Academic Appointments


2014-15 Courses


All Publications


  • All joint moments significantly contribute to trunk angular acceleration JOURNAL OF BIOMECHANICS Nott, C. R., Zajac, F. E., Neptune, R. R., Kautz, S. A. 2010; 43 (13): 2648-2652

    Abstract

    Computationally advanced biomechanical analyses of gait demonstrate the often counter-intuitive roles of joint moments on various aspects of gait such as propulsion, swing initiation, and balance. Each joint moment can produce linear and angular acceleration of all body segments (including those on which the moment does not directly act) due to the dynamic coupling inherent in the interconnected musculoskeletal system. This study presents quantitative relationships between individual joint moments and trunk control with respect to balance during gait to show that the ankle, knee, and hip joint moments all affect the angular acceleration of the trunk. We show that trunk angular acceleration is affected by all joints in the leg with varying degrees of dependence during the gait cycle. Furthermore, it is shown that inter-planar coupling exists and a two-dimensional analysis of trunk balance neglects important out-of-plane joint moments that affect trunk angular acceleration.

    View details for DOI 10.1016/j.jbiomech.2010.04.044

    View details for Web of Science ID 000282545900032

    View details for PubMedID 20646711

  • Merging of Healthy Motor Modules Predicts Reduced Locomotor Performance and Muscle Coordination Complexity Post-Stroke JOURNAL OF NEUROPHYSIOLOGY Clark, D. J., Ting, L. H., Zajac, F. E., Neptune, R. R., Kautz, S. A. 2010; 103 (2): 844-857

    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 coordination of human walking, nor how nervous system injury may alter the organization of motor modules and their biomechanical outputs. We first tested the hypothesis that muscle activation patterns during walking are produced through the variable activation of a small set of motor modules. In 20 healthy control subjects, EMG signals from eight leg muscles were measured across a range of walking speeds. Four motor modules identified through nonnegative matrix factorization were sufficient to account for variability of muscle activation from step to step and across speeds. Next, consistent with the clinical notion of abnormal limb flexion-extension synergies post-stroke, we tested the hypothesis that subjects with post-stroke hemiparesis would have altered motor modules, leading to impaired walking performance. In post-stroke subjects (n = 55), a less complex coordination pattern was shown. Fewer modules were needed to account for muscle activation during walking at preferred speed compared with controls. Fewer modules resulted from merging of the modules observed in healthy controls, suggesting reduced independence of neural control signals. The number of modules was correlated to preferred walking speed, speed modulation, step length asymmetry, and propulsive asymmetry. Our results suggest a common modular organization of muscle coordination underlying walking in both healthy and post-stroke subjects. Identification of motor modules may lead to new insight into impaired locomotor coordination and the underlying neural systems.

    View details for DOI 10.1152/jn.00825.2009

    View details for Web of Science ID 000274327900021

    View details for PubMedID 20007501

  • Effect of equinus foot placement and intrinsic muscle response on knee extension during stance GAIT & POSTURE Higginson, J. S., Zajac, F. E., Neptune, R. R., Kautz, S. A., Burgar, C. G., Delp, S. L. 2006; 23 (1): 32-36

    Abstract

    Equinus gait, a common movement abnormality among individuals with stroke and cerebral palsy, is often associated with knee hyperextension during stance. Whether there exists a causal mechanism linking equinus foot placement with knee hyperextension remains unknown. To investigate the response of the musculoskeletal system to equinus foot placement, a forward dynamic simulation of normal walking was perturbed by augmenting ankle plantarflexion by 10 degrees at initial contact. The subsequent effect on knee extension was assessed when the muscle forces were allowed, or not allowed, to change in response to altered kinematics and intrinsic force-length-velocity properties. We found that an increase in ankle plantarflexion at initial contact without concomitant changes in muscle forces caused the knee to hyperextend. The intrinsic force-length-velocity properties of muscle, particularly in gastrocnemius and vastus, diminished the effect of equinus posture alone, causing the abnormal knee extension to be less pronounced. We conclude that the effect of ankle position at initial contact on knee motion should be considered in the analysis of equinus gait.

    View details for DOI 10.1016/j.gaitpost.2004.11.011

    View details for Web of Science ID 000234166500005

    View details for PubMedID 16311192

  • Muscle contributions to support during gait in an individual with post-stroke hemiparesis JOURNAL OF BIOMECHANICS Higginson, J. S., Zajac, F. E., Neptune, R. R., Kautz, S. A., Delp, S. L. 2006; 39 (10): 1769-1777

    Abstract

    Walking requires coordination of muscles to support the body during single stance. Impaired ability to coordinate muscles following stroke frequently compromises walking performance and results in extremely low walking speeds. Slow gait in post-stroke hemiparesis is further complicated by asymmetries in lower limb muscle excitations. The objectives of the current study were: (1) to compare the muscle coordination patterns of an individual with flexed stance limb posture secondary to post-stroke hemiparesis with that of healthy adults walking very slowly, and (2) to identify how paretic and non-paretic muscles provide support of the body center of mass in this individual. Simulations were generated based on the kinematics and kinetics of a stroke survivor walking at his self-selected speed (0.3 m/s) and of three speed-matched, healthy older individuals. For each simulation, muscle forces were perturbed to determine the muscles contributing most to body weight support (i.e., height of the center of mass during midstance). Differences in muscle excitations and midstance body configuration caused paretic and non-paretic ankle plantarflexors to contribute less to midstance support than in healthy slow gait. Excitation of paretic ankle dorsiflexors and knee flexors during stance opposed support and necessitated compensation by knee and hip extensors. During gait for an individual with post-stroke hemiparesis, adequate body weight support is provided via reorganized muscle coordination patterns of the paretic and non-paretic lower limbs relative to healthy slow gait.

    View details for DOI 10.1016/j.jbiomech.2005.05.032

    View details for Web of Science ID 000239417900002

    View details for PubMedID 16046223

  • Gait differences between individuals with post-stroke hemiparesis and non-disabled controls at matched speeds GAIT & POSTURE Chen, G., Patten, C., Kothari, D. H., Zajac, F. E. 2005; 22 (1): 51-56

    Abstract

    Treadmill walking was used to assess the consistent gait differences between six individuals with post-stroke hemiparesis and six non-disabled, healthy controls at matched speeds. The hemiparetic subjects walked on the treadmill at their comfortable speeds, while each control walked at the same speed as the hemiparetic subject with whom he or she was matched. Kinematic and insole pressure data were collected from multiple, steady-state gait cycles. A large set of gait differences found between hemiparetic and non-disabled subjects was consistent with impaired swing initiation in the paretic limb (i.e., inadequate propulsion of the leg during pre-swing, increased percentage swing time, and reduced knee flexion at toe-off and mid-swing in the paretic limb) and related compensatory strategies (i.e., pelvic hiking and swing-phase propulsion and circumduction of the paretic limb). Exaggerated positive work associated with raising the trunk during pre-swing and swing of the paretic limb, consistent with pelvic hiking, contributed to increased mechanical energetic cost during walking. A second set of gait differences found was consistent with impaired single limb support on the paretic limb (i.e., shortened support time on the paretic limb) and related compensatory strategies (i.e., exaggerated propulsion of the non-paretic limb during pre-swing to shorten its swing time). Other significant gait differences included asymmetry in step length and increased step width. We conclude that consistent gait differences exist between hemiparetic and non-disabled subjects walking at matched speeds. The differences provide insights, concerning hemiparetic impairment and related compensatory strategies, that are in addition to the observation of slow walking speed.

    View details for DOI 10.1016/j.gaitpost.2004.06.009

    View details for Web of Science ID 000230807100007

    View details for PubMedID 15996592

  • Gait deviations associated with post-stroke hemiparesis: improvement during treadmill walking using weight support, speed, support stiffness, and handrail hold GAIT & POSTURE Chen, G., Patten, C., Kothari, D. H., Zajac, F. E. 2005; 22 (1): 57-62

    Abstract

    By comparing treadmill walking in hemiparetic and non-disabled individuals at matched speeds, Chen et al. [Chen G, Patten C, Kothari DH, Zajac FE. Gait differences between individuals with post-stroke hemiparesis and non-disabled controls at matched speeds. Gait Posture (2004)] identified gait deviations that were consistent with impaired swing initiation and single limb support in the paretic limb and related compensatory strategies. Treadmill training with harness support is a promising, task-oriented approach to restoring locomotor function in individuals with post-stroke hemiparesis. To provide a rationale for the proper selection of training parameters, we assessed the potential of body weight support, treadmill speed, support stiffness, and handrail hold to improve the identified gait deviations associated with hemiparesis during treadmill walking. In the six hemiparetic subjects studied, the adjustment of each training parameter was found to improve a specific set of the gait deviations. With increased body weight support or the addition of handrail hold, percentage single limb support time on the paretic limb increased and temporal symmetry improved. With increased treadmill speed, leg kinetic energy at toe-off in the paretic limb increased but remained low relative to values in the non-paretic limb. With increased support stiffness, the exaggerated energy cost associated with raising the trunk during pre-swing and swing of the paretic limb was improved. We conclude that the proper selection of training parameters can improve the gait pattern practiced by individuals with hemiparesis during treadmill training and may improve treatment outcome.

    View details for DOI 10.1016/j.gaitpost.2004.06.008

    View details for Web of Science ID 000230807100008

    View details for PubMedID 15996593

  • Muscle mechanical work requirements during normal walking: the energetic cost of raising the body's center-of-mass is significant JOURNAL OF BIOMECHANICS Neptune, R. R., Zajac, F. E., Kautz, S. A. 2004; 37 (6): 817-825

    Abstract

    Inverted pendulum models of walking predict that little muscle work is required for the exchange of body potential and kinetic energy in single-limb support. External power during walking (product of the measured ground reaction force and body center-of-mass (COM) velocity) is often analyzed to deduce net work output or mechanical energetic cost by muscles. Based on external power analyses and inverted pendulum theory, it has been suggested that a primary mechanical energetic cost may be associated with the mechanical work required to redirect the COM motion at the step-to-step transition. However, these models do not capture the multi-muscle, multi-segmental properties of walking, co-excitation of muscles to coordinate segmental energetic flow, and simultaneous production of positive and negative muscle work. In this study, a muscle-actuated forward dynamic simulation of walking was used to assess whether: (1). potential and kinetic energy of the body are exchanged with little muscle work; (2). external mechanical power can estimate the mechanical energetic cost for muscles; and (3.) the net work output and the mechanical energetic cost for muscles occurs mostly in double support. We found that the net work output by muscles cannot be estimated from external power and was the highest when the COM moved upward in early single-limb support even though kinetic and potential energy were exchanged, and muscle mechanical (and most likely metabolic) energetic cost is dominated not only by the need to redirect the COM in double support but also by the need to raise the COM in single support.

