Biomedical subjects

R V Baratta

Publications and source records attributed to R V Baratta.

At least 37 records · Page 2Linked to original sources

PubMed1998

The ligamento-muscular stabilizing system of the spine.

STUDY DESIGN: Electrical and mechanical stimulation of the lumbar supraspinous ligament of three patients with L4-L5 spinal deficits and of the feline model, respectively, was applied while recording electromyography on the multifidus muscles. OBJECTIVES: To determine if mechanoreceptors in the human spine can reflexively recruit muscle force to stabilize the lumbar spine, and to demonstrate, in the feline model, that such ligamento-muscular synergy is elicited by mechanical deformation of the lumbar supraspinous ligament (and possibly of other spinal ligaments), the facet joint capsule, and the disc. SUMMARY OF BACKGROUND DATA: The literature repeatedly confirms that ligaments have only a minor mechanical role in maintaining spine stability, and that muscular co-contraction of anterior and posterior muscles is the major stabilizing mechanism of the spine. The literature also points out that various sensory receptors are present in spinal ligaments, and that the ligaments are innervated by spinal and autonomic nerves. Data that describe how ligaments and muscles interact to provide stability to the spine were not found. METHODS: The supraspinous ligament at L2-L3 and L3-L4 was electrically stimulated in three patients undergoing surgery to correct deficits at L4-L5. Electromyography was performed from the multifidus muscles at L2-L3 and L3-L4, bilaterally. In 12 cats, the supraspinous ligaments from L1-L2 to L6-L7 were mechanically deformed, sequentially, while electromyography was performed from the multifidus muscles of the six levels. Loading of the ligament was applied before and after each of the two vertebrae were externally fixed to prevent motion. RESULTS: Electromyograms were recorded from the multifidus muscles, bilaterally, in the two of the three patients, demonstrating a direct relationship to receptors in the supraspinous ligament. Electromyograms were recorded from the feline multifidus muscle with mechanical loading of the supraspinal ligament at each of the L1-L2 to L6-L7 motion segments. In the free-spine condition the largest electromyographic discharge was present in the level of ligament deformation, and lower electromyographic discharge was recorded in two rostral and caudal segments. After immobilizing any two vertebrae, loading of the ligament resulted in electromyographic discharge in the muscles of the same level and at least one level above and/or below. CONCLUSIONS: Deformation or stress in the supraspinous ligament, and possibly in other spinal ligaments, recruits multifidus muscle force to stiffen one to three lumbar motion segments and prevent instability. Strong muscular activity is seen when loads that can cause permanent damage to the ligament are applied, indicating that spastic muscle activity and possibly pain can be caused by ligament overloading.

Animals↗

PubMed1998

Force feedback control of motor unit recruitment in isometric muscle.

The use of simple force feedback in an isometric muscle control system utilizing orderly recruitment of motor units is explored. Cat medial gastrocnemius motor units were stimulated with and without simple force feedback gain ranging from 0.7 to 0.9. Ramp, triangular, staircase, sinusoidal and bandwidth-limited pseudo-random input recruitment signals were used to study tracking accuracy through linear correlation in ramp and triangular signals, cross correlation in sinusoidal and random signals, and rise time and steady state error in staircase signals. Dramatic improvements were found in most tested tracking variables with the use of feedback; squared correlation coefficients increased from a mean of 0.93 to 0.99 for ramp signals and from 0.76 to 0.98 in triangular signals. Mean peak cross-correlations improved from 0.85 to 0.98 in random signals and from 0.93 to 0.98 for sinusoidal inputs, and mean time to peak cross-correlations decreased from 144 to 24 ms in random signals and from 156 to 25 ms in sine waves. Rise times in staircase signals decreased from a mean of 520 to 175 ms, and mean steady state error decreased from 12 to 3%. Significant effects of the triangle cycle time, sinusoidal frequency and staircase step were found on the performance of the muscle force control system. In addition, the possible effects of intrinsic feedback mechanisms on the control system were examined by repeating the closed loop part of the study but with the sciatic nerve cut proximally. The tracking results were essentially and statistically the same as in the closed loop condition. It was concluded that a simple feedback configuration provided superior tracking performance for a practical application in which orderly recruitment is used to control muscles; furthermore, it was concluded that this type of system would be virtually immune to external disturbances such as spasticity resulting from intact spinal neural feedback mechanisms found in paralyzed individuals.

