A dynamic model of the knee and lower limb for simulating rising movements

A two-dimensional dynamical model of the human body was developed and used to simulate muscle and knee-ligament loading during a fast rising movement. The hip, ankle, and toes were each modeled as a simple hinge joint. Relative movements of the femur, tibia, and patella in the sagittal plane were described using a more detailed representation of the knee. The geometry of the model bones was adapted from cadaver data. Eleven elastic elements described the geometric and mechanical properties of the knee ligaments and joint capsule. The patella was assumed to be massless. Smooth hypersurfaces were constructed and used to calculate the position and orientation of the patella during a forward integration of the model. Each hypersurface was formed by applying the principle of static equilibrium to approximate patellofemoral mechanics during the simulation. The model was actuated by 22 musculotendinous units, each unit represented as a three-element muscle in series with tendon. A first-order process was assumed to model muscle excitation-contraction dynamics. Dynamic optimization theory was used to calculate the pattern of muscle excitations that produces a coordinated rising movement from an initial squatting position in minimum time. The calculations support the contention that squatting is a relatively safe exercise for rehabilitation following ACL reconstruction. ACL forces remain less than 20 N for the duration of the task.     

Segmentation of foot and ankle complex based on kinematic criteria

Although various foot models were proposed for kinematics assessment using skin makers, no objective justification exists for the foot segmentations. This study proposed objective kinematic criteria to define which foot joints are relevant (dominant) in skin markers assessments. Among the studied joints, shank-hindfoot, hindfoot-midfoot and medial-lateral forefoot joints were found to have larger mobility than flexibility of their neighbour bonesets. The amplitude and pattern consistency of these joint angles confirmed their dominancy. Nevertheless, the consistency of the medial-lateral forefoot joint amplitude was lower. These three joints also showed acceptable sensibility to experimental errors which supported their dominancy. This study concluded that to be reliable for assessments using skin markers, the foot and ankle complex could be divided into shank, hindfoot, medial forefoot, lateral forefoot and toes. Kinematics of foot models with more segments must be more cautiously used.     

A Neuro-Muscular Elasto-Dynamic Model of the Human Arm Part 2: Musculotendon Dynamics and Related Stress Effects

In this paper we develop an elasto-dynamic model of the human arm that includes effects of neuro-muscular control uponelastic deformation in the limb.The elasto-dynamic model of the arm is based on hybrid parameter multiple body systemvariational projection principles presented in the companion paper.Though the technique is suitable for detailed bone and jointmodeling,we present simulations for simplified geometry of the bones,discretized as Rayleigh beams with elongation,whileallowing for large deflections.Motion of the upper extremity is simulated by incorporating muscle forces derived from aHill-type model of musculotendon dynamics.The effects of muscle force are modeled in two ways.In one approach,aneffective joint torque is calculated by multiplying the muscle force by a joint moment ann.A second approach models themuscle as acting along a straight line between the origin and insertion sites of the tendon.Simple arm motion is simulated byutilizing neural feedback and feedforward control.Simulations illustrate the combined effects of neural control strategies,models of muscle force inclusion,and elastic assumptions on joint trajectories and stress and strain development in the bone andtendon.     

A musculoskeletal foot model for clinical gait analysis

Several full body musculoskeletal models have been developed for research applications and these models may potentially be developed into useful clinical tools to assess gait pathologies. Existing full-body musculoskeletal models treat the foot as a single segment and ignore the motions of the intrinsic joints of the foot. This assumption limits the use of such models in clinical cases with significant foot deformities. Therefore, a three-segment musculoskeletal model of the foot was developed to match the segmentation of a recently developed multi-segment kinematic foot model. All the muscles and ligaments of the foot spanning the modeled joints were included. Muscle pathways were adjusted with an optimization routine to minimize the difference between the muscle flexion–extension moment arms from the model and moment arms reported in literature. The model was driven by walking data from five normal pediatric subjects (aged 10.6±1.57 years) and muscle forces and activation levels required to produce joint motions were calculated using an inverse dynamic analysis approach. Due to the close proximity of markers on the foot, small marker placement error during motion data collection may lead to significant differences in musculoskeletal model outcomes. Therefore, an optimization routine was developed to enforce joint constraints, optimally scale each segment length and adjust marker positions. To evaluate the model outcomes, the muscle activation patterns during walking were compared with electromyography (EMG) activation patterns reported in the literature. Model-generated muscle activation patterns were observed to be similar to the EMG activation patterns.     

