Biomechanical model calculation of muscle contraction forces: a double linear programming method

Advanced subject-specific neck musculoskeletal modeling unveils sex differences in muscle moment arm and cervical spine loading

Neck pain and injuries are growing healthcare burdens with women having a higher incidence rate and poorer treatment outcomes than males. A better understanding of sex differences in neck biomechanics, foundational for more targeted, effective prevention or treatment strategies, calls for more advanced subject-specific musculoskeletal modeling. Current neck musculoskeletal models are based on generic anatomy, lack subject specificity beyond anthropometric scaling, and are unable to accurately reproduce neck strengths exhibited in vivo without arbitrary muscle force scaling factors or residual torque actuators. In this work, subject-specific neck musculoskeletal models of 23 individuals (11 male, 12 female) were constructed by integrating multi-modality imaging and biomechanical measurements. Each model simulated maximal voluntary neck static exertions in three postures: neck flexion in a neutral posture, flexion in a 40° extended posture, and extension in a 40° flexed posture. Quantitative model validation showed close agreement between model-predicted muscle activation and EMG measurement. The models unveiled that (1) males have greater moment arms in one flexor muscle group and five extensor muscle groups, (2) females exhibited higher cervical spinal compression per unit exertion force in the flexed posture, and (3) the variability of compression force was much greater in females in all three exertions but most notably in the extension with a flexed "dropped head" position. These insights illuminated a plausible pathway from sex differences in neck biomechanics to sex disparities in the risk and prevalence of neck pain.

A computational musculoskeletal arm model for assessing muscle dysfunction in chronic obstructive pulmonary disease

Computational models have been used extensively to assess diseases and disabilities effects on musculoskeletal system dysfunction. In the current study, we developed a two degree-of-freedom subject-specific second-order task-specific arm model for characterizing upper-extremity function (UEF) to assess muscle dysfunction due to chronic obstructive pulmonary disease (COPD). Older adults (65 years or older) with and without COPD and healthy young control participants (18 to 30 years) were recruited. First, we evaluated the musculoskeletal arm model using electromyography (EMG) data. Second, we compared the computational musculoskeletal arm model parameters along with EMG-based time lag and kinematics parameters (such as elbow angular velocity) between participants. The developed model showed strong cross-correlation with EMG data for biceps (0.905, 0.915) and moderate cross-correlation for triceps (0.717, 0.672) within both fast and normal pace tasks among older adults with COPD. We also showed that parameters obtained from the musculoskeletal model were significantly different between COPD and healthy participants. On average, higher effect sizes were achieved for parameters obtained from the musculoskeletal model, especially for co-contraction measures (effect size = 1.650 ± 0.606, p < 0.001), which was the only parameter that showed significant differences between all pairwise comparisons across the three groups. These findings suggest that studying the muscle performance and co-contraction, may provide better information regarding neuromuscular deficiencies compared to kinematics data. The presented model has potential for assessing functional capacity and studying longitudinal outcomes in COPD.

An Analysis of Biomechanical Parameters in OTP Police Physical Intervention Techniques for Occupational Risk Prevention

(1) Background: a set of ergonomic parameters that are relevant for risk assessment methods for the prevention of occupational risks, such as REBA or NIOSH, have been measured by means of inertial sensors that allow capturing the movements of the human body. These methods base their assessment on a number of postural and dynamic parameters. In the case of police physical intervention techniques, trunk, legs, arms, forearms and wrists angles, joint contact force and sheer force at the L5-Pelvic junction, asymmetry (angle and factor), and muscle power are the more relevant parameters to be considered. (2) Method: The data have been collected by means of a motion capture suit equipped with 19 inertial sensors. The large amount of data and the 3-dimensional plots have been managed by a powerful software package specific for ergonomic analysis. The police physical intervention technique used was OTP. (3) Results: Five ergonomic parameters in a traditional police physical intervention technique have been analyzed. REBA scores and ergonomic metrics have been recorded and discussed with some prevention risk limits from the literature. (4) Conclusions: the usage of inertial sensors to capture the movements in OTPs provides a new and quite an efficient viewpoint for occupational risk research studies.

An EMG-Based Constitutive Law for Force Generation in Skeletal Muscle - Part II: Model Validation On the Ankle Joint Complex

This study evaluates the predictive ability of the skeletal muscle force model derived previously within the ankle joint complex. The model is founded in dimensional analysis, using electromyography and the muscle force-length, force-velocity, and force-frequency curves as inputs. Seventeen subjects (8 males, 9 females) performed five different exercises that activated the primary muscles crossing the ankle joint. Motion capture, force plate, and electromyography data were collected during these exercises. A constant, Km, was calculated for each muscle of each subject using four of the five exercises. The fifth exercise was used to validate the results by treating the moments due to muscle forces as known and all other components in Euler's second law as unknown. While muscle forces cannot be directly validated in vivo, methods can be developed to test these values with reasonable confidence. This study compared moments about the ankle joint due to the calculated muscle forces to the sum of the moments due to all other sources and the kinematic terms in the second Newton-Euler equation of rigid body motion. Average percent errors for each subject ranged from 4.2% to 15.5% with an average percent error across all subjects of 8.2% while maximum percent errors for each subject ranged from 33.3% to 78.0% with an overall average maximum of 52.4%. Future work will examine sensitivity analyses to identify potential simplifications to the model and solution process and will validate the model on a more complex joint.

An EMG-Based Constitutive Law for Force Generation in Skeletal Muscle - Part I: Model Development

PURPOSE

This paper proposes a new method for estimating skeletal muscle forces using a model derived from dimensional analysis. It incorporates electromyography signals and muscle force-length, force-velocity, and force frequency relationships as inputs. The purpose of this model is to provide more accurate estimates of individualized muscle forces to better predict surrounding musculoskeletal tissue and joint contact loading.

THEORY

The derivation begins with dimensional analysis and a selection of critical parameters that define muscle force generation. The resulting constitutive equation gives way to a unique application of inverse-dynamics, one which avoids the issue of indeterminacy when reaction moments and ligament loading are minimized in a joint. The ankle joint is used as an example for developing the equations that culminate into a system of linear equations.

DISCUSSION

A muscle force model capable of being calibrated and then used to predict joint contact and surrounding tissue loading is critical in advancing biomechanics research areas like injury prevention, performance optimization, and tissue engineering, among others. This model's foundation in dimensional analysis, along with its inclusion of electromyography signals, gives promise that it will be physiologically relevant and suitable for application-based studies.