    View details for DOI 10.1016/j.jbiomech.2003.11.001

    View details for Web of Science ID 000221894400004

    View details for PubMedID 15111069

  • Muscle force redistributes segmental power for body progression during walking GAIT & POSTURE Neptune, R. R., Zajac, F. E., Kautz, S. A. 2004; 19 (2): 194-205

    Abstract

    The ankle plantar flexors were previously shown to support the body in single-leg stance to ensure its forward progression [J. Biomech. 34 (2001) 1387]. The uni- (SOL) and biarticular (GAS) plantar flexors accelerated the trunk and leg forward, respectively, with each opposing the effect of the other. Around mid-stance their net effect on the trunk and the leg was negligible, consistent with the body acting as an inverted pendulum. In late stance, their net effect was to accelerate the leg and trunk forward, consistent with an active push-off. Because other muscles are active in the beginning and end of stance, we hypothesized that their active concentric and eccentric force generation also supports the body and redistributes segmental power to enable body forward progression. Muscle-actuated forward dynamical simulations that emulated observed walking kinematics and kinetics of young adult subjects were analyzed to quantify muscle contributions to the vertical and horizontal ground reaction force, and to the acceleration and mechanical power of the leg and trunk. The eccentric uniarticular knee extensors (vasti, VAS) and concentric uniarticular hip extensors (gluteus maximus, GMAX) were found to provide critical support to the body in the beginning of stance, before the plantar flexors became active. VAS also decelerated the forward motion of both the trunk and the leg. Afterwards when VAS shortens in mid-stance, it delivered the power produced to accelerate the trunk and also redistributed segmental power to the trunk by continuing to decelerate the leg. When present, rectus femoris (RF) activity in the beginning of stance had a minimal effect. But in late stance the lengthening RF accelerated the knee and hip into extension, which opposed swing initiation. Though RF was lengthening, it still accelerated the trunk forward by decelerating the leg and redistributing the leg segmental power to the trunk, as SOL does though it is shortening instead of lengthening. Force developed from highly stretched passive hip structures and active force produced by the uniarticular hip flexors assisted GAS in swing initiation. Hamstrings (HAM) decelerated the leg in late swing while lengthening and accelerated the leg in the beginning of stance while shortening. We conclude that the uniarticular knee and hip extensor muscles are critical to body support in the beginning of stance and redistribution of segmental power by muscles throughout the gait cycle is critical to forward progression of the trunk and legs.

    View details for DOI 10.1016/S0966-6362(03)00062-6

    View details for Web of Science ID 000220472600011

    View details for PubMedID 15013508

  • Biomechanics and muscle coordination of human walking Part II: Lessons from dynamical simulations and clinical implications GAIT & POSTURE Zajac, F. E., Neptune, R. R., Kautz, S. A. 2003; 17 (1): 1-17

    Abstract

    Principles of muscle coordination in gait have been based largely on analyses of body motion, ground reaction force and EMG measurements. However, data from dynamical simulations provide a cause-effect framework for analyzing these measurements; for example, Part I (Gait Posture, in press) of this two-part review described how force generation in a muscle affects the acceleration and energy flow among the segments. This Part II reviews the mechanical and coordination concepts arising from analyses of simulations of walking. Simple models have elucidated the basic multisegmented ballistic and passive mechanics of walking. Dynamical models driven by net joint moments have provided clues about coordination in healthy and pathological gait. Simulations driven by muscle excitations have highlighted the partial stability afforded by muscles with their viscoelastic-like properties and the predictability of walking performance when minimization of metabolic energy per unit distance is assumed. When combined with neural control models for exciting motoneuronal pools, simulations have shown how the integrative properties of the neuro-musculo-skeletal systems maintain a stable gait. Other analyses of walking simulations have revealed how individual muscles contribute to trunk support and progression. Finally, we discuss how biomechanical models and simulations may enhance our understanding of the mechanics and muscle function of walking in individuals with gait impairments.

    View details for Web of Science ID 000180824300001

    View details for PubMedID 12535721

  • Biomechanics and muscle coordination of human walking - Part I: Introduction to concepts, power transfer, dynamics and simulations GAIT & POSTURE Zajac, F. E., Neptune, R. R., Kautz, S. A. 2002; 16 (3): 215-232

    Abstract

    Current understanding of how muscles coordinate walking in humans is derived from analyses of body motion, ground reaction force and EMG measurements. This is Part I of a two-part review that emphasizes how muscle-driven dynamics-based simulations assist in the understanding of individual muscle function in walking, especially the causal relationships between muscle force generation and walking kinematics and kinetics. Part I reviews the strengths and limitations of Newton-Euler inverse dynamics and dynamical simulations, including the ability of each to find the contributions of individual muscles to the acceleration/deceleration of the body segments. We caution against using the concept of biarticular muscles transferring power from one joint to another to infer muscle coordination principles because energy flow among segments, even the adjacent segments associated with the joints, cannot be inferred from computation of joint powers and segmental angular velocities alone. Rather, we encourage the use of dynamical simulations to perform muscle-induced segmental acceleration and power analyses. Such analyses have shown that the exchange of segmental energy caused by the forces or accelerations induced by a muscle can be fundamentally invariant to whether the muscle is shortening, lengthening, or neither. How simulation analyses lead to understanding the coordination of seated pedaling, rather than walking, is discussed in this first part because the dynamics of pedaling are much simpler, allowing important concepts to be revealed. We elucidate how energy produced by muscles is delivered to the crank through the synergistic action of other non-energy producing muscles; specifically, that a major function performed by a muscle arises from the instantaneous segmental accelerations and redistribution of segmental energy throughout the body caused by its force generation. Part II reviews how dynamical simulations provide insight into muscle coordination of walking.

    View details for Web of Science ID 000180123100001

    View details for PubMedID 12443946

  • Mutability of bifunctional thigh muscle activity in pedaling due to contralateral leg force generation JOURNAL OF NEUROPHYSIOLOGY Kautz, S. A., Brown, D. A., Van der Loos, H. F., Zajac, F. E. 2002; 88 (3): 1308-1317

    Abstract

    Locomotion requires uninterrupted transitions between limb extension and flexion. The role of contralateral sensorimotor signals in executing smooth transitions is little understood even though their participation is crucial to bipedal walking. However, elucidating neural interlimb coordinating mechanisms in human walking is difficult because changes to contralateral sensorimotor activity also affect the ipsilateral mechanics. Pedaling, conversely, is ideal for studying bilateral coordination because ipsilateral mechanics can be independently controlled. In pedaling, the anterior and posterior bifunctional thigh muscles develop needed anterior and posterior crank forces, respectively, to dominate the flexion-to-extension and extension-to-flexion transitions. We hypothesized that contralateral sensorimotor activity substantially contributes to the appropriate activation of these bifunctional muscles during the limb transitions. Bilateral pedal forces and surface electromyograms (EMGs) from four thigh muscles were collected from 15 subjects who pedaled with their right leg against a right-crank servomotor, which emulated the mechanical load experienced in conventional two-legged coupled-crank pedaling. In one pedaling session, the contralateral (left) leg pseudo-pedaled (i.e., EMG activity and pedal forces were pedaling-like, but pedal force was not allowed to affect crank rotation). In other sessions, the mechanically decoupled contralateral leg was first relaxed and then produced rhythmic isometric force trajectories during either leg flexion or one of the two limb transitions of the pedaling leg. With contralateral force production in the extension-to-flexion transition (predominantly by the hamstrings), rectus femoris activity and work output increased in the pedaling leg during its flexion-to-extension transition, which occurs simultaneously with contralateral extension-to-flexion in conventional pedaling. Similarly, with contralateral force production in the other transition (i.e., flexion-to-extension; predominantly by rectus femoris), hamstrings activity and work output increased in the pedaling leg during its extension-to-flexion transition. Therefore rhythmic isometric force generation in the contralateral leg supported the ongoing bifunctional muscle activity and resulting work output in the pedaling leg. The results suggest that neural interlimb coordinating mechanisms fine-tune bifunctional muscle activity in rhythmic lower-limb tasks to ensure limb flexion/extension transitions are executed successfully.

    View details for DOI 10.1152/jn.00104.2002

    View details for Web of Science ID 000177764100023

    View details for PubMedID 12205152

  • Understanding muscle coordination of the human leg with dynamical simulations JOURNAL OF BIOMECHANICS Zajac, F. E. 2002; 35 (8): 1011-1018

    Abstract

    Muscles coordinate multijoint motion by generating forces that cause reaction forces throughout the body. Thus, a muscle can redistribute existing segmental energy by accelerating some segments and decelerating others. In the process, a muscle may also produce or absorb energy, in which case its summed energetic effect on the segments is positive or negative, respectively. This Borelli Lecture shows how dynamical simulations derived from musculoskeletal models reveal muscle-induced segmental energy redistribution and muscle co-functions and synergies. Synergy occurs when co-excited muscles distribute segmental energy differently to execute the motor task. In maximum height jumping, high vertical velocity at lift-off occurs desirably at full body extension because biarticular leg muscles redistribute the energy produced by the uniarticular leg muscles. In pedaling, synergistic ankle plantarflexor force generation during leg extension allows the high energy produced by the uniarticular hip and knee extensors to be delivered to the crank. An analogous less-powerful flexor synergy exists during leg flexion. Hamstrings reduce crank deceleration during the leg extension-to-flexion transition by not only producing energy but delivering it to the crank through its contribution to the tangential (accelerating) crank force, though this hamstrings function occurs at the opposite (flexion-extension) transition when pedaling backwards. In walking, the eccentric quadriceps activity in early stance not only decelerates the leg but also accelerates the trunk. In mid-stance, the uni- and biarticular plantarflexors, by having opposite segmental energetic effects, act in synergy to support the whole body, so segmental potential and kinetic energy exchange can occur. To conclude, the extraction of unmeasurable variables from dynamical simulations emulating task kinematics, kinetics, and EMGs shows how the production of force and energy by individual muscles contribute to the energy flow among the individual segments during task execution.

    View details for Web of Science ID 000177318000001

    View details for PubMedID 12126660

  • Nonuniform shortening in the biceps brachii during elbow flexion JOURNAL OF APPLIED PHYSIOLOGY Pappas, G. P., Asakawa, D. S., Delp, S. L., Zajac, F. E., Drace, J. E. 2002; 92 (6): 2381-2389

    Abstract

    This study tested the common assumption that skeletal muscle shortens uniformly in the direction of its fascicles during low-load contraction. Cine phase contrast magnetic resonance imaging was used to characterize shortening of the biceps brachii muscle in 12 subjects during repeated elbow flexion against 5 and 15% maximum voluntary contraction (MVC) loads. Mean shortening was relatively constant along the anterior boundary of the muscle and averaged 21% for both loading conditions. In contrast, mean shortening was nonuniform along the centerline of the muscle during active elbow flexion. Centerline shortening in the distal region of the biceps brachii (7.3% for 5% MVC and 3.7% for 15% MVC) was significantly less (P < 0.001) than shortening in the muscle midportion (26.3% for 5% MVC and 28.2% for 15% MVC). Nonuniform shortening along the centerline was likely due to the presence of an internal aponeurosis that spanned the distal third of the longitudinal axis of the biceps brachii. However, muscle shortening was also nonuniform proximal to the centerline aponeurosis. Because muscle fascicles follow the anterior contour and centerline of the biceps brachii, our results suggest that shortening is uniform along anterior muscle fascicles and nonuniform along centerline fascicles.

