Stabilizing function of antagonistic neuromusculoskeletal systems: an analytical investigation

 Under normal conditions human walking or running consists of stable cyclic movements. Minor perturbances such as a stone or a pothole do not disrupt the cycle, and the system returns to its prescribed trajectory. We investigated whether a pair of antagonistic muscles is able to stabilize the movement without neuronal feedback. The human is represented by a model consisting of a massless two-segment linkage system (leg) topped by a point mass. Both the extensor and flexor muscles are described by a Hill-type muscle model. Conditions for stability are calculated analytically based on the Ljapunov Theory and the results are illustrated by numerical examples. The activation functions of both the extensor and flexor muscles can be calculated for a prescribed trajectory to maintain the self-stabilizing ability of such a system. Experimental evidence supports the prediction. Our investigation shows that a moving center of rotation of the kneejoint, a biarticular flexor muscle group, the force-velocity relation, and the ascending limb of the force-length relation improves the self-stabilizing ability of human movement. Received: 24 March 1999 / Accepted: 20 February 2003 / Published online: 22 May 2003 Correspondence to: H. Wagner (e-mail: heiko.wagner@uni-jena.de, Tel.:+49-3641-945706) Acknowledgements. The authors wish to express their gratitude to Arnd Friedrichs and Lars Wendrock for their contribution to data acquisition and analysis. Veit Wank is acknowledged for making available for our use the x-ray photos of several knee joints. We would like to thank Anna N. Ahn for her very detailed and helpful comments. With support from DFG (Innovationskolleg “Motion Systems”).     

Molecular genetic studies of gene identification for sarcopenia

Sarcopenia, which is characterized by a progressive decrease of skeletal muscle mass and function with aging, is closely related to several common diseases (such as cardiovascular and airway diseases) and functional impairment/disability. Strong genetic determination has been reported for muscle mass and muscle strength, two most commonly recognized and studied risk phenotypes for sarcopenia, with heritability ranging from 30 to 85% for muscle strength and 45–90% for muscle mass. Sarcopenia has been the subject of increasing genetic research over the past decade. This review is designed to comprehensively summarize the most important and representative molecular genetic studies designed to identify genetic factors associated with sarcopenia. We have methodically reviewed whole-genome linkage studies in humans, quantitative trait loci mapping in animal models, candidate gene association studies, newly reported genome-wide association studies, DNA microarrays and microRNA studies of sarcopenia or related skeletal muscle phenotypes. The major results of each study are tabulated for easy comparison and reference. The findings of representative studies are discussed with respect to their influence on our present understanding of the genetics of sarcopenia. This is a comprehensive review of molecular genetic studies of gene identification for sarcopenia, and an overarching theme for this review is that the currently accumulating results are tentative and occasionally inconsistent and should be interpreted with caution pending further investigation. Consequently, this overview should enhance recognition of the need to validate/replicate the genetic variants underlying sarcopenia in large human cohorts and animal. We believe that further progress in understanding the genetic etiology of sarcopenia will provide valuable insights into important fundamental biological mechanisms underlying muscle physiology that will ultimately lead to improved ability to recognize individuals at risk for developing sarcopenia and our ability to treat this debilitating condition.     

Modelling, simulation and optimisation of a human vertical jump.

This paper describes an efficient biomechanical model of the human lower limb with the aim of simulating a real human jump movement consisting of an upword propulsion, a flying and a landing phase. A multiphase optimal control technique is used to solve the muscle force sharing problem. To understand how intermuscular control coordinates limb muscle excitations, the human body is reduced to a single lower limb consisting of three rigid bodies. The biomechanical system is activated by nine muscle-tendon actuators representing the basic properties of muscles during force generation. For the calculation of the minimal muscle excitations of the jump movement, the trajectory of the hip joint is given as a rheonomic constraint and the contact forces (ground reaction forces) are determined by force plates. Based on the designed musculoskeletal model and on the differential equations of the multibody system, muscle excitations and muscle forces necessary for a vertical jump movement are calculated. The validity of the system is assessed comparing the calculated muscle excitations with the registered surface electromyogramm (EMG) of the muscles. The achieved results indicate a close relationship between the predicted and the measured parameters.     

