Vertical adaptation of the center of mass in human running on uneven ground.

In running we are frequently confronted with different kinds of disturbances. Some require quick reactions and adaptations while others, like moderate changes in ground level, can be compensated passively. Monitoring the kinematics of the runner's center of mass (CoM) in such situations can reveal what global locomotion control strategies humans use and can help to distinguish between active and passive compensation methods. In this study single and permanent upward steps of 10 cm as well as drops of the same height were used as mechanical disturbances and the adaptations in the vertical oscillation of the runners CoM were analyzed. We found that runners visually perceiving uneven ground ahead substantially adapted their CoM in preparation by lifting it about 50% of step height or lowering it by about 40% of drop height, respectively. After contact on the changed ground level different adaptations depending on the situation occur. For persisting changes the adaptation to the elevated ground is completed after the first step on the new level. For single steps part of the adaptation takes place while returning to the ground. The consistent adaptations for the different situations support the idea that controlling the CoM by adapting leg parameters is a general control principle in running.

Determination of three-dimensional muscle architectures: validation of the DTI-based fiber tractography method by manual digitization.

In the last decade, diffusion tensor imaging (DTI) has been used increasingly to investigate three-dimensional (3D) muscle architectures. So far there is no study that has proved the validity of this method to determine fascicle lengths and pennation angles within a whole muscle. To verify the DTI method, fascicle lengths of m. soleus as well as their pennation angles have been measured using two different methods. First, the 3D muscle architecture was analyzed in vivo applying the DTI method with subsequent deterministic fiber tractography. In a second step, the muscle architecture of the same muscle was analyzed using a standard manual digitization system (MicroScribe MLX). Comparing both methods, we found differences for the median pennation angles (P < 0.001) but not for the median fascicle lengths (P = 0.216). Despite the statistical results, we conclude that the DTI method is appropriate to determine the global fiber orientation. The difference in median pennation angles determined with both methods is only about 1.2° (median pennation angle of MicroScribe: 9.7°; DTI: 8.5°) and probably has no practical relevance for muscle simulation studies. Determining fascicle lengths requires additional restriction and further development of the DTI method.

Extension and customization of self-stability control in compliant legged systems.

Several recent studies on the control of legged locomotion in animal and robot running focus on the influence of different leg parameters on gait stability. In a preceding investigation self-stability controls showing deadbeat behavior could be obtained by studying the dynamics of the system in dependence of the leg orientation carefully adjusted during the flight phase. Such controls allow to accommodate disturbances of the ground level without having to detect them. Here we further this method in two ways. Besides the leg orientation, we allow changes in leg stiffness during flight and show that this extension substantially improves the rejection of ground disturbances. In a human like example the tolerance of random variation in ground level over many steps increased from 3.5% to 35% of leg length. In single steps changes of about 70% leg length (either up or down) could be negotiated. The variable leg stiffness not only allows to start with flat leg orientations maximizing step tolerances but also increase the control subspace. This allows to customize self-stability controls and to consider physical and technical limitations found in animals and robots.

Nature as an engineer: one simple concept of a bio-inspired functional artificial muscle.

The biological muscle is a powerful, flexible and versatile actuator. Its intrinsic characteristics determine the way how movements are generated and controlled. Robotic and prosthetic applications expect to profit from relying on bio-inspired actuators which exhibit natural (muscle-like) characteristics. As of today, when constructing a technical actuator, it is not possible to copy the exact molecular structure of a biological muscle. Alternatively, the question may be put how its characteristics can be realized with known mechanical components. Recently, a mechanical construct for an artificial muscle was proposed, which exhibits hyperbolic force-velocity characteristics. In this paper, we promote the constructing concept which is made by substantiating the mechanical design of biological muscle by a simple model, proving the feasibility of its real-world implementation, and checking their output both for mutual consistency and agreement with biological measurements. In particular, the relations of force, enthalpy rate and mechanical efficiency versus contraction velocity of both the construct's technical implementation and its numerical model were determined in quick-release experiments. All model predictions for these relations and the hardware results are now in good agreement with the biological literature. We conclude that the construct represents a mechanical concept of natural actuation, which is suitable for laying down some useful suggestions when designing bio-inspired actuators.

Proof of concept of an artificial muscle: theoretical model, numerical model, and hardware experiment.

