Skip to Content

Newsletter Volume 6 - 2nd Quarter 2005

Modeling the Neuromechanical Events of Locomotion at Varying Gravitational Levels

CONTENTS

Case Study: Modeling the Neuromechanical Events of Locomotion at Varying Gravitational Levels

Software: LifeMOD™ v2005.1 New Product Release!

Other News : New Book Chapter: " The Virtual Knee" in Total Knee Arthroplasty, Springer pub.



This issue presents a study of the neuromechanical events of locomotion at varying gravitational levels. It is based on the collaborative work between BRG, the Department of Physiological Science and Brain Research Institute at UCLA and NASA's Jet Propulsion Laboratory [Day, 01] .


Also in this issue, learn how BRG.LifeMOD™ makes this technology accessible to all researchers and students of biomechanics. Additionally, we are pleased to announce the release of LifeMOD Version 2005.1 with many new functions and features including a new scalable muscle geometry database for the entire body and scaling muscle graphics. We invite you to download a free trial version of the software; try out one of our 17 easy-to-follow tutorials and begin building physics-based human models today.



MODELING THE NEUROMECHANICAL EVENTS OF LOCOMOTION
AT VARYING GRAVITATIONAL LEVELS

Introduction

Understanding neuromuscular dynamics and kinematics is a critical element in the development of astronaut training and safety procedures for missions requiring long-term exposure to low and 0G environments as well as for the development of effective clinical intervention strategies for many neuromuscular disorders. To achieve this one must fully integrate multiple sources of information about muscle interactions with the skeletal system, and how the nervous system controls these functions.

One source of information is a computer model that allows for accurate simulations of bipedal and quadrapedal locomotion at varying gravitational levels and speeds. Subsequently, the model can be used as an effective research tool in efforts to identify the critical control signals of a given locomotor system.

The most common definition of bipedal walking is a gait pattern in which at least one foot is always in contact with the ground and which has a period when both feet are simultaneously in contact with the ground. The latter condition is known as the double support phase. In running, the double support phase is replaced by a flight phase during which neither foot is in contact with the ground. In addition to foot-to-ground contact patterns, the mechanics of walking and running are different [McMahon, 87]. During walking the body's center of mass passes over each leg in an inverted pendulum motion as the feet contact the ground. During running, the mechanics change to a spring-mass pattern with the legs acting as springs on which the center of mass bounces with each stride.

Animals exhibit a preferred walking speed above which they normally switch to a running gait. The change from a walking to a running gait occurs abruptly rather than as a gradual transition [Thorstensson, 87]. Individual humans switch from walking to running at different absolute speeds, but at mechanically equivalent speeds [Kram, 97]. The transition occurs when a value known as the Froude number (see equation below) is



Based on this equation, the transition from a walking to a running gait should occur at slower speeds as gravitational levels decrease.

The purpose of the present study was to determine the feasibility of using a neuromechanical model of human locomotion based on a model previously published by Taga et al. [Taga, 91] to simulate gait at various speeds and gravitational levels. The results indicate that this model may be appropriate for studying walking at 1G but not for higher speed or lower G locomotion.

Methods

The musculoskeletal system and the environment with which it interacted were created as a 3-D model in BRG.LifeMOD™ [McGuan, 04] and was based on the work from Taga et al. [Taga, 91]. The model in BRG.LifeMOD was completely parameterized which allowed for easy manipulation of environmental conditions such as ground stiffness, surface grade and gravitational level.

Generally, the dynamic 3-D musculoskeletal model consisted of: a) five segments including a pelvis, 2 thighs and 2 shanks; b) six joints, two each at the hips, knees and ankles; and c) flexor and extensor "muscles" that generate active torques around the joints in proportion to the output of the neural system. Leg length was 1.1 m. Muscle forces were modeled as net torques about each joint. The model also included frictional torques at each joint and torques exerted by passive joint structures at the knees that limited the range of motion. The model is fully dynamic and subject to gravitational forces. Ground reaction forces from the foot-surface contact were automatically generated using an fat-pad contact algorithm available in BRG.LifeMOD.


Figure 1. BRG.LifeMOD locomotion model based on parameters from Taga publications.Figure 1. BRG.LifeMOD locomotion model based on parameters from Taga publications.

These mechanics must then be coupled to a neural controller that determines the force output that is applied at each instant to the segments of the legs. The neural controller must also receive afferent information about the positions and velocities of the segments, as well as about the external forces they are experiencing. This kind of two-way feedback process, in which the mechanics give information to the neural controller and the neural controller determines the force outputs that drive the mechanics, is modeled with a co-simulation coupling of BRG.LifeMOD and MatLab® (The MathWorks, Inc., Natick, MA).


Figure 2. A representation of how the neural oscillator pattern generator creates the extension/flexion torque patterns at the hip, knee and ankle.Figure 2. A representation of how the neural oscillator pattern generator creates the extension/flexion torque patterns at the hip, knee and ankle.

