The results of the present report show an effect of amplitude dependence of AEPs, with increasing stimulus intensity leading to larger N1 and P2 components, but not affecting P1. Similarly, intensity-dependent changes in hemodynamic activity were observed in both the auditory and prefrontal cortices, as reflected in block average and GLM analysis. These changes exhibited a spatial distribution that expanded with increasing intensity, as shown in the T-maps, and are consistent with patterns reported in previous fMRI studies. Notably, prefrontal fNIRS activity in the IFG displayed a delayed response relative to the auditory cortex, suggesting distinct temporal dynamics between sensory and higher-order regions. Spearman correlations show auditory and prefrontal positive associations, suggesting functional connectivity between these areas. For the neurovascular coupling results, Spearman correlation of AEPs and fNIRS residuals suggested functional relationships between frontal and auditory regions, for N1 and P2. N1 showed positive associations with channels in the STG and SFG but negative associations with the IFG for HbO, while HbR positive correlation was found near the SMG. P2 correlations were predominantly observed in frontal regions, with positive associations in the SFG and IFG for HbO and negative associations with SMG, AnG, SFG, and IFG for HbR. Together these findings provide insights into the complex mechanism underlying auditory processing and cognitive engagement in response to varying sound intensities, and the electrical and vascular responses that are involved.

The effect of the intensity on the amplitudes of the P2 and N1 AEPs was found in the present report, indicating that AEP amplitudes increase with stimulus intensity (50 dB, 70 dB, and 90 dB). This finding is consistent with previous studies (Hegerl and Juckel 1993; Hegerl et al. 2001), which also reported the amplitude dependence of intensity. The modulation of AEP amplitudes by intensity can be attributed to increased neural synchrony and/or enhanced neural recruitment at higher intensities, in part modulated by serotonergic innervations. It has been proposed that the serotonergic effect on the auditory cortex plays a critical role in amplifying/reducing the AEPs, where high serotonergic neurotransmission would result in a weak IDAP and low serotonergic neurotransmission would result in a strong IDAP (Hegerl et al. 2001). In the present report, since the population studied were healthy volunteers without any neurological disorder, the expected modulation in AEPs was found. The effect of the intensity on the AEPs has primarily been associated with areas exhibiting higher serotonergic innervations, such as the auditory cortex. Additionally, the involvement of prefrontal regions, including the OFC, has been suggested (Hegerl and Juckel 1993; Hegerl et al. 2001; Mavrogiorgou et al. 2017). The participation of these areas is further supported by the results that will be discussed in the following paragraphs.

The hemodynamic results from both the block average and GLM-derived beta analyses demonstrate an amplitude-dependent response in the auditory and prefrontal regions as stimulus intensity increases. These results are in line with the fMRI and fNIRS studies which have found an intensity effect not only in the auditory area but also in the dorsolateral prefrontal cortex and OFC (Hart et al. 2003; Neuner et al. 2014; Bauernfeind et al. 2018; Muñoz et al. 2023). The fNIRS hemodynamic response, as observed in the block average, exhibits amplitude modulation like the AEPs, particularly in the auditory cortex and the right IFG, with a similar trend observed in the left IFG. These findings are consistent with those reported in our previous study (Muñoz et al. 2023). Furthermore, the present study investigates the effect of latency, revealing significant differences in response latency across ROIs, ranging from 510 to 920 m, with earlier latencies observed in the auditory cortex and later latencies in the IFG. These latency differences have been linked to delayed neural activation, network dynamics including less synchronous inputs to higher-order areas, and even physiological differences in vasculature or blood flow (Bauernfeind et al. 2018). In this context, the observed latency differences could be reflecting the dynamic flow of information between these regions. Rapid auditory processing in the auditory cortex facilitates swift responses to sound stimuli (Ogawa et al. 2007), while higher-order cognitive processes, such as attentional modulation, contribute to delayed hemodynamic responses in the IFG due to the engagement of more complex neural networks. These latency patterns align with literature suggesting hierarchical information transfer from auditory sensory to frontal areas in animals and humans (Planke and Rommanski, 2014, de Heer et al. 2017; Braga et al., 2017; Nourski et al. 2018, Jang and Choi 2022; Hockley and Malmierca 2024), supporting the idea that slower responses in frontal cortices would reflect integrative processing and top-down modulation.

The T-maps of the beta values indicate that the number of activated channels increases with sound intensity, extending to broader areas within the auditory and prefrontal cortices at 70 and 90 dB. This expansion in the cortical activation with intensity is consistent with previous findings by Hall et al., (2001) and Neuner et al. (2014), who reported that higher intensities recruit more extensive cortical and subcortical regions. This phenomenon likely reflects greater excitation within the auditory and prefrontal cortices, aligning with fMRI studies that show heightened activation in these areas as sound levels increase (Hall et al. 2001; Hart et al. 2003). Similarly, the contrast analysis (Fig. 5b) shows the differential topographical activation when comparing the lower intensities (50 dB and 70 dB) with the highest intensity (90 dB), with pronounced differences near the IFG, and auditory-related structures near the STG, SMG and AnG. According to Jäncke et al., (1998) the network between the STG and the IFG, has been associated with the retrieval and rehearsal of auditory information, and in the present study, this network would be specifically related to encoding high-intensity auditory stimuli. The last statement would be supported by the Spearman correlation results in which positive associations were found in a series of auditory and prefrontal channels, suggesting a coupling of auditory processing with higher-order cognitive functions. These findings would indicate a complex interplay between sensory and cognitive networks, with increasing auditory stimulus intensity potentially enhancing the connectivity between auditory and prefrontal regions, which may support the process of attention and cognitive control during auditory processing (Bidet-Caulet et al. 2015; Panichello and Buschman 2021).

