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.@en

Background: Proprioception is important for regaining motor function in the paretic upper extremity after stroke. However, clinical assessments of proprioception are subjective and require verbal responses from the patient to applied proprioceptive stimuli. Cortical responses evoked by robotic wrist perturbations and measured by electroencephalography (EEG) may be an objective method to support current clinical assessments of proprioception. Objective: To establish whether evoked cortical responses reflect proprioceptive deficits as assessed by clinical scales and whether they predict upper extremity motor function at 26 weeks after stroke. Methods: Thirty-one patients with stroke were included. In week 1, 3, 5, 12, and 26 after stroke, the upper extremity sections of the Erasmus modified Nottingham Sensory Assessment (EmNSA-UE) and the Fugl-Meyer Motor Assessment (FM-UE) and the EEG responses (64 channels) to robotic wrist perturbations were measured. The extent to which proprioceptive input was conveyed to the affected hemisphere was estimated by the signal-to-noise ratio (SNR) of the evoked response. The relationships between SNR and EmNSA-UE as well as SNR and time after stroke were investigated using linear regression. Receiver-operating-characteristic curves were used to compare the predictive values of SNR and EmNSA-UE for predicting whether patients regained some selective motor control (FM-UE > 22) or whether they could only move their paretic upper extremity within basic limb synergies (FM-UE ≤ 22) at 26 weeks after stroke. Results: Patients (N = 7) with impaired proprioception (EmNSA-UE proprioception score < 8) had significantly smaller SNR than patients with unimpaired proprioception (N = 24) [EmNSA-UE proprioception score = 8, t(29) = 2.36, p = 0.03]. No significant effect of time after stroke on SNR was observed. Furthermore, there was no significant difference in the predictive value between EmNSA-UE and SNR for predicting motor function at 26 weeks after stroke. Conclusion: The SNR of the evoked cortical response does not significantly change as a function of time after stroke and differs between patients with clinically assessed impaired and unimpaired proprioception, suggesting that SNR reflects persistent damage to proprioceptive pathways. A similar predictive value with respect to EmNSA-UE suggests that SNR may be used as an objective predictor next to clinical sensory assessments for predicting motor function at 26 weeks after stroke.

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Cortical responses to continuous stimuli as recorded using either magneto- or electroencephalography (EEG) have shown power at harmonics of the stimulated
frequency, indicating nonlinear behavior. Even though the selection of analysis techniques depends on the linearity of the system under study, the importance of nonlinear contributions to cortical responses has not been formally
addressed.The goal of this paper is to quantify the nonlinear contributions to the cortical response obtained fromcontinuous sensory stimulation. EEG was used to record the cortical response evoked by continuousmovement of the wrist joint of healthy subjects applied with a robotic manipulator. Multisine stimulus signals (i.e., the sum of several sinusoids) elicit a periodic cortical response and allowto assess
the nonlinear contributions to the response.Wrist dynamics (relation between joint angle and torque) were successfully linearized, explaining 99% of the response. In contrast, the cortical response revealed a highly nonlinear relation;
where most power ( ∼ 80%) occurred at non-stimulated frequencies. Moreover, only 10% of the response could be explained using a nonparametric linear model. These results indicate that the recorded evoked cortical responses
are governed by nonlinearities and that linear methods do not suffice when describing the relation between mechanical stimulus and cortical response.@en

Objective: This paper introduces a generalized coherence framework for detecting and characterizing nonlinear interactions in the nervous system, namely cross-spectral coherence (CSC). CSC can detect different types of nonlinear interactions including harmonic and intermodulation coupling as present in static nonlinearities and also subharmonic coupling, which only occurs with dynamic nonlinearities. Methods: We verified the performance of CSC in model simulations with both static and dynamic nonlinear systems. We applied CSC to investigate nonlinear stimulus–response interactions in the human proprioceptive system. A periodic movement perturbation was imposed to the wrist when the subjects performed an isotonic wrist flexion. CSC analysis was performed between the perturbation and brain responses (electroencephalogram, EEG). Results: Both the simulation and the application demonstrated that CSC successfully detected different types of nonlinear interactions. High-order nonlinearities were revealed in the proprioceptive system, shown in harmonic and intermodulation coupling between the perturbation and EEG for all subjects. Subharmonic coupling was found in some subjects but not all. Conclusion: This paper provides a general tool to detect and characterize nonlinear nature and dynamics of the nervous system. The application of CSC on the experimental dataset indicates a complex nonlinear dynamics in the proprioceptive system. Significance: This novel framework 1) unveils the nonlinear neural dynamics in a more complete way than the existing coherence measures, and 2) is more suitable for estimating the input–output relation regarding both phase and amplitude compared to phase synchrony measures (which only consider phase coupling). Subharmonic coupling is reported in human proprioceptive system for the first time.@en

