Accuracy of dipole source reconstruction in the 3-layer BEM model against the 5-layer BEM-FMM model.

Objective: To compare cortical dipole fitting spatial accuracy between the widely used yet highly simplified 3-layer and modern more realistic 5-layer BEM-FMM models with and without adaptive mesh refinement (AMR) methods. Methods: We generate simulated noiseless 256-channel EEG data from 5-layer (7-compartment) meshes of 15 subjects from the Connectome Young Adult dataset. For each subject, we test four dipole positions, three sets of conductivity values, and two types of head segmentation. We use the boundary element method (BEM) with fast multipole method (FMM) acceleration, with or without (AMR), for forward modeling. Dipole fitting is carried out with the FieldTrip MATLAB toolbox. Results: The average position error (across all tested dipoles, subjects, and models) is ~4 mm, with a standard deviation of ~2 mm. The orientation error is ~20° on average, with a standard deviation of ~15°. Without AMR, the numerical inaccuracies produce a larger disagreement between the 3- and 5-layer models, with an average position error of ~8 mm (6 mm standard deviation), and an orientation error of 28° (28° standard deviation). Conclusions: The low-resolution 3-layer models provide excellent accuracy in dipole localization. On the other hand, dipole orientation is retrieved less accurately. Therefore, certain applications may require more realistic models for practical source reconstruction. AMR is a critical component for improving the accuracy of forward EEG computations using a high-resolution 5-layer volume conduction model. Significance: Improving EEG source reconstruction accuracy is important for several clinical applications, including epilepsy and other seizure-inducing conditions.

PyRates-A code-generation tool for modeling dynamical systems in biology and beyond.

The mathematical study of real-world dynamical systems relies on models composed of differential equations. Numerical methods for solving and analyzing differential equation systems are essential when complex biological problems have to be studied, such as the spreading of a virus, the evolution of competing species in an ecosystem, or the dynamics of neurons in the brain. Here we present PyRates, a Python-based software for modeling and analyzing differential equation systems via numerical methods. PyRates is specifically designed to account for the inherent complexity of biological systems. It provides a new language for defining models that mirrors the modular organization of real-world dynamical systems and thus simplifies the implementation of complex networks of interacting dynamic entities. Furthermore, PyRates provides extensive support for the various forms of interaction delays that can be observed in biological systems. The core of PyRates is a versatile code-generation system that translates user-defined models into "backend" implementations in various languages, including Python, Fortran, Matlab, and Julia. This allows users to apply a wide range of analysis methods for dynamical systems, eliminating the need for manual translation between code bases. PyRates may also be used as a model definition interface for the creation of custom dynamical systems tools. To demonstrate this, we developed two extensions of PyRates for common analyses of dynamic models of biological systems: PyCoBi for bifurcation analysis and RectiPy for parameter fitting. We demonstrate in a series of example models how PyRates can be used in combination with PyCoBi and RectiPy for model analysis and fitting. Together, these tools offer a versatile framework for applying computational modeling and numerical analysis methods to dynamical systems in biology and beyond.

Modeling the effects of transcranial magnetic stimulation on spatial attention.

Objectives. Transcranial magnetic stimulation (TMS) has been widely used to modulate brain activity in healthy and diseased brains, but the underlying mechanisms are not fully understood. Previous research leveraged biophysical modeling of the induced electric field (E-field) to map causal structure-function relationships in the primary motor cortex. This study aims at transferring this localization approach to spatial attention, which helps to understand the TMS effects on cognitive functions, and may ultimately optimize stimulation schemes.Approach. Thirty right-handed healthy participants underwent a functional magnetic imaging (fMRI) experiment, and seventeen of them participated in a TMS experiment. The individual fMRI activation peak within the right inferior parietal lobule (rIPL) during a Posner-like attention task defined the center target for TMS. Thereafter, participants underwent 500 Posner task trials. During each trial, a 5-pulse burst of 10 Hz repetitive TMS (rTMS) was given over the rIPL to modulate attentional processing. The TMS-induced E-fields for every cortical target were correlated with the behavioral modulation to identify relevant cortical regions for attentional orientation and reorientation.Main results. We did not observe a robust correlation between E-field strength and behavioral outcomes, highlighting the challenges of transferring the localization method to cognitive functions with high neural response variability and complex network interactions. Nevertheless, TMS selectively inhibited attentional reorienting in five out of seventeen subjects, resulting in task-specific behavioral impairments. The BOLD-measured neuronal activity and TMS-evoked neuronal effects showed different patterns, which emphasizes the principal distinction between the neural activity being correlated with (or maybe even caused by) particular paradigms, and the activity of neural populations exerting a causal influence on the behavioral outcome.Significance. This study is the first to explore the mechanisms of TMS-induced attentional modulation through electrical field modeling. Our findings highlight the complexity of cognitive functions and provide a basis for optimizing attentional stimulation protocols.

