Comparison of global and joint-to-joint methods for estimating the hip joint load and the muscle forces during walking

A three-dimensional musculoskeletal model of the lower limb was developed to study the influence of biarticular muscles on the muscle force distribution and joint loads during walking. A complete walking cycle was recorded for 9 healthy subjects using the standard optoelectronic motion tracking system. Ground contact forces were also measured using a 6-axes force plate. Inverse dynamics was used to compute net joint reactions (forces and torques) in the lower limb. A static optimization method was then used to estimate muscle forces. Two different approaches were used: in the first one named global method, the biarticular muscles exerted a torque on the two joints they spanned at the same time, and in the second one called joint-by-joint method, these biarticular muscles were divided into two mono-articular muscles with geometrical (insertion, origin, via points) and physiological properties remained unchanged. The hip joint load during the gait cycle was then calculated taking into account the effect of muscle contractions. The two approaches resulted in different muscle force repartition: the biarticular muscles were favoured over any set of single-joint muscles with the same physiological function when using the global method. While the two approaches yielded only little difference in the resultant hip load, the examination of muscle power showed that biarticular muscles could produce positive work at one joint and negative work at the other, transferring energy between body segments and thus decreasing the metabolic cost of movement.     

Muscle moment arm and normalized moment contributions as reference data for musculoskeletal elbow and wrist joint models

A geometric musculoskeletal model of the elbow and wrist joints was developed to calculate muscle moment arms throughout elbow flexion/extension, forearm pronation/supination, wrist flexion/extension and radial/ulnar deviation. Model moment arms were verified with data from cadaver specimen studies and geometric models available in the literature. Coefficients of polynomial equations were calculated for all moment arms as functions of joint angle, with special consideration to coupled muscles as a function of two joint angles. Additionally, a “normalized potential moment (NPM)” contribution index for each muscle across the elbow and wrist joints in four degrees-of-freedom was determined using each muscle's normalized physiological cross-sectional area (PCSA) and peak moment arm (MA). We hypothesize that (a) a geometric model of the elbow and wrist joints can represent the major attributes of MA versus joint angle from many literature sources of cadaver and model data and (b) an index can represent each muscle's normalized moment contribution to each degree-of-freedom at the elbow and wrist. We believe these data serve as a simple, yet comprehensive, reference for how the primary 16 muscles across the elbow and wrist contribute to joint moment and overall joint performance.     

The effects of sloped surfaces on locomotion: backward walking as a perturbation

The purpose of this study was to examine lower extremity kinetics and muscle activity during backward slope walking to clarify the relationship between joint moments and powers and muscle activity patterns observed in forward slope walking. Nine healthy volunteers walked backward on an instrumented ramp at three grades (-39% (-21 degrees ), 0% (level), +39% (+21 degrees )). EMG activity was recorded from major lower extremity muscles. Joint kinetics were obtained from kinematic and force platform data. The knee joint moment and power generation increased significantly during upslope walking; hip joint moment and power absorption increased significantly during downslope walking. When compared to data from forward slope walking, these backward walking data suggest that power requirements of a task dictate the muscle activity pattern needed to accomplish that movement. During downslope walking tasks, power absorption increased and changes in muscle activity patterns were directly related to the changes in the joint moment patterns. In contrast, during upslope walking tasks, power generation increased and changes in the muscle activity were related to the changes in the joint moments only at the 'primary' joint; at adjacent joints the changes in muscle activity were unrelated to the joint moment pattern. The 'paradoxical' changes in the muscle activity at the adjacent joints are possibly related to the activation of biarticular muscles required by the increased power generation at the primary joint. In total, these data suggest that changing power requirements at a joint impact the control of muscle activity at that and adjacent joints.     

