Are natural coordinates a useful tool in modeling planar biomechanical linkages?

The paper analyzes the use of natural coordinates in modeling and simulation of musculoskeletal models of the human body. A biomechanical model of the lower extremity of the human body was constructed for the analysis. It consists of three anatomical segments described by eight natural coordinates located at the joints. The developed model was applied to solve three classic dynamics problems of human motion: inverse dynamics, direct dynamics, and static optimization. The analysis covers the raising of a leg together with; the time characteristics of the resultant net torques at the basic joints of the leg (inverse dynamics), the time histories of natural coordinates and their velocities (direct dynamics) as well as the time-varying muscle force patterns (static optimization). In order to check the numerical efficiency of modeling in the natural coordinates' environment the results were compared with the ones received through generalized coordinates. Some conclusions drawn from this comparison and final remarks referring to the biomechanical identification of the analyzed motor task were included in the paper.     

An analytical model for the ergometer rowing: inverse multibody dynamics analysis

A model for the ergometer rowing exercise is presented in this paper. From the quantitative observations of a particular trajectory (motion), the model is used to determine the moment of the forces produced by the muscles about each joint. These forces are evaluated according to the continuous system of equations of motion. An inverse dynamics analysis is performed in order to predict the joint torques developed by the muscles during the execution of the task. An elementary multibody mechanical system is used as an example to discuss the assumptions and procedures adopted.     

An improved inverse dynamics formulation for estimation of external and internal loads during human sagittal plane movements

Planar musculoskeletal models are common in the inverse dynamics analysis of human movements such as walking, running and jumping. The continued interest in such models is justified by their simplicity and computational efficiency. Related to a human planar model, a unified formulation for both the flying and support phases of the sagittal plane movements is developed. The actuation involves muscle forces in the lower limbs and the resultant muscle torques in the other body joints. The dynamic equations, introduced in absolute coordinates of the segments, are converted into useful compact forms using the projective technique. The solution to a determinate inverse dynamics problem allows for the explicit determination of the external reactions (presumed to vanish during the flying phases) and the resultant muscle torques in all the model joints. The indeterminate inverse dynamics problem is then focused on the assessment of muscle forces and joint reaction forces selectively in the supporting lower limb. Numerical results of the inverse dynamics simulation of sample sagittal plane movements are reported to illustrate the validity and effectiveness of the improved formulation.     

Modelling, simulation and optimisation of a human vertical jump.

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

Modeling and inverse simulation of somersaults on the trampoline

This paper describes a biomechanical model for numerical simulation of front and back somersaults, without twist, performed on the trampoline. The developed mathematical formulation is used to solve an inverse dynamics problem, in which the moments of muscle forces at the joints that result in a given (measured) motion are determined. The nature of the stunts and the way the human body is maneuvered and controlled can be studied. The calculated torques can then be used as control signals for a dynamic simulation. This provides a way to check the inverse dynamics procedures, and influence of typical control errors on somersault performance can be studied. To achieve these goals, the nonlinear dynamical model of the trampolinist and the interacting trampoline bed has been identified, and a methodology for recording the actual somersault performances was proposed. Some results of numerical simulations are reported.     

Evidence of residual force enhancement for multi-joint leg extension

Force enhancement is a well accepted property of skeletal muscle and has been observed at all structural levels ranging from single myofibrils to voluntarily activated m. quadriceps femoris in vivo. However, force enhancement has not been studied for multi-joint movements like human leg extension; therefore knowledge about its relevance in daily living remains limited. The purpose of this study was to determine whether there is force enhancement during maximal voluntary multi-joint leg extension. Human leg extension was studied (n=22) on a motor driven leg press dynamometer where external reaction forces under the feet as well as activity of 8 lower extremity muscles were measured. In addition, torque in the ankle and knee joints was calculated using inverse dynamics. The steady-state isometric force, joint torques, and muscle activation after active stretch (20° stretch amplitude at 60°/s) were compared with the corresponding values obtained during isometric reference contractions. There was consistent force enhancement during and following stretch for both forces and joint torques. Potentiation during stretch reached values between 26% and 30%, while a significant force enhancement of 10.5–12.3% and 4.3–7.4% remained 0.5–1 and 2.5–3 s after stretch, respectively. During stretch, EMG signals of m. gastrocnemius medialis and lateralis were significantly increased, while following stretch all analyzed muscles showed the same activity as during the reference contractions. We conclude from these results that force enhancement exists in everyday movements and should be accounted for when analyzing or modelling human movement.     