Laminar neural dynamics of auditory evoked responses: Computational modeling of local field potentials in auditory cortex of non-human primates.

Evoked neural responses to sensory stimuli have been extensively investigated in humans and animal models both to enhance our understanding of brain function and to aid in clinical diagnosis of neurological and neuropsychiatric conditions. Recording and imaging techniques such as electroencephalography (EEG), magnetoencephalography (MEG), local field potentials (LFPs), and calcium imaging provide complementary information about different aspects of brain activity at different spatial and temporal scales. Modeling and simulations provide a way to integrate these different types of information to clarify underlying neural mechanisms. In this study, we aimed to shed light on the neural dynamics underlying auditory evoked responses by fitting a rate-based model to LFPs recorded via multi-contact electrodes which simultaneously sampled neural activity across cortical laminae. Recordings included neural population responses to best-frequency (BF) and non-BF tones at four representative sites in primary auditory cortex (A1) of awake monkeys. The model considered major neural populations of excitatory, parvalbumin-expressing (PV), and somatostatin-expressing (SOM) neurons across layers 2/3, 4, and 5/6. Unknown parameters, including the connection strength between the populations, were fitted to the data. Our results revealed similar population dynamics, fitted model parameters, predicted equivalent current dipoles (ECD), tuning curves, and lateral inhibition profiles across recording sites and animals, in spite of quite different extracellular current distributions. We found that PV firing rates were higher in BF than in non-BF responses, mainly due to different strengths of tonotopic thalamic input, whereas SOM firing rates were higher in non-BF than in BF responses due to lateral inhibition. In conclusion, we demonstrate the feasibility of the model-fitting approach in identifying the contributions of cell-type specific population activity to stimulus-evoked LFPs across cortical laminae, providing a foundation for further investigations into the dynamics of neural circuits underlying cortical sensory processing.

Spatiotemporal phase slip patterns for visual evoked potentials, covert object naming tasks, and insight moments extracted from 256 channel EEG recordings.

Phase slips arise from state transitions of the coordinated activity of cortical neurons which can be extracted from the EEG data. The phase slip rates (PSRs) were studied from the high-density (256 channel) EEG data, sampled at 16.384 kHz, of five adult subjects during covert visual object naming tasks. Artifact-free data from 29 trials were averaged for each subject. The analysis was performed to look for phase slips in the theta (4-7 Hz), alpha (7-12 Hz), beta (12-30 Hz), and low gamma (30-49 Hz) bands. The phase was calculated with the Hilbert transform, then unwrapped and detrended to look for phase slip rates in a 1.0 ms wide stepping window with a step size of 0.06 ms. The spatiotemporal plots of the PSRs were made by using a montage layout of 256 equidistant electrode positions. The spatiotemporal profiles of EEG and PSRs during the stimulus and the first second of the post-stimulus period were examined in detail to study the visual evoked potentials and different stages of visual object recognition in the visual, language, and memory areas. It was found that the activity areas of PSRs were different as compared with EEG activity areas during the stimulus and post-stimulus periods. Different stages of the insight moments during the covert object naming tasks were examined from PSRs and it was found to be about 512 ± 21 ms for the 'Eureka' moment. Overall, these results indicate that information about the cortical phase transitions can be derived from the measured EEG data and can be used in a complementary fashion to study the cognitive behavior of the brain.

Precise motor mapping with transcranial magnetic stimulation.

