ThB1.4
Proceedings of the 5th International IEEE EMBS Conference on Neural Engineering Cancun, Mexico, April 27 - May 1, 2011
Central and Peripheral Coding of Joint Position by Descending -Static Commands and Muscle Spindle Afferents Xin He1 and Ning Lan1, 2, Senior Member, IEEE
Abstract—The purpose of this study is to investigate plausible central and peripheral coding strategies of joint angle by descending commands and proprioceptive afferents in humans. Experimental evidence in both human and animal has shown that the firing rate of Ia afferents was linearly correlated to joint angle. Yet, experiments did not elucidate how Ia encoding of joint angle would be affected by co-activation, and how the peripheral neuromuscular system is informed of central representation of joint configuration. This study is aimed at addressing these issues using a realistic virtual arm (VA) model. In simulated experiments, elbow and shoulder angles of the VA are moved to different angular positions. The commands to muscles remain constant, or are adjusted with joint angle in linear and nonlinear fashions. The Ia afferents of muscles are evaluated in each case of modulation. Results show that Ia firing rates of mono-articular muscles can be fine-tuned to the characteristics of experimental recordings, while commands are nonlinearly modulated with joint angle. This suggests that commands could serve as the output of central encoding of joint information for posture and movement, and Ia afferents could be used to decode joint angle information faithfully.
I. INTRODUCTION
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evidence suggests that trajectory and final position of movement are planned separately, and are executed with dual controls [Lan et al. 2005; Ghez et al. 2007]. Other experimental evidence also suggests that the brain treats movement and position with distinct neural representations [Kurtzer et al. 2005]. Thus, movement and position control signals may be specified by motor cortex as static and dynamic commands to spinal motor neurons separately. A set of static alpha and gamma commands may be most relevant to maintaining a steady state joint position, while a set of dynamic alpha and gamma commands may control the acceleration and deceleration of movement. In so doing, questions arise as to how does the central nervous system (CNS) inform the periphery about the desired ECENT
Manuscript received on January 12, 2011. This work was supported in part by a grant from the Natural Science Foundation of China (No. 31070749). 1 Institute of Rehabilitation Engineering, the Med-X Research Institute, Shanghai Jiao Tong University, Shanghai, 200030, China 2 Division of Biokinesiology and Physical Therapy, School of Dentistry University of Southern California, Los Angeles, CA 90033, USA Xin He is with the Med-X Research Institute, Shanghai Jiao Tong University, 1954 Hua Shan Road, Shanghai, 200030, China (Email:
[email protected]). Ning Lan, Ph.D. is with Institute of Rehabilitation Engineering, the Med-X Research Institute, Shanghai Jiao Tong University, 1954 Hua Shan Road, Shanghai, 200030, China (Phone: 86-21-62933710, Fax: 86-21-62932302, Email:
[email protected]).
978-1-4244-4141-9/11/$25.00 ©2011 IEEE
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joint position, and can the joint position be decoded faithfully from proprioceptive afferents with fusimotor modulation of spindle sensitivity. The muscle spindle has a dual efferent and afferent function. Its fusimotor commands regulate the sensitivity of muscle spindle directly, and the sensory zone of spindle senses instantaneous muscle length and velocity, and feed the proprioception back to the spinal cord and brain via Ia and II afferents [Mileusnic et al. 2006]. To keep the spindle sensitive during muscle contraction, the brain may activate fusimotor control by descending gamma commands , and simultaneously execute the action by way of descending alpha command . At the same time, the brain needs to assess the outcome of the alpha activation of muscles through spindle afferents in order to estimate whether the alpha commands have properly driven the arm to the planned position. Therefore, we hypothesize that fusimotor control of spindle sensitivity may be used by the CNS to encode an internal representation of joint angles. Experimental studies of patterns of gamma motor activity during movement and posture in animals have shed some light to the function of fusimotor co-activation with commands. Direct recordings from gamma fibers in reduced preparations showed that there is in-phase modulation of activities with muscle EMGs during locomotion, providing firm evidence of co-activation during movement [Taylor et al. 2000, 2004, 2006]. Direct recording of Ia afferents from the dorsal ganglion cells of decerebrated cats indicated a robust linear relation between Ia afferents and joint angles [Stein et al. 2004]. With direct recording of spindle afferent, a range of wrist positions at rest and during movement were correlated with firing rates of primary afferents in wrist joint extensor of normal human subjects [Cordo et al. 2002]. With ramp-and-hold flexion movements at the wrist, and joint position was found linearly related to the steady-state firing rate during the hold period between ramps, i.e. during the posture maintenance phase, with a position sensitivity of . But modulation of spindle sensitivity during posture and movement was unknown in these experimental studies. Nonetheless, evidence in animals and intact subjects established partial clues to understand coding of joint positions by both fusimotor command and Ia afferent signals. Based on available empirical findings, we aimed at testing three plausible coding hypotheses of joint angles in central representation by commands and in peripheral decoding by Ia afferents. We tested these hypotheses using the realistic VA model developed previously [Song et al. 2008a]. Alpha
Fig. 1. The integrated VA model is driven by co-activation and generates joint kinematics as well as proprioceptions. VA model include 2 DOFs in the horizontal plane (shoulder F/E, elbow F/E) driven by 6 muscles, (PC, DP) for the shoulder joint, (BS, Tlt) for the elbow joint, and (Bsh, Tlh) cross both.