Critical analysis of musculoskeletal modelling complexity in multibody biomechanical models of the upper limb

The inverse dynamics technique applied to musculoskeletal models, and supported by optimisation techniques, is used extensively to estimate muscle and joint reaction forces. However, the solutions of the redundant muscle force sharing problem are sensitive to the detail and modelling assumptions of the models used. This study presents four alternative biomechanical models of the upper limb with different levels of discretisation of muscles by bundles and muscle paths, and their consequences on the estimation of the muscle and joint reaction forces. The muscle force sharing problem is solved for the motions of abduction and anterior flexion, acquired using video imaging, through the minimisation of an objective function describing muscle metabolic energy consumption. While looking for the optimal solution, not only the equations of motion are satisfied but also the stability of the glenohumeral and scapulothoracic joints is preserved. The results show that a lower level of muscle discretisation provides worse estimations regarding the muscle forces. Moreover, the poor discretisation of muscles relevant to the joint in analysis limits the applicability of the biomechanical model. In this study, the biomechanical model of the upper limb describing the infraspinatus by a single bundle could not solve the complete motion of anterior flexion. Despite the small differences in the magnitude of the forces predicted by the biomechanical models with more complex muscular systems, in general, there are no significant variations in the muscular activity of equivalent muscles.     

A neuromusculoskeletal tracking method for estimating individual muscle forces in human movement

A neuromusculoskeletal tracking (NMT) method was developed to estimate muscle forces from observed motion data. The NMT method combines skeletal motion tracking and optimal neuromuscular tracking to produce forward simulations of human movement quickly and accurately. The skeletal motion tracker calculates the joint torques needed to actuate a skeletal model and track observed segment angles and ground forces in a forward simulation of the motor task. The optimal neuromuscular tracker resolves the muscle redundancy problem dynamically and finds the muscle excitations (and muscle forces) needed to produce the joint torques calculated by the skeletal motion tracker. To evaluate the accuracy of the NMT method, kinematics and ground forces obtained from an optimal control (parameter optimization) solution for maximum-height jumping were contaminated with both random and systematic noise. These data served as input observations to the NMT method as well as an inverse dynamics analysis. The NMT solution was compared to the input observations, the original optimal solution, and a simulation driven by the inverse dynamics torques. The results show that, in contrast to inverse dynamics, the NMT method is able to produce an accurate forward simulation consistent with the optimal control solution. The NMT method also requires 3 orders-of-magnitude less CPU time than parameter optimization. The speed and accuracy of the NMT method make it a promising new tool for estimating muscle forces using experimentally obtained kinematics and ground force data.     

A model for insect locomotion in the horizontal plane: Feedforward activation of fast muscles, stability, and robustness

We develop a neuromechanical model for running insects that includes a simplified hexapedal leg geometry with agonist-antagonist muscle pairs actuating each leg joint. Restricting to dynamics in the horizontal plane and neglecting leg masses, we reduce the model to three degrees of freedom describing translational and yawing motions of the body. Muscles are driven by stylized action potentials characteristic of fast motoneurons, and modeled using an activation function and nonlinear length and shortening velocity dependence. Parameter values are based on measurements from depressor muscles and observations of kinematics and dynamics of the cockroach Blaberus discoidalis; in particular, motoneuronal inputs and muscle force levels are chosen to approximately achieve joint torques that are consistent with measured ground reaction forces. We show that the model has stable double-tripod gaits over the animal's speed range, that its dynamics at preferred speeds matches those observed, and that it maintains stable gaits, with low frequency yaw deviations, when subject to random perturbations in foot touchdown and lift-off timing and action potential input timing. We explain this in terms of the low-dimensional dynamics.     

