Moment arms of the human neck muscles in flexion, bending and rotation

There is a paucity of data available for the moment arms of the muscles of the human neck. The objective of the present study was to measure the moment arms of the major cervical spine muscles in vitro. Experiments were performed on five fresh-frozen human head-neck specimens using a custom-designed robotic spine testing apparatus. The testing apparatus replicated flexion-extension, lateral bending and axial rotation of each individual intervertebral joint in the cervical spine while all other joints were kept immobile. The tendon excursion method was used to measure the moment arms of 30 muscle sub-regions involving 13 major muscles of the neck about all three axes of rotation of each joint for the neutral position of the cervical spine. Significant differences in the moment arm were observed across sub-regions of individual muscles and across the intervertebral joints spanned by each muscle (p<0.05). Overall, muscle moment arms were larger in flexion-extension and lateral bending than in axial rotation, and most muscles had prominent moment arms in at least 2 out of the 3 joint motions investigated. This study emphasizes the importance of detailed representation of a muscle's architecture in prediction of its torque capacity about the individual joints of the cervical spine. The dataset produced may be useful in developing and validating computational models of the human neck.     

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.     

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.     

Muscle and external load contribution to knee joint contact loads during normal gait

Large knee adduction moments during gait have been implicated as a mechanical factor related to the progression and severity of tibiofemoral osteoarthritis and it has been proposed that these moments increase the load on the medial compartment of the knee joint. However, this mechanism cannot be validated without taking into account the internal forces and moments generated by the muscles and ligaments, which cannot be easily measured. Previous musculoskeletal models suggest that the medial compartment of the tibiofemoral joint bears the majority of the tibiofemoral load, with the lateral compartment unloaded at times during stance. Yet these models did not utilise explicitly measured muscle activation patterns and measurements from an instrumented prosthesis which do not portray lateral compartment unloading. This paper utilised an EMG-driven model to estimate muscle forces and knee joint contact forces during healthy gait. Results indicate that while the medial compartment does bear the majority of the load during stance, muscles provide sufficient stability to counter the tendency of the external adduction moment to unload the lateral compartment. This stability was predominantly provided by the quadriceps, hamstrings, and gastrocnemii muscles, although the contribution from the tensor fascia latae was also significant. Lateral compartment unloading was not predicted by the EMG-driven model, suggesting that muscle activity patterns provide useful input to estimate muscle and joint contact forces.     

Validation of lumbar spine loading from a musculoskeletal model including the lower limbs and lumbar spine

Low back mechanics are important to quantify to study injury, pain and disability. As in vivo forces are difficult to measure directly, modeling approaches are commonly used to estimate these forces. Validation of model estimates is critical to gain confidence in modeling results across populations of interest, such as people with lower-limb amputation. Motion capture, ground reaction force and electromyographic data were collected from ten participants without an amputation (five male/five female) and five participants with a unilateral transtibial amputation (four male/one female) during trunk-pelvis range of motion trials in flexion/extension, lateral bending and axial rotation. A musculoskeletal model with a detailed lumbar spine and the legs including 294 muscles was used to predict L4-L5 loading and muscle activations using static optimization. Model estimates of L4-L5 intervertebral joint loading were compared to measured intradiscal pressures from the literature and muscle activations were compared to electromyographic signals. Model loading estimates were only significantly different from experimental measurements during trunk extension for males without an amputation and for people with an amputation, which may suggest a greater portion of L4-L5 axial load transfer through the facet joints, as facet loads are not captured by intradiscal pressure transducers. Pressure estimates between the model and previous work were not significantly different for flexion, lateral bending or axial rotation. Timing of model-estimated muscle activations compared well with electromyographic activity of the lumbar paraspinals and upper erector spinae. Validated estimates of low back loading can increase the applicability of musculoskeletal models to clinical diagnosis and treatment.     

Evidence for a role of antagonistic cocontraction in controlling trunk stiffness during lifting

Activity of the abdominal muscles during symmetric lifting has been a consistent finding in many studies. It has been hypothesized that this antagonistic coactivation increases trunk stiffness to provide stability to the spine. To test this, we investigated whether abdominal activity in lifting is increased in response to destabilizing conditions.

Ten healthy male subjects lifted 35 l containers containing 15 l of water (unstable condition), or ice (stable condition). 3D-kinematics, ground reaction forces, and EMG of selected trunk muscles were recorded. Euler angles of the thorax relative to the pelvis were determined. Inverse dynamics was used to calculate moments about L5S1. Averaged normalized abdominal EMG activity was calculated to express coactivation and an EMG-driven trunk muscle model was used to estimate the flexor moment produced by these muscles and to estimate the L5S1 compression force.