The neural controller is a rudimentary pattern generator model of oscillators, running the various joints and coupled to each other to generate a patterned output was modeled in MatLab as a higher center and 12 oscillator units. There were two oscillators per joint, one controlling flexor torque and the other controlling extensor torque. Changing the magnitude of the higher center output constant resulted in changes in the speed of locomotion.


Figure 3. Co-simulation model. BRG.LifeMOD solves dynamics equations of the locomotion mechanics, while Matlab solves the equations of the neuroscillator control. Mechanics states (limb position, grx forces, etc) are passed from the BRG.LifeMOD model to Matlab, while Matlab returns hip, knee and ankle torques.Figure 3. Co-simulation model. BRG.LifeMOD solves dynamics equations of the locomotion mechanics, while Matlab solves the equations of the neuroscillator control. Mechanics states (limb position, grx forces, etc) are passed from the BRG.LifeMOD model to Matlab, while Matlab returns hip, knee and ankle torques.

Simulations were run with the higher center output constant set at values ranging from 2.5 to 8.5 and the gravitational level set at 1.0, 0.38 or 0.17G.

Results

At 1G, the model achieved stable bipedal locomotion at speeds ranging from 1.0 m/s with the higher center constant set at 4.0 to 2.0 m/s with the higher center constant set at 7.5. At speeds below 2.0 m/s the model exhibited a walking gait with a double support phase and inverted pendulum mechanics (Figs. 4a and 5a). At 2.0 m/s there was an abrupt change to a gait resembling running. The running gait had a flight phase, however, it maintained the inverted pendulum mechanics seen in walking rather than transitioning to the expected spring-mass mechanics (Figs. 4b and 5b). The Froude number equaled 0.37 at the transition point.

At gravitational levels simulating those found on the moon, 0.17G and Mars, 0.38G, the model was not able to achieve stable locomotion at a speed higher than 0.8 m/s. The gait pattern had a double support phase and inverted pendulum mechanics (Fig. 5c) as the Froude number would have predicted.


Figure 4. Ground reaction forces (y component) at locomotion speeds of: a) 1.2 m/s and b) 2.0 m/s. At the slower speed one foot is always in contact with the ground and there is a double support phase indicating that the model is using a walking gait. At the higher speed there is a flight phase indicating a running gait.Figure 4. Ground reaction forces (y component) at locomotion speeds of: a) 1.2 m/s and b) 2.0 m/s. At the slower speed one foot is always in contact with the ground and there is a double support phase indicating that the model is using a walking gait. At the higher speed there is a flight phase indicating a running gait.
Figure 5. Center of mass movement during locomotion at: a) 1G, 1.2 m/s, b) 1G, 2.0 m/s, c) 0.38G, 0.8 m/s. In an inverted pendulum gait the center of mass should be at its highest point at mid-stance. In a spring-mass gait the center of mass should be at its lowest point at midstance. The predicted (P) mid-stance point and actual (A) mid-stance point observed for each condition is indicated.Figure 5. Center of mass movement during locomotion at: a) 1G, 1.2 m/s, b) 1G, 2.0 m/s, c) 0.38G, 0.8 m/s. In an inverted pendulum gait the center of mass should be at its highest point at mid-stance. In a spring-mass gait the center of mass should be at its lowest point at midstance. The predicted (P) mid-stance point and actual (A) mid-stance point observed for each condition is indicated.

Discussion

It has been demonstrated that individuals have a preferred walking speed and that the transition from walking to running is abrupt [Thorstensson, 87]. These observations suggest that the neuromotor control strategy consists of a stable limit cycle for walking and that the transition to running represents a bifurcation to another stable limit cycle. The neural oscillator model described by Taga et al. [Taga, 91] exhibits these behaviors and is based on flexible control, rather than on an engineering control theory of planning and execution. Also, some physiological evidence suggests that the speed of locomotion is normally modulated by higher centers as in Taga's neural control system [Shik, 69].

However, while the neural control system in Taga's model mimics some of the characteristics of physiological behavior associated with locomotion, the musculoskeletal system demonstrates accurate gait mechanics only under limited conditions. In our simulations, the model was incapable of producing the spring-mass mechanics seen in bouncing gaits such as running at 1G and did not achieve stable locomotion in low G at a speed higher than 0.8 m/s.

A feature of the Taga model that may account for this deficit is that the torques generated at the joints are proportional to the output of the neural oscillators. This means that a muscle's torque production is assumed to be the same throughout the range of joint motion and the stress-strain properties of the muscle/tendon units are ignored.

As the joint angle changes, the mechanical advantage of a muscle changes [Lieber, 88]. Therefore, the same neural output to a muscle can produce dramatically different torques at different joint angles. In human running this is an important factor to consider because increases in speed are associated with increases in leg sweep [Farley, 93] which results in greater changes in joint angle.