Oxygen delivery by blood determines the maximal VO2 and work rate during whole body exercise in humans: in silico studies

It has been proposed by Saltin (J Exp Biol 115: 345-354, 1985) that oxygen delivery by blood is limiting for maximal work and oxygen consumption in humans during whole body exercise but not during single-muscle exercise. To test this prediction quantitatively, we developed a static (steady-state) computer model of oxygen transport to and within human skeletal muscle during single-muscle (quadriceps) exercise and whole body (cycling) exercise. The main system fluxes, namely cardiac output and oxygen consumption by muscle, are described as a function of the "primary" parameter: work rate. The model is broadly validated by comparison of computer simulations with various experimental data. In silico studies show that, when all other parameters and system properties are kept constant, an increase in the working muscle mass from 2.5 kg (single quadriceps) to 15 kg (two legs) causes, at some critical work intensity, a drop in oxygen concentration in muscle cells to (very near) zero, and therefore oxygen supply by blood limits maximal oxygen consumption and oxidative ATP production. Therefore, the maximal oxygen consumption per muscle mass is significantly higher during single-muscle exercise than during whole body exercise. The effect is brought about by a distribution of a limited amount of oxygen transported by blood in a greater working muscle mass during whole body exercise.     

An optimal control model for maximum-height human jumping

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

A quantitative trait locus on 13q14.2 for trunk strength.

Previous findings show strong evidence for the role of retinoblastoma (Rb) in myoblast proliferation and differentiation. However, it is not known whether variation in the retinoblastoma gene (RB1 ) is responsible for normal variation in human muscle strength. Therefore, a linkage analysis for quantitative traits was performed on 329 young male siblings from 146 families with muscle strength, using a polymorphic marker in RB1 (D13S153 on 13q14.2). Trunk strength, a general strength indicator that requires activation of large muscle groups, was measured on a Cybex TEF isokinetic dynamometer. We found evidence for linkage between locus D13S153 at 13q14.2 and several measurements of trunk flexion with LOD scores between 1.62 and 2.78 (.002< p <.0002). No evidence for linkage was found with trunk extension. This first exploration of the relationship between RB1 and human muscle strength through linkage analysis warrants efforts for further fine mapping of this region.     

Sensitivity of model predictions of muscle function to changes in moment arms and muscle-tendon properties: a Monte-Carlo analysis

Hill-type muscle models are commonly used in musculoskeletal models to estimate muscle forces during human movement. However, the sensitivity of model predictions of muscle function to changes in muscle moment arms and muscle-tendon properties is not well understood. In the present study, a three-dimensional muscle-actuated model of the body was used to evaluate the sensitivity of the function of the major lower limb muscles in accelerating the whole-body center of mass during gait. Monte-Carlo analyses were used to quantify the effects of entire distributions of perturbations in the moment arms and architectural properties of muscles. In most cases, varying the moment arm and architectural properties of a muscle affected the torque generated by that muscle about the joint(s) it spanned as well as the torques generated by adjacent muscles. Muscle function was most sensitive to changes in tendon slack length and least sensitive to changes in muscle moment arm. However, the sensitivity of muscle function to changes in moment arms and architectural properties was highly muscle-specific; muscle function was most sensitive in the cases of gastrocnemius and rectus femoris and insensitive in the cases of hamstrings and the medial sub-region of gluteus maximus. The sensitivity of a muscle's function was influenced by the magnitude of the muscle's force as well as the operating region of the muscle on its force-length curve. These findings have implications for the development of subject-specific models of the human musculoskeletal system.     

