Series Elastic Stiffness Research Articles

The force-length relation of the young adult human tibialis anterior.

Knowledge of the muscle's lengths at which maximum active isometric force is attained is important for predicting forces during movement. However, there is limited information about the in vivo force-length properties of a human muscle that plays crucial roles during locomotion; the tibialis anterior (TA). We therefore aimed to estimate TA's force-length relation from dorsiflexor torque-angle curves constructed from eight women and eight men. Participants performed maximal voluntary fixed-end contractions with their right ankle dorsiflexors from 0° to 30° plantar flexion. Muscle fascicle lengths were estimated from B-mode ultrasound images, and net ankle joint torques were measured using dynamometry. Fascicle forces were estimated by dividing maximal active torques by literature-derived, angle-specific tendon moment arm lengths while assuming a fixed 50% force contribution of TA to the total dorsiflexor force and accounting for fascicle angles. Maximal active torques were higher at 15° than 20° and 30° plantar flexion (2.4-6.4 Nm, p≤0.012), whereas maximal active TA fascicle forces were higher at 15° than 0°, 20° and 30° plantar flexion (25-61 N, p≤0.042), but not different between 15° and 10° plantar flexion (15 N, p=0.277). TA fascicle shortening magnitudes during fixed-end contractions were larger at 15° than 30° plantar flexion (3.9 mm, p=0.012), but less at 15° than 0° plantar flexion (-2.4 mm, p=0.001), with no significant differences (≤0.7 mm, p=0.871) between TA's superficial and deep muscle compartments. Series elastic element stiffness was lowest and highest at lengths 5% shorter and 5% longer than optimum fascicle length, respectively (-30 and 15 N/mm, p≤0.003). TA produced its maximum active force at 10-15° plantar flexion, and its normalized force-length relation had ascending and descending limbs that agreed with a simple scaled sarcomere model when active fascicle lengths from within TA's superficial or deep muscle compartment were considered. These findings can be used to inform the properties of the contractile and series elastic elements of Hill-type muscle models.

Mechanical design and preliminary tests of VS-AnkleExo

Exoskeletons and wearable robotic systems have advanced substantially over the last decade for gait assistance, rehabilitation and load-carrying purposes. Currently, there are commercially available devices with stiff actuators. However, these actuators cannot adapt to their unpredictable environments. Thus, compliant actuators like series elastic and variable stiffness actuators have been implemented in exoskeletons and active orthoses. This paper presents a novel design and experimental characterization of a compliant actuator with adjustable stiffness for a lower limb wearable ankle robot (VS-AnkleExo). The proposed actuator is designed to mimic the behavior of biological ankle and maximizes the compliance between user and robot during a gait cycle. The adjustable stiffness of actuator is achieved through a controllable transmission ratio mechanism. Both transparency and tracking performance experiments are performed to demonstrate reduced the user–robot interaction force and improved the tracking performance of the proposed actuator, respectively. Experimental results showed that interaction forces between the user and robot are minimized in the transparency experiments, while the actuators proposed are able to track the given torque signals at various frequencies in the tracking experiments.

Determinants of aponeurosis shape change during muscle contraction

Aponeuroses are sheet-like elastic tendon structures that cover a portion of the muscle belly and act as insertion sites for muscle fibers while free tendons connect muscles to bones. During shortening contractions, free tendons are loaded in tension and lengthen due to the force acting longitudinally along the muscle׳s line of action. In contrast, aponeuroses increase in length and width, suggesting that aponeuroses are loaded in directions along and orthogonal to the muscle׳s line of action. Because muscle fibers are isovolumetric, they must expand radially as they shorten, potentially generating a force that increases aponeurosis width. We hypothesized that increases in aponeurosis width result from radial expansion of shortening muscle fibers. We tested this hypothesis by combining in situ muscle-tendon measurements with high-speed biplanar fluoroscopy measurements of the turkey׳s lateral gastrocnemius (n=6) at varying levels of isotonic muscle contractions. The change in aponeurosis width during periods of constant force depended on both the amount of muscle shortening and the magnitude of force production. At low to intermediate forces, aponeurosis width increased in direct proportion to fiber shortening. At high forces, aponeurosis width increased to a lesser extent or in some cases, decreased slightly during fiber shortening. Our results demonstrate that forces generated from radial expansion of shortening muscle fibers tend to drive increases in aponeurosis width, whereas longitudinal forces tend to decrease aponeurosis width. Ultimately, it is these two opposing forces that drive changes in aponeurosis width and alter series elastic stiffness during a muscle contraction.

