Recruiting neural field theory for data augmentation in a motor imagery brain-computer interface.

We introduce a novel approach to training data augmentation in brain-computer interfaces (BCIs) using neural field theory (NFT) applied to EEG data from motor imagery tasks. BCIs often suffer from limited accuracy due to a limited amount of training data. To address this, we leveraged a corticothalamic NFT model to generate artificial EEG time series as supplemental training data. We employed the BCI competition IV '2a' dataset to evaluate this augmentation technique. For each individual, we fitted the model to common spatial patterns of each motor imagery class, jittered the fitted parameters, and generated time series for data augmentation. Our method led to significant accuracy improvements of over 2% in classifying the "total power" feature, but not in the case of the "Higuchi fractal dimension" feature. This suggests that the fit NFT model may more favorably represent one feature than the other. These findings pave the way for further exploration of NFT-based data augmentation, highlighting the benefits of biophysically accurate artificial data.

Geometric constraints on human brain function.

The anatomy of the brain necessarily constrains its function, but precisely how remains unclear. The classical and dominant paradigm in neuroscience is that neuronal dynamics are driven by interactions between discrete, functionally specialized cell populations connected by a complex array of axonal fibres1-3. However, predictions from neural field theory, an established mathematical framework for modelling large-scale brain activity4-6, suggest that the geometry of the brain may represent a more fundamental constraint on dynamics than complex interregional connectivity7,8. Here, we confirm these theoretical predictions by analysing human magnetic resonance imaging data acquired under spontaneous and diverse task-evoked conditions. Specifically, we show that cortical and subcortical activity can be parsimoniously understood as resulting from excitations of fundamental, resonant modes of the brain's geometry (that is, its shape) rather than from modes of complex interregional connectivity, as classically assumed. We then use these geometric modes to show that task-evoked activations across over 10,000 brain maps are not confined to focal areas, as widely believed, but instead excite brain-wide modes with wavelengths spanning over 60 mm. Finally, we confirm predictions that the close link between geometry and function is explained by a dominant role for wave-like activity, showing that wave dynamics can reproduce numerous canonical spatiotemporal properties of spontaneous and evoked recordings. Our findings challenge prevailing views and identify a previously underappreciated role of geometry in shaping function, as predicted by a unifying and physically principled model of brain-wide dynamics.

Neural field theory of adaptive effects on auditory evoked responses and mismatch negativity in multifrequency stimulus sequences.

Physiologically based neural field theory (NFT) of the corticothalamic system, including adaptation, is used to calculate the responses evoked by trains of auditory stimuli that differ in frequency. In oddball paradigms, fully distinguishable frequencies lead to different standard (common stimulus) and deviant (rare stimulus) responses; the signal obtained by subtracting the standard response from the deviant is termed the mismatch negativity (MMN). In this analysis, deviant responses are found to correspond to unadapted cortex, whereas the part of auditory cortex that processes the standard stimuli adapts over several stimulus presentations until the final standard response form is achieved. No higher-order memory processes are invoked. In multifrequency experiments, the deviant response approaches the standard one as the deviant frequency approaches that of the standard and analytic criteria for this effect to be obtained. It is shown that these criteria can also be used to understand adaptation in random tone sequences. A method of probing MMNs and adaptation in random tone sequences is suggested to makes more use of such data.

The music of the hemispheres: Cortical eigenmodes as a physical basis for large-scale brain activity and connectivity patterns.

Neuroscience has had access to high-resolution recordings of large-scale cortical activity and structure for decades, but still lacks a generally adopted basis to analyze and interrelate results from different individuals and experiments. Here it is argued that the natural oscillatory modes of the cortex-cortical eigenmodes-provide a physically preferred framework for systematic comparisons across experimental conditions and imaging modalities. In this framework, eigenmodes are analogous to notes of a musical instrument, while commonly used statistical patterns parallel frequently played chords. This intuitive perspective avoids problems that often arise in neuroimaging analyses, and connects to underlying mechanisms of brain activity. We envisage this approach will lead to novel insights into whole-brain function, both in existing and prospective datasets, and facilitate a unification of empirical findings across presently disparate analysis paradigms and measurement modalities.

