Diverse dynamics in interacting vortices systems through tunable conservative and non-conservative coupling strengths

Magnetic vortices are highly tunable, nonlinear systems with ideal properties for being applied in spin wave emission, data storage, and neuromorphic computing. However, their technological application is impaired by a limited understanding of non-conservative forces, that results in the open challenge of attaining precise control over vortex dynamics in coupled vortex systems. Here, we present an analytical model for the gyrotropic dynamics of coupled magnetic vortices within nano-pillar structures, revealing how conservative and non-conservative forces dictate their complex behavior. Validated by micromagnetic simulations, our model accurately predicts dynamic states, controllable through external current and magnetic field adjustments. The experimental verification in a fabricated nano-pillar device aligns with our predictions, and it showcases the system's adaptability in dynamical coupling. The unique dynamical states, combined with the system's tunability and inherent memory, make it an exemplary foundation for reservoir computing. This positions our discovery at the forefront of utilizing magnetic vortex dynamics for innovative computing solutions, marking a leap towards efficient data processing technologies.

Fusion of EEG and EMG signals for detecting pre-movement intention of sitting and standing in healthy individuals and patients with spinal cord injury

Introduction

Rehabilitation devices assist individuals with movement disorders by supporting daily activities and facilitating effective rehabilitation training. Accurate and early motor intention detection is vital for real-time device applications. However, traditional methods of motor intention detection often rely on single-mode signals, such as EEG or EMG alone, which can be limited by low signal quality and reduced stability. This study proposes a multimodal fusion method based on EEG-EMG functional connectivity to detect sitting and standing intentions before movement execution, enabling timely intervention and reducing latency in rehabilitation devices.

Methods

Eight healthy subjects and five spinal cord injury (SCI) patients performed cue-based sit-to-stand and stand-to-sit transition tasks while EEG and EMG data were recorded simultaneously. We constructed EEG-EMG functional connectivity networks using data epochs from the 1.5-s period prior to movement onset. Pairwise spatial filters were then designed to extract discriminative spatial network topologies. Each filter paired with a support vector machine classifier to classify future movements into one of three classes: sit-to-stand, stand-to-sit, or rest. The final prediction was determined using a majority voting scheme.

Results

Among the three functional connectivity methods investigated-coherence, Pearson correlation coefficient and mutual information (MI)-the MI-based EEG-EMG network showed the highest decoding performance (94.33%), outperforming both EEG (73.89%) and EMG (89.16%). The robustness of the fusion method was further validated through a fatigue training experiment with healthy subjects. The fusion method achieved 92.87% accuracy during the post-fatigue stage, with no significant difference compared to the pre-fatigue stage (p > 0.05). Additionally, the proposed method using pre-movement windows achieved accuracy comparable to trans-movement windows (p > 0.05 for both pre- and post-fatigue stages). For the SCI patients, the fusion method showed improved accuracy, achieving 87.54% compared to single- modality methods (EEG: 83.03%, EMG: 84.13%), suggesting that the fusion method could be promising for practical rehabilitation applications.

Conclusion

Our results demonstrated that the proposed multimodal fusion method significantly enhances the performance of detecting human motor intentions. By enabling early detection of sitting and standing intentions, this method holds the potential to offer more accurate and timely interventions within rehabilitation systems.

Influencing factors of corticomuscular coherence in stroke patients

Stroke, also known as cerebrovascular accident, is an acute cerebrovascular disease with a high incidence, disability rate, and mortality. It can disrupt the interaction between the cerebral cortex and external muscles. Corticomuscular coherence (CMC) is a common and useful method for studying how the cerebral cortex controls muscle activity. CMC can expose functional connections between the cortex and muscle, reflecting the information flow in the motor system. Afferent feedback related to CMC can reveal these functional connections. This paper aims to investigate the factors influencing CMC in stroke patients and provide a comprehensive summary and analysis of the current research in this area. This paper begins by discussing the impact of stroke and the significance of CMC in stroke patients. It then proceeds to elaborate on the mechanism of CMC and its defining formula. Next, the impacts of various factors on CMC in stroke patients were discussed individually. Lastly, this paper addresses current challenges and future prospects for CMC.

Multiscale Canonical Coherence for Functional Corticomuscular Coupling Analysis

Functional corticomuscular coupling (FCMC) probes multi-level information communication in the sensorimotor system. The canonical Coherence (caCOH) method has been leveraged to measure the FCMC between two multivariate signals within the single scale. In this paper, we propose the concept of multiscale canonical Coherence (MS-caCOH) to disentangle complex multi-layer information and extract coupling features in multivariate spaces from multiple scales. Then, we verified the reliability and effectiveness of MS-caCOH on two types of data sets, i.e., a synthetic multivariate data set and a real-world multivariate data set. Our simulation results showed that compared with caCOH, MS-caCOH enhanced coupling detection and achieved lower pattern recovery errors at multiple frequency scales. Further analysis on experimental data demonstrated that the proposed MS-caCOH method could also capture detailed multiscale spatial-frequency characteristics. This study leverages the multiscale analysis framework and multivariate method to give a new insight into corticomuscular coupling analysis.