Background: Cortical damage after stroke can drastically impair sensory and motor function of the upper limb, affecting the execution of activities of daily living and quality of life. Motor impairment after stroke has been thoroughly studied, however sensory impairment and its relation to movement control has received less attention. Integrity of the somatosensory system is essential for feedback control of human movement, and compromised integrity due to stroke has been linked to sensory impairment.
Methods: The goal of this study is to assess the integrity of the somatosensory system in individuals with chronic hemiparetic stroke with different levels of sensory impairment, through a combination of robotic joint manipulation
and high-density electroencephalogram (EEG). A robotic wrist manipulator applied continuous periodic disturbances to the affected limb, providing somatosensory (proprioceptive and tactile) stimulation while challenging task execution. The integrity of the somatosensory system was evaluated during passive and active tasks, defined as ‘relaxed wrist’ and ‘maintaining 20% maximum wrist flexion’, respectively. The evoked cortical responses in the EEG were quantified using the power in the averaged responses and their signal-to-noise ratio.
Results: Thirty individuals with chronic hemiparetic stroke and ten unimpaired individuals without stroke participated in this study. Participants with stroke were classified as having severe, mild, or no sensory impairment, based on the Erasmus modification of the Nottingham Sensory Assessment. Under passive conditions, wrist manipulation resulted in contralateral cortical responses in unimpaired and chronic stroke participants with mild and no sensory impairment. In participants with severe sensory impairment the cortical responses were strongly reduced in amplitude, which related to anatomical damage. Under active conditions, participants with mild sensory impairment showed reduced responses compared to the passive condition, whereas unimpaired and chronic stroke participants without sensory impairment did not show this reduction.
Conclusions: Robotic continuous joint manipulation allows studying somatosensory cortical evoked responses during the execution of meaningful upper limb control tasks. Using such an approach it is possible to quantitatively
assess the integrity of sensory pathways; in the context of movement control this provides additional information required to develop more effective neurorehabilitation therapies.@en

The contributions of the cerebral cortex to human balance control are clearly demonstrated by the profound impact of cortical lesions on the ability to maintain standing balance. The cerebral cortex is thought to regulate subcortical postural centers to maintain upright balance and posture under varying environmental conditions and task demands. However, the cortical mechanisms that support standing balance remain elusive. Here, we present an EEG-based analysis of cortical oscillatory dynamics during the preparation and execution of balance responses with distinct postural demands. In our experiment, participants responded to backward movements of the support surface either with one forward step or by keeping their feet in place. To challenge the postural control system, we applied participant-specific high accelerations of the support surface such that the postural demand was low for stepping responses and high for feet-in-place responses. We expected that postural demand modulated the power of intrinsic cortical oscillations. Independent component analysis and time-frequency domain statistics revealed stronger suppression of alpha (9–13 Hz) and low-gamma (31–34 Hz) rhythms in the supplementary motor area (SMA) when preparing for feet-in-place responses (i.e., high postural demand). Irrespective of the response condition, support-surface movements elicited broadband (3–17 Hz) power increase in the SMA and enhancement of the theta (3–7 Hz) rhythm in the anterior prefrontal cortex (PFC), anterior cingulate cortex (ACC), and bilateral sensorimotor cortices (M1/S1). Although the execution of reactive responses resulted in largely similar cortical dynamics, comparison between the bilateral M1/S1 showed that stepping responses corresponded with stronger suppression of the beta (13–17 Hz) rhythm in the M1/S1 contralateral to the support leg. Comparison between response conditions showed that feet-in-place responses corresponded with stronger enhancement of the theta (3–7 Hz) rhythm in the PFC. Our results provide novel insights into the cortical dynamics of SMA, PFC, and M1/S1 during the control of human balance.

