Impedance characteristics of a neuromusculoskeletal model of the human arm I. Posture control

The mechanical impedance of neuromusculoskeletal models of the human arm is studied in this paper. The model analysis provides a better understanding of the contributions of possible intrinsic and reflexive components of arm impedance, makes clear the limitations of second-order mass-viscosity-stiffness models and reveals possible task effects on the impedance. The musculoskeletal model describes planar movements of the upper arm and forearm, which are moved by six lumped muscles with nonlinear dynamics. The motor control system is represented by a neural network which combines feedforward and feedback control. It is optimized for the control of movements or for posture control in the presence of external forces. The achieved impedance characteristics depend on the conditions during the learning process. In particular, the impedance is adapted in a suitable way to the frequency content and direction of external forces acting on the hand during an isometric task. The impedance characteristics of a model, which is optimized for movement control, are similar to experimental data in the literature. The achieved stiffness is, to a large extent, reflexively determined whereas the approximated viscosity is primarily due to intrinsic attributes. It is argued that usually applied Hill-type muscle models do not properly represent intrinsic muscle stiffness. Received: 14 October 1997 / Accepted in revised form: 18 May 1999     

A benchtop biorobotic platform for in vitro observation of muscle-tendon dynamics with parallel mechanical assistance from an elastic exoskeleton

We present a novel biorobotic framework comprised of a biological muscle-tendon unit (MTU) mechanically coupled to a feedback controlled robotic environment simulation that mimics in vivo inertial/gravitational loading and mechanical assistance from a parallel elastic exoskeleton. Using this system, we applied select combinations of biological muscle activation (modulated with rate-coded direct neural stimulation) and parallel elastic assistance (applied via closed-loop mechanical environment simulation) hypothesized to mimic human behavior based on previously published modeling studies. These conditions resulted in constant system-level force-length dynamics (i.e., stiffness), reduced biological loads, increased muscle excursion, and constant muscle average positive power output—all consistent with laboratory experiments on intact humans during exoskeleton assisted hopping. Mechanical assistance led to reduced estimated metabolic cost and MTU apparent efficiency, but increased apparent efficiency for the MTU + Exo system as a whole. Findings from this study suggest that the increased natural resonant frequency of the artificially stiffened MTU + Exo system, along with invariant movement frequencies, may underlie observed limits on the benefits of exoskeleton assistance. Our novel approach demonstrates that it is possible to capture the salient features of human locomotion with exoskeleton assistance in an isolated muscle-tendon preparation, and introduces a powerful new tool for detailed, direct examination of how assistive devices affect muscle-level neuromechanics and energetics.     

Directional preference of activation of abdominal and paraspinal muscles during position-control tasks in sitting

Controversy exists in the literature regarding antagonist activity of trunk muscles during different types of trunk loading, and the direction-specificity of activation of trunk muscles, particularly the deeper trunk muscles. This study aimed to systematically compare activation of a range of trunk muscles between directions of statically applied loads, and to consider the impact of breathing in this activation. In a semi-seated position, 13 healthy male participants resisted moderate inertial loads applied to the trunk in eight different directions. Intramuscular electromyography was recorded from eight abdominal and back muscles on the right side during 1 s prior to peak inspiration/expiration. All muscles demonstrated a directional preference of activation. No muscle displayed antagonistic activation during loading conditions of an intensity that exceded that recorded in upright sitting without a load. During these moderate intensity sustained efforts, trunk muscle activation varied little between respiratory phases. Antagonistic muscle activation of amplitude equivalent to the activation recorded in upright sitting without load is sufficient to maintain control of the spine during predictable and sustained low load tasks.     

Tremor and other oscillations in neuromuscular systems

A model has been analyzed which is based on recent experimental evidence concerning the properties of muscles and the sensory feedback pathways from muscles. Damped oscillations can arise in the absence of sensory feedback due to the interaction of a muscle with inertial loads. These mechanical oscillations can have a wide range of frequencies depending on the inertial and elastic loads that are attached to the muscle. Small amounts of sensory feedback will tend to reduce deviations from a steady muscle length, but larger amounts of feedback can produce oscillations. The frequency of these reflex oscillations is determined by the properties of the muscle and feedback pathway, and is rather independent of load. If the strength of the sensory feedback is sufficient, either the mechanical oscillations or the reflex oscillations or both can grow, rather than decay, with time. The growth of these oscillations is limited by saturation non-linearities in the muscle receptors and the muscle itself, so that the oscillations approach a steady amplitude and frequency. Using typical properties of muscles and spinal reflex pathways, the frequency of reflex oscillations will be within the range 8–12 Hz found for physiological tremor. With the longer latency found for supraspinal reflexes, oscillations will occur in the range 4–6 Hz which is characteristic of Parkinson's and cerebellar diseases. The role of longer latency reflexes in the generation of these tremors is discussed.     