Mechanical Design and Control Method for SEA and VSA-based Exoskeleton Devices for Elbow Joint Rehabilitation

Robot-aided rehabilitation training allows patients to receive a more effective and stable rehabilitation process. Exoskeleton devices are superior to the endpoint manipulators and cable suspension devices on the aspect that they can train and measure the angle and torque on each joint of impaired limbs. For robotic devices, physical safety should be guaranteed since the robot-assisted training relies on high human-robot interaction especially for exoskeletons. Traditional robotic devices mainly introduce the stiffness actuator, while the high levels of kinetic energy of robots will induce unsafe. For guaranteeing the safety of patients, compliant actuator such as the series elastic actuator (SEA) and variable stiffness actuator (VSA) design has been involved into these devices. The added compliance can make robots intrinsically safe and realize the energy-efficient actuation. The VSA used a variable stiffness elastic component instead of a constant stiffness elastic component, and VSAs is deemed to a kind of SEAs. A closed-loop interaction control method was used for SEAs to generate low impedance. By comparison, the VSA realizes adaptable compliance properties with inherent mechanical design. Thus, for SEAs, an additional mechanism is needed to adjust the output stiffness. In this paper, two kinds of compliant exoskeleton devices designed with the SEA and VSA respectively are introduced. The mechanical design and control method for each device are introduced; especially the design for guaranteeing patients’ safety.

Neural representation of muscle dynamics in voluntary movement control

Several theories of motor control posit that the nervous system has access to a neural representation of muscle dynamics. Yet, this has not been tested experimentally. Should such a representation exist, it was hypothesized that subjects who learned to control a virtual limb using virtual muscles would improve performance faster and show greater generalization than those who learned with a less dynamically complex virtual force generator. Healthy adults practiced using their biceps brachii activity to move a myoelectrically controlled virtual limb from rest to a standard target position with maximum speed and accuracy. Throughout practice, generalization was assessed with untrained target trials and sensitivity to actuator dynamics was probed by unexpected actuator model switches. In a muscle model subject group (n = 10), the biceps electromyographic signal activated a virtual muscle that pulled on the virtual limb with a force governed by muscle dynamics, defined by a nonlinear force-length-velocity relation and series elastic stiffness. A force generator group (n = 10) performed the same task, but the actuation force was a linear function of the biceps activation signal. Both groups made significant errors with unexpected actuator dynamics switches, supporting task sensitivity to actuator dynamics. The muscle model group improved performance as fast as the force generator group and showed greater generalization in early practice, despite using an actuator with more complex dynamics. These results are consistent with a preexisting neural representation of muscle dynamics, which may have offset any learning challenges associated with the more dynamically complex virtual muscle model.