Comparison of Predictions Between an EMG-Assisted Approach and Two Optimization-Driven Approaches for Lumbar Spine Loading During Walking With Backpack Loads

OBJECTIVE

The efficacy of two optimization-driven biomechanical modeling approaches has been compared with an electromyography-assisted optimization (EMGAO) approach to predict lumbar spine loading while walking with backpack loads.

BACKGROUND

The EMGAO approach adopts more variables in the optimization process and is complex in data collection and processing, whereas optimization-driven approaches are simple and include the fewest possible variables. However, few studies have been conducted on the efficacy of using the optimization-driven approach to predict lumbar spine loading while walking with backpack loads.

METHOD

Anthropometric information of 10 healthy male adults as well as their kinematic, kinetic, and electromyographic data acquired while they walked with various backpack loads (no-load, 5%, 10%, 15%, and 20% of body weight) served as inputs into the model for predicting lumbosacral joint compression forces. The efficacy of two optimization-driven models, namely double linear optimization with constraints on muscle intensity and single linear optimization without any constraints, was investigated by comparing the resulting force profile with that provided by a current EMGAO approach.

RESULTS

The double and single linear optimization approaches predicted mean deviations in peak force of -5.1%, and -19.2% as well as root-mean-square differences in force profile of 16.2%, and 25.4%, respectively.

CONCLUSION

The double linear optimization approach was a relatively comparable estimator to the EMGAO approach in terms of its consistency, slight bias, and efficiency for predicting peak lumbosacral joint compression forces.

APPLICATION

The double linear optimization approach is a useful biomechanical model for estimating peak lumbar compression forces while walking with backpack loads.

Modified electromyography-assisted optimization approach for predicting lumbar spine loading while walking with backpack loads

This study modified an electromyography-assisted optimization approach for predicting lumbar spine loading while walking with backpack loads. The modified-electromyography-assisted optimization approach eliminated the electromyography measurement at maximal voluntary contraction and adopted a linear electromyography-force relationship. Moreover, an optimal lower boundary condition for muscle gain was introduced to constrain the trunk muscle co-activation. Anthropometric information of 10 healthy young men as well as their kinematic, kinetic, and electromyography data obtained while walking with backpack loads were used as inputs in this study. A computational algorithm was used to find and analyse the sensitivity of the optimal lower boundary condition for achieving minimum deviation of the modified-electromyography-assisted optimization approach from the electromyography-assisted optimization approach for predicting lumbosacral joint compression force. Results validated that the modified-electromyography-assisted optimization approach (at optimal lower boundary condition of 0.92) predicted on average, a non-significant deviation in peak lumbosacral joint compression force of -18 N, a standard error of 9 N, and a root mean square difference in force profile of 73.8 N. The modified-electromyography-assisted optimization approach simplified the experimental process by eliminating the electromyography measurement at maximal voluntary contraction and provided comparable estimations for lumbosacral joint compression force that is also applicable to patients or individuals having difficulty in performing the maximal voluntary contraction activity.

Normal force distribution and posture of a hand pressing on a flat surface

Hand strength data are needed to understand and predict hand postures and finger loads while placing the hand on an object or surface. This study aims to analyze the effect of hand posture and surface orientation on hand force while pressing a flat surface. Twelve participants, 6 females and 6 males ages 19-25, performed three exertions (100%, 30% and 10% MVC- Maximum Voluntary Contraction) perpendicular to a plate in 4 angles (-45°, 0°, 45° and 90° with respect to the horizontal plane) at elbow height. Exertions involved pushing in two postures: (1) whole hand and (2) constrained to only using the fingertips. Inter-digit joint angles were recorded to map hand and finger motions and estimate joint moments for each condition. Participants exerted twice the force when pushing with whole hand vs. fingertips. 72-75% of the total force was exerted over the base of the palm, while only 11-13% with the thumb for exertions at 90°, 45° or 0° plate angles. Males maximum force for pushing at 0°, 45° and 90° plates averaged 49% higher than females for the whole hand and 62% for the fingertips (p < 0.01). There was no significant sex difference (p > 0.05) for the -45° plate. Thumb joint loads were generally higher than the other individual fingers (p < 0.05) in all % MVC and accounted for 12% of total force during whole hand exertions. On average, joint moments were 30% higher during fingertip conditions vs. whole hand. Thumb and finger joint moment magnitudes when pushing the plate at 100% MVC indicated that Metacarpophalangeal (MCP) joint moments were higher (p < 0.05) than Distal Interphalangeal joints (DIP) and Proximal Interphalangeal joints (PIP) under whole hand and fingertips conditions.

Co-Activation, Estimated Anterior and Posterior Cruciate Ligament Forces, and Motor Unit Activation Strategies during the Time Course of Fatigue

This study aimed to combine co-activation as well as anterior and posterior cruciate ligament force estimations with the motor unit activation strategies employed by the primary muscles that are involved in the movement at the knee joint. Fourteen male subject performed 25 maximal concentric isokinetic leg extension muscle actions at 120 s⁻¹. Electromyographic and mechanomyographic signals from the vastus lateralis and bicep femoris, as well as force, were used to measure co-activation, and estimated anterior and posterior ligament forces during the time course of fatigue. There were decreases in quadriceps force and increases in hamstring force during the 25 leg extensions. The posterior cruciate ligament force was greater than the anterior cruciate ligament force during each leg extension. Both the posterior and anterior cruciate ligament forces decreased during the 25 leg extensions. Each muscle indicated unique neuromuscular responses, which may explain the decreases in quadriceps force and increases in the hamstring force. The combination of anterior and posterior cruciate ligament force estimation and motor unit activation strategies helped to provide a better understanding of the fatigue-related mechanism that was utilized to avoid injury and increase or maintain joint stability during the time course of fatigue.

Estimation of Muscle Contraction Forces and Joint Reaction Forces at the Low Back and Shoulder during Drywall Installation

Construction workers performing drywall installation are exposed to a variety of ergonomic hazards, including heavy material handling, repetitive motions and awkward postures. The rates of musculoskeletal injuries and disorders among drywall installers are very high, especially at the low back and shoulder. The unique characteristics of the work environment in the construction industry do not allow for applying objective ergonomic assessment instruments. Thus, biomechanical models and computer simulations were combined for a more comprehensive evaluation of ergonomic hazards. Utilizing Monte-Carlo simulation to generate the input for biomechanical models based on information from PATH (Posture, Activity, Tools, and Handling), a work-sampling based approach, the present study estimated the required muscle contraction forces and joint reaction forces at the low back and shoulder during a simulated 8-hour drywall installation workday. The results of this study also provided a database for future evaluations of ergonomic interventions on drywall installation work.

