Introduction

The xxx event-related potential (ERP) and field (ERF) of the electroencephalogram (EEG) and magnetoencephalogram (MEG), respectively, appear as a series of waves triggered by a stimulus event. First described by \citet{Davis1939}, these waves are thought to represent stimulus-related activations which are stationary, time-locked to stimulus presentation, and buried in ongoing oscillations and other large-amplitude activity unrelated to stimulus processing. Thus, to cancel out the noise unrelated to the stimulus, ERPs and ERFs are obtained through stimulus repetition and averaging of the resulting single-trial EEG/MEG signals. The event-related response starts with small-amplitude, early-latency waves in the first 8 ms from stimulus onset; these are followed by mid-latency waves in the 8-40 ms range and by large-amplitude long-latency waves (e.g., \cite{Picton1980}). In the passive recording condition, when the subject is not engaged in a task involving the stimuli, the most prominent waves of the auditory ERP are the long-latency P1, N1, and P2 responses, peaking at approximately 50, 100, and 200 ms, respectively. Their respective ERF counterparts are termed the P1m, N1m, and P2m. These responses function as landmarks as they can be identified in the ERP/ERF of most subjects. Hence, the fact that the morphology of the event-related responses varies greatly from subject to subject (see, for example, \citet{Matysiak2013} and \citet{Koenig2015}) is powerful feature enabling fundamental studies of signal processing in the AC.
Despite the straightforwardness of the method, decades of use, and improvements in localization methods, we still have a poor understanding of how event-related responses are generated and what they signify. The general biophysics of EEG and MEG generation and the neural processes giving rise to currents in the brain contributing to these signals are well known \citep{Sarvas1987,Williamson1981}. According to this, EEG \citep{Buzaski2012,Einevoll2013,Mitzdorf1985,Mitzdorf1994} and MEG \citep{Hamalainen1993,Okada1997} represent primarily a weighted sum of synchronised synaptic activities of pyramidal neural populations. With pyramidal neurons being the predominant cell type in cortex, cortical columns are characterized by the apical dendrites of these cells running in parallel, and in a perpendicular direction to the cortical surface. The activity of excitatory synapses on these dendrites translates into electrical current (cations \(Ca^{2+}\) and \(Na^{+}\)) flowing into the apical dendrites, then along the dendrites as the primary/lead current, and out through the passive leak channels into the extracellular space, where the resulting volume current completes the circuit. The primary current along many synchronously activated cells gives rise to a magnetic field which is visible in MEG and whose strength depends on the orientation and distance of the primary current in relation to the sensor. Similarly, the extracellular sinks and sources separated along the axis of the dendrites contribute to an open electric field which can be picked up in EEG and local field potential (LFP) measurements. In contrast, inhibitory neurons, with shorter dendrites and a symmetric dendritic structure, contribute to a closed field which does not show up in EEG and MEG. Traditionally, inhibitory synapses onto pyramidal cells were thought to contribute only minimally to EEG/MEG, with the reversal potentials of these synapses being close to the resting membrane potential \citep{Bartos2007,Mitzdorf1985}. Accordingly, an activated inhibitory synapse leads to minimal cross-membrane currents and hence a minimal contribution to EEG and MEG. However, when pyramidal neurons are actively spiking, for example when spontaneous activity occurs, the membrane potential is elevated and so inhibitory synapses can significantly contribute to EEG and MEG generation \citep{Trevelyan2009,Glickfield2009,Bazelot2010}.
