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.     

Coupled objective function to study the role of abdominal muscle forces in lifting using the kinematics-driven model

To circumvent the existing shortcoming of optimisation algorithms in trunk biomechanical models, both agonist and antagonist trunk muscle stresses to different powers are introduced in a novel objective function to evaluate the role of abdominal muscles in trunk stability and spine compression. This coupled objective function is introduced in our kinematics-driven finite element model to estimate muscle forces and to identify the role of abdominal muscles in upright standing while lifting symmetrically a weight at different heights. Predictive equations for the compression and buckling forces are developed. Results are also compared with the conventional objective function that neglects abdominal muscle forces. An overall optimal solution involving smaller spinal compression but higher trunk stability is automatically attained when choosing muscle stress powers at and around 3. Results highlight the internal oblique muscle as the most efficient abdominal muscle during the tasks investigated. The estimated relative forces in abdominal muscles are found to be in good agreement with the respective ratios of recorded electromyography activities.     

Trunk muscle activation and associated lumbar spine joint shear forces under different levels of external forward force applied to the trunk.

High anterior intervertebral shear loads could cause low back injuries and therefore the neuromuscular system may actively counteract these forces. This study investigated whether, under constant moment loading relative to L3L4, an increased externally applied forward force on the trunk results in a shift in muscle activation towards the use of muscles with more backward directed lines of action, thereby reducing the increase in total joint shear force. Twelve participants isometrically resisted forward forces, applied at several locations on the trunk, while moments were held constant relative to L3L4. Surface EMG and lumbar curvature were measured, and an EMG-driven muscle model was used to calculate compression and shear forces at all lumbar intervertebral joints. Larger externally applied forward forces resulted in a flattening of the lumbar lordosis and a slightly more backward directed muscle force. Furthermore, the overall muscle activation increased. At the T12L1 to L3L4 joint, resulting joint shear forces remained small (less than 200N) because the average muscle force pulled backward relative to those joints. However, at the L5S1 joint the average muscle force pulled the trunk forward so that the increase in muscle force with increasing externally applied forward force caused a further rise in shear force (by 102.1N, SD=104.0N), resulting in a joint shear force of 1080.1N (SD=150.4N) at 50Nm moment loading. It is concluded that the response of the neuromuscular system to shear force challenges tends to increase rather than reduce the shear loading at the lumbar joint that is subjected to the highest shear forces.     

Sensitivity of muscle and intervertebral disc force computations to variations in muscle attachment sites

Abstract

The current paper aims at assessing the sensitivity of muscle and intervertebral disc force computations against potential errors in modeling muscle attachment sites. We perturbed each attachment location in a complete and coherent musculoskeletal model of the human spine and quantified the changes in muscle and disc forces during standing upright, flexion, lateral bending, and axial rotation of the trunk. Although the majority of the muscles caused minor changes (less than 5%) in the disc forces, certain muscle groups, for example, quadratus lumborum, altered the shear and compressive forces as high as 353% and 17%, respectively. Furthermore, percent changes were higher in the shear forces than in the compressive forces. Our analyses identified certain muscles in the rib cage (intercostales interni and intercostales externi) and lumbar spine (quadratus lumborum and longissimus thoracis) as being more influential for computing muscle and disc forces. Furthermore, the disc forces at the L4/L5 joint were the most sensitive against muscle attachment sites, followed by T6/T7 and T12/L1 joints. Presented findings suggest that modeling muscle attachment sites based on solely anatomical illustrations might lead to erroneous evaluation of internal forces and promote using anatomical datasets where these locations were accurately measured. When developing a personalized model of the spine, certain care should also be paid especially for the muscles indicated in this work.     

Investigation of optimal follower load path generated by trunk muscle coordination

It has been reported that the center of rotation of each vertebral body is located posterior to the vertebral body center. Moreover, it has been suggested that an optimized follower load (FL) acts posterior to the vertebral body center. However, the optimal position of the FL with respect to typical biomechanical characteristics regarding spinal stabilization, such as joint compressive force, shear force, joint moment, and muscle stress, has not been studied. A variation in the center of rotation of each vertebra was formulated in a three-dimensional finite element model of the lumbar spine with 117 pairs of trunk muscles. Then, the optimal translation of the FL path connecting the centers of rotations was estimated by solving the optimization problem that was to simultaneously minimize the compressive forces, the shear forces, and the joint moments or to minimize the cubic muscle stresses. An upright neutral standing position and a standing position with 200N in both hands were considered. The FL path moved posterior, regardless of the optimization criteria and loading conditions. The FL path moved 5.0 and 7.8mm posterior in upright standing and 4.1mm and 7.0mm posterior in standing with 200N in hands for each optimization scheme. In addition, it was presented that the optimal FL path may have advantages in comparison to the body center FL path. The present techniques may be important in understanding the spine stabilization function of the trunk muscles.     