Effects of elastic loads on the contractions of cat muscles

The nerves to plantaris and soleus muscles in the cat were stimulated with maximal single shocks and with random stimulus trains which produced partially fused contractions. In order to obtain information on the mechanism of muscular contraction, the effects of allowing the muscles to shorten against various elastic loads were studied in the time domain and in the frequency domain. When springs of increasing stiffness were placed in series with the muscle, the twitch tension increased greatly. The gain of the frequency response curve was also much greater with stiffer springs. The shape of the frequency response curve for plantaris muscle could usually be described by that expected for a second-order system with two real time constants or rate constants. The rate constants changed in qualitatively similar ways in response to increased stiffness of an elastic load, increased muscle length and increased mean rate of nerve stimulation. These results are in agreement with the hypothesis that the linear responses of muscles working against elastic loads are determined by the values of two rate constants. Thus, of the many processes associated with contraction, only two are rate-limiting: one associated with the viscoelastic properties of muscle and the second associated with the reuptake of Ca into the sarcoplasmic reticulum. Non-linear aspects of muscular contraction are also discussed. These are more prominent in soleus muscle than in plantaris muscle.Graduate student of the Medical Research Council of Canada.Formerly a Post-doctoral Fellow of the Muscular Dystrophy Association of Canada.     

Reduced nucleus pulposus glycosaminoglycan content alters intervertebral disc dynamic viscoelastic mechanics

The intervertebral disc functions over a range of dynamic loading regimes including axial loads applied across a spectrum of frequencies at varying compressive loads. Biochemical changes occurring in early degeneration, including reduced nucleus pulposus glycosaminoglycan content, may alter disc mechanical behavior and thus may contribute to the progression of degeneration. The objective of this study was to determine disc dynamic viscoelastic properties under several equilibrium loads and loading frequencies, and further, to determine how reduced nucleus glycosaminoglycan content alters dynamic mechanics. We hypothesized that (1) dynamic stiffness would be elevated with increasing equilibrium load and increasing frequency, (2) the disc would behave more elastically at higher frequencies, and finally, (3) dynamic stiffness would be reduced at low equilibrium loads under all frequencies due to nucleus glycosaminoglycan loss. We mechanically tested control and chondroitinase ABC injected rat lumbar motion segments at several equilibrium loads using oscillatory loading at frequencies ranging from 0.05 to 5 Hz. The rat lumbar disc behaved non-linearly with higher dynamic stiffness at elevated compressive loads irrespective of frequency. Phase angle was not affected by equilibrium load, although it decreased as frequency was increased. Reduced glycosaminoglycan decreased dynamic stiffness at low loads but not at high equilibrium loads and led to increased phase angle at all loads and frequencies. The findings of this study demonstrate the effect of equilibrium load and loading frequencies on dynamic disc mechanics and indicate possible mechanical mechanisms through which disc degeneration can progress.     

Dynamic analysis of load carriage biomechanics during level walking

This paper describes an investigation into the biomechanical effects of load carriage dynamics on human locomotion performance. A whole body, inverse dynamics gait model has been developed which uses only kinematic input data to define the gait cycle. To provide input data, three-dimensional gait measurements have been conducted to capture whole body motion while carrying a backpack. A nonlinear suspension model is employed to describe the backpack dynamics. The model parameters for a particular backpack system can be identified using a dynamic load carriage test-rig. Biomechanical assessments have been conducted based on combined gait and pack simulations. It was found that the backpack suspension stiffness and damping have little effect on human locomotion energetics. However, decreasing suspension stiffness offers important biomechanical advantages. The peak values of vertical pack force, acting on the trunk, and lower limb joint loads are all moderated. This would reduce shoulder strap pressures and the risk of injury when heavy loads are carried.     

