Simulation of Biomechanical Experiments in OpenSim I. Symeonidis, G. Kavadarli, E. Schuller, and S. Peldschus Institution of Legal Medicine, Munich University, Germany Abstract— Biomechanical experiments produce large amounts of data that is complicated to visualize analyze and interpret. Simulation of an experiment can provide a framework to integrate all the different measured parameters in the subject and can help to understand their influence in the model. OpenSim software is used for this purpose. Opensim is free open-source software, developed in Stanford University, which can simulate active musculoskeletal models and provide information about muscle activity during a motion. In this paper the analysis of an experiment concerning the volunteer’s head neck reaction during motorcycle’s braking is presented. Keywords— muscle, simulation, biomechanics.
I. INTRODUCTION During a biomechanical experiment several parameters are measured like: kinematics, electromyography and ground reaction force. These measurements produce a large amount of data that is then analyzed to provide indicators about a diagnosis or to support hypothesis about the studied subject. Since the focus of the study is usually a human the complicated musculoskeletal structure, the anthropometric differences and the variance in its behavior during a measurement produce a further problem because of the additional variability of the recorded data of the measurement; making the results difficult to compare with normative data or to extract a conclusion. The OpenSim software provides a platform to study each experiment individually and to understand the cause and effect relationship in musculoskeletal systems [1]. An application to the analysis of an experiment is presented as an example of this method.
emerges from motorcycle braking at a certain traveling speed was simulated with backward motion of the MGD with a constant acceleration. A helmet was also used with a weight of 1 kg. The acceleration of the sled was measured with a uniaxial accelerometer. An optoelectronic motion capture system was used to capture the motion of the volunteer. Reflective markers were placed on several anatomical landmarks of the volunteer's body. Especially for the head and neck, markers were placed on the prominent process of the seventh cervical vertebrae (C7), on the occipital protuberance, on the sternum, and on the tragus of each ear. The motion of the markers was recorded with eight high speed cameras with red light strobes. Their frame rate was set to 1000Hz. A surface EMG device with eight channels was used to measure the muscle activity of three neck (splenius capitis, sternocleidomastoid and posterior cervical muscles) and one arm (lateral head of triceps brachii) muscles, with the reference electrode placed on the mastoid process. The volunteer’s instrumentation is presented in figure 1.
II. EXPERIMENT The experiment was performed to study the kinematics’ behavior of the volunteers during motorcycle braking [2]. The focuses of the study is the head neck biomechanics and in more detail the relationship between the muscle activity in the neck and the kinematics of the head during motorcycle braking. A Device was built that could reproduce the Geometry of a Motorcycle (MGD). The MGD included only the motorcycle - rider interface. The MGD was mounted on a sled; a construction with a falling weight was used to accelerate the sled with a stable acceleration of 0.4g. The deceleration that
Fig. 1 Subject setup for the experiment The EMG signal was rectified and onsets were calculated, then it was filtered with a band pass filter to minimize the measurement noise and finally a low pass filter was applied to create an envelope of the signal. The motion capture data was treated as presented in [3]. The EMG and the motion capture data were synchronized so the muscle activation in relation to the neck kinematics could be studied; results are shown in figure 2.
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Table 1 Inertial properties of the head-neck bones [8] mass (kg) head
Ixx Iyy Izz (kg/mm²) (kg/mm²) (kg/mm²)
4.690
18100
23600
17300
c1
0.22
220
220
420
c2
0.25
250
250
480
c3
0.24
240
240
465
c4
0.23
230
230
440
c5
0.23
230
230
450
c6
0.24
240
240
470
c7
0.22
220
220
430
With the latest current version of OpenSim, 2.01 loads can be defined in musculoskeletal models. This way the sled deceleration was simulated. A constant force acting on the center of mass of the torso was applied, that produces the same average acceleration (figure 3) based on Newton’s second law. Fig. 2 The EMG activity of the sternocleidomastoid, splenius capitis, posterior cervical and triceps muscles for left and right side synchronized with the C7 and occiput rotation from the initial posture [9]
III. SIMULATION The Opensim software was used to simulate the experiment presented previously. Opensim is a free opensource code that unifies a multibody dynamics engine with a detailed muscle simulation code and an optimization algorithm. The multibody system has rigid skeletal bones paired with muscles that are used as constrains and actuators and it is able to synthesize the equations of motion for this system. The muscle simulation part includes a detailed Hill muscle model [4,5,6] and additionally parameters that describe the penation angle, maximum contraction velocity, damping, optimal fiber length, tendon slack length, tendon force-length curve and wrapping surfaces. The actuators redundancy (more muscles from the available degrees of freedom) creates an indeterminate problem to resolve directly with an inverse dynamic analysis. For this reason static optimization is performed. For the study of head and neck biomechanics the model proposed from [7] with some modifications to the maximum muscle forces of individual muscles and the addition of the inertial properties of the skeletal structures of interest, was used. Markers were placed at the same anatomical points like the experiment. Additional weight was placed on the head to represent the helmet.