The Influence of Intrinsic Muscle Properties on Musculoskeletal System Stability: A Modelling Study

The objective of this study is to investigate how the intrinsic mechanical properties of muscles will affect the musculoskeletal system stability. A typical musculoskeletal joint driven by a pair of antagonist muscles confined only in the sigittal plane was constructed. The dynamic characteristics of the flexor and extensor muscles induced by neural inputs were represented by three dynamic processes: neural excitation, muscle activation and muscle contraction dynamics. The muscle contraction mechanics was described using a modified Hill's model with a Contractile Element (CE), a parallel elastic element and a serial elastic element. Additionally, the change of muscle Physiological Cross-Sectional Area (PCSA) and pennation angle during muscle contraction were also considered. A set of dynamic simulations were conducted by applying an external impulsive force at the distal part of the musculoskeletal system. Sensitivity analysis was conducted to investigate the effect of the CE's force-length relationship, the CE's force-velocity relationship, the force-length relationship of the serial elastic element, the parallel elastic element and the pennation angle on the system stability. The results show that the muscles with full intrinsic mechanical properties are sufficient to stabilize the system subject to an impulsive force perturbation without reflexive changes in activations. To guarantee a self-stabilizing ability, a proper CE's force-velocity relationship, the existence of a series elastic element and a sufficient muscle co-contraction level are necessary. This study would provide insight into the intrinsic design and function of the musculoskeletal system, and also give implications for the design of bionic actuators, biomimetic robotics and prosthetic devices.     

The relation between the resultant moments at a joint and the moments measured by an isokinetic dynamometer

Isokinetic dynamometers have frequently been used to determine in vivo properties of human skeletal muscles. In these investigations the moments recorded by the dynamometer were often (implicitly) assumed to be the same as the joint moments produced by muscles. This assumption may have contributed to the conflicting results about in vivo muscle properties of human skeletal muscles that are reported in the literature. The purpose of this paper is to present a method for calculating the resultant joint moments from the moments recorded using a Cybex II dynamometer and to determine the differences between these two moments for some typical exercise conditions. The differences between these these moments are shown to be due to (a) gravitational effects, (b) inertial effects, and (c) non-rigidity of the Cybex arm/shank-foot system. The results obtained suggest that the moments recorded using the dynamometer should not be used to derive muscle properties without taking into account the relationship between the resultant joint moments and the moments measured using an isokinetic dynamometer.     

The contribution of muscle properties in the control of explosive movements

Explosive movements such as throwing, kicking, and jumping are characterized by high velocity and short movement time. Due to the fact that latencies of neural feedback loops are long in comparison to movement times, correction of deviations cannot be achieved on the basis of neural feedback. In other words, the control signals must be largely preprogrammed. Furthermore, in many explosive movements the skeletal system is mechanically analogous to an inverted pendulum; in such a system, disturbances tend to be amplified as time proceeds. It is difficult to understand how an inverted-pendulum-like system can be controlled on the basis of some form of open loop control (albeit during a finite period of time only). To investigate if actuator properties, specifically the force-length-velocity relationship of muscle, reduce the control problem associated with explosive movement tasks such as human vertical jumping, a direct dynamics modeling and simulation approach was adopted. In order to identify the role of muscle properties, two types of open loop control signals were applied: STIM(t), representing the stimulation of muscles, and MOM(t), representing net joint moments. In case of STIM control, muscle properties influence the joint moments exerted on the skeleton; in case of MOM control, these moments are directly prescribed. By applying perturbations and comparing the deviations from a reference movement for both types of control, the reduction of the effect of disturbances due to muscle properties was calculated. It was found that the system is very sensitive to perturbations in case of MOM control; the sensitivity to perturbations is markedly less in case of STIM control. It was concluded that muscle properties constitute a peripheral feedback system that has the advantage of zero time delay. This feedback system reduces the effect of perturbations during human vertical jumping to such a degree that when perturbations are not too large, the task may be performed successfully without any adaptation of the muscle stimulation pattern.     