Springs in Swimming Animals

Animals can lower the metabolic cost of swimming by using appropriatelytuned, elastic springs. Jet-powered invertebrates use springsthat lie in functional parallel to their swimming muscles topower half the locomotor cycle. The parallel geometry constrainsthe spring to be non-linearly elastic; muscle power is divertedto load the spring only when swimming muscles are not capableof producing maximal hydrodynamic thrust. The springs of jellyfishand scallops are forced at or near their resonant frequency,producing large energy savings. Measuring the contribution ofelastic energy storage to jet-powered locomotion has been facilitatedby the relatively simple geometries of invertebrate locomotorsystems. In contrast, complex musculoskeletal systems and kinematicshave complicated the study of springs in swimming vertebrates.Skins, tendons and axial skeletons of some vertebrate swimmershave appropriate mechanical properties to act as springs. Todate, though, there exist just a handful of studies that haveinvestigated the mechanical behaviors of these locomotor structuresin swimming vertebrates, and these data have yet to be integratedwith measures of swimming power. Integrating mechanical, kinematic,hydrodynamic and metabolic data are required to understand morefully the role of elastic springs in vertebrate swimming energetics.     

An analysis of the sources of musculoskeletal system impedance

When antagonistic muscles co-contract, the impedance of musculoskeletal systems to applied loads is known to increase. In this paper a physiologically-based, higher-order, nonlinear antagonistic muscle-joint model is utilized to clarify the sources of impedance modulation during a variety of tasks, ranging from resisting transient loads to holding steady loads to making fast movements in unpredictable surroundings. It is shown that impedance modulation occurs automatically as a function of the specific operating ranges utilized during a given task by each of four different muscle-joint mechanical relations. The relative contribution of each relation depends on the type of task, with impedance during quasi-static conditions sensitive to muscle tension-length and sometimes joint parallel elastic properties and during dynamic tasks dominated by the series element and muscle force-velocity properties. Elimination of any of these causes a decrease in built-in biomechanical capabilities. These findings raise questions concerning past theories on stiffness-impedance modulation which appear to underestimate the role of inherent biomechanical properties.     

Spinal stability and role of passive stiffness in dynamic squat and stoop lifts

The spinal stability and passive-active load partitioning under dynamic squat and stoop lifts were investigated as the ligamentous stiffness in flexion was altered. Measured in vivo kinematics of subjects lifting 180 N at either squat or stoop technique was prescribed in a nonlinear transient finite element model of the spine. The Kinematics-driven approach was utilized for temporal estimation of muscle forces, internal spinal loads and system stability. The finite element model accounted for nonlinear properties of the ligamentous spine, wrapping of thoracic extensor muscles and trunk dynamic characteristics while subject to measured kinematics and gravity/external loads. Alterations in passive properties of spine substantially influenced muscle forces, spinal loads and system stability in both lifting techniques, though more so in stoop than in squat. The squat technique is advocated for resulting in smaller spinal loads. Stability of spine in the sagittal plane substantially improved with greater passive properties, trunk flexion and load. Simulation of global extensor muscles with curved rather than straight courses considerably diminished loads on spine and increased stability throughout the task.     

Changes in muscle activity in response to different impact forces affect soft tissue compartment mechanical properties

Electromyographic (EMG) activity is associated with several tasks prior to landing in walking and running including positioning the leg, developing joint stiffness and possibly control of soft tissue compartment vibrations. The concept of muscle tuning suggests one reason for changes in muscle activity pattern in response to small changes in impact conditions, if the frequency content of the impact is close to the natural frequency of the soft tissue compartments, is to minimize the magnitude of soft tissue compartment vibrations. The mechanical properties of the soft tissue compartments depend in part on muscle activations and thus it was hypothesized that changes in the muscle activation pattern associated with different impact conditions would result in a change in the acceleration transmissibility to the soft tissue compartments. A pendulum apparatus was used to systematically administer impacts to the heel of shod male participants. Wall reaction forces, EMG of selected leg muscles, soft tissue compartment and shoe heel cup accelerations were quantified for two different impact conditions. The transmissibility of the impact acceleration to the soft tissue compartments was determined for each subject/soft tissue compartment/shoe combination. For this controlled impact situation it was shown that changes in the damping properties of the soft tissue compartments were related to changes in the EMG intensity and/or mean frequency of related muscles in response to a change in the impact interface conditions. These results provide support for the muscle tuning idea--that one reason for the changes in muscle activity in response to small changes in the impact conditions may be to minimize vibrations of the soft tissue compartments that are initiated at heel-strike.     