Contributions of muscle forces and toe-off kinematics to peak knee flexion during the swing phase of normal gait: an induced position analysis

A three-dimensional dynamic simulation of walking was used together with induced position analysis to determine how kinematic conditions at toe-off and muscle forces following toe-off affect peak knee flexion during the swing phase of normal gait. The flexion velocity of the swing-limb knee at toe-off contributed 30 degrees to the peak knee flexion angle; this was larger than any contribution from an individual muscle or joint moment. Swing-limb muscles individually made large contributions to knee angle (i.e., as large as 22 degrees), but their actions tended to balance one another, so that the combined contribution from all swing-limb muscles was small (i.e., less than 3 degrees of flexion). The uniarticular muscles of the swing limb made contributions to knee flexion that were an order of magnitude larger than the biarticular muscles of the swing limb. The results of the induced position analysis make clear the importance of knee flexion velocity at toe-off relative to the effects of muscle forces exerted after toe-off in generating peak knee flexion angle. In addition to improving our understanding of normal gait, this study provides a basis for analyzing stiff-knee gait, a movement abnormality in which knee flexion in swing is diminished.     

Dynamic coordinate data for describing muscle-tendon paths: a mathematical approach

When modelling the musculoskeletal system over a range of joint angles the use of fixed points to describe muscle-tendon paths has inherent limitations. These result in fewer deflection points and the use of effective insertions to accommodate both relative marker movement and avoid muscle paths contacting bony structures. Model performance is dependent on the joint angle relative to the anatomical position where the muscle-tendon paths were defined. The present study proposes a scheme for the implementation of dynamic coordinates for describing muscle-tendon paths. For each muscle-tendon element a plane is defined in which the muscle-tendon complex acts when crossing a given joint. The muscle-tendon plane is dependent on 3D segment orientations and describes one degree of freedom, while the remaining two degrees of freedom are described by polar coordinates and locate the dynamic point in the muscle-tendon plane. The dynamic approach is implemented on four muscles of the lower limb in modelled and simulated joint movements and offers a significant improvement on previous approaches based on fixed deflection points. The scheme accommodates compound 3D rotations about joint axes, is not computationally difficult or require large data sets, and does not impose limitations on the number of points that may be defined along a muscle-tendon path.     

A muscle-path-plane method for representing muscle contraction during joint movement

Traditional muscle paths (the straight-line model and the viapoint-line model) emphasise either the mechanical properties that arouse joint movement or the morphological characteristics of the muscles. To consider both the factors, a muscle-path-plane (MPP) method is introduced to model the paths of muscles during joint movement. This method is based on the premise that there is a MPP, constructed by origin, insertion and MPP control point, which represents the major direction of the muscle contraction for an arbitrary joint configuration at any time. Then, we can calculate the functions and the lengths of the muscle paths during instantaneous joint movement in MPP by mathematical approaches. Taking the triceps brachii as an example, the lengths of its paths during elbow flexion are calculated and compared with the relative studies reported in the literature. It is concluded that this method can provide an insight into the simulation of the muscle contraction.     

Mechanical demand and multijoint control during landing depend on orientation of the body segments relative to the reaction force.

The purpose of this study was to determine how diverse momentum conditions and anatomical orientation at contact influences mechanical loading and multijoint control of the reaction force during landings. Male collegiate gymnasts (n=6) performed competition style landings (n=3) of drop jumps, front saltos, and back saltos from a platform (0.72 m) onto landing mats (0.12 m). Kinematics (200 fps), reaction forces (800 Hz) and muscle activation patterns (surface EMG, 1600 Hz) of seven lower extremity muscles were collected simultaneously. Between-task differences in segment orientation relative to the reaction force contributed to significant between-task differences in knee and hip net joint moments (NJM) during the impact phase. During the stabilization phase, ankle, knee, and hip NJMs acted to control joint flexion. Between-task differences in muscle activation patterns indicated that gymnasts scaled biarticular muscle activation to accommodate for between-task differences in NJM after contact. Activation of muscles on both sides of the joint suggests that impedance like control was used to stabilize the joints and satisfy the mechanical demand imposed on the lower extremity. Between-subject differences in the set of muscles used to control total body center of mass (TBCM) trajectory and achieve lower extremity NJMs suggests that control of multijoint movements involving impact needs to incorporate mechanical objectives at both the total body and local level. The functional consequences of such a control structure may prove to be an asset to gymnasts, particularly when required to perform a variety of landing tasks under a variety of environmental constraints.     