Analysis of Variance↗

PubMed1998

Ligamento-muscular protective reflex in the lumbar spine of the feline.

A ligamento-muscular protective reflex in the lumbar spine was demonstrated in a feline model. Stimulating electrodes were applied to the supraspinous ligament between several lumbar vertebra (L1 to L6) while recording myoelectric discharge from the paraspinal muscles at the L3, L4 and L5, bilaterally. Electromyographic (EMG) activity was present in the paraspinal muscles bilaterally, upon stimulation of the supraspinous ligament, in six preparations. The EMG discharge was strongest in the muscles one level below that of the stimulated ligament, whereas weaker EMG signals were recorded from as far as two levels above and below. The mean time delay between the application of the stimulus to the ligament to the resulting EMG ranged from 2.52 to 2.77 ms at all levels. Stimulation of the supraspinous ligament in the L6 segment resulted in a weak reflex response, and stimulation in the L7 segment did not produce any EMG activity. It was concluded that mechanoreceptors in the supraspinous ligament at the L1/6 levels may initiate sensory signals upon strain of the ligament, during flexion. This, in turn, causes contraction of the paraspinal muscles, bilaterally, to extend the spine and prevent possible damage to the ligament while maintaining stability. The results may add to the understanding of low back pain, and to the formulation of surgical procedures which could spare the neural supply of the ligament, allowing advanced physiotherapeutic modalities to be implemented for post-surgical rehabilitation.

Animals↗

PubMed1998

Frequency domain-based models of skeletal muscle.

Models of skeletal muscle based on its response to sinusoidal stimulation have been in use since the late 1960s. In these methods, cyclic excitation at varying frequencies is used to determine force or muscle length amplitude and phase as functions of excitation frequency. These functions can then be approximated by models consisting of combinations of poles and zeros and pure time delays without the need to combine force-length or force-velocity relationships. The major findings of a series of frequency response studies undertaken in our laboratory revealed that: The frequency response models for isometric force including orderly recruitment of motor units were relatively invariant of the particular strategy or oscillation level employed. A critically damped second order model with corner frequency near 2 Hz and a pure time delay best described the relationship between input stimulation and output isometric force. The frequency response models for load-moving muscles consisted of an overall gain which is a function of mass, dependent mostly on the width of the length-force relation at a given load (force), and a frequency-dependent gain component independent of load mass. The phase lag between input and output was also independent of load. Muscle function and architecture are the primary determinants of its isometric force frequency response. Tendon viscoelasticity (excluding the aponeurosis) has no significant effect on isometric force dynamic response, but does have a minor effect on load-moving dynamic response. The effect of tendon in reducing or augmenting the load-moving muscle response bandwidth is muscle-dependent. The joint produces decreased high frequency gain and uniformly increased phase lags between input excitation and output force in isometric conditions. The joint acts as a lag network in load-moving conditions, increasing the phase lag without significant effect on the gain. Despite its inherent non-linear properties, the joint does not significantly deteriorate output signal quality in either isometric or load-moving conditions. Co-contraction strategy has a significant effect on the dynamic response of the joint. These frequency-based models have shown to be robust as long as the excitation type and mechanical conditions under which they are obtained are not varied. They are particularly useful for the design of neuroprostheses, where a dynamic description of muscle output as a function of stimulus input under given conditions is desirable.

Algorithms↗

PubMed1998

Methods to reduce the variability of EMG power spectrum estimates.

Three methods that can significantly reduce the variability of the EMG power density spectrum (PDS) variable by eliminating artifactual components are described. Two methods, one that allows the subtraction of power line noise in the time domain and one which allows the subtraction of system noise in the frequency domain from the EMG, were shown to be effective in helping to accurately estimate the median frequency (MF) of the PDS, and especially during low level contractions (0-25% maximal voluntary contraction, MVC) when the signal-to-noise ratio is unfavorable. The techniques eliminate the artifactual effects of system and power line noises from the EMG recordings throughout the force range (0-100% MVC) while preserving the native EMG power at all frequencies. It was also shown that if a technique to train subjects to produce their true MVC is employed, the absolute force/torque produced could be as much as 30% higher than in untrained MVC. The effect of true MVC production was also shown to be significant when interpretation of PDS variables are correlated to the processes which produce contraction.

Algorithms↗

PubMed1998

Open-loop tracking performance of a limb joint controlled by random, periodic, and abrupt electrical stimulation inputs to the antagonist muscle pair.