Fig. 3 Sled acceleration (blue) and average value (green) The simulation model is presented in figure 4.
Fig. 4 Model
setup for the simulation, skeleton(white), muscles(red), markers(yellow), force(green)
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Finally, the simulation procedure as presented in Table 2 was followed. Table 2 Simulation procedure Steps
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perform a simulation of the motion based on the muscle activation and the external loads. This way a complete description of the motion can be established from the ground up.
Action Scaling of the musculoskeletal model to the subjects anthropometry using a static posture from the kinematics acquired with the motion capture system. Inverse kinematics (joint angles and translations of the models’ segments) are calculated from the kinematics of the subject.
1 2
Inverse dynamics (joint moments) are calculated from the kinematics of the model
3
Residual reduction algorithm is applied to make the data of the kinematics and the forces measured during the test more dynamically consistent. Computed muscle control uses a static optimization criterion to distribute the joint torques to several muscles Forward dynamics simulation that uses the calculated muscle activations to drive the model in the performance of the subject during the experiment.
4 5 6
Fig. 5 Pitch joint moments on the cervical vertebrae joints
Scaling is performed based on a combination of: •
•
measured distances between the markers on the subject and the markers on the model taken from a pose of the subject right before the initiation of the experiment and manually-specified scale factors based on anthropometric measurements.
The inverse kinematics are calculated from a weighted least squares problem that finds the pose with the minimum distance of the subject’s and model’s markers. The inverse dynamics calculate the forces and moments at each joint responsible for a given movement. From the kinematics describing the movement of a model and kinetics, external loads applied to the model, an inverse dynamics analysis is performed. The equations of motion of the system are synthesized and solved in the inverse dynamics sense, to calculate the forces and moments at each joint. An example of the results is shown at figure 5 for the pitch moments at the cervical vertebrae joints. Static optimization is used as an extension to inverse dynamics that further resolves the joint moments into individual muscle forces at each instant in time according to the muscle model. Constraint functions are used like the selection of ideal force generators muscles based on their moment arms or their Hill muscle properties (velocity length - force surface) while the optimization process is minimizing the objective function of muscle activation. After the muscle activations have been calculated from the static optimization, the forward dynamics module can
IV. CONCLUSIONS The difficulty to study the relationship between the muscle activity and the produced motions in complicated dynamic systems like the neck has several challenges. • • •
The anatomical structure of the neck with several joints with complicated geometry that produce a large number of degrees of freedom. The even larger number of actuators (muscles) that produce a problem of redundancy. The muscle activation and co-activation mechanics.
These issues can be studied in more detail and produce a better biomechanical insight, using a simulation of each experiment individually like the one proposed from OpenSim, instead of analyzing directly the captured signals for all the experiments. In this way the nervous system coordination of muscle activation can be analyzed and a small insight about the muscle recruitment from the nervous system can be gained. Even though, a big gap due to the model’s individual component validity has to be closed, to be able to output reliable results.
ACKNOWLEDGMENT This research was performed during founding from the EU Marie Curie Project MYMOSA.
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6. Zajac, F. E. Muscle and tendon: properties, models, scaling, and application to biomechanics and motor control. In: CRC Critical Reviews in Biomedical Engineering, edited by J. R. Bourne. Boca Raton, FL: CRC, 1989, vol. 17, p. 359–411 7. Vasavada A, Li S, Delp SL, Influence of Muscle Morphometry and Moment Arms on the Moment-Generating Capacity of Human Neck Muscles, Spine, 23:4:412-422, 1998 8. Jager, M. K. J. de (1996). Mathematical head-neck models for acceleration impacts. Ph.D thesis, University of Eindhoven, Nederlands 9. Symeonidis I., Kavadarli G.,Brenna C., Zhao Z., Fraga F., van Roij L., Schuller E., Peldschus S., Developing a method to simulate injury mechanisms in motorcycle crashes, J of biological physics and chemistry [in press] 10. Opennsim 2.01 User’s Guide at https://simtk.org/home/opensim Author: Institute: Street: City: Country: Email:
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Symeonidis Ioannis Institution of Legal Medicine, University of Munich Nussbaumstr 26 Munich Germany
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