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).     

Optimal compliant-surface jumping: a multi-segment model of springboard standing jumps

A multi-segment model is used to investigate optimal compliant-surface jumping strategies and is applied to springboard standing jumps. The human model has four segments representing the feet, shanks, thighs, and trunk-head-arms. A rigid bar with a rotational spring on one end and a point mass on the other end (the tip) models the springboard. Board tip mass, length, and stiffness are functions of the fulcrum setting. Body segments and board tip are connected by frictionless hinge joints and are driven by joint torque actuators at the ankle, knee, and hip. One constant (maximum isometric torque) and three variable functions (of instantaneous joint angle, angular velocity, and activation level) determine each joint torque. Movement from a nearly straight motionless initial posture to jump takeoff is simulated. The objective is to find joint torque activation patterns during board contact so that jump height can be maximized. Minimum and maximum joint angles, rates of change of normalized activation levels, and contact duration are constrained. Optimal springboard jumping simulations can reasonably predict jumper vertical velocity and jump height. Qualitatively similar joint torque activation patterns are found over different fulcrum settings. Different from rigid-surface jumping where maximal activation is maintained until takeoff, joint activation decreases near takeoff in compliant-surface jumping. The fulcrum-height relations in experimental data were predicted by the models. However, lack of practice at non-preferred fulcrum settings might have caused less jump height than the models' prediction. Larger fulcrum numbers are beneficial for taller/heavier jumpers because they need more time to extend joints.     

Contributions of the individual muscles of the shoulder to glenohumeral joint stability during abduction

The aim of this study was to determine the relative contributions of the deltoid and rotator cuff muscles to glenohumeral joint stability during arm abduction. A three-dimensional model of the upper limb was used to calculate the muscle and joint-contact forces at the shoulder for abduction in the scapular plane. The joints of the shoulder girdle-sternoclavicular joint, acromioclavicular joint, and glenohumeral joint-were each represented as an ideal three degree-of-freedom ball-and-socket joint. The articulation between the scapula and thorax was modeled using two kinematic constraints. Eighteen muscle bundles were used to represent the lines of action of 11 muscle groups spanning the glenohumeral joint. The three-dimensional positions of the clavicle, scapula, and humerus during abduction were measured using intracortical bone pins implanted into one subject. The measured bone positions were inputted into the model, and an optimization problem was solved to calculate the forces developed by the shoulder muscles for abduction in the scapular plane. The model calculations showed that the rotator cuff muscles (specifically, supraspinatus, subscapularis, and infraspinatus) by virtue of their lines of action are perfectly positioned to apply compressive load across the glenohumeral joint, and that these muscles contribute most significantly to shoulder joint stability during abduction. The middle deltoid provides most of the compressive force acting between the humeral head and the glenoid, but this muscle also creates most of the shear, and so its contribution to joint stability is less than that of any of the rotator cuff muscles.     

Biological Jumping Mechanism Analysis and Modeling for Frog Robot

This paper presents a mechanical model of jumping robot based on the biological mechanism analysis of frog. By biological observation and kinematic analysis the frog jump is divided into take-offphase, aerial phase and landing phase. We find the similar trajectories of hindlimb joints during jump, the important effect of foot during take-off and the role of forelimb in supporting the body. Based on the observation, the frog jump is simplified and a mechanical model is put forward. The robot leg is represented by a 4-bar spring/linkage mechanism model, which has three Degrees of Freedom （DOF） at hip joint and one DOF （passive） at tarsometatarsal joint on the foot. The shoulder and elbow joints each has one DOF for the balancing function of arm. The ground reaction force of the model is analyzed and compared with that of frog during take-off. The results show that the model has the same advantages of low likelihood of premature lift-off and high efficiency as the frog. Analysis results and the model can be employed to develop and control a robot capable of mimicking the jumping behavior of frog.     