The ability of the cat's ankle joint to track various input signals when controlled by electrically elicited motor unit recruitment, firing rate and antagonist muscle coactivation was examined. Pseudo-random, sinusoidal and staircase signals were used to control the soleus and tibialis anterior muscles isometrically and with a 250-g pendulum. Tracking was evaluated through cross correlation for pseudo-random and sinusoidal signals, and by rise time and steady-state error in step signals. Better tracking was obtained in isometric conditions than in load-moving conditions. Pseudo-random signals resulted in 250-ms delay between input and isometric torque output. For load-moving conditions, 340-ms and 400-ms delay in torque and angle were obtained. For sinusoids, delays decreased from 240 ms at 0.5 Hz, to 140 ms at 2 Hz in isometric conditions. Time delays for angle were between 300 and 400 ms, decreasing as frequency increased. Poor cross correlation was found for torque in load-moving conditions, because of pendulum nonlinear dynamics. Step size was not uniform in staircase trials, with steady-state errors between 9% and 39%, and rise times between 200 and 1000 ms. It is concluded that open-loop joint control results in poor tracking, presumably because it is devoid of feedback mechanisms.

Analysis of Variance↗

PubMed1997

Method to impact in vivo rabbit femoral cartilage with blows of quantifiable stress.

The purpose of this study was to develop a technique by which a known stress could be applied uniformly across the femoral cartilage of a rabbit as a model for the development of post-traumatic arthritis. A system to impact the cartilage was designed that consisted of an apparatus to deliver a blow of quantifiable force, a method to apply the stress uniformly over the impact area, and a way to accurately measure the impact area. The knee joints of cadaveric New Zealand White rabbits were surgically exposed with the knee flexed so that the distal femoral articular surface was perpendicular to an impactor. With the knee fixed in position, a cup containing polymethylmethacrylate bone cement was applied to create an exact contour of the femoral surface, and the cement was allowed to cure. The form was then rested on the rabbit knee, and a drop tower released a weight of known mass from a known height onto an impactor (instrumented with strain gauges to measure the compressive force) that was attached to the cup. The area of the impacted surface was determined and, with the measured force, was used to calculate an accurate estimate of the impact stress. This method can be performed under sterile conditions, and therefore it is well suited for survival experiments in which the long-term effects of impact to cartilage will be studied.

Animals↗

PubMed1997

Force, velocity and energy dynamics of nine load-moving muscles.

Nine architecturally different muscles of the cat's hindlimb were investigated with respect to the kinetic energy, the potential energy, and the force variations associated with shortening contractions against gravitational loads. Insight about the energy dynamics of contractile muscle can provide a unifying concept for models of muscle performance capability. In this study, it was found that as contractions shortened from passive equilibrium against a constant mass load, acceleration and deceleration phases appeared. These phase were associated with muscular force variations of up to 25% of the mass weight in fast twitch muscles at low loads. In contrast, slow twitch muscles were associated with less than 10% force variations when shortening against a gravitational load. It also was found that optimal loads exist which maximize each muscle's ability to impart kinetic and potential energy, these optimal loads tend to be in the mid-force range for highly pennate muscle and in the low-force range for justform muscles. It was concluded that the kinetic energy provided by each muscle is a small percentage of that calculated from its length-force relationship, especially at low loads. This study confirms that the efficiency of kinetic energy conversion is very low at low loads (gradually improving as the loads increase) and thereby substantiates early experiments with heat and metabolic energy.

Animals↗

PubMed1997

Evaluation of antagonist coactivation strategies elicited from electrically stimulated muscles under load-moving conditions.

Muscle coactivation strategies that produce ankle dorsiflexion and plantar flexion were elicited by electrical stimulation of the tibialis anterior (TA) and soleus (SOL) muscles of the cat, and examined under several loading conditions. Four different load types were used: free-limb motion (no load), fly-wheel, and two pendulums, each with a different lever arm. Three types of coactivation strategies were considered. The first coactivation strategy consisted of antagonist activity that decreased as the agonist activity increased. The second strategy consisted of increasing antagonist activity with increasing agonist activity. And, in the third strategy, antagonist coactivation decreased at low force levels, then increased at high force levels. The three strategies were evaluated based on the joint angle's peak-to-peak movement and its ability to track a linear input command given by the correlation coefficient of the output signal versus linear input. Results showed that increasing antagonist activity resulted in decreasing peak-to-peak angle and a decreased signal tracking capability for each load condition. The latter, however, was not as obvious in the flywheel load (as compared with free-moving and pendulum conditions). A decreasing peak-to-peak torque for pendulum loads was also observed with increasing antagonist activity. In all loading conditions, maximal peak-to-peak angle and torque were present when a moderate degree of antagonist activity was engaged, and signal tracking capability improved with earlier engagement of the antagonist muscles. It is suggested that strategies using a combination of low-level coactivation, as described in the physiological literature and previous functional electrical stimulation (FES) studies, could satisfactorily address the issues of controllability and efficiency while maintaining long-term joint integrity.