Increased Residual Force Enhancement in Older Adults Is Associated with a Maintenance of Eccentric Strength

Despite an age-related loss of voluntary isometric and concentric strength, muscle strength is well maintained during lengthening muscle actions (i.e., eccentric strength) in old age. Additionally, in younger adults during lengthening of an activated skeletal muscle, the force level observed following the stretch is greater than the isometric force at the same muscle length. This feature is termed residual force enhancement (RFE) and is believed to be a combination of active and passive components of the contractile apparatus. The purpose of this study was to provide an initial assessment of RFE in older adults and utilize aging as a muscle model to explore RFE in a system in which isometric force production is compromised, but structural mechanisms of eccentric strength are well-maintained. Therefore, we hypothesised that older adults will experience greater RFE compared with young adults. Following a reference maximal voluntary isometric contraction (MVC) of the dorsiflexors in 10 young (26.1±2.7y) and 10 old (76.0±6.5y) men, an active stretch was performed at 15°/s over a 30° ankle joint excursion ending at the same muscle length as the reference MVCs (40° of plantar flexion). Any additional torque compared with the reference MVC therefore represented RFE. In older men RFE was ∼2.5 times greater compared to young. The passive component of force enhancement contributed ∼37% and ∼20% to total force enhancement, in old and young respectively. The positive association (R 2 = 0.57) between maintained eccentric strength in old age and RFE indicates age-related mechanisms responsible for the maintenance of eccentric strength likely contributed to the observed elevated RFE. Additionally, as indicated by the greater passive force enhancement, these mechanisms may be related to increased muscle series elastic stiffness in old age.

Differential adaptations during growth spurt and in young adult rat muscles

During the post-weaning growth and maturation period (25/90 days after birth), rat limb muscles are submitted to specific adaptations. Our aim was to characterize the mechanical properties of two muscles that are opposite in terms of fibre-type distribution, the soleus and the extensor digitorum longus (EDL) muscles of male Wistar rats. Results showed a fast-to-slow fibre-type transition in soleus while no modification in fibre-type distribution was observed in EDL. A growth-induced increase in muscle force was observed. Soleus underwent an increase in twitch kinetics, but EDL showed no modification. Resistance to fatigue was higher in 90-day-old soleus but not modified in the EDL. Surprisingly, analysis of maximal shortening velocity showed a decrease in both soleus and EDL. Finally, tension/extension curves indicated a growth-induced increase in series elastic stiffness in the two muscles. These results suggest that during this growth period, skeletal muscles are submitted to differential adaptations. Moreover, whereas adaptation of biomechanical properties observed can be explained partly by an adaptation of fibre profile in soleus, this is not the case for EDL. It is suggested that changes in muscle architecture, which are often disregarded, could explain some variations in mechanical properties, especially when muscles undergo an increase in both mass and length.

The inverted pendulum model of bipedal standing cannot be stabilized through direct feedback of force and contractile element length and velocity at realistic series elastic element stiffness

Control of bipedal standing is typically analyzed in the context of a single-segment inverted pendulum model. The stiffness K (SE) of the series elastic element that transmits the force generated by the contractile elements of the ankle plantarflexors to the skeletal system has been reported to be smaller in magnitude than the destabilizing gravitational stiffness K ( g ). In this study, we assess, in case K (SE) + K ( g ) < 0, if bipedal standing can be locally stable under direct feedback of contractile element length, contractile element velocity (both sensed by muscle spindles) and muscle force (sensed by Golgi tendon organs) to alpha-motoneuron activity. A theoretical analysis reveals that even though positive feedback of force may increase the stiffness of the muscle-tendon complex to values well over the destabilizing gravitational stiffness, dynamic instability makes it impossible to obtain locally stable standing under the conditions assumed.

The passive, human calf muscles in relation to standing: the short range stiffness lies in the contractile component.