We describe a routine to precisely localize cortical muscle representations within the primary motor cortex with transcranial magnetic stimulation (TMS) based on the functional relation between induced electric fields at the cortical level and peripheral muscle activation (motor-evoked potentials; MEPs). Besides providing insights into structure-function relationships, this routine lays the foundation for TMS dosing metrics based on subject-specific cortical electric field thresholds. MEPs for different coil positions and orientations are combined with electric field modeling, exploiting the causal nature of neuronal activation to pinpoint the cortical origin of the MEPs. This involves constructing an individual head model using magnetic resonance imaging, recording MEPs via electromyography during TMS and computing the induced electric fields with numerical modeling. The cortical muscle representations are determined by relating the TMS-induced electric fields to the MEP amplitudes. Subsequently, the coil position to optimally stimulate the origin of the identified cortical MEP can be determined by numerical modeling. The protocol requires 2 h of manual preparation, 10 h for the automated head model construction, one TMS session lasting 2 h, 12 h of computational postprocessing and an optional second TMS session lasting 30 min. A basic level of computer science expertise and standard TMS neuronavigation equipment suffices to perform the protocol.

White matter brain structure predicts language performance and learning success.

Individual differences in the ability to process language have long been discussed. Much of the neural basis of these, however, is yet unknown. Here we investigated the relationship between long-range white matter connectivity of the brain, as revealed by diffusion tractography, and the ability to process syntactically complex sentences in the participants' native language as well as the improvement thereof by multiday training. We identified specific network motifs by singular value decomposition that indeed related white matter structural connectivity to individual language processing performance. First, for two such motifs, one in the left and one in the right hemisphere, their individual prevalence significantly predicted the individual language performance, suggesting an anatomical predisposition for the individual ability to process syntactically complex sentences. Both motifs comprise a number of cortical regions, but seem to be dominated by areas known for the involvement in working memory rather than the classical language network itself. Second, we identified another left hemispheric network motif, whose change of prevalence over the training period significantly correlated with the individual change in performance, thus reflecting training induced white matter plasticity. This motif comprises diverse cortical areas including regions known for their involvement in language processing, working memory and motor functions. The present findings suggest that individual differences in language processing and learning can be explained, in part, by individual differences in the brain's white matter structure. Brain structure may be a crucial factor to be considered when discussing variations in human cognitive performance, more generally.

Rate and oscillatory switching dynamics of a multilayer visual microcircuit model.

The neocortex is organized around layered microcircuits consisting of a variety of excitatory and inhibitory neuronal types which perform rate- and oscillation-based computations. Using modeling, we show that both superficial and deep layers of the primary mouse visual cortex implement two ultrasensitive and bistable switches built on mutual inhibitory connectivity motives between somatostatin, parvalbumin, and vasoactive intestinal polypeptide cells. The switches toggle pyramidal neurons between high and low firing rate states that are synchronized across layers through translaminar connectivity. Moreover, inhibited and disinhibited states are characterized by low- and high-frequency oscillations, respectively, with layer-specific differences in frequency and power which show asymmetric changes during state transitions. These findings are consistent with a number of experimental observations and embed firing rate together with oscillatory changes within a switch interpretation of the microcircuit.

Comparison of the performance and reliability between improved sampling strategies for polynomial chaos expansion.

As uncertainty and sensitivity analysis of complex models grows ever more important, the difficulty of their timely realizations highlights a need for more efficient numerical operations. Non-intrusive Polynomial Chaos methods are highly efficient and accurate methods of mapping input-output relationships to investigate complex models. There is substantial potential to increase the efficacy of the method regarding the selected sampling scheme. We examine state-of-the-art sampling schemes categorized in space-filling-optimal designs such as Latin Hypercube sampling and L1-optimal sampling and compare their empirical performance against standard random sampling. The analysis was performed in the context of L1 minimization using the least-angle regression algorithm to fit the GPCE regression models. Due to the random nature of the sampling schemes, we compared different sampling approaches using statistical stability measures and evaluated the success rates to construct a surrogate model with relative errors of <0.1%, <1%, and <10%, respectively. The sampling schemes are thoroughly investigated by evaluating the y of surrogate models constructed for various distinct test cases, which represent different problem classes covering low, medium and high dimensional problems. Finally, the sampling schemes are tested on an application example to estimate the sensitivity of the self-impedance of a probe that is used to measure the impedance of biological tissues at different frequencies. We observed strong differences in the convergence properties of the methods between the analyzed test functions.