Inverse and forward dynamics: models of multi-body systems

Connected multi-body systems exhibit notoriously complex behaviour when driven by external and internal forces and torques. The problem of reconstructing the internal forces and/or torques from the movements and known external forces is called the 'inverse dynamics problem', whereas calculating motion from known internal forces and/or torques and resulting reaction forces is called the 'forward dynamics problem'. When stepping forward to cross the street, people use muscle forces that generate angular accelerations of their body segments and, by virtue of reaction forces from the street, a forward acceleration of the centre of mass of their body. Inverse dynamics calculations applied to a set of motion data from such an event can teach us how temporal patterns of joint torques were responsible for the observed motion. In forward dynamics calculations we may attempt to create motion from such temporal patterns, which is extremely difficult, because of the complex mechanical linkage along the chains forming the multi-body system. To understand, predict and sometimes control multi-body systems, we may want to have mathematical expressions for them. The Newton-Euler, Lagrangian and Featherstone approaches have their advantages and disadvantages. The simulation of collisions and the inclusion of muscle forces or other internal forces are discussed. Also, the possibility to perform a mixed inverse and forward dynamics calculation are dealt with. The use and limitations of these approaches form the conclusion.     

An EMG-driven musculoskeletal model to estimate muscle forces and knee joint moments in vivo

This paper examined if an electromyography (EMG) driven musculoskeletal model of the human knee could be used to predict knee moments, calculated using inverse dynamics, across a varied range of dynamic contractile conditions. Muscle-tendon lengths and moment arms of 13 muscles crossing the knee joint were determined from joint kinematics using a three-dimensional anatomical model of the lower limb. Muscle activation was determined using a second-order discrete non-linear model using rectified and low-pass filtered EMG as input. A modified Hill-type muscle model was used to calculate individual muscle forces using activation and muscle tendon lengths as inputs. The model was calibrated to six individuals by altering a set of physiologically based parameters using mathematical optimisation to match the net flexion/extension (FE) muscle moment with those measured by inverse dynamics. The model was calibrated for each subject using 5 different tasks, including passive and active FE in an isokinetic dynamometer, running, and cutting manoeuvres recorded using three-dimensional motion analysis. Once calibrated, the model was used to predict the FE moments, estimated via inverse dynamics, from over 200 isokinetic dynamometer, running and sidestepping tasks. The inverse dynamics joint moments were predicted with an average R(2) of 0.91 and mean residual error of approximately 12 Nm. A re-calibration of only the EMG-to-activation parameters revealed FE moments prediction across weeks of similar accuracy. Changing the muscle model to one that is more physiologically correct produced better predictions. The modelling method presented represents a good way to estimate in vivo muscle forces during movement tasks.     

Inter-joint coupling effects on muscle contributions to endpoint force and acceleration in a musculoskeletal model of the cat hindlimb

The biomechanical principles underlying the organization of muscle activation patterns during standing balance are poorly understood. The goal of this study was to understand the influence of biomechanical inter-joint coupling on endpoint forces and accelerations induced by the activation of individual muscles during postural tasks. We calculated induced endpoint forces and accelerations of 31 muscles in a 7 degree-of-freedom, three-dimensional model of the cat hindlimb. To test the effects of inter-joint coupling, we systematically immobilized the joints (excluded kinematic degrees of freedom) and evaluated how the endpoint force and acceleration directions changed for each muscle in 7 different conditions. We hypothesized that altered inter-joint coupling due to joint immobilization of remote joints would substantially change the induced directions of endpoint force and acceleration of individual muscles. Our results show that for most muscles crossing the knee or the hip, joint immobilization altered the endpoint force or acceleration direction by more than 90° in the dorsal and sagittal planes. Induced endpoint forces were typically consistent with behaviorally observed forces only when the ankle was immobilized. We then activated a proximal muscle simultaneous with an ankle torque of varying magnitude, which demonstrated that the resulting endpoint force or acceleration direction is modulated by the magnitude of the ankle torque. We argue that this simple manipulation can lend insight into the functional effects of co-activating muscles. We conclude that inter-joint coupling may be an essential biomechanical principle underlying the coordination of proximal and distal muscles to produce functional endpoint actions during motor tasks.     