A Biomechanical Investigation of the Asymmetric Multiplier in the Revised NIOSH Lifting Equation

There is growing evidence, from epidemiological and biomechanical sources, that lifting performed in asymmetric postures is a risk factor for the development of a musculoskeletal injury. In the recent update of the NIOSH Lifting Guide, a linear Asymmetric Multiplier was added to account for this type of risk. The present study addresses the form of this Multiplier through analysis of several asymmetric lifting tasks. Both spinal loading and a derived metric of muscle injury risk were calculated as a function of asymmetry angle. The results suggest that there is a non-linear increase in injury risk with respect to asymmetry. Only moderate increases in risk were predicted for asymmetry of 0°–30°, and sharply increasing risk as asymmetry reaches 90°, implying that ergonomic intervention should be concentrated on tasks with the highest asymmetries.

Trunk Muscle Activations While Resisting Asymmetric Loads in a Laterally Bent Trunk Posture

Asymmetric material handling frequently results in lateral bending of the torso. Each of these factors have been linked via epidemiological investigations to the incidence of low back disorders (LBD). Very little literature is available which describes the response of the trunk muscles in situations which would be analogous to handling materials while bent to the side. Such activities are observed frequently in industrial settings, especially during the initial and final portions of a lift. The objective of the current study was to describe the internal response of the trunk muscles as asymmetric loads were applied to the laterally bent torso. Specifically, this investigation quantified the electromyographic activities (EMG) of 8 trunk muscles under conditions where the trunk was isometrically loaded while the trunk was maintained in a 20 degree laterally bent posture. Moments with a magnitudes of 20 and 40 Nm were applied to fifteen subjects. The direction of the external moments was varied in 30 degree increments completely around the subjects. The EMG data indicates that the muscles showed the greatest activity when they were in opposition to the load's sagittal and frontal plane moment. The muscle showing the largest response was the External Oblique. Significant activity was also observed under conditions in which muscles were creating an antagonistic moment in either the sagittal plane, the frontal plane, or in both planes.

Modelling Muscle and Joint Forces at the Glenohumeral Joint: Overview of a Current Study

A biomechanical model of the glenohumeral joint has been developed to investigate muscle and joint loading during real life three-dimensional activities. Based on a rigid body mechanics approach, the model incorporates algorithms to correct for curved muscle paths and bone geometry, providing realistic muscle orientation over a wide range of limb positions. An optimization routine has been incorporated, minimizing overall maximum muscle stress in the 26 individual muscle elements considered. The model utilizes anatomical muscle and bone data, subject anthropometric data, kinematics measured using a six-camera Vicon motion analysis system and hand loading measured using a force-plate and mobile six-component strain gauged force transducer developed for this project. A study of real life three-dimensional activities has been conducted using five fit male subjects. Normalized, averaged muscle and joint loading have been calculated for each activity. Muscle activation appears in good agreement with published electromyographic studies. Overall joint compressive and shear forces of up to 5 and 1.5 times body weight respectively have been calculated.

An integrated biomechanical modeling approach to the ergonomic evaluation of drywall installation

Three different methodologies: work sampling, computer simulation and biomechanical modeling, were integrated to study the physical demands of drywall installation. PATH (Posture, Activity, Tools, and Handling), a work-sampling based method, was used to quantify the percent of time that the drywall installers were conducting different activities with different body segment (trunk, arm, and leg) postures. Utilizing Monte-Carlo simulation to convert the categorical PATH data into continuous variables as inputs for the biomechanical models, the required muscle contraction forces and joint reaction forces at the low back (L4/L5) and shoulder (glenohumeral and sternoclavicular joints) were estimated for a typical eight-hour workday. To demonstrate the robustness of this modeling approach, a sensitivity analysis was conducted to examine the impact of some quantitative assumptions that have been made to facilitate the modeling approach. The results indicated that the modeling approach seemed to be the most sensitive to both the distribution of work cycles for a typical eight-hour workday and the distribution and values of Euler angles that are used to determine the "shoulder rhythm." Other assumptions including the distribution of trunk postures did not appear to have a significant impact on the model outputs. It was concluded that the integrated approach might provide an applicable examination of physical loads during the non-routine construction work, especially for those operations/tasks that have certain patterns/sequences for the workers to follow.

An optimization-based method for prediction of lumbar spine segmental kinematics from the measurements of thorax and pelvic kinematics

Given measurement difficulties, earlier modeling studies have often used some constant ratios to predict lumbar segmental kinematics from measurements of total lumbar kinematics. Recent imaging studies suggested distribution of lumbar kinematics across its vertebrae changes with trunk rotation, lumbar posture, and presence of load. An optimization-based method is presented and validated in this study to predict segmental kinematics from measured total lumbar kinematics. Specifically, a kinematics-driven biomechanical model of the spine is used in a heuristic optimization procedure to obtain a set of segmental kinematics that, when prescribed to the model, were associated with the minimum value for the sum of squared predicted muscle stresses across all the lower back muscles. Furthermore, spinal loads estimated using the predicted kinematics by the present method were compared with those estimated using constant ratios. Predicted segmental kinematics were in good agreement with those obtained by imaging with an average error of ~10%. Compared with those obtained using constant ratios, predicted spinal loads using segmental kinematics obtained here were in general smaller. In conclusion, the proposed method offers an alternative tool for improving model-based estimates of spinal loads where image-based measurement of lumbar kinematics is not feasible.

Comparative evaluation of six quantitative lifting tools to estimate spine loads during static activities

Different lifting analysis tools are commonly used to assess spinal loads and risk of injury. Distinct musculoskeletal models with various degrees of accuracy are employed in these tools affecting thus their relative accuracy in practical applications. The present study aims to compare predictions of six tools (HCBCF, LSBM, 3DSSPP, AnyBody, simple polynomial, and regression models) for the L4-L5 and L5-S1 compression and shear loads in twenty-six static activities with and without hand load. Significantly different spinal loads but relatively similar patterns for the compression (R(2) > 0.87) were computed. Regression models and AnyBody predicted intradiscal pressures in closer agreement with available in vivo measurements (RMSE ≈ 0.12 MPa). Due to the differences in predicted spinal loads, the estimated risk of injury alters depending on the tool used. Each tool is evaluated to identify its shortcomings and preferred application domains.