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 frontal plane model of the lumbar spine subjected to a follower load: implications for the role of muscles

Compression on the lumbar spine is 1000 N for standing and walking and is higher during lifting. Ex vivo experiments show it buckles under a vertical load of 80-100 N. Conversely, the whole lumbar spine can support physiologic compressive loads without large displacements when the load is applied along a follower path that approximates the tangent to the curve of the lumbar spine. This study utilized a two-dimensional beam-column model of the lumbar spine in the frontal plane under gravitational and active muscle loads to address the following question: Can trunk muscle activation cause the path of the internal force resultant to approximate the tangent to the spinal curve and allow the lumbar spine to support compressive loads of physiologic magnitudes? The study identified muscle activation patterns that maintained the lumbar spine model under compressive follower load, resulting in the minimization of internal shear forces and bending moments simultaneously at all lumbar levels. The internal force resultant was compressive, and the lumbar spine model, loaded in compression along the follower load path, supported compressive loads of physiologic magnitudes with minimal change in curvature in the frontal plane. Trunk muscles may coactivate to generate a follower load path and allow the ligamentous lumbar spine to support physiologic compressive loads.     

Total trunk muscle force and spinal compression are lower in asymmetric moments as compared to pure extension moments.

The aim of the present study was to test the assumption that asymmetric trunk loading requires a higher total muscle force and consequently entails a higher compression forces on the spine as compared to symmetric loading. When the trunk musculature is modelled in sufficient detail, optimisation shows that there is no mechanical necessity for an increase in total muscle force (or compression force) with task asymmetry. A physiologically based optimisation does also not predict an increase in total muscle force or spinal loading with asymmetry. EMG data on 14 trunk muscles collected in eight subjects showed antagonistic coactivity to be present in both conditions. However, estimates of total muscle force based on the EMG were lower when producing an asymmetric moment. In conclusion, producing an asymmetric moment appears to cause slightly lower forces on the lumbosacral joint as compared to a symmetric moment. Only lateral shear forces increase with asymmetry but these remain well below failure levels.     

Mechanically simulated muscle forces strongly stabilize intact and injured upper cervical spine specimens

Although muscles are assumed to be capable of stabilizing the spinal column in vivo, they have only rarely been simulated in vitro. Their effect might be of particular importance in unstable segments. The present study therefore tests the hypothesis that mechanically simulated muscle forces stabilize intact and injured cervical spine specimens. In the first step, six human occipito-cervical spine specimens were loaded intact in a spine tester with pure moments in lateral bending (+/- 1.5 N m), flexion-extension (+/- 1.5 N m) and axial rotation (+/- 0.5 N m). In the second step, identical flexibility tests were carried out during constant traction of three mechanically simulated muscle pairs: splenius capitits (5 N), semispinalis capitis (5 N) and longus colli (15 N). Both steps were repeated after unilateral and bilateral transection of the alar ligaments. The muscle forces strongly stabilized C0-C2 in all loading and injury states. This was most obvious in axial rotation, where a reduction of range of motion (ROM) and neutral zone to <50% (without muscles=100%) was observed. With increasing injury the normalized ROM (intact condition=100%) increased with and without muscles approximately to the same extend. With bilateral injury this increase was 125-132% in lateral bending, 112%-119% in flexion-extension and 103-116% in axial rotation. Mechanically simulated cervical spine muscles strongly stabilized intact and injured cervical spine specimens. Nevertheless, it could be shown that in vitro flexibility tests without muscle force simulation do not necessarily lead to an overestimation of spinal instability if the results are normalized to the intact state.     

