Identifying mutual information transfer in the brain with differential-algebraic modeling: Evidence for fast oscillatory coupling between cortical somatosensory areas 3b and 1

Correspondence between thalamic injury-induced changes in resting-state fMRI of monkeys and their sensorimotor behaviors and neural activities

Resting state functional MRI (rsfMRI) exploits variations in blood-oxygenation-level-dependent (BOLD) signals to infer resting state functional connectivity (FC) within and between brain networks. However, there have been few reports quantifying and validating the results of rsfMRI analyses with other metrics of brain circuits. We measured longitudinal changes in FC both within and between brain networks in three squirrel monkeys after focal lesions of the thalamic ventroposterior lateral nucleus (VPL) that were intended to disrupt the input to somatosensory cortex and impair manual dexterity. Local field potential signals were recorded to assess electrophysiological changes during each animal's recovery, and behavioral performances were measured longitudinally using a sugar-pellet grasping task. Finally, end-point histological evaluations were performed on brain tissue slices to quantify the VPL damage. The rsfMRI data analysis showed significant decrease in FC measures both within and between networks immediately post-injury, which started to recover at different time-points for each animal. The trajectories of FC recovery for each animal mirrored their individual behavioral recovery time-courses. Electrophysiological measurements of inter-electrode coherences and end-point histological measures also aligned well with the graded injury effects measured using rsfMRI-based FC. A simple algorithm employing FC measures from the somatosensory network could accurately predict each monkeys' behavioral recovery timeframe after four weeks post-injury. Whole brain between-network FC measures further revealed that the injury effects were not limited to thalamocortical connections but were rather more widespread. Overall, this study provides evidence of the validity of rsfMRI based FC measures as indicators of the functional integrity and behavioral relevance following an injury to a specific brain circuit.

Standardized Kalman filtering for dynamical source localization of concurrent subcortical and cortical brain activity

OBJECTIVE

We introduce standardized Kalman filtering (SKF) as a new spatiotemporal method for tracking brain activity. Via the Kalman filtering scheme, the computational workload is low, and by spatiotemporal standardization, we reduce the depth bias of non-standardized Kalman filtering (KF).

METHODS

We describe the standardized KF methodology for spatiotemporal tracking from the Bayesian perspective. We construct a realistic simulation setup that resembles activity due to somatosensory evoked potential (SEP) to validate the proposed methodology before we run our tests using real SEP data.

RESULTS

In the experiments, SKF was compared with standardized low-resolution brain electromagnetic tomography (sLORETA) and the non-standardized KF. SKF localized the cortical and subcortical SEP originators appropriately and tracked P20/N20 originators for investigated signal-to-noise ratios (25, 15, and 5 dB). sLORETA distinguished those for 25 and 15 dB suppressing the subcortical originators. KF tracked only the evolution of cortical activity but mislocalized it.

CONCLUSIONS

The numerical results suggest that SKF inherits the estimation accuracy of sLORETA and traceability of KF while producing focal estimates for SEP originators.

SIGNIFICANCE

SKF could help study time-evolving brain activities and localize landmarks with a deep contributor or when there is no prior knowledge of evolution.

Non-Equilibrium Enhancement of Classical Information Transmission

Information transmission plays a crucial role across various fields, including physics, engineering, biology, and society. The efficiency of this transmission is quantified by mutual information and its associated information capacity. While studies in closed systems have yielded significant progress, understanding the impact of non-equilibrium effects on open systems remains a challenge. These effects, characterized by the exchange of energy, information, and materials with the external environment, can influence both mutual information and information capacity. Here, we delve into this challenge by exploring non-equilibrium effects using the memoryless channel model, a cornerstone of information channel coding theories and methodology development. Our findings reveal that mutual information exhibits a convex relationship with non-equilibriumness, quantified by the non-equilibrium strength in transmission probabilities. Notably, channel information capacity is enhanced by non-equilibrium effects. Furthermore, we demonstrate that non-equilibrium thermodynamic cost, characterized by the entropy production rate, can actually improve both mutual information and information channel capacity, leading to a boost in overall information transmission efficiency. Our numerical results support our conclusions.

Can individually targeted and optimized multi-channel tDCS outperform standard bipolar tDCS in stimulating the primary somatosensory cortex?