Recently, the hyperbolic Hill-type force-velocity relation was derived from basic physical components. It was shown that a contractile element CE consisting of a mechanical energy source (active element AE), a parallel damper element (PDE), and a serial element (SE) exhibits operating points with hyperbolic force-velocity dependency. In this paper, the contraction dynamics of this CE concept were analyzed in a numerical simulation of quick release experiments against different loads. A hyperbolic force-velocity relation was found. The results correspond to measurements of the contraction dynamics of a technical prototype. Deviations from the theoretical prediction could partly be explained by the low stiffness of the SE, which was modeled analog to the metal spring in the hardware prototype. The numerical model and hardware prototype together, are a proof of this CE concept and can be seen as a well-founded starting point for the development of Hill-type artificial muscles. This opens up new vistas for the technical realization of natural movements with rehabilitation devices.

Musculoskeletal support of lumbar spine stability.

Using a biomechanical model and experimental data the self-stabilising behaviour of antagonistic trunk muscles was analyzed. The biomechanical model is constituted of a pair of antagonistic Hill-type muscles, their geometric arrangement with respect to the spine, and the instantaneous centre of rotation in frontal plane. Using Ljapunov's theory, the stability of certain motion and loading situations was analyzed. Applying a sensitivity analysis, the influence of different muscle properties and the geometric arrangement on stability was investigated. The simulations revealed that the stability of spinal movements depended primarily on the geometrical arrangement of muscles and the position of the centre of rotation of the spine, the latter was affected in turn by the activities of the profound muscles. To stabilize the situations simulated oblique muscle arrangements were necessary. In order to define an instantaneous centre of rotation in the lower region of the spine negative attachment angles (medio-lateral decline) of muscles were necessary, corresponding to the real anatomy of obliquus externus muscles. More cranially located instantaneous centres of rotation required positive attachment angles for stability, corresponding to obliquus internus or multifidus muscles. Furthermore, the fibre-type distribution of muscles influenced the stability of the system, i.e. a high percentage of fast-twitch-fibres supported the stabilisation. Conclusions drawn from the simulations were supported by experimental data. Sudden loads and quick-release perturbations with two different amplitudes were applied to the upper body of ten male subjects. In comparison to sudden load situations preactivation of muscles due to an external load, i.e. quick-release perturbation, led to significantly less dependency of the amplitude of deflection on the amplitude of the perturbation. This observation relates to the self-stabilising properties of the musculoskeletal system. In conclusion, training seems to be advantageous if directed towards not only enhancing the endurance capacity of the muscles, but also increasing the cross-sectional area of oblique fast-twitch-fibres. Training should also improve the co-ordination of deep and superficial trunk muscles. These findings may influence physiotherapy and training programs for low back pain patients.

ISOFIT: a model-based method to measure muscle-tendon properties simultaneously.

Estimation of muscle parameters specifying force-length and force-velocity behavior requires in general a large number of sophisticated experiments often including a combination of isometric, isokinetic, isotonic, and quick-release experiments. This study validates a simpler method (ISOFIT) to determine muscle properties by fitting a Hill-type muscle model to a set of isovelocity data. Muscle properties resulting from the ISOFIT method agreed well with muscle properties determined separately in in vitro measurements using frog semitendinosus muscles. The force-length curve was described well by the results of the model. The force-velocity curve resulting from the model coincided with the experimentally determined curve above approximately 20% of maximum isometric force (correlation coefficient R>0.99). At lower forces and thus higher velocities the predicted curve underestimated velocity. The stiffness of the series elastic component determined with direct experiments was approximately 10% lower than that determined by the ISOFIT method. Use of the ISOFIT method can decrease experimental time up to 80% and reduce potential changes in muscle parameters due to fatigue.

Stable operation of an elastic three-segment leg.

Quasi-elastic operation of joints in multi-segmented systems as they occur in the legs of humans, animals, and robots requires a careful tuning of leg properties and geometry if catastrophic counteracting operation of the joints is to be avoided. A simple three-segment model has been used to investigate the segmental organization of the leg during repulsive tasks like human running and jumping. The effective operation of the muscles crossing the knee and ankle joints is described in terms of rotational springs. The following issues were addressed in this study: (1) how can the joint torques be controlled to result in a spring-like leg operation? (2) how can rotational stiffnesses be adjusted to leg-segment geometry? and (3) to what extend can unequal segment lengths and orientations be advantageous? It was found that: (1) the three-segment leg tends to become unstable at a certain amount of bending expressed by a counterrotation of the joints; (2) homogeneous bending requires adaptation of the rotational stiffnesses to the outer segment lengths; (3) nonlinear joint torque-displacement behaviour extends the range of stable leg bending and may result in an almost constant leg stiffness; (4) biarticular structures (like human gastrocnemius muscle) and geometrical constraints (like heel strike) support homogeneous bending in both joints; (5) unequal segment lengths enable homogeneous bending if asymmetric nominal angles meet the asymmetry in leg geometry; and (6) a short foot supports the elastic control of almost stretched knee positions. Furthermore, general leg design strategies for animals and robots are discussed with respect to the range of safe leg operation.