Using short duration perturbations, previous attempts to measure the intrinsic ankle stiffness during human standing have revealed a substantial stabilizing contribution (65-90% normalized to load stiffness 'mgh'). Others regard this method as unsuitable for the low-frequency conditions of quiet standing and believe the passive contribution to be small (10-15%). This latter view, consistent with a linear Hill-type model, argues that during standing, the contractile portion of the muscle is much less stiff than the tendon. Here, for upright subjects, we settle this issue by measuring the stiffness of the contractile portion of the passive calf muscles using low-frequency ankle rotations. Using ultrasound we tracked the changes in muscle contractile length and partitioned the ankle rotation into contractile and extra-contractile (series elastic) portions. Small ankle rotations of 0.15 and 0.4 deg show a contractile to series elastic stiffness ratio (K(ce)/K(se)) of 12 +/- 9 and 6.3 +/- 10, respectively, with both elements displaying predominantly elastic behaviour. Larger, 7 deg rotations reveal the range of this ratio. It declines in a non-linear way from a high value (K(ce)/K(se) = 18 +/- 11) to a low value (K(ce)/K(se) = 1 +/- 0.4) as rotation increases from 0.1 to 7 deg. There is a marked transition at around 0.5 deg. The series elastic stiffness (K(se)/mgh) remains largely constant (77 +/- 13%) demonstrating the contractile component origin of passive, short range stiffness. The linear Hill-type model does not describe the range-related stiffness relevant to the progression from quiet standing to perturbed balance and movement and can lead to inaccurate predictions regarding human balance.

Is Achilles tendon compliance optimised for maximum muscle efficiency during locomotion?

Tendon elasticity is important for economical locomotion; however it is unknown whether tendon stiffness is appropriate to achieve an optimal efficiency in various muscles. Here we test the hypothesis that the Achilles tendon is of an appropriate stiffness to maximise medial gastrocnemius muscle efficiency during locomotion with different power requirements. To test this hypothesis we used a three element Hill muscle model to determine how muscle fascicles would be required to change length if the series elastic element stiffness is varied, whilst the limb kinematics and muscle properties are held constant. We applied a model of muscle energetics to these data to predict muscle efficiency for a range of stiffness values in both walking and running conditions. We also compared the model results to in vivo data collected using ultrasonography. The muscle model predicted that optimal series elastic element stiffness for maximising efficiency is equal or slightly higher than that of the average Achilles tendon in running and walking, respectively. Although the peak efficiency values for running (26%) and walking (27%) are similar, the range of stiffness values achieving high efficiency in running is much smaller than that during walking. These results suggest that a compliant tendon, such as the Achilles tendon, is required for efficient running. Such a finding is important, because it describes how the stiffness of a tendon may be adapted to achieve optimal efficiency for particular athletic pursuits. The influence of varying tendon stiffness on kinematic performance may, however, play an important role in determining the efficiency of the muscle.

Electromechanical Delay and Series Elastic Musculotendinous Stiffness in the Triceps Surae

Electromechanical Delay and Series Elastic Musculotendinous Stiffness in the Triceps Surae

Mechanics of human triceps surae muscle in walking, running and jumping.

Length changes of the muscle-tendon complex (MTC) during activity are in part the result of length changes of the active muscle fibres, the contractile component (CC), and also in part the result of stretch of elastic structures [series-elastic component (SEC)]. We used a force platform and kinematic measurements to determine force and length of the human calf muscle during walking, running and squat jumping. The force-length relation of the SEC was determined in dynamometer experiments on the same four subjects. Length of the CC was calculated as total muscle-tendon length minus the force dependent length of the SEC. The measured relations between force and length or velocity were compared with the individually determined force-length and force-velocity relations of the CC. In walking or running the negative work performed in the eccentric phase was completely stored as elastic energy. This elastic energy was released in the concentric phase, at speeds well exceeding the maximum shortening speed predicted by the Hill force-velocity relation. Speed of the CC, in contrast, was positive and low, well within the range predicted by the measured force-velocity properties and compatible with a favourable muscular efficiency. These effects were also present in purely concentric contractions, like the squatted jump. Contractile component length usually started at the far end of the force-length relation. Inter-individual differences in series-elastic stiffness were reflected in the force and length recordings during natural activity.