Animals↗

PubMed1997

The influence of antagonist muscle control strategies on the isometric frequency response of the cat's ankle joint.

This study investigated the effect of various strategies to control the interaction between agonist and antagonist muscles on the frequency response of the isometric cat ankle joint actuated by the tibialis anterior (TA) and soleus (SOL) muscles. Some strategies were based on the physiologic need for increasing joint stability during forceful contractions; with these strategies, the proportional rate of physiologic antagonist activity was termed antagonist gain. Other strategies were based on the electrical stimulation literature, which advocates co-contraction at low force levels. The range of crossover of antagonist activity to the agonist's domain was termed overlap. Strategies consisting of 0%, 10%, and 20% antagonist gain were combined with 0%, 50%, and 100% overlap for a total of nine strategies. These were applied to the TA and SOL using sinusoidal input signals varying in frequency from 0.4 to 6 Hz. Gain and phase Bode plots were constructed through the use of the fast Fourier transforms (FFT's); and analysis of variance determined the significance of differences in gain and phase across frequencies. Best-fit models consisting of four poles and two zeroes were used to fit the experimental data and compared against an analytical model of muscles acting independently across the joint. Harmonic distortion was calculated to evaluate signal quality. It was found that changing the overlap and the antagonist gain produces significant changes in the dynamic response of the two-muscle joint system. The analytical approach to modeling such a system tends to consistently overestimate gain. It is suggested that signal quality is optimal when a moderate amount of antagonist gain (10%) is engaged, with overlap of 50% to smooth transitions between opposing movements. It is expected that this type of strategy will achieve optimum signal quality while preserving the long-term integrity of the joint.

Analysis of Variance↗

PubMed1997

Reciprocating gait orthosis powered with electrical muscle stimulation (RGO II). Part I: Performance evaluation of 70 paraplegic patients.

Seventy paraplegics were fitted with an improved Reciprocating Gait Orthosis powered with or without (low-level injury) electrical stimulation of the thigh muscles (RGO II) as a secondary rehabilitation phase after the acute period. The patients comprised a broad cross-section of the paraplegic population applying for medical services and varied in age from 16 to 55 years, time since injury ranging from less than 1 to 15 years, injury levels ranging from C-6/7 to T-11/12, and varying levels of spasticity, contractures, scoliosis and other related medical and physiologic problems. The success/failure ratio was dependent on the injury level, which was 1:1 for paraplegics with injury level at C-6/7; 1.67:1 for those with injury of T-1/3; and about 4:1 for paraplegics with injury level from T-3 to T-12. Lack of motivation and medical problems unrelated to the RGO II treatment were the primary reasons for failure. The duration of treatment (outpatient service three times per week) ranged from 2 to 48 weeks (mean: 16). Forty-one patients who completed the RGO II rehabilitation and were sent home with the orthosis for independent use (for at least 6 months and up to 3 years) were surveyed by a staff member for analysis of the meaning and impact of the RGO II on the patient's life and health, and potential problems. It was shown that 80.5% of the 41 patients were regular users and 19.5% were non-users. Thirty-eight of the 41 patients declined an offer to return the RGO II equipment for a full refund, while three patients were willing to return the orthosis. It was concluded that the RGO II is viable orthosis for restoring standing and limited walking in paraplegics while providing sufficient function, safety, and reliability. The most appropriate patients for the use of such an orthosis consist primarily of those with T-3 to T-12 injury level and good motivation, although highly selected patients with higher injury levels also can benefit from its use. Regular use of the RGO II, even for exercise only, had a general positive impact on the patients' health and outlook.

Adolescent↗

PubMed1997

Reciprocating gait orthosis powered with electrical muscle stimulation (RGO II). Part II: Medical evaluation of 70 paraplegic patients.