BACKGROUND

Transcranial direct current stimulation (tDCS) has emerged as a non-invasive neuro-modulation technique. Most studies show that anodal tDCS increases cortical excitability, however, with variable outcomes. Previously, we have shown in computer simulations that our multi-channel tDCS (mc-tDCS) approach, the distributed constrained maximum intensity (D-CMI) method can potentially lead to better controlled tDCS results due to the improved directionality of the injected current at the target side for individually optimized D-CMI montages.

OBJECTIVE

In this study, we test the application of the D-CMI approach in an experimental study to stimulate the somatosensory P20/N20 target source in Brodmann area 3b and compare it with standard bipolar tDCS and sham conditions.

METHODS

We applied anodal D-CMI, the standard bipolar and D-CMI based Sham tDCS for 10 min to target the 20 ms post-stimulus somatosensory P20/N20 target brain source in Brodmann area 3b reconstructed using combined magnetoencephalography (MEG) and electroencephalography (EEG) source analysis in realistic head models with calibrated skull conductivity in a group-study with 13 subjects. Finger-stimulated somatosensory evoked fields (SEF) were recorded and the component at 20 ms post-stimulus (M20) was analyzed before and after the application of the three tDCS conditions in order to read out the stimulation effect on Brodmann area 3b.

RESULTS

Analysis of the finger stimulated SEF M20 peak before (baseline) and after tDCS shows a significant increase in source amplitude in Brodmann area 3b for D-CMI (6-16 min after tDCS), while no significant effects are found for standard bipolar (6-16 min after tDCS) and sham (6-16 min after tDCS) stimulation conditions. For the later time courses (16-26 and 27-37 min post-stimulation), we found a significant decrease in M20 peak source amplitude for standard bipolar and sham tDCS, while there was no effect for D-CMI.

CONCLUSION

Our results indicate that targeted and optimized, and thereby highly individualized, mc-tDCS can outperform standard bipolar stimulation and lead to better control over stimulation outcomes with, however, a considerable amount of additional work compared to standard bipolar tDCS.

Reconstructing subcortical and cortical somatosensory activity via the RAMUS inverse source analysis technique using median nerve SEP data

This study concerns reconstructing brain activity at various depths based on non-invasive EEG (electroencephalography) scalp measurements. We aimed at demonstrating the potential of the RAMUS (randomized multiresolution scanning) technique in localizing weakly distinguishable far-field sources in combination with coinciding cortical activity. As we have shown earlier theoretically and through simulations, RAMUS is a novel mathematical method that by employing the multigrid concept, allows marginalizing noise and depth bias effects and thus enables the recovery of both cortical and subcortical brain activity. To show this capability with experimental data, we examined the 14-30 ms post-stimulus somatosensory evoked potential (SEP) responses of human median nerve stimulation in three healthy adult subjects. We aim at reconstructing the different response components by evaluating a RAMUS-based estimate for the primary current density in the nervous tissue. We present source reconstructions obtained with RAMUS and compare them with the literature knowledge of the SEP components and the outcome of the unit-noise gain beamformer (UGNB) and standardized low-resolution brain electromagnetic tomography (sLORETA). We also analyzed the effect of the iterative alternating sequential technique, the optimization technique of RAMUS, compared to the classical minimum norm estimation (MNE) technique. Matching with our previous numerical studies, the current results suggest that RAMUS could have the potential to enhance the detection of simultaneous deep and cortical components and the distinction between the evoked sulcal and gyral activity.

Parametrizing the Conditionally Gaussian Prior Model for Source Localization with Reference to the P20/N20 Component of Median Nerve SEP/SEF

In this article, we focused on developing the conditionally Gaussian hierarchical Bayesian model (CG-HBM), which forms a superclass of several inversion methods for source localization of brain activity using somatosensory evoked potential (SEP) and field (SEF) measurements. The goal of this proof-of-concept study was to improve the applicability of the CG-HBM as a superclass by proposing a robust approach for the parametrization of focal source scenarios. We aimed at a parametrization that is invariant with respect to altering the noise level and the source space size. The posterior difference between the gamma and inverse gamma hyperprior was minimized by optimizing the shape parameter, while a suitable range for the scale parameter can be obtained via the prior-over-measurement signal-to-noise ratio, which we introduce as a new concept in this study. In the source localization experiments, the primary generator of the P20/N20 component was detected in the Brodmann area 3b using the CG-HBM approach and a parameter range derived from the existing knowledge of the Tikhonov-regularized minimum norm estimate, i.e., the classical Gaussian prior model. Moreover, it seems that the detection of deep thalamic activity simultaneously with the P20/N20 component with the gamma hyperprior can be enhanced while using a close-to-optimal shape parameter value.