Work behaviors of artificial muscle based on cation driven polypyrrole

A soft actuator mimicking natural muscles (artificial muscle) has been developed using a flexible conducting polymer of polypyrrole films, which were driven by electrical stimulus in a saline solution. The work characteristics were studied under various load stresses and found to behave like natural muscles. The artificial muscles shrunk and stiffened by the positive electrical stimulus by 2-3% at the maximum force of 5 MPa, and relaxed by application of negative voltages. At larger load stresses, the artificial muscle shrunk slowly as natural muscles do. The driving current also lasted longer at larger loads, indicating that the muscle sensed the magnitude of the load stress. During contraction of the muscle, the conversion efficiency from the electrical input and mechanical output energies was estimated to be around 0.06%. The maximum volumetric work was approximately estimated to be 100 kJ m(-3). These figures are unexpectedly small compared with those of natural muscles.     

Gravitational force modulates muscle activity during mechanical oscillation of the tibia in humans

Mechanical oscillation (vibration) is an osteogenic stimulus for bone in animal models and may hold promise as an anti-osteoporosis measure in humans with spinal cord injury (SCI). However, the level of reflex induced muscle contractions associated with various loads (g force) during limb segment oscillation is uncertain. The purpose of this study was to determine whether certain gravitational loads (g forces) at a fixed oscillation frequency (30 Hz) increases muscle reflex activity in individuals with and without SCI. Nine healthy subjects and two individuals with SCI sat with their hip and knee joints at 90° and the foot secured on an oscillation platform. Vertical mechanical oscillations were introduced at 0.3, 0.6, 1.2, 3 and 5g force for 20 s at 30 Hz. Non-SCI subjects received the oscillation with and without a 5% MVC background contraction. Peak soleus and tibialis anterior (TA) EMG were normalized to M-max. Soleus and TA EMG were <2.5% of M-max in both SCI and non-SCI subjects. The greatest EMG occurred at the highest acceleration (5g). Low magnitude mechanical oscillation, shown to enhance bone anabolism in animal models, did not elicit high levels of reflex muscle activity in individuals with and without SCI. These findings support the g force modulated background muscle activity during fixed frequency vibration. The magnitude of muscle activity was low and likely does not influence the load during fixed frequency oscillation of the tibia.     

Some pharmacological properties of neuromuscular transmission in the oviduct of the locust,Locusta migratoria

The effects of various pharmacological agents on neurally evoked contractions of the visceral muscles of the oviduct of Locusta migratoria have been examined. The pentapeptide, proctolin, at low concentrations (10^?11 M?10^?10 M), induced an increase in the amplitude of neurally evoked contractions and basal tonus, and induced the appearance and increased the frequency of myogenic contractions. Glutamate, at 10^?4 M, produced a small transient contraction which in some preparations was accompanied by a reduction in amplitude of neurally evoked contractions. Octopamine, at 10^?6 M, reduced the amplitude of neurally evoked contractions and also resulted in a relaxation of the muscles. The octopaminergic effects were inhibited by the α-aminergic antagonist phentolamine. Neurally evoked contractions were unaffected by dopamine, 5-HT or the acetylcholine receptor antagonists atropine and hexamethonium. Acetylcholine increased the amplitude of neurally evoked contractions, but only at the high concentration of 10^?3 M. The possible role of proctolin and glutamate as excitatory neuro-transmitters and the inhibitory action of octopamine is discussed.     