A review of combined functional neuroimaging and motion capture for motor rehabilitation

BACKGROUND

Technological advancements in functional neuroimaging and motion capture have led to the development of novel methods that facilitate the diagnosis and rehabilitation of motor deficits. These advancements allow for the synchronous acquisition and analysis of complex signal streams of neurophysiological data (e.g., EEG, fNIRS) and behavioral data (e.g., motion capture). The fusion of those data streams has the potential to provide new insights into cortical mechanisms during movement, guide the development of rehabilitation practices, and become a tool for assessment and therapy in neurorehabilitation.

RESEARCH OBJECTIVE

This paper aims to review the existing literature on the combined use of motion capture and functional neuroimaging in motor rehabilitation. The objective is to understand the diversity and maturity of technological solutions employed and explore the clinical advantages of this multimodal approach.

METHODS

This paper reviews literature related to the combined use of functional neuroimaging and motion capture for motor rehabilitation following the PRISMA guidelines. Besides study and participant characteristics, technological aspects of the used systems, signal processing methods, and the nature of multimodal feature synchronization and fusion were extracted.

RESULTS

Out of 908 publications, 19 were included in the final review. Basic or translation studies were mainly represented and based predominantly on healthy participants or stroke patients. EEG and mechanical motion capture technologies were most used for biomechanical data acquisition, and their subsequent processing is based mainly on traditional methods. The system synchronization techniques at large were underreported. The fusion of multimodal features mainly supported the identification of movement-related cortical activity, and statistical methods were occasionally employed to examine cortico-kinematic relationships.

CONCLUSION

The fusion of motion capture and functional neuroimaging might offer advantages for motor rehabilitation in the future. Besides facilitating the assessment of cognitive processes in real-world settings, it could also improve rehabilitative devices' usability in clinical environments. Further, by better understanding cortico-peripheral coupling, new neuro-rehabilitation methods can be developed, such as personalized proprioceptive training. However, further research is needed to advance our knowledge of cortical-peripheral coupling, evaluate the validity and reliability of multimodal parameters, and enhance user-friendly technologies for clinical adaptation.

A Multidimensional Visible Evaluation Model for Stroke Rehabilitation: A Pilot Study

Efficient rehabilitation state evaluation is important to the design of rehabilitation strategies after stroke. However, most traditional evaluations have depended on subjective clinical scales, which do not entail quantitative evaluation of the motor function. Functional corticomuscular coupling (FCMC) can be used to quantitatively describe the rehabilitation state. However, how to apply FCMC to clinical evaluation still needs to be studied. In this study, we propose a visible evaluation model which can combine the FCMC indicators with a Ueda score to comprehensively evaluate the motor function. In this model, we first calculated the FCMC indicators based on our previous study, including transfer spectral entropy (TSE), wavelet package transfer entropy (WPTE) and multiscale transfer entropy (MSTE). We then apply Pearson correlation analysis to determine which FCMC indicators are significantly correlated with the Ueda score. Then, we simultaneously introduced a radar map to present the selected FCMC indicators and the Ueda score, and described the relation between them. Finally, we calculated the comprehensive evaluation function (CEF) of the radar map and applied it as a comprehensive score of the rehabilitation state. To verify the model's effectiveness, we synchronously collected the electroencephalogram (EEG) and electrocardiogram (EMG) data from stroke patients under the steady-state force task and evaluated the state by the model. This model visualized the evaluation results by constructing a radar map and presented the physiological electrical signal features and the clinical scales at the same time. The CEF indicator calculated from this model was significantly correlated with the Ueda score (P= $0.001< 0.01$ ). This research provides a new approach to evaluation and rehabilitation training after stroke, and explicates possible pathomechanisms.

Nociceptive Intra-epidermal Electric Stimulation Evokes Steady-State Responses in the Secondary Somatosensory Cortex

Recent studies have established the presence of nociceptive steady-state evoked potentials (SSEPs), generated in response to thermal or intra-epidermal electric stimuli. This study explores cortical sources and generation mechanisms of nociceptive SSEPs in response to intra-epidermal electric stimuli. Our method was to stimulate healthy volunteers (n = 22, all men) with 100 intra-epidermal pulse sequences. Each sequence had a duration of 8.5 s, and consisted of pulses with a pulse rate between 20 and 200 Hz, which was frequency modulated with a multisine waveform of 3, 7 and 13 Hz (n = 10, 1 excluded) or 3 and 7 Hz (n = 12, 1 excluded). As a result, evoked potentials in response to stimulation onset and contralateral SSEPs at 3 and 7 Hz were observed. The SSEPs at 3 and 7 Hz had an average time delay of 137 ms and 143 ms respectively. The evoked potential in response to stimulation onset had a contralateral minimum (N1) at 115 ms and a central maximum (P2) at 300 ms. Sources for the multisine SSEP at 3 and 7 Hz were found through beamforming near the primary and secondary somatosensory cortex. Sources for the N1 were found near the primary and secondary somatosensory cortex. Sources for the N2-P2 were found near the supplementary motor area. Harmonic and intermodulation frequencies in the SSEP power spectrum remained below a detectable level and no evidence for nonlinearity of nociceptive processing, i.e. processing of peripheral firing rate into cortical evoked potentials, was found.