Investigation of the Peculiarities of Two-joint Muscles Using a 3 DOF Model of the Human Upper Limb in the Sagittal Plane: an Optimization Approach

Abstract

The purpose of this paper is an investigation of the peculiarities of biarticular muscles by means of modelling and analytical solution of the indeterminate problem. The basic model includes 10 muscle elements performing flexio/extensio in the shoulder, elbow and wrist. Four of them are biarticular muscles. Two modifications of the model with only monoarticular muscles are developed. The indeterminate problem is solved analytically using the objective criterion σc_iF_i ² where F( is the module of the i-th muscle force and Cj is a weight coefficient. The predicted muscle forces, joint reactions and moments are compared in-between the basic model and its two modifications for different joint angles, external loading and weight coefficients. The main conclusions are: it is impossible to formulate strict advantages of the biarticular muscles under quasistatical conditions, their peculiarities depend on limb position, external loading and neural control; in general, monoarticular muscles are more powerful than biarticular ones; the biarticular muscles fine tune muscle coordination, their control is more precise and graceful; the presence of biarticular muscles leads to an increase of the joint reactions and moments, thus stabilizing the limb.     

Scaling of peak moment arms of elbow muscles with upper extremity bone dimensions.

It is often assumed that moment arms scale with size and can be normalized by body segment lengths or limb circumferences. However, quantitative scaling relationships between moment arms and anthropometric dimensions are generally not available. We hypothesized that peak moment arms of the elbow flexor and extensor muscles scale with the shorter distance (D(s)) between the elbow flexion axis and a muscle's origin and insertion. To test this hypothesis, we estimated moment arms of six muscles that cross the elbow, digitized muscle attachment sites and bone surface geometry, and estimated the location of the elbow flexion axis in 10 upper extremity cadaveric specimens which ranged in size from a 5'0" female to a 6'4" male. D(s) accurately reflected the differences in peak moment arms across different muscles, explaining 93-99% of the variation in peaks between muscles in the same specimen. D(s) also explained between 55% and 88% of the interspecimen variation in peak moment arms for brachioradialis, biceps, and ECRL. Triceps peak moment arm was significantly correlated to the anterior-posterior dimension of the ulna measured at the olecranon (r(2)=0.61, p=0.008). Radius length provides a good measure of the interspecimen variation in peaks for brachioradialis, biceps, and ECRL. However, bone lengths were not significantly correlated to triceps moment arm or anterior-posterior bone dimensions. This work advances our understanding of the variability and scaling dimensions for elbow muscle moment arms across subjects of different sizes.     

Error propagation from kinematic data to modeled muscle-tendon lengths during walking

Kinematic data from 3D gait analysis together with musculoskeletal modeling techniques allow the derivation of muscle-tendon lengths during walking. However, kinematic data are subject to soft tissue artifacts (STA), referring to skin marker displacements during movement. STA are known to significantly affect the computation of joint kinematics, and would therefore also have an effect on muscle-tendon lengths which are derived from the segmental positions. The present study aimed to introduce an analytical approach to calculate the error propagation from STA to modeled muscle-tendon lengths. Skin marker coordinates were assigned uncorrelated, isotropic error functions with given standard deviations accounting for STA. Two different musculoskeletal models were specified; one with the joints moving freely in all directions, and one with the joints constrained to rotation but no translation. Using reference kinematic data from two healthy boys (mean age 9 y 5 m), the propagation of STA to muscle-tendon lengths was quantified for semimembranosus, gastrocnemius and soleus. The resulting average SD ranged from 6% to 50% of the normalized muscle-tendon lengths during gait depending on the muscle, the STA magnitudes and the musculoskeletal model. These results highlight the potential impact STA has on the biomechanical analysis of modeled muscle-tendon lengths during walking, and suggest the need for caution in the clinical interpretation of muscle-tendon lengths derived from joint kinematics.     

