Description of motor control using inverse models

Humans can perform complicated movements like writing or running without giving them much thought. The scientific understanding of principles guiding the generation of these movements is incomplete. How the nervous system ensures stability or compensates for injury and constraints – are among the unanswered questions today. Furthermore, only through movement can a human impose their will and interact with the world around them. Damage to a part of the motor control system can lower a person’s quality of life. Understanding how the central nervous system (CNS) forms control signals and executes them helps with the construction of devices and rehabilitation techniques. This allows the user, at least in part, to bypass the damaged area or replace its function, thereby improving their quality of life. CNS forms motor commands, for example a locomotor velocity or another movement task. These commands are thought to be processed through an internal model of the body to produce patterns of motor unit activity. An example of one such network in the spinal cord is a central pattern generator (CPG) that controls the rhythmic activation of synergistic muscle groups for overground locomotion. The descending drive from the brainstem and sensory feedback pathways initiate and modify the activity of the CPG. The interactions between its inputs and internal dynamics are still under debate in experimental and modelling studies. Even more complex neuromechanical mechanisms are responsible for some non-periodic voluntary movements. Most of the complexity stems from internalization of the body musculoskeletal (MS) system, which is comprised of hundreds of joints and muscles wrapping around each other in a sophisticated manner. Understanding their control signals requires a deep understanding of their dynamics and principles, both of which remain open problems. This dissertation is organized into three research chapters with a bottom-up investigation of motor control, plus an introduction and a discussion chapter. Each of the three research chapters are organized as stand-alone articles either published or in preparation for submission to peer-reviewed journals. Chapter two introduces a description of the MS kinematic variables of a human hand. In an effort to simulate human hand motor control, an algorithm was defined that approximated the moment arms and lengths of 33 musculotendon actuators spanning 18 degrees of freedom. The resulting model could be evaluated within 10 microseconds and required less than 100 KB of memory. The structure of the approximating functions embedded anatomical and functional features of the modelled muscles, providing a meaningful description of the system. The third chapter used the developments in musculotendon modelling to obtain muscle activity profiles controlling hand movements and postures. The agonist-antagonist coactivation mechanism was responsible for producing joint stability for most degrees of freedom, similar to experimental observations. Computed muscle excitations were used in an offline control of a myoelectric prosthesis for a single subject. To investigate the higher-order generation of control signals, the fourth chapter describes an analytical model of CPG. Its parameter space was investigated to produce forward locomotion when controlled with a desired speed. The model parameters were varied to produce asymmetric locomotion, and several control strategies were identified. Throughout the dissertation the balance between analytical, simulation, and phenomenological modelling for the description of simple and complex behavior is a recurrent theme of discussion

Analytical CPG model driven by limb velocity input generates accurate temporal locomotor dynamics

The ability of vertebrates to generate rhythm within their spinal neural networks is essential for walking, running, and other rhythmic behaviors. The central pattern generator (CPG) network responsible for these behaviors is well-characterized with experimental and theoretical studies, and it can be formulated as a nonlinear dynam- ical system. The underlying mechanism responsible for locomotor behavior can be expressed as the process of leaky integration with resetting states generating appropriate phases for changing body velocity. The low-dimensional input to the CPG model generates the bilateral pattern of swing and stance modulation for each limb and is consistent with the desired limb speed as the input command. To test the minimal configuration of required parameters for this model, we reduced the system of equations representing CPG for a single limb and provided the analytical solution with two complementary methods. The analytical and empirical cycle durations were similar (R2 = 0.99) for the full range of walking speeds. The structure of solution is consistent with the use of limb speed as the input domain for the CPG network. Moreover, the reciprocal interaction between two leaky integration processes representing a CPG for two limbs was sufficient to capture fundamental experimental dynamics associated with the control of heading direction. This analysis provides further support for the embedded velocity or limb speed representation within spinal neural pathways involved in rhythm generation

Microstimulation of human somatosensory cortex evokes task-dependent, spatially patterned responses in motor cortex

The primary motor (M1) and somatosensory (S1) cortices play critical roles in motor control but the signaling between these structures is poorly understood. To fill this gap, we recorded – in three participants in an ongoing human clinical trial (NCT01894802) for people with paralyzed hands – the responses evoked in the hand and arm representations of M1 during intracortical microstimulation (ICMS) in the hand representation of S1. We found that ICMS of S1 activated some M1 neurons at short, fixed latencies consistent with monosynaptic activation. Additionally, most of the ICMS-evoked responses in M1 were more variable in time, suggesting indirect effects of stimulation. The spatial pattern of M1 activation varied systematically: S1 electrodes that elicited percepts in a finger preferentially activated M1 neurons excited during that finger’s movement. Moreover, the indirect effects of S1 ICMS on M1 were context dependent, such that the magnitude and even sign relative to baseline varied across tasks. We tested the implications of these effects for brain-control of a virtual hand, in which ICMS conveyed tactile feedback. While ICMS-evoked activation of M1 disrupted decoder performance, this disruption was minimized using biomimetic stimulation, which emphasizes contact transients at the onset and offset of grasp, and reduces sustained stimulation

Approximating complex musculoskeletal biomechanics using multidimensional autogenerating polynomials.

Computational models of the musculoskeletal system are scientific tools used to study human movement, quantify the effects of injury and disease, plan surgical interventions, or control realistic high-dimensional articulated prosthetic limbs. If the models are sufficiently accurate, they may embed complex relationships within the sensorimotor system. These potential benefits are limited by the challenge of implementing fast and accurate musculoskeletal computations. A typical hand muscle spans over 3 degrees of freedom (DOF), wrapping over complex geometrical constraints that change its moment arms and lead to complex posture-dependent variation in torque generation. Here, we report a method to accurately and efficiently calculate musculotendon length and moment arms across all physiological postures of the forearm muscles that actuate the hand and wrist. Then, we use this model to test the hypothesis that the functional similarities of muscle actions are embedded in muscle structure. The posture dependent muscle geometry, moment arms and lengths of modeled muscles were captured using autogenerating polynomials that expanded their optimal selection of terms using information measurements. The iterative process approximated 33 musculotendon actuators, each spanning up to 6 DOFs in an 18 DOF model of the human arm and hand, defined over the full physiological range of motion. Using these polynomials, the entire forearm anatomy could be computed in <10 μs, which is far better than what is required for real-time performance, and with low errors in moment arms (below 5%) and lengths (below 0.4%). Moreover, we demonstrate that the number of elements in these autogenerating polynomials does not increase exponentially with increasing muscle complexity; complexity increases linearly instead. Dimensionality reduction using the polynomial terms alone resulted in clusters comprised of muscles with similar functions, indicating the high accuracy of approximating models. We propose that this novel method of describing musculoskeletal biomechanics might further improve the applications of detailed and scalable models to describe human movement