Modeling Spinal Sensorimotor Control for Reach Task

Proceedings of the 2005 IEEE Engineering in Medicine and Biology 27th Annual Conference Shanghai, China, September 1-4, 2005

Modeling Spinal Sensorimotor Control for Reach Task N. Lan1, D. Song2, M. Mileusnic2, and J. Gordon1 Depts. of Biokinesiology and Physical Therapy, and 2Biomedical Engineering University of Southern California, Los Angeles, CA 90089, USA 1

been corroborated by behavioral studies in deafferented patients [Gordon et al. 1995]. The focus of this paper is to describe a model of the spinal sensorimotor control system that is capable of generating multiple joint reaching movements in humans in the framework of the dual control hypothesis.

Abstract Abstract – The spinal sensorimotor control system executes movement instructions from the central controller in the brain that plans the task in terms of global requirements. Spinal circuits serve as a local regulator that tunes the neuromuscular apparatus to an optimal state for task execution. We hypothesize that reach tasks are controlled by a set of feedforward and feedback descending commands for trajectory and final posture, respectively. This paper presents the use of physiologically realistic models of the spinal sensorimotor system to demonstrate the feasibility of such dual control for reaching movements.

Model of the Spinal Sensorimotor System

Keywords: sensorimotor control, modeling, simulation, reach, movement and posture

Introduction The neuromuscular system is a versatile device that can perform a variety of skilled tasks under the control of the brain. One of the most common tasks is to transport the hand to desired places in space by moving the arm. The mechanism of neural control of reaching tasks has been a subject of intensive experimental studies. It has proven difficult to identify the relative contributions of the various internal components of the sensorimotor control system. Recent advances in computer modeling and simulation of physiologically realistic models can provide insight into phenomena that are not directly observable, making it possible to formulate and test stronger hypotheses In control of motor tasks, arm movement and final posture are planned differently in the brain [Kurtzer et al. 2005]. We hypothesize that the spinal circuits responsible for proprioceptive reflexes regulate the equilibrium state of the final posture, and that the dynamics of movement are controlled by a programmed feedforward command to those same circuits. To execute a reach task involving a multijoint arm, the nervous system may first set proper spinal reflex gains for regulating the equilibrium state of each joint via a Ȗ motoneuron command to intrafusal muscle fibers of the spindle receptors. Joint movement may then be initiated via an D command to muscles. The dual nature of reaching task control has 0-7803-8740-6/05/$20.00 ©2005 IEEE.

A hierarchical model can be used to characterize reach task control taking place in the sensorimotor system. Figure 1A shows the structure of the system from task planning to movement execution. Figure 1B illustrates the spinal circuits connecting a pair of antagonist muscles around a joint, including stretch reflex, reciprocal inhibition, as well as recurrent inhibition of Renshaw cells. Two descending commands impinge upon the D and J motoneuron pools, respectively. Figure 1C depicts the interaction among muscle, joint and proprioceptors. The sensor outputs are thus not simply representative of the contractile state of muscles. Task Inputs Afferent Signal

Ne(t)

J(Teq(t))

Nf(t)

J(Teq(t))

Efferent Signal TASK PLANNING

D

D

Renshaw cells

J

OPTIMAL CONTROLLER

Spindles

Flexor

J

uf(t)

ue(t)

Extensor

GTO GTO Segment Bone

SPINAL REGULATOR

(C)

lt

SENSORS

MUSCLES

Lmt

lp

lf ls

JOINTS

(A)

(B)

lp

SPINDLE

MUSCLE

lt JOINT

Movements

Figure 1, hierarchical model of sensorimotor control system.

A skeletal model of the right arm is developed using software package SIMM (Musculographics, Inc.), which is shown in Figure 2. The arm model has anatomically realistic feature of bony structures, muscle origin and insertion points, as well as musculotendon paths. 14 muscles are included in the model, controlling 5 degrees of freedom of motion, i.e. shoulder flexion and extension, abduction and adduction, and rotation; elbow flexion and extension; as well as forearm supination and pronation.

4404

A virtual muscleTM model [Cheng et al. 2000] is used to actuate the arm skeleton. The compliant nature of muscle provides a basic stability for the arm, since muscles often operate in the positive stiffness range of

simulink blocks seamlessly to construct a complete spinal sensorimotor model.

