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

Fascicle dynamics of the tibialis anterior muscle reflect whole-body walking economy

Humans can inherently adapt their gait pattern in a way that minimizes the metabolic cost of transport, or walking economy, within a few steps, which is faster than any known direct physiological sensor of metabolic energy. Instead, walking economy may be indirectly sensed through mechanoreceptors that correlate with the metabolic cost per step to make such gait adaptations. We tested whether velocity feedback from tibialis anterior (TA) muscle fascicles during the early stance phase of walking could potentially act to indirectly sense walking economy. As participants walked within a range of steady-state speeds and step frequencies, we observed that TA fascicles lengthen on almost every step. Moreover, the average peak fascicle velocity experienced during lengthening reflected the metabolic cost of transport of the given walking condition. We observed that the peak TA muscle activation occurred earlier than could be explained by a short latency reflex response. The activation of the TA muscle just prior to heel strike may serve as a prediction of the magnitude of the ground collision and the associated energy exchange. In this scenario, any unexpected length change experienced by the TA fascicle would serve as an error signal to the nervous system and provide additional information about energy lost per step. Our work helps provide a biomechanical framework to understand the possible neural mechanisms underlying the rapid optimization of walking economy.

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.

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.

Assessing Neural Connectivity and Associated Time Delays of Muscle Responses to Continuous Position Perturbations

Both linear and nonlinear electromyographic (EMG) connectivity has been reported during the expression of stretch reflexes, though it is not clear whether they are generated by the same neural pathways. To answer this question, we aim to distinguish linear and nonlinear connectivity, as well as their delays in muscle responses, resulting from continuous elbow joint perturbations. We recorded EMG from Biceps Brachii muscle when eight able-bodied participants were performing a steady elbow flexion torque while simultaneously receiving a continuous position perturbation. Using a recently developed phase coupling metric, we estimated linear and nonlinear connectivity as well as their associated delays between Biceps EMG responses and perturbations. We found that the time delay for linear connectivity (24.5 ± 5.4 ms) is in the range of short-latency stretch reflex period (< 35 ms), while that for nonlinear connectivity (53.8 ± 3.2 ms) is in the range of long-latency stretch reflex period (40-70 ms). These results suggest that the estimated linear connectivity between EMG and perturbations is very likely generated by the mono-synaptic spinal stretch reflex loop, while the nonlinear connectivity may be associated with multi-synaptic supraspinal stretch reflex loops. As such, this study provides new evidence of the nature of neural connectivity related to the stretch reflex.