Model and in vivo studies on human trunk load partitioning and stability in isometric forward flexions

To resolve the trunk redundancy to determine muscle forces, spinal loads, and stability margin in isometric forward flexion tasks, combined in vivo-numerical model studies was undertaken. It was hypothesized that the passive resistance of both the ligamentous spine and the trunk musculature plays a crucial role in equilibrium and stability of the system. Fifteen healthy males performed free isometric trunk flexions of approximately 40 degrees and approximately 65 degrees +/- loads in hands while kinematics by skin markers and EMG activity of trunk muscles by surface electrodes were measured. A novel kinematics-based approach along with a nonlinear finite element model were iteratively used to calculate muscle forces and internal loads under prescribed measured postures and loads considered in vivo. Stability margin was investigated using nonlinear, linear buckling, and perturbation analyses under various postures, loads and alterations in ligamentous stiffness. Flexion postures significantly increased activity in extensor muscles when compared with standing postures while no significant change was detected in between flexed postures. Compression at the L5-S1 substantially increased from 570 and 771 N in upright posture, respectively, for +/-180 N, to 1912 and 3308 N at approximately 40 degrees flexion, and furthermore to 2332 and 3850 N at approximately 65 degrees flexion. Passive ligamentous/muscle components resisted up to 77% of the net moment. In flexion postures, the spinal stability substantially improved due both to greater passive stiffness and extensor muscle activities so that, under 180 N, no muscle stiffness was required to maintain stability. The co-activity of abdominal muscles and the muscle stiffness were of lesser concern to maintain stability in forward flexion tasks as compared with upright tasks. An injury to the passive system, on one hand, required a substantial compensatory increase in active muscle forces which further increased passive loads and, hence, the risk of injury and fatigue. On the other hand, it deteriorated the system stability which in turn could require greater additional muscle activation. This chain of events would place the entire trunk active-passive system at higher risks of injury, fatigue and instability.     

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.     

Effects of geometric individualisation of a human spine model on load sharing: neuro-musculoskeletal simulation reveals significant differences in ligament and muscle contribution

In spine research, two possibilities to generate models exist: generic (population-based) models representing the average human and subject-specific representations of individuals. Despite the increasing interest in subject specificity, individualisation of spine models remains challenging. Neuro-musculoskeletal (NMS) models enable the analysis and prediction of dynamic motions by incorporating active muscles attaching to bones that are connected using articulating joints under the assumption of rigid body dynamics. In this study, we used forward-dynamic simulations to compare a generic NMS multibody model of the thoracolumbar spine including fully articulated vertebrae, detailed musculature, passive ligaments and linear intervertebral disc (IVD) models with an individualised model to assess the contribution of individual biological structures. Individualisation was achieved by integrating skeletal geometry from computed tomography and custom-selected muscle and ligament paths. Both models underwent a gravitational settling process and a forward flexion-to-extension movement. The model-specific load distribution in an equilibrated upright position and local stiffness in the L4/5 functional spinal unit (FSU) is compared. Load sharing between occurring internal forces generated by individual biological structures and their contribution to the FSU stiffness was computed. The main finding of our simulations is an apparent shift in load sharing with individualisation from an equally distributed element contribution of IVD, ligaments and muscles in the generic spine model to a predominant muscle contribution in the individualised model depending on the analysed spine level.

     

Effects of lumbo-pelvic rhythm on trunk muscle forces and disc loads during forward flexion: A combined musculoskeletal and finite element simulation study

Previous in-vivo studies suggest that the ratio of total lumbar rotation over pelvic rotation (lumbo-pelvic rhythm) during trunk sagittal movement is essential to evaluate spinal loads and discriminate between low back pain and asymptomatic population. Similarly, there is also evidence that the lumbo-pelvic rhythm is key for evaluation of realistic muscle and joint reaction forces and moments predicted by various computational musculoskeletal models. This study investigated the effects of three lumbo-pelvic rhythms defined based on in-vivo measurements on the spinal response during moderate forward flexion (60°) using a combined approach of musculoskeletal modeling of the upper body and finite element model of the lumbosacral spine. The muscle forces and joint loads predicted by the musculoskeletal model, together with the gravitational forces, were applied to the finite element model to compute the disc force and moment, intradiscal pressure, annular fibers strain, and load-sharing. The results revealed that a rhythm with high pelvic rotation and low lumbar flexion involves more global muscles and increases the role of the disc in resisting spinal loads, while its counterpart, with low pelvic rotation, recruits more local muscles and engages the ligaments to lower the disc loads. On the other hand, a normal rhythm that has balanced pelvic and lumbar rotations yields almost equal disc and ligament load-sharing and results in more balanced synergy between global and local muscles. The lumbo-pelvic rhythm has less effect on the intradiscal pressure and annular fibers strain. This work demonstrated that the spinal response during forward flexion is highly dependent on the lumbo-pelvic rhythm. It is therefore, essential to adapt this parameter instead of using the default values in musculoskeletal models for accurate prediction of muscle forces and joint reaction forces and moments. The findings provided by this work are expected to improve knowledge of spinal response during forward flexion, and are clinically relevant towards low back pain treatment and disc injury prevention.     