Standard cell-based implementation of a digital optoelectronic neural-network hardware.

A standard cell-based implementation of a digital optoelectronic neural-network architecture is presented. The overall structure of the multilayer perceptron network that was used, the optoelectronic interconnection system between the layers, and all components required in each layer are defined. The design process from VHDL-based modeling from synthesis and partly automatic placing and routing to the final editing of one layer of the circuit of the multilayer perceptrons are described. A suitable approach for the standard cell-based design of optoelectronic systems is presented, and shortcomings of the design tool that was used are pointed out. The layout for the microelectronic circuit of one layer in a multilayer perceptron neural network with a performance potential 1 magnitude higher than neural networks that are purely electronic based has been successfully designed.

The function of resilin in beetle wings.

This account shows the distribution of elastic elements in hind wings in the scarabaeid Pachnoda marginata and coccinellid Coccinella septempunctata (both Coleoptera). Occurrence of resilin, a rubber-like protein, in some mobile joints together with data on wing unfolding and flight kinematics suggest that resilin in the beetle wing has multiple functions. First, the distribution pattern of resilin in the wing correlates with the particular folding pattern of the wing. Second, our data show that resilin occurs at the places where extra elasticity is needed, for example in wing folds, to prevent material damage during repeated folding and unfolding. Third, resilin provides the wing with elasticity in order to be deformable by aerodynamic forces. This may result in elastic energy storage in the wing.

A finite-element model for the mechanical analysis of skeletal muscles.

In the present paper, a finite-element model for simulating muscle mechanics is described. Based on nonlinear continuum mechanics an algorithm is proposed that includes the contractile active and passive properties of skeletal muscle. Stress in the muscle is assumed to result from the superposition of a passive and an active part. The passive properties are described by a hyperelastic constitutive material law whereas the active part depends on the fibre length, shortening velocity and an activation function. The constraint of approximate incompressibility of the muscle element is satisfied as a property of the constitutive equations. Because of the nonlinear behaviour of the material and the highly dynamical performance an incremental procedure including iterative methods is used. The advantage of the model over previous formulations is the possibility to integrate the element into an engineering standard finite-element programme ANSYS using advanced numerical tools. The model allows simulations of muscle recruitment, calculations of stress and strain distributions and predictions of muscle shape. Other possible applications are studies of the muscle architecture, the effect of inertia and impacts. First, simple examples are presented.

Reduced muscle vascular resistance in intrauterine growth restricted newborn piglets.

It has been shown that asymmetrical intrauterine growth restriction is denoted by disproportional reduction of muscle mass compared to body weight reduction. However, the effects of IUGR on regional vascular resistance and blood flow of skeletal muscles and their contractile function have not been studied until now. Therefore, muscle blood flow (MBF) and isometric force output of serial stimulated hindlimb plantar flexors was measured in thiopental -anesthetized normal weight (NW; n = 9) and intrauterine growth restricted (IUGR; n = 9) one-day-old piglets. Additionally, muscle vascular resistance (MVR) and thyroid hormones were estimated. MBF was found to be markedly increased in IUGR piglets by 36% with a concomitant MVR reduction of 37% (p < 0.05). Isometric force of the plantar flexors was considerably higher in NW than in IUGR piglets (p < 0.05). However, amount of muscle fatigue was more pronounced in NW piglets (9.1+/-2.8%) than was in IUGR piglets (3.7+/-2.3%) (p < 0.05). Furthermore, specific tension of NW muscles (18.8+/-0.7 N/cm2) was significantly lower than for IUGR muscles (21.2+/-0.9 N/cm2) (P<0.05). IUGR newborn piglets exhibited increased plasma levels of thyroxine (T4) (p < 0.05), whereas triiodothyronine (T3) showed similar values in both animal groups. These data clearly indicate that muscle hemodynamics and contractile function are more developed in newborn IUGR piglets. Furthermore it is suggested that the improved tolerance to fatigue during isometric contractions may indicate an increased oxidative capacity of calf muscles due to intrauterine growth restriction.