An important feature of spring-mass gaits is that mechanical energy is stored as strain energy in the muscle-tendon units. This strain energy is recovered during each step at minimal metabolic cost to the system resulting in more efficient locomotion [Biewener, 98]. Therefore, the Taga model may seriously underestimate net joint torques during running because it does not have the capability of conserving and returning muscle-tendon strain energy.

This study suggests the importance of coupling a neural control system model with a musculoskeletal system model that is based on accurate morphology and physiology when studying human movement dynamics. It appears that this coupling becomes even more important when factors related to gravitational load and speed of locomotion are to be considered.

References
  • 1998_Biewener_6 Biewener, A. A., D. D. Konieczynski and R. V. Baudinette. In Vivo Muscle Force-Length Behavior During Steady-Speed Hopping in Tammar Wallabies. J. Exp. Biol. 201: 1681-94, 1998.
  • 2000_Day_6Day, M.K., Monti, R.J., Vallance, K., McGuan, S.P., Roy, R.R., Edgerton, V.R., Modeling the Neuromechanical Events of Locomotion at Varying Gravitational Levels. J. Grav. Phys., 2001.
  • 1993_Farley_6 Farley, C. T., J. Glasheen and T. A. McMahon. Running Springs: Speed and Animal Size. J. Exp. Biol. 185: 71-86, 1993.
  • 1997_Kram_6Kram, R., A. Domingo and D. P. Ferris. Effect of Reduced Gravity on the Preferred Walk-Run Transition Speed. J. Exp. Biol. 200: 821-6, 1997.
  • 1988_Lieber_6Lieber, R. L. and J. L. Boakes. Sarcomere Length And Joint Kinematics During Torque Production In Frog Hindlimb. Am. J. Physiol. 254: C759-68, 1988.
  • 2004_McGuan_7S. 2004 BRG.LifeMOD™ 2004 Users Manual, Biomechanics Research Group, Inc.
  • 1987_McMahon_6McMahon, T. A., G. Valiant and E. C. Frederick. Groucho Running. J. Appl. Physiol. 62: 2326-37, 1987.
  • 1969_Shik_6Shik, M. L., F. V. Severin and G. N. Orlovsky. Control Of Walking And Running By Means Of Electrical Stimulation Of The Mesencephalon. Electroenceph. and Clin. Neurophysiol. 26: 549, 1969.
  • 1991_Taga_6Taga, G., Y. Yamaguchi and H. Shimizu. Self-Organized Control Of Bipedal Locomotion By Neural Oscillators In Unpredictable Environment. Biol. Cybernetics 65: 147-59, 1991.
  • 1987_Thorstens_6Thorstensson, A. and H. Roberthson. Adaptations To Changing Speed In Human Locomotion: Speed Of Transition Between Walking And Running. Acta Physiol. Scand. 131: 211-4, 1987.


SOFTWARE

The BRG is pleased to announce the release of LifeMOD™ version 2005.1. This new release makes state-of-the-art human modeling accessible to every investigator interested in the physics behind human motion. The release includes a new muscle parameters library which includes data on physiological cross sectional areas, maximum tissue stresses, etc. for each of the 212 muscles included in LifeMOD. These properties also scale based on the body size, weight, age and gender. In addition the user may affect the muscle output from 5 times normal to 0 to perform muscle imbalance or weakened studies.


A new graphical animation feature has been introduced which allows for the scaling of the muscle graphics and joint graphics based on force and torque magnitudes.


A new generalized contact algorithm which permits general contact between any two surfaces has been introduced. This allows for sophisticated modeling of knee joints, as well as external contacts between the body and the environment.


Due to the tremendous response we received from our users for our "trainable" muscles, we have introduced several more muscle groups to ensure LifeMOD's position as the most powerful, versatile and ease-to-use full-body human modeling package available today.


This new version is a direct result from an ongoing and rigorous user dialogue, partnerships with our research community, and the inclusion of much functionality developed by our professional staff to solve the world's most demanding biomechanics issues. View Examples...



SERVICES

The Biomechanics Research Group Inc. is a service-based organization chartered to empower our customers to capture a level of ROI from their technology investment in ways they've never imagined. We are committed to customer service, product excellence and continuous quality improvement in all we do. We provide training, modeling and simulation expertise. Contact us for more information.



OTHER NEWS

New publication: "Chapter 24: The Virtual Knee" in Total Knee Arthoplasty, Springer 2005. See PDF

2005 Korean Cad/Cam Conference Keynote Address "Achieving Commercial Success in Biomechanics Simulation" by Shawn McGuan President/Ceo of BRG.

Recorded webinar: "Virtual Product Development for Biomechanics Applications" by Shawn McGuan.

Check out our new model repository! We would like to sincerely thank those who have contributed to the LifeMOD™ body of knowledge. We pledge to do our best to increase the technical capabilities of LifeMOD while developing new ways to educate the community.



If you would like further information on our software and services, please contact us.


Copyright© 2005 LifeModeler, Inc.