Analytic Model for Feature Maps in the Primary Visual Cortex.

A compact analytic model is proposed to describe the combined orientation preference (OP) and ocular dominance (OD) features of simple cells and their mutual constraints on the spatial layout of the combined OP-OD map in the primary visual cortex (V1). This model consists of three parts: (i) an anisotropic Laplacian (AL) operator that represents the local neural sensitivity to the orientation of visual inputs; and (ii) obtain a receptive field (RF) operator that models the anisotropic spatial projection from nearby neurons to a given V1 cell over scales of a few tenths of a millimeter and combines with the AL operator to give an overall OP operator; and (iii) a map that describes how the parameters of these operators vary approximately periodically across V1. The parameters of the proposed model maximize the neural response at a given OP with an OP tuning curve fitted to experimental results. It is found that the anisotropy of the AL operator does not significantly affect OP selectivity, which is dominated by the RF anisotropy, consistent with Hubel and Wiesel's original conclusions that orientation tuning width of V1 simple cell is inversely related to the elongation of its RF. A simplified and idealized OP-OD map is then constructed to describe the approximately periodic local OP-OD structure of V1 in a compact form. It is shown explicitly that the OP map can be approximated by retaining its dominant spatial Fourier coefficients, which are shown to suffice to reconstruct its basic spatial structure. Moreover, this representation is a suitable form to analyze observed OP maps compactly and to be used in neural field theory (NFT) for analyzing activity modulated by the OP-OD structure of V1. Application to independently simulated V1 OP structure shows that observed irregularities in the map correspond to a spread of dominant coefficients in a circle in Fourier space. In addition, there is a strong bias toward two perpendicular directions when only a small patch of local map is included. The bias is decreased as the amount of V1 included in the Fourier transform is increased.

Cortical depth-dependent modeling of visual hemodynamic responses.

A physiologically based three-dimensional (3D) hemodynamic model is developed to predict the experimentally observed blood oxygen level dependent (BOLD) responses versus the cortical depth induced by visual stimuli. Prior 2D approximations are relaxed in order to analyze 3D blood flow dynamics as a function of cortical depth. Comparison of the predictions with experimental data for evoked stimuli demonstrates that the full 3D model performs at least as well as previous approaches while remaining parsimonious. In particular, the 3D model requires significantly fewer assumptions and model parameters than previous models such that there is no longer need to define depth-specific parameter values for spatial spreading, peak amplitude, and hemodynamic velocity.

Neural Field Theory of Evoked Response Sequences and Mismatch Negativity With Adaptation.

Physiologically based neural field theory of the corticothalamic system is used to calculate the responses evoked by trains of auditory stimuli that correspond to different cortical locations via the tonotopic map. The results are shown to account for standard and deviant evoked responses to frequent and rare stimuli, respectively, in the auditory oddball paradigms widely used in human cognitive studies, and the so-called mismatch negativity between them. It also reproduces a wide range of other effects and variants, including the mechanism by which a change in standard responses relative to deviants can develop through adaptation, different responses when two deviants are presented in a row or a standard is presented after two deviants, relaxation of standard responses back to deviant form after a stimulus-free period, and more complex sequences. Some cases are identified in which adaptation does not account for the whole difference between standard and deviant responses. The results thus provide a systematic means to determine how much of the response is due to adaptation in the system comprising the primary auditory cortex and medial geniculate nucleus, and how much requires involvement of higher-level processing.

Determination of Dynamic Brain Connectivity via Spectral Analysis.

