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

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

Investigation of optimal follower load path generated by trunk muscle coordination

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

The effect of lateral eccentricity on failure loads,kinematics, and canal occlusions of the cervical spine in axial loading

Current neck injury criteria do not include limits for lateral bending combined with axial compression and this has been observed as a clinically relevant mechanism, particularly for rollover motor vehicle crashes. The primary objectives of this study were to evaluate the effects of lateral eccentricity (the perpendicular distance from the axial force to the centre of the spine) on peak loads, kinematics, and spinal canal occlusions of subaxial cervical spine specimens tested in dynamic axial compression (0.5 m/s). Twelve 3-vertebra human cadaver cervical spine specimens were tested in two groups: low and high eccentricity with initial eccentricities of 1 and 150% of the lateral diameter of the vertebral body. Six-axis loads inferior to the specimen, kinematics of the superior-most vertebra, and spinal canal occlusions were measured. High speed video was collected and acoustic emission (AE) sensors were used to define the time of injury. The effects of eccentricity on peak loads, kinematics, and canal occlusions were evaluated using unpaired Student t-tests. The high eccentricity group had lower peak axial forces (1544±629 vs. 4296±1693 N), inferior displacements (0.2±1.0 vs. 6.6±2.0 mm), and canal occlusions (27±5 vs. 53±15%) and higher peak ipsilateral bending moments (53±17 vs. 3±18 Nm), ipsilateral bending rotations (22±3 vs. 1±2°), and ipsilateral displacements (4.5±1.4 vs. −1.0±1.3 mm, p<0.05 for all comparisons). These results provide new insights to develop prevention, recognition, and treatment strategies for compressive cervical spine injuries with lateral eccentricities.     

Abdominal muscle activation changes if the purpose is to control pelvis motion or thorax motion

The aim of this study was to compare trunk muscular recruitment and lumbar spine kinematics when motion was constrained to either the thorax or the pelvis. Nine healthy women performed four upright standing planar movements (rotations, anterior–posterior translations, medial–lateral translations, and horizontal circles) while constraining pelvis motion and moving the thorax or moving the pelvis while minimizing thorax motion, and four isometric trunk exercises (conventional curl-up, reverse curl-up, cross curl-up, and reverse cross curl-up). Surface EMG (upper and lower rectus abdominis, lateral and medial aspects of external oblique, internal oblique, and latissimus dorsi) and 3D lumbar displacements were recorded. Pelvis movements produced higher EMG amplitudes of the oblique abdominals than thorax motions in most trials, and larger lumbar displacements in the medial–lateral translations and horizontal circles. Conversely, thorax movements produced larger rotational lumbar displacement than pelvis motions during rotations and higher EMG amplitudes for latissimus dorsi during rotations and anterior–posterior translations and for lower rectus abdominis during the crossed curl-ups. Thus, different neuromuscular compartments appear when the objective changes from pelvis to thorax motion. This would suggest that both movement patterns should be considered when planning spine stabilization programs, to optimize exercises for the movement and muscle activations desired.     

Evaluation of an electromagnetic position tracking device for measuring in vivo, dynamic joint kinematics

An electromagnetic position tracking device was evaluated to determine its static and dynamic accuracy and reliability for applications related to measuring in vivo joint kinematics. The device detected the position and orientation of small coiled sensors, maintained in an electromagnetic field. System output was measured against known translations or rotations throughout the measurement volume. Average translational errors during static testing were 0.1 +/- 0.04, 0.2 +/- 0.17, and 0.8 +/- 0.81 mm (mean+/-SD) for sensors 50, 300, and 550 mm away from the field generator, respectively. Average rotational errors were 0.4 +/- 0.31 degrees, 0.4 +/- 0.21 degrees, and 0.9 +/- 0.85 degrees (mean +/- SD) for sensors located at the same distances. Since we intended to use this system in an animal walking on a treadmill, we incrementally moved the sensors under various treadmill conditions. The effects of treadmill operation on translational accuracy were found to be negligible. The effects of dynamic motions on sensor-to-sensor distance were also assessed for future data collection in the animal. Sensor-to-sensor distance showed standard deviations of 2.6 mm and a range of 13 mm for the highest frequency tested (0.23 Hz). We conclude that this system is useful for static or slow dynamic motions, but is of limited use for obtaining gait kinematics at higher speeds.     

