Muscle-driven finite element simulation of human foot movements

This paper describes a finite element scheme for realistic muscle-driven simulation of human foot movements. The scheme is used to simulate human ankle plantar flexion. A three-dimensional anatomically detailed finite element model of human foot and lower leg is developed and the idea of generating natural foot movement based entirely on the contraction of the plantar flexor muscles is used. The bones, ligaments, articular cartilage, muscles, tendons, as well as the rest soft tissues of human foot and lower leg are included in the model. A realistic three-dimensional continuum constitutive model that describes the biomechanical behaviour of muscles and tendons is used. Both the active and passive properties of muscle tissue are accounted for. The materials for bones and ligaments are considered as homogeneous, isotropic and linearly elastic, whereas the articular cartilage and the rest soft tissues (mainly fat) are defined as hyperelastic materials. The model is used to estimate muscle tissue deformations as well as stresses and strains that develop in the lower leg muscles during plantar flexion of the ankle. Stresses and strains that develop in Achilles tendon during such a movement are also investigated.     

Muscle-driven finite element simulation of human foot movements

This paper describes a finite element scheme for realistic muscle-driven simulation of human foot movements. The scheme is used to simulate human ankle plantar flexion. A three-dimensional anatomically detailed finite element model of human foot and lower leg is developed and the idea of generating natural foot movement based entirely on the contraction of the plantar flexor muscles is used. The bones, ligaments, articular cartilage, muscles, tendons, as well as the rest soft tissues of human foot and lower leg are included in the model. A realistic three-dimensional continuum constitutive model that describes the biomechanical behaviour of muscles and tendons is used. Both the active and passive properties of muscle tissue are accounted for. The materials for bones and ligaments are considered as homogeneous, isotropic and linearly elastic, whereas the articular cartilage and the rest soft tissues (mainly fat) are defined as hyperelastic materials. The model is used to estimate muscle tissue deformations as well as stresses and strains that develop in the lower leg muscles during plantar flexion of the ankle. Stresses and strains that develop in Achilles tendon during such a movement are also investigated.     

A biomechanical model of the foot: the role of muscles,tendons, and ligaments

A biomechanical model of the foot is developed and analyzed to determine the distribution of support under the metatarsal heads, the tension in the plantar aponeurosis, and the bending moment at each of the joints of the foot. This model is an extension of our earlier work to include the role of muscles, tendons, and ligaments. Two cases are presented: in the first the center of gravity of the body is over the mid foot, and in the second, the center of gravity is anterior, over the metatarsals, and no support is provided by the heel. The model shows the extent to which the muscles reduce the force in the supporting ligaments at each of the joints and decrease the tension in the plantar aponeurosis, and that this effect is more pronounced when the center of gravity of the body is moved forward.     

Deformation and stress distribution of the human foot after plantar ligaments release: A cadaveric study and finite element analysis

The majority of foot deformities are related to arch collapse or instability, especially the longitudinal arch. Although the relationship between the plantar fascia and arch height has been previously investigated, the stress distribution remains unclear. The aim of this study was to explore the role of the plantar ligaments in foot arch biomechanics. We constructed a geometrical detailed three-dimensional (3-D) finite element (FE) model of the human foot and ankle from computer tomography images. The model comprised the majority of joints in the foot as well as bone segments, major ligaments, and plantar soft tissue. Release of the plantar fascia and other ligaments was simulated to evaluate the corresponding biomechanical effects on load distribution of the bony and ligamentous structures. These intrinsic ligaments of the foot arch were sectioned to simulate different pathologic situations of injury to the plantar ligaments, and to explore bone segment displacement and stress distribution. The validity of the 3-D FE model was verified by comparing results with experimentally measured data via the displacement and von Mise stress of each bone segment. Plantar fascia release decreased arch height, but did not cause total collapse of the foot arch. The longitudinal foot arch was lost when all the four major plantar ligaments were sectioned simultaneously. Plantar fascia release was compromised by increased strain applied to the plantar ligaments and intensified stress in the midfoot and metatarsal bones. Load redistribution among the centralized metatarsal bones and focal stress relief at the calcaneal insertion were predicted. The 3-D FE model indicated that plantar fascia release may provide relief of focal stress and associated heel pain. However, these operative procedures may pose a risk to arch stability and clinically may produce dorsolateral midfoot pain. The initial strategy for treating plantar fasciitis should be non-operative.     

