Neural and Computational Modeling of Movement Control

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Review
04 June 2015
Major remaining gaps in models of sensorimotor systems
Gerald E. Loeb
 and 
George A. Tsianos
Schematic of major structures likely to be required for a reasonably complete model of sensorimotor control of learned voluntary behaviors. Gray elements denote well-modeled subsystems (discussed herein only by reference); blue denotes substantial progress but with important functional gaps; green denotes attempts to model based on incomplete data; red denotes no quantitative models to date. Musculoskeletal systems (MS) interact with the World via Skin interfaces that contain large numbers of Tactile mechanoreceptors. Other sources of neurally mediated feedback include large numbers of Proprioceptive mechanoreceptors in muscles and various connective tissues plus chemoreceptors that provide information related to Energy consumption, fatigue, and injury. All of these somatosensory signals inform both the spinal cord and the brain and are known to play critical roles in both learning and performance of skilled motor behaviors. Various computational models have been described for individual subsystems of the brain but these models do not include specific models of how they interact with each other or with their ascending and descending projections from and to the various subsystems in the spinal cord.

Experimental descriptions of the anatomy and physiology of individual components of sensorimotor systems have revealed substantial complexity, making it difficult to intuit how complete systems might work. This has led to increasing efforts to develop and employ mathematical models to study the emergent properties of such systems. Conversely, the development of such models tends to reveal shortcomings in the experimental database upon which models must be constructed and validated. In both cases models are most useful when they point up discrepancies between what we think we know and possibilities that we may have overlooked. This overview considers those components of complete sensorimotor systems that currently appear to be potentially important but poorly understood. These are generally omitted completely from modeled systems or buried in implicit assumptions that underlie the design of the model.

8,474 views
24 citations
Original Research
11 November 2014
Spinal circuits can accommodate interaction torques during multijoint limb movements
Thomas Buhrmann
 and 
Ezequiel A. Di Paolo
Model of two-joint planar arm actuated by antagonistic muscles under control of spinal interneurons. Shown are two spinal circuits, one for each pair of antagonistic muscles. Connections are drawn between interneurons regulating muscles acting on the same joint, as well as those coupling adjacent joints (only one direction is shown for simplicity; the structure of Ib connections between segments is symmetric in the model). Ia pathways are shown in red, Ib pathways in orange, and Renshaw cells in gray. Flexor related circuitry is drawn as solid and extensor as dashed lines. Excitatory synapses are displayed as triangles and inhibitory synapses as disks. Those that during optimization can be of either type are drawn as squares. Three types of signals descend from higher centers (blue). These are: the stretch reflex threshold λd (implying appropriate coordination of α and γ fusimotor drives, see section on threshold control); a coactivation signal λco to the α-MNs, and a GO-signal distributed to all spinal neurons (each receiving this signal via its own weighted connection, not shown here). The topology of the circuits is symmetric, but synaptic strengths can be assigned asymmetrically. The topology is also identical for the two joints, though for clarity some connections of the shoulder joint are omitted in the figure. Muscles wrap around joint capsules of radius r1,2 and insert into arm segments of lengths l1,2.

The dynamic interaction of limb segments during movements that involve multiple joints creates torques in one joint due to motion about another. Evidence shows that such interaction torques are taken into account during the planning or control of movement in humans. Two alternative hypotheses could explain the compensation of these dynamic torques. One involves the use of internal models to centrally compute predicted interaction torques and their explicit compensation through anticipatory adjustment of descending motor commands. The alternative, based on the equilibrium-point hypothesis, claims that descending signals can be simple and related to the desired movement kinematics only, while spinal feedback mechanisms are responsible for the appropriate creation and coordination of dynamic muscle forces. Partial supporting evidence exists in each case. However, until now no model has explicitly shown, in the case of the second hypothesis, whether peripheral feedback is really sufficient on its own for coordinating the motion of several joints while at the same time accommodating intersegmental interaction torques. Here we propose a minimal computational model to examine this question. Using a biomechanics simulation of a two-joint arm controlled by spinal neural circuitry, we show for the first time that it is indeed possible for the neuromusculoskeletal system to transform simple descending control signals into muscle activation patterns that accommodate interaction forces depending on their direction and magnitude. This is achieved without the aid of any central predictive signal. Even though the model makes various simplifications and abstractions compared to the complexities involved in the control of human arm movements, the finding lends plausibility to the hypothesis that some multijoint movements can in principle be controlled even in the absence of internal models of intersegmental dynamics or learned compensatory motor signals.

6,752 views
29 citations
Stiffness modulation and mini-max feedback control (MMFC). (A) Adaptation of stiffness geometry to unstable dynamics. The stiffness changes to the red dotted ellipse from the initial blue solid form. The long and short axes of the ellipse represent the directions of maximal and minimal stiffness, respectively. (B) Block diagram of MMFC with uncertainty.
Original Research
24 September 2014

We propose a mini-max feedback control (MMFC) model as a robust approach to human motor control under conditions of uncertain dynamics, such as structural uncertainty. The MMFC model is an expansion of the optimal feedback control (OFC) model. According to this scheme, motor commands are generated to minimize the maximal cost, based on an assumption of worst-case uncertainty, characterized by familiarity with novel dynamics. We simulated linear dynamic systems with different types of force fields–stable and unstable dynamics–and compared the performance of MMFC to that of OFC. MMFC delivered better performance than OFC in terms of stability and the achievement of tasks. Moreover, the gain in positional feedback with the MMFC model in the unstable dynamics was tuned to the direction of instability. It is assumed that the shape modulations of the gain in positional feedback in unstable dynamics played the same role as that played by end-point stiffness observed in human studies. Accordingly, we suggest that MMFC is a plausible model that predicts motor behavior under conditions of uncertain dynamics.

10,078 views
19 citations
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