Vertebral size, bone density, and strength in men and women matched for age and areal spine BMD

To explore the possible mechanisms underlying sex-specific differences in skeletal fragility that may be obscured by two-dimensional areal bone mineral density (aBMD) measures, we compared quantitative computed tomography (QCT)-based vertebral bone measures among pairs of men and women from the Framingham Heart Study Multidetector Computed Tomography Study who were matched for age and spine aBMD. Measurements included vertebral body cross-sectional area (CSA, cm(2) ), trabecular volumetric BMD (Tb.vBMD, g/cm(3) ), integral volumetric BMD (Int.vBMD, g/cm(3) ), estimated vertebral compressive loading and strength (Newtons) at L3 , the factor-of-risk (load-to-strength ratio), and vertebral fracture prevalence. We identified 981 male-female pairs (1:1 matching) matched on age (± 1 year) and QCT-derived aBMD of L3 (± 1%), with an average age of 51 years (range 34 to 81 years). Matched for aBMD and age, men had 20% larger vertebral CSA, lower Int.vBMD (-8%) and Tb.vBMD (-9%), 10% greater vertebral compressive strength, 24% greater vertebral compressive loading, and 12% greater factor-of-risk than women (p < 0.0001 for all), as well as higher prevalence of vertebral fracture. After adjusting for height and weight, the differences in CSA and volumetric bone mineral density (vBMD) between men and women were attenuated but remained significant, whereas compressive strength was no longer different. In conclusion, vertebral size, morphology, and density differ significantly between men and women matched for age and spine aBMD, suggesting that men and women attain the same aBMD by different mechanisms. These results provide novel information regarding sex-specific differences in mechanisms that underlie vertebral fragility.

PREDICTION OF MUSCLE FORCES USING STATIC OPTIMIZATION FOR DIFFERENT CONTRACTILE CONDITIONS

In this study, we introduced a novel cost function for the prediction of individual muscle forces for a one degree-of-freedom musculoskeletal system. Unlike previous models, the new approach incorporates the instantaneous contractile conditions represented by the force-length and force-velocity relationships and accounts for physiological properties such as fiber type distribution and physiological cross-sectional area (PCSA) in the cost function. Using this cost function, it is possible to predict experimentally observed features of force-sharing among synergistic muscles that cannot be predicted using the classical approaches. Specifically, the new approach allows for predictions of force-sharing loops of agonistic muscles in one degree-of-freedom systems and for simultaneous increases in force in one muscle and decreases in a corresponding agonist. We concluded that the incorporation of the contractile conditions in the weighting of cost functions provides a natural way to incorporate observed force-sharing features in synergistic muscles that have eluded satisfactory description.

The ratio of thoracic to lumbar compression force is posture dependent

Despite the evidence suggesting that between 8% and 55% of manual labourers experience thoracic pain, research on spinal loading during occupational tasks has been almost invariably limited to the lumbar spine. In this study, we determined the ratio of thoracic to lumbar compression force and the relative risk of injury to each region in various postures. Compressive forces on the spine were calculated based on previously reported thoracic and lumbar intradiscal pressures and disc cross-sectional areas. Flexion postures were associated with an approximate doubling in lumbar compression force but only small increases (or even decreases) in thoracic compression. The ratio of thoracic to lumbar compression was above the tolerance ratio (i.e. the ratio of thoracic to lumbar compressive strength) during upright postures and below the tolerance ratio during flexion postures, indicating that upright postures may pose a greater relative risk of injury to the thoracic spine than to the lumbar spine. Practitioner summary: Previously reported thoracic and lumbar in vivo disc pressures during various postures were compared. The ratio of thoracic and lumbar compression increased during upright postures and decreased in flexed postures, indicating that upright postures may pose a greater risk of injury to the thoracic spine than to the lumbar spine.

Study protocol title: a prospective cohort study of low back pain

BACKGROUND

Few prospective cohort studies of workplace low back pain (LBP) with quantified job physical exposure have been performed. There are few prospective epidemiological studies for LBP occupational risk factors and reported data generally have few adjustments for many personal and psychosocial factors.

METHODS/DESIGN

A multi-center prospective cohort study has been incepted to quantify risk factors for LBP and potentially develop improved methods for designing and analyzing jobs. Due to the subjectivity of LBP, six measures of LBP are captured: 1) any LBP, 2) LBP ≥ 5/10 pain rating, 3) LBP with medication use, 4) LBP with healthcare provider visits, 5) LBP necessitating modified work duties and 6) LBP with lost work time. Workers have thus far been enrolled from 30 different employment settings in 4 diverse US states and performed widely varying work. At baseline, workers undergo laptop-administered questionnaires, structured interviews, and two standardized physical examinations to ascertain demographics, medical history, psychosocial factors, hobbies and physical activities, and current musculoskeletal disorders. All workers' jobs are individually measured for physical factors and are videotaped. Workers are followed monthly for the development of low back pain. Changes in jobs necessitate re-measure and re-videotaping of job physical factors. The lifetime cumulative incidence of low back pain will also include those with a past history of low back pain. Incident cases will exclude prevalent cases at baseline. Statistical methods planned include survival analyses and logistic regression.

DISCUSSION

Data analysis of a prospective cohort study of low back pain is underway and has successfully enrolled over 800 workers to date.

The effect of thoracic kyphosis and sagittal plane alignment on vertebral compressive loading

To better understand the biomechanical mechanisms underlying the association between hyperkyphosis of the thoracic spine and risk of vertebral fracture and other degenerative spinal pathology, we used a previously validated musculoskeletal model of the spine to determine how thoracic kyphosis angle and spinal posture affect vertebral compressive loading. We simulated an age-related increase in thoracic kyphosis (T(1) -T(12) Cobb angle 50-75 degrees) during two different activities (relaxed standing and standing with 5-kg weights in the hands) and three different posture conditions: (1) an increase in thoracic kyphosis with no postural adjustment (uncompensated posture); (2) an increase in thoracic kyphosis with a concomitant increase in pelvic tilt that maintains a stable center of mass and horizontal eye gaze (compensated posture); and (3) an increase in thoracic kyphosis with a concomitant increase in lumbar lordosis that also maintains a stable center of mass and horizontal eye gaze (congruent posture). For all posture conditions, compressive loading increased with increasing thoracic kyphosis, with loading increasing more in the thoracolumbar and lumbar regions than in the mid-thoracic region. Loading increased the most for the uncompensated posture, followed by the compensated posture, with the congruent posture almost completely mitigating any increases in loading with increased thoracic kyphosis. These findings indicate that both thoracic kyphosis and spinal posture influence vertebral loading during daily activities, implying that thoracic kyphosis measurements alone are not sufficient to characterize the impact of spinal curvature on vertebral loading.

Predictive equations for lumbar spine loads in load-dependent asymmetric one- and two-handed lifting activities

BACKGROUND

Asymmetric lifting activities are associated with low back pain.