Medical evaluation was performed on a group of paraplegics who were trained to walk with the Reciprocating Gait Orthosis powered with electrical muscle stimulation (RGO II). The evaluation included changes in spasticity, cholesterol level, bone metabolism, cardiac output and stroke volume, vital capacity, knee extensors torque, and heart rate at the end of a 30-meter walk. After an average of 14 weeks of training during which patients walked for 3 hours per week, significant reductions in spasticity, total cholesterol and low-density lipids, hydroxyproline/creatinine ratio, and increased knee extensor torque were evident. The data also showed that improvements occurred in the calcium/creatinine ratio, serum calcium and alkaline phosphatase levels, cardiac output and stroke volume, and vital capacity, yet these improvements were not statistically significant. The final heart rate at the end of a 30-meter walk showed that the RGO II required only a moderate level of exertion, which was found to be the lowest among the other mechanical or muscle stimulation orthoses available to paraplegics. It was concluded that the limited but reasonable level of functional regain provided by the RGO II is associated with a general improvement in the paraplegic's physiological condition if used for a minimum of 3 to 4 hours per week.

Bone Resorption↗

PubMed1996

Evaluation of isometric antagonist coactivation strategies of electrically stimulated muscles.

The performance of various coactivation strategies to control agonist-antagonist muscles in functional electrical stimulation (FES) applications was examined in a cat model using the tibialis anterior and soleus muscles to produce ankle isometric dorsiflexion and plantarflexion torques, respectively. Three types of coactivation strategies were implemented and tested. The first strategy was based on coactivation maps described in the literature as consisting of decreasing antagonistic activity as the input command to the agonist was increased. The second type of strategy was based on the physiologic coactivation data collected from normal subjects exhibiting joint stabilization during the full range of contractions. These strategies included scaled increasing antagonist activity and therefore joint stiffness with increasing agonist input command. A third strategy was devised which at low force levels mimicked the strategies described in the literature and at high force levels resembled strategies exhibited by normal subjects. The three strategies were evaluated based on their ability to track a linear or sinusoidal input command and their efficiency of torque transmission across the joint. Coactivation strategies using increasing antagonist activity resulted in decreased maximal joint torque and efficiency, decreased signal tracking capability for linear inputs, and increased harmonic distortion for sinusoidal inputs. Peak efficiency and tracking ability appeared when a moderate degree of antagonist activity was engaged near the neutral joint position. Signal tracking quality improved with earlier engagement of the antagonist muscles. Our results suggest that strategies combining low-level coactivation as described in the physiological literature and previous FES studies could satisfactorily address the issues of controllability, efficiency, and long-term joint integrity.

Animals↗

PubMed1996

Load, length, and velocity of load-moving tibialis anterior muscle of the cat.

Three-dimensional relationships of load, length, and velocity of shortening of the tibialis anterior muscle in the cat were derived experimentally and fitted with an analytic model. Gravitational loads were applied to the isolated muscle, which arrived at an equilibrium with the passive forces before supramaximal tetanic stimulation was delivered to its nerve. Recordings of initial passive muscle length at equilibrium and length changes throughout the shortening phase up to the final length at active equilibrium were taken and numerically differentiated to obtain each load's instantaneous velocity. A three-dimensional surface was constructed by using instantaneous length and the corresponding velocity for each of several loads. Maximal velocity of shortening was shown to gradually decrease, occurring earlier in the shortening phase (at larger muscle lengths) as loads increased. Whereas load-velocity curves were hyperbolic for middle and short muscle lengths, they were nonmonotonic during shortening above the optimal length. The model was found to correlate well with the experimental data (R = 0.98) and allowed for prediction of both muscle performance boundaries and instantaneous shortening velocity for a given length across the physiological load spectrum, thus offering a realistic estimation of the contractile properties exhibited by the tibialis anterior muscle in functions similar to naturally occurring movements against gravitational loads, which are accelerated and decelerated during the movement.

Animals↗

PubMed1995

Motor unit recruitment strategy of knee antagonist muscles in a step-wise, increasing isometric contraction.

The purpose of this study was to determine if differences exist between the control strategies of two antagonist thigh muscles during knee flexion and extension muscular coactivation. Surface myoelectric signal (MES) of the quadriceps (rectus femoris) and the hamstrings (semitendinosus) were obtained from both muscles while performing step-wise increasing contractions during flexion and extension with the knee at 1.57 rad of flexion (90 degrees). The median frequency of the power density spectrum, which is related to the average muscle fiber action potential conduction velocity and therefore to motor unit recruitment, was calculated from each MES. The results suggest that, in all the subjects tested, when the muscle acts as antagonist most motor units are recruited up to 50% of the maximal voluntary force, whereas when the muscle acts as antagonist motor units are recruited up to 40% of the maximal voluntary force. The force range past 40-50% of the maximal force is also characterized by differences between the agonist/antagonist.