Modulation of soleus H-reflex during dorsal and plantar flexions in the human ankle joint

Recording of the H-reflex was used to study the changes in the reflex excitability of soleus motoneurons during dorsal and plantar flexions of the ipsilateral and contralateral feet performed with different strengths by 15 healthy subjects. The dorsiflexion of the ipsilateral foot was accompanied by the “classic” reciprocal inhibition of the soleus motoneurons, the degree of the inhibition being directly proportional to the strength of the contraction of pretibial muscles and depending on the presence of foot support. The plantar flexion of the ipsilateral foot was accompanied by changes in reflex excitability, which were inversely proportional to the strength of the flexion. This was apparently related to the activation of a mechanism protecting the muscle against excessive contraction. The dorsal and plantar flexions of the contralateral foot were accompanied by similar changes in the reflex excitability of soleus motoneurons, namely, an increase in the case of weak contraction and a decrease in the case of strong contraction. However, the increase in reflex excitability during contralateral dorsiflexion was smaller and its decrease began at a weaker contraction than in the case of contralateral plantar flexion. The changes in the reflex excitability of soleus motoneurons during movements of the contralateral foot, which were also strength-dependent, confirmed the presence of cross-projections that are likely to be part of the generator of the central pattern of lower limb movement coordination.     

Is the attenuation effect on the ankle muscles activity from the EMG biofeedback generalized to – or compensated by – other lower limb muscles during standing?

Biofeedback based on electromyograms (EMGs) has been recently proposed to reduce exaggerated postural activity. Whether the effect of EMG biofeedback on the targeted muscles generalizes to – or is compensated by – other muscles is still an open question we address here. Fourteen young individuals were tested in three 60 s standing trials, without and with EMG-audio feedback: (i) collectively from soleus and medial gastrocnemius and (ii) from medial gastrocnemii. The Root Mean Square (RMS) of bipolar EMGs sampled from postural muscles bilaterally was computed to assess the degree of activity and postural sway was assessed from the center of pressure (CoP). In relation to standing at naturally, EMG-audio feedback from soleus and medial gastrocnemii decreased plantar flexors’ activity (∼10 %) but at the cost of increased amplitude of tibialis anterior (∼5%) and vasti muscles (∼20 %) accompanied by a posterior shift of the mean CoP position. However, EMG-audio feedback from medial gastrocnemii reduced only plantar flexors’ activity (∼5%) when compared to standing at naturally. Current results suggest the EMG biofeedback has the potential to reduce calf muscles’ activity without loading other postural muscles especially when using medial gastrocnemii as feedback source, with implications on postural training aimed at assisting individuals in activating more efficiently postural muscles during standing.     

Three-dimensional dynamical capabilities of the human masticatory muscles

Many habitual human jaw movements are non-symmetrical. Generally, it is observed that when the lower incisors move to one side the contralateral condyle moves forwards onto the articular eminence, whereas the ipsilateral condyle stays in the mandibular fossa, moving slightly to the ipsilateral side. These jaw movements are the result of contractions of active masticatory muscles and guided by the temporomandibular joints, their ligaments and passive elastic properties of the muscles. It is not known whether the movements are primarily dependent on passive guidance, active muscle control or both. Therefore, the objective of this study was to analyse the interplay between these factors during non-symmetrical jaw movements. A six-degrees-of-freedom dynamical biomechanical model of the human masticatory system was used. The movements were not restricted to a priori defined joint axes. Jaw movement simulations were performed by unilateral activity of the muscles. The ligaments or the passive elastic properties of the muscles could be removed during these simulations. Laterodeviations conform to naturally observed ones could be generated by unilateral muscle contractions. The movement of the lower incisors was hardly affected by the absence of passive elastic muscle properties or temporomandibular ligaments. The latter, however, influenced the movement of the condyles. The movements could be understood by analysing the combination of forces and torques with respect to the centre of gravity of the lower jaw. In addition, the loading of the condyles appeared to be an important determinant for the movement. This analysis emphasizes that the movements of the jaw are primarily dependent on the orientation of the contributing muscles with respect to this centre of gravity and not on the temporomandibular ligaments or passive elastic muscle properties.     

