Borelli Lecture from the American Society of Biomechanics Conference 2001Understanding muscle coordination of the human leg with dynamical simulations
Introduction
Muscles participate critically in the execution of human motor tasks. When muscle strength, power, or coordination is impaired, task execution is compromised. So what is the exact role of a muscle in a specific task?
Fortunately for us, a muscle can perform many mechanical functions. A muscle can develop force and power, and over time produce work output. Or it can dissipate mechanical energy if its active fibers are stretched. When its tendon, aponeurosis, and other in-series elastic elements are stretched, energy is stored. The force–length–velocity property of muscle can stabilize movement with its impedance-like function before reflexes become operative (Brown and Loeb, 2000; Gerritsen et al., 1998; Loeb et al., 1999). Less appreciated is a muscle's critical role to redistribute mechanical energy among the body segments during task execution (Fregly and Zajac, 1996; Neptune et al., 2001).
Muscles redistribute the net mechanical energy of the body segments because each muscle force causes reaction forces throughout the body with the net effect being to accelerate some segments and decelerate others. If the segments are not at rest, segmental energy increases in the accelerated segments and decreases in the decelerated ones. If a muscle is isometric while generating force, the net energy change among the segments caused by the muscle is zero, although energy distribution among segments can occur. The isometric force generated by the muscle can cause energy to increase in some segments and decrease in others by the same amount. This function of a muscle to cause energy to be exchanged among segments, whether the muscle is isometric, eccentric, or concentric, can be more important to task execution than its role in producing energy and delivering that energy to the segments (Zajac et al., 2002a).
By working co-functionally, or synergistically, muscles coordinate force generation so individual segments gain and lose energy consonant with the task. Usually no one muscle can cause the required segmental energetic exchanges. At times, multiple muscles will cause similar segmental exchanges to occur by accelerating the same segments and decelerating others. The co-excited muscles are then called co-functional (Zajac et al., 2002a). Co-functional muscle activity may be required, for example, when segmental energetic exchanges are so high that force production in one muscle is insufficient.
At other times co-excited muscles work synergistically but not co-functionally; i.e., the segments accelerated by muscles differ causing oppositely directed segmental exchanges to occur (Zajac et al., 2002a). Such synergistic muscle activity may occur, for example, when one muscle produces the energy required in task execution but is unable to deliver it to a target segment because its force does not accelerate the segment; instead its force acts to accelerate other segments. Another muscle, which may not produce energy, may be co-excited because its generation of force opposes the acceleration of the other segments while accelerating the target segment. In this example of muscle synergy, therefore, one muscle produces the energy and another causes opposing segmental accelerations and decelerations so the energy reaches the target segment.
Unfortunately, the contributions of individual muscle forces to the reaction forces throughout the body and to the acceleration and deceleration of segments cannot be measured. In fact, rarely can the muscle forces in humans (or animals) be recorded, much less from many muscles simultaneously (however, see Gregor et al., 1987; Herzog et al., 1993). Given that we are usually limited to measurements of muscle (EMG) activity, the kinematics of the movement, and the forces exerted by the body on contact objects (e.g., the ground in walking), many musculoskeletal variables escape direct observation. But fortunately these and other kinetic quantities can be estimated from dynamical musculoskeletal simulations.
In the context of segmental energy redistribution, this paper summarizes some of the results found from simulations of motor tasks by me and my collaborators over the past 25 yr. Jumping is reviewed somewhat, but pedaling and walking are emphasized because concepts can be espoused better. The concept that a muscle can act to accelerate all joints (even unspanned ones) into rotation and that a biarticular muscle can act to accelerate one of its spanned joints into rotation opposite to its anatomical classification (i.e., opposite to its joint moment) are not reviewed here (see Zajac, 1993; Zajac and Gordon, 1989).
