The rhythms of steady posture: Motor commands as spatially organized oscillation patterns
Introduction
Neural oscillations in the beta band (15–30 Hz) have long been implicated in the planning and execution of voluntary movement [1], [2], but how those oscillations relate to specific muscle movements is unknown. We present a theoretical model of the descending motor system which proposes a neural mechanism by which spatial patterns of beta band oscillations in motor cortex may be translated into muscle activity. We argue that specific patterns of beta oscillations in cortex are spatially filtered by the pyramidal tract neurons of the descending motor tract to selectively shape the motor drive to the muscles (Fig. 1). The proposed mechanism suggests a functional role for neural oscillations in which the ensuing movements need not be rhythmic. This decoupling of the cortical rhythm from the movement rhythm distinguishes the proposed model from central pattern generator models where oscillations in the spinal cord are typically translated directly into rhythmic muscle movements (see [3], [4] for reviews). We demonstrate this principle by modeling propagating waves of cortical beta oscillations controlling steady postures in a simulated biomechanical limb joint. The aim is to explore a putative role for motor rhythms [5], [6] that goes beyond the generation of rhythmic locomotion and tackles the problem of translating cortical activity into motor output (see [7] for a recent discussion).
The neurophysiology of beta oscillations in the descending motor system is complex. In primary and pre-motor cortex, the spectral power of the beta rhythm is most pronounced during the maintenance of steady motor output and rapidly attenuates at the onset of movement to rebound strongly after movement termination [10]. These event-related fluctuations in power are thought to reflect dynamic reorganization of the phases of oscillatory activity at the neuronal scale [11]. Task-specific beta oscillations are also observed in the pyramidal tract neurons [12], which form the major output of primary motor cortex and directly innervate the motor neurons in the spine. These descending beta oscillations are weakly coherent with the activity of spinal motor neurons and can also be observed non-invasively as corticomuscular coherence between electromyograph (EMG) activity and electroencephalograph (EEG) or magnetoencepholgraph (MEG) activity [13], [14]. Corticomuscular coherence may have a functional role by enabling more efficient recruitment of spinal motor neurons [15] or effective corticospinal interaction [16]. It is thought that beta-band oscillations favor the stationary motor state [17], [18], [19] since the presence of beta oscillations is inversely proportional to the likelihood that a new voluntary action will need to be processed and performed [20].
Cortical beta oscillations are not necessarily spatially uniform. Propagating waves of beta oscillations have recently been observed in the primary and pre-motor cortices of primates and humans during delayed-reaching tasks [21], [22], [23]. These waves are most prominent during states of motor readiness and are attenuated during movement concomitant with the general reduction of beta power. The phase of the propagating wave is reset at the onset of the instruction cue, suggesting a role for information transfer from pre-frontal decision-making areas [21]. On average, the direction of wave propagation tends to follow the direction of the underlying cytoarchitecture but there is substantial variation between individual waves. It has been suggested that the propagating wave corresponds to the proximal-to-distal sequencing of muscle recruitment in the reaching task [24]. In the present paper, we speculate that the morphological properties of waves may serve as the neural basis for encoding motor commands.
Propagating waves contain potential information in their wavelength, orientation, amplitude, phase and speed. For simplicity, we consider only wavelength and orientation since those properties are known to be governed by the topology of lateral inhibitory connections in neural field models [25], [26], [27]. Previous numerical studies have shown that manipulating the strength of lateral inhibition induces transitions between waves and coherent synchrony among coupled oscillators [28]. Introducing anisotropy into the inhibitory coupling permits control over the spatial orientation of waves to encode motor commands [29]. The orientation of those waves can be discriminated (decoded) by the extensive dendritic arbors of the pyramidal tract neurons to selectively drive motor unit activity [8]. That motor unit activity can in turn drive muscle movement in a simulated biomechanical limb [30].
The present study combines the previous findings [28], [29], [30], [8] into a combined set of simulations that demonstrate the entire chain of events from cortex to limb. The full model comprises two parallel motor tracts that each descend from the cortex to independently drive antagonist muscles in a single biomechanical joint which is restricted to planar movements with one degree of freedom. Waves and synchrony are elicited in the cortical model by manipulating the lateral inhibitory connectivity. The descending motor tracts are each tuned to respond to cortical waves at orthogonal orientations. The orientation of waves in the cortical model thus governs the descending motor drive to the muscles. Cortical synchrony is assumed to encode motor rest. We use this model to demonstrate how spatial oscillation patterns in motor cortex can be translated into steady postures in a biomechanical joint. Furthermore, our model replicates some of the oscillatory aspects of motor neurophysiology. Namely, the gross reduction of beta power at movement onset and the weak but significant levels of corticomuscular coherence during steady motor output.
The full model is entirely feed-forward and so we present it in separate stages. Section 2 demonstrates the emergence of oriented waves and synchrony in the cortex when the strength of the lateral inhibitory connectivity is manipulated. Section 3 demonstrates how the dendritic arbors of the pyramidal tract neurons spatially filter the cortical wave patterns to shape the descending motor drive. Section 4 shows how the descending drive of the pyramidal tract neurons translates into motor unit activity. Section 5 describes how motor neuron activity is translated into muscle contractions which govern the movement of the biomechanical joint. Lastly, Section 6 compares the simulated coherence between oscillations in cortex and muscles against corticomuscular coherence observed in humans.