A Three-Dimensional Musculoskeletal Model of the Human Knee Joint. Part 1: Theoretical Construction

A three-dimensional model of the knee is developed to study the interactions between the muscles, ligaments, and bones during activity. The geometry of the distal femur, proximal tibia, and patella is based on cadaver data reported for an average-size knee. The shapes of the femoral condyles are represented by high-order polynomials: the tibial plateaux and patellar facets are approximated as flat surfaces. The contacting surfaces of the femur and tibia are modeled as deformable, while those of the femur and patella are assumed to be rigid. Interpenetration of the femur and tibia is taken into account by modeling cartilage as a thin, linear, elastic layer, mounted on rigid bone. Twelve elastic elements describe the geometry and mechanical properties of the cruciate ligaments, the collateral ligaments, and the posterior capsule. The model is actuated by thirteen musculotendinous units, each unit modeled as a three-element muscle in series with tendon. The path of each muscle is approximated as a straight line, except where it contacts and wraps around bone and other muscles; changes in muscle paths are taken into account using data obtained from MRI. In the first part of this paper, the model is used to simulate passive knee flexion. Quantitative comparisons of the model results with experimental data reported in the literature indicate that the relative movements of the bones and the geometry of the ligaments and muscles in the model are similar to those evident in the real knee. In Part II, the model is used to describe knee-ligament function during anterior-posterior draw, axial rotation, and isometric knee-extension and knee-flexion exercises.     

A Three-Dimensional Musculoskeletal Model of the Human Knee Joint. Part 1: Theoretical Construct

A three-dimensional model of the knee is developed to study the interactions between the muscles, ligaments, and bones during activity. The geometry of the distal femur, proximal tibia, and patella is based on cadaver data reported for an average-size knee. The shapes of the femoral condyles are represented by high-order polynomials; the tibial plateaux and patellar facets are approximated as flat surfaces. The contacting surfaces of the femur and tibia are modeled as deformable, while those of the femur and patella are assumed to be rigid. Interpenetration of the femur and tibia is taken into account by modeling cartilage as a thin, linear, elastic layer, mounted on rigid bone. Twelve elastic elements describe the geometry and mechanical properties of the cruciate ligaments, the collateral ligaments, and the posterior capsule. The model is actuated by thirteen musculotendinous units, each unit modeled as a three-element muscle in series with tendon. The path of each muscle is approximated as a straight line, except where it contacts and wraps around bone and other muscles; changes in muscle paths are taken into account using data obtained from MRI. In the first part of this paper, the model is used to simulate passive knee flexion. Quantitative comparisons of the model results with experimental data reported in the literature indicate that the relative movements of the bones and the geometry of the ligaments and muscles in the model are similar to those evident in the real knee. In Part II, the model is used to describe knee-ligament function during anterior-posterior draw, axial rotation, and isometric knee-extension and knee-flexion exercises.     

