Effect of intervertebral translational flexibilities on estimations of trunk muscle forces, kinematics, loads, and stability

Evaluation of trunk muscle coactivation predictions in multi-body models

Musculoskeletal simulations with muscle optimization aim to minimize muscle effort, hence are considered unable to predict the activation of antagonistic muscles. However, activation of antagonistic muscles might be necessary to satisfy the dynamic equilibrium. This study aims to elucidate under which conditions coactivation can be predicted, to evaluate factors modulating it, and to compare the antagonistic activations predicted by the lumbar spine model with literature data. Simple 2D and 3D models, comprising of 2 or 3 rigid bodies, with simple or multi-joint muscles, were created to study conditions under which muscle coactivity is predicted. An existing musculoskeletal model of the lumbar spine developed in AnyBody was used to investigate the effects of modeling intra-abdominal pressure (IAP), linear/cubic and load/activity-based muscle recruitment criterion on predicted coactivation during forward flexion and lateral bending. The predicted antagonist activations were compared to reported EMG data. Muscle coactivity was predicted with simplified models when multi-joint muscles were present or the model was three-dimensional. During forward flexion and lateral bending, the coactivation ratio predicted by the model showed good agreement with experimental values. Predicted coactivation was negligibly influenced by IAP but substantially reduced with a force-based recruitment criterion. The conditions needed in multi-body models to predict coactivity are: three-dimensionality or multi-joint muscles, unless perfect antagonists. The antagonist activations are required to balance 3D moments but do not reflect other physiological phenomena, which might explain the discrepancies between model predictions and experimental data. Nevertheless, the findings confirm the ability of the multi-body trunk models to predict muscle coactivity and suggest their overall validity.

Validation of an EMG submaximal method to calibrate a novel dynamic EMG-driven musculoskeletal model of the trunk: Effects on model estimates

BACKGROUND

Multijoint EMG-assisted optimization models are reliable tools to predict muscle forces as they account for inter- and intra-individual variations in activation. However, the conventional method of normalizing EMG signals using maximum voluntary contractions (MVCs) is problematic and introduces major limitations. The sub-maximal voluntary contraction (SVC) approaches have been proposed as a remedy, but their performance against the MVC approach needs further validation particularly during dynamic tasks.

METHODS

To compare model outcomes between MVC and SVC approaches, nineteen healthy subjects performed a dynamic lifting task with two loading conditions.

RESULTS

Results demonstrated that these two approaches produced highly correlated results with relatively small absolute and relative differences (<10 %) when considering highly-aggregated model outcomes (e.g. compression forces, stability indices). Larger differences were, however, observed in estimated muscle forces. Although some model outcomes, e.g. force of abdominal muscles, were statistically different, their effect sizes remained mostly small (η_G² ≤ 0.13) and in a few cases moderate (η_G² ≤ 0.165).

CONCLUSION

The findings highlight that the MVC calibration approach can reliably be replaced by the SVC approach when the true MVC exertion is not accessible due to pain, kinesiophobia and/or the lack of proper training.

Computational lumbar spine models: A literature review

BACKGROUND

Computational spine models of various types have been employed to understand spine function, assess the risk that different activities pose to the spine, and evaluate techniques to prevent injury. The areas in which these models are applied has expanded greatly, potentially beyond the appropriate scope of each, given their capabilities. A comprehensive understanding of the components of these models provides insight into their current capabilities and limitations.

METHODS

The objective of this review was to provide a critical assessment of the different characteristics of model elements employed across the spectrum of lumbar spine modeling and in newer combined methodologies to help better evaluate existing studies and delineate areas for future research and refinement.

FINDINGS

A total of 155 studies met selection criteria and were included in this review. Most current studies use either highly detailed Finite Element models or simpler Musculoskeletal models driven with in vivo data. Many models feature significant geometric or loading simplifications that limit their realism and validity. Frequently, studies only create a single model and thus can't account for the impact of subject variability. The lack of model representation for certain subject cohorts leaves significant gaps in spine knowledge. Combining features from both types of modeling could result in more accurate and predictive models.

INTERPRETATION

Development of integrated models combining elements from different model types in a framework that enables the evaluation of larger populations of subjects could address existing voids and enable more realistic representation of the biomechanics of the lumbar spine.