Accelerated contractile function and improved fatigue resistance of calf muscles in newborn piglets with IUGR.

Asymmetrical intrauterine growth restriction is denoted by disproportional reduction of muscle mass compared with body weight reduction. However, effects on contractile function or tissue development of skeletal muscles were not studied until now. Therefore, isometric force output of serial-stimulated hindlimb plantar flexors was measured in thiopental-anesthetized normal weight (NW) and intrauterine growth-restricted (IUGR) 1-day-old piglets under conditions of normal, reduced (aortic cross clamping), and reestablished (clamp release) blood supply (measured by colored microspheres technique). Furthermore, muscle fiber type distribution was determined after histochemical staining, specific muscle force of the plantar flexors [quotient from absolute force divided by muscle mass (N/g)] was calculated, and glycogen content and morphometric data of the investigated muscles were estimated. Regional blood flow of hindlimb muscles was similar in NW (6 +/- 2 ml. min(-1). 100 g(-1)) and IUGR piglets (8 +/- 1 ml. min(-1). 100 g(-1)). Isometric muscle contractions induced a marked increase in regional blood flow of 4.1-fold in NW and 5-fold in stimulated hindlimb muscles of IUGR piglets (baseline blood flow). Specific force of NW piglet muscles (5.2 +/- 0.2 N/g) was significantly lower than IUGR piglet muscles (6.1 +/- 0.6 N/g; P < 0.05). Isometric muscle contractions (NW: 32.7 +/- 4.7 N; IUGR: 21.7 +/- 4.0 N) resulted in a higher rate of force decrease in the calf muscles of NW animals compared with IUGR piglets (8 +/- 2 vs. 3 +/- 1%; P < 0. 01). Functional restoration of contractile performance after hindlimb recirculation was nearly complete in IUGR piglets (98 +/- 1%), whereas in NW piglets a deficit of 9 +/- 3% was found (P < 0. 01). Muscle fiber type estimation revealed an increased proportion of type I fibers in flexor digitalis superficialis and gastrocnemius medialis in IUGR piglets (P < 0.05). These data clearly indicate that contractile function is accelerated in newborn IUGR piglets.

Optimum take-off techniques and muscle design for long jump.

A two-segment model based on Alexander (1990; Phil. Trans. R. Soc. Lond. B 329, 3-10) was used to investigate the action of knee extensor muscles during long jumps. A more realistic representation of the muscle and tendon properties than implemented previously was necessary to demonstrate the advantages of eccentric force enhancement and non-linear tendon properties. During the take-off phase of the long jump, highly stretched leg extensor muscles are able to generate the required vertical momentum. Thereby, serially arranged elastic structures may increase the duration of muscle lengthening and dissipative operation, resulting in an enhanced force generation of the muscle-tendon complex. To obtain maximum performance, athletes run at maximum speed and have a net loss in mechanical energy during the take-off phase. The positive work done by the concentrically operating muscle is clearly less than the work done by the surrounding system on the muscle during the eccentric phase. Jumping performance was insensitive to changes in tendon compliance and muscle speed, but was greatly influenced by muscle strength and eccentric force enhancement. In agreement with a variety of experimental jumping performances, the optimal jumping technique (angle of attack) was insensitive to the approach speed and to muscle properties (muscle mass, the ratio of muscle fibre to tendon cross-sectional area, relative length of fibres and tendon). The muscle properties also restrict the predicted range of the angle of the velocity vector at take-off.

Dynamics of the long jump.

A mechanical model is proposed which quantitatively describes the dynamics of the centre of gravity (c.g.) during the take-off phase of the long jump. The model entails a minimal but necessary number of components: a linear leg spring with the ability of lengthening to describe the active peak of the force time curve and a distal mass coupled with nonlinear visco-elastic elements to describe the passive peak. The influence of the positions and velocities of the supported body and the jumper's leg as well as of systemic parameters such as leg stiffness and mass distribution on the jumping distance were investigated. Techniques for optimum operation are identified: (1) There is a minimum stiffness for optimum performance. Further increase of the stiffness does not lead to longer jumps. (2) For any given stiffness there is always an optimum angle of attack. (3) The same distance can be achieved by different techniques. (4) The losses due to deceleration of the supporting leg do not result in reduced jumping distance as this deceleration results in a higher vertical momentum. (5) Thus, increasing the touch-down velocity of the jumper's supporting leg increases jumping distance.

