A biomechanical model on muscle forces in the transfer of spinal load to the pelvis and legs.

Based on musculoskeletal anatomy of the lower back, abdominal wall, pelvis and upper legs, a biomechanical model has been developed on forces in the load transfer through the pelvis. The aim of this model is to obtain a tool for analyzing the relations between forces in muscles, ligaments and joints in the transfer of gravitational and external load from the upper body via the sacroiliac joints to the legs in normal situations and pathology. The study of the relation between muscle coordination patterns and forces in pelvic structures, in particular the sacroiliac joints, is relevant for a better understanding of the aetiology of low back pain and pelvic pain. The model comprises 94 muscle parts, 6 ligaments and 6 joints. It enables the calculation of forces in pelvic structures in various postures. The calculations are based on a linear/non-linear optimization scheme. To gain a better understanding of the function of individual muscles and ligaments, deviant properties of these structures can be preset. The model is validated by comparing calculations with EMG data from the literature. For agonistic muscles, good agreement is found between model calculations and EMG data. Antagonistic muscle activity is underestimated by the model. Imposed activity of modelled antagonistic muscles has a minor effect on the mutual proportions of agonistic muscle activities. Simulation of asymmetric muscle weakness shows higher activity of especially abdominal muscles.     

A review of biomechanical models

This paper surveys biomechanical models of the nonimpact type, involving the musculo-skeletal system. Models of bones, joints and body segments, including human gait and motion of the whole body are discussed. In particular, stress analysis of bone, calculation of ligament and muscle forces across joints and the kinetics and kinematics of locomotion are discussed. The models are described in terms of the method of formulation, the method of solution and the realism of the results obtained. There is a need for more data on material properties of various body tissues and more experimental research to develop techniques for validating many of the models. Further work on the selection of appropriate objective functions for indeterminate problems is also required.     

A global optimization method for prediction of muscle forces of human musculoskeletal system

Inverse dynamic optimization is a popular method for predicting muscle and joint reaction forces within human musculoskeletal joints. However, the traditional formulation of the optimization method does not include the joint reaction moment in the moment equilibrium equation, potentially violating the equilibrium conditions of the joint. Consequently, the predicted muscle and joint reaction forces are coordinate system-dependent. This paper presents an improved optimization method for the prediction of muscle forces and joint reaction forces. In this method, the location of the rotation center of the joint is used as an optimization variable, and the moment equilibrium equation is formulated with respect to the joint rotation center to represent an accurate moment constraint condition. The predicted muscle and joint reaction forces are independent of the joint coordinate system. The new optimization method was used to predict muscle forces of an elbow joint. The results demonstrated that the joint rotation center location varied with applied loading conditions. The predicted muscle and joint reaction forces were different from those predicted by using the traditional optimization method. The results further demonstrated that the improved optimization method converged to a minimum for the objective function that is smaller than that reached by using the traditional optimization method. Therefore, the joint rotation center location should be involved as a variable in an inverse dynamic optimization method for predicting muscle and joint reaction forces within human musculoskeletal joints.     

Méthodes biomécaniques avancées pour le calcul des moments articulaires et des forces musculaires

Taking into account the growing number of musculoskeletal pathologies, more and more clinical studies are nowadays based on the evaluation of the 3D joint moments. The calculation of these joint moments requires a rigorous experimental protocol set-up, and the development of advanced kinematic and inverse dynamic methods, taking into account the functional centres and axes and the personalized inertial characteristics of the subject. Moreover, starting from the measurement of the lever arms of the muscles and implementing a numerical technique for optimization, it is possible to improve the analysis in order to evaluate the muscular forces and the contact forces on the joints.     

Joint moments and contact forces in the foot during walking

The net force and moment of a joint have been widely used to understand joint disease in the foot. Meanwhile, it does not reflect the physiological forces on muscles and contact surfaces. The objective of the study is to estimate active moments by muscles, passive moments by connective tissues and joint contact forces in the foot joints during walking. Joint kinematics and external forces of ten healthy subjects (all males, 24.7 ± 1.2 years) were acquired during walking. The data were entered into the five-segment musculoskeletal foot model to calculate muscle forces and joint contact forces of the foot joints using an inverse dynamics-based optimization. Joint reaction forces and active, passive and net moments of each joint were calculated from muscle and ligament forces. The maximum joint reaction forces were 8.72, 4.31, 2.65, and 3.41 body weight (BW) for the ankle, Chopart’s, Lisfranc and metatarsophalangeal joints, respectively. Active and passive moments along with net moments were also obtained. The maximum net moments were 8.6, 8.4, 5.4 and 0.8%BW∙HT, respectively. While the trend of net moment was very similar between the four joints, the magnitudes and directions of the active and passive moments varied between joints. The active and passive moments during walking could reveal the roles of muscles and ligaments in each of the foot joints, which was not obvious in the net moment. This method may help narrow down the source of joint problems if applied to clinical studies.     