Spectral analysis based on neural field theory is used to analyze dynamic connectivity via methods based on the physical eigenmodes that are the building blocks of brain dynamics. These approaches integrate over space instead of averaging over time and thereby greatly reduce or remove the temporal averaging effects, windowing artifacts, and noise at fine spatial scales that have bedeviled the analysis of dynamical functional connectivity (FC). The dependences of FC on dynamics at various timescales, and on windowing, are clarified and the results are demonstrated on simple test cases, demonstrating how modes provide directly interpretable insights that can be related to brain structure and function. It is shown that FC is dynamic even when the brain structure and effective connectivity are fixed, and that the observed patterns of FC are dominated by relatively few eigenmodes. Common artifacts introduced by statistical analyses that do not incorporate the physical nature of the brain are discussed and it is shown that these are avoided by spectral analysis using eigenmodes. Unlike most published artificially discretized "resting state networks" and other statistically-derived patterns, eigenmodes overlap, with every mode extending across the whole brain and every region participating in every mode-just like the vibrations that give rise to notes of a musical instrument. Despite this, modes are independent and do not interact in the linear limit. It is argued that for many purposes the intrinsic limitations of covariance-based FC instead favor the alternative of tracking eigenmode coefficients vs. time, which provide a compact representation that is directly related to biophysical brain dynamics.

Modal-Polar Representation of Evoked Response Potentials in Multiple Arousal States.

An expansion of the corticothalamic transfer function into eigenmodes and resonant poles is used to derive a simple formula for evoked response potentials (ERPs) in various states of arousal. The transfer function corresponds to the cortical response to an external stimulus, which encodes all the information and properties of the linear system. This approach links experimental observations of resonances and characteristic timescales in brain activity with physically based neural field theory (NFT). The present work greatly simplifies the formula of the analytical ERP, and separates its spatial part (eigenmodes) from the temporal part (poles). Within this framework, calculations involve contour integrations that yield an explicit expression for ERPs. The dominant global mode is considered explicitly in more detail to study how the ERP varies with time in this mode and to illustrate the method. For each arousal state in sleep and wake, the resonances of the system are determined and it is found that five poles are sufficient to study the main dynamics of the system in waking eyes-open and eyes-closed states. Similarly, it is shown that six poles suffice to reproduce ERPs in rapid-eye movement sleep, sleep state 1, and sleep state 2 states, whereas just four poles suffice to reproduce the dynamics in slow wave sleep. Thus, six poles are sufficient to preserve the main global ERP dynamics of the system for all states of arousal. These six poles correspond to the dominant resonances of the system at slow-wave, alpha, and beta frequencies. These results provide the basis for simplified analytic treatment of brain dynamics and link observations more closely to theory.

Brain dynamics and structure-function relationships via spectral factorization and the transfer function.

It is shown how the brain's linear transfer function provides a means to systematically analyze brain connectivity and dynamics, and to infer connectivity, eigenmodes, and activity measures such as spectra, evoked responses, coherence, and causality, all of which are widely used in brain monitoring. In particular, the Wilson spectral factorization algorithm is outlined and used to efficiently obtain linear transfer functions from experimental two-point correlation functions. The algorithm is tested on a series of brain-like structures of increasing complexity which include time delays, asymmetry, two-dimensionality, and complex network connectivity. These tests are used to verify the algorithm is suitable for application to brain dynamics, specify sampling requirements for experimental time series, and to verify that its runtime is short enough to obtain accurate results for systems of similar size to current experiments. The results can equally well be applied to inference of the transfer function in complex linear systems other than brains.

Neural Field Theory of Evoked Response Potentials With Attentional Gain Dynamics.