Lower extremity extension force and electromyography properties as a function of knee angle and their relation to joint torques: implications for strength diagnostics

The purpose of this study was to evaluate whether and how isometric multijoint leg extension strength can be used to assess athletes' muscular capability within the scope of strength diagnosis. External reaction forces (Fext) and kinematics were measured (n = 18) during maximal isometric contractions in a seated leg press at 8 distinct joint angle configurations ranging from 30 to 100° knee flexion. In addition, muscle activation of rectus femoris, vastus medialis, biceps femoris c.l., gastrocnemius medialis, and tibialis anterior was obtained using surface electromyography (EMG). Joint torques for hip, knee, and ankle joints were computed by inverse dynamics. The results showed that unilateral Fext decreased significantly from 3,369 ± 575 N at 30° knee flexion to 1,015 ± 152 N at 100° knee flexion. Despite maximum voluntary effort, excitation of all muscles as measured by EMG root mean square changed with knee flexion angles. Moreover, correlations showed that above-average Fext at low knee flexion is not necessarily associated with above-average Fext at great knee flexion and vice versa. Similarly, it is not possible to deduce high joint torques from high Fext just as above-average joint torques in 1 joint do not signify above-average torques in another joint. From these findings, it is concluded that an evaluation of muscular capability by means of Fext as measured for multijoint leg extension is strongly limited. As practical recommendation, we suggest analyzing multijoint leg extension strength at 3 distinct knee flexion angles or at discipline-specific joint angles. In addition, a careful evaluation of muscular capacity based on measured Fext can be done for knee flexion angles ≥ 80°. For further and detailed analysis of single muscle groups, the use of inverse dynamic modeling is recommended.     

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.     

Kinematic and kinetic analysis of the fouetté turn in classical ballet

The fouetté turn in classical ballet dancing is a continuous turn with the whipping of the gesture leg and the arms and the bending and stretching of the supporting leg. The knowledge of the movement intensities of both legs for the turn would be favorable for the conditioning of the dancer's body. The purpose of this study was to estimate the intensities. The hypothesis of this study was that the intensities were higher in the supporting leg than in the gesture leg. The joint torques of both legs were determined in the turns performed by seven experienced female classical ballet dancers with inverse dynamics using three high-speed cine cameras and a force platform. The hip abductor torque, knee extensor and plantar flexor torques of the supporting leg were estimated to be exerted up to their maximum levels and the peaks of the torques were larger than the peaks of their matching torques of the gesture leg. Thus, the hypothesis was partly supported. Training of the supporting leg rather than the gesture leg would help ballet dancers perform many revolutions of the fouetté turn continuously.     

Biomechanical Analysis of the Human Finger Extensor Mechanism during Isometric Pressing