Cross-frequency phase-amplitude coupling in repetitive movements in patients with Parkinson's disease.

Bradykinesia is a cardinal motor symptom in Parkinson's disease (PD), the pathophysiology of which is not fully understood. We analyzed the role of cross-frequency coupling of oscillatory cortical activity in motor impairment in patients with PD and healthy controls. High-density EEG signals were recorded during various motor activities and at rest. Patients performed a repetitive finger-pressing task normally, but were slower than controls during tapping. Phase-amplitude coupling (PAC) between ß (13-30 Hz) and broadband γ (50-150 Hz) was computed from individual EEG source signals in the premotor, primary motor, and primary somatosensory cortices, and the primary somatosensory complex. In all four regions, averaging the entire movement period resulted in higher PAC in patients than in controls for the resting condition and the pressing task (similar performance between groups). However, this was not the case for the tapping tasks where patients performed slower. This suggests the strength of state-related ß-γ PAC does not determine Parkinsonian bradykinesia. Examination of the dynamics of oscillatory EEG signals during motor transitions revealed a distinctive motif of PAC rise and decay around press onset. This pattern was also present at press offset and slow tapping onset, linking such idiosyncratic PAC changes to transitions between different movement states. The transition-related PAC modulation in patients was similar to controls in the pressing task but flattened during slow tapping, which related to normal and abnormal performance, respectively. These findings suggest that the dysfunctional evolution of neuronal population dynamics during movement execution is an important component of the pathophysiology of Parkinsonian bradykinesia.NEW & NOTEWORTHY Our findings using noninvasive EEG recordings provide evidence that PAC dynamics might play a role in the physiological cortical control of movement execution and may encode transitions between movement states. Results in patients with Parkinson's disease suggest that bradykinesia is related to a deficit of the dynamic regulation of PAC during movement execution rather than its absolute strength. Our findings may contribute to the development of a new concept of the pathophysiology of bradykinesia.

The effect of meninges on the electric fields in TES and TMS. Numerical modeling with adaptive mesh refinement.

BACKGROUND: When modeling transcranial electrical stimulation (TES) and transcranial magnetic stimulation (TMS) in the brain, the meninges - dura, arachnoid, and pia mater - are often neglected due to high computational costs. OBJECTIVE: We investigate the impact of the meningeal layers on the cortical electric field in TES and TMS while considering the headreco segmentation as the base model. METHOD: We use T1/T2 MRI data from 16 subjects and apply the boundary element fast multipole method with adaptive mesh refinement, which enables us to accurately solve this problem and establish method convergence at reasonable computational cost. We compare electric fields in the presence and absence of various meninges for two brain areas (M1HAND and DLPFC) and for several distinct TES and TMS setups. RESULTS: Maximum electric fields in the cortex for focal TES consistently increase by approximately 30% on average when the meninges are present in the CSF volume. Their effect on the maximum field can be emulated by reducing the CSF conductivity from 1.65 S/m to approximately 0.85 S/m. In stark contrast to that, the TMS electric fields in the cortex are only weakly affected by the meningeal layers and slightly (∼6%) decrease on average when the meninges are included. CONCLUSION: Our results quantify the influence of the meninges on the cortical TES and TMS electric fields. Both focal TES and TMS results are very consistent. The focal TES results are also in a good agreement with a prior relevant study. The solver and the mesh generator for the meningeal layers (compatible with SimNIBS) are available online.

Resting-State fMRI Functional Connectivity Strength Predicts Local Activity Change in the Dorsal Cingulate Cortex: A Multi-Target Focused rTMS Study.

