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Research Papers

Simulation of Movement in Three-Dimensional Musculoskeletal Human Lumbar Spine Using Directional Encoding-Based Neurocontrollers

[+] Author and Article Information
Bahman Nasseroleslami

Department of Biology,
Northeastern University,
134 Mugar Life Sciences,
360 Huntington Avenue,
Boston, MA 02115
e-mail: nasseroleslami@gmail.com

Gholamreza Vossoughi

Center of Excellence in Design,
Robotics, and Automation,
School of Mechanical Engineering,
Sharif University of Technology,
Azadi Avenue,
P.O. Box 145888-9496,
Tehran, Iran
e-mail: vossough@sharif.edu

Mehrdad Boroushaki

Department of Energy Engineering,
Sharif University of Technology,
Azadi Avenue,
P.O. Box 11155-8639,
Tehran, Iran
e-mail: boroushaki@sharif.edu

Mohamad Parnianpour

Biomechanics Laboratory,
School of Mechanical Engineering,
Sharif University of Technology,
Azadi Avenue,
P.O. Box 11365-9567,
Tehran, Iran
e-mail: parnianpour@sharif.edu

Definition of agonist/antagonist is based on the acceleration phase of movement.

1Corresponding author.

Manuscript received October 5, 2013; final manuscript received April 20, 2014; accepted manuscript posted May 14, 2014; published online July 24, 2014. Assoc. Editor: Kenneth Fischer.

J Biomech Eng 136(9), 091010 (Jul 24, 2014) (10 pages) Paper No: BIO-13-1466; doi: 10.1115/1.4027664 History: Received October 05, 2013; Revised April 20, 2014; Accepted May 14, 2014

Despite development of accurate musculoskeletal models for human lumbar spine, the methods for prediction of muscle activity patterns in movements lack proper association with corresponding sensorimotor integrations. This paper uses the directional information of the Jacobian of the musculoskeletal system to orchestrate adaptive critic-based fuzzy neural controller modules for controlling a complex nonlinear redundant musculoskeletal system. The proposed controller is used to control a 3D 3-degree of freedom (DOF) musculoskeletal model of trunk, actuated by 18 muscles. The controller is capable of learning to control from sensory information, without relying on pre-assumed model parameters. Simulation results show satisfactory tracking of movements and the simulated muscle activation patterns conform to previous EMG experiments and optimization studies. The proposed controller can be used as a computationally inexpensive muscle activity generator to distinguish between neural and mechanical contributions to movement and for study of sensory versus motor origins of motor function and dysfunction in human spine.

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Figures

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Fig. 1

Simplified three-dimensional model of torso as a rigid inverted pendulum actuated by muscles. Front view (left) and side view (right) of musculoskeletal system. The joint at the bottom is considered as frictionless spherical joint, placed at the center of inertial coordinate system. The body coordinate system is placed at the center of gravity (C.G) of the pendulum. RA, EO, IO, ES, and LD stand for rectus abdominis, external oblique, internal oblique, erector spinae, and latissimus dorsi, respectively. Musculature data from Ref. [30].

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Fig. 2

Critic-based fuzzy neurocontroller unit in SISO control loop. The NFC block is the neurofuzzy controller block described in Appendix A1 (See the “Supplemental Data” tab for this paper on the ASME Digital Collection.) re and rα are the tracking error critic signal and control effort critic signal, which are functions of error (e) and control effort (α), respectively. θ and θref are actual output and reference position signals. The structure of the NFC block is shown in Fig. A1.

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Fig. 3

Directional encoding based array of fuzzy neurocontroller units. Each neurofuzzy controller (NFC) unit (illustrated in Fig. 2) is fed with the corresponding directionally encoded error signal to generate the output αm (Critic signals in Fig. 2 are not shown). The Jacobian neural network provides the Directional Encoders that perform the dot-product and controller agents with the required directional information (J→m) and gain (jm). The Jacobian neural network computes the needed data as a function of desired states of system, θ→ref. Training of the Jacobian network is achieved through supervised learning, whose required signals are received from the musculoskeletal model (see Fig. 4). Solid lines depict the control signals while dashed lines show learning signals. θ→ is the actual position of the musculoskeletal model. The figure explains the structure of Controller block in Fig. 4.