Muscle forces predicted using optimization methods are coordinate system dependent

Optimization methods are widely used to predict in vivo muscle forces in musculoskeletal joints. Moment equilibrium at the joint center (usually chosen as the origin of the joint coordinate system) has been used as a constraint condition for optimization procedures and the joint reaction moments were assumed zero. This study, through the use of a three-dimensional elbow model, investigated the effect of coordinate system origin (joint center) location on muscle forces predicted using a nonlinear static optimization method. The results demonstrated that moving the origin of the coordinate system medially and laterally along the flexion-extension axis caused dramatic variations in the predicted muscle forces. For example, moving the origin of the coordinate system from a position 5mm medial to 5mm lateral of the geometric elbow center caused the predicted biceps force to vary from 12% to 46% and the brachialis force to vary from 80% to 34% of the total muscle loading. The joint reaction force reduced by 24% with this medial to lateral variation of the coordinate system origin location. This data revealed that the muscle forces predicted using the optimization method are sensitive to the coordinate system origin location due to the zero joint reaction moment assumption in the moment constraint condition. For accurate prediction of muscle load distributions using optimization methods, it is necessary to determine the accurate coordinate system origin location where the condition of a zero joint reaction moment is satisfied.     

Hip joint contact force in the emu (Dromaius novaehollandiae) during normal level walking

The emu is a large, (bipedal) flightless bird that potentially can be used to study various orthopaedic disorders in which load protection of the experimental limb is a limitation of quadrupedal models. An anatomy-based analysis of normal emu walking gait was undertaken to determine hip contact forces for comparison with human data. Kinematic and kinetic data captured for two laboratory-habituated emus were used to drive the model. Muscle attachment data were obtained by dissection, and bony geometries were obtained by CT scan. Inverse dynamics calculations at all major lower-limb joints were used in conjunction with optimization of muscle forces to determine hip contact forces. Like human walking gait, emu ground reaction forces showed a bimodal distribution over the course of the stance phase. Two-bird averaged maximum hip contact force was approximately 5.5 times body weight, directed nominally axially along the femur. This value is only modestly larger than optimization-based hip contact forces reported in literature for humans. The interspecies similarity in hip contact forces makes the emu a biomechanically attractive animal in which to model loading-dependent human orthopaedic hip disorders.     

An improved multi-joint EMG-assisted optimization approach to estimate joint and muscle forces in a musculoskeletal model of the lumbar spine

Muscle force partitioning methods and musculoskeletal system simplifications are key modeling issues that can alter outcomes, and thus change conclusions and recommendations addressed to health and safety professionals. A critical modeling concern is the use of single-joint equilibrium to estimate muscle forces and joint loads in a multi-joint system, an unjustified simplification made by most lumbar spine biomechanical models. In the context of common occupational tasks, an EMG-assisted optimization method (EMGAO) is modified in this study to simultaneously account for the equilibrium at all lumbar joints (M-EMGAO). The results of this improved approach were compared to those of its conventional single-joint equivalent (S-EMGAO) counterpart, the latter method being applied to the same lumbar joints but one at a time. Despite identical geometrical configurations and passive contributions used in both models, computed outcomes clearly differed between single- and multi-joint methods, especially at larger trunk flexed postures and during asymmetric lifting. Moreover, muscle forces predicted by L5-S1 single-joint analyses do not maintain mechanical equilibrium at other spine joints crossed by the same muscles. Assuming that the central nervous system does not attempt to balance the external moments one joint at a time and that a given muscle cannot exert different forces at different joints, the proposed multi-joint method represents a substantial improvement over its single-joint counterpart. This improved approach, hence, resolves trunk muscle forces with biological integrity but without compromising mechanical equilibrium at the lumbar joints.     