METHODS

A finite element biomechanical model is used to estimate spinal loads during one- and two-handed asymmetric static lifting activities. Model input variables are thorax flexion angle, load magnitude as well as load sagittal and lateral positions while response variables are L4-L5 and L5-S1 disc compression and shear forces. A number of levels are considered for each input variable and all their possible combinations are introduced into the model. Robust yet user-friendly predictive equations that relate model responses to its inputs are established.

FINDINGS

Predictive equations with adequate goodness-of-fit (R(2) ranged from ~94% to 99%, P≤0.001) that relate spinal loads to task (input) variables are established. Contour plots are used to identify combinations of task variable levels that yield spine loads beyond the recommended limits. The effect of uncertainties in the measurements of asymmetry-related inputs on spinal loads is studied.

INTERPRETATION

A number of issues regarding the NIOSH asymmetry multiplier are discussed and it is concluded that this multiplier should depend on the trunk posture and be defined in terms of the load vertical and horizontal positions. Due to an imprecise adjustment of the handled load magnitude this multiplier inadequately controls the biomechanical loading of the spine. Ergonomists and bioengineers, faced with the dilemma of using either complex but more accurate models on one hand or less accurate but simple models on the other hand, have hereby easy-to-use predictive equations that quantify spinal loads under various occupational tasks.

Potential of the Pseudo-Inverse Method as a Constrained Static Optimization for Musculo-Tendon Forces Prediction

Inverse dynamics combined with a constrained static optimization analysis has often been proposed to solve the muscular redundancy problem. Typically, the optimization problem consists in a cost function to be minimized and some equality and inequality constraints to be fulfilled. Penalty-based and Lagrange multipliers methods are common optimization methods for the equality constraints management. More recently, the pseudo-inverse method has been introduced in the field of biomechanics. The purpose of this paper is to evaluate the ability and the efficiency of this new method to solve the muscular redundancy problem, by comparing respectively the musculo-tendon forces prediction and its cost-effectiveness against common optimization methods. Since algorithm efficiency and equality constraints fulfillment highly belong to the optimization method, a two-phase procedure is proposed in order to identify and compare the complexity of the cost function, the number of iterations needed to find a solution and the computational time of the penalty-based method, the Lagrange multipliers method and pseudo-inverse method. Using a 2D knee musculo-skeletal model in an isometric context, the study of the cost functions isovalue curves shows that the solution space is 2D with the penalty-based method, 3D with the Lagrange multipliers method and 1D with the pseudo-inverse method. The minimal cost function area (defined as the area corresponding to 5% over the minimal cost) obtained for the pseudo-inverse method is very limited and along the solution space line, whereas the minimal cost function area obtained for other methods are larger or more complex. Moreover, when using a 3D lower limb musculo-skeletal model during a gait cycle simulation, the pseudo-inverse method provides the lowest number of iterations while Lagrange multipliers and pseudo-inverse method have almost the same computational time. The pseudo-inverse method, by providing a better suited cost function and an efficient computational framework, seems to be adapted to the muscular redundancy problem resolution in case of linear equality constraints. Moreover, by reducing the solution space, this method could be a unique opportunity to introduce optimization methods for a posteriori articulation of preference in order to provide a palette of solutions rather than a unique solution based on a lot of hypotheses.

QCT measures of bone strength at the thoracic and lumbar spine: the Framingham Study

We used volumetric quantitative computed tomography (QCT) scans to evaluate volumetric bone density (vBMD), geometry, and strength in the thoracic (T8 to T10) and lumbar (L3 to L5) spine and determined how these parameters varied with age, sex, and spinal region. Participants included 690 participants of the Framingham Study, 40 to 87 years old (mean, 61 years). In both women and men, trabecular vBMD declined with age similarly for lumbar and thoracic regions, whereas cortical vBMD and integral vBMD, vertebral strength, and compressive force declined more at the lumbar spine than thoracic spine (interaction, p < 0.01). Notably, in men, cortical vBMD increased (β = 0.0004, p = 0.01), and vertebral strength did not change (β = 1.9305, p = 0.66) at the thoracic spine with age. In both women and men, vertebral cross-sectional area increased less and the factor-of-risk increased more with age at the lumbar than at the thoracic region (interaction, p < 0.01). For example, in women, the factor-of-risk for forward flexion increased (worsened) with age 6.8-fold more in the lumbar spine (β = 0.0157), compared with the thoracic spine (β = 0.0023). vBMD and vertebral strength declined more and the factor-of-risk increased more with age in women than men (interaction, p < 0.01). For instance, integral vBMD for the lumbar spine declined 36% from 40 to 75 years of age in women compared with 18% in men. There was little or no age-related change in the forces applied to the thoracic vertebrae in either women or men. Age-related changes were greater in the lumbar spine than in the thoracic region and greater in women than men. Whereas women lost bone density and strength at both the thoracic and lumbar spine, in men, vertebral strength declined only at the lumbar spine. Our study confirms the importance of evaluating determinants of vertebral strength in both the thoracic and lumbar spine and in both women and men to understand mechanisms underlying the structural failure of vertebral bodies with aging.

Developing physical exposure-based back injury risk models applicable to manual handling jobs in distribution centers

Using our ultrasound-based "Moment Monitor," exposures to biomechanical low back disorder risk factors were quantified in 195 volunteers who worked in 50 different distribution center jobs. Low back injury rates, determined from a retrospective examination of each company's Occupational Safety and Health Administration (OSHA) 300 records over the 3-year period immediately prior to data collection, were used to classify each job's back injury risk level. The analyses focused on the factors differentiating the high-risk jobs (those having had 12 or more back injuries/200,000 hr of exposure) from the low-risk jobs (those defined as having no back injuries in the preceding 3 years). Univariate analyses indicated that measures of load moment exposure and force application could distinguish between high (n = 15) and low (n = 15) back injury risk distribution center jobs. A three-factor multiple logistic regression model capable of predicting high-risk jobs with very good sensitivity (87%) and specificity (73%) indicated that risk could be assessed using the mean across the sampled lifts of the peak forward and or lateral bending dynamic load moments that occurred during each lift, the mean of the peak push/pull forces across the sampled lifts, and the mean duration of the non-load exposure periods. A surrogate model, one that does not require the Moment Monitor equipment to assess a job's back injury risk, was identified although with some compromise in model sensitivity relative to the original model.