This study investigated the effects of the finger extensor mechanism on the bone-to-bone contact forces at the interphalangeal and metacarpal joints and also on the forces in the intrinsic and extrinsic muscles during finger pressing. This was done with finger postures ranging from very flexed to fully extended. The role of the finger extensor mechanism was investigated by using two alternative finger models, one which omitted the extensor mechanism and another which included it. A six-camera three-dimensional motion analysis system was used to capture the finger posture during maximum voluntary isometric pressing. The fingertip loads were recorded simultaneously using a force plate system. Two three-dimensional biomechanical finger models, a minimal model without extensor mechanism and a full model with extensor mechanism (tendon network), were used to calculate the joint bone-to-bone contact forces and the extrinsic and intrinsic muscle forces. If the full model is assumed to be realistic, then the results suggest some useful biomechanical advantages provided by the tendon network of the extensor mechanism. It was found that the forces in the intrinsic muscles (interosseus group and lumbrical) are significantly reduced by 22% to 61% due to the action of the extensor mechanism, with the greatest reductions in more flexed postures. The bone-to-bone contact force at the MCP joint is reduced by 10% to 41%. This suggests that the extensor mechanism may help to reduce the risk of injury at the finger joints and also to moderate the forces in intrinsic muscles. These apparent biomechanical advantages may be a result of the extensor mechanism''s distinctive interconnected fibrous structure, through which the contraction of the intrinsic muscles as flexors of the MCP joint can generate extensions at the DIP and PIP joints.     

A method for biomechanical analysis of bicycle pedalling

This paper reports a new method, which enables a detailed biomechanical analysis of the lower limb during bicycling. The method consists of simultaneously measuring both the normal and tangential pedal forces, the EMGs of eight leg muscles, and the crank arm and pedal angles. Data were recorded for three male subjects of similar anthropometric characteristics. Subjects rode under different pedalling conditions to explore how both pedal forces and pedalling rates affect the biomechanics of the pedalling process. By modelling the leg-bicycle as a five bar linkage and driving the linkage with the measured force and kinematic data, the joint moment histories due to pedal forces only (i.e. no motion) and motion only (i.e. no pedal forces) were generated. Total moments were produced by superimposing the two moment histories. The separate moment histories, together with the pedal forces and EMG results, enable a detailed biomechanical analysis of bicycle pedalling. Inasmuch as the results are similar for all three subjects, the analysis for one subject is discussed fully. One unique insight gained via this new method is the functional role that individual leg muscles play in the pedalling process.     

Finger joint coordination during tapping

We investigated finger joint coordination during tapping by characterizing joint kinematics and torques in terms of muscle activation patterns and energy profiles. Six subjects tapped with their index finger on a computer keyswitch as if they were typing on the middle row of a keyboard. Fingertip force, keyswitch position, kinematics of the metacarpophalangeal (MCP) and the proximal and distal interphalangeal (IP) joints, and intramuscular electromyography of intrinsic and extrinsic finger muscles were measured simultaneously. Finger joint torques were calculated based on a closed-form Newton–Euler inverse dynamic model of the finger. During the keystroke, the MCP joint flexed and the IP joints extended before and throughout the loading phase of the contact period, creating a closing reciprocal motion of the finger joints. As the finger lifted, the MCP joint extended and the interphalangeal (IP) joints flexed, creating an opening reciprocal motion. Intrinsic finger muscle and extrinsic flexor activities both began after the initiation of the downward finger movement. The intrinsic finger muscle activity preceded both the IP joint extension and the onset of extrinsic muscle activity. Only extrinsic extensor activity was present as the finger was lifted. While both potential energy and kinetic energy are present and large enough to overcome the work necessary to press the keyswitch, the motor control strategies utilize the muscle forces and joint torques to ensure a successful keystroke.     

Three-dimensional model to predict muscle forces and their relation to motor variances in reaching arm movements

A three-dimensional (3-D) arm movement model is presented to simulate kinematic properties and muscle forces in reaching arm movements. Healthy subjects performed reaching movements repetitively either with or without a load in the hand. Joint coordinates were measured. Muscle moment arms, 3-D angular acceleration, and moment of inertias of arm segments were calculated to determine 3-D joint torques. Variances of hand position, arm configuration, and muscle activities were calculated. Ratios of movement variances observed in the two conditions (load versus without load) showed no differences for hand position and arm configuration variances. Virtual muscle force variances for all muscles except deltoid posterior and EMG variances for four muscles increased significantly by moving with the load. The greatly increased variances in muscle activity did not imply equally high increments in kinematic variances. We conclude that enhanced muscle cooperation through synergies helps to stabilize movement at the kinematic level when a load is added.