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Fig. 4

Simplified block diagram of the proposed controller for motor command generation. The arrangement of modules is a simplified model inspired from Refs. [16,17]. Solid lines depict the control signals while dashed lines show learning signals. Only the nongray elements are directly discussed in this study. The controller block contains the controller structure of Fig. 3. The State Estimator computes an estimation of system states from sensory signals. The Next State Planner (NSP) plans the next state of system based on the default and target system state. (θt is the target state, θd the desired state of system, α the generated muscle activation level, L the sensory information vectors of muscle length, and θest the estimated system states from sensory information). The structure of the Controller block is shown in Fig. 3.

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Fig. 5

Tracking performance of the controller in point-to-point movement. The movement is the flexion between upright 0 deg to 55.4 deg flexion with 1.0 s duration. Minimum jerk is used as desired trajectory. The exact values of the Jacobian are used for simulation (i.e., a perfectly trained Jacobian network).

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Fig. 6

Muscles activation levels in upright 0 deg–55.4 deg flexion point-to-point movement for right-hand side muscles (see Fig. 5), generated by the controller. RA, EO, IO, ES, and LD stand for rectus abdominis, external oblique, internal oblique, erector spinae, and latissimus dorsi, respectively.

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Fig. 7

Scaling of the predicted muscle activity patterns by movement duration. For all simulations the point-to-point trunk movement from upright 0 deg to 55.4 deg flexion is simulated with the minimum-jerk trajectory. RA and ES stand for rectus abdominis and erector spinae, respectively. Notice the tendency of the second agonist burst to vanish in slower movement.

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Fig. 8

(a) Muscles activation level in 51.1 deg to upright 0 deg extension point-to-point movement for right-hand side muscles, generated by controller for 1.0 s duration. RA, EO, IO, ES, and LD stand for rectus abdominis, external oblique, internal oblique, erector spinae, and latissimus dorsi, respectively. (b) Experimental RMS filtered EMG activity of right rectus abdominis and lumbar erector spinae muscles, in 51.1 deg to upright 0 deg extension point-to-point movement with the same duration. The figure is reproduced here for comparison from the report by Ross [25], used with permission.

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Fig. 9

Effect of learning in Jacobian neural network on control performance. The tracking performance in upright 0 deg to 55.4 deg flexion point-to-point movement (see Fig. 5), after different stages of training is shown. The controller performance is compared in different stages of training when a mean squared error (MSE) performance of 9, 8, 3, and 0.1 (× 10-4 rad2/12) is obtained for the Jacobian network.

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Fig. 10

Comparison of activation patterns, generated by DE-NFC, with static optimization (data from Ref. [6]) for upright 0 deg to 55.4 deg flexion movement with durations of 1.0 s (Fig. 9). (a) Activation levels of prime flexor, RA. (b) Activation levels of prime extensor, ES. The movements are point-to-point movements with minimum-jerk trajectory as the reference. The optimization results, with sum of the squared activation as cost function, are from Ref. [6] and are computed using the same dynamic model with all the main considered muscle groups present, as well as some extra muscle vectors included in modeling. The third burst of the triphasic pattern (AG2), which is only (correctly) predicted by the DE-NFC method is indicated in the figure. (c) Example of experimental EMG activity in trunk flexion movements, showing the three-burst EMG pattern that occurs in some but not all trunk flexion trials. Reproduced for qualitative comparison from Ref. [43] (Copyright © 1987 by John Wiley & Sons, Inc., reprinted by permission). The vertical line shows the movement onset. Note that the time reference and scale, as well as the movement amplitude and duration is not directly comparable to the simulation results.

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