Evaluation of the influence of muscle deactivation on other muscles and joints during gait motion

When any muscle in the human musculoskeletal system is damaged, other muscles and ligaments tend to compensate for the role of the damaged muscle by exerting extra effort. It is beneficial to clarify how the roles of the damaged muscles are compensated by other parts of the musculoskeletal system from the following points of view: From a clinical point of view, it will be possible to know how the abnormal muscle and joint forces caused by the acute compensations lead to further physical damage to the musculoskeletal system. From the viewpoint of rehabilitation, it will be possible to know how the role of the damaged muscle can be compensated by extra training of the other muscles. A method to evaluate the influence of muscle deactivation on other muscles and joints is proposed in this report. Methodology based on inverse dynamics and static optimization, which is applicable to arbitrary motion was used in this study. The evaluation method was applied to gait motion to obtain matrices representing (1) the dependence of muscle force compensation and (2) the change to bone-on-bone contact forces. These matrices make it possible to evaluate the effects of deactivation of one of the muscles of the musculoskeletal system on the forces exerted by other muscles as well as the change to the bone-on-bone forces when the musculoskeletal system is performing the same motion. Through observation of this matrix, it was found that deactivation of a muscle often results in increment/decrement of force developed by muscles with completely different primary functions and bone-on-bone contact force in different parts of the body. For example, deactivation of the iliopsoas leads to a large reduction in force by the soleus. The results suggest that acute deactivation of a muscle can result in damage to another part of the body. The results also suggest that the whole musculoskeletal system must go through extra retraining in the case of damage to certain muscles.     

Load-sharing in the lumbosacral spine in neutral standing & flexed postures – A combined finite element and inverse static study

Understanding load-sharing in the spine during in-vivo conditions is critical for better spinal implant design and testing. Previous studies of load-sharing that considered actual spinal geometry applied compressive follower load, with or without moment, to simulate muscle forces. Other studies used musculoskeletal models, which include muscle forces, but model the discs by simple beams or spherical joints and ignore the articular facet joints.This study investigated load-sharing in neutral standing and flexed postures using a detailed Finite Element (FE) model of the ligamentous lumbosacral spine, where muscle forces, gravity loads and intra-abdominal pressure, as predicted by a musculoskeletal model of the upper body, are input into the FE model. Flexion was simulated by applying vertebral rotations following spine rhythm measured in a previous in-vivo study, to the musculoskeletal model. The FE model predicted intradiscal pressure (IDP), strains in the annular fibers, contact forces in the facet joints, and forces in the ligaments. The disc forces and moments were determined using equilibrium equations, which considered the applied loads, including muscle forces and IDP, as well as forces in the ligaments and facet joints predicted by the FE model. Load-sharing was calculated as the portion of the total spinal load carried along the spine by each individual spinal structure. The results revealed that spinal loads which increased substantially from the upright to the flexed posture were mainly supported by the discs in the upright posture, whereas the ligaments’ contribution in resisting shear, compression, and moment was more significant in the flexed posture.     

Simulating the response of a standing operator to vibration stress by means of a biomechanical model

Under vibration stress the compressive forces transmitted in the joints of a standing operator are composed of nearly static and oscillating force parts. Because these forces can hardly be measured they were assessed by means of a biomechanical model. In the model, 27 rigid bodies with 103 degrees of freedom represent the segments of the human body. 106 force elements imitate the muscles of the trunk and the legs. At first, the model parameter were varied so that for the simulated sitting posture the model fits the seat-to-head transmissibility given in the literature and in ISO/CD 5982. For the standing posture, the transfer functions between the ground acceleration and the oscillating forces in the ankle, the knee, the hip, and the motion segment L3-L4 were computed. According to the moduli of these functions the forces in the ankles are higher than those in the knees or the hips and they nearly come up to the forces in the lumbar spine. Further the results of the simulation indicate that under equal vibration stress in the standing and the sitting posture the differences between the compressive forces in the lumbar spine are small.     