EMG optimization in OpenSim: A model for estimating lower back kinetics in gait

Participant-specific musculoskeletal models are needed to accurately estimate lower back internal kinetic demands and injury risk. In this study we developed the framework for incorporating an electromyography optimization (EMGopt) approach within OpenSim (https://simtk.org/projects/emg_opt_tool) and evaluated lower back demands estimated from the model during gait. Kinematic, external kinetic, and EMG data were recorded from six participants as they performed walking and carrying tasks on a treadmill. For evaluation, predicted lumbar vertebral joint forces were compared to those from a generic static optimization approach (SOpt) and to previous studies. Further, model-estimated muscle activations were compared to recorded EMG, and model sensitivity to day-to-day EMG variability was evaluated. Results showed the vertebral joint forces from the model were qualitatively similar in pattern and magnitude to literature reports. Compared to SOpt, the EMGopt approach predicted larger joint loads (p<.01) with muscle activations better matching individual participant EMG patterns. L5/S1 vertebral joint forces from EMGopt were sensitive to the expected variability of recorded EMG, but the magnitude of these differences (±4%) did not impact between-task comparisons. Despite limitations inherent to such models, the proposed musculoskeletal model and EMGopt approach appears well-suited for evaluating internal lower back demands during gait tasks.

Evaluating stability of human spine in static tasks: a combined in vivo-computational study

Various interpretations and parameters have been proposed to assess spinal stability such as antagonist muscle coactivity, trunk stiffness and spinal buckling load; however, the correlation between these parameters remains unknown. We evaluated spinal stability during different tasks while changing the external moment and load height and investigated likely relationships between different EMG- and model-based parameters (e.g., EMG coactivity ratio, trunk stiffness, force coactivity ratio) and stability margins. EMG and kinematics of 40 young healthy subjects were recorded during various quasi-static tasks. Muscle forces, trunk stiffness and stability margins were calculated by a nonlinear subject-specific EMG-assisted-optimization musculoskeletal model of the trunk. The load elevation and external moment increased muscle activities and trunk stiffness while all stability margins (i.e., buckling loads) decreased. The force coactivity ratio was strongly correlated with the hand-load stability margin (i.e., additional weight in hands to initiate instability; R² = 0.54) demonstrating the stabilizing role of abdominal muscles. The total trunk stiffness (Pearson's r = 0.96) and the sum of EMGs of back muscles (Pearson's r = 0.65) contributed the most to the T1 stability margin (i.e., additional required load at T1 for instability/buckling). Force coactivity ratio and trunk stiffness can be used as alternative spinal stability metrics.

Biomechanical effects of lumbar fusion surgery on adjacent segments using musculoskeletal models of the intact, degenerated and fused spine

Adjacent segment disorders are prevalent in patients following a spinal fusion surgery. Postoperative alterations in the adjacent segment biomechanics play a role in the etiology of these conditions. While experimental approaches fail to directly quantify spinal loads, previous modeling studies have numerous shortcomings when simulating the complex structures of the spine and the pre/postoperative mechanobiology of the patient. The biomechanical effects of the L4–L5 fusion surgery on muscle forces and adjacent segment kinetics (compression, shear, and moment) were investigated using a validated musculoskeletal model. The model was driven by in vivo kinematics for both preoperative (intact or severely degenerated L4–L5) and postoperative conditions while accounting for muscle atrophies. Results indicated marked changes in the kinetics of adjacent L3–L4 and L5–S1 segments (e.g., by up to 115% and 73% in shear loads and passive moments, respectively) that depended on the preoperative L4–L5 disc condition, postoperative lumbopelvic kinematics and, to a lesser extent, postoperative changes in the L4–L5 segmental lordosis and muscle injuries. Upper adjacent segment was more affected post-fusion than the lower one. While these findings identify risk factors for adjacent segment disorders, they indicate that surgical and postoperative rehabilitation interventions should focus on the preservation/restoration of patient’s normal segmental kinematics.