An inverse optimization approach for determining weights of joint displacement objective function for upper body kinematic posture prediction

Human posture prediction can often be formulated as a nonlinear multiobjective optimization (MOO) problem. The joint displacement function is considered as a benchmark of human performance measures. When the joint displacement function is used as the objective function, posture prediction is a MOO problem. The weighted-sum method is commonly used to find a Pareto solution of this MOO problem. Within the joint displacement function, the relative value of the weights associated with each joint represents the relative importance of that joint. Usually, weights are determined by trial and error approaches. This paper presents a systematic approach via an inverse optimization approach to determine the weights for the joint displacement function in posture prediction. This inverse optimization problem can be formulated as a bi-level optimization problem. The design variables are joint angles and weights. The cost function is the summation of the differences between two set of joint angles (the design variables and the realistic posture). Constraints include (1) normalized weights within limits and (2) an inner optimization problem to solve for joint angles (predicted posture). Additional constraints such as weight limits and weight linear equality constraints, obtained through observations, are also implemented in the formulation to test the method. A 24 degree of freedom human upper body model is used to study the formulation and visualize the prediction. An in-house motion capture system is used to obtain the realistic posture. Four different percentiles of subjects are selected to run the experiment. The set of weights for the general seated posture prediction is obtained by averaging all weights for all subjects and all tasks. On the basis of obtained set of weights, the predicted postures match the experimental results well.

A biomechanical model for estimating loads on thoracic and lumbar vertebrae

BACKGROUND

Biomechanical models are commonly used to estimate loads on the spine. Current models have focused on understanding the etiology of low back pain and have not included thoracic vertebral levels. Using experimental data on the stiffness of the thoracic spine, ribcage, and sternum, we developed a new quasi-static stiffness-based biomechanical model to calculate loads on the thoracic and lumbar spine during bending or lifting tasks.

METHODS

To assess the sensitivity of the model to our key assumptions, we determined the effect of varying ribcage and sternal stiffness, maximum muscle stress, and objective function on predicted spinal loads. We compared estimates of spinal loading obtained with our model to previously reported in vivo intradiscal pressures and muscle activation patterns.

FINDINGS

Inclusion of the ribs and sternum caused an average decrease in vertebral compressive force of 33% for forward flexion and 18% in a lateral moment task. The impact of maximum muscle stress on vertebral force was limited to a narrow range of values. Compressive forces predicted by our model were strongly correlated to in vivo intradiscal pressure measurements in the thoracic (r=0.95) and lumbar (r=1) spine. Predicted trunk muscle activity was also strongly correlated (r=0.95) with previously published EMG data from the lumbar spine.

INTERPRETATION

The consistency and accuracy of the model predictions appear to be sufficient to justify the use of this model for investigating the relationships between applied loads and injury to the thoracic spine during quasi-static loading activities.

Evaluation of change in muscle activity as a result of posterior lumbar spine surgery using a dynamic modeling system

STUDY DESIGN

A commercially available musculoskeletal model of the lumbar spine was modified to study the change in muscle activation as a result of posterior lumbar surgery at the L3-L4 and L4-L5 segments.

OBJECTIVE

To evaluate how graded resection of the lumbar paraspinal muscles as a result of posterior lumbar surgery affects muscle activity for a variety of movement tasks.

SUMMARY OF BACKGROUND DATA

Several in vivo studies compare the change in functional outcome of the paraspinal muscles following surgery. However, due to limitations that exist with current in vivo methods no study to date has been able to quantitatively examine how the function of individual muscles in the lumbar spine change in response to different levels of injury.

METHODS

A multibody dynamic musculoskeletal model of the lumbar spine was modified to measure muscle activity using a parametric examination of change in the cross-sectional area of muscles affected by posterior lumbar surgery.

RESULTS

This study shows that the reduction in muscle cross-sectional area as a result of posterior lumbar surgery at L3-L4 and L4-L5 results in a change in trunk muscle activity where the greatest change occurs during axial rotation and lateral bending. The results suggest that preservation of the posterior paraspinal musculature results in greater preservation of the normal muscle activity than traditional open techniques.

CONCLUSION

Preservation of the paraspinal musculature associated with minimally invasive surgical approaches to the lumbar better preserve postoperative muscle activity. This study suggests that there is a positive correlation between the reduction of paraspinal muscle cross-sectional area following posterior lumbar spine surgery and the alteration in trunk muscle activity.

Multi-objective optimization-based method for kinematic posture prediction: development and validation

Posture prediction plays an important role in product design and manufacturing. There is a need to develop a more efficient method for predicting realistic human posture. This paper presents a method based on multi-objective optimization (MOO) for kinematic posture prediction and experimental validation. The predicted posture is formulated as a multi-objective optimization problem. The hypothesis is that human performance measures (cost functions) govern how humans move. Twelve subjects, divided into four groups according to different percentiles, participated in the experiment. Four realistic in-vehicle tasks requiring both simple and complex functionality of the human simulations were chosen. The subjects were asked to reach the four target points, and the joint centers for the wrist, elbow, and shoulder and the joint angle of the elbow were recorded using a motion capture system. We used these data to validate our model. The validation criteria comprise R-square and confidence intervals. Various physics factors were included in human performance measures. The weighted sum of different human performance measures was used as the objective function for posture prediction. A two-domain approach was also investigated to validate the simulated postures. The coefficients of determinant for both within-percentiles and cross-percentiles are larger than 0.70. The MOO-based approach can predict realistic upper body postures in real time and can easily incorporate different scenarios in the formulation. This validated method can be deployed in the digital human package as a design tool.

Effect of chain wheel shape on crank torque, freely chosen pedal rate, and physiological responses during submaximal cycling

The development of noncircular chain wheels for the enhancement of cycling performance has been in progress for a long time and continues apace. In this study we tested whether submaximal cycling using a non-circular (Biopace) versus a circular chain wheel resulted in lower peak crank torque at preset pedal rates as well as resulting in lower pedal rate and metabolic response at freely chosen pedal rate. Ten trained cyclists (mean+/-SD: 27+/-3 years of age, 182+/-4 cm tall, 77.5+/-7.0 kg of body mass, and peak oxygen uptake of 61.7+/-4.4 ml kg(-1) min(-1)) cycled with a Biopace and a circular chain wheel at 180 W at 65 and 90 rpm for recording of crank torque profiles, and at their freely chosen pedal rate for recording of pedal rate and metabolic response, including oxygen uptake and blood lactate concentration. Crank torque profiles were similar between the two chain wheels during cycling at preset pedal rates. During cycling at the freely chosen pedal rate (being 93+/-6 and 93+/-4 rpm for the Biopace and circular chain wheel, respectively), blood lactate concentration was significantly different between the two chain wheels, being on average 0.2 mmol l(-1) lower with the Biopace chain wheel. A musculoskeletal simulation model supported the idea that a contributing factor to the observed difference in blood lactate concentration may be slightly reduced muscle activity around the phase where peak crank torque occurs during cycling with the Biopace chain wheel. In that particular phase of the crank revolution, the observed slightly lower muscle activity may result from larger transfer of energy from the legs to the crank.