Concentration independent modulation of local micromechanics in a fibrin gel

Methods for tuning extracellular matrix (ECM) mechanics in 3D cell culture that rely on increasing the concentration of either protein or cross-linking molecules fail to control important parameters such as pore size, ligand density, and molecular diffusivity. Alternatively, ECM stiffness can be modulated independently from protein concentration by mechanically loading the ECM. We have developed a novel device for generating stiffness gradients in naturally derived ECMs, where stiffness is tuned by inducing strain, while local mechanical properties are directly determined by laser tweezers based active microrheology (AMR). Hydrogel substrates polymerized within 35 mm diameter Petri dishes are strained non-uniformly by the precise rotation of an embedded cylindrical post, and exhibit a position-dependent stiffness with little to no modulation of local mesh geometry. Here we present the device in the context of fibrin hydrogels. First AMR is used to directly measure local micromechanics in unstrained hydrogels of increasing fibrin concentration. Changes in stiffness are then mapped within our device, where fibrin concentration is held constant. Fluorescence confocal imaging and orbital particle tracking are used to quantify structural changes in fibrin on the micro and nano levels respectively. The micromechanical strain stiffening measured by microrheology is not accompanied by ECM microstructural changes under our applied loads, as measured by confocal microscopy. However, super-resolution orbital tracking reveals nanostructural straightening, lengthening, and reduced movement of fibrin fibers. Furthermore, we show that aortic smooth muscle cells cultured within our device are morphologically sensitive to the induced mechanical gradient. Our results demonstrate a powerful cell culture tool that can be used in the study of mechanical effects on cellular physiology in naturally derived 3D ECM tissues.     

Activity of deep abdominal muscles increases during submaximal flexion and extension efforts but antagonist co-contraction remains unchanged

Lumbo-pelvic stability relies, amongst other factors, on co-contraction of the lumbo-pelvic muscles. However, during submaximal trunk flexion and extension efforts, co-contraction of antagonist muscles is limited. It was predicted that activity of the deeper lumbo-pelvic muscles that are often excluded from analysis (transversus abdominis (TrA) and the deep fascicles of multifidus (DM)), would increase with load in each direction. In eleven healthy subjects, electromyographic activity (EMG) was recorded from eight trunk muscles using surface and fine-wire electrodes. Subjects performed isometric flexion and extension efforts to submaximal loads of 50, 100, 150 and 200 N and a maximal voluntary contraction (MVC). Loading tasks were then repeated in trials in which subjects knew that the load would release at an unpredictable time. Compared to the starting position, EMG of all muscles, except DM, increased during MVC efforts in both directions. During the flexion and extension submaximal tasks, there was no increased co-contraction of antagonist muscles. However, TrA EMG increased in both directions. In the unpredictable trials, EMG of all lumbo-pelvic muscles except TrA was decreased. These findings provide further support for a contribution of TrA to lumbo-pelvic stability. In submaximal tasks, TrA activation may enhance stability as a strategy to improve trunk stiffness without requiring a concurrent increase in activity of the larger torque producing trunk muscles.     

Locomotor function shapes the passive mechanical properties and operating lengths of muscle

Locomotor muscles often perform diverse roles, functioning as motors that produce mechanical energy, struts that produce force and brakes that dissipate mechanical energy. In many vertebrate muscles, these functions are not mutually exclusive and a single muscle often performs a range of mechanically diverse tasks. This functional diversity has obscured the relationship between a muscle''s locomotor function and its mechanical properties. I use hopping in toads as a model system for comparing muscles that primarily produce mechanical energy with muscles that primarily dissipate mechanical energy. During hopping, hindlimb muscles undergo active shortening to produce mechanical energy and propel the animal into the air, whereas the forelimb muscles undergo active lengthening to dissipate mechanical energy during landing. Muscles performing distinct mechanical functions operate on different regions of the force–length curve. These findings suggest that a muscle''s operating length may be shaped by potential trade-offs between force production and sarcomere stability. In addition, the passive force–length properties of hindlimb and forelimb muscles vary, suggesting that passive stiffness functions to restrict the muscle''s operating length in vivo. These results inform our understanding of vertebrate muscle variation by providing a clear link between a muscle''s locomotor function and its mechanical properties.     