    View details for DOI 10.1152/japplphysiol.00843.2001

    View details for Web of Science ID 000175739200021

    View details for PubMedID 12015351

  • Contributions of the individual ankle plantar flexors to support, forward progression and swing initiation during walking JOURNAL OF BIOMECHANICS Neptune, R. R., Kautz, S. A., Zajac, F. E. 2001; 34 (11): 1387-1398

    Abstract

    Walking is a motor task requiring coordination of many muscles. Previous biomechanical studies, based primarily on analyses of the net ankle moment during stance, have concluded different functional roles for the plantar flexors. We hypothesize that some of the disparities in interpretation arise because of the effects of the uniarticular and biarticular muscles that comprise the plantar flexor group have not been separated. Furthermore, we believe that an accurate determination of muscle function requires quantification of the contributions of individual plantar flexor muscles to the energetics of individual body segments. In this study, we examined the individual contributions of the ankle plantar flexors (gastrocnemius (GAS); soleus (SOL)) to the body segment energetics using a musculoskeletal model and optimization framework to generate a forward dynamics simulation of normal walking at 1.5 m/s. At any instant in the gait cycle, the contribution of a muscle to support and forward progression was defined by its contribution to trunk vertical and horizontal acceleration, respectively, and its contribution to swing initiation by the mechanical energy it delivers to the leg in pre-swing (i.e., double-leg stance prior to toe-off). GAS and SOL were both found to provide trunk support during single-leg stance and pre-swing. In early single-leg stance, undergoing eccentric and isometric activity, they accelerate the trunk vertically but decelerate forward trunk progression. In mid single-leg stance, while isometric, GAS delivers energy to the leg while SOL decelerates it, and SOL delivers energy to the trunk while GAS decelerates it. In late single-leg stance through pre-swing, though GAS and SOL both undergo concentric activity and accelerate the trunk forward while decelerating the downward motion of the trunk (i.e., providing forward progression and support), they execute different energetic functions. The energy produced from SOL accelerates the trunk forward, whereas GAS delivers almost all its energy to accelerate the leg to initiate swing. Although GAS and SOL maintain or accelerate forward motion in mid single-leg stance through pre-swing, other muscles acting at the beginning of stance contribute comparably to forward progression. In summary, throughout single-leg stance both SOL and GAS provide vertical support, in mid single-leg stance SOL and GAS have opposite energetic effects on the leg and trunk to ensure support and forward progression of both the leg and trunk, and in pre-swing only GAS contributes to swing initiation.

    View details for Web of Science ID 000171955400003

    View details for PubMedID 11672713

  • Bicycle drive system dynamics: Theory and experimental validation JOURNAL OF BIOMECHANICAL ENGINEERING-TRANSACTIONS OF THE ASME Fregly, B. J., Zajac, F. E., Dairaghi, C. A. 2000; 122 (4): 446-452

    Abstract

    Bicycle pedaling has been studied from both a motor control and an equipment setup and design perspective. In both cases, although the dynamics of the bicycle drive system may have an influence on the results, a thorough understanding of the dynamics has not been developed. This study pursued three objectives related to developing such an understanding. The first was to identify the limitations of the inertial/frictional drive system model commonly used in the literature. The second was to investigate the advantages of an inertial/frictional/compliant model. The final objective was to use these models to develop a methodology for configuring a laboratory ergometer to emulate the drive system dynamics of road riding. Experimental data collected from the resulting road-riding emulator and from a standard ergometer confirmed that the inertial/frictional model is adequate for most studies of road-riding mechanics or pedaling coordination. However, the compliant model was needed to reproduce the phase shift in crank angle variations observed experimentally when emulating the high inertia of road riding. This finding may be significant for equipment setup and design studies where crank kinematic variations are important or for motor control studies where fine control issues are of interest.

    View details for Web of Science ID 000167111100020

    View details for PubMedID 11036570

  • Contralateral movement and extensor force generation alter flexion phase muscle coordination in pedaling JOURNAL OF NEUROPHYSIOLOGY Ting, L. H., Kautz, S. A., Brown, D. A., Zajac, F. E. 2000; 83 (6): 3351-3365

    Abstract

    The importance of bilateral sensorimotor signals in coordination of locomotion has been demonstrated in animals but is difficult to ascertain in humans due to confounding effects of mechanical transmission of forces between the legs (i.e., mechanical interleg coupling). In a previous pedaling study, by eliminating mechanical interleg coupling, we showed that muscle coordination of a unipedal task can be shaped by interlimb sensorimotor pathways. Interlimb neural pathways were shown to alter pedaling coordination as subjects pedaling unilaterally exhibited increased flexion-phase muscle activity compared with bilateral pedaling even though the task mechanics performed by the pedaling leg(s) in the unilateral and bilateral pedaling tasks were identical. To further examine the relationship between contralateral sensorimotor state and ipsilateral flexion-phase muscle coordination during pedaling, subjects in this study pedaled with one leg while the contralateral leg either generated an extensor force or relaxed as a servomotor either held that leg stationary or moved it in antiphase with the pedaling leg. In the presence of contralateral extensor force generation, muscle activity in the pedaling leg during limb flexion was reduced. Integrated electromyographic activity of the pedaling-leg hamstring muscles (biceps femoris and semimembranosus) during flexion decreased by 25-30%, regardless of either the amplitude of force generated by the nonpedaling leg or whether the leg was stationary or moving. In contrast, rectus femoris and tibialis anterior activity during flexion decreased only when the contralateral leg generated high rhythmic force concomitant with leg movement. The results are consistent with a contralateral feedforward mechanism triggering flexion-phase hamstrings activity and a contralateral feedback mechanism modulating rectus femoris and tibialis anterior activity during flexion. Because only muscles that contribute to flexion as a secondary function were observed, it is impossible to know whether the modulatory effect also acts on primary, unifunctional, limb flexors or is specific to multifunctional muscles contributing to flexion. The influence of contralateral extensor-phase sensorimotor signals on ipsilateral flexion may reflect bilateral coupling of gain control mechanisms. More generally, these interlimb neural mechanisms may coordinate activity between muscles that perform antagonistic functions on opposite sides of the body. Because pedaling and walking share biomechanical and neuronal control features, these mechanisms may be operational in walking as well as pedaling.

    View details for Web of Science ID 000087574000015

    View details for PubMedID 10848554

  • Muscle contributions to specific biomechanical functions do not change in forward versus backward pedaling JOURNAL OF BIOMECHANICS Neptune, R. R., Kautz, S. A., Zajac, F. E. 2000; 33 (2): 155-164

    Abstract

    Previous work had identified six biomechanical functions that need to be executed by each limb in order to produce a variety of pedaling tasks. The functions can be organized into three antagonistic pairs: an Ext/Flex pair that accelerates the foot into extension or flexion with respect to the pelvis, an Ant/Post pair that accelerates the foot anteriorly or posteriorly with respect to the pelvis, and a Plant/Dorsi pair that accelerates the foot into plantarflexion or dorsiflexion. Previous analyses of experimental data have inferred that muscles perform the same function during different pedaling tasks (e.g. forward versus backward pedaling) because the EMG timing was similar, but they did not present rigorous biomechanical analyses to assess whether a muscle performed the same biomechanical function, and if so, to what degree. Therefore, the objective of this study was to determine how individual muscles contribute to these biomechanical functions during two different motor tasks, forward and backward pedaling, through a theoretical analysis of experimental data. To achieve this objective, forward and backward pedaling simulations were generated and a mechanical energy analysis was used to examine how muscles generate, absorb or transfer energy to perform the pedaling tasks. The results showed that the muscles contributed to the same primary Biomechanical functions in both pedaling directions and that synergistic performance of certain functions effectively accelerated the crank. The gluteus maximus worked synergistically with the soleus, the hip flexors worked synergistically with the tibialis anterior, and the vasti and hamstrings functioned independently to accelerate the crank. The rectus femoris used complex biomechanical mechanisms including negative muscle work to accelerate the crank. The negative muscle work was used to transfer energy generated elsewhere (primarily from other muscles) to the pedal reaction force in order to accelerate the crank. Consistent with experimental data, a phase shift was required from those muscles contributing to the Ant/Post functions as a result of the different limb kinematics between forward and backward pedaling, although they performed the same biomechanical function. The pedaling simulations proved necessary to interpret the experimental data and identify motor control mechanisms used to accomplish specific motor tasks, as the mechanisms were often complex and not always intuitively obvious.

    View details for Web of Science ID 000084838600003

    View details for PubMedID 10653028

  • In vivo tracking of the human patella using cine phase contrast magnetic resonance imaging JOURNAL OF BIOMECHANICAL ENGINEERING-TRANSACTIONS OF THE ASME Sheehan, F. T., Zajac, F. E., Drace, J. E. 1999; 121 (6): 650-656

    Abstract

    Improper patellar tracking is often considered to be the cause of patellar-femoral pain. Unfortunately, our knowledge of patellar-femoral-tibial (knee) joint kinematics is severely limited due to a lack of three-dimensional, noninvasive, in vivo measurement techniques. This study presents the first large-scale, dynamic, three-dimensional, noninvasive, in vivo study of nonimpaired knee joint kinematics during volitional leg extensions. Cine-phase contrast magnetic resonance imaging was used to measure the velocity profiles of the patella, femur, and tibia in 18 unimpaired knees during leg extensions, resisted by a 34 N weight. Bone displacements were calculated through integration and then converted into three-dimensional orientation angles. We found that the patella displaced laterally, superiorly, and anteriorly as the knee extended. Further, patellar flexion lagged knee flexion, patellar tilt was variable, and patellar rotation was fairly constant throughout extension.

    View details for Web of Science ID 000084592900014

    View details for PubMedID 10633267

  • Ankle and hip postural strategies defined by joint torques GAIT & POSTURE Runge, C. F., Shupert, C. L., Horak, F. B., Zajac, F. E. 1999; 10 (2): 161-170

    Abstract

    Previous studies have identified two discrete strategies for the control of posture in the sagittal plane based on EMG activations, body kinematics, and ground reaction forces. The ankle strategy was characterized by body sway resembling a single-segment-inverted pendulum and was elicited on flat support surfaces. In contrast, the hip strategy was characterized by body sway resembling a double-segment inverted pendulum divided at the hip and was elicited on short or compliant support surfaces. However, biomechanical optimization models have suggested that hip strategy should be observed in response to fast translations on a flat surface also, provided the feet are constrained to remain in contact with the floor and the knee is constrained to remain straight. The purpose of this study was to examine the experimental evidence for hip strategy in postural responses to backward translations of a flat support surface and to determine whether analyses of joint torques would provide evidence for two separate postural strategies. Normal subjects standing on a flat support surface were translated backward with a range of velocities from fast (55 cm/s) to slow (5 cm/s). EMG activations and joint kinematics showed pattern changes consistent with previous experimental descriptions of mixed hip and ankle strategy with increasing platform velocity. Joint torque analyses revealed the addition of a hip flexor torque to the ankle plantarflexor torque during fast translations. This finding indicates the addition of hip strategy to ankle strategy to produce a continuum of postural responses. Hip torque without accompanying ankle torque (pure hip strategy) was not observed. Although postural control strategies have previously been defined by how the body moves, we conclude that joint torques, which indicate how body movements are produced, are useful in defining postural control strategies. These results also illustrate how the biomechanics of the body can transform discrete control patterns into a continuum of postural corrections.