Hormonal aspects of the muscle-bone unit

Osteoporotic fractures are the result of low density and especially inferior bone quality (microarchitecture) caused by both internal (genes, hormones) and external (life style) influences. Bone mechanosensors are extremely important for the overall integrity of the skeleton, because in response to mechanical load they activate its modeling, resulting in an increase in bone density and strength. The largest physiological loads are caused by muscle contractions. Bone mass in adult men has a closer relationship to muscle mass than is case in women. The sexual differences in the relationship between bone and muscle mass are also apparent in children. Based on the mechanostatic theory, the muscle-bone unit has been defined as a functional system whose components are under the common control of the hormones of the somatotropin-IGF-I axis, sexual steroids, certain adipose tissue hormones and vitamin D. The osteogenic effects of somatotropin-IGF-I system are based on the stimulation of bone formation, as well as increase in muscle mass. Moreover, somatotropin decreases the bone mechanostat threshold and reinforces the effect of physical stress on bone formation. The system, via the muscle-bone unit, plays a significant role in the development of the childhood skeleton as well as in its stability during adulthood. The muscle and bone are also the targets of androgens, which increase bone formation and the growth of muscle mass in men and women, independently of IGF-I. The role of further above-mentioned hormones in regulation of this unified functional complex is also discussed.     

A dynamic simulator to evaluate distal radio-ulnar joint kinematics

In order to perform cadaveric biomechanical studies of the human forearm and distal radio-ulnar joint, a dynamic simulator has been constructed. The device is based upon a Plexiglas frame, to which the ulna is secured in a vertical orientation and the humerus in a horizontal orientation. The hand is secured in a sliding bar linkage to a stepper-motor that is used to rotate the forearm. The tendons to be loaded are connected to pneumatic actuators that provide agonist and antagonist muscle loading resulting in torque along the forearm axis. The muscle loading profiles and magnitudes are programmable as a function of the pronation-supination position and direction. A magnetic tracking system is used to collect three-dimensional kinematics data of up to four segments, in conjunction with the muscle tendon loads, forearm torque and other prescribed experimental measures. All functions are under PC control using custom software written with LabVIEW (National Instruments, Austin, TX). For the DRUJ testing, the validity of the tendon loading protocol to produce physiologic torque/rotation patterns was verified using in vivo data. The relationship of individual muscle forces to forearm torque was determined by a cadaveric study.     

Contractile properties of the human diaphragm in vivo

The mechanical properties of the human diaphragm have been studied at fractional residual capacity in normal seated subjects with closed glottis. The transdiaphragmatic pressure (Pdi) developed in response to single shocks or to trains of stimuli at increasing frequency was approximately 3 times greater during bilateral than unilateral stimulation. During unilateral phrenic nerve stimulation the Pdi twitches increased as the interval (0-200 ms) of a preceding conditioning stimulus to the contralateral phrenic nerve was decreased suggesting that the two hemidiaphragms are mechanically coupled in series. The contraction time and half-relaxation time of single bilateral twitches as well as the Pdi-frequency relationship (5-35 Hz) during bilateral tetanic stimulation indicate that the contractile properties of the human diaphragm are intermediate between those of fast- and slow-twitch muscle fibers. The results suggest that the contractile properties of the human diaphragm are well illustrated by single bilateral twitches recorded from the relaxed muscle, but that the responses to unilateral stimulation are misleading due to distortion by abnormal changes in the muscle geometry.     

Expression of vascular endothelial growth factor during the development of cardiac hypertrophy in spontaneously hypertensive rats

We have recently demonstrated that lipids, particularly cholesterol, covalently bound to apolipoprotein B (apoB) are a stable marker of low density lipoprotein (LDL) oxidation (Tertov et al. 1995). The present study is an attempt to assess the relationship between the degree of LDL oxidation, evaluated by the content of apoB-bound cholesterol and the ability of LDL to induce cholesterol accumulation in cultured human aortic intimal smooth muscle cells, i.e. LDL atherogenicity. Native LDL was oxidized in vitro by copper ions, 2,2-azobis-(2-aminopropane hydrochloride), or sodium hypochlorite. Minimum degree of LDL in vitro oxidation necessary to convert LDL into atherogenic one was accompanied by an increase of apoB-bound cholesterol to the level much higher than that usually observed in freshly isolated atherogenic LDL from human blood. Moreover, elimination of LDL aggregates from in vitro oxidized LDL preparations by gel filtration led to loss of its atherogenic properties. Thus, the ability to induce cholesterol accumulation in cells, i.e. the atherogenicity of in vitro oxidized LDL is a result of LDL aggregation but not oxidation. We also studied the relationship between LDL atherogenicity and apoB-bound cholesterol content in LDL freshly isolated from healthy subjects and normo- and hypercholesterolemic patients with coronary atherosclerosis. The ability of human LDL to induce cholesterol accumulation in aortic smooth muscle cells did not correlate with the degree of in vivo LDL oxidation (r = 0.12, n = 90). It is concluded that LDL atherogenicity does not depend on the degree of lipid peroxidation in LDL particle.     