A 3D lower limb musculoskeletal model for simultaneous estimation of musculo-tendon,joint contact,ligament and bone forces during gait

Musculo-tendon forces and joint reaction forces are typically estimated using a two-step method, computing first the musculo-tendon forces by a static optimization procedure and then deducing the joint reaction forces from the force equilibrium. However, this method does not allow studying the interactions between musculo-tendon forces and joint reaction forces in establishing this equilibrium and the joint reaction forces are usually overestimated. This study introduces a new 3D lower limb musculoskeletal model based on a one-step static optimization procedure allowing simultaneous musculo-tendon, joint contact, ligament and bone forces estimation during gait. It is postulated that this approach, by giving access to the forces transmitted by these musculoskeletal structures at hip, tibiofemoral, patellofemoral and ankle joints, modeled using anatomically consistent kinematic models, should ease the validation of the model using joint contact forces measured with instrumented prostheses. A blinded validation based on four datasets was made under two different minimization conditions (i.e., C1 – only musculo-tendon forces are minimized, and C2 – musculo-tendon, joint contact, ligament and bone forces are minimized while focusing more specifically on tibiofemoral joint contacts). The results show that the model is able to estimate in most cases the correct timing of musculo-tendon forces during normal gait (i.e., the mean coefficient of active/inactive state concordance between estimated musculo-tendon force and measured EMG envelopes was C1: 65.87% and C2: 60.46%). The results also showed that the model is potentially able to well estimate joint contact, ligament and bone forces and more specifically medial (i.e., the mean RMSE between estimated joint contact force and in vivo measurement was C1: 1.14BW and C2: 0.39BW) and lateral (i.e., C1: 0.65BW and C2: 0.28BW) tibiofemoral contact forces during normal gait. However, the results remain highly influenced by the optimization weights that can bring to somewhat aphysiological musculo-tendon forces.     

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.     

Treatment of children scoliosis by corrective brace with regulated force effect

Rigid structural spine scoliosis of a child and even non progressive congenital scoliosis (e.g. isolated hemivertebra) can be treated by hypercorrective brace in full day regime. The article shows the new type of corrective brace with adjustable force effect. The brace consists of 3 stiff parts connected by joints and telescopes. The parts of brace are made from plastic according to plaster form of child trunk. The joints allow only mutual turning brace parts at frontal plane. The special telescopes were developed which operated with prescribed forces, it means the brace and trunk parts are mutually turned at prescribed moments. The article shows the algorithm for calculation of spine stress state, and spine curve correction for given brace with adjusted telescope forces. The second algorithm calculates the telescope forces for demanded spine curve correction. The computer program can be used for computer aid design of brace forces. The force effect of the new type of brace is demonstrated on a 14 months old boy with congenital scoliosis of lumbar spine (hemivertebra L1 and L3 on the right side). Curvature measured according to Coob was changed after application of this brace from 47.5° to 32.0°.     

A general-purpose framework to simulate musculoskeletal system of human body: using a motion tracking approach*

Computation of muscle force patterns that produce specified movements of muscle-actuated dynamic models is an important and challenging problem. This problem is an undetermined one, and then a proper optimization is required to calculate muscle forces. The purpose of this paper is to develop a general model for calculating all muscle activation and force patterns in an arbitrary human body movement. For this aim, the equations of a multibody system forward dynamics, which is considered for skeletal system of the human body model, is derived using Lagrange–Euler formulation. Next, muscle contraction dynamics is added to this model and forward dynamics of an arbitrary musculoskeletal system is obtained. For optimization purpose, the obtained model is used in computed muscle control algorithm, and a closed-loop system for tracking desired motions is derived. Finally, a popular sport exercise, biceps curl, is simulated by using this algorithm and the validity of the obtained results is evaluated via EMG signals.     

Joint reaction forces at the first MTP joint in a normal elderly population

The calculation of net ankle, knee, and hip joint reaction forces is an often applied procedure in the analysis of gait. Except for very few studies, joint reaction forces have not been measured in other joints such as the fingers, wrist, elbow, shoulder and toes. In this study the joint reaction forces between the metatarsal head and the proximal phalanx and the metatarsal head and the sesamoids are calculated for the push off phase during gait. The results of ten normal elderly subjects show that the maximum resultant loads of the two articulations lie close to the longitudinal axis of the metatarsal. The knowledge of the magnitude and direction of the joint reaction forces of a normal elderly population will be essential for the design of an optimal fixation of an artificial anatomical first MTP joint.     