    View details for Web of Science ID 000083160600008

    View details for PubMedID 10502650

  • Locomotor strategy for pedaling: Muscle groups and biomechanical functions JOURNAL OF NEUROPHYSIOLOGY Raasch, C. C., Zajac, F. E. 1999; 82 (2): 515-525

    Abstract

    A group of coexcited muscles alternating with another group is a common element of motor control, including locomotor pattern generation. This study used computer simulation to investigate human pedaling with each muscle assigned at times to a group. Simulations were generated by applying patterns of muscle excitations to a musculoskeletal model that includes the dynamic properties of the muscles, the limb segments, and the crank load. Raasch et al. showed that electromyograms, pedal reaction forces, and limb and crank kinematics recorded during maximum-speed start-up pedaling could be replicated with two signals controlling the excitation of four muscle groups (1 group alternating with another to form a pair). Here a four-muscle-group control also is shown to replicate steady pedaling. However, simulations show that three signals controlling six muscle groups (i.e., 3 pairs) is much more biomechanically robust, such that a wide variety of forward and backward pedaling tasks can be executed well. We found the biomechanical functions necessary for pedaling, and how these functions can be executed by the muscle groups. Specifically, the phasing of two pairs with respect to limb extension and flexion and the transitions between extension and flexion do not change with pedaling direction. One pair of groups (uniarticular hip and knee extensors alternating with their anatomic antagonists) generates the energy required for limb and crank propulsion during limb extension and flexion, respectively. In the second pair, the ankle plantarflexors transfer the energy from the limb inertia to the crank during the latter part of limb extension and the subsequent limb extension-to-flexion transition. The dorsiflexors alternate with the plantarflexors. The phasing of the third pair (the biarticular thigh muscles) reverses with pedaling direction. In forward pedaling, the hamstring is excited during the extension-to-flexion transition and in backward pedaling during the opposite transition. In both cases hamstrings propel the crank posteriorly through the transition. Rectus femoris alternates with hamstrings and propels the crank anteriorly through the transitions. With three control signals, one for each pair of groups, different cadences (or power outputs) can be achieved by adjusting the overall excitatory drive to the pattern generating elements, and different pedaling goals (e.g., smooth, or energy-efficient pedaling; 1- or 2-legged pedaling) by adjusting the relative excitation levels among the muscle groups. These six muscle groups are suggested to be elements of a general strategy for pedaling control, which may be generally applicable to other human locomotor tasks.

    View details for Web of Science ID 000082038000001

    View details for PubMedID 10444651

  • Phase reversal of biomechanical functions and muscle activity in backward pedaling JOURNAL OF NEUROPHYSIOLOGY Ting, L. H., Kautz, S. A., Brown, D. A., Zajac, F. E. 1999; 81 (2): 544-551

    Abstract

    Computer simulations of pedaling have shown that a wide range of pedaling tasks can be performed if each limb has the capability of executing six biomechanical functions, which are arranged into three pairs of alternating antagonistic functions. An Ext/Flex pair accelerates the limb into extension or flexion, a Plant/Dorsi pair accelerates the foot into plantarflexion or dorsiflexion, and an Ant/Post pair accelerates the foot anteriorly or posteriorly relative to the pelvis. Because each biomechanical function (i.e., Ext, Flex, Plant, Dorsi, Ant, or Post) contributes to crank propulsion during a specific region in the cycle, phasing of a muscle is hypothesized to be a consequence of its ability to contribute to one or more of the biomechanical functions. Analysis of electromyogram (EMG) patterns has shown that this biomechanical framework assists in the interpretation of muscle activity in healthy and hemiparetic subjects during forward pedaling. Simulations show that backward pedaling can be produced with a phase shift of 180 degrees in the Ant/Post pair. No phase shifts in the Ext/Flex and Plant/Dorsi pairs are then necessary. To further test whether this simple yet biomechanically viable strategy may be used by the nervous system, EMGs from 7 muscles in 16 subjects were measured during backward as well as forward pedaling. As predicted, phasing in vastus medialis (VM), tibialis anterior (TA), medial gastrocnemius (MG), and soleus (SL) were unaffected by pedaling direction, with VM and SL contributing to Ext, MG to Plant, and TA to Dorsi. In contrast, phasing in biceps femoris (BF) and semimembranosus (SM) were affected by pedaling direction, as predicted, compatible with their contribution to the directionally sensitive Post function. Phasing of rectus femoris (RF) was also affected by pedaling direction; however, its ability to contribute to the directionally sensitive Ant function may only be expressed in forward pedaling. RF also contributed significantly to the directionally insensitive Ext function in both forward and backward pedaling. Other muscles also appear to have contributed to more than one function, which was especially evident in backward pedaling (i.e. , BF, SM, MG, and TA to Flex). We conclude that the phasing of only the Ant and Post biomechanical functions are directionally sensitive. Further, we suggest that task-dependent modulation of the expression of the functions in the motor output provides this biomechanics-based neural control scheme with the capability to execute a variety of lower limb tasks, including walking.

    View details for Web of Science ID 000078832800014

    View details for PubMedID 10036258

  • Role of vestibular information in initiation of rapid postural responses EXPERIMENTAL BRAIN RESEARCH Runge, C. F., Shupert, C. L., Horak, F. B., Zajac, F. E. 1998; 122 (4): 403-412

    Abstract

    Patients with bilateral vestibular loss have difficulty maintaining balance without stepping when standing in tandem, on compliant surfaces, across narrow beams, or on one foot, especially with eyes closed. Normal individuals (with no sensory impairment) maintain balance in these tasks by employing quick, active hip rotation (a "hip strategy"). The absence of a hip strategy in vestibular patients responding to translations of a short support surface has previously been taken as evidence that the use of hip strategy requires an intact vestibular system. However, many tasks requiring hip strategy alter one or a combination of important system characteristics, such as initial state of the body (tandem stance), dynamics (compliant surfaces), or biomechanical limits of stability (narrow beams). Therefore, the balance deficit in these tasks may result from a failure to account for these support surface alterations when planning and executing sensorimotor responses. In this study, we tested the hypothesis that vestibular information is critical to trigger a hip strategy even on an unaltered support surface, which imposes no changes on the system characteristics. We recorded the postural responses of vestibular patients and control subjects with eyes closed to rearward support surface translations of varying velocity, in erect stance on a firm, flat surface. Subjects were instructed to maintain balance without stepping, if possible. Faster translation velocities (25 cm/s or more) produced a consistent pattern of early hip torque (first 400 ms) in control subjects (i.e., a hip strategy). Most of the patients with bilateral vestibular loss responded to the same translation velocities with similar torques. Contrary to our hypothesis, we conclude that vestibular function is not necessary to trigger a hip strategy. We postulate, therefore, that the balance deficit previously observed in vestibular patients during postural tasks that elicit a hip strategy may have been due to the sensorimotor consequences of the system alterations imposed by the postural tasks used in those studies. Preliminary results from two younger patients who lost vestibular function as infants indicate that age, duration of vestibular loss, and/or the timing of the loss may also be factors that can influence the use of hip strategy as a rapid postural response.

    View details for Web of Science ID 000076462900004

    View details for PubMedID 9827859

  • Sensorimotor state of the contralateral leg affects ipsilateral muscle coordination of pedaling JOURNAL OF NEUROPHYSIOLOGY Ting, L. H., Raasch, C. C., Brown, D. A., Kautz, S. A., Zajac, F. E. 1998; 80 (3): 1341-1351

    Abstract

    The objective of this study was to determine if independent central pattern generating elements controlling the legs in bipedal and unipedal locomotion is a viable theory for locomotor propulsion in humans. Coordinative coupling of the limbs could then be accomplished through mechanical interactions and ipsilateral feedback control rather than through central interlimb neural pathways. Pedaling was chosen as the locomotor task to study because interlimb mechanics can be significantly altered, as pedaling can be executed with the use of either one leg or two legs (cf. walking) and because the load on the limb can be well-controlled. Subjects pedaled a modified bicycle ergometer in a two-legged (bilateral) and a one-legged (unilateral) pedaling condition. The loading on the leg during unilateral pedaling was designed to be identical to the loading experienced by the leg during bilateral pedaling. This loading was achieved by having a trained human "motor" pedal along with the subject and exert on the opposite crank the torque that the subject's contralateral leg generated in bilateral pedaling. The human "motor" was successful at reproducing each subject's one-leg crank torque. The shape of the motor's torque trajectory was similar to that of subjects, and the amount of work done during extension and flexion was not significantly different. Thus the same muscle coordination pattern would allow subjects to pedal successfully in both the bilateral and unilateral conditions, and the afferent signals from the pedaling leg could be the same for both conditions. Although the overall work done by each leg did not change, an 86% decrease in retarding (negative) crank torque during limb flexion was measured in all 11 subjects during the unilateral condition. This corresponded to an increase in integrated electromyography of tibialis anterior (70%), rectus femoris (43%), and biceps femoris (59%) during flexion. Even given visual torque feedback in the unilateral condition, subjects still showed a 33% decrease in negative torque during flexion. These results are consistent with the existence of an inhibitory pathway from elements controlling extension onto contralateral flexion elements, with the pathway operating during two-legged pedaling but not during one-legged pedaling, in which case flexor activity increases. However, this centrally mediated coupling can be overcome with practice, as the human "motor" was able to effectively match the bilateral crank torque after a longer practice regimen. We conclude that the sensorimotor control of a unipedal task is affected by interlimb neural pathways. Thus a task performed unilaterally is not performed with the same muscle coordination utilized in a bipedal condition, even if such coordination would be equally effective in the execution of the unilateral task.