Figure 3(a) structure of spindle model

Figure 3(b) model of intrafusal fiber (Mileusnic et al. 2005) Figure 2, graphic model of the arm in SIMM

their fascicle lengths. The properties of muscle activation and contraction dynamics, as well as recruitment of different types of muscle fibers, are carefully considered in the muscle model. Proprioceptor models are also embedded in the SIMM model. Figure 3 shows the structure of the spindle model under development. The model captures the most important physiologic properties of an animal muscle spindle, such as dynamic and static fusimotor innervations, primary and secondary afferents and nonlinear viscosity. Three kinds of intrafusal fibers are included in Figure 3(a), each having the similar structure shown in Figure 3(b). Parameters of the spindle model are determined by fitting model outputs to experimental data of spindle afferents [Mileusnic et al. 2005]. A linear model of Golgi Tendon Organ (GTO) will be used to describe force feedback. The skeletal arm, virtual muscle and proprioceptor models are integrated into a single Simulink block by a software tool, MMS (or Musculoskeletal Modeling in Simulink), for dynamic simulation. The dynamics module of the SIMM model contains the C code of equations of motion for the arm. The MMS wraps the C code of equations of motion by an S-function of Matlab, combines it with the virtual muscle and proprioceptor models, and converts the integrated model into a simulink block as shown in Figure 4. This system block can be connected with other

Figure 4, simulink block of the integrated arm model

Dual Control of Reaching Movements The sensorimotor system model will be used in demonstrate the feasibility of dual control for reach tasks. Figure 5 illustrates the block diagram of dual control for a single joint, in which a pair of antagonist muscles is controlled by an D command and a continuously modulated J command. The D command determines the background activation of both antagonist muscles, while the J command steers the balance of activation between the two antagonists in the time course of reaching, and specifies the final target position corresponding to its steady state value. The interneuronal network (INN in Figure 5) of the propriospinal system [Perrot-Deseilligny, 1996] preprocesses the D and J commands before they are distributed to the D and J motonuronal pools. The

4405

Figure 5, diagram of dual control for reach task in a single joint.

brain controller sets the spinal reflex gains mostly by pre-synaptic inhibition to the mono-synaptic reflexes, and by interneurons interposed in the pathways of disynaptic reflexes. Experimental evidence appears to suggest that J-static and J-dynamic controls play different roles in movement control [Prochazka, 1989; Taylor et al. 2004]. Simulation studies demonstrated that J-static activity is associated with regulation of final equilibrium position [Lan et al. 2005]. It would, thus, be possible to separate the contributions of Jstatic and J-dynamic controls for reaching tasks using simulation studies.

Figure 6 illustrates the moment arm ratio of biceps at shoulder and elbow joints. In a large range of the elbow angle, the action of biceps at the elbow is greater than that at the shoulder, i.e. the ratio is less than 1. The mechanical coupling of biceps muscle is not constant across the shoulder and elbow angles, implying that its effect on arm posture control can be very complicated.

Multi-Joint Posture Control A controllability issue of the neuromuscular system is the uniqueness of posture control, due to the fact that there are a greater number of muscles than that are required for actuating the degrees of freedom in the arm. With a pair of antagonist muscles around a single joint, it has been shown possible to provide a unique control of final equilibrium angle of the joint with properly tuned spinal reflex gains [Lan et al. 2005]. Furthermore, the equilibrium joint angle is uniquely correlated to the level of J-static activity. The existence of a unique relation between the J-static activity and the final equilibrium position suggests a possible avenue to specify the final target position of reaching via the descending J-static command. Such unique relation can be extended for controlling final target posture of a multi-joint arm. However, multi-joint posture control is complicated by the presence of multi-articular muscles, such as biceps that cross the elbow and shoulder joints. Activation of bi-articular muscles will make the equilibrium angles of shoulder and elbow joints depend on each other, and thus losing independent control of them.

Figure 6, coupling ratio of biceps at shoulder and elbow joints

A plausible strategy for multi-joint postural control may be to activate single joint muscles only. Evidence of end-point stiffness modulation in voluntary force production [Perreault et al. 2001] indicates that in postural control, single joint muscles are mostly activated to modulate end-point stiffness of the hand, while the biceps remain at a minimal level of activation. A simulation analysis also suggests that bi-articular muscles do not have significant advantages over single joint muscles in stabilizing the arm [Lan, 2002]. Thus, it is justifiable to assume that the more effective strategy for multi-joint postural task is to activate single joint muscles.