Fibre operating lengths of human lower limb muscles during walking

Muscles actuate movement by generating forces. The forces generated by muscles are highly dependent on their fibre lengths, yet it is difficult to measure the lengths over which muscle fibres operate during movement. We combined experimental measurements of joint angles and muscle activation patterns during walking with a musculoskeletal model that captures the relationships between muscle fibre lengths, joint angles and muscle activations for muscles of the lower limb. We used this musculoskeletal model to produce a simulation of muscle-tendon dynamics during walking and calculated fibre operating lengths (i.e. the length of muscle fibres relative to their optimal fibre length) for 17 lower limb muscles. Our results indicate that when musculotendon compliance is low, the muscle fibre operating length is determined predominantly by the joint angles and muscle moment arms. If musculotendon compliance is high, muscle fibre operating length is more dependent on activation level and force-length-velocity effects. We found that muscles operate on multiple limbs of the force-length curve (i.e. ascending, plateau and descending limbs) during the gait cycle, but are active within a smaller portion of their total operating range.     

Estimation of cat medial gastrocnemius fascicle lengths during dynamic contractions

In typical muscle models, it is often assumed that the contractile element (fascicle) length depends exclusively on the instantaneous muscle-tendon length and the instantaneous muscle force. In order to test whether the instantaneous fascicle length during dynamic contractions can be predicted from muscle-tendon length and force, fascicle lengths, muscle-tendon lengths, and muscle forces were directly measured in cat medial gastrocnemii during isometric and dynamic contractions. Two theoretical muscle models were developed: model A was based on force-time data obtained during the activation phase and model D on force-time data obtained during the deactivation phase of isometric contractions. To test the models, instantaneous fascicle lengths were predicted from muscle-tendon lengths and forces during dynamic contractions that simulated cat locomotion for speeds ranging from 0.4 to 1.6m/s. The theoretically predicted fascicle lengths were compared with the experimentally measured fascicle lengths. It was found that fascicle lengths were not uniquely associated with muscle-tendon lengths and forces; that is, for a given muscle-tendon length and force, fascicle lengths varied depending on the contractile history. Consequently, models A and D differed in fascicle length predictions; model D (maximum average error=8.5%) was considerably better than model A (maximum average error=22.3%). We conclude from this study that it is not possible to predict the exact fascicle lengths from muscle-tendon lengths and forces alone, however, adequate predictions seem possible based on such a model. The relationship between fascicle length and muscle force and muscle-tendon length is complex and highly non-linear, thus, it appears unlikely that accurate fascicle length predictions can be made without some reference contractions in which fascicle length, muscle-tendon length, and force are measured simultaneously.     

Load on the upper extremity in manual wheelchair propulsion

To study joint contributions in manual wheelchair propulsion, we developed a three-dimensional model of the upper extremity. The model was applied to data collected in an experiment on a wheelchair ergometer in which mechanical advantage (MA) was manipulated. Five male able-bodied subjects performed two wheelchair exercise tests (external power output P_ext = 0.25–0.50 W · kg⁻¹) against increasing speeds (1.11–1.39–1.67 m.s⁻¹), which simulated MA of 0.58–0.87. Results indicated a decrease in mechanical efficiency (ME) with increasing MA that could not be related to applied forces or joint torques. Increase in P_ext was related to increases in joint torques. On the average, the highest torques were noted in shoulder flexion and adduction (35.6 and 24.6 N · m at MA = 0.58 and P_ext= 0.50 W · kg⁻¹). Peak elbow extension and flexion torques were −10.6 and 8.5 N · m. Based on the combination of torques and electromyographic (EMG) records of upper extremity muscles, anterior deltoid and pectoralis muscles are considered the prime movers in manual wheelchair propulsion. Coordinative aspects of manual wheelchair propulsion concerning the function of (biarticular) muscles in directing the propulsive forces and the redistribution of joint torques in a closed chain are discussed. We found no conclusive evidence for the role of elbow extensors in direction of propulsive forces.     