Moment dependency of the series elastic stiffness in the human plantar flexors measured in vivo

The moment dependency of the series elastic stiffness (SES) in the human plantar flexors was investigated in vivo with the quick release method. At an ankle moment of 100 N m produced with either voluntary or electrical stimulation we found non-significantly different SES of 506±72 and 529±125 N m rad −1, respectively. It has recently been proposed that the amount of series elastic tissue involved in plantar flexion changes with the moment level produced by the plantar flexors (Hof, J. Biomech 31 (1998) 793). However, our results indicate that the amount of series elastic tissue involved in plantar flexions remained constant with changing moment levels. We therefore propose that the series elastic component (SEC) in human plantar flexors act as one structure or rather one combination of anatomical structures which is engaged at all muscle activation levels, and that the mechanical properties (i.e. the stress–strain function) are determined by the combined tissue mechanical properties. Additionally, our results demonstrated that the SES in the human plantar flexors at moments levels up to about isometric maximum did not reach an asymptote where the stiffness is independent of moment, i.e. SEC of the plantar flexors is, during many daily activities, loaded for the greatest part in the non-linear part of the stress–strain function.

Muscle and joint elastic properties during elbow flexion in Duchenne muscular dystrophy.

1. Maximal voluntary contraction (MVC), series elastic stiffness and total joint stiffness during elbow flexion were investigated in healthy boys and in boys with Duchenne muscular dystrophy (DMD) in order to assess changes in mechanical properties induced by the disease. 2. Two methods were used to perform stiffness measurements: (i) the application of sinusoidal perturbations to the joint during flexion efforts, allowing the calculation of total joint stiffness; (ii) the use of quick-release movements of the elbow, which had previously been maintained in isometric contraction, allowing the calculation of series elastic stiffness. In each case, stiffness was linearly related to torque, leading to the calculation of a normalized stiffness index as the slope of this stiffness-torque relationship. 3. As expected, mean MVC was found to be much higher for healthy boys (20.02 +/- 5.20 N m) than for DMD patients (3.09 +/- 2.44 N m). Furthermore, the results showed that it was possible to characterize healthy and DMD children by virtue of the mechanical properties measured. Mean series elastic stiffness index was higher for DMD children (142.55 +/- 136.58 rad(-1)) than for healthy subjects (4.39 +/- 2.53 rad(-1)). The same holds for mean total joint stiffness index: 43.68 +/- 67.58 rad(-1) for DMD children and 2.26 +/- 0.70 rad(-1) for healthy subjects. In addition, increases in stiffness were more marked in DMD patients exhibiting high levels of muscle weakness. 4. These changes are interpreted in terms of the adaptation of the properties of the muscles and joint involved, i.e. muscle fibres, tendons, peri- and intra-articular structures.

Effect of passive stretching and jogging on the series elastic muscle stiffness and range of motion of the ankle joint.

To determine the effect of stretching and jogging on the series elastic muscle stiffness of the plantar flexors and on the range of dorsiflexion at the ankle joint. 24 healthy subjects participated in this study. Each subject undertook all of the following protocols, in random order: (1) stretching protocol: five 30 s static stretches with 30 s rest between stretches; (2) aerobic jogging protocol: subjects ran on a treadmill for 10 min at 60% of their maximum age predicted heart rate; (3) combined protocol: subjects ran first and then stretched. A damped oscillation technique was used to measure the series elastic stiffness of the plantar flexors. Dorsiflexion of the ankle was assessed with a weights and pulley system that moved the ankle joint from a neutral position into dorsiflexion passively. Electromyography was used to monitor the activity of the plantar and dorsiflexors during these procedures. The statistical analysis of these data involved an analysis of covariance. For decreasing series elastic muscle stiffness running was more effective than stretching (P < 0.05). In contrast, the results for range of motion showed that the combination protocol and the stretching only protocol were more effective than the running only protocol (P < 0.05) for increasing dorsiflexion range of motion at the ankle. Both jogging and static stretching exercises appear to be beneficial to individuals participating in sporting activities.