Mechanical performance of artificial pneumatic muscles to power an ankle-foot orthosis

We developed a powered ankle-foot orthosis that uses artificial pneumatic muscles to produce active plantar flexor torque. The purpose of this study was to quantify the mechanical performance of the orthosis during human walking. Three subjects walked at a range of speeds wearing ankle-foot orthoses with either one or two artificial muscles working in parallel. The orthosis produced similar total peak plantar flexor torque and network across speeds independent of the number of muscles used. The orthosis generated approximately 57% of the peak ankle plantar flexor torque during stance and performed approximately 70% of the positive plantar flexor work done during normal walking. Artificial muscle bandwidth and force-length properties were the two primary factors limiting torque production. The lack of peak force and work differences between single and double muscle conditions can be explained by force-length properties. Subjects altered their ankle kinematics between conditions resulting in changes in artificial muscle length. In the double muscle condition greater plantar flexion yielded shorter artificial muscles lengths and decreased muscle forces. This finding emphasizes the importance of human testing in the design and development of robotic exoskeleton devices for assisting human movement. The results of this study outline the mechanical performance limitations of an ankle-foot orthosis powered by artificial pneumatic muscles. This orthosis could be valuable for gait rehabilitation and for studies investigating neuromechanical control of human walking.     

Activation of human plantar flexor muscles increases after electromyostimulation training.

Neuromuscular adaptations of the plantar flexor muscles were assessed before and subsequent to short-term electromyostimulation (EMS) training. Eight subjects underwent 16 sessions of isometric EMS training over 4 wk. Surface electromyographic (EMG) activity and torque obtained under maximal voluntary and electrically evoked contractions were analyzed to distinguish neural adaptations from contractile changes. After training, plantar flexor voluntary torque significantly increased under isometric conditions at the training angle (+8.1%, P < 0.05) and at the two eccentric velocities considered (+10.8 and +13.1%, P < 0.05). Torque gains were accompanied by higher normalized soleus EMG activity and, in the case of eccentric contractions, also by higher gastrocnemii EMG (P < 0.05). There was an 11.9% significant increase in both plantar flexor maximal voluntary activation (P < 0.01) and postactivation potentiation (P < 0.05), whereas contractile properties did not change after training. In the absence of a change in the control group, it was concluded that an increase in neural activation likely mediates the voluntary torque gains observed after short-term EMS training.     

Anatomy of the feeding apparatus of the lemon shark,Negaprion brevirostris

The anatomy of the feeding apparatus of the lemon shark, Negaprion brevirostris, is investigated by gross dissection, computer axial tomography, and histological staining. The muscles and ligaments of the head associated with feeding are described. The upper and lower jaws are suspended by the hyoid arch, which in turn is braced against the chondrocranium by a complex series of ligaments. In addition, various muscles and the integument contribute to the suspension and stability of the jaws. The dual jaw joint is comprised of lateral and medial quadratomandibular joints that resist lateral movement of the upper and lower jaws on one another. This is important during feeding involving vigorous head shaking. An elastic ethmoplatine ligament that unites the anterior portion of the upper jaw to the neurocranium is involved with upper jaw retraction. The quadratomandibularis muscle is divided into four divisions with a bipinnate fiber arrangement of the two large superficial divisions. This arrangement would permit a relatively greater force per unit volume and reduce muscle bulging of the jaw adductor muscle in the spatially confined cheek region. Regions of relatively diffuse integumental ligaments overlying the adductor mandibulae complex and the levator palatoquadrati muscle, interspersed with localized regions of longer tendonlike attachments between the skin and the underlying muscle, permit greater musculoskeletal movement relative to the skin. The nomenclature of the hypobranchial muscles is discussed. In this shark they are comprised of the unsegmented coracomandibularis and coracohyoideus, and the segmented coracoarcualis. © 1995 Wiley-Liss, Inc.     

Sensorimotor control of the spine.

The spinal viscoelastic structures including disk, capsule and ligaments were reviewed with special focus on their sensory motor functions. Afferent capable of monitoring proprioceptive and kinesthetic information are abundant in the disc, capsule and ligament. Electrical stimulation of the lumbar afferents in the discs, capsules and ligaments seem to elicit reflex contraction of the multifidus and also longissimus muscles. The muscular excitation is pronounced in the level of excitation and with weaker radiation 1 to 2 levels above and below. Similarly, mechanical stimulation of the spinal viscoelastic tissues excites the muscles with higher excitation intensity when more than one tissue (ligaments and discs for example) is stimulated. Overall, it seems that spinal structures are well suited to monitor sensory information as well as to control spinal muscles and probably also provide kinesthetic perception to the sensory cortex.     