Randomized Multiresolution Scanning in Focal and Fast E/MEG Sensing of Brain Activity with a Variable Depth

We focus on electro-/magnetoencephalography imaging of the neural activity and, in particular, finding a robust estimate for the primary current distribution via the hierarchical Bayesian model (HBM). Our aim is to develop a reasonably fast maximum a posteriori (MAP) estimation technique which would be applicable for both superficial and deep areas without specific a priori knowledge of the number or location of the activity. To enable source distinguishability for any depth, we introduce a randomized multiresolution scanning (RAMUS) approach in which the MAP estimate of the brain activity is varied during the reconstruction process. RAMUS aims to provide a robust and accurate imaging outcome for the whole brain, while maintaining the computational cost on an appropriate level. The inverse gamma (IG) distribution is applied as the primary hyperprior in order to achieve an optimal performance for the deep part of the brain. In this proof-of-the-concept study, we consider the detection of simultaneous thalamic and somatosensory activity via numerically simulated data modeling the 14-20 ms post-stimulus somatosensory evoked potential and field response to electrical wrist stimulation. Both a spherical and realistic model are utilized to analyze the source reconstruction discrepancies. In the numerically examined case, RAMUS was observed to enhance the visibility of deep components and also marginalizing the random effects of the discretization and optimization without a remarkable computation cost. A robust and accurate MAP estimate for the primary current density was obtained in both superficial and deep parts of the brain.

Primary somatosensory contextual modulation is encoded by oscillation frequency change

OBJECTIVE

This study characterized thalamo-cortical communication by assessing the effect of context-dependent modulation on the very early somatosensory evoked high-frequency oscillations (HF oscillations).

METHODS

We applied electrical stimuli to the median nerve together with an auditory oddball paradigm, presenting standard and deviant target tones representing differential cognitive contexts to the constantly repeated electrical stimulation. Median nerve stimulation without auditory stimulation served as unimodal control.

RESULTS

A model consisting of one subcortical (near thalamus) and two cortical (Brodmann areas 1 and 3b) dipolar sources explained the measured HF oscillations. Both at subcortical and the cortical levels HF oscillations were significantly smaller during bimodal (somatosensory plus auditory) than unimodal (somatosensory only) stimulation. A delay differential equation model was developed to investigate interactions within the 3-node thalamo-cortical network. Importantly, a significant change in the eigenfrequency of Brodmann area 3b was related to the context-dependent modulation, while there was no change in the network coupling.

CONCLUSION

This model strongly suggests cortico-thalamic feedback from both cortical Brodmann areas 1 and 3b to the thalamus. With the 3-node network model, thalamo-cortical feedback could be described.

SIGNIFICANCE

Frequency encoding plays an important role in contextual modulation in the somatosensory thalamo-cortical network.

High frequency oscillations evoked by peripheral magnetic stimulation

The analysis of somatosensory evoked potentials (SEP) and / or fields (SEF) is a well-established and important tool for investigating the functioning of the peripheral and central human nervous system. A standard technique to evoke SEPs / SEFs is the stimulation of the median nerve by using a bipolar electrical stimulus. We aim at an alternative stimulation technique enabling stimulation of deep nerve structures while reducing patient stress and error susceptibility. In the current study, we apply a commercial transcranial magnetic stimulation system for peripheral magnetic stimulation of the median nerve. We compare the results of simultaneously recorded EEG signals to prove applicability of our technique to evoke SEPs including low frequency components (LFC) as well as high frequency oscillations (HFO). Therefore, we compare amplitude, latency and time-frequency characteristics of the SEP of 14 healthy volunteers after electric and magnetic stimulation. Both low frequency components and high frequency oscillations were detected. The HFOs were superimposed onto the primary cortical response N20. Statistical analysis revealed significantly lower amplitudes and increased latencies for LFC and HFO components after magnetic stimulation. The differences indicate the inability of magnetic stimulation to elicit supramaximal responses. A psycho-perceptual evaluation showed that magnetic stimulation was less unpleasant for 12 out of the 14 volunteers. In conclusion, we showed that LFC and HFO components related to median nerve stimulation can be evoked by peripheral magnetic stimulation.