Disrupted cortico-peripheral interactions in motor disorders

Motor disorders may arise from neurological damage or diseases at different levels of the hierarchical motor control system and side-loops. Altered cortico-peripheral interactions might be essential characteristics indicating motor dysfunctions. By integrating cortical and peripheral responses, top-down and bottom-up cortico-peripheral coupling measures could provide new insights into the motor control and recovery process. This review first discusses the neural bases of cortico-peripheral interactions, and corticomuscular coupling and corticokinematic coupling measures are addressed. Subsequently, methodological efforts are summarized to enhance the modeling reliability of neural coupling measures, both linear and nonlinear approaches are introduced. The latest progress, limitations, and future directions are discussed. Finally, we emphasize clinical applications of cortico-peripheral interactions in different motor disorders, including stroke, neurodegenerative diseases, tremor, and other motor-related disorders. The modified interaction patterns and potential changes following rehabilitation interventions are illustrated. Altered coupling strength, modified coupling directionality, and reorganized cortico-peripheral activation patterns are pivotal attributes after motor dysfunction. More robust coupling estimation methodologies and combination with other neurophysiological modalities might more efficiently shed light on motor control and recovery mechanisms. Future studies with large sample sizes might be necessary to determine the reliabilities of cortico-peripheral interaction measures in clinical practice.

Multiscale Wavelet Transfer Entropy with Application to Corticomuscular Coupling Analysis

OBJECTIVE

Functional coupling between the motor cortex and muscle activity is commonly detected and quantified by cortico-muscular coherence (CMC) or Granger causality (GC) analysis, which are applicable only to linear couplings and are not sufficiently sensitive: some healthy subjects show no significant CMC and GC, and yet have good motor skills. The objective of this work is to develop measures of functional cortico-muscular coupling that have improved sensitivity and are capable of detecting both linear and non-linear interactions.

METHODS

A multiscale wavelet transfer entropy (TE) methodology is proposed. The methodology relies on a dyadic stationary wavelet transform to decompose electroencephalogram (EEG) and electromyogram (EMG) signals into functional bands of neural oscillations. Then, it applies TE analysis based on a range of embedding delay vectors to detect and quantify intra- and cross-frequency band cortico-muscular coupling at different time scales.

RESULTS

Our experiments with neurophysiological signals substantiate the potential of the developed methodologies for detecting and quantifying information flow between EEG and EMG signals for subjects with and without significant CMC or GC, including non-linear cross-frequency interactions, and interactions across different temporal scales. The obtained results are in agreement with the underlying sensorimotor neurophysiology.

CONCLUSION

These findings suggest that the concept of multiscale wavelet TE provides a comprehensive framework for analyzing cortex-muscle interactions.

SIGNIFICANCE

The proposed methodologies will enable developing novel insights into movement control and neurophysiological processes more generally.

Assessing the Usage of Indirect Motor Pathways Following a Hemiparetic Stroke

A hallmark impairment in a hemiparetic stroke is a loss of independent joint control resulting in abnormal co-activation of shoulder abductor and elbow flexor muscles in their paretic arm, clinically known as the flexion synergy. The flexion synergy appears while generating shoulder abduction (SABD) torques as lifting the paretic arm. This likely be caused by an increased reliance on contralesional indirect motor pathways following damage to direct corticospinal projections. The assessment of functional connectivity between brain and muscle signals, i.e., brain-muscle connectivity (BMC), may provide insight into such changes to the usage of motor pathways. Our previous model simulation shows that multi-synaptic connections along the indirect motor pathway can generate nonlinear connectivity. We hypothesize that increased usage of indirect motor pathways (as increasing SABD load) will lead to an increase of nonlinear BMC. To test this hypothesis, we measured brain activity, muscle activity from shoulder abductors when stroke participants generate 20% and 40% of maximum SABD torque with their paretic arm. We computed both linear and nonlinear BMC between EEG and EMG. We found dominant nonlinear BMC at contralesional/ipsilateral hemisphere for stroke, whose magnitude increased with the SABD load. These results supported our hypothesis and indicated that nonlinear BMC could provide a quantitative indicator for determining the usage of indirect motor pathways following a hemiparetic stroke.

Multiscale Transfer Spectral Entropy for Quantifying Corticomuscular Interaction

Corticomuscular coupling reflects nonlinear interactions and multi-layer neural information transmission between the motor cortex and effector muscle in the sensorimotor system. Transfer spectral entropy (TSE) method has been used to describe corticomuscular coupling within single scale. As an extension of TSE, multiscale transfer spectral entropy (MSTSE) is proposed in this paper to depict multi-layer of neural information transfer between two coupling signals. The reliability and effectiveness of MSTSE were verified on data generated by nonlinear numerical models and those of a force tracking task. Compared with TSE, MSTSE is more robust to the embedding dimension and performs optimally in the detection of the coupling properties. Further analysis of the physiological signals showed that the MSTSE provided more detailed band characteristics than the single scale TSE measurement. MSTSE indicates significant coupling scattered in alpha, beta and low gamma bands during the force tracking task. Besides, the coupling strength in the descending direction of the beta band was significantly higher than that in the ascending direction. This study constructs multi-scale coupling information to provide a new perspective for exploring corticomuscular interaction.