Moreover, the internal fNIRS correlations reveal negative and positive correlations between auditory and visual channels in HbO and HbR, respectively. These seemingly contradictory results can be explained by the physiological properties of the oxygenated and deoxygenated hemoglobin. In HbO the total blood flow is distributed prioritizing certain regions, it is possible that with greater activation in the auditory channel (by increasing the intensity of the stimulus), more oxygen is captured in that region, while in the visual channel, the HbO does not increase in the same proportion. As the brain reallocates resources to enhance auditory processing during high-intensity stimuli, the reduced HbO in the visual domain can lead to an accumulation of deoxyhemoglobin, as the oxygen supply does not increase in the same proportion as metabolic demand (Pinti et al. 2020). This dynamic is particularly relevant in tasks involving multisensory stimulation, where sensory modalities compete for limited cognitive resources. In the present study, participants were engaged in watching a mute movie while auditory stimuli were delivered, highlighting the competition between sensory channels.

Additionally, the intra-regional positive correlations found in the Spearman Correlation would suggest an influence of regional cortical blood flow, this could imply that beyond neurovascular coupling, local vascular dynamics would contribute to the hemodynamic response. In this regard, it has been suggested that hemodynamic changes are driven by a complex interaction of cerebral blood flow (CBF), cerebral blood volume (CBV), the cerebral metabolic rate of oxygen (CMRO2), and vascular density, thus, this interaction would play an important role in the amplitude, and temporality (as discussed before) of the HRF (Kim and Ogawa 2012; Vigneau-Roy et al. 2014). Frontal areas, for instance, have been proposed to have a higher vascular density (Vigneau-Roy et al. 2014), therefore differences in neurovascular coupling efficiency could emerge from these variables, potentially complicating the interpretation of fNIRS signals in terms of neuronal activity alone.

Source analyses of AEPs have shown that N1 and P2 typically follow a frontocentral scalp distribution (Näätänen and Picton 1987; Alcaini et al. 1994; Hyde 1997). Consistent with these findings, Spearman correlation analysis of residuals in the present study revealed significant correlations for the N1 component, specifically involving two auditory channels near the STG and SMG, as well as two frontal channels near the SFG and IFG. Notably, for HbO the auditory and SFG channels showed positive correlations whereas the IFG channel exhibited negative correlations. Physiologically, the N1 amplitude is associated with the processes of detection and attention triggering (Hyde 1997). Accordingly, the positive correlations observed in N1 amplitude (i.e., more negative values) with the STG and SFG channels (decrease in HbO) would reflect a localized reduction in metabolic demand, potentially influenced by attentional reallocation driven by sensory gating mechanisms. These processes are particularly relevant within the context of the current experimental design, which involves the presentation of tone sequences in blocks. Although sensory gating is not analyzed in the present study, it can be inferred from the observed reduction in amplitude of the potentials, as can be seen in Fig. 2c. Sensory gating or repetition suppression is a fundamental neural process that filters out redundant or irrelevant stimuli, allowing the brain to focus on salient sensory information (Freedman et al. 1996). In this context, the observed relationship suggests that early auditory processing (reflected in N1) is associated with the modulation of hemodynamic responses in frontal and auditory areas, thereby facilitating the suppression of irrelevant sensory input. Similarly, the negative correlation between N1 and HbO in IFG would suggest recruitment of the IFG for top-down control, increasing its metabolic demand. The IFG is known to play a critical role in switching attention and inhibitory processing (Aron et al. 2004; Hampshire et al. 2010), which aligns with the concept of filtering out irrelevant stimuli through sensory gating mechanisms.

Furthermore, the positive correlation between N1 and the left auditory channel of the SMG suggests an active process in this more posterior auditory area, consistent with an early auditory triggering, where the increase in amplitude of N1 was correlated with increased activity in this channel. Notably, this correlation in the left auditory cortex specifically for deoxygenated hemoglobin was also found in our previous study (Muñoz et al. 2023) and was linked to neurovascular coupling, understood as the dynamic interplay between neural activity and hemodynamic vascular responses, where electrical activity drives corresponding changes in cerebral blood flow to meet metabolic demands (Attwell et al 2010; Schei et al. 2012). Given that the N1 component is considered a marker of auditory processing, reflecting both the detection of auditory stimuli and the allocation of attentional resources (Näätänen and Picton 1987), the engagement of auditory and frontal sources would indicate that early sensory signals in the auditory cortex interact dynamically with the SFG and IFG, supporting a framework where sensory and cognitive processes are integrated to optimize perception.