Modelling of cortical and thalamic 600 Hz activity by means of oscillatory networks

The purpose of this study is to investigate information processing in the primary somatosensory system with the help of oscillatory network modelling. Specifically, we consider interactions in the oscillatory 600Hz activity between the thalamus and the cortical Brodmann areas 3b and 1. This type of cortical activity occurs after electrical stimulation of peripheral nerves such as the median nerve. Our measurements consist of simultaneous 31-channel MEG and 32-channel EEG recordings and individual 3D MRI data. We perform source localization by means of a multi-dipole model. The dipole activation time courses are then modelled by a set of coupled oscillators, described by linear second-order ordinary delay differential equations (DDEs). In particular, a new model for the thalamic activity is included in the oscillatory network. The parameters of the DDE system are successfully fitted to the data by a nonlinear evolutionary optimization method. To activate the oscillatory network, an individual input function is used, based on measurements of the propagated stimulation signal at the biceps. A significant feedback from the cortex to the thalamus could be detected by comparing the network modelling with and without feedback connections. Our finding in humans is supported by earlier animal studies. We conclude that this type of rhythmic brain activity can be modelled by oscillatory networks in order to disentangle feed forward and feedback information transfer.

Nonlinear interactions of high-frequency oscillations in the human somatosensory system

OBJECTIVE

The source of somatosensory evoked high-frequency activity at about 600 Hz is still not completely clear. Hence, we aimed to study the influence of double stimulation on the human somatosensory system by analyzing both the low-frequency activity and the high-frequency oscillations (HFOs) at about 600 Hz.

METHODS

We used median nerve stimulation at seven interstimuli intervals (ISIs) with a high time resolution between 2.4 and 4.8 ms to investigate the N15, N20 and superimposed HFOs. Simultaneously, the electroencephalogram and the magnetoencephalogram of 12 healthy participants were recorded. Subsequently, the source analysis of precortical and cortical dipoles was performed.

RESULTS

The difference computations of precortical dipole activation curves showed in both the low- and high-frequency range a correlation between the ISI and the latency of the second stimulus response. The cortical low-frequency response showed a similar behavior. Contrarily, in the second response of cortical HFOs this latency shift could not be confirmed. We found amplitude fluctuations that were dependent on the ISI in the low-frequency activity and the HFOs. These nonlinear interactions occurred at ISIs, which differ by one full HFO period (1.6 ms).

CONCLUSIONS

Low-frequency activity and HFOs originate from different generators. Precortical and cortical HFOs are independently generated. The amplitude fluctuations dependent on ISI indicate nonlinear interference between successive stimuli.

SIGNIFICANCE

Information processing in human somatosensory system includes nonlinearity.

Analysis and modeling of time-variant amplitude-frequency couplings of and between oscillations of EEG bursts

Low-frequency (0.5-2.5 Hz) and individually defined high-frequency (7-11 or 8-12 Hz; 11-15 or 14-18 Hz) oscillatory components of the electroencephalogram (EEG) burst activity derived from thiopental-induced burst-suppression patterns (BSP) were investigated in seven sedated patients (17-26 years old) with severe head injury. The predominant high-frequency burst oscillations (>7 Hz) were detected for each patient by means of time-variant amplitude spectrum analysis. Thereafter, the instantaneous envelope (IE) and the instantaneous frequency (IF) were computed for these low- and high-frequency bands to quantify amplitude-frequency dependencies (envelope-envelope, envelope-frequency, and frequency-frequency correlations). Time-variant phase-locking, phase synchronization, and quadratic phase couplings are associated with the observed amplitude-frequency characteristics. Additionally, these time-variant analyses were carried out for modeled burst patterns. Coupled Duffing oscillators were adapted to each EEG burst and by means of these models data-based burst simulations were generated. Results are: (1) strong envelope-envelope correlations (IE courses) can be demonstrated; (2) it can be shown that a rise of the IE is associated with an increase of the IF (only for the frequency bands 0.5-2.5 and 7-11 or 8-12 Hz); (3) the rise characteristics of all individually averaged envelope-frequency courses (IE-IF) are strongly correlated; (4) for the 7-11 or 8-12 Hz oscillation these associations are weaker and the variation between the time courses of the patients is higher; (5) for both frequency ranges a quantitative amplitude-frequency dependency can be shown because higher IE peak maxima are accompanied by stronger IF changes; (6) the time range of significant phase-locking within the 7-11 or 8-12 Hz frequency bands and of the strongest quadratic phase couplings (between 0.5-2.5 and 7-11 or 8-12 Hz) is between 0 and 1,000 ms; (7) all phase coupling characteristics of the modeled bursts accord well with the corresponding characteristics of the measured EEG burst data. All amplitude-frequency dependencies and phase locking/coupling properties described here are known from and can be discussed using coupled Duffing oscillators which are characterized by autoresonance properties.

