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Functional connectivity and GABAergic signaling modulate the enhancement effect of neurostimulation on mathematical learning [1]

['George Zacharopoulos', 'Wellcome Centre For Integrative Neuroimaging', 'Department Of Experimental Psychology', 'University Of Oxford', 'Oxford', 'United Kingdom', 'School Of Psychology', 'Swansea University', 'Swansea', 'Masoumeh Dehghani']

Date: 2025-07 

Effortful learning and practice are integral to academic attainment in areas like reading, language, and mathematics, shaping future career prospects, socioeconomic status, and health outcomes. However, academic learning outcomes often exhibit disparities, with initial cognitive advantages leading to further advantages (the Matthew effect). One of the areas in which learners frequently exhibit difficulties is mathematical learning. Neurobiological research has underscored the involvement of the dorsolateral prefrontal cortex (dlPFC), the posterior parietal cortex (PPC), and the hippocampus in mathematical learning. However, their causal contributions remain unclear. Moreover, recent findings have highlighted the potential role of excitation/inhibition (E/I) balance in neuroplasticity and learning. To deepen our understanding of the mechanisms driving mathematical learning, we employed a novel approach integrating double-blind excitatory neurostimulation—high-frequency transcranial random noise stimulation (tRNS)—and examined its effect at the behavioral, functional, and neurochemical levels. During a 5-day mathematical learning paradigm (n = 72) active tRNS was applied over the dlPFC or the PPC, and we compared the effects versus sham tRNS. Individuals exhibiting stronger positive baseline frontoparietal connectivity demonstrated greater improvement in calculation learning. Subsequently, utilizing tRNS to modulate frontoparietal connectivity, we found that participants with weaker positive baseline frontoparietal connectivity, typically associated with poorer learning performance, experienced enhanced learning outcomes following dlPFC-tRNS only. Further analyses revealed that dlPFC-tRNS improved learning outcomes for participants who showed reductions in dlPFC GABA when it was accompanied by a reduced positive frontoparietal connectivity, but this effect was reversed for participants who showed increased positive frontoparietal connectivity. Our multimodal approach elucidates the causal role of the dlPFC and frontoparietal network in a critical academic learning skill, shedding light on the interplay between functional connectivity and GABAergic modulation in the efficacy of brain-based interventions to augment learning outcomes, particularly benefiting individuals who would learn less optimally based on their neurobiological profile.

Competing interests: I have read the journal's policy and the author RCK of this manuscript has the following competing interests: RCK serves on the scientific advisory boards of Neuroelectrics Inc., Innosphere Inc., is the founder and shareholder of Cognite Neurotechnology Ltd., and is an Editorial Board Member at PLOS Biology.

Funding: Funding: This research was supported by the European Research Council (Learning&Achievement 338065 to RCK, https://erc.europa.eu/ ) and the Wellcome Trust (0883781 to RCK, https://wellcome.org/ ). The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.

Introduction

Academic learning has profound implications for individuals and society at large [1–3]. However, not all individuals benefit equally from educational opportunities, a phenomenon referred to as the Matthew effect [4] in education. This cognitive disparity is a significant societal issue, exacerbating inequalities in learning and perpetuating gaps in education, which, in turn, limit access to future resources and opportunities. Mathematical learning, in particular, presents a considerable barrier for many. For instance, an organisation for economic cooperation and development (OECD) report from 2016 revealed that 24%−29% of adults in developed countries such as the United States, the United Kingdom, Germany, and France possess mathematical skills at or below the level expected of 5–7-year-olds [5]. This widespread deficiency in mathematical skills has extensive consequences, including higher unemployment, reduced economic growth, poorer health outcomes, diminished political engagement, and lower levels of trust in others [5]. In our increasingly science, technology, engineering, mathematics (STEM)-oriented societies, the repercussions of low mathematical competence are likely to intensify [6].

Longitudinal studies suggest that mathematical abilities are relatively stable from childhood through adulthood, driven primarily by biological rather than environmental factors [7–9]. Genetic research has identified correlations between mathematical abilities and genes associated with potassium channels, which are essential for neuronal excitability. Variations in these genes are linked to learning disabilities and neurodevelopmental delays, underscoring their role in neuronal excitability and synaptic plasticity [10–12]. However, despite these insights, the causal mechanisms underpinning mathematical learning remain poorly understood, with much of the existing research focusing on neural correlates rather than causal factors [13–16].

Non-invasive neurostimulation techniques offer a promising avenue for exploring the causal mechanisms of mathematical learning by modulating cortical excitability and neurochemicals involved in cognitive processing [17–19]. To advance our understanding of the neurobiological underpinnings of mathematical learning, we employed a double-blind excitatory neurostimulation protocol—high-frequency (100–640 Hz) transcranial random noise stimulation (tRNS)—in conjunction with proton Magnetic Resonance Spectroscopy (1H-magnetic resonance spectroscopy (MRS)) and resting-state functional magnetic resonance imaging (fMRI) over a 5-day mathematical learning paradigm involving 72 healthy young adults. The dorsolateral prefrontal cortex (dlPFC) and the posterior parietal cortex (PPC) were selected as voxels of interest (VOIs) based on their established roles in skill acquisition and mathematical proficiency [20–27].

Neurocognitive models have suggested that arithmetic information is processed in a multimodal and distributed manner in the human brain. Accounts based on Bayesian meta-analytic models identified the canonical circuit of arithmetic problem solving [28], which consists of brain regions that are mostly localized to the dorsal aspects of the PPC, ventral temporal-occipital cortex (VTOC), and the prefrontal cortex (PFC), including the premotor cortex and the inferior and middle frontal gyri [29].