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Neural systems can present various types of nonlinear input-output relationships, such as harmonic, subharmonic, and/or intermodulation coupling. This paper aims to introduce a general framework in frequency domain for detecting and characterizing nonlinear coupling in neural systems, called the cross-frequency coherence framework (CFCF). CFCF is an extension of classic coherence based on higher-order statistics. We demonstrate an application of CFCF for identifying nonlinear interactions in human motion control. Our results indicate that CFCF can effectively characterize nonlinear properties of the afferent sensory pathway. We conclude that CFCF contributes to identifying nonlinear transfer in neural systems.@en

Communication between neuronal populations is facilitated by synchronization of their oscillatory activity. Although nonlinearity has been observed in the sensorimotor system, its nonlinear connectivity has not been widely investigated yet. This study investigates nonlinear connectivity during the human stretch reflex based on neuronal synchronization. Healthy participants generated isotonic wrist flexion while receiving a periodic mechanical perturbation to the wrist. Using a novel cross-frequency phase coupling metric, we estimate directional nonlinear connectivity, including time delay, from the perturbation to brain and to muscle, as well as from brain to muscle. Nonlinear phase coupling is significantly stronger from the perturbation to the muscle than to the brain, with a shorter time delay. The time delay from the perturbation to the muscle is 33 ms, similar to the reported latency of the spinal stretch reflex at the wrist. Source localization of nonlinear phase coupling from the brain to the muscle suggests activity originating from the motor cortex, although its effect on the stretch reflex is weak. As such nonlinear phase coupling between the perturbation and muscle activity is dominated by the spinal reflex loop. This study provides new evidence of nonlinear neuronal synchronization in the stretch reflex at the wrist joint with respect to spinal and transcortical loops.@en

Communication between neuronal populations is facilitated by synchronization of their oscillatory activity. Although nonlinearity has been observed in the sensorimotor system, its nonlinear connectivity has not been widely investigated yet. This study investigates nonlinear connectivity during the human stretch reflex based on neuronal synchronization. Healthy participants generated isotonic wrist flexion while receiving a periodic mechanical perturbation to the wrist. Using a novel cross-frequency phase coupling metric, we estimate directional nonlinear connectivity, including time delay, from the perturbation to brain and to muscle, as well as from brain to muscle. Nonlinear phase coupling is significantly stronger from the perturbation to the muscle than to the brain, with a shorter time delay. The time delay from the perturbation to the muscle is 33 ms, similar to the reported latency of the spinal stretch reflex at the wrist. Source localization of nonlinear phase coupling from the brain to the muscle suggests activity originating from the motor cortex, although its effect on the stretch reflex is weak. As such nonlinear phase coupling between the perturbation and muscle activity is dominated by the spinal reflex loop. This study provides new evidence of nonlinear neuronal synchronization in the stretch reflex at the wrist joint with respect to spinal and transcortical loops.@en

Interaction between distant neuronal populations is essential for communication within the nervous system and can occur as a highly nonlinear process. To better understand the functional role of neural interactions, it is important to quantify the nonlinear connectivity in the nervous system. We introduce a general approach to measure nonlinear connectivity through phase coupling: the multi-spectral phase coherence (MSPC). Using simulated data, we compare MSPC with existing phase coupling measures, namely n : m synchronization index and bi-phase locking value. MSPC provides a system description, including (i) the order of the nonlinearity, (ii) the direction of interaction, (iii) the time delay in the system, and both (iv) harmonic and (v) intermodulation coupling beyond the second order; which are only partly revealed by other methods. We apply MSPC to analyze data from a motor control experiment, where subjects performed isotonic wrist flexions while receiving movement perturbations. MSPC between the perturbation, EEG and EMG was calculated. Our results reveal directional nonlinear connectivity in the afferent and efferent pathways, as well as the time delay (43±8ms) between the perturbation and the brain response. In conclusion, MSPC is a novel approach capable to assess high-order nonlinear interaction and timing in the nervous system.@en

Interaction between distant neuronal populations is essential for communication within the nervous system and can occur as a highly nonlinear process. To better understand the functional role of neural interactions, it is important to quantify the nonlinear connectivity in the nervous system. We introduce a general approach to measure nonlinear connectivity through phase coupling: the multi-spectral phase coherence (MSPC). Using simulated data, we compare MSPC with existing phase coupling measures, namely n : m synchronization index and bi-phase locking value. MSPC provides a system description, including (i) the order of the nonlinearity, (ii) the direction of interaction, (iii) the time delay in the system, and both (iv) harmonic and (v) intermodulation coupling beyond the second order; which are only partly revealed by other methods. We apply MSPC to analyze data from a motor control experiment, where subjects performed isotonic wrist flexions while receiving movement perturbations. MSPC between the perturbation, EEG and EMG was calculated. Our results reveal directional nonlinear connectivity in the afferent and efferent pathways, as well as the time delay (43±8ms) between the perturbation and the brain response. In conclusion, MSPC is a novel approach capable to assess high-order nonlinear interaction and timing in the nervous system.@en