Previous resting state functional magnetic resonance imaging (RS-fMRI) studies suggested that repetitive transcranial magnetic stimulation (rTMS) can modulate local activity in distant areas via functional connectivity (FC). A brain region has more than one connection with the superficial cortical areas. The current study proposed a multi-target focused rTMS protocol for indirectly stimulating a deep region, and to investigate 1) whether FC strength between stimulation targets (right middle frontal gyrus [rMFG] and right inferior parietal lobule [rIPL]) and effective region (dorsal anterior cingulate cortex [dACC]) can predict local activity changes of dACC and 2) whether multiple stimulation targets can focus on the dACC via FC. A total of 24 healthy participants received rTMS with two stimulation targets, both showing strong FC with the dACC. There were four rTMS conditions (>1 week apart, 10 Hz, 1800 pulses for each): rMFG-target, rIPL-target, Double-targets (900 pulses for each target), and Sham. The results failed to validate the multi-target focused rTMS hypothesis. But rMFG-target significantly decreased the local activity in the dACC. In addition, stronger dACC-rMFG FC was associated with a greater local activity change in the dACC. Future studies should use stronger FC to focus stimulation effects on the deep region.

Mean-field approximations of networks of spiking neurons with short-term synaptic plasticity.

Low-dimensional descriptions of spiking neural network dynamics are an effective tool for bridging different scales of organization of brain structure and function. Recent advances in deriving mean-field descriptions for networks of coupled oscillators have sparked the development of a new generation of neural mass models. Of notable interest are mean-field descriptions of all-to-all coupled quadratic integrate-and-fire (QIF) neurons, which have already seen numerous extensions and applications. These extensions include different forms of short-term adaptation considered to play an important role in generating and sustaining dynamic regimes of interest in the brain. It is an open question, however, whether the incorporation of presynaptic forms of synaptic plasticity driven by single neuron activity would still permit the derivation of mean-field equations using the same method. Here we discuss this problem using an established model of short-term synaptic plasticity at the single neuron level, for which we present two different approaches for the derivation of the mean-field equations. We compare these models with a recently proposed mean-field approximation that assumes stochastic spike timings. In general, the latter fails to accurately reproduce the macroscopic activity in networks of deterministic QIF neurons with distributed parameters. We show that the mean-field models we propose provide a more accurate description of the network dynamics, although they are mathematically more involved. Using bifurcation analysis, we find that QIF networks with presynaptic short-term plasticity can express regimes of periodic bursting activity as well as bistable regimes. Together, we provide novel insight into the macroscopic effects of short-term synaptic plasticity in spiking neural networks, as well as two different mean-field descriptions for future investigations of such networks.

Efficient high-resolution TMS mapping of the human motor cortex by nonlinear regression.

Transcranial magnetic stimulation (TMS) is a powerful tool to investigate causal structure-function relationships in the human brain. However, a precise delineation of the effectively stimulated neuronal populations is notoriously impeded by the widespread and complex distribution of the induced electric field. Here, we propose a method that allows rapid and feasible cortical localization at the individual subject level. The functional relationship between electric field and behavioral effect is quantified by combining experimental data with numerically modeled fields to identify the cortical origin of the modulated effect. Motor evoked potentials (MEPs) from three finger muscles were recorded for a set of random stimulations around the primary motor area. All induced electric fields were nonlinearly regressed against the elicited MEPs to identify their cortical origin. We could distinguish cortical muscle representation with high spatial resolution and localized them primarily on the crowns and rims of the precentral gyrus. A post-hoc analysis revealed exponential convergence of the method with the number of stimulations, yielding a minimum of about 180 random stimulations to obtain stable results. Establishing a functional link between the modulated effect and the underlying mode of action, the induced electric field, is a fundamental step to fully exploit the potential of TMS. In contrast to previous approaches, the presented protocol is particularly easy to implement, fast to apply, and very robust due to the random coil positioning and therefore is suitable for practical and clinical applications.

On the Role of Arkypallidal and Prototypical Neurons for Phase Transitions in the External Pallidum.