Gamma, fast, and ultrafast waves of the brain: their relationships with epilepsy and behavior

Gamma waves, defined as rhythms from 25 to 100 Hz, are reviewed along with fast (100-400 Hz) and ultrafast (400-800 Hz) activity. Investigations on animals, especially those involving interneurons from the hippocampus, are reviewed. Gamma waves and fast rhythms likely play a role in neural communication, reflecting information from the external world to the brain. These rhythms become evident when the GABA-A system shifts from excitation to inhibition; are seen mainly in the hippocampus, the dentate gyrus, and CA(1)-CA(3) system; and are likely involved in long-term memory and cognitive task performance. These waves are also involved in spreading depression, but especially with epileptiform activity, progressively increasing in frequency from the pre-ictal to the ictal state. After status epilepticus, their presence predicts the development of spontaneous seizures. Gamma waves and fast activity have been studied in all sensory modalities, especially visual systems, providing a mechanism for awareness and processing of visual objects. In humans, gamma waves develop in the young, peak at 4-5 years of age, and are observed especially during alertness and after sensory stimulation. These fast rhythms are seen in the majority of seizures, especially in infantile spasms and during ictal activity in extratemporal and regional onsets, and, if low in amplitude, seem to be a good prognostic sign after seizure surgery. They have been studied in all sensory systems and are associated with selective attention, transient binding of cognitive features, and conscious perception of the external world.

Short-latency median-nerve somatosensory-evoked potentials and induced gamma-oscillations in humans

Recent studies have suggested that cortical gamma-oscillations are tightly linked with various forms of physiological activity. In the present study, the dynamic changes of intracranially recorded median-nerve somatosensory-evoked potentials (SEPs) and somatosensory-induced gamma-oscillations were animated on a three-dimensional MR image, and the temporal and spatial characteristics of these activities were analysed in 10 children being evaluated for epilepsy surgery. Visual and quantitative assessments revealed that short-latency SEPs and somatosensory-induced gamma-oscillations predominantly involved the post-central gyrus and less intensely involved the pre-central gyrus and the anterior parietal lobule. Formation of a dipole of N20 peak with opposite polarities across the central sulcus was well delineated in animation movies. High-frequency (100-250 Hz) somatosensory-induced gamma-oscillations emerged in the post-central gyrus at 13.6-17.5 ms after median-nerve stimulation, gradually slowed down in frequency around and below 100 Hz, and progressively involved the neighbouring areas. A substantial proportion of somatosensory-induced gamma-oscillations was initially phase-locked and the proportion of a non-phase-locked component gradually increased over time. The primary motor hand areas proven by cortical stimulation frequently coincided with the sites showing the largest N20 peak and the largest somatosensory-induced gamma oscillations. In vivo animation of SEPs and somatosensory-induced gamma oscillations both may be utilized to localize the primary sensory-motor hand area in pre-surgical evaluation. The dipole on SEPs is consistent with the previously accepted notion that the cortices along the central sulcus are activated. The high-frequency somatosensory-induced gamma-oscillations in the post-central gyrus may represent the initial neural processing for external somatosensory stimuli, whereas the subsequent lower-frequency oscillations might represent the reafferent cortical activity occurring in larger cortical networks.