Abdominal coactivation was significantly higher when lifting the unstable load. This coincided with significant increases in estimated moments produced by the antagonist muscles and in estimated compression forces on the L5S1 disc, except at the instant of the peak moment about L5S1. The lifting style was not affected by load instability as evidenced by the absence of effects on moments about L5S1 and angles of the thorax relative to the pelvis. The data support the interpretation of abdominal cocontraction during lifting as subserving spinal stability. An alternative function of the increased trunk stiffness due to cocontraction might be to achieve more precise control over the trajectory of lifted weight in order to avoid sloshing of the water mass in the box and the consequent perturbations.     

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.     

Development of a novel MATLAB-based framework for implementing mechanical joint stability constraints within OpenSim musculoskeletal models

The Static Optimization (SO) solver in OpenSim estimates muscle activations and forces that only equilibrate applied moments. In this study, SO was enhanced through an open-access MATLAB interface, where calculated muscle activations can additionally satisfy crucial mechanical stability requirements. This Stability-Constrained SO (SCSO) is applicable to many OpenSim models and can potentially produce more biofidelic results than SO alone, especially when antagonistic muscle co-contraction is required to stabilize body joints. This hypothesis was tested using existing models and experimental data in the literature. Muscle activations were calculated by SO and SCSO for a spine model during two series of static trials (i.e. simulation 1 and 2), and also for a lower limb model (supplementary material 2). In simulation 1, symmetric and asymmetric flexion postures were compared, while in simulation 2, various external load heights were compared, where increases in load height did not change the external lumbar flexion moment, but necessitated higher EMG activations. During the tasks in simulation 1, the predicted muscle activations by SCSO demonstrated less average deviation from the EMG data (6.8% −7.5%) compared to those from SO (10.2%). In simulation 2, SO predicts constant muscle activations and forces, while SCSO predicts increases in the average activations of back and abdominal muscles that better match experimental data. Although the SCSO results are sensitive to some parameters (e.g. musculotendon stiffness), when considering the strategy of the central nervous system in distributing muscle forces and in activating antagonistic muscles, the assigned activations by SCSO are more biofidelic than SO.     

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.     

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.     

Spinal stability and role of passive stiffness in dynamic squat and stoop lifts

The spinal stability and passive-active load partitioning under dynamic squat and stoop lifts were investigated as the ligamentous stiffness in flexion was altered. Measured in vivo kinematics of subjects lifting 180 N at either squat or stoop technique was prescribed in a nonlinear transient finite element model of the spine. The Kinematics-driven approach was utilized for temporal estimation of muscle forces, internal spinal loads and system stability. The finite element model accounted for nonlinear properties of the ligamentous spine, wrapping of thoracic extensor muscles and trunk dynamic characteristics while subject to measured kinematics and gravity/external loads. Alterations in passive properties of spine substantially influenced muscle forces, spinal loads and system stability in both lifting techniques, though more so in stoop than in squat. The squat technique is advocated for resulting in smaller spinal loads. Stability of spine in the sagittal plane substantially improved with greater passive properties, trunk flexion and load. Simulation of global extensor muscles with curved rather than straight courses considerably diminished loads on spine and increased stability throughout the task.     

Trunk response analysis under sudden forward perturbations using a kinematics-driven model

Accurate quantification of the trunk transient response to sudden loading is crucial in prevention, evaluation, rehabilitation and training programs. An iterative dynamic kinematics-driven approach was used to evaluate the temporal variation of trunk muscle forces, internal loads and stability under sudden application of an anterior horizontal load. The input kinematics is hypothesized to embed basic dynamic characteristics of the system that can be decoded by our kinematics-driven approach. The model employs temporal variation of applied load, trunk forward displacement and surface EMG of select muscles measured on two healthy and one chronic low-back pain subjects to a sudden load. A finite element model accounting for measured kinematics, nonlinear passive properties of spine, detailed trunk musculature with wrapping of global extensor muscles, gravity load and trunk biodynamic characteristics is used to estimate the response under measured sudden load. Results demonstrate a delay of ～200 ms in extensor muscle activation in response to sudden loading. Net moment and spinal loads substantially increase as muscles are recruited to control the trunk under sudden load. As a result and due also to the trunk flexion, system stability significantly improves. The reliability of the kinematics-driven approach in estimating the trunk response while decoding measured kinematics is demonstrated. Estimated large spinal loads highlight the risk of injury that likely further increases under larger perturbations, muscle fatigue and longer delays in activation.     