Elastic mechanisms in primate locomotion

Tendons that stretch elastically and recoil, as the forces on them rise and fall, can save energy in running by enabling the animal to make do with shorter or slower muscle fascicles, that can generate force more economically. Non-human primates have rather long fascicles and thick tendons in their distal leg muscles and so seem poorly adapted to save energy in this way. Additional savings are made possible by the elastic compliance of ligaments in the foot. Though tendon and ligament compliance tend to save energy, the compliance of branches tends to increase the energy cost of arboreal locomotion.     

Different plantar flexors neuromuscular and mechanical characteristics depending on the preferred running form

Two main types of endurance runners have been identified: aerial runners (AER), who have a larger flight time, and terrestrial runners (TER), who have a longer ground contact time. The purpose of this study was to assess the neuromuscular characteristics of plantar flexors between AER and TER runners. Twenty-four well-trained runners participated in the experiment. They were classified either in a TER or AER group according to the Volodalen® scale. Plantar flexors’ maximal rate of force development (RFD) and maximal voluntary contraction force (MVC) were assessed. Percutaneous electrical stimulation was delivered to the posterior tibial nerve to evoke maximal M-waves and H-reflexes of the triceps surae muscles. These responses, as well as voluntary activation, muscle potentiation, and V-waves, were recorded by superimposing stimulations to MVCs. RFD was significantly higher in AER than in TER, while MVC remained unchanged. This was accompanied by higher myoelectrical activity recorded in the soleus muscle. While M-waves and other parameters remained unchanged, maximal H-reflex was significantly higher in AER than in TER, still in soleus only. The present study raised the possibility of different plantar flexors’ neuromuscular characteristics according to running profile. These differences seemed to be focused on the soleus rather than on the gastrocnemii.     

Relation between the ankle joint angle and the maximum isometric force of the toe flexor muscles

The purpose of this study was to investigate the relationships between the ankle joint angle and maximum isometric force of the toe flexor muscles. Toe flexor strength and electromyography activity of the foot muscles were measured in 12 healthy men at 6 different ankle joint angles with the knee joint at 90 deg in the sitting position. To measure the maximum isometric force of the toe flexor muscles, subjects exerted maximum force on a toe grip dynamometer while the activity levels of the intrinsic and extrinsic plantar muscles were measured. The relation between ankle joint angle and maximum isometric force of the toe flexor muscles was determined, and the isometric force exhibited a peak when the ankle joint was at 70–90 deg on average. From this optimal neutral position, the isometric force gradually decreased and reached its nadir in the plantar flexion position (i.e., 120 deg). The EMG activity of the abductor hallucis (intrinsic plantar muscle) and peroneus longus (extrinsic plantar muscle) did not differ at any ankle joint angles. The results of this study suggest that the force generation of toe flexor muscles is regulated at the ankle joint and that changes in the length-tension relations of the extrinsic plantar muscle could be a reason for the force-generating capacity at the metatarsophalangeal joint when the ankle joint angle is changed.     

Are coupled rotations in the lumbar spine largely due to the osseo-ligamentous anatomy?--a modeling study

Prior studies have found that primary rotations in the lumbar spine are accompanied by coupled out-of-plane rotations. However, it is not clear whether these accompanying rotations are primarily due to passive (discs, ligaments and facet joints) or active (muscles) spinal anatomy. The aim of this study was to use a finite element (FE) model of the lumbar spine to predict three-dimensional coupled rotations between the lumbar vertebrae, due to passive spinal structures alone. The FE model was subjected to physiologically observed whole lumbar spine rotations about in vivo centres of rotation. Model predictions were validated by comparison of intra-discal pressures and primary rotations with in vivo measurements and these showed close agreement. Predicted coupled rotations matched in vivo measurements for all primary motions except lateral bending. We suggest that coupled rotations accompanying primary motions in the sagittal (flexion/extension) and transverse (axial rotation) planes are primarily due to passive spinal structures. For lateral bending the muscles most likely play a key role in the coupled rotation of the spine.     