Applications of biomechanics for prevention of work-related musculoskeletal disorders

This paper summarises applications of biomechanical principles and models in industry to control musculoskeletal disorders of the low back and upper extremity. Applications of 2-D and 3-D biomechanical models to estimate compressive force on the low back, the strength requirements of jobs, application of guidelines for overhead work and application of strain index and threshold limit value to address distal upper extremity musculoskeletal disorders are presented. Several case studies applied in the railroad industry, manufacturing, healthcare and warehousing are presented. Finally, future developments needed for improved biomechanical applications in industry are discussed. The information presented will be of value to practising ergonomists to recognise how biomechanics has played a significant role in identifying causes of musculoskeletal disorders and controlling them in the workplace. In particular, the information presented will help practising ergonomists with how physical stresses can be objectively quantified.

The evolving role of biomechanics in prevention of overexertion injuries

This paper describes occupational biomechanics as an evolving body of knowledge that has required not only a sophisticated development of fundamental biomechanical principles and human failure data, but also has required epidemiological information to enable a more complete understanding of how certain types of musculoskeletal injuries can be caused by specific physical work requirements. It also is argued that even with adequate biomechanical and epidemiological information, the ability to change working conditions and manual task requirements in companies required management and workers to become organised into formal ergonomics teams that could be trained and empowered to reduce the known biomechanical risk factors present in various jobs. It is demonstrated that in the last 35 years occupational biomechanics research continues to provide the intellectual machine that is driving the development of important ergonomics guidelines. Despite these successes, however, some major limitations in contemporary biomechanics knowledge are discussed, particularly related to situations where high-speed motions and repetitions are involved. Finally, the evolving importance and limitations in occupational biomechanical simulation models for proactive ergonomics are presented.

An integer programming model for optimizing shoulder rehabilitation

Strength restoration is one goal of shoulder rehabilitation following rotator cuff repair surgery. However, the time spent in a physical rehabilitation setting is limited. The objective of this study was to develop a novel mathematical formulation for determining the optimal shoulder rehabilitation exercise protocol to restore normal shoulder strength given a time-constrained rehabilitation session. Strength gain was modeled using a linear dose-response function and biomechanical parameters of the shoulder musculature. Two different objective functions were tested: (1) one based on a least squares support vector machine using healthy and pathologic shoulder strengths (normative objective function), and (2) one which seeks to match the strength of the contralateral shoulder (contralateral objective function). The normative objective function was subject-independent and the optimal protocol consisted of four sets each of adduction and external rotation. The contralateral objective function was subject-specific and the typical optimal protocol consisted of various set combinations of abduction and internal and external rotation. These results are only partially consistent with current practice. Improvement of the current model is dependent on a better understanding of strength training adaptation and shoulder rehabilitation.

Estimation of compressive forces on lumbar spine from categorical posture data

To combine estimates of trunk posture and force into an integrated measure of load on the low back, continuous variables for body angles were estimated by assuming specified distributions within corresponding posture categories with Monte-Carlo (MC) simulation. The estimated posture angles were compared with reference measurements from the Lumbar Motion Monitor and inclinometers. The lumbar compression estimates, generated from simulated posture angles and from direct measurement, were compared. Trunk flexion showed high correlation between direct measurements and simulated angles, as did L5/S1 compression. The MC approach to extracting continuous posture angles from categorized observations did not appear to introduce large error in the variables used to estimate spinal compressive forces. When instrumentation methods of postural assessment are not feasible, a simulation approach combined with biomechanical modelling could be used to integrate multiple external exposure variables into estimates of compressive forces acting on the low back.

The assessment of ankle joint forces during the postural balance control movement

The purpose of this study was to calculate three-dimensional angular displacements, moments and joint reaction forces of the ankle joint during the waist pulling, and then, we assessed the reaction forces and bone-on-bone forces within ankle joint during postural balance control movement. With experiments and MATLAB simulation we could calculate ankle joint kinematic and kinetic data. The results presented in this study will be useful data for understanding the injury mechanism of ankle joint during postural balance control.

Model-based estimation of muscle forces exerted during movements

Estimation of individual muscle forces during human movement can provide insight into neural control and tissue loading and can thus contribute to improved diagnosis and management of both neurological and orthopaedic conditions. Direct measurement of muscle forces is generally not feasible in a clinical setting, and non-invasive methods based on musculoskeletal modeling should therefore be considered. The current state of the art in clinical movement analysis is that resultant joint torques can be reliably estimated from motion data and external forces (inverse dynamic analysis). Static optimization methods to transform joint torques into estimates of individual muscle forces using musculoskeletal models, have been known for several decades. To date however, none of these methods have been successfully translated into clinical practice. The main obstacles are the lack of studies reporting successful validation of muscle force estimates, and the lack of user-friendly and efficient computer software. Recent advances in forward dynamics methods have opened up new opportunities. Forward dynamic optimization can be performed such that solutions are less dependent on measured kinematics and ground reaction forces, and are consistent with additional knowledge, such as the force-length-velocity-activation relationships of the muscles, and with observed electromyography signals during movement. We conclude that clinical applications of current research should be encouraged, supported by further development of computational tools and research into new algorithms for muscle force estimation and their validation.

Effects of EMG processing on biomechanical models of muscle joint systems: Sensitivity of trunk muscle moments, spinal forces, and stability

Biomechanical models are in use to estimate parameters such as contact forces and stability at various joints. In one class of these models, surface electromyography (EMG) is used to address the problem of mechanical indeterminacy such that individual muscle activation patterns are accounted for. Unfortunately, because of the stochastical properties of EMG signals, EMG based estimates of muscle force suffer from substantial estimation errors. Recent studies have shown that improvements in muscle force estimation can be achieved through adequate EMG processing, specifically whitening and high-pass (HP) filtering of the signals. The aim of this paper is to determine the effect of such processing on outcomes of a biomechanical model of the lumbosacral joint and surrounding musculature. Goodness of fit of estimated muscle moments to net moments and also estimated joint stability significantly increased with increasing cut-off frequencies in HP filtering, whereas no effect on joint contact forces was found. Whitening resulted in moment estimations comparable to those obtained from optimal HP filtering with cut-off frequencies over 250 Hz. Moreover, compared to HP filtering, whitening led to a further increase in estimated joint-stability. Based on theoretical models and on our experimental results, we hypothesize that the processing leads to an increase in pick-up area. This then would explain the improvements from a better balance between deep and superficial motor unit contributions to the signal.