A generalized neural field model of large-scale activity in the corticothalamic system is used to predict standard evoked potentials. This model embodies local feedbacks that modulate the gains of neural activity as part of the response to incoming stimuli and thus enables both activity changes and effective connectivity changes to be calculated as parts of a generalized evoked response, and their relative contributions to be determined. The results show that incorporation of gain modulations enables a compact and physically justifiable description of the differences in gain between background-EEG and standard-ERP conditions, with the latter able to be initiated from the background state, rather than requiring distinct parameters as in earlier work. In particular, top-down gains are found to be reduced during an ERP, consistent with recent theoretical suggestions that the role of internal models is diminished in favor of external inputs when the latter change suddenly. The static-gain and modulated-gain system transfer functions are analyzed via control theory in terms of system resonances that were recently shown to implement data filtering whose gain adjustments can be interpreted as attention. These filters are shown to govern early and late features in standard evoked responses and their gain parameters are shown to be dynamically adjusted in a way that implements a form of attention. The results show that dynamically modulated resonant filters responsible for the low-frequency oscillations in an evoked potential response have different parameters than those responsible for low-frequency resting EEG responses, while both responses share similar mid- and high-frequency resonant filters. These results provide a biophysical mechanism by which oscillatory activity in the theta, alpha, and beta frequency ranges of an evoked response are modulated as reflections of attention; notably theta is enhanced and alpha suppressed during the latter parts of the ERP. Furthermore, the model enables the part of the ERP response induced by gain modulations to be estimated and interpreted in terms of attention.

Modeling melanopsin-mediated effects of light on circadian phase, melatonin suppression, and subjective sleepiness.

A physiologically based model of arousal dynamics is improved to incorporate the effects of the light spectrum on circadian phase resetting, melatonin suppression, and subjective sleepiness. To account for these nonvisual effects of light, melanopic irradiance replaces photopic illuminance that was used previously in the model. The dynamic circadian oscillator is revised according to the melanopic irradiance definition and tested against experimental circadian phase resetting dose-response and phase response data. Melatonin suppression function is recalibrated against melatonin dose-response data for monochromatic and polychromatic light sources. A new light-dependent term is introduced into the homeostatic weight component of subjective sleepiness to represent the direct alerting effect of light; the new term responds to light change in a time-dependent manner and is calibrated against experimental data. The model predictions are compared to a total of 14 experimental studies containing 26 data sets for 14 different spectral light profiles. The revised melanopic model shows on average 1.4 times lower prediction error for circadian phase resetting compared to the photopic-based model, 3.2 times lower error for melatonin suppression, and 2.1 times lower error for subjective sleepiness. Overall, incorporating melanopic irradiance allowed simulation of wavelength-dependent responses to light and could explain the majority of the observations. Moving forward, models of circadian phase resetting and the direct effects of light on alertness and sleep need to use nonvisual photoreception-based measures of light, for example, melanopic irradiance, instead of the traditionally used illuminance based on the visual system.

Neural Field Theory of Corticothalamic Attention With Control System Analysis.

Neural field theory is used to analyze attention by extending an existing model of the large-scale activity in the corticothalamic system to incorporate local feedbacks that modulate the gains of neural connectivity as part of the response to incoming stimuli. Treatment of both activity changes and connectivity changes as part of a generalized response enables generalized linear transfer functions of the combined response to be derived. These are then analyzed and interpreted via control theory in terms of stimulus-driven changes in system resonances that were recently shown to implement data filtering and prediction of the inputs. Using simple visual stimuli as a test case, it is shown that the gain response can implement attention by evaluating two main features of the stimuli: the magnitude and the rate of change, by increasing the weight placed on the rate of change in response to sudden changes, while reducing the contribution of stimuli value in tandem. These changes of filter parameters are shown to improve the prediction of the upcoming stimuli based on its recent time course. This outcome is analogous to controller-parameter tuning for performance enhancement in engineering control theory.

Feasibility of functional magnetic resonance imaging of ocular dominance and orientation preference in primary visual cortex.

A recent hemodynamic model is extended and applied to simulate and explore the feasibility of detecting ocular dominance (OD) and orientation preference (OP) columns in primary visual cortex by means of functional magnetic resonance imaging (fMRI). The stimulation entails a short oriented bar stimulus being presented to one eye and mapped to cortical neurons with corresponding OD and OP selectivity. Activated neurons project via patchy connectivity to excite other neurons with similar OP in nearby visual fields located preferentially along the direction of stimulus orientation. The resulting blood oxygen level dependent (BOLD) response is estimated numerically via the model's spatiotemporal hemodynamic response function. The results are then used to explore the feasibility of detecting spatial OD-OP modulation, either directly measuring BOLD or by using Wiener deconvolution to filter the image and estimate the underlying neural activity. The effect of noise is also considered and it is estimated that direct detection can be robust for fMRI resolution of around 0.5 mm, whereas detection with Wiener deconvolution is possible at a broader range from 0.125 mm to 1 mm resolution. The detection of OD-OP features is strongly dependent on hemodynamic parameters, such as low velocity and high damping reduce response spreads and result in less blurring. The short-bar stimulus that gives the most detectable response is found to occur when neural projections are at 45 relative to the edge of local OD boundaries, which provides a constraint on the OD-OP architecture even when it is not fully resolved.