Effects of the rib cage on thoracic spine flexibility.

Besides protecting the internal organs of the thorax, the rib cage is the site of numerous muscle attachments. It also decreases the overall flexibility of the thoracic spine. This study developed finite element (FE) models of the thoracic spine with and without the rib cage, and the effects of the rib cage on thoracic spine flexibility were determined. The numerical models were validated by comparing the maximum rotation of the models for several loading cases with experimental data in the literature. After adapting the material properties for the discs and ligaments, the calculated maximum rotations differed from the measured median values by less than 1 degrees without the rib cage and by less than 2.5 degrees with it. The rib cage decreased the mean flexibility of the thoracic spine by 23% to 47%, depending on the loading plane. Assuming the ribs to be rigid beams required a corresponding reduction of ligament stiffnesses in order to achieve the same agreement of the maximum rotations with the measured median values. Interconnecting the FE thoracic spine model plus rib cage with the existing detailed FE lumbar spine model improves the simulation of force directions of muscles attached to the rib cage or thoracolumbar spine. In addition, such a model is suitable for determining the effects of lumbar spine implants on spinal balance.     

Comparative accuracy of radiostereometric and optical tracking systems

This study aims to quantify and compare the accuracy of traditional radiostereometric analysis (RSA), fluoroscopic RSA (fRSA), and optical tracking systems. Three phantoms were constructed, each having three stainless steel spheres and three reflective markers. One phantom was mounted to the base of a precision cross-slide table, one to the base of a precision rotation table, and the third was mounted to each moveable tabletop. Two dial-gauges, rigidly mounted to the cross-slide table and rotation table, quantified translations and rotations. Two fluoroscopy units placed orthogonally tracked the steel spheres while a four-camera optical motion capture system tracked the reflective markers in three-dimensional space. RSA was performed with both digital radiography and fluoroscopy. Three axes of translation were tested: parallel to one fluoroscopy image, parallel to the other fluoroscopy image, and at approximately 45° to each image. One axis of rotation was tested. Intraclass correlation coefficients indicated excellent agreement between the actual (dial-gauge) and measured translations for all modalities (ICCs>0.99) and excellent agreement between actual and measured rotations for RSA and fRSA (ICCs>0.99). Standard errors of measurement ranged from 0.032 mm and 0.121° for RSA, to 0.040 mm and 0.229° for fRSA, and to 0.109 mm and 0.613° for optical tracking. Differences between actual and measured translations along the 45° axis were significantly smaller than the two parallel axes. These findings suggest that under ideal conditions, accuracy of fRSA is comparable to traditional RSA, and superior to optical tracking. Accuracy is highest when measured at 45° to the fluoroscopy units.     

Influence of glenohumeral mismatch on bone strains and implant displacements in implanted glenoïds. An in vitro experimental study on cadaveric scapulae

In shoulder arthroplasty, there is no consensus about the ideal mismatch between a prosthetic humeral head and a glenoïd component. Thus, investigations into mismatch effects from a biomechanical point of view can be useful. The aim of this in vitro study was to help us understand mismatch influence on bone strains, translational forces in the joint and implant/bone displacements in implanted scapulae.

Five fresh cadaveric scapulae were implanted with a cemented keeled polyethylene implant. The lower part of the scapulae was embedded and the loadings were carried out using five metallic spheres simulating mismatches of 0, 2, 4, 5 and 6 mm. Loadings included a constant compressive preload of 392 N and an anterior, posterior, inferior and superior translation of 2.5 mm. We measured the transversal force necessary to produce the imposed translation, the strains at six locations around the peripheral cortex of the glenoïd using strain gages and the relative implant/bone displacements using CCD cameras.