Prolonged myosin binding increases muscle stiffness in Drosophila models of Freeman-Sheldon syndrome

Freeman-Sheldon syndrome (FSS) is characterized by congenital contractures resulting from dominant point mutations in the embryonic isoform of muscle myosin. To investigate its disease mechanism, we used Drosophila models expressing FSS myosin mutations Y583S or T178I in their flight and jump muscles. We isolated these muscles from heterozygous mutant Drosophila and performed skinned fiber mechanics. The most striking mechanical alteration was an increase in active muscle stiffness. Y583S/+ and T178I/+ fibers’ elastic moduli increased 70 and 77%, respectively. Increased stiffness contributed to decreased power generation, 49 and 66%, as a result of increased work absorbed during the lengthening portion of the contractile cycle. Slower muscle kinetics also contributed to the mutant phenotype, as shown by 17 and 32% decreases in optimal frequency for power generation, and 27 and 41% slower muscle apparent rate constant 2πb. Combined with previous measurements of slower in vitro actin motility, our results suggest a rate reduction of at least one strongly bound cross-bridge cycle transition that increases the time myosin spends strongly bound to actin, t_on. Increased t_on was further supported by decreased ATP affinity and a 16% slowing of jump muscle relaxation rate in T178I heterozygotes. Impaired muscle function caused diminished flight and jump ability of Y583S/+ and T178I/+ Drosophila. Based on our results, assuming that our model system mimics human skeletal muscle, we propose that one mechanism driving FSS is elevated muscle stiffness arising from prolonged t_on in developing muscle fibers.     

A mathematical analysis of the force-stiffness characteristics of muscles in control of a single joint system

Feldman (1966) has proposed that a muscle endowed with its spinal reflex system behaves as a non-linear spring with an adjustable resting length. In contrast, because of the length-tension properties of muscles, many researchers have modeled them as non-linear springs with adjustable stiffness. Here we test the merits of each approach: Initially, it is proven that the adjustable stiffness model predicts that isometric muscle force and stiffness are linearly related. We show that this prediction is not supported by data on the static stiffness-force characteristics of reflexive muscles, where stiffness grows non-linearly with force. Therefore, an intact muscle-reflex system does not behave as a non-linear spring with an adjustable stiffness. However, when the same muscle is devoid of its reflexes, the data shows that stiffness grows linearly with force. We aim to understand the functional advantage of the non-linear stiffness-force relationship present in the reflexive muscle. Control of an inverted pendulum with a pair of antagonist muscles is considered. Using an active-state muscle model we describe force development in an areflexive muscle. From the data on the relationship of stiffness and force in the intact muscle we derive the length-tension properties of a reflexive muscle. It is shown that a muscle under the control of its spinal reflexes resembles a non-linear spring with an adjustable resting length. This provides independent evidence in support of the Feldman hypothesis of an adjustable resting length as the control parameter of a reflexive muscle, but it disagrees with his particular formulation. In order to maintain stability of the single joint system, we prove that a necessary condition is that muscle stiffness must grow at least linearly with force at isometric conditions. This shows that co-contraction of antagonist muscles may actually destabilize the limb if the slope of this stiffness-force relationship is less than an amount specified by the change in the moment arm of the muscle as a function of joint configuration. In a reflexive muscle where stiffness grows faster than linearly with force, co-contraction will always lead to an increase in stiffness. Furthermore, with the reflexive muscles, the same level of joint stiffness can be produced by much smaller muscle forces because of the non-linear stiffness-force relationship. This allows the joint to remain stable at a fraction of the metabolic energy cost associated with maintaining stability with areflexive muscles.This work was supported in part by grant no. 1R01 NS 24926 from the NIH (Michael Arbib, PI). R.S. was supported by an IBM Graduate Fellowship in Computer Science     

Muscle activity and spine load during pulling exercises: Influence of stable and labile contact surfaces and technique coaching

This study examined pulling exercises performed on stable surfaces and unstable suspension straps. Specific questions included: which exercises challenged particular muscles, what was the magnitude of resulting spine load, and did technique coaching influence results. Fourteen males performed pulling tasks while muscle activity, external force, and 3D body segment motion were recorded. These data were processed and input to a sophisticated and anatomically detailed 3D model that used muscle activity and body segment kinematics to estimate muscle force, in this way the model was sensitive to each individual’s choice of motor control for each task. Muscle forces and linked segment joint loads were used to calculate spine loads. There were gradations of muscle activity and spine load characteristics to every task. It appears that suspension straps alter muscle activity less in pulling exercises, compared to studies reporting on pushing exercises. The chin-up and pull-up exercises created the highest spine load as they required the highest muscle activation, despite the body “hanging” under tractioning gravitational load. Coaching shoulder centration through retraction increased spine loading but undoubtedly adds proximal stiffness. An exercise atlas of spine compression was constructed to help with the decision making process of exercise choice for an individual.