Neural Field Theory of Corticothalamic Prediction With Control Systems Analysis.

Neural field theory is used to model and analyze realistic corticothalamic responses to simple visual stimuli. This yields system transfer functions that embody key features in common with those of engineering control systems, which enables interpretation of brain dynamics in terms of data filters. In particular, these features assist in finding internal signals that represent input stimuli and their changes, which are exactly the types of quantities used in control systems to enable prediction of future input signals, and adjustment of gains which is argued to be the analog of attention in control theory. Corticothalamic dynamics are shown to be analogous to the classical proportional-integral-derivative (PID) filters that are widely used in engineering.

NFTsim: Theory and Simulation of Multiscale Neural Field Dynamics.

A user ready, portable, documented software package, NFTsim, is presented to facilitate numerical simulations of a wide range of brain systems using continuum neural field modeling. NFTsim enables users to simulate key aspects of brain activity at multiple scales. At the microscopic scale, it incorporates characteristics of local interactions between cells, neurotransmitter effects, synaptodendritic delays and feedbacks. At the mesoscopic scale, it incorporates information about medium to large scale axonal ranges of fibers, which are essential to model dissipative wave transmission and to produce synchronous oscillations and associated cross-correlation patterns as observed in local field potential recordings of active tissue. At the scale of the whole brain, NFTsim allows for the inclusion of long range pathways, such as thalamocortical projections, when generating macroscopic activity fields. The multiscale nature of the neural activity produced by NFTsim has the potential to enable the modeling of resulting quantities measurable via various neuroimaging techniques. In this work, we give a comprehensive description of the design and implementation of the software. Due to its modularity and flexibility, NFTsim enables the systematic study of an unlimited number of neural systems with multiple neural populations under a unified framework and allows for direct comparison with analytic and experimental predictions. The code is written in C++ and bundled with Matlab routines for a rapid quantitative analysis and visualization of the outputs. The output of NFTsim is stored in plain text file enabling users to select from a broad range of tools for offline analysis. This software enables a wide and convenient use of powerful physiologically-based neural field approaches to brain modeling. NFTsim is distributed under the Apache 2.0 license.

Quantitative theory of deep brain stimulation of the subthalamic nucleus for the suppression of pathological rhythms in Parkinson's disease.

Deep brain stimulation (DBS) of the subthalamic nucleus (STN) is modeled to explore the mechanisms of this effective, but poorly understood, treatment for motor symptoms of drug-refractory Parkinson's disease and dystonia. First, a neural field model of the corticothalamic-basal ganglia (CTBG) system is developed that reproduces key clinical features of Parkinson's disease, including its characteristic 4-8 Hz and 13-30 Hz electrophysiological signatures. Deep brain stimulation of the STN is then modeled and shown to suppress the pathological 13-30 Hz (beta) activity for physiologically realistic and optimized stimulus parameters. This supports the idea that suppression of abnormally coherent activity in the CTBG system is a major factor in DBS therapy for Parkinson's disease, by permitting normal dynamics to resume. At high stimulus intensities, nonlinear effects in the target population mediate wave-wave interactions between resonant beta activity and the stimulus pulse train, leading to complex spectral structure that shows remarkable similarity to that seen in steady-state evoked potential experiments.

Prediction of Cognitive Performance and Subjective Sleepiness Using a Model of Arousal Dynamics.