Sulfide increases labile iron pool in RD4 cells

A linkage between sulfur and iron metabolism has been suggested since sulfide has the ability to release iron from ferritin in the presence of iron acceptors in vitro. Nevertheless, this linkage is still lacking evidence in vivo as well as in cellular models. In this study we have treated human RD4 skeletal muscle cells with sodium sulfide and measured the level of the labile iron pool (LIP) as well as the intracellular sulfide concentration. We have also detected the amounts of L-ferritin protein as well as the iron regulatory protein 2 (IRP2). The sulfide treatment resulted in a 100% increase in the amount of LIP after 1 and 2 h. We also found that the raise of the LIP levels was coupled to an elevation of the amounts of intracellular sulfide that increased by 60%. The bioavailability of the released iron was confirmed by a 100% increase in L-ferritin protein as well as a 60% decrease of the IRP2 protein levels. These results suggest that there is a linkage between sulfur metabolism and intracellular iron regulation in mammalian cells.     

Muscle architectural properties in the common marmoset (<Emphasis Type="Italic">Callithrix jacchus</Emphasis>)

The common marmoset, Callithrix jacchus, is a small New World monkey that has recently gained attention as an important experimental animal model in the field of neuroscience as well in rehabilitative and regenerative medicine. This attention reflects the closer phylogenetic relationship between humans and common marmosets compared to that between humans and other experimental animals. When studying the neuronal mechanism behind various types of neurological motor disorders using the common marmoset, possible differences in muscle parameters (e.g., the force-generating capacity of each of the muscles) between the common marmoset and other animals must be taken into account to permit accurate interpretation of observed motor behavior. Differences in the muscle architectural properties are expected to affect biomechanics, and hence to affect neuronal control of body movements. Therefore, we dissected the forelimbs and hind limbs of two common marmosets, including systematic analysis of the muscle mass, fascicle length, and physiological cross-sectional area (PCSA). Comparisons of the mass fractions and PCSA fractions of the forelimb and hind limb musculature among the common marmoset, human, Japanese macaque, and domestic cat demonstrated that the overall muscle architectural properties of the forelimbs and hind limbs in the common marmoset are very similar to those of the Japanese macaque, a typical quadrupedal primate. However, muscle architectural properties of the common marmoset differ from those of the domestic cat, which has relatively larger hamstrings and pedal digital flexor muscles. Compared to humans, the common marmoset exhibits relatively smaller shoulder protractor, retractor, and abductor muscles and larger elbow extensor and rotator-cuff muscles in the forelimb, and smaller plantarflexor muscles in the hind limb. These differences in the muscle architectural properties must be taken into account when interpreting motor behaviors such as locomotion and arm-reaching movements in the common marmoset.     

Limitations to maximum sprinting speed imposed by muscle mechanical properties

It has been suggested that the force-velocity relationship of skeletal muscle plays a critical limiting role in the maximum speed at which humans can sprint. However, this theory has not been tested directly, and it is possible that other muscle mechanical properties play limiting roles as well. In this study, forward dynamics simulations of human sprinting were generated using a 2D musculoskeletal model actuated by Hill muscle models. The initial simulation results compared favorably to kinetic, kinematic, and electromyographic data recorded from sprinting humans. Muscle mechanical properties were then removed in isolation to quantify their effect on maximum sprinting speed. Removal of the force-velocity, excitation-activation, and force-length relationships increased the maximum speed by 15, 8, and 4%, respectively. Removal of the series elastic force-extension relationship decreased the maximum speed by 26%. Each relationship affected both stride length and stride frequency except for the force-length relationship, which mainly affected stride length. Removal of all muscular properties entirely (optimized joint torques) increased speed (+22%) to a greater extent than the removal of any single contractile property. The results indicate that the force-velocity relationship is indeed the most important contractile property of muscle regarding limits to maximum sprinting speed, but that other muscular properties also play important roles. Interactions between the various muscular properties should be considered when explaining limits to maximal human performance.     

