Felix E. Zajac

Bio: Felix E. Zajac is an academic researcher from Stanford University. The author has contributed to research in topics: Gait (human) & Ground reaction force. The author has an hindex of 42, co-authored 79 publications receiving 15646 citations. Previous affiliations of Felix E. Zajac include Veterans Health Administration & United States Department of Veterans Affairs.

Muscle and tendon: properties, models, scaling, and application to biomechanics and motor control

Abstract: Skeletal muscles transform neural control signals into forces that act upon the body segments to effect a coordinated motor task. This transformation is complex, not only because the properties of muscles are complex, but because the tendon affects the transmission of muscle force to the skeleton. This review focuses on how to synthesize basic properties of muscle and tendon to construct models applicable to studies of coordination. After a review of the properties of muscle and tendon, their integrated ability to generate force statically and dynamically is studied by formulating a generic model of the "musculotendon actuator", which has only one parameter, the ratio of tendon length at rest to muscle fiber length at rest. To illustrate the utility of the model, it is analyzed to show how this one parameter specifies whether excitation-contraction or musculotendon contraction is the rate-limiting process of force generation, whether elastic energy is stored in tendon or muscle, and whether hip- and knee-extensor actuators function as springs or dashpots during walking.

An interactive graphics-based model of the lower extremity to study orthopaedic surgical procedures

Abstract: A model is developed of the human lower extremity to study how changes in musculoskeletal geometry and musculotendon parameters affect muscle force and its moment about the joints. The lines of action of 43 musculotendon actuators were defined based on their anatomical relationships to three-dimensional bone surface representations. A model for each actuator was formulated to compute its isometric force-length relation. The kinematics of the lower extremity were defined by modeling the hip, knee, ankle, subtalar, and metatarsophalangeal joints. Thus, the force and joint moment that each musculotendon actuator develops can be computed for any body position. The joint moments calculated with the model compare well with experimentally measured isometric joint moments. A graphical interface to the model has also been developed. It allows the user to visualize the musculoskeletal geometry and to manipulate the model parameters to study the biomechanical consequences of orthopaedic surgical procedures. For example, tendon transfer and lengthening procedures can be simulated by adjusting the model parameters according to various surgical techniques. Results of the simulated surgeries can be analyzed quickly in terms of postsurgery muscle forces and other biomechanical variables. >

Merging of Healthy Motor Modules Predicts Reduced Locomotor Performance and Muscle Coordination Complexity Post-Stroke

Abstract: Evidence suggests that the nervous system controls motor tasks using a low-dimensional modular organization of muscle activation. However, it is not clear if such an organization applies to coordin...

OpenSim: Open-Source Software to Create and Analyze Dynamic Simulations of Movement

Abstract: Dynamic simulations of movement allow one to study neuromuscular coordination, analyze athletic performance, and estimate internal loading of the musculoskeletal system. Simulations can also be used to identify the sources of pathological movement and establish a scientific basis for treatment planning. We have developed a freely available, open-source software system (OpenSim) that lets users develop models of musculoskeletal structures and create dynamic simulations of a wide variety of movements. We are using this system to simulate the dynamics of individuals with pathological gait and to explore the biomechanical effects of treatments. OpenSim provides a platform on which the biomechanics community can build a library of simulations that can be exchanged, tested, analyzed, and improved through a multi-institutional collaboration. Developing software that enables a concerted effort from many investigators poses technical and sociological challenges. Meeting those challenges will accelerate the discovery of principles that govern movement control and improve treatments for individuals with movement pathologies.

Spinal and Supraspinal Factors in Human Muscle Fatigue

Abstract: Muscle fatigue is an exercise-induced reduction in maximal voluntary muscle force. It may arise not only because of peripheral changes at the level of the muscle, but also because the central nervous system fails to drive the motoneurons adequately. Evidence for “central” fatigue and the neural mechanisms underlying it are reviewed, together with its terminology and the methods used to reveal it. Much data suggest that voluntary activation of human motoneurons and muscle fibers is suboptimal and thus maximal voluntary force is commonly less than true maximal force. Hence, maximal voluntary strength can often be below true maximal muscle force. The technique of twitch interpolation has helped to reveal the changes in drive to motoneurons during fatigue. Voluntary activation usually diminishes during maximal voluntary isometric tasks, that is central fatigue develops, and motor unit firing rates decline. Transcranial magnetic stimulation over the motor cortex during fatiguing exercise has revealed focal cha...

Postural Orientation and Equilibrium: What Do We Need to Know About Neural Control of Balance to Prevent Falls?