Elbow and wrist joint contact forces during occupational pick and place activities

A three-dimensional, mathematical model of the elbow and wrist joints, including 15 muscle units, 3 ligaments and 4 joint forces, has been developed. A new strain gauge transducer has been developed to measure functional grip forces. The device measures radial forces divided into six components and forces of up to 250N per segment can be measured with an accuracy of +/-1%. Ten normal volunteers were asked to complete four tasks representing occupational activities, during which time their grip force was monitored. Together with kinematic information from the six-camera Vicon data, the moment effect of these loads at the joints was calculated. These external moments are assumed to be balanced by the internal moments, generated by the muscles, passive soft tissue and bone contact. The effectiveness of the body's internal structures in generating joint moments was assessed by studying the geometry of a simplified model of the structures, where information about the lines of action and moment arms of muscles, tendons and ligaments is contained. The assumption of equilibrium between these external and internal joint moments allows formulation of a set of equations from which muscle and joint forces can be calculated. A two stage, linear optimisation routine minimising the overall muscle stress and the sum of the joint forces has been used to overcome the force-sharing problem. Humero-ulnar forces of up to 1600N, humero-radial forces of up to 800N and wrist joint forces of up to 2800N were found for moderate level activity. The model was validated by comparison with other studies.     

Elevation and orientation of external loads influence trunk neuromuscular response and spinal forces despite identical moments at the L5–S1 level

A wide range of loading conditions involving external forces with varying magnitudes, orientations and locations are encountered in daily activities. Here we computed the effect on trunk biomechanics of changes in force location (two levels) and orientation (5 values) in 4 subjects in upright standing while maintaining identical external moment of 15 Nm, 30 N m or 45 Nm at the L5–S1. Driven by measured kinematics and gravity/external loads, the finite element models yielded substantially different trunk neuromuscular response with moderate alterations (up to 24% under 45 Nm moment) in spinal loads as the load orientation varied. Under identical moments, compression and shear forces at the L5–S1 as well as forces in extensor thoracic muscles progressively decreased as orientation of external forces varied from downward gravity (90°) all the way to upward (−25°) orientation. In contrast, forces in local lumbar muscles followed reverse trends. Under larger horizontal forces at a lower elevation, lumbar muscles were much more active whereas extensor thoracic muscle forces were greater under smaller forces at a higher elevation. Despite such differences in activity pattern, the spinal forces remained nearly identical (<6% under 45 Nm moment). The published recorded surface EMG data of extensor muscles trend-wise agreed with computed local muscle forces as horizontal load elevation varied but were overall different from results in both local and global muscles when load orientation altered. Predictions demonstrate the marked effect of external force orientation and elevation on the trunk neuromuscular response and spinal forces and questions attempts to estimate spinal loads based only on consideration of moments at a spinal level.     

Role of trunk muscles in generating follower load in the lumbar spine of neutral standing posture