A model of arousal dynamics is applied to predict objective performance and subjective sleepiness measures, including lapses and reaction time on a visual Performance Vigilance Test (vPVT), performance on a mathematical addition task (ADD), and the Karolinska Sleepiness Scale (KSS). The arousal dynamics model is comprised of a physiologically based flip-flop switch between the wake- and sleep-active neuronal populations and a dynamic circadian oscillator, thus allowing prediction of sleep propensity. Published group-level experimental constant routine (CR) and forced desynchrony (FD) data are used to calibrate the model to predict performance and sleepiness. Only the studies using dim light (<15 lux) during alertness measurements and controlling for sleep and entrainment before the start of the protocol are selected for modeling. This is done to avoid the direct alerting effects of light and effects of prior sleep debt and circadian misalignment on the data. The results show that linear combination of circadian and homeostatic drives is sufficient to predict dynamics of a variety of sleepiness and performance measures during CR and FD protocols, with sleep-wake cycles ranging from 20 to 42.85 h and a 2:1 wake-to-sleep ratio. New metrics relating model outputs to performance and sleepiness data are developed and tested against group average outcomes from 7 (vPVT lapses), 5 (ADD), and 8 (KSS) experimental protocols, showing good quantitative and qualitative agreement with the data (root mean squared error of 0.38, 0.19, and 0.35, respectively). The weights of the homeostatic and circadian effects are found to be different between the measures, with KSS having stronger homeostatic influence compared with the objective measures of performance. Using FD data in addition to CR data allows us to challenge the model in conditions of both acute sleep deprivation and structured circadian misalignment, ensuring that the role of the circadian and homeostatic drives in performance is properly captured.

A unified model of melatonin, 6-sulfatoxymelatonin, and sleep dynamics.

A biophysical model of the key aspects of melatonin synthesis and excretion has been developed, which is able to predict experimental dynamics of melatonin in plasma and saliva, and of its urinary metabolite 6-sulfatoxymelatonin (aMT6s). This new model is coupled to an established model of arousal dynamics, which predicts sleep and circadian dynamics based on light exposure and times of wakefulness. The combined model thus predicts melatonin levels over the sleep-wake/dark-light cycle and enables prediction of melatonin-based circadian phase markers, such as dim light melatonin onset (DLMO) and aMT6s acrophase under conditions of normal sleep and circadian misalignment. The model is calibrated and tested against group average data from 10 published experimental studies and is found to reproduce quantitatively the key dynamics of melatonin and aMT6s, including the timing of release and amplitude, as well as response to controlled lighting and shift work.

Suppression of Parkinsonian Beta Oscillations by Deep Brain Stimulation: Determination of Effective Protocols.

A neural field model of the corticothalamic-basal ganglia system is developed that describes enhanced beta activity within subthalamic and pallidal circuits in Parkinson's disease (PD) via system resonances. A model of deep brain stimulation (DBS) of typical clinical targets, the subthalamic nucleus (STN) and globus pallidus internus (GPi), is added and studied for several distinct stimulation protocols that are used for treatment of the motor symptoms of PD and that reduce pathological beta band activity (13-30 Hz) in the corticothalamic-basal ganglia network. The resulting impact of DBS on enhanced beta activity in the STN and GPi, as well as cortico-subthalamic and cortico-pallidal coherence, are studied. Both STN-DBS and GPi-DBS are found to be effective for suppressing peak STN and GPi power in the beta band, with GPi-DBS being slightly more effective in both the STN and the GPi for all stimulus protocols tested. The largest decrease in cortico-STN coherence is observed during STN-DBS, whereas GPi-DBS is most effective for reducing cortico-GPi coherence. A reduction of the pathologically large STN connection strengths that define the parkinsonian state results in enhanced 6 Hz activity and could thus represent a compensatory mechanism that has the side effect of driving parkinsonian tremor-like oscillations. This model provides a method for systematically testing effective DBS protocols that agrees with experimental and clinical findings. Furthermore, the model suggests GPi-DBS and STN-DBS have distinct impacts on elevated synchronization between the basal ganglia and motor cortex in PD.