Previous accounts for how arithmetic information is mastered indicated that the development of numerical and arithmetic abilities is enabled by a significant increase in working memory [30]. Indeed, the role of working memory and executive functions is a crucial feature in several theoretical models of cognitive learning, in general, and arithmetic learning in particular (A Triarchic Theory of Learning, [20]). These models predict that mathematical procedures (calculation), which rely heavily on executive functions including working memory, attention processes, inhibition, and shifting [31] are typically associated with the dlPFC [32]. This view, which is supported by previous work on the acquisition of arithmetic expertise in normally developing children and adults, revealed that a positive shift in arithmetic competence corresponds to a shift from effortful processing that engages the prefrontal regions, such as the dlPFC, to skilled and fast retrieval that involves parietal regions such as the PPC [21]. This is because repeating the arithmetic problems strengthens a direct retrieval of the correct solution from memory (e.g., 23 × 8 = 184). Concurrently, the demand on quantity-based processing and complex processes, such as working memory (e.g., 23 × 8 = [20 × 8] + [3 × 8] = 160 + 24 = 184), monitoring and attention, sustained by frontal areas, is diminished [21]. Accordingly, we hypothesize that tRNS over the dlPFC, while participants learn to apply a new algorithm, will improve calculation learning. Based on a previous tRNS study using the same paradigm as in this work we predict that the effect will be found for reaction times (RTs), rather than accuracy [33]. In contrast, we do not expect to find a reliable tRNS (over the dlPFC) effect for drill learning, which does not require the application of mathematical procedures. However, tRNS over the PPC may improve drill learning, but not calculation learning. While in a previous study no effect was found when tRNS was applied over the PPC during calculation and drill learning [33], the same parietal montage and tRNS parameters as in our study [33] improved performance in a vocabulary learning task, which involves some component of drill learning [34].

Apart from the aforementioned dissociated roles of the frontal and the parietal regions, these regions, which are co-activated during arithmetic tasks [29], form the frontoparietal networks that support the manipulation of numerical information, which is crucial for calculation learning. Apart from frontoparietal networks, the frontohippocampal networks are involved in creating associative memories and connecting new information with existing knowledge, which contributes to the development of long-term memories that enable generalization beyond specific problem characteristics [35]. Taking these results together with previous work showing that cortico-hippocampal connectivity is involved in mathematical learning [36], we hypothesize that frontoparietal connectivity is associated mainly with calculation learning, while frontohippocampal connectivity is associated with both drill and calculation learning performance.

Beyond the brain regions and networks involved in mathematical learning, previous studies, have highlighted the crucial role of excitatory and inhibitory neural circuits in shaping neural excitation/inhibition (E/I) balance. E/I balance governs the onset and closure of sensitive periods in brain development and skill acquisition [37–39]. For example, in humans, research on visual procedural learning has utilized glutamate and GABA measurements to quantify E/I balance, associating high E/I with plasticity (the capacity for change in learning mechanisms) and lower E/I with stability (the resistance to change in these mechanisms) [40]. Effective learning requires an initial phase of plasticity, followed by a phase of stability to consolidate knowledge and prevent interference from subsequent learning experiences [40]. However, the role of plasticity and stability in more complex learning domains, such as mathematics, remains underexplored [41]. In this study, we employed tRNS due to its potential to change the levels of excitation and inhibition [41–44]. Similar to previous neuroimaging studies we noninvasively quantified excitation and inhibition using glutamate and GABA, respectively [45–47]. tRNS, due to its potential excitatory effect, has been suggested to enhance plasticity with a continuous effect beyond the stimulation session, as indicated by lasting effects beyond the stimulation period (e.g., weeks to months; [33,34,42,48–52]. Our approach is further motivated by the association between individual variability in glutamate and GABA levels and mathematical attainment [15]. Therefore, we hypothesize that changes in glutamate and GABA levels will predict calculation and drill learning.

Participants engaged in a 5-day mathematical learning task, solving new arithmetic problems through either calculation (algorithm-based) or drill (rote memorization) [53,54] (Fig 1). The calculation method required the integration of declarative, procedural, and conceptual knowledge, all of which are critical for mathematical learning [55]. To provide a comprehensive network-level understanding of frontoparietal stimulation, we utilized resting-state fMRI to assess the functional connectivity between our predefined regions throughout the learning process.

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TIFF original image Download: Fig 1. Task procedure. Calculation and drill problems were presented to the participants in different blocks on each learning day (see Materials and methods). (A) Calculation problems (denoted by “§”) began with the presentation of a problem, a brief mask, and an unlimited input duration. Upon giving the correct response, the participant was presented with a new problem. Incorrect responses led to the repetition of the same problem until the correct response was provided. (B) Drill problems (denoted by “♯”) were presented as a combination of two operands and an outcome. In contrast to the calculation problems, in the drill problems, the underlying algorithm to derive the result by calculation was not known. The combination had to be memorized and reproduced after masking. Both presentation time and response input time decreased from one session to the next, overall. Problems were repeated when answered incorrectly. https://doi.org/10.1371/journal.pbio.3003200.g001

We hypothesize that participants who exhibit a greater increase in inhibitory neurochemical levels over the 5 days will benefit more from tRNS, as this indicates a more rapid transition from plasticity to stability, thereby facilitating better learning outcomes. Additionally, given the established link between neurochemical concentrations and functional connectivity [16,45,56], we explored the interplay between neurochemicals (GABA and glutamate) and functional connectivity to elucidate the complex mechanisms underlying mathematical learning.

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[1] Url: https://journals.plos.org/plosbiology/article?id=10.1371/journal.pbio.3003200

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