P < 0.01). Then, we estimated the critical cluster statistics by summarizing the test statistics at every node per cluster. These actual critical values were compared with the distribution of the dummy critical values obtained by repeating the process described above 10,000 times while randomly permuting the performance (Hedges’ g) values before computing PEI. The test significance (p_cluster) is the proportion of dummy values equal to or more extreme than the actual critical value.

Control Statistical Analyses.

We performed a leave-one-out analysis to test the sensitivity of the meta-modeling to study outliers. The relationship between electric fields and Hedges’ g (denoted as performance-to-electric field index or PEI) maps were recalculated 28 times, each time leaving out the data from one experimental study. Subsequently, we calculated the average, variance (in %), and SD of 28 subanalyses and correlated them with the main analysis.

Further, we tested whether putative outliers in the outcome measures could bias our main results. For that, we recalculated the causal maps using the variation of the performance-to-electric field index that employs nonparametric rank-order statistics (Spearman) that is less sensitive for outliers and accounts for possible monotonic but nonlinear interactions.

Next, we investigated the effect of unequal sample sizes over studies on our main results. We again recalculated PEI, this time weighted by study sample size (recruitment number per study). Finally, we performed another weighted PEI analysis, controlling for the number of accuracy vs. performance time outcomes. Specifically, the theta tACS dataset consisted of 133 outcomes for accuracy and 41 for PT, giving a weighting factor of 0.31 (=41/133) for accuracy. For gamma, 60 accuracy and 45 PT outcomes resulted in the weighting factors of 0.75 for accuracy. For all control analyses, we estimated a linear correlation with the original result to estimate the agreement between them.

Functional Map Similarity.

To generate a functional meta-analytic map of WM derived from the fMRI, we used the large-scale automated synthesis of human functional neuroimaging data (NeuroSynth) (58). We extracted the association test map for the term working memory, which automatically summarizes voxels reported more often across 1,091 articles that include the term relative to the articles that do not. The meta-analysis parameters were kept to default (FDR-corrected P values ≤ 0.01). The maps were binarized for spatial similarity analysis.

The causal functional WM maps from our study were converted to volume space and binarized separately for the theta cluster, positive gamma cluster, and negative gamma cluster. Then, the Dice similarity coefficient was estimated between the fMRI map and our causal maps. The significance of the coefficient was estimated using the permutation test by comparing the coefficient values with the dummy distribution. The dummy distribution was obtained by randomly permuting the voxels of the fMRI map and reestimating the Dice coefficient 10,000 times.

Target Optimization.

We performed the electrode montage optimization to propose the tACS parameters for targeting the brain areas according to our causal functional maps. This was done following the SimNIBS 3.2 framework using the method for distributed target optimization proposed by Ruffini et al. (105) and implemented by Saturnino et al. (59). We separately considered theta, negative gamma, and positive gamma maps and used the exemplary anatomic dataset Ernie within SimNIBS 3.2 as the individual head model. The lead field matrix was generated for the middle level of the neocortical gray matter using the PARDISO solver and standard tissue conductivities. We set the target electric field strength at 0.3 V/m. The optimization aimed to achieve the target strength of the normal component of the induced electric field (normal E) inside the cluster of interest while minimizing normal E outside. We constrained optimization to use 8 or fewer electrodes, a current intensity of 2 mA or less per electrode, and 4 mA or less in total for safety.

Supplementary Material

Appendix 01 (PDF)

Data, Materials, and Software Availability

Functional maps data have been deposited in Zenodo (10.5281/zenodo.10651639) (106). All study data are included in the article and/or SI Appendix.