Calibration and validation of a novel hybrid model of the lumbosacral spine in ArtiSynth-The passive structures

In computational biomechanics, two separate types of models have been used predominantly to enhance the understanding of the mechanisms of action of the lumbosacral spine (LSS): Finite element (FE) and musculoskeletal multibody (MB) models. To combine advantages of both models, hybrid FE-MB models are an increasingly used alternative. The aim of this paper is to develop, calibrate, and validate a novel passive hybrid FE-MB open-access simulation model of a ligamentous LSS using ArtiSynth. Based on anatomical data from the Male Visible Human Project, the LSS model is constructed from the L1-S1 rigid vertebrae interconnected with hyperelastic fiber-reinforced FE intervertebral discs, ligaments, and facet joints. A mesh convergence study, sensitivity analyses, and systematic calibration were conducted with the hybrid functional spinal unit (FSU) L4/5. The predicted mechanical responses of the FSU L4/5, the lumbar spine (L1-L5), and the LSS were validated against literature data from in vivo and in vitro measurements and in silico models. Spinal mechanical responses considered when loaded with pure moments and combined loading modes were total and intervertebral range of motions, instantaneous axes and centers of rotation, facet joint contact forces, intradiscal pressures, disc bulges, and stiffnesses. Undesirable correlations with the FE mesh were minimized, the number of crisscrossed collagen fiber rings was reduced to five, and the individual influences of specific anatomical structures were adjusted to in vitro range of motions. Including intervertebral motion couplings for axial rotation and nonlinear stiffening under increasing axial compression, the predicted kinematic and structural mechanics responses were consistent with the comparative data. The results demonstrate that the hybrid simulation model is robust and efficient in reproducing valid mechanical responses to provide a starting point for upcoming optimizations and extensions, such as with active skeletal muscles.

A novel coupled musculoskeletal finite element model of the spine - Critical evaluation of trunk models in some tasks

Spine musculoskeletal (MS) models make simplifying assumptions on the intervertebral joint degrees-of-freedom (rotational and/or translational), representation (spherical or beam-like joints), and properties (linear or nonlinear). They also generally neglect the realistic structure of the joints with disc nuclei/annuli, facets, and ligaments. We aim to develop a novel MS model where trunk muscles are incorporated into a detailed finite element (FE) model of the ligamentous T12-S1 spine thus constructing a gold standard coupled MS-FE model. Model predictions are compared under some tasks with those of our earlier spherical joints, beam joints, and hybrid (uncoupled) MS-FE models. The coupled model predicted L4-L5 intradiscal pressures (R² ≅ 0.97, RMSE ≅ 0.27 MPa) and L1-S1 centers of rotation (CoRs) in agreement to in vivo data. Differences in model predictions grew at larger trunk flexion angles; at the peak (80°) flexion the coupled model predicted, compared to the hybrid model, much smaller global/local muscle forces (~38%), segmental (~44%) and disc (~22%) compression forces but larger segmental (~9%) and disc (~17%) shear loads, ligament forces at the lower lumbar levels (by up to 57%) and facet forces at all levels. The spherical/beam joints models predicted much greater muscle forces and segmental loads under larger flexion angles. Unlike the spherical joints model with fixed CoRs, the beam joints model predicted CoRs closer (RMSE = 2.3 mm in flexion tasks) to those of the coupled model. The coupled model offers a great potential for future studies towards improvement of surgical techniques, management of musculoskeletal injuries and subject-specific simulations.

Comparison of different lifting analysis tools in estimating lower spinal loads - Evaluation of NIOSH criterion

Excessive loads on the human spine is recognized as a risk factor for back injuries/pain. Various lifting analysis tools such as musculoskeletal models, regression equations and NIOSH (National Institute for Occupational Safety and Health) lifting equation (NLE) have been proposed to evaluate and mitigate associated risks during manual material handling activities. Present study aims to compare predicted spinal loads from 5 different lifting analysis tools as well as to critically evaluate the NIOSH recommended weight limit (RWL). Spinal loads were estimated under different symmetric/asymmetric lifting tasks in which hand-load mass at each task was set based on RWL from NLE. Estimated intradiscal pressures (IDPs) of various tools were also compared with in vivo measurements. We compared RWL by NLE versus our estimations of RWL calculated from our regression equations using biomechanical criteria (compression <3400 N with/without shear <1000, 1250 or 1500 N). Our regression equations followed by OpenSim, AnyBody, simple polynomial and 3DSSPP satisfactorily predicted L4-L5 IDPs. Lifting analysis tools estimated comparable spinal compression forces (mean Pearson's r = 0.80; standard deviation of relative difference = 26%) while in shear, differences were greater (mean Pearson's r = 0.68; standard deviation of relative difference = 56%). NLE estimations of RWL were conservative in comparison with our estimations for lean individuals (BMI < 25 kg/m²) when compression <3400 N and shear <1250 N were considered as the biomechanical criteria. For heavier individuals, however, NLE estimations of RWL generated spinal compression >3400 N (NIOSH biomechanical safety threshold) as well as shear >1000 N. Although RWLs estimated by NLE was body weight independent, body weight substantially altered RWLs estimated from our regression equations. For improved estimation of the risk of injury, more accurate failure criteria for spinal segments are essential.