    View details for Web of Science ID 000076233500026

    View details for PubMedID 9744943

  • Large index-fingertip forces are produced by subject-independent patterns of muscle excitation JOURNAL OF BIOMECHANICS Valero-Cuevas, F. J., Zajac, F. E., Burgar, C. G. 1998; 31 (8): 693-703

    Abstract

    Are fingertip forces produced by subject-independent patterns of muscle excitation? If so, understanding the mechanical basis underlying these muscle coordination strategies would greatly assist surgeons in evaluating options for restoring grasping. With the finger in neutral ad- abduction and flexed 45 degrees at the MCP and PIP, and 10 degrees at DIP joints, eight subjects attempted to produce maximal voluntary forces in four orthogonal directions perpendicular to the distal phalanx (palmar, dorsal, lateral and medial) and in one direction collinear with it (distal). Forces were directed within 4.7 +/- 2.2 degrees (mean +/- S.D.) of target and their magnitudes clustered into three distinct levels (p < 0.05; post hoc pairwise RMANOVA). Palmar (27.9 +/- 4.1 N), distal (24.3 +/- 8.3 N) and medial (22.9 +/- 7.8 N) forces were highest, lateral (14.7 +/- 4.8 N) was intermediate, and dorsal (7.5 +/- 1.5 N) was lowest. Normalized fine-wire EMGs from all seven muscles revealed distinct muscle excitation groups for palmar, dorsal and distal forces (p < 0.05; post hoc pairwise RMANOVA). Palmar force used flexors, extensors and dorsal interosseous; dorsal force used all muscles; distal force used all muscles except for extensors; medial and lateral forces used all muscles including significant co-excitation of interossei. The excitation strategies predicted to achieve maximal force by a 3-D computer model (four pinjoints, inextensible tendons, extensor mechanism and isometric force models for all seven muscles) reproduced the observed use of extensors and absence of palmar interosseous to produce palmar force (to regulate net joint flexion torques), the absence of extensors for distal force, and the use of intrinsics (strong MCP flexors) for dorsal force. The model could not predict the interossei co-excitation seen for medial and lateral forces, which may be a strategy to prevent MCP joint damage. The model predicts distal force to be most sensitive to dorsal interosseous strength, and palmar and distal forces to be very sensitive to MCP and PIP flexor moment arms, and dorsal force to be sensitive to the moment arm of and the tension allocation to the PIP extensor tendon of the extensor mechanism.

    View details for Web of Science ID 000076383100003

    View details for PubMedID 9796669

  • Bilateral integration of sensorimotor signals during pedaling NEURONAL MECHANISMS FOR GENERATING LOCOMOTOR ACTIVITY Ting, L. H., Kautz, S. A., Brown, D. A., Van der Loos, H. F., Zajac, F. E. 1998; 860: 513-516

    View details for Web of Science ID 000078450500057

    View details for PubMedID 9928350

  • Using cine phase contrast magnetic resonance imaging to non-invasively study in vivo knee dynamics JOURNAL OF BIOMECHANICS Sheehan, F. T., Zajac, F. E., Drace, J. E. 1998; 31 (1): 21-26

    Abstract

    We tested the accuracy and feasibility of using cine phase contrast magnetic resonance imaging (cine-PC MRI) to non-invasively measure three-dimensional, in vivo, skeletal velocity. Bone displacement was estimated by integrating the velocity measurements. Cine-PC MRI was originally developed to directly and non-invasively measure in vivo blood and heart velocity. Since no standard of reference exists for in vivo measurement of trabecular bone motion, a motion phantom (consisting of a series of paired gears that moved a sample box containing a human femoral bone sample) was built to assess the accuracy of tracking trabecular bone with cine-PC MRI. The in-plane, average absolute displacement errors were 0.55 +/- 0.38 and 0.36 +/- 0.27 mm in the x- and y-direction, respectively. Thus, estimates of bone position based on the integration of bone velocity measurements are affected little by the magnetic properties of bone [Majumdar and Genant (1995) Osteoporos International 5, 79-92]. The velocity profiles of the patella, femur and tibia were measured in five healthy subjects during leg extensions. Extension was resisted by a 34 N weight. Subjects maintained a consistent motion rate (35 +/- 0.5 cycles min(-1)) and motion artifacts were minimal. Our results indicate that patellar flexion lags knee flexion and the patella tilts laterally and then medially as the knee extends. We conclude cine-PC MRI is a promising technique for the non-invasive measurement of in vivo skeletal dynamics and, based on our previous work, muscular dynamics as well.

    View details for Web of Science ID 000073974600003

    View details for PubMedID 9596534

  • Muscle coordination of maximum-speed pedaling JOURNAL OF BIOMECHANICS Raasch, C. C., Zajac, F. E., Ma, B. M., Levine, W. S. 1997; 30 (6): 595-602

    Abstract

    A simulation based on a forward dynamical musculoskeletal model was computed from an optimal control algorithm to understand uni- and bi-articular muscle coordination of maximum-speed startup pedaling. The muscle excitations, pedal reaction forces, and crank and pedal kinematics of the simulation agreed with measurements from subjects. Over the crank cycle, uniarticular hip and knee extensor muscles provide 55% of the propulsive energy, even though 27% of the amount they produce in the downstroke is absorbed in the upstroke. Only 44% of the energy produced by these muscles during downstroke is delivered to the crank directly. The other 56% is delivered to the limb segments, and then transferred to the crank by the ankle plantarflexors. The plantarflexors, especially soleus, also prevent knee hyperextension, by slowing the knee extension being produced during downstroke by the other muscles, including hamstrings. Hamstrings and rectus femoris make smooth pedaling possible by propelling the crank through the stroke transitions. Other simulations showed that pedaling can be performed well by partitioning all the muscles in a leg into two pairs of phase-controlled alternating functional groups, with each group also alternating with its contralateral counterpart. In this scheme, the uniarticular hip/knee extensor muscles (one group) are excited during downstroke, and the uniarticular hip/knee flexor muscles (the alternating group) during upstroke. The ankle dorsiflexor and rectus femoris muscles (one group of the other pair) are excited near the transition from upstroke to downstroke, and the ankle plantarflexors and hamstrings muscles (the alternating group) during the downstroke to upstroke transition. We conclude that these alternating functional muscle groups might represent a centrally generated primitive for not only pedaling but also other locomotor tasks as well.

    View details for Web of Science ID A1997WZ33100008

    View details for PubMedID 9165393

  • Crank inertial load has little effect on steady-state pedaling coordination JOURNAL OF BIOMECHANICS Fregly, B. J., Zajac, F. E., Dairaghi, C. A. 1996; 29 (12): 1559-1567

    Abstract

    Inertial load can affect the control of a dynamic system whenever parts of the system are accelerated or decelerated. During steady-state pedaling, because within-cycle variations in crank angular acceleration still exist, the amount of crank inertia present (which varies widely with road-riding gear ratio) may affect the within-cycle coordination of muscles. However, the effect of inertial load on steady-state pedaling coordination is almost always assumed to be negligible, since the net mechanical energy per cycle developed by muscles only depends on the constant cadence and workload. This study test the hypothesis that under steady-state conditions, the net joint torques produced by muscles at the hip, knee, and ankle are unaffected by crank inertial load. To perform the investigation, we constructed a pedaling apparatus which could emulate the low inertial load of a standard ergometer or the high inertial load of a road bicycle in high gear. Crank angle and bilateral pedal force and angle data were collected from ten subjects instructed to pedal steadily (i.e., constant speed across cycles) and smoothly (i.e., constant speed within a cycle) against both inertias at a constant workload. Virtually no statistically significant changes were found in the net hip and knee muscle joint torques calculated from an inverse dynamics analysis. Though the net ankle muscle joint torque, as well as the one- and two-legged crank torque, showed statistically significant increases at the higher inertia, the changes were small. In contrast, large statistically significant reductions were found in crank kinematic variability both within a cycle and between cycles (i.e., cadence), primarily because a larger inertial load means a slower crank dynamic response. Nonetheless, the reduction in cadence variability was somewhat attenuated by a large statistically significant increase in one-legged crank torque variability. We suggest, therefore, that muscle coordination during steady-state pedaling is largely unaffected, though less well regulated, when crank inertial load is increased.

    View details for Web of Science ID A1996VT91600007

    View details for PubMedID 8945654

  • A state-space analysis of mechanical energy generation, absorption, and transfer during pedaling JOURNAL OF BIOMECHANICS Fregly, B. J., Zajac, F. E. 1996; 29 (1): 81-90

    Abstract

    Seated ergometer pedaling is a motor task ideal for studying basic mechanisms of human bipedal coordination because, in contrast to standing and walking, fewer degrees of freedom are being controlled and upright balance is not a factor. As a step toward understanding how individual muscles coordinate pedaling, we investigated how individual net muscle joint torques and non-muscular (e.g. centripetal, coriolis, and gravity) forces of the lower limbs generate, absorb, and transfer mechanical energy in order to propel the crank and recover the limb. This was accomplished using a mechanical power analysis derived entirely from the closed-form state-space dynamical equations of a two-legged pedaling model that accounted for both the limb segmental and crank load dynamics. Based on a pedaling simulation that reproduced experimental kinematic and kinetic trajectories, we found that the net ankle and hip extensor joint torques function 'synergistically' to deliver energy to the crank during the downstroke. The net hip extensor joint torque generates energy to the limb, while the net ankle extensor joint torque transfers this energy from the limb to the crank. In contrast, net knee extensor and flexor joint torques function 'independently' by generating energy to the crank through the top and bottom of the stroke, respectively. The net ankle joint torque transfers and the net knee joint torque generates energy to the crank by contributing to the driving component of the pedal reaction force. During the upstroke, net ankle extensor joint torque transfers energy from the crank to the limb to restore the potential energy of the limb. In both halves of the crank cycle, gravity forces augment the crank-limb energy transfer performed by the net ankle extensor joint torque.

    View details for Web of Science ID A1996TM44400010

    View details for PubMedID 8839020

  • ESTIMATING NET JOINT TORQUES FROM KINESIOLOGICAL DATA USING OPTIMAL LINEAR-SYSTEM THEORY IEEE TRANSACTIONS ON BIOMEDICAL ENGINEERING Runge, C. F., Zajac, F. E., Allum, J. H., RISHER, D. W., Bryson, A. E., Honegger, F. 1995; 42 (12): 1158-1164

    Abstract

    Net joint torques (NJT) are frequently computed to provide insights into the motor control of dynamic biomechanical systems. An inverse dynamics approach is almost always used, whereby the NJT are computed from 1) kinematic measurements (e.g., position of the segments), 2) kinetic measurements (e.g., ground reaction forces) that are, in effect, constraints defining unmeasured kinematic quantities based on a dynamic segmental model, and 3) numerical differentiation of the measured kinematics to estimate velocities and accelerations that are, in effect, additional constraints. Due to errors in the measurements, the segmental model, and the differentiation process, estimated NJT rarely produce the observed movement in a forward simulation when the dynamics of the segmental system are inherently unstable (e.g., human walking). Forward dynamic simulations are, however, essential to studies of muscle coordination. We have developed an alternative approach, using the linear quadratic follower (LQF) algorithm, which computes the NJT such that a stable simulation of the observed movement is produced and the measurements are replicated as well as possible. The LQF algorithm does not employ constraints depending on explicit differentiation of the kinematic data, but rather employs those depending on specification of a cost function, based on quantitative assumptions about data confidence. We illustrate the usefulness of the LQF approach by using it to estimate NJT exerted by standing humans perturbed by support-surface movements. We show that unless the number of kinematic and force variables recorded is sufficiently high, the confidence that can be placed in the estimates of the NJT, obtained by any method (e.g., LQF, or the inverse dynamics approach), may be unsatisfactorily low.