Trajectory Control during Reaching Trajectory control of a multi-joint limb must take into account the nonlinear dynamics in the planning of the reach by the central controller in the brain. An

4406

internal model of the limb would allow accurate programming of the descending commands for trajectory control. Optimal performance criteria may be adopted to guide the formation (or learning) of the motor program. Dynamic optimization has shown that a minimal effort criterion prescribes a tri-phasic pulse of feedforward D command for multi-joint reach task that displays a near straight hand path, and the familiar tri-phasic EMG bursts between antagonists [Lan, 1997].

extent. Movement trajectory emerges as a result of interaction of musculoskeletal dynamics with an optimal feedforward control. The spinal reflexes are tuned to regulate the equilibrium state of the final target posture of reach. We will test the dual control hypothesis using simulation studies combined with experimental data of normal and abnormal reaching movements in human subjects [Gordon et al. 1995]. The sensorimotor control model is also useful to test alternative hypotheses of motor control for reach tasks, and control strategies of other motor tasks, such as cyclic movements.

Acknowledgement

(a) reaching movements

This work is supported by the National Science Foundation under a grant IBN-0352117, and partially by the Whitaker Foundation. Part of the work was developed at the Alfred E. Mann Institute for Biomedical Engineering at USC.

(b) shoulder muscles

References

(c) elbow muscles

(d) bi-articular muscles

Figure 7, patterns of first phase of muscle activation in movements of different directions.

Simulation analysis further reveals that the pulse height of the D command is a global variable that determines the speed of movements, and is nearly insensitive to movement directions. The latter is specified, instead, by a separate command of the final target position. Figure 7(a) shows the simulation of a set of two joint, planar reach movements in different directions, where the pulse heights for each pair of antagonist muscles remain nearly at the same level across all directions. Figure 7(b), (c) and (d) give the first phase of muscle activity (or EMG) for shoulder, elbow and bi-articular muscles. It is clear that the first phase of muscle activities is tuned in a sinusoidal pattern with movement directions. It is possible to investigate with the model the role of the propriospinal network in shaping the EMG patterns of reach movements in different directions.

Discussions This paper presents a model of spinal sensorimotor system and a dual control hypothesis of reach tasks. Modeling studies have suggested that the global variables in planning reach tasks are the final target position and movement speed. The final target position prescribes both movement direction and

Chen EJ, Brown IE, and Loeb GE, Virtual muscle: a computa-tional approach to understanding the effects of muscle properties on motor control, J. Neurosci, Methods, 101:117-130, 2000. Gordon J, Ghilard MF, and Ghez C, Impairments of reaching movements in patients without proprioception, I. Spatial errors, J. Neurophyiol., vol.73(1):347-360, 1995. Kurtzer I, Herter TM, and Scott SH, Random changes in cortical load representation suggests distinct control of posture and movement, Nature Neurosci., 8(4):498-540, 2005. Lan N, Analysis of an optimal control model of multi-joint arm movements, Biol. Cybern., 76:107-117, 1997. Lan N, Stability analysis for posture control in a two joint limb system, IEEE Trans. NSRE, 10(4): 249-259, 2002. Lan N., Li Y., Sun Y. and Yang FS, Reflex regulation of antagonist muscles for control of joint equilibrium position, IEEE Trans. NSRE, 13(1):60-71, 2005. Mileusnic M, Brown IE, Lan N, and Loeb GE, A model of fusimotor control of the mammalian muscle spindle, to be submitted, 2005. Perreault EJ, Kirsch RF, and Crago PE, Effects of voluntary force generation on the elastic components of endpoint stiffness, Exp. Brain Res., 141:312-323, 2001. Pierrot-Deseilligny E, Transmission of the cortical command for human voluntary movement through cervical propriospinal premotorneurons, Progress in Nuerobiology, 48:489-517, 1996. Prochazka A., Sensorimotor gain control: a basic strategy of motor systems? Progress in Neurobiology, 33:281307, 1989. Taylar A, Durbaba R, and Ellaway PH, Direct and indirect assessment of J-motor firing patterns, Can. J. Physiol. Pharmacol., 82:793-802, 2004.

4407