Lumbar spine loads are reduced for activities of daily living when using a braced arm-to-thigh technique

PURPOSE

To evaluate the effect of the braced arm-to-thigh technique (BATT) (versus self-selected techniques) on three-dimensional trunk kinematics and spinal loads for three common activities of daily living (ADLs) simulated in the laboratory: weeding (gardening), reaching for an object in a low cupboard, and car egress using the two-legs out technique.

METHODS

Ten young healthy males performed each task using a self-selected technique, and then using the BATT. The pulling action of weeding was simulated using a magnet placed on a steel plate. Cupboard and car egress tasks were simulated using custom apparatus representing the dimensions of a kitchen cabinet and a medium-sized Australian car, respectively. Three-dimensional trunk kinematics and L4/L5 spinal loads were estimated using the Lifting Full-Body OpenSim model and compared between techniques. Paired t-tests were used to compare peak values between methods (self-selected vs BATT).

RESULTS

The BATT significantly reduced peak extension moments (13-51%), and both compression (27-45%) and shear forces (31-62%) at L4/L5, compared to self-selected techniques for all three tasks (p < 0.05). Lateral bending angles increased with the BATT for weeding and cupboard tasks, but these changes were expected as the BATT inherently introduces asymmetric trunk motion.

CONCLUSION

The BATT substantially reduced L4/L5 extension moments, and L4/L5 compression and shear forces, compared to self-selected methods, for three ADLs, in a small cohort of ten young healthy males without prior history of back pain. These study findings can be used to inform safe procedures for these three ADLs, as the results are considered representative of a mature population.

Estimation of Trunk Muscle Forces Using a Bio-Inspired Control Strategy Implemented in a Neuro-Osteo-Ligamentous Finite Element Model of the Lumbar Spine

Low back pain (LBP), the leading cause of disability worldwide, remains one of the most common and challenging problems in occupational musculoskeletal disorders. The effective assessment of LBP injury risk, and the design of appropriate treatment modalities and rehabilitation protocols, require accurate estimation of the mechanical spinal loads during different activities. This study aimed to: (1) develop a novel 2D beam-column finite element control-based model of the lumbar spine and compare its predictions for muscle forces and spinal loads to those resulting from a geometrically matched equilibrium-based model; (2) test, using the foregoing control-based finite element model, the validity of the follower load (FL) concept suggested in the geometrically matched model; and (3) investigate the effect of change in the magnitude of the external load on trunk muscle activation patterns. A simple 2D continuous beam-column model of the human lumbar spine, incorporating five pairs of Hill's muscle models, was developed in the frontal plane. Bio-inspired fuzzy neuro-controllers were used to maintain a laterally bent posture under five different external loading conditions. Muscle forces were assigned based on minimizing the kinematic error between target and actual postures, while imposing a penalty on muscular activation levels. As compared to the geometrically matched model, our control-based model predicted similar patterns for muscle forces, but at considerably lower values. Moreover, irrespective of the external loading conditions, a near (<3°) optimal FL on the spine was generated by the control-based predicted muscle forces. The variation of the muscle forces with the magnitude of the external load within the simulated range at the L1 level was found linear. This work presents a novel methodology, based on a bio-inspired control strategy, that can be used to estimate trunk muscle forces for various clinical and occupational applications toward shedding light on the ever-elusive LBP etiology.