Allophonic perception of VOT contrasts in Spanish children with dyslexia

INTRODUCTION

Previous studies have evidenced a different mode of speech perception in dyslexia, characterized by the use of allophonic rather than phonemic units. People with dyslexia perceive phonemic features (such as voicing) less accurately than typical readers, but they perceive allophonic features (i.e., language-independent differences between speech sounds) more accurately.

METHOD

In this study, we investigated the perception of voicing contrasts in a sample of 204 Spanish children with or without dyslexia. Identification and discrimination data were collected for synthetic sounds varying along three different voice onset time (VOT) continua (ba/pa, de/te, and di/ti). Empirical data will be contrasted with a mathematical model of allophonic perception building up from neural oscillations and auditory temporal processing.

RESULTS

Children with dyslexia exhibited a general deficit in categorical precision; that is, they discriminated among phonemically contrastive pairs (around 0-ms VOT) less accurately than did chronological age controls, irrespective of the stimulus continuum. Children with dyslexia also exhibited a higher sensitivity in the discrimination of allophonic features (around ±30-ms VOT), but only for the stimulus continuum that was based on a nonlexical contrast (ba/pa).

CONCLUSION

Fitting the neural network model to the data collected for this continuum suggests that allophonic perception is due to a deficit in "subharmonic coupling" between high-frequency oscillations. Relationships with "temporal sampling framework" theory are discussed.

Nonlinear System Identification of Neural Systems from Neurophysiological Signals

The human nervous system is one of the most complicated systems in nature. Complex nonlinear behaviours have been shown from the single neuron level to the system level. For decades, linear connectivity analysis methods, such as correlation, coherence and Granger causality, have been extensively used to assess the neural connectivities and input-output interconnections in neural systems. Recent studies indicate that these linear methods can only capture a certain amount of neural activities and functional relationships, and therefore cannot describe neural behaviours in a precise or complete way. In this review, we highlight recent advances in nonlinear system identification of neural systems, corresponding time and frequency domain analysis, and novel neural connectivity measures based on nonlinear system identification techniques. We argue that nonlinear modelling and analysis are necessary to study neuronal processing and signal transfer in neural systems quantitatively. These approaches can hopefully provide new insights to advance our understanding of neurophysiological mechanisms underlying neural functions. These nonlinear approaches also have the potential to produce sensitive biomarkers to facilitate the development of precision diagnostic tools for evaluating neurological disorders and the effects of targeted intervention.

Multisine frequency modulation of intra-epidermal electric pulse sequences: A novel tool to study nociceptive processing

A sustained sensory stimulus with a periodic variation of intensity creates an electrophysiological brain response at associated frequencies, referred to as the steady-state evoked potential (SSEP). The SSEPs elicited by the periodic stimulation of nociceptors in the skin may represent activity of a brain network that is primarily involved in nociceptive processing. Exploring the behavior of this network could lead to valuable insights regarding the pathway from nociceptive stimulus to pain perception. We present a method to directly modulate the pulse rate of nociceptive afferents in the skin with a multisine waveform through intra-epidermal electric stimulation. The technique was demonstrated in healthy volunteers. Each subject was stimulated using a pulse sequence modulated by a multisine waveform of 3, 7 and 13 Hz. The EEG was analyzed for the presence of the base frequencies and associated (sub)harmonics. Topographies showed significant central and contralateral SSEP responses at 3, 7 and 13 Hz in respectively 7, 4 and 3 out of the 9 participants included for analysis. As such, we found that intra-epidermal stimulation with a multisine frequency modulated pulse sequence can generate nociceptive SSEPs. The possibility to stimulate the nociceptive system using multisine frequency modulated pulses offers novel opportunities to study the temporal dynamics of nociceptive processing.

Nonlinear Modeling of Cortical Responses to Mechanical Wrist Perturbations Using the NARMAX Method

OBJECTIVE

Nonlinear modeling of cortical responses (EEG) to wrist perturbations allows for the quantification of cortical sensorimotor function in healthy and neurologically impaired individuals. A common model structure reflecting key characteristics shared across healthy individuals may provide a reference for future clinical studies investigating abnormal cortical responses associated with sensorimotor impairments. Thus, the goal of our study is to identify this common model structure and therefore to build a nonlinear dynamic model of cortical responses, using nonlinear autoregressive-moving-average model with exogenous inputs (NARMAX).

METHODS

EEG was recorded from ten participants when receiving continuous wrist perturbations. A common model structure detection method was developed for identifying a common NARMAX model structure across all participants, with individualized parameter values. The results were compared to conventional subject-specific models.