gamma co-activation strategy was adopted as model input to represent descending commands of motor cortex, and a dynamic simulation procedure was designed for testing plausible hypotheses. Understanding the coding strategies will be useful to further investigate neural control of movements [Alstermark et al. 2007; Lan et al. 2009; Du et al. 2010] by combining simulation with experiments.
capture a more realistic recruitment property of mammalian muscle as well. We modified the input port of the VM block to allow command inputs to each muscle. Each VM model was embedded with a spindle model, that has and muscle fiber length inputs and primary (Ia), secondary (II) afferent outputs [Mileusnic et al. 2006]. We simplified the sensorimotor system by excluding the spinal reflexes in the VA model to eliminate the effects of proprioception regulation in position control. The VM model was implemented in MATLAB/SIMULINK environment, and then integrated to the realistic VA model (Fig. 1). The VA model could be easily modified to include spinal circuitry to form a closed-loop model in future study. Experimental studies may encounter difficulties, in which many variables of crucial interest are unobservable. With model simulation, a large set of information could be obtained to reveal relations among variables that would not be possible to discover using animal experiments.
II. METHODS AND MATERIALS A. The Virtual Arm Model An integrated, sensorimotor virtual arm (VA) model has been developed for simulation studies of control of human arm movements [Song et al. 2008a]. The behaviors of the VA model have been evaluated and were found consistent with a wide range of physiological phenomena. In this study, three pairs of representative antagonist muscles were selected to actuate the VA model that kept the arm in horizontal plane (Fig. 1). These muscles were two pairs of mono-articular muscles for elbow and shoulder joints respectively, and one pair of bi-articular muscles cross both joints. Deltoid posterior (DP) and pectoralis major (clavicle portion, PC) were selected for shoulder joint; brachialis (BS) and triceps lateral (Tlt) were used for elbow joint; and biceps short (Bsh) and triceps long (Tlh) were bi-articular muscles. This subset of muscles has been typical in a large number of studies with the similar joint configuration. In this study, we updated the virtual arm (VA) [Song et al. 2008a] with a new version of virtual muscle (VM) [Song et al. 2008b] in order to improve computational efficiency, and to
Fig. 2. Nine sets of normalized
B. Alpha Gamma ( ) Co-activation We utilized different patterns of co-activation as inputs to drive the VA to different static joint configurations. The gamma command is regarded as the output of the internal representation of joint configuration in the brain. Alpha commands activate muscle fibers, while gamma commands actuate the spindle simultaneously. Each set of constant motor commands ( ) of mono-articular muscles stabilized the VA model at an equilibrium position in posture maintenance tasks. Alpha commands of bi-articular muscles were set to zero as they induce complex joint torques at both
motor commands (0~1) stabilize the VA at 9 different EP positions.
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shoulder and elbow joints. The signal dependent noise (SDN) in natural neuromuscular recruitment [Jones et al. 2004] was added to the alpha motor commands. To test fusimotor control strategies, three patterns of commands with constant, linear and parabolic relation to joint angles were evaluated respectively. The spindle afferents corresponding to different patterns were investigated at nine positions in the workspace of the arm (Fig. 2).
curves (Fig. 5 (a, b)). Results suggest that Ia afferents of mono-articular muscles could still be correlated with joint angles in a linear way as shown in Fig. 5 (c, d). The outcome of this strategy best fits all experimental data available so far. Although, the relationship between is nonlinear, it remains a monotonic curve. It implies that may still be used to encode joint position uniquely.