    View details for Web of Science ID A1995TJ29200002

    View details for PubMedID 8550057

  • MODELING AND SIMULATION OF PARAPLEGIC AMBULATION IN A RECIPROCATING GAIT ORTHOSIS JOURNAL OF BIOMECHANICAL ENGINEERING-TRANSACTIONS OF THE ASME Tashman, S., Zajac, F. E., Perkash, I. 1995; 117 (3): 300-308

    Abstract

    We developed a three dimensional, four segment, eight-degree-of-freedom model for the analysis of paraplegic ambulation in a reciprocating gait orthosis (RGO). Model development was guided by experimental analysis of a spinal cord injured individual walking in an RGO with the additional assistance of arm crutches. Body forces and torques required to produce a dynamic simulation of the RGO gait swing phase were found by solving an optimal control problem to track the recorded kinematics and ground reaction forces. We found that high upper body forces are required, not only during swing but probably also during double support to compensate for the deceleration of the body during swing, which is due to the pelvic thrust necessary to swing the leg forward. Other stimulations showed that upper body forces and body deceleration during swing can be reduced substantially by producing a ballistic swing. Functional neuromuscular stimulation of the hip musculature during double support would then be required, however, to establish the initial conditions needed in a ballistic swing.

    View details for Web of Science ID A1995RZ15400009

    View details for PubMedID 8618383

  • COMPENSATING FOR CHANGES IN MUSCLE LENGTH IN TOTAL HIP-ARTHROPLASTY - EFFECTS ON THE MOMENT GENERATING CAPACITY OF THE MUSCLES CLINICAL ORTHOPAEDICS AND RELATED RESEARCH Vasavada, A. N., Delp, S. L., Maloney, W. J., Schurman, D. J., Zajac, F. E. 1994: 121-133

    Abstract

    Alterations in the location of the hip center may change the lengths and moment arms of the muscles, and thereby affect their capacity to generate force and moment about the hip. This study demonstrates some of the differences between compensating and not compensating for changes in muscle length that arise from displacement of the hip center. A computer model was developed to estimate the maximum isometric moment generating capacity of the hip muscles under two conditions. In the compensated condition, the hip center was displaced, but the muscles were restored to their original lengths and orientations by altering proximal femoral geometry. In the uncompensated condition, femoral geometry remained constant; thus, muscle lengths and orientations changed with displacement of the hip center. The computer simulations showed large differences between the two conditions. For example, a 2-cm superior displacement of the hip center decreased the moment generating capacity of the hip abductors 18% with compensation and 49% without compensation. Similarly, a 1-cm medial displacement of the hip center increased the moment generating capacity of the abductors 17% with compensation, but decreased it 4% without compensation. In contrast, a 1-cm inferior displacement decreased the moment generating capacity of flexors 6% with compensation, but increased it 12% without compensation. The results presented here demonstrate that compensating for changes in muscle length can be important in terms of preserving the moment generating capacity of the muscles when the hip center is displaced superiorly and medially, but not when the hip center is displaced in the inferior direction.

    View details for Web of Science ID A1994NL07400020

    View details for PubMedID 8168289

  • HUMAN STANDING POSTURE - MULTIJOINT MOVEMENT STRATEGIES BASED ON BIOMECHANICAL CONSTRAINTS Kuo, A. D., Zajac, F. E. ELSEVIER SCIENCE PUBL B V. 1993: 349-358
  • HUMAN STANDING POSTURE - MULTIJOINT MOVEMENT STRATEGIES BASED ON BIOMECHANICAL CONSTRAINTS PROGRESS IN BRAIN RESEARCH Kuo, A. D., Zajac, F. E. 1993; 97: 349-358

    Abstract

    We developed a theoretical framework for studying coordination strategies in standing posture. The framework consists of a musculoskeletal model of the human lower extremity in the sagittal plane and a technique to visualize, geometrically, how constraints internal and external to the body affect movement. The set of all feasible accelerations (i.e., the "feasible acceleration set" or FAS) that muscles can induce at positions near upright were calculated. We found that musculoskeletal mechanics dictate that independent control of joints is relatively difficult to achieve. When muscle activations are constrained so the knees stay straight, to approximate the typical postural response to perturbation, the corresponding subset of the feasible acceleration set greatly favors a combination of ankle and hip movement in the ratio 1:3 (called the "hip strategy"). Independent control of these two joints remains difficult to achieve. When near the boundary of instability, the orientation and shape of this subset show that the movement strategy necessary to maintain stability, without taking a step, is quite restricted. Hypothesizing that regulation of center-of-mass position is crucial to maintaining balance, we examined the feasible set of center-of-mass accelerations. When the knees must be kept straight, the acceleration of the center of mass is severely limited vertically, but not horizontally. We also found that the "ankle strategy", involving rotation about the ankles only, requires more muscle activation than the "hip strategy" for a given amount of horizontal acceleration. Our model therefore predicts that the hip strategy is most effective at controlling the center of mass with minimal muscle activation ("neural effort").

    View details for Web of Science ID A1993LZ35700039

    View details for PubMedID 8234760

  • A BIOMECHANICAL ANALYSIS OF MUSCLE STRENGTH AS A LIMITING FACTOR IN STANDING POSTURE JOURNAL OF BIOMECHANICS Kuo, A. D., Zajac, F. E. 1993; 26: 137-150

    Abstract

    We developed a method for studying muscular coordination and strength in multijoint movements and have applied it to standing posture. The method is based on a musculoskeletal model of the human lower extremity in the sagittal plane and a technique to visualize, geometrically, how constraints internal and external to the body affect movement. We developed an algorithm to calculate the set of all feasible accelerations (i.e., the 'feasible acceleration set', or FAS) that muscles can induce. For the ankle, knee, and hip joints in the sagittal plane, this set is a polyhedron in three dimensions. Using the volume of the FAS as an indicator of overall mobility, we found that strengthening muscles on the posterior side (as opposed to the anterior) of the body would cause greater increases in mobility. Employing the experimental observations of others, we also found that acceleration constraints greatly reduce the range of feasible accelerations. We then defined a set of four basic acceleration vectors which, when used in various combinations, can produce the repertoire of postural movements. We used linear programming to find the maximum magnitudes of these vectors, and the sensitivity of these magnitudes to muscle strength, thereby delineating those muscles which, if strengthened, would cause the greatest increase in the body's ability to generate the basic acceleration vectors. For our particular model, those muscle groups were found to be hamstrings, tibialis anterior, rectus femoris, and gastrocnemius. These muscle groups would be of great importance in cases involving severely reduced muscle strength. This methodology may therefore be useful for purposes such as design of functional electrical stimulation controllers or exercises for persons at risk for falling.

    View details for Web of Science ID A1993LB36700012

    View details for PubMedID 8505348

  • MUSCLE COORDINATION OF MOVEMENT - A PERSPECTIVE JOURNAL OF BIOMECHANICS Zajac, F. E. 1993; 26: 109-124

    Abstract

    Multijoint movement requires the coordination of many muscles. Because multijoint movement is complex, kinesiological data must be analyzed and interpreted in the context of forward dynamical models rich enough to study coordination; otherwise, principles will remain elusive. The complexity arises because a muscle acts to accelerate all joints and segments, even joints it does not span and segments to which it does not attach. A biarticular muscle can even act to accelerate one of the joints it spans opposite to its anatomical classification. For example, gastrocnemius may act to accelerate the knee into extension during upright standing. One powerful forward dynamical modeling method to study muscle coordination is optimal control theory because simulations of movement can be produced. These simulations can either attempt to replicate experimental data, without hypothesizing the purpose of the motor task, or otherwise generate muscle and movement trajectories that best accomplish the hypothesized task. Application of the theory to the study of maximum-height jumping has provided insight into the biomechanical principles of jumping, such as: (i) jump height is more sensitive to muscle strength than to muscle speed, and insensitive to musculotendon compliance; (ii) uniarticular muscles generate the propulsive energy and biarticular muscles fine-tune the coordination; and (iii) countermovement is often desirable, even in squat jumps, because it seems both to prolong the duration of upwards propulsion, and to give muscles time to develop force so the body can move upwards initially with high acceleration. The effort necessary to develop forward dynamical models has been so high, however, that model-generated data of jumping or any other task are meager. An interactive computer workstation environment is proposed whereby users can develop neuromusculoskeletal control models, generate simulations of motor tasks, and display both kinesiological and modeling data more easily (e.g., animations). By studying a variety of motor tasks well, each within a theoretical framework, hopefully muscle coordination principles will soon emerge.

    View details for Web of Science ID A1993LB36700010

    View details for PubMedID 8505346

  • WHAT IS THE NATURE OF THE FEEDFORWARD COMPONENT IN MOTOR CONTROL BEHAVIORAL AND BRAIN SCIENCES Kuo, A. D., Zajac, F. E. 1992; 15 (4): 767-767
  • FORCE-GENERATING AND MOMENT-GENERATING CAPACITY OF LOWER-EXTREMITY MUSCLES BEFORE AND AFTER TENDON LENGTHENING CLINICAL ORTHOPAEDICS AND RELATED RESEARCH Delp, S. L., Zajac, F. E. 1992: 247-259
  • How musculotendon architecture and joint geometry affect the capacity of muscles to move and exert force on objects: a review with application to arm and forearm tendon transfer design. journal of hand surgery Zajac, F. E. 1992; 17 (5): 799-804

    Abstract

    This commentary reviews musculotendon architecture and the relation between architectural parameters and the force, speed, and excursion capacity of musculotendon units. It is hoped that this review will help provide the framework within which to appreciate the importance of the data presented by Lieber et al. Muscle fiber pennation hardly affects musculotendon output of forearm and hand muscles. Instead, physiologic cross-sectional area and muscle fiber length affect force capacity and speed and excursion capacity, respectively. How muscles with equal mass can have different force, speed, and excursion capacities is explained. Since the moment arm of a muscle (the shortest distance from the musculotendon unit to the joint center of rotation) transforms muscle output into musculotendon output, it is shown why the capacity for a muscle to exert force on an object, as during grasping, is directly proportional to its moment arm and why the range of joint movement and speed over which muscles exert force is inversely proportional to the moment arm. Finally, tendon, being not stiff in forearm and hand musculotendon units, also affects their output. Criteria are given for designing tendon transfer reconstructions from architectural data and moment arm data to best replicate the biomechanical function of the replaced muscle. To have the same capacity for imparting movement to objects and exerting force on them, the donor muscle should have the same moment arm/physiologic cross-sectional area product, the same fiber length/moment arm ratio, and the same tendon length/muscle fiber length ratio as the replaced muscle.