Section snippets
Creating dynamical simulations
Creating a muscle-driven simulation of a motor task requires two basic steps: (1) the formulation of a dynamical model of the musculoskeletal system and its interaction with the environment (e.g., the ground in walking); and (2) a method to find the muscle excitations to be applied as inputs to the model (Pandy, 2001; Zajac, 1993; Zajac and Winters, 1990). A simulation is evaluated by how well the simulated kinematics, kinetics, and muscle excitation pattern agree with the measured kinematics,
Jumping
Our interest in the propulsion phase of maximum height jumping from the squat, which was the first motor task simulated by us, originated from this task's tractability to theoretical and experimental investigation (Pandy et al., 1990; Zajac and Levine, 1979). Because the task is dominated by sagittal plane leg dynamics, we could focus on testing our concepts of musculoskeletal modeling and simulation using optimal control theory as a basis. Our reasoning was that, if successful, we would then
Pedaling
Pedaling fascinated us because experiments could be conceptualized and implemented to elucidate bilateral neuro-locomotor mechanisms (Ting et al (1998a), Ting et al (1998b), Ting et al (2000)), and pedaling is highly amenable to simulation and biomechanical analysis (Neptune et al., 2000; Raasch and Zajac, 1999). Propulsion is again dominated by sagittal-plane dynamics.
The uniarticular knee (VAS) and hip (GMAX) extensors produce high work output during leg extension (Fig. 1 VAS, GMAX: filled
Walking
Using the concepts and methodologies developed to understand muscle coordination of pedaling, we are now applying them to understand how muscles coordinate energy flow in walking based on dynamical simulations of the whole gait cycle (Neptune et al., 2001). Because energy flow is dominated by forward progression of the body segments, we feel that sagittal-plane simulations are reasonably sufficient for understanding the function of many leg muscles.
Walking kinematics requires muscles to
Concluding remarks
Muscles coordinate human movement because the forces generated by them develop mechanical energy and mechanisms for energy exchange among the segments. Task kinematics dictate the required exchanges. Muscles also have to produce energy because seldom is the energetic state of the whole system constant, and frictional losses are common to many motor tasks. Individual muscle-control of the energy flow among segments is, unfortunately, impossible to measure.
Energy flow can be computed, however,
Acknowledgements
Thanks to Steve Kautz and Rick Neptune for reviewing the manuscript. This Borelli Award would not have been received without the endless discussions and untiring effort of my collaborators, including: Dave Brown, George Chen, Scott Delp, BJ Fregly, Mike Gordon, Melissa Gross, Rod Hentz, Jill Higginson, Steve Kautz, Gon Khang, Art Kuo, Bill Levine, Pete Loan, Wendy Murray, Rick Neptune, Marcus Pandy, George Pappas, Chris Raasch, Kit Runge, Lisa Schutte, Fran Sheehan, Scott Tashman, Lena Ting,
References (34)
- et al.
Storage and utilization of elastic strain energy during jumping
Journal of Biomechanics
(1993) - et al.
A graphics-based software system to develop and analyze models of musculoskeletal structures
Computers in Biology and Medicine
(1995) - et al.
A state-space analysis of mechanical energy generation, absorption, and transfer during pedaling
Journal of Biomechanics
(1996) The complete optimization of the human motion
Mathematical Biosciences
(1976)A complete set of control equations for the human musculo-skeletal system
Journal of Biomechanics
(1977)- et al.
Forces in gastrocnemius, soleus, and plantaris tendons of the freely moving cat
Journal of Biomechanics
(1993) - et al.
Muscle contributions to specific biomechanical functions do not change in forward versus backward pedaling
Journal of Biomechanics
(2000) - et al.
Contributions of the individual ankle plantar flexors to support, forward progression and swing initiation during normal walking
Journal of Biomechanics
(2001) - et al.
Optimal muscular coordination strategies for jumping
Journal of Biomechanics
(1991) - et al.
An optimal control model for maximum-height human jumping
Journal of Biomechanics
(1990)