In contrast, the P2 component shows correlations mainly with frontal activity for the HbO and HbR within IFG and SFG, and also posterior auditory channels near the SMG and AnG for HbR. The correlations were positive for HbO and negative for HbR across all regions, suggesting that an increase in amplitudes of the P2 potential is correlated with the increase in HbO values and decrease in HbR values, i.e., activation in these areas. This functional association of P2 with frontal activity aligns with our previous study (Muñoz et al. 2023). Currently, the sources for P2 are discussed, but functionally has been linked to attentional targeting, perceptual learning, and inhibitory processes for irrelevant stimuli (Paiva et al. 2016). In this sense, similar to N1, the involvement of the IFG and SFG, would be crucial for top-down control, facilitating the modulation of attention and inhibition of distractions (Aron et al. 2004; Hampshire et al. 2010; Wegrzyn et al. 2017). The greater number of observed correlations of P2 with frontal activity (IFG and SFG) suggest a stronger involvement of top-down control mechanisms compared to N1. Thus, P2 would reflect the process of refining attention and integrating sensory information with cognitive demands, supporting sustained attentional engagement, and facilitating learning and adaptation to auditory stimuli. Although N1 and P2 are both related to frontal and auditory cortices, their distinct roles highlight two complementary but functionally distinct mechanisms of auditory-cognitive processing. N1 would reflect early sensory encoding and an early attentional capture, and P2 would reflect a later stage of attentional regulation, engaging both auditory and prefrontal regions in a broader network interaction. This distinction underscores the dynamic interplay between sensory and cognitive processes, where early sensory responses driven by the auditory cortex trigger top-down regulatory mechanisms.

A critical aspect of our analysis is the removal of the global response in each channel and electrode, to isolate stimulus-specific activity while preserving functionally relevant neurovascular coupling patterns. Is well known that the fNIRS signal has a lower signal-to-noise-ratio than fMRI, and is more contaminated by physiological artifacts (Cui et al. 2011; Tachtsidis, and Scholkmann 2016), in this sense some studies have tried to address this limitation (Zhang et al. 2016). In the present study, our approach is based on the premise that global trends in both EEG and fNIRS signals often reflect systemic noise, inter-individual variability, or non-neural contributions, which can obscure meaningful neural-vascular interactions. By extracting residuals, i.e., the variance that remains after accounting for these global trends, we aim to enhance the specificity of our analysis to activity directly linked to auditory stimulation. Importantly, the correlations observed in our study align with well-established neuroanatomical and functional relationships, particularly between auditory and prefrontal regions, further supporting the validity of the residual-based approach. Rather than distorting neurovascular coupling, removing the global response channel by channel and electrode by electrode seeks to refine the detection of functionally relevant interactions by minimizing individual confounds and allowing for a more precise interpretation of the relationship between electrophysiological activity and hemodynamic responses.

One limitation of the present study is the spatial discrepancy between EEG and fNIRS recordings, as EEG captures activity from central electrodes (FCz, FC1, FC2, Cz), although influenced by the volume conduction influences from other brain areas, while fNIRS optodes covered auditory, prefrontal, and visual cortices with a better spatial resolution than EEG. Despite this discrepancy, the observed correlations between residual AEPs and fNIRS signals provide insights into neurovascular coupling. Functional connectivity between auditory and prefrontal regions has been well-documented, with studies showing that higher-order cognitive processes, such as attention and auditory perception, engage distributed networks (Jäncke et al. 1998). Additionally, the residual-based approach used in this study helps isolate stimulus-specific relationships by reducing confounding effects from individual variations in AEP and fNIRS values. While future studies with high-density EEG and improved source localization techniques could refine the spatial alignment of EEG and fNIRS signals, the present findings offer evidence of functionally relevant neurovascular interactions, particularly in auditory and prefrontal cortices, where stimulus intensity effects were observed.

These findings contribute to an integrated, dual-modality perspective on auditory processing by combining EEG and fNIRS to examine how auditory stimulus intensity shapes both neural and vascular responses. This multimodal approach allows for a more comprehensive understanding of neurovascular coupling, capturing both the fast electrophysiological dynamics and the spatial distribution of hemodynamic activity. Specifically, the observed functional associations between auditory and prefrontal regions suggest that higher stimulus intensities not only engage auditory processing but also recruit non-auditory functions, such as attentional control and higher-order cognitive processes, which are mediated by the prefrontal cortex and are distinctly related to the N1 and P2 AEP functions. This interaction highlights the integration of sensory and cognitive systems in processing auditory stimuli. Given the extensive literature on IDAP in clinical population studies, this type of multimodal analysis could be applied to various disorders, such as ADHD or affective disorders, potentially aiding in targeting serotonergic pathways through non-invasive brain stimulation or pharmacological interventions. Limitations of the study are the penetration of fNIRS only at the cerebral cortex level, that most participants are right-handed, and that when co-recording the two signals the EEG noise-to-ratio and different confounds such as the use of tone blocks could alter the results.