Abstract: Postural control is no longer considered simply a summation of static reflexes but, rather, a complex skill based on the interaction of dynamic sensorimotor processes. The two main functional goals of postural behaviour are postural orientation and postural equilibrium. Postural orientation involves the active alignment of the trunk and head with respect to gravity, support surfaces, the visual surround and internal references. Sensory information from somatosensory, vestibular and visual systems is integrated, and the relative weights placed on each of these inputs are dependent on the goals of the movement task and the environmental context. Postural equilibrium involves the coordination of movement strategies to stabilise the centre of body mass during both self-initiated and externally triggered disturbances of stability. The specific response strategy selected depends not only on the characteristics of the external postural displacement but also on the individual’s expectations, goals and prior experience. Anticipatory postural adjustments, prior to voluntary limb movement, serve to maintain postural stability by compensating for destabilising forces associated with moving a limb. The amount of cognitive processing required for postural control depends both on the complexity of the postural task and on the capability of the subject’s postural control system. The control of posture involves many different underlying physiological systems that can be affected by pathology or sub-clinical constraints. Damage to any of the underlying systems will result in different, context-specific instabilities. The effective rehabilitation of balance to improve mobility and to prevent falls requires a better understanding of the multiple mechanisms underlying postural control.

An interactive graphics-based model of the lower extremity to study orthopaedic surgical procedures

Abstract: A model is developed of the human lower extremity to study how changes in musculoskeletal geometry and musculotendon parameters affect muscle force and its moment about the joints. The lines of action of 43 musculotendon actuators were defined based on their anatomical relationships to three-dimensional bone surface representations. A model for each actuator was formulated to compute its isometric force-length relation. The kinematics of the lower extremity were defined by modeling the hip, knee, ankle, subtalar, and metatarsophalangeal joints. Thus, the force and joint moment that each musculotendon actuator develops can be computed for any body position. The joint moments calculated with the model compare well with experimentally measured isometric joint moments. A graphical interface to the model has also been developed. It allows the user to visualize the musculoskeletal geometry and to manipulate the model parameters to study the biomechanical consequences of orthopaedic surgical procedures. For example, tendon transfer and lengthening procedures can be simulated by adjusting the model parameters according to various surgical techniques. Results of the simulated surgeries can be analyzed quickly in terms of postsurgery muscle forces and other biomechanical variables. >

Sensorimotor integration in human postural control

Abstract: It is generally accepted that human bipedal upright stance is achieved by feedback mechanisms that generate an appropriate corrective torque based on body-sway motion detected primarily by visual, vestibular, and proprioceptive sensory systems. Because orientation information from the various senses is not always available (eyes closed) or accurate (compliant support surface), the postural control system must somehow adjust to maintain stance in a wide variety of environmental conditions. This is the sensorimotor integration problem that we investigated by evoking anterior-posterior (AP) body sway using pseudorandom rotation of the visual surround and/or support surface (amplitudes 0.5-8 degrees ) in both normal subjects and subjects with severe bilateral vestibular loss (VL). AP rotation of body center-of-mass (COM) was measured in response to six conditions offering different combinations of available sensory information. Stimulus-response data were analyzed using spectral analysis to compute transfer functions and coherence functions over a frequency range from 0.017 to 2.23 Hz. Stimulus-response data were quite linear for any given condition and amplitude. However, overall behavior in normal subjects was nonlinear because gain decreased and phase functions sometimes changed with increasing stimulus amplitude. "Sensory channel reweighting" could account for this nonlinear behavior with subjects showing increasing reliance on vestibular cues as stimulus amplitudes increased. VL subjects could not perform this reweighting, and their stimulus-response behavior remained quite linear. Transfer function curve fits based on a simple feedback control model provided estimates of postural stiffness, damping, and feedback time delay. There were only small changes in these parameters with increasing visual stimulus amplitude. However, stiffness increased as much as 60% with increasing support surface amplitude. To maintain postural stability and avoid resonant behavior, an increase in stiffness should be accompanied by a corresponding increase in damping. Increased damping was achieved primarily by decreasing the apparent time delay of feedback control rather than by changing the damping coefficient (i.e., corrective torque related to body-sway velocity). In normal subjects, stiffness and damping were highly correlated with body mass and moment of inertia, with stiffness always about 1/3 larger than necessary to resist the destabilizing torque due to gravity. The stiffness parameter in some VL subjects was larger compared with normal subjects, suggesting that they may use increased stiffness to help compensate for their loss. Overall results show that the simple act of standing quietly depends on a remarkably complex sensorimotor control system.