RESULTS

The proposed method achieved 93.91% variance accounted for (VAF) when implementing a one-step-ahead prediction and around 50% VAF for a k-step ahead prediction (k = 3), without a substantial drop of VAF as compare to subject-specific models. The estimated common structure suggests that the measured cortical response is a mixed outcome of the nonlinear transformation of external inputs and local neuronal interactions or inherent neuronal dynamics at the cortex.

CONCLUSION

The proposed method well determined the common characteristics across subjects in the cortical responses to wrist perturbations.

SIGNIFICANCE

It provides new insights into the human sensorimotor nervous system in response to somatosensory inputs and paves the way for future translational studies on assessments of sensorimotor impairments using our modeling approach.

Estimating multiple latencies in the auditory system from auditory steady-state responses on a single EEG channel

The latency of the auditory steady-state response (ASSR) may provide valuable information regarding the integrity of the auditory system, as it could potentially reveal the presence of multiple intracerebral sources. To estimate multiple latencies from high-order ASSRs, we propose a novel two-stage procedure that consists of a nonparametric estimation method, called apparent latency from phase coherence (ALPC), followed by a heuristic sequential forward selection algorithm (SFS). Compared with existing methods, ALPC-SFS requires few prior assumptions, and is straightforward to implement for higher-order nonlinear responses to multi-cosine sound complexes with their initial phases set to zero. It systematically evaluates the nonlinear components of the ASSRs by estimating multiple latencies, automatically identifies involved ASSR components, and reports a latency consistency index. To verify the proposed method, we performed simulations for several scenarios: two nonlinear subsystems with different or overlapping outputs. We compared the results from our method with predictions from existing, parametric methods. We also recorded the EEG from ten normal-hearing adults by bilaterally presenting superimposed tones with four frequencies that evoke a unique set of ASSRs. From these ASSRs, two major latencies were found to be stable across subjects on repeated measurement days. The two latencies are dominated by low-frequency (LF) (near 40 Hz, at around 41-52 ms) and high-frequency (HF) (> 80 Hz, at around 21-27 ms) ASSR components. The frontal-central brain region showed longer latencies on LF components, but shorter latencies on HF components, when compared with temporal-lobe regions. In conclusion, the proposed nonparametric ALPC-SFS method, applied to zero-phase, multi-cosine sound complexes is more suitable for evaluating embedded nonlinear systems underlying ASSRs than existing methods. It may therefore be a promising objective measure for hearing performance and auditory cortex (dys)function.

Slowly activating outward membrane currents generate input-output sub-harmonic cross frequency coupling in neurons

A major challenge in understanding spike-time dependent information encoding in the neural system is the non-linear firing response to inputs of the individual neurons. Hence, quantitative exploration of the putative mechanisms of this non-linear behavior is fundamental to formulating the theory of information transfer in the neural system. The objective of this simulation study was to evaluate and quantify the effect of slowly activating outward membrane current, on the non-linearity in the output of a one-compartment Hodgkin-Huxley styled neuron. To evaluate this effect, the peak conductance of the slow potassium channel (g_K-slow) was varied from 0% to 200% of its normal value in steps of 33%. Both cross- and iso-frequency coupling between the input and the output of the simulated neuron was computed using a generalized coherence measure, i.e., n:m coherence. With increasing g_K-slow, the amount of sub-harmonic cross-frequency coupling, where the output frequencies (1-8 Hz) are lower than the input frequencies (15-35 Hz), increased progressively whereas no change in iso-frequency coupling was observed. Power spectral and phase-space analysis of the neuronal membrane voltage vs. slow potassium channel activation variable showed that the interaction of the slow channel dynamics with the fast membrane voltage dynamics generates the observed sub-harmonic coupling. This study provides quantitative insights into the role of an important membrane mechanism i.e. the slowly activating outward current in generating non-linearities in the output of a neuron.

Cross-frequency and iso-frequency estimation of functional corticomuscular coupling after stroke

Functional corticomuscular coupling (FCMC) between the brain and muscles has been used for motor function assessment after stroke. Two types, iso-frequency coupling (IFC) and cross-frequency coupling (CFC), are existed in sensory-motor system for healthy people. However, in stroke, only a few studies focused on IFC between electroencephalogram (EEG) and electromyogram (EMG) signals, and no CFC studies have been found. Considering the intrinsic complexity and rhythmicity of the biological system, we first used the wavelet package transformation (WPT) to decompose the EEG and EMG signals into several subsignals with different frequency bands, and then applied transfer entropy (TE) to analyze the IFC and CFC relationship between each pair-wise subsignal. In this study, eight stroke patients and eight healthy people were enrolled. Results showed that both IFC and CFC still existed in stroke patients (EEG → EMG: 1:1, 3:2, 2:1; EMG → EEG: 1:1, 2:1, 2:3, 3:1). Compared with the stroke-unaffected side and healthy controls, the stroke-affected side yielded lower alpha, beta and gamma synchronization (IFC: beta; CFC: alpha, beta and gamma). Further analysis indicated that stroke patients yielded no significant difference of the FCMC between EEG → EMG and EMG → EEG directions. Our study indicated that alpha and beta bands were essential to concentrating and maintaining the motor capacities, and provided a new insight in understanding the propagation and function in the sensory-motor system.