Effects of spaceflight, simulated spaceflight and countermeasures on single muscle fiber physiology

Since the first human flew in space in 1961, there has been extensive scientific interest in the responses of the human body and how it adapts to this unique environment. From the available data, it appears that all major systems in the human body undergo an adaptive change while in a microgravity environment. In particular the human muscle system appears to undergo loss of muscle mass and strength which greatly influences the maximal work capacity of the muscle. Recently, our research group has been involved in a series of whole muscle and cellular studies during periods of short duration space flight, bed rest, and unilateral lower limb suspension (ULLS) in an attempt to elucidate the changes that are occurring in the whole muscle and single muscle fiber contractile properties with unloading. In addition, various countermeasure activities for skeletal muscle have been part of the space flights and ground-based studies. The intention of this paper will be to briefly review our findings in whole muscle, cellular, and countermeasure effectiveness with human muscle.     

Carnosine and anserine concentrations in the quadriceps femoris muscle of healthy humans

The content of anserine and carnosine in the lateral portion of the quadriceps femoris muscle of 50 healthy, human subjects has been studied. Anserine was undetectable in all muscle samples examined. Muscle carnosine values for the group conformed to a normal distribution with a mean (SD) value of 20.0 (4.7) mmol.kg-1 of dry muscle mass. The concentration of carnosine was significantly higher in the muscle of male subjects (21.3, 4.2 mmol.kg-1 dry mass) than in females of a similar age and training status (17.5, 4.8 mmol.kg-1 dry mass) (P less than 0.005). The test-retest reliability of measures was determined on a subgroup of 17 subjects. No significant difference in mean carnosine concentration was found between the two trials [21.5 (4.0) and 22.0 (5.2) mmol.kg-1 dry muscle mass; P greater than 0.05]. The importance of carnosine as a physicochemical buffer within human muscle was examined by calculating its buffering ability over the physiological pH range. From the range of carnosine concentrations observed (7.2-30.7 mmol.kg-1 dry muscle mass), it was estimated that the dipeptide could buffer between 2.4 and 10.1 mmol H+.kg-1 dry mass over the physiological pH range 7.1-6.5, contributing, on average, approximately 7% to the total muscle buffering. This suggests that in humans, in contrast to many other species, carnosine is of only limited importance in preventing the reduction in pH observed during high intensity exercise.     

Are fixed limb inertial models valid for dynamic simulations of human movement?

During human movement, muscle activation and limb movement result in subtle changes in muscle mass distribution. Muscle mass redistribution can affect limb inertial properties and limb dynamics, but it is not currently known to what extent. The objectives of this study were to investigate: (1) how physiological alterations of muscle and tendon length affect limb inertial characteristics, and (2) how such changes affect dynamic simulations of human movement. To achieve these objectives, a digital model of a human leg, custom software, and Software for interactive musculoskeletal modeling were used to simulate mass redistribution of muscle–tendon structures within a limb segment during muscle activation and joint movement. Thigh and shank center of mass and moments of inertia for different muscle activation and joint configurations were determined and compared. Limb inertial parameters representing relaxed muscles and fully active muscles were input into a simulated straight-leg movement to evaluate the effect inertial parameter variations could have on movement simulation results. Muscle activation and limb movement altered limb segment center of mass and moments of inertia by less than 0.04 cm and 1.2%, respectively. These variations in limb inertial properties resulted in less than 0.01% change in maximum angular velocity for a simulated straight-leg hip flexion task. These data demonstrate that, for the digital human leg model considered, assuming static quantities for segment center of masses and moments of inertia in movement simulations appear reasonable and induce minimal errors in simulated movement dynamics.