Estimation of muscle response using three-dimensional musculoskeletal models before impact situation: a simulation study

When car crash experiments are performed using cadavers or dummies, the active muscles' reaction on crash situations cannot be observed. The aim of this study is to estimate muscles' response of the major muscle groups using three-dimensional musculoskeletal model by dynamic simulations of low-speed sled-impact. The three-dimensional musculoskeletal models of eight subjects were developed, including 241 degrees of freedom and 86 muscles. The muscle parameters considering limb lengths and the force-generating properties of the muscles were redefined by optimization to fit for each subject. Kinematic data and external forces measured by motion tracking system and dynamometer were then input as boundary conditions. Through a least-squares optimization algorithm, active muscles' responses were calculated during inverse dynamic analysis tracking the motion of each subject. Electromyography for major muscles at elbow, knee, and ankle joints was measured to validate each model. For low-speed sled-impact crash, experiment and simulation with optimized and unoptimized muscle parameters were performed at 9.4 m/h and 10 m/h and muscle activities were compared among them. The muscle activities with optimized parameters were closer to experimental measurements than the results without optimization. In addition, the extensor muscle activities at knee, ankle, and elbow joint were found considerably at impact time, unlike previous studies using cadaver or dummies. This study demonstrated the need to optimize the muscle parameters to predict impact situation correctly in computational studies using musculoskeletal models. And to improve accuracy of analysis for car crash injury using humanlike dummies, muscle reflex function, major extensor muscles' response at elbow, knee, and ankle joints, should be considered.     

Joint contact loading in forefoot and rearfoot strike patterns during running

Research concerning forefoot strike pattern (FFS) versus rearfoot strike pattern (RFS) running has focused on the ground reaction force even though internal joint contact forces are a more direct measure of the loads responsible for injury. The main purpose of this study was to determine the internal loading of the joints for each strike pattern. A secondary purpose was to determine if converted FFS and RFS runners can adequately represent habitual runners with regards to the internal joint loading. Using inverse dynamics to calculate the net joint moments and reaction forces and optimization techniques to estimate muscle forces, we determined the axial compressive loading at the ankle, knee, and hip. Subjects consisted of 15 habitual FFS and 15 habitual RFS competitive runners. Each subject ran at a preferred running velocity with their habitual strike pattern and then converted to the opposite strike pattern. Plantar flexor muscle forces and net ankle joint moments were greater in the FFS running compared to the RFS running during the first half of the stance phase. The average contact forces during this period increased by 41.7% at the ankle and 14.4% at the knee joint during FFS running. Peak ankle joint contact force was 1.5 body weights greater during FFS running (p<0.05). There was no evidence to support a difference between habitual and converted running for joint contact forces. The increased loading at the ankle joint for FFS is an area of concern for individuals considering altering their foot strike pattern.     

Estimation of muscle forces during natural movement of man on the basis of minimization of various functions

Forces exerted by 11 muscles of lower extremities of a man in squat jump were determined using 4-link planar muscular-skeletal model. The research project was performed in two stages: 1) kinematic data were used for the calculation of control moments in joints, 2) determination of muscle forces as a result of minimization procedure of 5 objective functions with constraints to forces. The forces found were compared with corresponding EMG-activity of muscles. The highest correlation with EMG parameters was shown by the minimized sum of absolute powers of all muscles.     

Prediction of biomechanical parameters in the lumbar spine during static sagittal plane lifting.

A combined approach involving optimization and the finite element technique was used to predict biomechanical parameters in the lumbar spine during static lifting in the sagittal plane. Forces in muscle fascicles of the lumbar region were first predicted using an optimization-based force model including the entire lumbar spine. These muscle forces as well as the distributed upper body weight and the lifted load were then applied to a three-dimensional finite element model of the thoracolumbar spine and rib cage to predict deformation, the intradiskal pressure, strains, stresses, and load transfer paths in the spine. The predicted intradiskal pressures in the L3-4 disk at the most deviated from the in vivo measurements by 8.2 percent for the four lifting cases analyzed. The lumbosacral joint flexed, while the other lumbar joints extended for all of the four lifting cases studied (rotation of a joint is the relative rotation between its two vertebral bodies). High stresses were predicted in the posterolateral regions of the endplates and at the junctions of the pedicles and vertebral bodies. High interlaminar shear stresses were found in the posterolateral regions of the lumbar disks. While the facet joints of the upper two lumbar segments did not transmit any load, the facet joints of the lower two lumbar segments experienced significant loads. The ligaments of all lumbar motion segments except the lumbosacral junction provided only marginal moments. The limitations of the current model and possible improvements are discussed.