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Biomedical subjects

F E Zajac

Publications and source records attributed to F E Zajac.

At least 19 recordsLinked to original sources
PubMed1994

Compensating for changes in muscle length in total hip arthroplasty. Effects on the moment generating capacity of the muscles.

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.

Adaptation, Physiological↗
PubMed1993

Human standing posture: multi-joint movement strategies based on biomechanical constraints.

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").

Ankle Joint↗
PubMed1992

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.

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.

Arm↗
PubMed1992

Force- and moment-generating capacity of lower-extremity muscles before and after tendon lengthening.

A computer model of the human lower extremity was developed to study how surgical lengthening of tendon affects the force- and moment-generating capacity of the muscles. This model computes the maximum isometric force and the resulting joint moments that each muscle-tendon complex can develop at any body position. Tendon lengthenings were simulated by increasing the tendon length of each muscle-tendon complex and computing the change in the maximum isometric muscle force and joint moments at a specific body position. These simulations showed that the forces and moments developed by the ankle plantarflexors are extremely sensitive to changes in tendon length. For example, at a body position corresponding to the midstance phase of gait, the maximum isometric moment generated by soleus decreased 30% with a 1-cm increase in tendon length, and 85% with a 2-cm increase in tendon length. In contrast, 1- and 2-cm increases in iliopsoas tendon length decreased its hip flexion moment by only 4% and 9%, respectively. This article quantifies the sensitivity of muscle force and joint moments to changes in tendon length for the most commonly lengthened lower-extremity tendons. These results indicate how much each of these tendons should be lengthened to achieve an incremental decrease in muscle force or joint moment.

Ankle Joint↗
PubMed1991

Optimal muscular coordination strategies for jumping.

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.

Adult↗
PubMed1990

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.

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.

Ankle Joint↗
PubMed1990

An optimal control model for maximum-height human jumping.

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).

Biomechanical Phenomena↗
PubMed1990

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

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.

Biomechanical Phenomena↗
PubMed1990

Restoring unassisted natural gait to paraplegics via functional neuromuscular stimulation: a computer simulation study.

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.

Computer Simulation↗
PubMed1990

Biomechanical analysis of the Chiari pelvic osteotomy. Preserving hip abductor strength.

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.

Biomechanical Phenomena↗
PubMed1989

A planar model of the knee joint to characterize the knee extensor mechanism.

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.

Biomechanical Phenomena↗
PubMed1989

Paraplegic standing controlled by functional neuromuscular stimulation: Part I--computer model and control-system design.

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.

Biomechanical Phenomena↗
PubMed1989

Paraplegic standing controlled by functional neuromuscular stimulation: Part II--Computer simulation studies.

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.

Biomechanical Phenomena↗
PubMed1989

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

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.

Biomechanical Phenomena↗
PubMed1988

A mechanically decoupled two force component bicycle pedal dynamometer.

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.

Biomechanical Phenomena↗
PubMed1985

Thigh muscle activity during maximum-height jumps by cats.

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)

Animals↗
PubMed1985

Relationship among recruitment order, axonal conduction velocity, and muscle-unit properties of type-identified motor units in cat plantaris muscle.

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)

Animals↗