Functional morphology of the muscles in Philodina sp. (Rotifera: Bdelloidea)

Whole-mounts of Philodina sp., a bdelloid rotifer, were stained with fluorescent-labeled phalloidin to visualize the musculature. Several different muscle types were identified including incomplete circular bands, coronal retractors and foot retractors. Based on the position of the larger muscle bands in the body wall, their function during creeping locomotion and tun formation was inferred. Bdelloid creeping begins with the contraction of incomplete circular muscle bands against the hydrostatic pseudocoel, resulting in an anterior elongation of the body. One or more sets of ventral longitudinal muscles then contract bringing the rostrum into contact with the substrate, where it presumably attaches via adhesive glands. Different sets of ventral longitudinal muscles, foot and trunk retractors, function to pull the body forward. These same longitudinal muscle sets are also used in `tun' formation, in which the head and foot are withdrawn into the body. Three sets of longitudinal muscles supply the head region (anterior head segments) and function in withdrawal of the corona and rostrum. Two additional pairs of longitudinal muscles function to retract the anterior trunk segments immediately behind the head, and approximately five sets of longitudinal retractors are involved in the withdrawal of the foot and posterior toes. To achieve a greater understanding of rotifer behavior, it is important to elucidate the structural complexity of body wall muscles in rotifers. The utility of fluorescently-labeled phalloidin for the visualization of these muscles is discussed and placed in the context of rotifer functional morphology.     

Biomechanical analysis of primate bipedal walking by computer simulation

A computer simulation technique was applied to make clear the mechanical characteristics of primate bipedal walking. A primate body and the walking mechanism were modeled mathematically with a set of dynamic equations. Using a digital computer, the following were calculated from these equations by substituting measured displacements and morphological data of each segment of the primate: the acceleration, joint angle, center of gravity, foot force, joint moment, muscular force, transmitted force at the joint, electric activity of the muscle, generated power by the leg and energy expenditure in walking.The model was evaluated by comparing some of the calculated results with the experimental results such as foot force and electromyographic data, and improved in order to obtain the agreement between them.The level bipedal walking of man, chimpanzee and Japanese monkey and several types of synthesized walking were analyzed from the viewpoint of biomechanics.It is concluded that the bipedal walking of chimpanzee is nearer to that of man than to that of the Japanese monkey because of its propulsive mechanism, but it requires large muscular force for supporting the body weight.     

A multi-segment kinematic model of the foot with a novel definition of forefoot motion for use in clinical gait analysis during walking

A multi-segment kinematic model of the foot was developed for use in a gait analysis laboratory. The foot was divided into hindfoot, talus, midfoot and medial and lateral forefoot segments. Six functional joints were defined: ankle and subtalar joints, frontal and transverse plane motions of the hindfoot relative to midfoot, supination/pronation twist of the forefoot relative to midfoot and medial longitudinal arch height-to-length ratio. Twelve asymptomatic subjects were tested during barefoot walking with a six-camera optical stereometric system and auto-reflective markers organized in triads. Repeatability of the joint motions was tested using coefficients of multiple correlation. Ankle and subtalar joint motions and twisting of the forefoot were most repeatable. Hindfoot motions were least repeatable both within-subjects and between-subjects. Hindfoot and forefoot pronation in the frontal plane was found to coincide with dropping of the medial longitudinal arch between early to mid-stance, followed by supination and rising of the arch in late stance and swing phase. This multi-segment foot model addresses an unfortunate shortcoming in current gait analysis practice-the inability to measure motion within the foot. Such measurements are crucial if gait analysis is to remain relevant in the orthopaedic and rehabilitative treatment of the foot and ankle.     