The external pallidum (globus pallidus pars externa [GPe]) plays a central role for basal ganglia functions and dynamics and, consequently, has been included in most computational studies of the basal ganglia. These studies considered the GPe as a homogeneous neural population. However, experimental studies have shown that the GPe contains at least two distinct cell types (prototypical and arkypallidal cells). In this work, we provide in silico insight into how pallidal heterogeneity modulates dynamic regimes inside the GPe and how they affect the GPe response to oscillatory input. We derive a mean-field model of the GPe system from a microscopic spiking neural network of recurrently coupled prototypical and arkypallidal neurons. Using bifurcation analysis, we examine the influence of dopamine-dependent changes of intrapallidal connectivity on the GPe dynamics. We find that increased self-inhibition of prototypical cells can induce oscillations, whereas increased inhibition of prototypical cells by arkypallidal cells leads to the emergence of a bistable regime. Furthermore, we show that oscillatory input to the GPe, arriving from striatum, leads to characteristic patterns of cross-frequency coupling observed at the GPe. Based on these findings, we propose two different hypotheses of how dopamine depletion at the GPe may lead to phase-amplitude coupling between the parkinsonian beta rhythm and a GPe-intrinsic γ rhythm. Finally, we show that these findings generalize to realistic spiking neural networks of sparsely coupled Type I excitable GPe neurons.SIGNIFICANCE STATEMENT Our work provides (1) insight into the theoretical implications of a dichotomous globus pallidus pars externa (GPe) organization, and (2) an exact mean-field model that allows for future investigations of the relationship between GPe spiking activity and local field potential fluctuations. We identify the major phase transitions that the GPe can undergo when subject to static or periodic input and link these phase transitions to the emergence of synchronized oscillations and cross-frequency coupling in the basal ganglia. Because of the close links between our model and experimental findings on the structure and dynamics of prototypical and arkypallidal cells, our results can be used to guide both experimental and computational studies on the role of the GPe for basal ganglia dynamics in health and disease.

Functional brain plasticity during L1 training on complex sentences: Changes in gamma-band oscillatory activity.

The adult human brain remains plastic even after puberty. However, whether first language (L1) training in adults can alter the language network is yet largely unknown. Thus, we conducted a longitudinal training experiment on syntactically complex German sentence comprehension. Sentence complexity was varied by the depth of the center embedded relative clauses (i.e., single or double embedded). Comprehension was tested after each sentence with a question on the thematic role assignment. Thirty adult, native German speakers were recruited for 4 days of training. Magnetoencephalography (MEG) data were recorded and subjected to spectral power analysis covering the classical frequency bands (i.e., theta, alpha, beta, low gamma, and gamma). Normalized spectral power, time-locked to the final closure of the relative clause, was subjected to a two-factor analysis ("sentence complexity" and "training days"). Results showed that for the more complex sentences, the interaction of sentence complexity and training days was observed in Brodmann area 44 (BA 44) as a decrease of gamma power with training. Moreover, in the gamma band (55-95 Hz) functional connectivity between BA 44 and other brain regions such as the inferior frontal sulcus and the inferior parietal cortex were correlated with behavioral performance increase due to training. These results show that even for native speakers, complex L1 sentence training improves language performance and alters neural activities of the left hemispheric language network. Training strengthens the use of the dorsal processing stream with working-memory-related brain regions for syntactically complex sentences, thereby demonstrating the brain's functional plasticity for L1 training.

Ephaptic coupling in white matter fibre bundles modulates axonal transmission delays.

Axonal connections are widely regarded as faithful transmitters of neuronal signals with fixed delays. The reasoning behind this is that extracellular potentials caused by spikes travelling along axons are too small to have an effect on other axons. Here we devise a computational framework that allows us to study the effect of extracellular potentials generated by spike volleys in axonal fibre bundles on axonal transmission delays. We demonstrate that, although the extracellular potentials generated by single spikes are of the order of microvolts, the collective extracellular potential generated by spike volleys can reach several millivolts. As a consequence, the resulting depolarisation of the axonal membranes increases the velocity of spikes, and therefore reduces axonal delays between brain areas. Driving a neural mass model with such spike volleys, we further demonstrate that only ephaptic coupling can explain the reduction of stimulus latencies with increased stimulus intensities, as observed in many psychological experiments.

Spatiotemporal features of ß-γ phase-amplitude coupling in Parkinson's disease derived from scalp EEG.