Anatomy and biomechanics of the back muscles in the lumbar spine with reference to biomechanical modeling

STUDY DESIGN

This article describes the development of a musculoskeletal model of the human lumbar spine with focus on back muscles. It includes data from literature in a structured form.

OBJECTIVE

To review the anatomy and biomechanics of the back muscles related to the lumbar spine with relevance for biomechanical modeling.

SUMMARY OF BACKGROUND DATA

To reduce complexity, muscle units have been incorporated in an abridged manner, reducing their actions more or less to a single force equivalent. In early models of the lumbar spine, this may have been a necessary step to reduce complexity and, thereby, calculation time. The muscles of the spine are well described in the literature, but mainly qualitatively. Most of the literature provides a description of the structures without precise data of fiber length, muscle length, cross-sectional areas, moment arms, forces, etc. The predicted output of musculoskeletal models is very much dependent on the input parameters. The information needed to improve models consists of better approximations of the attachments to the vertebrae, and more precise data.

METHOD

Review of literature.

RESULTS

The predicted output of musculoskeletal models is very much dependent on the input parameters. Moderate changes in the assumed muscle line-of-action (i.e., moment arm) could substantially alter the magnitudes of predicted muscle and spinal forces, while the choice of optimization formulation is less sensitive.

CONCLUSIONS

Input parameters, moment arms, as well as physiologic cross-sectional areas have a profound effect on the predicted muscle forces. Therefore, it is important to choose the values for moment arm and physiologic cross-sectional area carefully because they are essential input parameters to biomechanical models.

Sensitivity of kinematics-based model predictions to optimization criteria in static lifting tasks

The effect of eight different cost functions on trunk muscle forces, spinal loads and stability was investigated. Kinematics-based approach combined with nonlinear finite element modeling and optimization were used to model in vivo measurements on isometric forward flexions at approximately 40 degrees and approximately 65 degrees in sagittal plane with or without a load of 180N in hands. Four nonlinear (summation stress(3), summation stress(2), summation force(2) and muscle fatigue) and four linear (summation stress, summation force, axial compression and double-linear) criteria were considered. Predicted muscle activities were compared with measured EMG data. All predictions, irrespective of the cost function used, satisfied required kinetic, kinematics and stability conditions all along the spine. Four criteria (summation stress(3), summation stress(2), fatigue and double-linear) predicted muscle activities that qualitatively matched measured EMG data. The fatigue and double-linear criteria were inadequate in predicting greater forces in larger muscles with no consideration for their moment arms. Nearly the same stability margin was computed under these four cost functions. At the lower lumbar levels, the compression forces differed by <20% and the shear forces by <14% as various cost functions were considered. Smaller axial compression and anterior shear forces (by less than or approximately equal 6%) were computed when only the active components rather than the total muscle forces were taken as unknown in the summation stress(3) cost function. Overall, one single cost function of summation stress(2) or summation stress(3) rather than a multi-criteria one was found sufficient and adequate in yielding plausible results comparable with measured EMG activities and disc pressure.

Representing and identifying alternative movement techniques for goal-directed manual tasks

Differences in motion patterns subserving the same movement goal can be identified qualitatively. These alternatives, which may characterize 'movement techniques' (e.g., the stoop and the squat lifting technique), may be associated with significantly different biomechanical constraints and physiological responses. Despite the widely shared understanding of the significance of alternative movement techniques, quantitative representation and identification of movement techniques have received little attention, especially for three-dimensional whole-body motions. In an attempt to systematically differentiate movement techniques, this study introduces a quantitative index termed joint contribution vector (JCV) representing a motion in terms of contributions of individual joint degrees-of-freedom to the achievement of the task goal. Given a set of uncharacterized (unlabeled) motions represented by joint angle trajectories (motion capture data), the JCV and statistical clustering methods enable automated motion classification to uncover a taxonomy of alternative movement techniques. The results of our motion data analyses show that the JCV was able to characterize and discern stoop and squat lifting motions, and also to identify movement techniques for a three-dimensional, whole-body, one-handed load-transfer task. The JCV index would facilitate consideration of alternative movement techniques in a variety of applications, including work method comparison and selection, and human motion modeling and simulation.

Constraining spine stability levels in an optimization model leads to the prediction of trunk muscle cocontraction and improved spine compression force estimates

A major limitation of optimization models of the spine has been the inability to accurately predict trunk muscle co-activity. Antagonist muscle activity is thought to be necessary to maintain adequate levels of spine stability but, in turn, creates increased loading on the spine. It is thus hypothesized that the CNS attempts to optimize the relationship between spine loading and spine stability in determining muscular activation patterns. This study presents an optimization model of the spine in which stability was constrained to target levels predicted from regression equations of independent loading variables. Objective functions were set to either minimize the sum of the cubed muscle forces or minimize the sum of the squared intervertebral forces at the L4-L5 disc level. Results demonstrate that the inclusion of stability constraints in optimization simulations produced realistic predictions of antagonist muscle activity and predictions of spine compression levels that agree more closely with EMG-based estimates, compared to simulations in which stability was unconstrained. It was concluded that spinal stability is a vital consideration for the CNS when dictating trunk muscle recruitment patterns.

Combination of finite element modeling and optimization for the study of lumbar spine biomechanics considering the 3D thorax-pelvis orientation

A model of the lumbar spine capable of taking into account realistic loads derived from human activity would be of great benefit in studying its normal biomechanical functioning as well as its in vivo behavior in injured and surgically altered states. This paper proposes a method to analyze the mechanical response of the lumbar spine subjected to loads derived from human activity, combining a non-linear finite element model (FEM) and an optimization-based force predicting algorithm. Loads borne by the lumbar spine at the T12-L1 level (joint loads) are first predicted with the optimization algorithm and then applied to the FEM, while a boundary condition prescribing the relative L1-sacrum rotation is imposed onto the FEM to account for three-dimensional physiological thorax-pelvis orientation. The prescribed rotation is achieved through the application of moments on L1. To account for the effect of these moments on lumbar joint loads, an iteration between the optimization technique and the FEM computation has been carried out. This method provides two main benefits over previous studies: first, it allows for the application of any 3D loading condition while considering the real 3D rotation measured between the thorax and the pelvis, and second, it makes it possible to estimate the moments that must be applied on L1 in order to maintain this rotation, taking them into account when predicting joint loads. As an example application of the method, results are presented for the lumbar spine mechanical response at the time of peak T12-L1 joint force during walking.