Analysing the effect of wearable lift-assist vest in squat lifting task using back muscle EMG data and musculoskeletal model

The most common disorders of the musculoskeletal system are low back disorders. They cause significant direct and indirect costs to different societies especially in lifting occupations. To reduce the risk of low back disorders, mechanical lifting aids have been used to decrease low back muscle forces. But there are very few direct ways to calculate muscle forces and examine the effect of personal lift-assist devices, so biomechanical models ought to be used to examine the quality of these devices for assisting back muscles in lifting tasks. The purpose of this study is to examine the effect of a designed wearable lift-assist vest (WLAV) in the reduction of erector spinae muscle forces during symmetric squat lifting tasks. Two techniques of muscle calculation were used, the electromyography-based method and the optimization-based model. The first uses electromyography data of erector spinae muscles and its linear relationship with muscle force to estimate their forces, and the second uses a developed musculoskeletal model to calculate back muscle forces using an optimization-based method. The results show that these techniques reduce the average value of erector spinae muscle forces by 45.38 (± 4.80) % and 42.03 (± 8.24) % respectively. Also, both methods indicated approximately the same behaviour in changing muscle forces during 10 to 60 degrees of trunk flexion using WLAV. The use of WLAV can help to reduce the activity of low back muscles in lifting tasks by transferring the external load effect to the assistive spring system utilized in it, so this device may help people lift for longer.

Investigation of lumbar spine biomechanics using global convergence optimization and constant loading path methods

Computational models and inverse dynamic optimization methods are used to predict in-vivo spinal loading. Spinal force is conventionally predicted using the constant loading path method, which is based on the concept that the physiological directions of the spine loads follow the same path of the spinal curve. However, the global convergence optimization method, in which the instantaneous center of rotation of the joint should be also predicted, is necessary for accurate prediction of joint forces of the human body. In this study, we investigate the joint forces, instantaneous centers of rotation, and muscle forces of the human lumbar spine using both global convergence optimization method and constant loading path method during flexion, upright standing, and extension postures. The joint forces predicted using the constant loading path method were 130%, 234%, and 253% greater than those predicted using the global convergence optimization method for the three postures. The instantaneous centers of rotation predicted using the global convergence optimization method were segment level-dependent and moved anteriorly in the flexion and posteriorly in the extension, whereas those predicted using the constant loading path method moved posteriorly in both the flexion and extension. The data indicated that compared to the global convergence optimization method, the constant loading path method introduces additional constraints to the spinal joint model, and thus, it results in greater joint and muscle forces.

Significance of spine stability criteria on trunk muscle forces following unilateral muscle weakening: A comparison between kinematics-driven and stability-based kinematics-driven musculoskeletal models

Two optimization-driven approaches were employed to develop kinematics-driven (KD) and stability-based kinematics-driven (SKD) musculoskeletal models of an adult thoracolumbar to ascertain the significance of spine stability in holding the upright-standing posture after muscular disuse atrophy. Both models were used to estimate muscle forces of the trunk with intact and unilaterally reduced longissimus thoracis pars thoracic (LGPT) and multifidus lumborum (MFL) muscles strength. A finite element model of the L5-S1 segment of the same kinematics was also developed to compare the joint stresses predicted by the KD and SKD models. Matching well with in vivo data, the SKD model predicted a 15% and 33% reduction in contralateral muscle forces to the 95% debilitated LGPT and MFL muscles, respectively. In contrast, the contralateral muscle force enhancement to the debilitated MFL muscle in the KD model was in contradiction with in vivo data, implying that the KD model is incapable of correctly predicting the muscular disorders. However, the similarity of both models' predictions of intradiscal pressures and intervertebral discs' stresses, which matched well with in vivo data, does indicate the feasibility of the KD model to investigate trunk muscle weakness effects on spinal loads, which could offer additional tools for research in ergonomics. Nonetheless, SKD models can be employed for assessment of contralateral muscle impotence in spinal neuromuscular disorders.

Validation of the AnyBody full body musculoskeletal model in computing lumbar spine loads at L4L5 level

In the panorama of available musculoskeletal modeling software, AnyBody software is a commercial tool that provides a full body musculoskeletal model which is increasingly exploited by numerous researchers worldwide. In this regard, model validation becomes essential to guarantee the suitability of the model in representing the simulated system. When focusing on lumbar spine, the previous works aimed at validating the AnyBody model in computing the intervertebral loads held several limitations, and a comprehensive validation is to be considered as lacking. The present study was aimed at extensively validating the suitability of the AnyBody model in computing lumbar spine loads at L4L5 level. The intersegmental loads were calculated during twelve specific exercise tasks designed to accurately replicate the conditions during which Wilke et al. (2001) measured in vivo the L4L5 intradiscal pressure. Motion capture data of one volunteer subject were acquired during the execution of the tasks and then imported into AnyBody to set model kinematics. Two different approaches in computing intradiscal pressure from the intersegmental load were evaluated. Lumbopelvic rhythm was compared with reference in vivo measurements to assess the accuracy of the lumbopelvic kinematics. Positive agreement was confirmed between the calculated pressures and the in vivo measurements, thus demonstrating the suitability of the AnyBody model. Specific caution needs to be taken only when considering postures characterized by large lateral displacements. Minor discrepancy was found assessing lumbopelvic rhythm. The present findings promote the AnyBody model as an appropriate tool to non-invasively evaluate the lumbar loads at L4L5 in physiological activities.