Abnormal phase-amplitude coupling between ß and broadband-γ activities has been identified in recordings from the cortex or scalp of patients with Parkinson's disease. While enhanced phase-amplitude coupling has been proposed as a biomarker of Parkinson's disease, the neuronal mechanisms underlying the abnormal coupling and its relationship to motor impairments in Parkinson's disease remain unclear. To address these issues, we performed an in-depth analysis of high-density EEG recordings at rest in 19 patients with Parkinson's disease and 20 age- and sex-matched healthy control subjects. EEG signals were projected onto the individual cortical surfaces using source reconstruction techniques and separated into spatiotemporal components using independent component analysis. Compared to healthy controls, phase-amplitude coupling of Parkinson's disease patients was enhanced in dorsolateral prefrontal cortex, premotor cortex, primary motor cortex and somatosensory cortex, the difference being statistically significant in the hemisphere contralateral to the clinically more affected side. ß and γ signals involved in generating abnormal phase-amplitude coupling were not strictly phase-phase coupled, ruling out that phase-amplitude coupling merely reflects the abnormal activity of a single oscillator in a recurrent network. We found important differences for couplings between the ß and γ signals from identical components as opposed to those from different components (originating from distinct spatial locations). While both couplings were abnormally enhanced in patients, only the latter were correlated with clinical motor severity as indexed by part III of the Movement Disorder Society Unified Parkinson's Disease Rating Scale. Correlations with parkinsonian motor symptoms of such inter-component couplings were found in premotor, primary motor and somatosensory cortex, but not in dorsolateral prefrontal cortex, suggesting motor domain specificity. The topography of phase-amplitude coupling demonstrated profound differences in patients compared to controls. These findings suggest, first, that enhanced phase-amplitude coupling in Parkinson's disease patients originates from the coupling between distinct neural networks in several brain regions involved in motor control. Because these regions included the somatosensory cortex, abnormal phase-amplitude coupling is not exclusively tied to the hyperdirect tract connecting cortical regions monosynaptically with the subthalamic nucleus. Second, only the coupling between ß and γ signals from different components appears to have pathophysiological significance, suggesting that therapeutic approaches breaking the abnormal lateral coupling between neuronal circuits may be more promising than targeting phase-amplitude coupling per se.

A Mean-Field Description of Bursting Dynamics in Spiking Neural Networks with Short-Term Adaptation.

Bursting plays an important role in neural communication. At the population level, macroscopic bursting has been identified in populations of neurons that do not express intrinsic bursting mechanisms. For the analysis of phase transitions between bursting and non-bursting states, mean-field descriptions of macroscopic bursting behavior are a valuable tool. In this article, we derive mean-field descriptions of populations of spiking neurons and examine whether states of collective bursting behavior can arise from short-term adaptation mechanisms. Specifically, we consider synaptic depression and spike-frequency adaptation in networks of quadratic integrate-and-fire neurons. Analyzing the mean-field model via bifurcation analysis, we find that bursting behavior emerges for both types of short-term adaptation. This bursting behavior can coexist with steady-state behavior, providing a bistable regime that allows for transient switches between synchronized and nonsynchronized states of population dynamics. For all of these findings, we demonstrate a close correspondence between the spiking neural network and the mean-field model. Although the mean-field model has been derived under the assumptions of an infinite population size and all-to-all coupling inside the population, we show that this correspondence holds even for small, sparsely coupled networks. In summary, we provide mechanistic descriptions of phase transitions between bursting and steady-state population dynamics, which play important roles in both healthy neural communication and neurological disorders.

A novel approach to localize cortical TMS effects.

Despite the widespread use of transcranial magnetic stimulation (TMS), the precise cortical locations underlying the resulting physiological and behavioral effects are still only coarsely known. To date, mapping strategies have relied on projection approaches (often termed "center of gravity" approaches) or maximum electric field value evaluation, and therefore localize the stimulated cortical site only approximately and indirectly. Focusing on the motor cortex, we present and validate a novel method to reliably determine the effectively stimulated cortical site at the individual subject level. The approach combines measurements of motor evoked potentials (MEPs) at different coil positions and orientations with numerical modeling of induced electric fields. We identify sharply bounded cortical areas, around the gyral crowns and rims of the motor hand area, as the origin of MEPs and show that the magnitude of the tangential component and the overall magnitude of the electric field are most relevant for the observed effect. To validate our approach, we identified the coil location and orientation that produces the maximal electric field at the predicted stimulation site, and then experimentally show that this location produces MEPs more efficiently than other tested locations/orientations. Moreover, we used extensive uncertainty and sensitivity analyses to verify the robustness of the method and identify the most critical model parameters. Our generic approach improves the localization of the cortical area effectively stimulated by TMS and may be transferred to other modalities such as language mapping.