Adult↗

PubMed1995

Force-velocity relations of nine load-moving skeletal muscles.

The relationship between maximal velocity and load was studied in nine muscles of the cat's hind limb using a technique in which the initial and final muscle lengths are determined by equilibrium of a suspended mass and the muscle's passive and active forces elicited by tetanic stimulation. The maximal velocities of shortening during contraction under each of various loads was used to fit a Hill model using the least-squares method. It was shown that different muscles varied significantly in their ability to generate maximal velocity over a range of loads. The tibialis anterior muscle generate the highest velocity (28.4 cms-1), whereas the tibialis posterior generated the lowest maximal velocity (4.2 cms-1). In general, muscles with predominantly fast twitch fibres and with the largest elongation/shortening range displaced the load at the highest velocities, as compared with muscles with predominantly slow twitch and short excursion range which respond with low velocities. The a/P0 ratio of Hill's equation, which defines the curvature of the force velocity, also varied widely, being most monotonic (0.927) for the soleus and the steepest (0.067) for the extensor digitorum longus, further suggesting that fibre composition is also highly influential on the force-velocity relations of the muscle.

Animals↗

PubMed1995

Architecture-based force-velocity models of load-moving skeletal muscles.

A predictive model of muscle force-velocity relationships is presented based on functional architectural variables. The parameters of Hill's equation describing muscle force-velocity relationship of nine muscles were estimated by their relationships with variables extracted from the whole-muscle length-force relationship and the percentage of slow-twitch fibres. Specifically, the maximal unloaded velocity (Vo) was estimated through multiple linear regression, from each muscle's fibre composition and the shortening range through which each muscle could produce active force. The maximal isometric force (Po) was also extracted from each muscle's length-force relationship. The ratio of Hill's dynamic constanta to Po and b to Vo, which determines the degree of curvature of the relation, was determined solely by the percent of slow-twitch fibres. This model was verified by fitting it to experimental force-velocity curves of nine different muscles in the cat's hindlimb. It was found that reasonable fits of force-velocity curves would be obtained with correlation coefficient in the range of 0.61 to 0.92, with an average of 0.82. The model predicted that muscles with relatively long shortening ranges would achieve higher maximal velocity, and that muscles with higher percentage of slow-twitch fibres had less pronounced curvature and lower maximal velocity in their force-velocity relationships. RELEVANCE: The results have direct implications in the design of neuroprosthetic limb control systems, which use electrical stimulation to restore function to muscles paralysed from spinal cord injury. The designer is enabled to optimally calibrate the controller according to the predicted individual force-velocity curves of different muscles by using the length-tension curves and fibre composition data available in the literature.

Journal Article↗

PubMed1995

The dynamic response of the cat ankle joint during load-moving contractions.

The dynamic response of the cat's ankle joint during load-moving activation of the medial gastrocnemius was determined. Sinusoidal-input oscillations of ankle plantar flexion were performed by the muscle at frequencies ranging from 0.4 to 5 Hz against a 10-N load acting via a cable through a pulley with a 2 cm radius. This was followed by sinusoidal muscle length changes against the same load while excluding the joint. The frequency responses of the two conditions were compared and decomposed in terms of their relative phase and gain, and best-fit pole-zero models to yield the dynamic model of the joint isolated from the muscle properties. The muscle displacement transfer function M(j omega) was characterized as two sets of double poles at 2.1 and 3.2 Hz, with a pair of zeros at 0.92 and 20 Hz, and pure time delay of 8 mS. The joint model J(j omega) was obtained by adding a pole at 5 Hz and a zero at 13 Hz. It was concluded that the ankle joint acts as a lag system, introducing significant increase in the phase lag between stimulus input and mechanical output without affecting the frequency-dependent attenuation of gain. Average harmonic distortion was less than 5% in all cases. This particular finding reveals that, despite its inherently nonlinear mechanical characteristics, the joint introduces no degradation in the simplified linear behavior of the muscle-joint system. This model is useful in the design of systems employing electrical stimulation to restore movement to limbs paralyzed by spinal cord injury or stroke.(ABSTRACT TRUNCATED AT 250 WORDS)

Animals↗