Force transmission via axial tendons in undulating fish: a dynamic analysis

Sonomicrometrics of in vivo axial strain of muscle has shown that the swimming fish body bends like a homogenous, continuous beam in all species except tuna. This simple beam-like behavior is surprising because the underlying tendon structure, muscle structure and behavior are complex. Given this incongruence, our goal was to understand the mechanical role of various myoseptal tendons. We modeled a pumpkinseed sunfish, Lepomis gibbosus, using experimentally-derived physical and mechanical attributes, swimming from rest with steady muscle activity. Axially oriented muscle-tendons, transverse and axial myoseptal tendons, as suggested by current morphological knowledge, interacted to replicate the force and moment distribution. Dynamic stiffness and damping associated with muscle activation, realistic muscle force generation, and force distribution following tendon geometry were incorporated. The vertebral column consisted of 11 rigid vertebrae connected by joints that restricted bending to the lateral plane and endowed the body with its passive viscoelasticity. In reaction to the acceleration of the body in an inviscid fluid and its internal transmission of moment via the vertebral column, the model predicted the kinematic response. Varying only tendon geometry and stiffness, four different simulations were run. Simulations with only intrasegmental tendons produced unstable axial and lateral tail forces and body motions. Only the simulation that included both intra- and intersegmental tendons, muscle-enhanced segment stiffness, and a stiffened caudal joint produced stable and large lateral and axial forces at the tail. Thus this model predicts that axial tendons function within a myomere to (1) convert axial force to moment (moment transduction), (2) transmit axial forces between adjacent myosepta (segment coupling), and, intersegmentally, to (3) distribute axial forces (force entrainment), and (4) stiffen joints in bending (flexural stiffening). The fact that all four functions are needed to produce the most realistic swimming motions suggests that axial tendons are essential to the simple beam-like behavior of fish.     

Effect of optimization criterion on spinal force estimates during asymmetric lifting

Optimization-based muscle force prediction models of the lumbar region are used in research and ergonomic practice, usually as a subroutine of a job analysis software package. Various optimization criteria have been put forward for use in rationally selecting a set of muscle forces to satisfy moment equilibrium, including the sum of cubed muscle contraction intensities and a double linear programming procedure for minimizing the spinal compression force and maximum muscle contraction intensity. A laboratory study was conducted to determine whether these two model formulations produce significantly different estimates of spinal forces for a dynamic asymmetric lift. Although statistically significant differences were found between the predictions of the two models, the difference in peak spinal compression force was only 1.1%.     

Links between the mechanics of ventilation and spine stability

Spine stability is ensured through isometric coactivation of the torso muscles; however, these same muscles are used cyclically to assist ventilation. Our objective was to investigate this apparent paradoxical role (isometric contraction for stability or rhythmic contraction for ventilation) of some selected torso muscles that are involved in both ventilation and support of the spine. Eight, asymptomatic, male subjects provided data on low back moments, motion, muscle activation, and hand force. These data were input to an anatomically detailed, biologically driven model from which spine load and a lumbar spine stability index was obtained. Results revealed that subjects entrained their torso stabilization muscles to breathe during demanding ventilation tasks. Increases in lung volume and back extensor muscle activation coincided with increases in spine stability, whereas declines in spine stability were observed during periods of low lung inflation volume and simultaneously low levels of torso muscle activation. As a case study, aberrant ventilation motor patterns (poor muscle entrainment), seen in one subject, compromised spine stability. Those interested in rehabilitation of patients with lung compromise and concomitant back troubles would be assisted with knowledge of the mechanical links between ventilation during tasks that impose spine loading.     

A continuous dynamic beam model for swimming fish

When a fish swims in water, muscle contraction, controlled by the nervous system, interacts with the body tissues and the surrounding fluid to yield the observed movement pattern of the body. A continuous dynamic beam model describing the bending moment balance on the body for such an interaction during swimming has been established. In the model a linear visco-elastic assumption is made for the passive behaviour of internal tissues, skin and backbone, and the unsteady fluid force acting on the swimming body is calculated by the 3D waving plate theory. The body bending moment distribution due to the various components, in isolation and acting together, is analysed. The analysis is based on the saithe (Pollachius virens), a carangiform swimmer. The fluid reaction needs a bending moment of increasing amplitude towards the tail and near-standing wave behaviour on the rear-half of the body. The inertial movement of the fish results from a wave of bending moment with increasing amplitude along the body and a higher propagation speed than that of body bending. In particular, the fluid reaction, mainly designed for propulsion, can provide a considerable force to balance the local momentum change of the body and thereby reduce the power required from the muscle. The wave of passive visco-elastic bending moment, with an amplitude distribution peaking a little before the mid-point of the fish, travels with a speed close to that of body bending. The calculated muscle bending moment from the whole dynamic system has a wave speed almost the same as that observed for EMG-onset and a starting instant close to that of muscle activation, suggesting a consistent matching between the muscle activation pattern and the dynamic response of the system in steady swimming. A faster wave of muscle activation, with a variable phase relation between the strain and activation cycle, appears to be designed to fit the fluid reaction and, to a lesser extent, the body inertia, and is limited by the passive internal tissues. Higher active stress is required from caudal muscle, as predicted from experimental studies on fish muscle. In general, the active force development by muscle does not coincide with the propulsive force generation on the tail. The stiffer backbone may play a role in transmitting force and deformation to maintain and adjust the movement of the body and tail in water.     