    View details for PubMedID 1401783

  • HOW MUSCULOTENDON ARCHITECTURE AND JOINT GEOMETRY AFFECT THE CAPACITY OF MUSCLES TO MOVE AND EXERT FORCE ON OBJECTS - A REVIEW WITH APPLICATION TO ARM AND FOREARM TENDON TRANSFER DESIGN JOURNAL OF HAND SURGERY-AMERICAN VOLUME Zajac, F. E. 1992; 17A (5): 799-804
  • AN ANALYSIS OF BIOMECHANICAL CONSTRAINTS ON THE COORDINATION OF STANDING POSTURE Kuo, A. D., Zajac, F. E. UNIV OREGONBOOKS. 1992: A344-A347
  • OPTIMAL MUSCULAR COORDINATION STRATEGIES FOR JUMPING JOURNAL OF BIOMECHANICS Pandy, M. G., Zajac, F. E. 1991; 24 (1): 1-10

    Abstract

    This paper presents a detailed analysis of an optimal control solution to a maximum height squat jump, based upon how muscles accelerate and contribute power to the body segments during the ground contact phase of jumping. Quantitative comparisons of model and experimental results expose a proximal-to-distal sequence of muscle activation (i.e. from hip to knee to ankle). We found that the contribution of muscles dominates both the angular acceleration and the instantaneous power of the segments. However, the contributions of gravity and segmental motion are insignificant, except the latter become important during the final 10% of the jump. Vasti and gluteus maximus muscles are the major energy producers of the lower extremity. These muscles are the prime movers of the lower extremity because they dominate the angular acceleration of the hip toward extension and the instantaneous power of the trunk. In contrast, the ankle plantarflexors (soleus, gastrocnemius, and the other plantarflexors) dominate the total energy of the thigh, though these muscles also contribute appreciably to trunk power during the final 20% of the jump. Therefore, the contribution of these muscles to overall jumping performance cannot be neglected. We found that the biarticular gastrocnemius increases jump height (i.e. the net vertical displacement of the center of mass of the body from standing) by as much as 25%. However, this increase is not due to any unique biarticular action (e.g. proximal-to-distal power transfer from the knee to the ankle), since jumping performance is similar when gastrocnemius is replaced with a uniarticular ankle plantarflexor.

    View details for Web of Science ID A1991FC28500001

    View details for PubMedID 2026629

  • RESTORING UNASSISTED NATURAL GAIT TO PARAPLEGICS VIA FUNCTIONAL NEUROMUSCULAR STIMULATION - A COMPUTER-SIMULATION STUDY IEEE TRANSACTIONS ON BIOMEDICAL ENGINEERING Yamaguchi, G. T., Zajac, F. E. 1990; 37 (9): 886-902

    Abstract

    Functional neuromuscular stimulation (FNS) of paralyzed muscles has enabled spinal-cord-injured patients to regain a semblance of lower-extremity control, for example to ambulate while relying heavily on the use of walkers. Given the limitations of FNS, specifically low muscle strengths, high rates of fatigue, and a limited ability to modulate muscle excitations, it remains unclear, however, whether FNS can be developed as a practical means to control the lower extremity musculature to restore aesthetic, unsupported gait to paraplegics. A computer simulation of FNS-assisted bipedal gait shows that it is difficult, but possible to attain undisturbed, level gait at normal speeds provided the electrically-stimulated ankle plantarflexors exhibit either near-normal strengths or are augmented by an orthosis, and at least seven muscle-groups in each leg are stimulated. A combination of dynamic programming and an open-loop, trial-and-error adjustment process was used to find a suboptimal set of discretely-varying muscle stimulation patterns needed for a 3-D, 8 degree-of-freedom dynamic model to sustain a step. An ankle-foot orthosis was found to be especially useful, as it helped to stabilize the stance leg and simplified the task of controlling the foot during swing. It is believed that the process of simulating natural gait with this model will serve to highlight difficulties to be expected during laboratory and clinical trials.

    View details for Web of Science ID A1990EB52600008

    View details for PubMedID 2227975

  • AN INTERACTIVE GRAPHICS-BASED MODEL OF THE LOWER-EXTREMITY TO STUDY ORTHOPEDIC SURGICAL-PROCEDURES IEEE TRANSACTIONS ON BIOMEDICAL ENGINEERING Delp, S. L., Loan, J. P., HOY, M. G., Zajac, F. E., Topp, E. L., Rosen, J. M. 1990; 37 (8): 757-767

    Abstract

    We have developed a model of the human lower extremity to study how surgical 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. We developed a graphical interface to the model that 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. Just as interactive graphics have enhanced engineering design and analysis, we have found that graphics-based musculoskeletal models are effective tools for designing and analyzing surgical procedures.

    View details for Web of Science ID A1990DV77000003

    View details for PubMedID 2210784

  • BIOMECHANICAL ANALYSIS OF THE CHIARI PELVIC OSTEOTOMY - PRESERVING HIP ABDUCTOR STRENGTH CLINICAL ORTHOPAEDICS AND RELATED RESEARCH Delp, S. L., BLECK, E. E., Zajac, F. E., Bollini, G. 1990: 189-198

    Abstract

    Although the Chiari osteotomy is usually effective in reducing pain, many patients are left with a long-term limp. The postoperative limp can at times be caused by hip abductors that have strength insufficient to counteract the torque from body weight during single-leg stance. To study how the surgical technique affects the hip abductor muscles, a biomechanical model was developed that computes the postsurgery pelvic geometry and the resulting hip abductor torque given three surgical parameters: angulation of the osteotomy, distance of medical displacement, and angle of internal rotation. The computer simulations of the Chiari osteotomy showed that some sets of surgical parameters conserve abductor torque while others greatly reduce it. Simulated surgeries with high angulation and large medial displacement reduce gluteus medius abductor torque by up to 65%. Therefore, this combination of surgical parameters may account for some instances of the postoperative limp. In the model, high angulation reduces the length of the gluteus medius and is the primary cause of reduced abductor strength. Simulated horizontal osteotomies (0 degrees to 10 degrees) were found to best conserve both muscle length and abductor torque.

    View details for Web of Science ID A1990DB35400027

    View details for PubMedID 2323130

  • AN OPTIMAL-CONTROL MODEL FOR MAXIMUM-HEIGHT HUMAN JUMPING JOURNAL OF BIOMECHANICS Pandy, M. G., Zajac, F. E., Sim, E., Levine, W. S. 1990; 23 (12): 1185-1198

    Abstract

    To understand how intermuscular control, inertial interactions among body segments, and musculotendon dynamics coordinate human movement, we have chosen to study maximum-height jumping. Because this activity presents a relatively unambiguous performance criterion, it fits well into the framework of optimal control theory. The human body is modeled as a four-segment, planar, articulated linkage, with adjacent links joined together by frictionless revolutes. Driving the skeletal system are eight musculotendon actuators, each muscle modeled as a three-element, lumped-parameter entity, in series with tendon. Tendon is assumed to be elastic, and its properties are defined by a stress-strain curve. The mechanical behavior of muscle is described by a Hill-type contractile element, including both series and parallel elasticity. Driving the musculotendon model is a first-order representation of excitation-contraction (activation) dynamics. The optimal control problem is to maximize the height reached by the center of mass of the body subject to body-segmental, musculotendon, and activation dynamics, a zero vertical ground reaction force at lift-off, and constraints which limit the magnitude of the incoming neural control signals to lie between zero (no excitation) and one (full excitation). A computational solution to this problem was found on the basis of a Mayne-Polak dynamic optimization algorithm. Qualitative comparisons between the predictions of the model and previously reported experimental findings indicate that the model reproduces the major features of a maximum-height squat jump (i.e. limb-segmental angular displacements, vertical and horizontal ground reaction forces, sequence of muscular activity, overall jump height, and final lift-off time).

    View details for Web of Science ID A1990EV47500001

    View details for PubMedID 2292598

  • A MUSCULOSKELETAL MODEL OF THE HUMAN LOWER-EXTREMITY - THE EFFECT OF MUSCLE, TENDON, AND MOMENT ARM ON THE MOMENT ANGLE RELATIONSHIP OF MUSCULOTENDON ACTUATORS AT THE HIP, KNEE, AND ANKLE JOURNAL OF BIOMECHANICS HOY, M. G., Zajac, F. E., Gordon, M. E. 1990; 23 (2): 157-169

    Abstract

    We have developed a musculoskeletal model of the human lower extremity for computer simulation studies of musculotendon function and muscle coordination during movement. This model incorporates the salient features of muscle and tendon, specifies the musculoskeletal geometry and musculotendon parameters of 18 musculotendon actuators, and defines the active isometric moment of these actuators about the hip, knee, and ankle joints in the sagittal plane. We found that tendon slack length, optimal muscle-fiber length, and moment arm are different for each actuator, thus each actuator develops peak isometric moment at a different joint angle. The joint angle where an actuator produces peak moment does not necessarily coincide with the joint angle where: (1) muscle force peaks, (2) moment arm peaks, or (3) the in vivo moment developed by maximum voluntary contractions peaks. We conclude that when tendon is neglected in analyses of musculotendon force or moment about joints, erroneous predictions of human musculotendon function may be stated, not only in static situations as studied here, but during movement as well.

    View details for Web of Science ID A1990CU01000005

    View details for PubMedID 2312520

  • PARAPLEGIC STANDING CONTROLLED BY FUNCTIONAL NEUROMUSCULAR STIMULATION .2. COMPUTER-SIMULATION STUDIES IEEE TRANSACTIONS ON BIOMEDICAL ENGINEERING Khang, G., Zajac, F. E. 1989; 36 (9): 885-894

    Abstract

    We simulated two types of body motion. First, the body position is assumed to be initially perturbed from the upright position, and all muscles are assumed inactive at the initial position. The control law developed in the preceding paper drives the body segments to the standing position. Arm movements are then applied to the body to investigate how performance is affected by an external disturbance. Simulated body motion indicated that the current output-feedback control law functions well. The body can recover upright posture from a highly flexed position, and the controller can then maintain the body near the vertical during arm movements. The simulation results showed three consistent activation patterns based on energy minimization: 1) no antagonistic muscle pairs are coactivated, 2) strong muscles are recruited before weak ones, and 3) fast muscles are recruited before slow ones. The reason for the second and third observations is that energy liberation rate depends heavily on the relative amount of muscle activation. Since the current control law requires muscles to generate specific joint torques at a prescribed time, strong muscles do not have to be activated as much as weak ones, and recruiting a fast muscle at low activation level consumes less energy than recruiting a slow one at high activation level. Although the output-feedback control law functions well according to our simulation results, the static optimization process would, in practice, take too much computational time to make it practical. Based on the consistent activation patterns found in our simulations, we therefore developed a simpler (suboptimal) activation-distribution scheme that takes much less time and still gives nearly identical performance.