A mathematical model of hind-limb control in cats when walking backward

The “walking backward” mode was achieved within a single model of cat hind-limb locomotion with the balance maintenance only due to a change in the controlling actions (in addition to the “forward walking” mode). The skeletal part of the model contains the spine, pelvis, and two limbs consisting of the thigh, shin, and foot. The hip joint and spine mount in the thoracic region have three degrees of freedom; the knee and ankle joints have one degree of freedom. The pelvis is rigidly connected to the spine. Control is performed by model muscles (flexors and extensors of the thigh, shin, and foot). The muscle activation is performed by the effects that are typical for motoneurons that control the muscles. The feet in the support phase touch the treadmill, which moves at a constant speed. The model qualitatively reproduces multiple characteristics of feline movements during forward and backward walking (supporting its validity).     

A quantitative assessment of the "tendon" action of two-joint muscles]

Two-joint muscles are able to transmit mechanical energy between the links of the body having no common joint ("tendon action" of the muscles). It is proposed to calculate difference between control moment power in a joint and the sum of powers developed by all muscles serving this joint in order to determine the direction and rate of mechanical energy transfer through the two-joint muscles. It was shown that in the shock-absorbing phase of support in running two-joint muscles the energy transfers from distal to proximal links (from foot to thigh, and from shank to pelvis), in take-off phase-from proximal links to distal ones (from pelvis to shank, and from thigh to foot).     

Longer moment arm results in smaller joint moment development, power and work outputs in fast motions

Effects of moment arm length on kinetic outputs of a musculoskeletal system (muscle force development, joint moment development, joint power output and joint work output) were evaluated using computer simulation. A skeletal system of the human ankle joint was constructed: a lower leg segment and a foot segment were connected with a hinge joint. A Hill-type model of the musculus soleus (m. soleus), consisting of a contractile element and a series elastic element, was attached to the skeletal system. The model of the m. soleus was maximally activated, while the ankle joint was plantarflexed/dorsiflexed at a variation of constant angular velocities, simulating isokinetic exercises on a muscle testing machine. Profiles of the kinetic outputs (muscle force development, joint moment development, joint power output and joint work output) were obtained. Thereafter, the location of the insertion of the m. soleus was shifted toward the dorsal/ventral direction by 1cm, which had an effect of lengthening/shortening the moment arm length, respectively. The kinetic outputs of the musculoskeletal system during the simulated isokinetic exercises were evaluated with these longer/shorter moment arm lengths. It was found that longer moment arm resulted in smaller joint moment development, smaller joint power output and smaller joint work output in the larger plantarflexion angular velocity region (>120 degrees/s). This is because larger muscle shortening velocity was required with longer moment arm to achieve a certain joint angular velocity. Larger muscle shortening velocity resulted in smaller muscle force development because of the force-velocity relation of the muscle. It was suggested that this phenomenon should be taken into consideration when investigating the joint moment-joint angle and/or joint moment-joint angular velocity characteristics of experimental data.     

Pelvic function in anuran jumping: Interspecific differences in the kinematics and motor control of the iliosacral articulation during take‐off and landing