Effect of potassium channel noise on nerve discharge based on the Chay model

BACKGROUND:

The nervous system senses and transmits information through the firing behavior of neurons, and this process is affected by various noises. However, in the previous study of the influence of noise on nerve discharge, the channel of some noise effects is not clear, and the difference from other noises was not examined.

OBJECTIVE:

To construct ion channel noise which is more biologically significant, and to clarify the basic characteristics of the random firing rhythm of neurons generated by different types of noise acting on ion channels.

Method:

Based on the dynamics of the ion channel, we constructed ion channel noise. We simulated the nerve discharge based on the Chay model of potassium ion channel noise, and used the nonlinear time series analysis method to measure the certainty and randomness of nerve discharge.

RESULTS:

In the Chay model with potassium ion noise, the chaotic rhythm defined by the original model could be effectively unified with the random rhythm simulated by the previous random Chay model into a periodic bifurcation process.

CONCLUSION:

This method clarified the influence of ion channel noise on nerve discharge, better understood the randomness of nerve discharge and provided a more reasonable explanation for the mechanism of nerve discharge.

Quantifying Altered Neural Connectivity of the Stretch Reflex in Chronic Hemiparetic Stroke

Post-stroke flexion synergy limits arm/hand function and is also linked to hyperactive stretch reflexes or spasticity. It is implicated in the increased role of indirect motor pathways following damage to direct corticospinal projections. We hypothesized that this maladaptive neuroplasticity also affects stretch reflexes. Specifically, multi-synaptic interactions in indirect motor pathways may increase nonlinear neural connectivity and time lag between stretch and reflex muscle response. Continuous position perturbations were applied to the elbow joint when eleven participants with stroke generated two levels of shoulder abduction (SABD) torques with their paretic arm to induce synergy-related spasticity. Likewise, the perturbations were applied to eleven control subjects while performing SABD and elbow flexion levels matching the synergy torques in stroke. We quantified linear and non-linear connectivity and the corresponding time lags between perturbations and muscle activity. Enhanced nonlinear connectivity with a prolonged time lag was found in stroke as compared to controls. Non-linear connectivity and time lag also increased with the expression of the flexion synergy, as induced by greater SABD load levels, in stroke. This study provides new evidence of changes in neural connectivity and long-latency time lag in the stretch reflex response post-stroke. The results suggest the contribution of indirect motor pathways to synergy-related spasticity.

Position-Cortical Coherence as a Marker of Afferent Pathway Integrity Early Poststroke: A Prospective Cohort Study

Background. Addressing the role of somatosensory impairment, that is, afferent pathway integrity, in poststroke motor recovery may require neurophysiological assessment. Objective. We investigated the longitudinal construct validity of position-cortical coherence (PCC), that is, the agreement between mechanically evoked wrist perturbations and electroencephalography (EEG), as a measure of afferent pathway integrity. Methods. PCC was measured serially in 48 patients after a first-ever ischemic stroke in addition to Fugl-Meyer motor assessment of the upper extremity (FM-UE) and Nottingham Sensory Assessment hand-finger subscores (EmNSA-HF, within 3 and at 5, 12, and 26 weeks poststroke. Changes in PCC over time, represented by percentage presence of PCC (%PCC), mean amplitude of PCC over the affected (Amp-A) and nonaffected hemisphere (Amp-N) and a lateralization index (L-index), were analyzed, as well as their association with FM-UE and EmNSA-HF. Patients were retrospectively categorized based on FM-UE score at baseline and 26 weeks poststroke into high- and low-baseline recoverers and non-recoverers. Results. %PCC increased from baseline to 12 weeks poststroke (β = 1.6%, CI = 0.32% to 2.86%, P = .01), which was no longer significant after adjusting for EmNSA-HF and FM-UE. A significant positive association was found between %PCC, Amp-A, and EmNSA-HF. Low-baseline recoverers (n = 8) showed longitudinally significantly higher %PCC than high-baseline recoverers (n = 23). Conclusions. We demonstrated the longitudinal construct validity of %PCC and Amp-A as a measure of afferent pathway integrity. A high %PCC in low-baseline recoverers suggests that this measure also contains information on cortical excitability. Use of PCC as an EEG-based measure to address the role of somatosensory integrity to motor recovery poststroke requires further attention.

Quantifying the Nonlinear Interaction in the Nervous System Based on Phase-Locked Amplitude Relationship

OBJECTIVE

This paper introduces the Cross-frequency Amplitude Transfer Function (CATF), a model-free method for quantifying nonlinear stimulus-response interaction based on phase-locked amplitude relationship.

METHOD

The CATF estimates the amplitude transfer from input frequencies at stimulation signal to their harmonics/intermodulation at the response signal. We first verified the performance of CATF in simulation tests with systems containing a static nonlinear function and a linear dynamic, i.e., Hammerstein and Wiener systems. We then applied the CATF to investigate the second-order nonlinear amplitude transfer in the human proprioceptive system from the periphery to the cortex.