Predicted pattern of human muscle activity during clenching derived from a computer assisted model: symmetric vertical bite forces

A computer assisted three-dimensional model of the jaw, based on linear programming, is presented. The upper and lower attachments of the muscles of mastication have been measured on a single human skull and divided into thirteen independent units on each side--a total of 26 muscle elements. The direction (in three dimensions) and maximum forces that could be developed by each muscle element, the bite reaction and two joint reactions are included in the model. It is shown for symmetrical biting that a model which minimizes the sum of the muscle forces used to produce a given bite force activates muscles in a way which corresponds well with previous observations on human subjects. A model which minimizes the joint reactions behaves differently and is rejected. An analysis of the way the chosen model operates suggests that there are two types of jaw muscles, power muscles and control muscles. Power muscles (superficial masseter, medial pterygoid and some of temporalis) produce the bite force but tend to displace the condyle up or down the articular eminence. This displacement is prevented by control muscles (oblique temporalis and lateral pterygoid) which have very poor moment arms for generating usual bite forces, but are efficient for preventing condylar slide. The model incorporates the concept that muscles consist of elements which can contract independently. It predicts that those muscle elements with longer moment arms relative to the joint are the first to be activated and, as the bite force increases, a ripple of activity spreads into elements with shorter moment arms. In general, the model can be used to study the three-dimensional activity in any system of joints and muscles.     

Lifting over an obstacle: effects of one-handed lifting and hand support on trunk kinematics and low back loading

Mechanical loading of the low back during lifting is a common cause of low back pain. In this study two-handed lifting is compared to one-handed lifting (with and without supporting the upper body with the free hand) while lifting over an obstacle. A 3-D linked segment model was combined with an EMG-assisted trunk muscle model to quantify kinematics and joint loads at the L5S1 joint. Peak total net moments (i.e., the net moment effect of all muscles and soft tissue spanning the joint) were found to be 10+/-3% lower in unsupported one-handed lifting compared to two-handed lifting, and 30+/-8% lower in supported compared to unsupported one-handed lifting. L5S1 joint forces also showed reductions, but not of the same magnitude (18+/-8% and 15+/-10%, respectively, for compression forces, and 15+/-17% and 11+/-14% respectively, for shear forces). Those reductions of low back load were mainly caused by a reduction of trunk and load moment arms relative to the L5S1 joint during peak loading, and, in the case of hand support, by a support force of about 250 N. Stretching one leg backward did not further reduce low back load estimates. Furthermore, one-handed lifting caused an 6+/-8 degrees increase in lateral flexion, a 9+/-5 degrees increase in twist and a 6+/-6 degrees decrease in flexion. Support with the free hand caused a small further increase in lumbar twisting. It is concluded that one-handed lifting, especially with hand support, reduces L5S1 loading but increases asymmetry in movements and moments about the lumbar spine.     

Abdominal muscles dominate contributions to vertebral joint stiffness during the push-up

The goal of this study was to quantify the relative contributions of each muscle group surrounding the spine to vertebral joint rotational stiffness (VJRS) during the push-up exercise. Upper-body kinematics, three-dimensional hand forces and lumbar spine postures, and 14 channels (bilaterally from rectus abdominis, external oblique, internal oblique, latissimus dorsi, thoracic erector spinae, lumbar erector spinae, and multifidus) of trunk electromyographic (EMG) activity were collected from 11 males and used as inputs to a biomechanical model that determined the individual contributions of 10 muscle groups surrounding the lumbar spine to VJRS at five lumbar vertebral joints (L1-L2 to L5-S1). On average, the abdominal muscles contributed 64.32 +/- 8.50%, 86.55 +/- 1.13%, and 83.84 +/- 1.95% to VJRS about the flexion/extension, lateral bend, and axial twist axes, respectively. Rectus abdominis contributed 43.16 +/- 3.44% to VJRS about the flexion/extension axis at each lumbar joint, and external oblique and internal oblique, respectively contributed 52.61 +/- 7.73% and 62.13 +/- 8.71% to VJRS about the lateral bend and axial twist axes, respectively, at all lumbar joints with the exception of L5-S1. Owing to changes in moment arm length, the external oblique and internal oblique, respectively contributed 55.89% and 50.01% to VJRS about the axial twist and lateral bend axes at L5-S1. Transversus abdominis, multifidus, and the spine extensors contributed minimally to VJRS during the push-up exercise. The push-up challenges the abdominal musculature to maintain VJRS. The orientation of the abdominal muscles suggests that each muscle primarily controls the rotational stiffness about a single axis.