Contribution of mono- and biarticular muscles to extending knee joint moments in runners and cyclists.

Motor actions are governed by coordinated activation of mono- and biarticular muscles. This study considered differences in mono- and biarticular knee extensors between runners and cyclists in the context of adaptations to task-specific movement requirements. Two hypotheses were tested: 1) the length-at-use hypothesis, which is that muscle adapts to have it operate around optimal length; and 2) the contraction-mode hypothesis, which is that eccentrically active muscles prefer to operate on the ascending limb of the length-force curve. Ten runners and ten cyclists performed maximal, isometric knee extensions on a dynamometer at five knee and four hip joint angles. This approach allowed the separation of the contribution of mono- and biarticular extensors. Three major differences occurred: 1) compared with runners, monoarticular extensors of cyclists reach optimal length at larger muscle length; 2) in runners, optimal length of the biarticular extensor is shifted to larger lengths; and 3) the moment generated by monoarticular extensor was larger in cyclists. Mono- and biarticular extensors respond to different adaptation triggers in runners and cyclists. Monoarticular muscles seem to adapt to the length-at-use, whereas biarticular muscles were found to be sensitive to the contraction-mode hypothesis.     

The influence of stimulation frequency and ankle joint angle on the moment exerted by human dorsiflexor muscles.

The purpose of this study was to investigate the force-frequency relationships and the post-tetanic twitch potentiation as a function of joint angle (i.e. muscle length) in human skeletal muscles under isometric conditions. The dorsiflexor muscles of healthy subjects were stimulated at different ankle joint angles by means of constant frequency bursts at seven submaximal frequencies (50, 33, 25, 20, 16, 12, 8 Hz) with a duration of two seconds. Particular attention has been focused on the stability of recruitment in the range of joint angles examined. The results show that moment-frequency curves of human dorsiflexors change as a function of ankle angle: especially for the lower stimulation frequency range (8, 12, 16, 20 Hz), the normalized moment increases from dorsiflexion to plantar flexion (i.e. with increasing muscle length) resulting in a leftward shift of the normalized moment-frequency curves. Post-tetanic twitch potentiation is shown to be ankle joint dependent as well.     

Modeling the length dependence of isometric force in human quadriceps muscles

Functional electrical stimulation is used to restore movement and function of paralyzed muscles by activating skeletal muscle artificially. An accurate and predictive mathematical model can facilitate the design of stimulation patterns that produce the desired force. The present study is a first step in developing a mathematical model for non-isometric muscle contractions. The goals of this study were to: (1) identify how our isometric force model's parameters vary with changes in knee joint angle, (2) identify the best knee flexion angle to parameterize this model, and (3) validate the model by comparing experimental data to predictions in response to a wide range of stimulation frequencies and muscle lengths. Results showed that by parabolically varying one of the free parameters with knee joint angle and fixing the other parameters at the values identified at 40 degrees of knee flexion, the model could predict the force responses to a wide range of stimulation frequencies and patterns at different muscle lengths. This work showed that the current isometric force model is capable of predicting the changes in skeletal muscle force at different muscle lengths.     

A noninvasive technique for in vivo measurement of joint torques of biarticular muscles.

The objective of this work was to develop a noninvasive method to measure the joint torques produced by biarticular muscles at two joints simultaneously. During intramuscular stimulation of the cat medial gastrocnemius (MG) muscle, torques at the ankle and knee joints were calculated from forces measured in two dimensions at the end point of the cat paw under isometric conditions. The method was verified by the known anatomical properties of cat MG muscle and the tibialis anterior (TA) muscle. The MG muscle was shown to produce a significant flexion torque at the knee, besides an extension torque at the ankle. This was in agreement with its anatomical arrangement. The TA muscle produced primarily an ankle flexion torque. The small knee torque, due to measurement errors, yielded an estimate of measurement accuracy of 3.0 +/- 2.1% (n = 52). The coupling ratio of the MG muscle, defined as T(ankle)/T(knee), varied significantly with both knee and ankle angles. The profile of MG mechanical coupling agreed qualitatively with changes in limb configuration. The method can be used to measure recruitment properties of electrically stimulated biarticular muscles, and may potentially be used to study the biomechanics of biarticular coupling.     