Although the anuran pelvis is thought to be adapted for jumping, the function of the iliosacral joint has seen little direct study. Previous work has contrasted the basal “ lateral‐bender ” pelvis from the “ rod‐like ” pelvis of crown taxa hypothesized to function as a sagittal hinge to align the trunk with take‐off forces. We compared iliosacral movements and pelvic motor patterns during jumping in the two pelvic types. Pelvic muscle activity patterns, iliosacral anteroposterior (AP) movements and sagittal bending of the pelvis during the take‐off and landing phases were quantified in lateral bender taxa Ascaphus (Leiopelmatidae) and Rhinella (Bufonidae) and the rod‐like Lithobates (Ranidae). All three species exhibit sagittal extension during take‐off, therefore, both pelvic types employ a sagittal hinge. However, trunk elevation occurs significantly earlier in the anuran rod‐like pelvis. Motor patterns confirm that the piriformis muscles depress the urostyle while the longissimus dorsi muscles elevate the trunk during take‐off. However, the coccygeoiliacus muscles also produce anterior translation of the sacrum on the ilia. A new model illustrates how AP translation facilitates trunk extension in the lateral‐bender anurans that have long been thought to have limited sagittal bending. During landing, AP translation patterns are similar because impact forces slide the sacrum from its posterior to anterior limits. Sagittal flexion during landing differs among the three taxa depending on the way the species land. AP translation during landing may dampen impact forces especially in Rhinella in which pelvic function is tuned to forelimb‐landing dynamics. The flexibility of the lateral‐bender pelvis to function in sagittal bending and AP translation helps to explain the retention of this basal configuration in many anurans. The novel function of the rod‐like pelvis may be to increase the rate of trunk elevation relative to faster rates of energy release from the hindlimbs enabling them to jump farther. J. Morphol. 277:1539–1558, 2016. © 2016 Wiley Periodicals, Inc.     

Ankle and midfoot kinetics during normal gait: a multi-segment approach

Multi-segment foot models are increasingly being used to evaluate intra and inter-segment foot kinematics such as the motion between the hindfoot/tibia (ankle) and the forefoot/hindfoot (midfoot) during walking. However, kinetic analysis have been mainly restricted to one-segment foot models and could be improved by considering a multi-segment approach. Therefore, the aims of this study were to (1) implement a kinetic analysis of the ankle and theoretical midfoot joints using the existing Oxford Foot Model (OFM) through a standard inverse dynamics approach using only marker, force plate and anthropometric data and (2) to compare OFM ankle joint kinetics to those output by the one-segment foot plugin-gait model (PIG). 10 healthy adolescents fitted with both the OFM and PIG markers performed barefoot comfortable speed walking trials over an instrumented walkway. The maximum ankle power generation was significantly reduced by approximately 40% through OFM calculations compared to PIG estimates (p<0.001). This result was not caused by a decrease in OFM computed joint moments, but by a reduction in the angular velocity between the tibia/hindfoot (OFM) compared to the tibia/foot (PIG) (p<0.001). Additionally, analysis revealed considerable midfoot loading. One-segment foot models overestimate ankle power, and may also overestimate the contribution of the triceps surae. A multi-segment approach may help quantify the important contribution of the midfoot ligaments and musculature to power generation. We therefore recommend the use of multi-segment foot models to estimate ankle and midfoot kinetics, especially when surgical decision-making is based on the results of three-dimensional gait analysis.     

Automated muscle wrapping using finite element contact detection

Realistic muscle path representation is essential to musculoskeletal modeling of joint function. Algorithms predicting these muscle paths typically rely on a labor intensive predefinition of via points or underlying geometries to guide wrapping for given joint positions. While muscle wrapping using anatomically precise three-dimensional (3D) finite element (FE) models of bone and muscle has been achieved, computational expense and pre-processing associated with this approach exclude its use in applications such as subject-specific modeling. With the intention of combining advantageous features of both approaches, an intermediate technique relying on contact detection capabilities of commercial FE packages is presented. We applied the approach to the glenohumeral joint, and validated the method by comparison against existing experimental data. Individual muscles were modeled as a straight series of deformable beam elements and bones as anatomically precise 3D rigid bodies. Only the attachment locations and a default orientation of the undeformed muscle segment were pre-defined. The joint was then oriented in a static position of interest. The muscle segment free end was then moved along the shortest Euclidean path to its origin on the scapula, wrapping the muscle along bone surfaces by relying on software contact detection. After wrapping for a given position, the resulting moment arm was computed as the perpendicular distance from the line of action vector to the humeral head center of rotation.This approach reasonably predicted muscle length and moment arm for 27 muscle segments when compared to experimental measurements over a wide range of shoulder motion. Artificial via points or underlying contact geometries were avoided, contact detection and multiobject wrapping on the bone surfaces were automatic, and low computational cost permitted wrapping of individual muscles within seconds on a standard desktop PC. These advantages may be valuable for both general and subject-specific musculoskeletal modeling.     