Stabilizing function of skeletal muscles: an analytical investigation.

Stability is the ability of a system to return to its original state after a disturbance. Taking vertical oscillations of the centre of mass of a human bending his legs as an example we prove that the intrinsic mechanical properties of musculature can stabilize the oscillatory movement (preflex) without reflexive changes in activation. The human is represented by a model consisting of a massless two-segment linkage system (knee) topped by a point mass. Conditions for stability are calculated analytically based on the theory of Ljapunov and the results are illustrated by numerical examples. In order to guarantee a self-stabilizing ability of the muscle-skeletal system, the muscle properties such as force-length relationship, force-velocity relationship and the muscle geometry must be tuned to the geometric properties of the linkage system.

Dynamic and static stability in hexapedal runners.

Stability is fundamental to the performance of terrestrial locomotion. Running cockroaches met the criteria for static stability over a wide range of speeds, yet several locomotor variables changed in a way that revealed an increase in the importance of dynamic stability as speed increased. Duty factors (the fraction of time that a leg spends on the ground relative to the stride period) decreased to 0.5 and below with an increase in speed. The duration of double support (i.e. when both tripods, or all six legs, were on the ground) decreased significantly with an increase in speed. All legs had similar touch-down phases in the tripod, but the shortest leg, the front one, lifted off before the middle and the rear leg, so that only two legs of the tripod were in contact with the ground at the highest speeds. Per cent stability margin (the shortest distance from the center of gravity to the boundaries of support, normalized to the maximum possible stability margin) decreased with increasing speed from 60% at 10 cms-1 to values less than zero at speeds faster than 50 cms-1, indicating instances of static instability at fast speeds. The center of mass moved rearward or posteriorly with respect to the base of support as speed increased. Moments about the center of mass, as shown by the center of pressure (the equivalent of a single 'effective' leg), were variable, but were balanced by opposing moments over a stride. Thus, hexapods can exploit the advantages of both static and dynamic stability. Static or quasi-static assumptions alone were insufficient to explain straight-ahead, constant-speed locomotion and may hinder discovery of behaviors that are dynamic, where kinetic energy and momentum can act as a bridge from one step to the next.

NOTE ON THE CALCULATION OF PROPELLER EFFICIENCY USING ELONGATED BODY THEORY

The elongated body theory has been widely used for calculations of the hydrodynamic propulsive performance of swimming fish. In the biological literature, terms containing the slope of the amplitude function at the tail end have been neglected in the calculations of thrust and efficiency, and a slope of zero has been assumed. However, some fishes, such as saithe and trout, have non-zero values of the slope near the tail end and, when this term is taken into account, the efficiency may be reduced by as much as 20 % and approaches the result given by the three-dimensional waving plate theory. The inclusion of the slope in the efficiency considerations results in an optimum ratio of the swimming speed to the wave speed that is clearly less than 1. It is suggested that the slope terms should be included in the estimation of propulsive performance for fish swimming with variable amplitude.

Hopping frequency in humans: a test of how springs set stride frequency in bouncing gaits.

The storage and recovery of elastic energy in muscle-tendon springs is important in running, hopping, trotting, and galloping. We hypothesized that animals select the stride frequency at which they behave most like simple spring-mass systems. If higher or lower frequencies are used, they will not behave like simple spring-mass systems, and the storage and recovery of elastic energy will be reduced. We tested the hypothesis by having humans hop forward on a treadmill over a range of speeds and hop in place over a range of frequencies. The body was modeled as a simple spring-mass system, and the properties of the spring were measured by use of a force platform. Our subjects used nearly the same frequency (the "preferred frequency," 2.2 hops/s) when they hopped forward on a treadmill and when they hopped in place. At this frequency, the body behaved like a simple spring-mass system. Contrary to our predictions, it also behaved like a simple spring-mass system when the subjects hopped at higher frequencies, up to the maximum they could achieve. However, at the higher frequencies, the time available to apply force to the ground (the ground contact time) was shorter, perhaps resulting in a higher cost of generating muscular force. At frequencies below the preferred frequency, as predicted by the hypothesis, the body did not behave in a springlike manner, and it appeared likely that the storage and recovery of elastic energy was reduced. The combination of springlike behavior and a long ground contact time at the preferred frequency should minimize the cost of generating muscular force.