Section snippets
Cortical model
Oscillatory neural activity within a patch of primary motor cortex was modeled using a array of Kuramoto oscillators [31] with anisotropic inhibitory surround spatial coupling [11] and periodic boundary conditions. The dynamics of each oscillator was thus defined aswhere θx is the phase of the oscillatory neural activity at spatial position and ωx is its intrinsic frequency. The inhibitory surround coupling was modeled by the anisotropic
Pyramidal tract neurons
We modeled the pyramidal tract neurons of the descending motor pathway to demonstrate how cortical wave activity may be selectively translated into motor drive. Pyramidal tract neurons occupy layer 5 of motor cortex and have extensive lateral dendritic connections with a spatial reach of approximately 300 μm [36], [37], [38]. Furthermore, their axons descend the spinal cord to monosynaptically innervate motor neurons. Gabor filters have previously been used to model neural responses to spatial
Motor neurons
Our model of the descending motor tract comprises a pool of pyramidal tract neurons that collectively innervate a pool of motor neurons that in turn innervate a single muscle (Fig. 1d). Each motor neuron was modeled as a leaky integrate-and-fire neuron with stochastic membrane resets following the methods of Boonstra and Breakspear [45]. The dynamics of the membrane potential Vj of each motor neuron was thus defined aswhere is an all-or-none connection from
Biomechanical joint movement
Following Heitmann, Ferns and Breakspear [30], the biomechanical joint was represented by a two-link planar model of an arm in which only the elbow joint was actuated by muscles. The shoulder joint was reduced to a passive pivot from which the limb hung freely under gravity. Movement in the elbow was driven by a pair of antagonist muscles where the muscle model replicated the passive force–length–velocity relationships of muscle tissue. These non-linear relationships greatly influence the
Corticomuscular coherence
Corticomuscular coherence measures the degree by which oscillations in the electromyogram correlate with oscillations in the motor cortex (see [53] for a review). Weak but statistically significant levels of coherence between 0.01 and 0.1 are typically observed in the beta bandwidth during steady hold tasks [15]. In our model, corticomusclar coherence was estimated by computing the average magnitude squared coherence between the local field potential at n=100 randomly chosen locations on cortex
Discussion
Our model demonstrates a putative neural mechanism by which the descending motor system translates spatial patterns of oscillatory cortical activity into muscle movements. Steady postures were achieved in the biomechanical joint using an oscillatory cortical mechanism that operated in the beta band (15–30 Hz). The simulation results verify the proposal that cortical processes can exploit oscillatory mechanisms to encode non-rhythmic movement. The use of oscillations to control steady postures
Acknowledgments
SH and BE acknowledge funding by USA National Science Foundation (NSF) award (1219753). SH, TB and MB acknowledge funding by Australian Research Council (ARC) Thinking Systems Grant (TS0669860). TB acknowledges funding by the Netherlands Organization for Scientific Research (NWO (45110-030)).
Stewart Heitmann is a post-doctoral research associate in the Department of Mathematics at the University of Pittsburgh. He also holds honours degrees in Computer Science (1994) and Psychology (2007) from the University of Sydney. He obtained his Ph.D. from the School of Psychiatry at the University of New South Wales (2013). He is interested in the functional role of oscillations in neural computation, specifically in relation to motor control.
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Stewart Heitmann is a post-doctoral research associate in the Department of Mathematics at the University of Pittsburgh. He also holds honours degrees in Computer Science (1994) and Psychology (2007) from the University of Sydney. He obtained his Ph.D. from the School of Psychiatry at the University of New South Wales (2013). He is interested in the functional role of oscillations in neural computation, specifically in relation to motor control.
Tjeerd Boonstra is a research fellow in Movement Neuroscience at the University of New South Wales in Sydney, Australia. He obtained a master degree in Psychology from the University in Amsterdam (2003) and a Ph.D. in Human Movement Science from the VU University Amsterdam (2007). He moved to Australia in 2007, where he is now the head of the EEG lab at the Black Dog Institute. His research focuses on brain dynamics, complex networks and neural synchronization.
Pulin Gong is a senior lecturer at University of Sydney (USyd), where he is the head of the Theoretical and Computational Neuroscience Group. Before joining USyd in 2009, Dr Gong was a staff scientist at RIKEN Brain Science Institute in Japan. Dr Gongs research focuses on understanding complex cortical dynamics and their information processing principles in the brain.
Michael Breakspear completed his medical training (1994), Ph.D. (2003) and post-doctoral training in Physics (2003–6) at the University of Sydney before joining the School of Psychiatry at UNSW. He moved to QIMR Berghofer in 2009 where he leads the Systems Neuroscience Group. He is a consultant psychiatrist and chair of research for Metro North Mental Health and a psychiatrist in the Forensic Mental Health Service.
Bard Ermentrout completed his Ph.D. (1979) at the University of Chicago and postdoctoral training at the National Institutes of Health before joining the Mathematics Department at the University of Pittsburgh. He is currently a Distinguished University Professor of Computational Biology and Professor of Mathematics.