Skeletal muscle stiffness in static and dynamic contractions

Series elastic stiffness of rat gastrocnemius medialis muscle was determined by means of sinusoidal movements (180 Hz, 0.25% of muscle length) for various contraction conditions. The effects of muscle length, activation level, velocity, prestretch, and temperature on the force-stiffness relationship were investigated. All force-stiffness curves were transformed to a linear force-α curve (Ettema and Huijing, 1993; Morgan, 1977) to distinguish mathematically two series elastic components; a force dependent and force independent compliance. For all isometric conditions a typical force-stiffness curve was found, where stiffness increased with force, and this increase levelled off at higher forces. Stiffness in dynamic shortening and lengthening contractions is related to force in a completely different way than in isometric condition. An increase in temperature caused a decrease in muscle stiffness for a given force, and the effects of muscle length, activation level, and prestretch were small. It was concluded that the series elastic component of skeletal-muscle-tendon complex is probably located in more than two morphologically identifiable elements. Furthermore, we concluded that using a single series elastic element in muscle modelling is not appropriate to describe muscle behaviour under all conditions that occur during in vivo activation.

Frequency response of rat gastrocnemius medialis in small amplitude vibrations

The effect of vibration frequency during small amplitude (∼0.25% of muscle-tendon complex length) vibrations on muscle stiffness and phase angle of the rat gastrocnemius medialis muscle ( n = 7) was investigated at four different force levels. Frequencies varying from 5 to 180 Hz were studied. Furthermore, series elastic stiffness was determined as a function of muscle force. The experiments were also simulated, using a Hill-type muscle model representing the fundamental characteristics of the experimental muscles. The frequency response found in the experiments deviated from the simulation results: stiffness and phase were lowest at about 30 Hz, whereas the simulations showed a rapid asymptotic increase of stiffness and decrease of phase angle with increasing frequency. The values levelled off at about 60 Hz. The discrepancy between experimental and simulation results is thought to be due to changes of the contractile properties of muscle, especially at low movement frequencies, where the contractile machinery has a significant influence on muscle stiffness. At frequencies of 120 Hz and above, the muscle stiffness resembled series elastic stiffness in both experimental muscles and simulations. This suggests that the contractile element contracts approximately isometrically. Functional implications of the frequency response are discussed.

Stiffness of the fastrocnemius medialis muscle-tendon complex and isolated tendon of the rat measured by sinusoidal length changes

STFFNESS OF THB GASTROCNBMIUS MEDIALIS MUSCLE-TBNDGN COMPLBX AND ISGLA‘IED TENDON OF THE RAT MEASURED BY SINUSOIDAL LENGTH CHANGES Gertjau J.C. Ettema and Peter A. Huijing Faculteit der Beweglngswetenschappen Vxije Uulverslteit Amsterdam, Van der Boechorststraat 9,108l BT Amsterdam, The Netherlands The aim of the present investigation was to determine at which frequencies of small sinusoidal leugth changes the. muscle-tendon complex acts within it’s short range stiffness. Furthermore, the relation between force aud stiffness for the muscle-tendon complex as well as for the isolated ten&n was studied. Sinusoidal length changes (frequency: 10 120 Hz, amplitude: 0.05 0.1 mm, and stepwlse length changes (+0.2 and -0.2 mm) were imposed on four GM muscle-tendon complexes of the Wlstar rat during isometric tetaulc contractions at several muscle lengths. Isometric fonze levels ranged from maximal isometric force (Fo) to about 5% Fo. Sinusoidal length changes were also imposed on two isolated teudous (GM aud Tibialis Anterior). All measurements were done at 27O C. Elastic stiffness (ES) (Butler, D.L. et al. in Handbook of engiueetiug in medicine and biology, pp 279-314,1978) of the muscle-tendon complex was compared to series elastic stiffhess as determined by means of step-wise length changes (SS). For the 80 and 120 Hz movements ES was similar to SS, whereas for the lower frequencies (10 60 Hz) much lower ES values are found, indicating leugth changes of the coutmctlle machinery. Force responses of both muscle-tendon complex and isolated tendon were merely elastic of nature. only at extreme low force levels a considerable visco-elastlc behaviour was found. The stiffness of the muscle-tendon complex as well as the stiffness of the isolated tendon continued to increase with force, even at force levels near Fo. This is in contradiction with the generally accepted opinion that tendluous stiffness is constaut at force levels above 30% Fo. The current results indicate that using sinusoidal movements of small amplitudes a frequency of 80 to 120 Hz is sufficient for an acamte determination of the series elastic (short range) stiffness of the rat GM.