RESULT

The simulation demonstrated that the CATF is a general method, which can well quantify nonlinear stimulus-response amplitude transfer for different orders of nonlinearity in Wiener or Hammerstein system configurations. Applied to the human proprioceptive system, we found a complicated nonlinear system behavior with substantial amplitude transfer from the periphery stimulation to cortical response signals in the alpha band. This complicated system behavior may be associated with the nonlinear behavior of the muscle spindle and the dynamic interaction in the thalamocortical radiation.

CONCLUSION

This paper provides a new tool to identify nonlinear interaction in the nervous system.

SIGNIFICANCE

The results provide novel insight of nonlinear dynamics in the human proprioceptive system.

Cross-Frequency Coupling in Descending Motor Pathways: Theory and Simulation

Coupling of neural oscillations is essential for the transmission of cortical motor commands to motoneuron pools through direct and indirect descending motor pathways. Most studies focus on iso-frequency coupling between brain and muscle activities, i.e., cortico-muscular coherence, which is thought to reflect motor command transmission in the mono-synaptic corticospinal pathway. Compared to this direct pathway, indirect corticobulbospinal motor pathways involve multiple intermediate synaptic connections via spinal interneurons. Neuronal processing of synaptic inputs can lead to modulation of inter-spike intervals which produces cross-frequency coupling. This theoretical study aims to evaluate the effect of the number of synaptic layers in descending pathways on the expression of cross-frequency coupling between supraspinal input and the cumulative output of the motoneuron pool using a computer simulation. We simulated descending pathways as various layers of interneurons with a terminal motoneuron pool using Hogdkin–Huxley styled neuron models. Both cross- and iso-frequency coupling between the supraspinal input and the motorneuron pool output were computed using a novel generalized coherence measure, i.e., n:m coherence. We found that the iso-frequency coupling is only dominant in the mono-synaptic corticospinal tract, while the cross-frequency coupling is dominant in multi-synaptic indirect motor pathways. Furthermore, simulations incorporating both mono-synaptic direct and multi-synaptic indirect descending pathways showed that increased reliance on a multi-synaptic indirect pathway over a mono-synaptic direct pathway enhances the dominance of cross-frequency coupling between the supraspinal input and the motorneuron pool output. These results provide the theoretical basis for future human subject study quantitatively assessing motor command transmission in indirect vs. direct pathways and its changes after neurological disorders such as unilateral brain injury.

A Novel Approach for Modeling Neural Responses to Joint Perturbations Using the NARMAX Method and a Hierarchical Neural Network

The human nervous system is an ensemble of connected neuronal networks. Modeling and system identification of the human nervous system helps us understand how the brain processes sensory input and controls responses at the systems level. This study aims to propose an advanced approach based on a hierarchical neural network and non-linear system identification method to model neural activity in the nervous system in response to an external somatosensory input. The proposed approach incorporates basic concepts of Non-linear AutoRegressive Moving Average Model with eXogenous input (NARMAX) and neural network to acknowledge non-linear closed-loop neural interactions. Different from the commonly used polynomial NARMAX method, the proposed approach replaced the polynomial non-linear terms with a hierarchical neural network. The hierarchical neural network is built based on known neuroanatomical connections and corresponding transmission delays in neural pathways. The proposed method is applied to an experimental dataset, where cortical activities from ten young able-bodied individuals are extracted from electroencephalographic signals while applying mechanical perturbations to their wrist joint. The results yielded by the proposed method were compared with those obtained by the polynomial NARMAX and Volterra methods, evaluated by the variance accounted for (VAF). Both the proposed and polynomial NARMAX methods yielded much better modeling results than the Volterra model. Furthermore, the proposed method modeled cortical responded with a mean VAF of 69.35% for a three-step ahead prediction, which is significantly better than the VAF from a polynomial NARMAX model (mean VAF 47.09%). This study provides a novel approach for precise modeling of cortical responses to sensory input. The results indicate that the incorporation of knowledge of neuroanatomical connections in building a realistic model greatly improves the performance of system identification of the human nervous system.

Causal Shannon-Fisher Characterization of Motor/Imagery Movements in EEG

The electroencephalogram (EEG) is an electrophysiological monitoring method that allows us to glimpse the electrical activity of the brain. Neural oscillations patterns are perhaps the best salient feature of EEG as they are rhythmic activities of the brain that can be generated by interactions across neurons. Large-scale oscillations can be measured by EEG as the different oscillation patterns reflected within the different frequency bands, and can provide us with new insights into brain functions. In order to understand how information about the rhythmic activity of the brain during visuomotor/imagined cognitive tasks is encoded in the brain we precisely quantify the different features of the oscillatory patterns considering the Shannon–Fisher plane H×F. This allows us to distinguish the dynamics of rhythmic activities of the brain showing that the Beta band facilitate information transmission during visuomotor/imagined tasks.