A model-based study of passive joint properties on muscle effort during static stance

This study examined the impact of lower extremity joint stiffnesses and simulated joint contractures on the muscle effort required to maintain static standing postures after a spinal cord injury (SCI). Static inverse computer simulations were performed with a three-dimensional 15 degree of freedom musculoskeletal model placed in 1600 different standing postures. The required lower extremity muscle forces were calculated through an optimization routine that minimized the sum of the muscle stresses squared, which was used as an index of the muscle effort required for each standing posture. Joint stiffnesses were increased and decreased by 100 percent of their nominal values, and contractures were simulated to determine their effects on the muscle effort for each posture. Nominal muscle and passive properties for an individual with a SCI determined the baseline muscle effort for comparisons. Stiffness changes for the ankle plantar flexion/dorsiflexion, hip flexion/extension, and hip abduction/adduction directions had the largest effect on reducing muscle effort by more than 5 percent, while changes in ankle inversion/eversion and knee flexion/extension had the least effect. For erect standing, muscle effort was reduced by more than 5 percent when stiffness was decreased at the ankle plantar flexion/dorsiflexion joint or hip flexion/extension joint. With simulated joint contractures, the postural workspace area decreased and muscle effort was not reduced by more than 5 percent for any posture. Using this knowledge, methods can be developed through the use of orthoses, physical therapy, surgery or other means to appropriately augment or diminish these passive moments during standing with a neuroprosthesis.     

Simulation of lower limb axial arterial length change during locomotion

The effect of external forces on axial arterial wall mechanics has conventionally been regarded as secondary to hemodynamic influences. However, arteries are similar to muscles in terms of the manner in which they traverse joints, and their three-dimensional geometrical requirements for joint motion. This study considers axial arterial shortening and elongation due to motion of the lower extremity during gait, ascending stairs, and sitting-to-standing motion. Arterial length change was simulated by means of a graphics based anatomic and kinematic model of the lower extremity. This model estimated the axial shortening to be as much as 23% for the femoropopliteal arterial region and as much as 21% for the iliac artery. A strong correlation was observed between femoropopliteal artery shortening and maximum knee flexion angle (r2=0.8) as well as iliac artery shortening and maximum hip angle flexion (r2=0.9). This implies a significant mechanical influence of locomotion on arterial behavior in addition to hemodynamics factors. Vascular tissue has high demands for axial compliance that should be considered in the pathology of atherosclerosis and the design of vascular implants.     

Activity of mono- and biarticular leg muscles during sprint running

A cinematographic recording of the movements of the lower limbs together with simultaneous emg tracings from nine lower limb muscles were obtained from two male track sprinters during three phases of a 100 m sprint run. The extensor muscles of the hip joint were found to be the primary movers by acceleration of the body's center of gravity (C.G.) during the ground phase of the running cycle. The extensors of the knee joint were also important in this, but to a minor extent, while the plantar flexors of the ankle joint showed the least contribution. The biarticular muscles functioned in a way different from the monoarticular muscles in the sense that they perform eccentric work during the flight and recovery phases and concentric work during the whole ground phase (support), whereas the monoarticular muscles are restricted first to eccentric work and then to concentric work during the ground phase. Furthermore, the biarticular muscles show variation (and rate of variation) in muscle length to a larger extent than the monoarticular muscles. Paradoxical muscle actions appear to take place around the knee joint, where the hamstring muscles, m. gastrocnemius, m. vastus laterialis and m. vastus medialis act as synergists by extending the knee joint during the last part of the ground phase.