Interindividual differences in leg muscle mass and pyruvate kinase activity correlate with interindividual differences in jumping performance of Hyla multilineata

Frog jumping is an excellent model system for examining the structural basis of interindividual variation in burst locomotor performance. Some possible factors that affect jump performance, such as total body size, hindlimb length, muscle mass, and muscle mechanical and biochemical properties, were analysed at the interindividual (intraspecies) level in the tree frog Hyla multilineata. The aim of this study was to determine which of these physiological and anatomical variables both vary between individuals and are correlated with interindividual variation in jump performance. The model produced via stepwise linear regression analysis of absolute data suggested that 62% of the interindividual variation in maximum jump distance could be explained by a combination of interindividual variation in absolute plantaris muscle mass, total hindlimb muscle mass (excluding plantaris muscle), and pyruvate kinase activity. When body length effects were removed, multiple regression indicated that the same independent variables explained 43% of the residual interindividual variation in jump distance. This suggests that individuals with relatively large jumping muscles and high pyruvate kinase activity for their body size achieved comparatively large maximal jump distances for their body size.     

In vivo tests of an improved method for functional location of the subtalar joint axis

The subtalar joint is important in frontal plane movement and posture of the hindfoot. Abnormal subtalar joint moments caused by muscle forces and the ground reaction force acting on the foot are thought to play a role in various foot deformities. Calculating joint moments typically requires knowledge of the location of the joint axis; however, location of the subtalar axis from measured movement is difficult because the talus cannot be tracked using skin-mounted markers. The accuracy of a novel technique for locating the subtalar axis was assessed in vivo using magnetic resonance imaging. The method was also tested with skin-mounted markers and video motion analysis. The technique involves applying forces to the foot that cause pure subtalar joint motion (with negligible talocrural joint motion), and then using helical axis decomposition of the resulting tibiocalcaneal motion. The resulting subtalar axis estimates differed by 6° on average from the true best-fit subtalar axes in the MRI tests. Motion was found to have been applied primarily about the subtalar joint with an average of only 3° of talocrural joint motion. The proposed method provides a potential means for obtaining subject-specific subtalar axis estimates which can then be used in inverse dynamic analyses and subject-specific musculoskeletal models.     

Measurement of multi-segment foot joint angles during gait using a wearable system

Usually the measurement of multi-segment foot and ankle complex kinematics is done with stationary motion capture devices which are limited to use in a gait laboratory. This study aimed to propose and validate a wearable system to measure the foot and ankle complex joint angles during gait in daily conditions, and then to investigate its suitability for clinical evaluations. The foot and ankle complex consisted of four segments (shank, hindfoot, forefoot, and toes), with an inertial measurement unit (3D gyroscopes and 3D accelerometers) attached to each segment. The angles between the four segments were calculated in the sagittal, coronal, and transverse planes using a new algorithm combining strap-down integration and detection of low-acceleration instants. To validate the joint angles measured by the wearable system, three subjects walked on a treadmill for five minutes at three different speeds. A camera-based stationary system that used a cluster of markers on each segment was used as a reference. To test the suitability of the system for clinical evaluation, the joint angle ranges were compared between a group of 10 healthy subjects and a group of 12 patients with ankle osteoarthritis, during two 50-m walking trials where the wearable system was attached to each subject. On average, over all joints and walking speeds, the RMS differences and correlation coefficients between the angular curves obtained using the wearable system and the stationary system were 1 deg and 0.93, respectively. Moreover, this system was able to detect significant alteration of foot and ankle function between the group of patients with ankle osteoarthritis and the group of healthy subjects. In conclusion, this wearable system was accurate and suitable for clinical evaluation when used to measure the multi-segment foot and ankle complex kinematics during long-distance walks in daily life conditions.