The leap from biophysics of ERP and ERF generation to an understanding of the experimentally measured waveforms is more complex. A sensory stimulus (the event) sets off a series of neural activations propagating from the sensory organ to cortex. Cortical activations can be observed locally, in intracortical measurements, as increased spiking when, for example, the weak thalamocortical signal activates the local feedback circuits in cortical columns of the primary areas \citep{Douglas1995}. Short-latency ERPs and LFPs co-vary with pharmacological manipulation of inhibition \citep{Bruyns2017} and computational modelling can account for adaptation effects of long-latency ERPs purely in terms of interactions across cortical layers in primary auditory cortex \citep{Wang2013}. However, it seems unlikely that purely local LFP events in primary fields could represent the full intracortical counterpart of ERPs, which emerge as a superposition of activity across larger swathes of cortex. Specifically, anatomical studies in monkey show that auditory cortex is organized hierarchically, with primary, core fields connecting to each other and to surrounding secondary, belt fields which, in turn, are connected with parabelt fields \citep{Kaas2000,Hackett2014}. Physiological evidence suggests that this hierarchical structure is reflected in feedforward activations progressing along the core-belt axis \citep{Rauschecker1997}. This suggests that cortical activations generating event-related responses should have spatial as well as temporal dynamics, and this is supported by localization studies. \citet{Luetkenhoener1998} modelling the long-latency auditory ERF from a human subject with a single equivalent current dipole (ECD) found that the ECD location was non-stationary across the entire ERF: during the P1m, it lies on Heschl’s gyrus (HG) from where it slides to the planum temporale (PT) during the N1m and shifts back to HG during the P2m. \citet{Inui2006} performed multi-dipole analysis in a 120-ms post-stimulus window using six ECDs and found that activity propagates along a roughly medial-lateral axis from HG to the superior temporal gyrus (STG). This was interpreted in terms of core-belt-parabelt activation. Similar results were reported by \citet{Yvert2005} who used minimum current estimate (MCE) analysis of recordings from intracerebral electrodes in human auditory cortex. Activity started in HG and Heschl’s sulcus (HS) at around 20 ms. The P1 time range (30-50 ms) was characterized by multiple areas becoming activated along medio-lateral and postero-anterior axes of propagation, successively involving HG and HS, PT, and STG. Subsequently, activation cycled back so that the rising slope of N1 coincided with a similar series of activations as during P1.
The above results point to event-related responses having both a temporal as well as a spatial dynamics whereby foci of activity in cortex shift over time. This addition of a spatial dimension to event-related responses adds to the descriptive palette but as such gives no deeper insight into what is going on. There have been a number of approaches for gaining such insight. Research in the 1970’s and 80’s used the concept of the ERP component, whereby the response is the linear sum of separable components, each generated by a spatially defined generator which also has a well-defined information processing function, such as stimulus onset detection or change detection (for reviews, see \citet{Naatanen1987} and \citet{bookNaatanen1992}). However, it has proven difficult to perform component separation in a reliable way and to map components to anatomical structure \citep{May2010}.
This emphasis on localization of activity was later complemented by considerations on connection strengths. In the framework of dynamical causal modelling (DCM), the event-related response is considered to arise out of a network of a small number of nodes arranged in a hierarchical structure and each representing an extended cortical area such as the primary or secondary auditory cortex \citep{Friston2003,David2006}. Stimulation-specific modulations in the response then arises out of changes in the strengths of connections, classified as bottom-up, lateral, or top-down. Such changes have been interpreted in the framework of predictive coding, whereby cortex attempts to predict incoming stimuli and in doing so generates prediction signals via top-down inhibitory connections. When there is a mismatch between stimulus and prediction, excitatory bottom-up connections relay a prediction error signal. In this view, the N1(m) signifies excitatory activity carrying the prediction error from auditory cortex towards frontal areas. In contrast, the P2(m) is due to inhibitory, feedback activity carrying the top-down prediction information \citep{Garrido2007}.
It appears then that we have a range of mutually exclusive explanations for event-related responses. First, these can be understood as arising purely locally, as the result of intralaminar dynamics within cortical columns \citep{Wang2013}. Second, they can be seen to represent the linear sum of activity in a limited number of component generators, each performing an independent information processing task \citep{Naatanen1987}. Third, they might arise out of a limited number of cortical areas interacting with each other in the performance of the singular task of predictive coding \citep{Friston2003}. The spatial resolutions of these explanations seem to lie at the extremes, ranging from the single column to treating entire areas as single nodes (see also \citet{Ritter2013}). These explanations are not designed to represent transformations occurring in auditory cortex, because the internal dynamics of auditory cortex as a distributed system are not included. For this purpose, a more mechanistic view on how AC processes and represents sound is needed. Such a view should probably be based on the structure of the auditory cortex, which also opens up the possibility of accounting for the spatial dynamics occurring within the temporal lobe, as described above.
Thus, the purpose of the current study is to plug the resolution gap in explaining the auditory event-related response by using a mechanistic model encapsulating the anatomical structure of AC. As a starting point we use a previously developed model of AC \citep{May2010,May2013} and explore how the internal structure of auditory cortex and its dynamics might account for the generation of ERPs and ERFs. This analysis, then, lets us explore the origin of the subject-specificity of event-related responses: Why do subjects have unique ERP/ERF morphology? Can this be fully accounted for in terms of individual curvature of AC and its modulating effect on the EEG and MEG? Or do subjects also have unique dynamics of the auditory cortex?