Stress analysis of the standing foot following surgical plantar fascia release

Plantar fascia release is a surgical alternative for patients who suffer chronic heel pain due to plantar fasciitis and are unaffected by conservative treatment. A computational (finite element) model for analysis of the structural behavior of the human foot during standing was utilized to investigate the biomechanical effects of releasing the plantar fascia. The model integrates a system of five planar structures in the directions of the foot rays. It was built according to accurate geometric data of MRI, and includes linear and non-linear elements that represent bony, cartilaginous, ligamentous and fatty tissues. The model was successfully validated by comparing its resultant ground reactions with foot-ground pressure measurements and its predicted displacements with those observed in radiological tests. Simulation of plantar fascia release (partial or total) was accomplished by gradually removing parts of the fascia in the model. The results showed that total fascia release causes extensive arch deformation during standing, which is greater than normal deformation by more than 2.5mm. Tension stresses carried by the long plantar ligaments increased significantly, and may exceed the normal average stress by more than 200%. Since the contribution of the plantar fascia to the foot's load-bearing ability is of major importance, its release must be very carefully considered, and the present model may be used to help surgeons decide upon the desired degree of release.     

Biomechanical model study of pelvic belt influence on muscle and ligament forces

Many patients with low back and/or pelvic girdle pain feel relief after application of a pelvic belt. External compression might unload painful ligaments and joints, but the exact mechanical effect on pelvic structures, especially in (active) upright position, is still unknown. In the present study, a static three-dimensional (3-D) pelvic model was used to simulate compression at the level of anterior superior iliac spine and the greater trochanter. The model optimised forces in 100 muscles, 8 ligaments and 8 joints in upright trunk, pelvis and upper legs using a criterion of minimising maximum muscle stress. Initially, abdominal muscles, sacrotuberal ligaments and vertical sacroiliac joints (SIJ) shear forces mainly balanced a trunk weight of 500N in upright position. Application of 50N medial compression force at the anterior superior iliac spine (equivalent to 25N belt tension force) deactivated some dorsal hip muscles and reduced the maximum muscle stress by 37%. Increasing the compression up to 100N reduced the vertical SIJ shear force by 10% and increased SIJ compression force with 52%. Shifting the medial compression force of 100N in steps of 10N to the greater trochanter did not change the muscle activation pattern but further increased SIJ compression force by 40% compared to coxal compression. Moreover, the passive ligament forces were distributed over the sacrotuberal, the sacrospinal and the posterior ligaments. The findings support the cause-related designing of new pelvic belts to unload painful pelvic ligaments or muscles in upright posture.     

Force output during and following active stretches of rat plantar flexor muscles: effect of velocity of ankle rotation

During the development of force deficits by repeated stretches, velocity-sensitive changes in the extra force produced during and after subsequent stretching has not been studied. In the present study, repeated dorsiflexion of the foot of rats with maximally contracting plantar flexor muscles was performed at two angular velocities [0.87 (slow muscle stretch) and 10.47rads(-1) (fast muscle stretch)] to examine the active force of the muscles during and following dorsiflexion. Dorsiflexion was performed 30 times with a rest period of 3min between the stretches to minimize muscle fatigue. The ability of rat plantar flexor muscles to produce additional force during the stretch was not velocity sensitive. In contrast, repeated dorsiflexion with fast muscle stretches, but not with slow muscle stretches, resulted in an increase in the force decay with time following the stretches (i.e. increased stress relaxation), as indicated by a change in the time constant of force decay during stress relaxation. Apparently, the stress-relaxation of rat plantar flexor muscles is sensitive to angular velocity of ankle movements; repeated fast, but not slow dorsiflexion, alters the stress relaxation process of active skeletal muscles exposed to stretches which create a force deficit. The change in time constant of force decay during stress relaxation in response to a series of repeated stretches might provide information on the sarcomere length distribution in skeletal muscles.