Dynamic cortical participation during bilateral, cyclical ankle movements: Effects of Parkinson's disease

Parkinson’s disease (PD) is known to increase asymmetry and variability of bilateral movements. However, the mechanisms of such abnormalities are not fully understood. Here, we aimed to investigate whether kinematic abnormalities are related to cortical participation during bilateral, cyclical ankle movements, which required i) maintenance of a specific frequency and ii) bilateral coordination of the lower limbs in an anti-phasic manner. We analyzed electroencephalographic and electromyographic signals from nine men with PD and nine aged-matched healthy men while they sat and cyclically dorsi- and plantarflexed their feet. This movement was performed at a similar cadence to normal walking under two conditions: i) self-paced and ii) externally paced by a metronome. Participants with PD exhibited reduced range of motion and more variable bilateral coordination. However, participants with and without PD did not differ in the magnitude of corticomuscular coherence between the midline cortical areas and tibialis anterior and medial gastrocnemius muscles. This finding suggests that either the kinematic abnormalities were related to processes outside linear corticomuscular communication or PD-related changes in neural correlates maintained corticomuscular communication but not motor performance.

Unveiling neural coupling within the sensorimotor system: directionality and nonlinearity

Neural coupling between the central nervous system and the periphery is essential for the neural control of movement. Corticomuscular coherence is a popular linear technique to assess synchronised oscillatory activity in the sensorimotor system. This oscillatory coupling originates from ascending somatosensory feedback and descending motor commands. However, corticomuscular coherence cannot separate this bidirectionality. Furthermore, the sensorimotor system is nonlinear, resulting in cross‐frequency coupling. Cross‐frequency oscillations cannot be assessed nor exploited by linear measures. Here, we emphasise the need of novel coupling measures, which provide directionality and acknowledge nonlinearity, to unveil neural coupling in the sensorimotor system. We highlight recent advances in the field and argue that assessing directionality and nonlinearity of neural coupling will break new ground in the study of the control of movement in healthy and neurologically impaired individuals.

Modeling the Nonlinear Cortical Response in EEG Evoked by Wrist Joint Manipulation

Joint manipulation elicits a response from the sensors in the periphery which, via the spinal cord, arrives in the cortex. The average evoked cortical response recorded using electroencephalography was shown to be highly nonlinear; a linear model can only explain 10% of the variance of the evoked response, and over 80% of the response is generated by nonlinear behavior. The goal of this paper is to obtain a nonparametric nonlinear dynamic model, which can consistently explain the recorded cortical response requiring little a priori assumptions about model structure. Wrist joint manipulation was applied in ten healthy participants during which their cortical activity was recorded and modeled using a truncated Volterra series. The obtained models could explain 46% of the variance of the evoked cortical response, thereby demonstrating the relevance of nonlinear modeling. The high similarity of the obtained models across participants indicates that the models reveal common characteristics of the underlying system. The models show predominantly high-pass behavior, which suggests that velocity-related information originating from the muscle spindles governs the cortical response. In conclusion, the nonlinear modeling approach using a truncated Volterra series with regularization, provides a quantitative way of investigating the sensorimotor system, offering insight into the underlying physiology.

Nonlinear Coupling between Cortical Oscillations and Muscle Activity during Isotonic Wrist Flexion

Coupling between cortical oscillations and muscle activity facilitates neuronal communication during motor control. The linear part of this coupling, known as corticomuscular coherence, has received substantial attention, even though neuronal communication underlying motor control has been demonstrated to be highly nonlinear. A full assessment of corticomuscular coupling, including the nonlinear part, is essential to understand the neuronal communication within the sensorimotor system. In this study, we applied the recently developed n:m coherence method to assess nonlinear corticomuscular coupling during isotonic wrist flexion. The n:m coherence is a generalized metric for quantifying nonlinear cross-frequency coupling as well as linear iso-frequency coupling. By using independent component analysis (ICA) and equivalent current dipole source localization, we identify four sensorimotor related brain areas based on the locations of the dipoles, i.e., the contralateral primary sensorimotor areas, supplementary motor area (SMA), prefrontal area (PFA) and posterior parietal cortex (PPC). For all these areas, linear coupling between electroencephalogram (EEG) and electromyogram (EMG) is present with peaks in the beta band (15–35 Hz), while nonlinear coupling is detected with both integer (1:2, 1:3, 1:4) and non-integer (2:3) harmonics. Significant differences between brain areas is shown in linear coupling with stronger coherence for the primary sensorimotor areas and motor association cortices (SMA, PFA) compared to the sensory association area (PPC); but not for the nonlinear coupling. Moreover, the detected nonlinear coupling is similar to previously reported nonlinear coupling of cortical activity to somatosensory stimuli. We suggest that the descending motor pathways mainly contribute to linear corticomuscular coupling, while nonlinear coupling likely originates from sensory feedback.

Multimodal Source Imaging: Basic Methods, Signal Processing Techniques, and Applications

Multimodal source imaging is an emerging field in biomedical engineering. Its central goal is to combine different imaging modalities in a single model or data representation, such that the combination provides an enhanced insight into the underlying physiological organ, compared to each modality separately. It requires advanced signal acquisition and processing techniques and has applications in cognitive neuroscience, clinical neuroscience and electrocardiology. Therefore, it belongs to the heart of biomedical engineering.