    View details for Web of Science ID A1989AN08200002

    View details for PubMedID 2789178

  • PARAPLEGIC STANDING CONTROLLED BY FUNCTIONAL NEUROMUSCULAR STIMULATION .1. COMPUTER-MODEL AND CONTROL-SYSTEM DESIGN IEEE TRANSACTIONS ON BIOMEDICAL ENGINEERING Khang, G., Zajac, F. E. 1989; 36 (9): 873-884

    Abstract

    We have developed a planar computer model to investigate paraplegic standing induced by functional neuromuscular stimulation. The model consists of nonlinear musculotendon dynamics (pulse train activation dynamics and musculotendon actuator dynamics), nonlinear body-segmental dynamics, and a linear output-feedback control law. The model of activation dynamics is an analytic expression that characterizes the relation between the stimulus parameters (pulse width and interpulse interval) and the muscle activation. Hill's classic two-element muscle model was modified into a musculotendon actuator model in order to account for the effects of submaximal activation and tendon elasticity on development of force by the actuator. The three body-segmental, multijoint model accounts for the anterior-posterior movements of the head and trunk, the thigh, and the shank. We modeled arm movement as an external disturbance and imposed the disturbance to the body-segmental dynamics by means of a quasistatic analysis. Linearization, and at times linear approximation of the computer model, enabled us to compute a constant, linear feedback-gain matrix, whose output is the net activation needed by a dynamical joint-torque actuator. Motivated by an assumption that minimization of energy expenditure lessens muscle fatigue, we developed an algorithm that then computes how to distribute the net activation among all the muscles crossing the joint. In part II, the combined feedback control strategy is applied to the nonlinear model of musculotendon and body-segmental dynamics to study how well the body ought to maintain balance should the feedback control strategy be employed.

    View details for Web of Science ID A1989AN08200001

    View details for PubMedID 2789177

  • MUSCLE AND TENDON - PROPERTIES, MODELS, SCALING, AND APPLICATION TO BIOMECHANICS AND MOTOR CONTROL CRITICAL REVIEWS IN BIOMEDICAL ENGINEERING Zajac, F. E. 1989; 17 (4): 359-411

    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.

    View details for Web of Science ID A1989AT16800002

    View details for PubMedID 2676342

  • A PLANAR MODEL OF THE KNEE-JOINT TO CHARACTERIZE THE KNEE EXTENSOR MECHANISM JOURNAL OF BIOMECHANICS Yamaguchi, G. T., Zajac, F. E. 1989; 22 (1): 1-10

    Abstract

    A simple planar static model of the knee joint was developed to calculate effective moment arms for the quadriceps muscle. A pathway for the instantaneous center of rotation was chosen that gives realistic orientations of the femur relative to the tibia. Using the model, nonlinear force and moment equilibrium equations were solved at one degree increments for knee flexion angles from 0 (full extension) to 90 degrees, yielding patellar orientation, patellofemoral contact force and patellar ligament force and direction with respect to both the tibial insertion point and the tibiofemoral contact point. The computer-derived results from this two-dimensional model agree with results from more complex models developed previously from experimentally obtained data. Due to our model's simplicity, however, the operation of the patellar mechanism as a lever as well as a spacer is clearly illustrated. Specifically, the thickness of the patella was found to increase the effective moment arm significantly only at flexions below 35 degrees even though the actual moment arm exhibited an increase throughout the flexion range. Lengthening either the patella or the patellar ligament altered the force transmitted from the quadriceps to the patellar ligament, significantly increasing the effective moment arm at flexions greater than 25 degrees. We conclude that the levering action of the patella is an essential mechanism of knee joint operation at moderate to high flexion angles.

    View details for Web of Science ID A1989R773500001

    View details for PubMedID 2914967

  • DETERMINING MUSCLES FORCE AND ACTION IN MULTI-ARTICULAR MOVEMENT EXERCISE AND SPORT SCIENCES REVIEWS/SERIES Zajac, F. E., Gordon, M. E. 1989; 17: 187-230

    View details for Web of Science ID A1989AB14500006

    View details for PubMedID 2676547

  • A MECHANICALLY DECOUPLED 2 FORCE COMPONENT BICYCLE PEDAL DYNAMOMETER JOURNAL OF BIOMECHANICS NEWMILLER, J., Hull, M. L., Zajac, F. E. 1988; 21 (5): 375-?

    Abstract

    A design is presented for a bicycle pedal dynamometer that measures both normal and tangential forces (i.e. driving forces). Mechanical decoupling is used to reduce the cross-sensitivity of the dynamometer to loads doing no work to propel the bicycle. This obviates the need to measure all six loads for accurate data reduction. A compact strain ring is the transducer element, and a monolithic design eliminates mechanical hysteresis between the strain ring and the dynamometer frame. The angular orientation of the dynamometer with respect to the crank arm is determined with a continuous-rotation potentiometer. Design criteria and design implementation are discussed, sample data are presented, and the performance of the dynamometer is evaluated.

    View details for Web of Science ID A1988P366800005

    View details for PubMedID 3417690

  • THIGH MUSCLE-ACTIVITY DURING MAXIMUM-HEIGHT JUMPS BY CATS JOURNAL OF NEUROPHYSIOLOGY Zajac, F. E. 1985; 53 (4): 979-994

    Abstract

    Cats were trained to jump from a force plate and touch a cotton ball suspended as high as 1.6 m. Force-plate reaction forces and double-joint hamstring muscle activity observed early in propulsion varied from one maximal jump to another. This variability is consistent with theory (31, 32, 42); that is, different coordination strategies can be implemented prior to the heels losing contact with the force plate (heel-off). Single-joint hip extensor and double-joint posterior thigh (hip extensor-knee flexor) muscles were coactivated prior to heel-off. This coactivation is probably partially responsible for the observed backward rotation of the trunk. Forepaws, observed to contact the force plate prior to heel-off, probably assist the hindlimbs in generating trunk rotation. Both single-joint knee extensor and hip extensor muscles exhibited greatest activation between heel-off and body lift-off. Single-joint flexor muscles were inactive throughout propulsion. Double-joint posterior thigh muscles were deactivated at heel-off and remained inactivated until lift-off. These observations agree with the theoretical notion that muscles should be either fully activated, inactivated, or switched from one extreme to the other (i.e., bang-bang control) between heel-off and body lift-off (31, 32, 42, 44). All seven muscles studied shortened while activated. Using computations based on muscle geometry, fiber architecture, and joint angle trajectories, I propose that sarcomeres shorten along the flat and ascending regions of the force-length curve. De- and inactivation of double-joint posterior thigh muscles between heel-off and lift-off coincided with muscle stretch. The reason for inactivation of these muscles is that the negative work that would have been generated had these muscles stayed activated would have hindered propulsion. Contractions preceded by active stretch were not observed. Enhancement of positive work by previous storage of energy in elastic musculotendinous structures is thus not used by cat thigh musculature in jumps starting from the squat. Adductor femoris, semimembranosus anterior, and biceps femoris anterior muscles were activated synergistically as one group yet differently from the synergistic activation of gracilis, semitendinosus, and biceps femoris posterior muscles. The separation of these muscles into two groups based on their activation patterns during jumping is compatible with the classification of these muscles into hip extensor and knee flexor muscle groups, respectively, based on their reflex patterns (37), spinal cord reflex connectivity (18, 30), and firing patterns during locomotion (20).(ABSTRACT TRUNCATED AT 400 WORDS)

    View details for Web of Science ID A1985AGF8400008

    View details for PubMedID 3998801

  • RELATIONSHIP AMONG RECRUITMENT ORDER, AXONAL CONDUCTION-VELOCITY, AND MUSCLE-UNIT PROPERTIES OF TYPE-IDENTIFIED MOTOR UNITS IN CAT PLANTARIS MUSCLE JOURNAL OF NEUROPHYSIOLOGY Zajac, F. E., Faden, J. S. 1985; 53 (5): 1303-1322

    Abstract

    A strict interpretation of the size-principle hypothesis (37, 39-41) is that a muscle's motor units should be recruited in an ascending order according to both the size of their motoneurons and the size of their innervated muscle units (for reviews see Refs. 9, 39, 73). Studies of large mixed muscles in the cat hindlimb, however, have shown that motor axonal conduction velocity and tetanic tension, which are frequently considered indices of motoneuron and muscle-unit size, respectively, are uncorrelated in the fast-twitch (type F) motor-unit subpopulation (12, 13, 23, 24, 30, 32, 63, 71, 79). Attempting to focus on type F units, we compared the recruitment order of 42 pairs of cat plantaris (PL) motor units with both axonal conduction velocity and tetanic tension as well as with other muscle-unit properties. Single PL alpha-motor axons were functionally isolated in intact L7 ventral root filaments of decerebrate cats. Tension responses produced by stimulating each isolated motor axon were used to find the tetanic tension of the muscle unit and to classify the unit (12) as either type S (slow twitch, fatigue resistant), type FR (fast twitch, fatigue resistant), type FI (fast twitch, intermediate fatigability), or type FF (fast twitch, highly fatigable). Conduction velocity of each isolated axon was computed from measurements of axonal conduction time and length. The axon's reflex discharges were recorded from the proximal end of the cut filament and compared with the discharges of another PL axon residing in a different, previously cut filament of the same cat. The recruitment order of each motor-unit pair studied was found during reflexes elicited by homonymous muscle stretch, tendon taps, or single shocks at group I intensity to the PL nerve. If either axon of the pair failed to discharge, as often was the case with the high-threshold type F units, the monosynaptic reflex was facilitated by a 500-pps conditioning train applied proximal to a complete reversible cooling block of the PL nerve. In all 42 pairs studied, the weaker motor unit had the lower functional threshold for recruitment. Recruitment also invariably followed the order S greater than FR greater than FI greater than FF units. The motor unit of a pair with the higher resistance to fatigue thus always had the lower functional threshold. In 21 of the 22 pairs containing at least one type S motor unit, the unit with the slower-conducting motor axon had the lower functional threshold for recruitment.(ABSTRACT TRUNCATED AT 400 WORDS)

    View details for Web of Science ID A1985AHM3600010

    View details for PubMedID 2987433

  • DEPENDENCE OF JUMPING PERFORMANCE ON MUSCLE PROPERTIES WHEN HUMANS USE ONLY CALF MUSCLES FOR PROPULSION JOURNAL OF BIOMECHANICS Zajac, F. E., WICKE, R. W., Levine, W. S. 1984; 17 (7): 513-523

    Abstract

    Using optimal control techniques, maximum height jumps were simulated for humans who held their body rigid except for the ankle. Three dynamic models of ankle torque generation based on known calf muscle properties were used. Force and kinematics obtained from the simulations using nominal and perturbed parameters were compared with data obtained from humans who had performed this type of jump. One torque model incorporated the series elastic, force-length and force-velocity properties of muscle. Our results suggest that higher jumps would be achieved by those who have the most compliant and fastest contracting muscles. It was also found that height attained depended much more on the ability of muscles to generate isometric force at long lengths than at short lengths. Studies of forward and strictly vertical jumps using similar computer methods suggest that for any maximal jump the optimal strategy is first to achieve a unique state (position, velocity and acceleration) with the feet flat on the ground, and then to maximally activate one's calf muscles until lift-off.

    View details for Web of Science ID A1984TG34400006

    View details for PubMedID 6480625

  • ANKLE CONTROLS THAT PRODUCE A MAXIMAL VERTICAL JUMP WHEN OTHER JOINTS ARE LOCKED IEEE TRANSACTIONS ON AUTOMATIC CONTROL Levine, W. S., Zajac, F. E., BELZER, M. R., ZOMLEFER, M. R. 1983; 28 (11): 1008-1016