C. Procedure of Dynamic Simulation Each simulation began with a set of constant ( ) inputs. This stage lasted for ten seconds to allow the system to stabilize at an equilibrium point. The SDN was then added to the alpha motor commands to simulate intrinsic motor noise for another ten seconds. SDN in alpha activation evoked stochastic variations in muscular force, muscle length, as well as in primary and secondary afferents of muscle spindle. To evaluate the dynamic response of simulation, the mean values of activation, Ia and II afferents were calculated using data records from last five seconds. We evaluated the afferent outputs of muscle spindle within a range of equilibrium joint angle by adjusting commands. The equilibrium angle and gamma static ( relations were hypothesized to be zero order, first order, and second order. The resultant relations between joint angle and Ia afferents, i.e. ( ) curve, were examined under the three conditions. An outcome that can fit experimental data best was used as a criterion to judge whether to accept or reject a hypothesis.
Fig. 3. Constant curve (a, b) and Ia afferents response of mono-articular muscle spindles (c, d) at each position.
III. RESULTS We tested three hypotheses of fusimotor control strategies in posture maintenance tasks. Internal representation of joint angles is assumed to be expressed by commands. The commands were fit to zero-order, first-order, and second-order polynomials of joint angles respectively, and the dynamic responses of each mono-articular muscle spindle were presented here. Hypothesis 1: command is constant within the entire range of joint angle (Fig. 3 (a, b)). The primary afferents of mono-articular muscle spindles show excellent linear relationship with joint angles (Fig. 3 (c, d)). The Ia afferents of extensor DP and Tlt are positively proportional to the joint angles, and Ia afferents of flexor PC and BS are negatively proportional to joint angles. Although excellent linear relations in are obtained with this strategy, experimental evidence did not indicate that commands remain constant across the entire range of joint angles. Hypothesis 2: command is linearly modulated with joint angle (Fig. 4 (a, b)). The Ia afferents of mono-articular muscle spindles are not linearly and monotonically related to joint angles as is shown in Fig. 4 (c, d).Thus, the outcome of this strategy does not fit to observed linear relations in [Stein et al. 2004; Cordo et al. 2002]. Hypothesis 3: command is nonlinearly modulated with joint angle , and the relation is fitted to quadratic
Fig. 4. Linear curve (a, b) and Ia afferents response of mono-articular muscle spindles (c, d) at each position.
Fig. 5. Quadratic curve (a, b) and Ia afferents response of mono-articular muscle spindles (c, d) at each position.
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The primary afferents of bi-articular muscle spindles was also obtained in these simulations. But data did not provide complete information to establish a relation with the two joint angles of span. The curve presented in Fig.6 revealed only a part of the 3D function. Further simulation will be needed to elucidate the complex relationship in bi-articular muscles. IV. DISCUSSION In this study, three hypotheses were tested regarding the central and peripheral coding strategies of joint angles. The first set of simulation rejected the hypothesis that a constant command may be a plausible neural strategy in spite of its excellent linear relation. Experimental evidence clearly showed that a dynamic pattern of modulation was observed to co-vary with command and joint angles during movements [Taylor et al. 2000, 2004, 2006]. A linear relation was considered as a possible assumption [Lan et al. 2005], in which a linear spindle model was used. In the test of second hypothesis of this study, the linear modulation did not yield a well regulated linear relation, as was observed in experimental recordings [Stein et al. 2004; Cordo et al. 2002]. This outcome may be attributed to the nonlinear property of spindle model used in the VA model. Thus, the linear hypothesis of correlation was also rejected. Therefore, we tested the third hypothesis, in which a nonlinear modulation of commands was examined. The results suggested that a second order nonlinear relation between command and joint angle was necessary, in order for the Ia afferent to be linearly correlated with joint angle. In this case, the Ia afferents of mono-articular muscles appeared to be linearly modulated by joint angles, while the corresponding activations was still monotonically correlated to joint angles. This result implies that the brain could learn the nonlinear monotonic curve, and use the command to specify desired joint angle, while maintaining the ability to faithfully decode angular information from Ia afferents.
Fig. 6. A monotonic nonlinear relation between bi-articular command and both joints (a), and Ia afferents response of bi-articular muscle spindles (b) at each position.
31070749) and a research fund of a key project (Project 985-II) from SJTU. REFERENCES [1] [2] [3]
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V. CONCLUSION
[10]
We have tested three hypotheses regarding fusimotor control strategies of mono-articular muscles to encode and decode joint angle information. Results suggest that a linear relation with an average sensitivity of ( ) between Ia afferents and joint angle could be obtained by modulating the with joint angle nonlinearly according to a parabolic curve. Thus, the brain may learn the parabolic curve to encode joint angle internally, and to decode actual angular information from the linear relation. Further investigation will be focus on bi-articular muscles and the effects of spinal reflex regulation.
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ACKNOWLEDGMENT Materials of this paper are based on the work supported by a grant from the Natural Science Foundation of China (No.
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