Isometric trunk extensor endurance in young females

Series elastic stiffness of rat gastrocnemius medialis muscle was determined by means of sinusoidal movements (180 Hz, 0.25% of muscle length) for various contraction conditions. The effects of muscle length, activation level, velocity, prestretch, and temperature on the force-stiffness relationship were investigated. All force-stiffness curves were transformed to a linear force-α curve (Ettema and Huijing, 1993; Morgan, 1977) to distinguish mathematically two series elastic components; a force dependent and force independent compliance. For all isometric conditions a typical force-stiffness curve was found, where stiffness increased with force, and this increase levelled off at higher forces. Stiffness in dynamic shortening and lengthening contractions is related to force in a completely different way than in isometric condition. An increase in temperature caused a decrease in muscle stiffness for a given force, and the effects of muscle length, activation level, and prestretch were small. It was concluded that the series elastic component of skeletal-muscle-tendon complex is probably located in more than two morphologically identifiable elements. Furthermore, we concluded that using a single series elastic element in muscle modelling is not appropriate to describe muscle behaviour under all conditions that occur during in vivo activation.

Instantaneous force-velocity-length relations in the intact human heart

The contractile state of the left ventricle was analyzed in 10 patients using measurements of instantaneous ascending aortic blood flow velocity, left ventricular pressure and end-diastolic volume. Instantaneous left ventricular volume at 10 msec intervals was derived by subtracting the cumulative volumes (integral of flow) ejected during each sampling interval from angiographically derived end-diastolic volume. Circumferential fiber shortening velocity and wall force were calculated as flow rate/4πr 2 and left ventricular pressure × πr 2, respectively. The instantaneous radius (r) was calculated by assuming a spherical model for the left ventricle. Applying a Hill model for muscle contraction, contractile element velocity was calculated as the sum of circumferential fiber shortening velocity and series elastic element velocity. Series elastic element velocity was calculated from the time rate of change of wall force (dF/dt) and series elastic element stiffness. Instantaneous force-velocity-length relations were clearly different in five patients with normal left ventricular function (Group I) from those in five patients with impaired left ventricular function (Group II). Peak contractile element velocity averaged 28.2 cm/sec or 1.35 circumferences per second (circ/sec) in Group I and 19.4 cm/sec ( P < 0.01) or 1.01 circ/sec ( P < 0.01) in Group II. Also, both peak and mean circumferential fiber shortening velocity were greater in Group I (averages 35.1 cm/sec or 2.12 circ/sec; and 21.4 cm/sec or 1.28 circ/sec, respectively) than in Group II (averages 24.3 cm/sec [ P < 0.05] or 1.41 circ/sec [ P < 0.05]; 15.4 cm/sec [ P < 0.025] or 0.85 circ/sec [ P < 0.01], respectively). Three patients in Group II had normal hemodynamics and peak circumferential fiber shortening velocity values; however, at comparable forces circumferential fiber shortening velocity was always less in this group ( P < 0.005). Circumferential fiber shortening velocity at peak force was higher in each Group I patient (averages 21.2 cm/sec or 1.13 circ/sec) than in Group II patients (averages 14.3 cm/sec [ P < 0.005] or 0.77 circ/sec [ P < 0.01]).