Curved muscles in biomechanical models of the spine: a systematic literature review

Early biomechanical spine models represented the trunk muscles as straight-line approximations. Later models have endeavoured to accurately represent muscle curvature around the torso. However, only a few studies have systematically examined various techniques and the logic underlying curved muscle models. The objective of this review was to systematically categorise curved muscle representation techniques and compare the underlying logic in biomechanical models of the spine. Thirty-five studies met our selection criteria. The most common technique of curved muscle path was the 'via-point' method. Curved muscle geometry was commonly developed from MRI/CT database and cadaveric dissections, and optimisation/inverse dynamics models were typically used to estimate muscle forces. Several models have attempted to validate their results by comparing their approach with previous studies, but it could not validate of specific tasks. For future needs, personalised muscle geometry, and person- or task-specific validation of curved muscle models would be necessary to improve model fidelity. Practitioner Summary: The logic underlying the curved muscle representations in spine models is still poorly understood. This literature review systematically categorised different approaches and evaluated their underlying logic. The findings could direct future development of curved muscle models to have a better understanding of the biomechanical causal pathways of spine disorders.

A biologically-assisted curved muscle model of the lumbar spine: Model structure

BACKGROUND

Biomechanical models have been developed to assess the spine tissue loads of individuals. However, most models have assumed trunk muscle lines of action as straight-lines, which might be less reliable during occupational tasks that require complex lumbar motions. The objective of this study was to describe the model structure and underlying logic of a biologically-assisted curved muscle model of the lumbar spine.

METHODS

The developed model structure including curved muscle geometry, separation of active and passive muscle forces, and personalization of muscle properties was described. An example of the model procedure including data collection, personalization, and data evaluation was also illustrated.

FINDINGS

Three-dimensional curved muscle geometry was developed based on a predictive model using magnetic resonance imaging and anthropometric measures to personalize the model for each individual. Calibration algorithms were able to reverse-engineer personalized muscle properties to calculate active and passive muscle forces of each individual.

INTERPRETATION

This biologically-assisted curved muscle model will significantly increase the accuracy of spinal tissue load predictions for the entire lumbar spine during complex dynamic occupational tasks. Personalized active and passive muscle force algorithms will help to more robustly investigate person-specific muscle forces and spinal tissue loads.

Prediction of magnetic resonance imaging-derived trunk muscle geometry with application to spine biomechanical modeling

BACKGROUND

Accurate geometry of the trunk musculature is essential for reliably estimating spinal loads in biomechanical models. Currently, many models employ straight muscle path assumptions that yield far less accurate tissue loads, particularly in extreme postures. Precise muscle moment-arms and physiological cross-sectional areas are important when incorporating curved muscle geometry in biomechanical models. The objective of this study was to develop a predictive model of moment arms and physiological cross-sectional areas of trunk musculature at multiple levels in the thoracic/lumbar spine as a function of anthropometric measures.

METHODS

Based on magnetic resonance imaging data from thirty subjects (10 male and 20 female) reported in a previous study, a polynomial regression analysis was conducted to estimate the muscle moment-arms and physiological cross-sectional areas of trunk muscles through thoracic/lumbar spine as a function of vertebral level, gender, age, height, and body mass.

FINDINGS

Gender, body mass, and height were the best predictors of muscle moment-arms and physiological cross-sectional areas. The predictability of muscle parameters tended to be higher for erector spinae than other muscles. Most muscles showed a curved muscle path along the thoracic/lumbar spine.

INTERPRETATION

The polynomial regression model of the muscle geometry in this study generally showed good predictability compared to previous reports. The predictive model in this study will be useful to develop personalized biomechanical models that incorporate curved trunk muscle geometries.