Recently, experimental results have demonstrated that the load carrying capacity of the human spine substantially increases under the follower load condition. Thus, it is essential to prove that a follower load can be generated in vivo by activating the appropriate muscles in order to demonstrate the possibility that the stability of the spinal column could be maintained through a follower load mechanism. The aim of this study was to analyze the coordination of the trunk muscles in order to understand the role of the muscles in generating the follower load. A three-dimensional finite element model of the lumbar spine was developed from T12 to S1 and 117 pairs of trunk muscles (58 pairs of superficial muscles and 59 pairs of deep muscles) were considered. The follower load concept was mathematically represented as an optimization problem. The muscle forces required to generate the follower load were predicted by solving the optimization problem. The corresponding displacements and rotations at all nodes were estimated along with the follower forces, shear forces, and joint moments acting on those nodes. In addition, the muscle forces and the corresponding responses were investigated when the activations of the deep muscles or the superficial muscles were restricted to 75% of the maximum activation, respectively. Significantly larger numbers of deep muscles were involved in the generation of the follower load than the number of superficial muscles, regardless of the restriction on muscle activation. The shear force and the resultant joint moment are more influenced by the change in muscle activation in the superficial muscles. A larger number of deep trunk muscles were activated in order to maintain the spinal posture in the lumbar spine. In addition, the deep muscles have a larger capability to reduce the shear force and the resultant joint moment with respect to the perturbation of the external load or muscle fatigue compared to the superficial muscles.     

Trunk strength,muscle activity and spinal loads in maximum isometric flexion and extension exertions: A combined in vivo-computational study

Determination of the trunk maximum voluntary exertion moment capacity and associated internal spinal forces could serve in proper selection of workers for specific occupational task requirements, injury prevention and treatment outcome evaluations. Maximum isometric trunk exertion moments in flexion and extension along with surface EMG of select trunk muscles are measured in 12 asymptomatic subjects. Subsequently and under individualized measured harness-subject forces, kinematics and upper trunk gravity, an iterative kinematics-driven finite element model is used to compute muscle forces and spinal loads in 4 of these subjects. Different co-activity and intra-abdominal pressure levels are simulated. Results indicate significantly larger maximal resistant moments and spinal compression/shear forces in extension exertions than flexion exertions. The agonist trunk muscles reach their maximum force generation (saturation) to greater extent in extension exertions compared to flexion exertions. Local lumbar extensor muscles are highly active in extension exertions and generate most of the internal spinal forces. The maximum exertion attempts produce large spinal compression and shear loads that increase with the antagonist co-activity level but decrease with the intra-abdominal pressure. Intra-abdominal pressure decreases agonist muscle forces in extension exertions but generally increase them in flexion exertions.     

Directional preference of activation of abdominal and paraspinal muscles during position-control tasks in sitting

Controversy exists in the literature regarding antagonist activity of trunk muscles during different types of trunk loading, and the direction-specificity of activation of trunk muscles, particularly the deeper trunk muscles. This study aimed to systematically compare activation of a range of trunk muscles between directions of statically applied loads, and to consider the impact of breathing in this activation. In a semi-seated position, 13 healthy male participants resisted moderate inertial loads applied to the trunk in eight different directions. Intramuscular electromyography was recorded from eight abdominal and back muscles on the right side during 1 s prior to peak inspiration/expiration. All muscles demonstrated a directional preference of activation. No muscle displayed antagonistic activation during loading conditions of an intensity that exceded that recorded in upright sitting without a load. During these moderate intensity sustained efforts, trunk muscle activation varied little between respiratory phases. Antagonistic muscle activation of amplitude equivalent to the activation recorded in upright sitting without load is sufficient to maintain control of the spine during predictable and sustained low load tasks.     

A comparative study of two trunk biomechanical models under symmetric and asymmetric loadings

Despite recent advances in modeling of the human spine, simplifying assumptions are still required to tackle complexities. Such assumptions need to be scrutinized to assess their likely impacts on predictions. A comprehensive comparison of muscle forces and spinal loads estimated by a single-joint (L5–S1) optimisation-assisted EMG-driven (EMGAO) and a multi-joint Kinematics-driven (KD) model of the spine under symmetric (symmetric trunk flexion from neutral upright to maximum forward flexion) and asymmetric (holding a load at various heights in the right hand) activities is carried out. Regardless of the task simulated, the KD model predicted greater activities in extensor muscles as compared to the EMGAO model. Such differences in the symmetric tasks was due mainly to the distinct approaches to resolve the redundancy while in the asymmetric tasks they were due also to the different methods used to estimate joint moments. Shear and compression forces were generally higher in the KD model. Differences in predictions between these modeling approaches varied depending on the task simulated and the joint considered in the single-joint EMGAO model. The EMGAO model should incorporate a multi-joint strategy to satisfy equilibrium at different levels while the KD model should benefit from recorded EMG activities of the antagonistic muscles to supplement input measured kinematics.