Generally, the increase of mismatch reduced the translational forces, the strains around the glenoïd and, except for the anterior loading, the relative implant/bone displacements. Few and even no significant differences were observed when the mismatch varied from 0 to 2 mm; the number of significant differences increased when the mismatch varied from 0 to 4 mm and from 0 to 5 mm; the results obtained for a 0–6 mm variation in mismatch were comparable to those obtained for a 0–5 mm variation.

This study underlines that the mismatch has a significant effect on bone strains, relative implant/bone displacements and induced translational forces when a compressive preload and imposed translations were applied on implanted scapulae.     

Accuracy of mobile biplane X-ray imaging in measuring 6-degree-of-freedom patellofemoral kinematics during overground gait

The aim of this study was to evaluate the accuracy with which mobile biplane X-ray imaging can be used to measure patellofemoral kinematics of the intact knee during overground gait. A unique mobile X-ray imaging system tracked and recorded biplane fluoroscopic images of two human cadaver knees during simulated overground walking at a speed of 0.7 m/s. Six-degree-of-freedom patellofemoral kinematics were calculated using a bone volumetric model-based method and the results then compared against those derived from a gold-standard bead-based method. RMS errors for patellar anterior translation, superior translation and lateral shift were 0.19 mm, 0.34 mm and 0.37 mm, respectively. RMS errors for patellar flexion, lateral tilt and lateral rotation were 1.08°, 1.15° and 1.46°, respectively. The maximum RMS error for patellofemoral translations was approximately one-half that reported previously for tibiofemoral translations using the same mobile X-ray imaging system while the maximum RMS error for patellofemoral rotations was nearly two times larger than corresponding errors reported for tibiofemoral rotations. The lower accuracy in measuring patellofemoral rotational motion is likely explained by the symmetric nature of the patellar geometry and the smaller size of the patella compared to the tibia.     

A finite helical axis as a landmark for kinematic reference of the knee

Reference coordinates based on the finite helical axis for flexion of the knee from 0 to 90 deg are proposed. Six degree-of-freedom tracking allows the use of such a helical axis as a kinematic landmark for knee motion representation. Data from five human subjects in vivo are presented as a path of finite helical axes for flexion of the knee from 20 to 80 deg. The finite helical axis rotates by an average of 11.4 deg, the centrode translates an average of 19.8 mm, and the total axial translation averages 0.1 mm during flexion from 20 to 80 deg. Error due to the transducer was measured on a fixed-pivot pendulum and found to be 1.0 deg and 1.9 mm rms for the helical axis orientation and position, respectively, and 0.1 mm for the axial translation. Reproducibility and soft tissue effects on the measurements were repeatable to 4.0 deg and 2.7 mm rms in orientation and position, respectively, and 0.1 mm for the axial translations. Soft tissue errors averaged 4.9 deg and 3.6 mm in position and orientation, and 0.3 mm in the axial translations.     

Structural behavior of human lumbar spinal motion segments

The objectives of this study were to obtain linearized stiffness matrices, and assess the linearity and hysteresis of the motion segments of the human lumbar spine under physiological conditions of axial preload and fluid environment. Also, the stiffness matrices were expressed in the form of an 'equivalent' structure that would give insights into the structural behavior of the spine. Mechanical properties of human cadaveric lumbar L2-3 and L4-5 spinal motion segments were measured in six degrees of freedom by recording forces when each of six principal displacements was applied. Each specimen was tested with axial compressive preloads of 0, 250 and 500 N. The displacements were four slow cycles of +/-0.5mm in anterior-posterior and lateral displacements, +/-0.35 mm axial displacement, +/-1.5 degrees lateral rotation and +/-1 degrees flexion-extension and torsional rotations. There were significant increases with magnitude of preload in the stiffness, hysteresis area (but not loss coefficient) and the linearity of the load-displacement relationship. The mean values of the diagonal and primary off-diagonal stiffness terms for intact motion segments increased significantly relative to values with no preload by an average factor of 1.71 and 2.11 with 250 and 500 N preload, respectively (all eight tests p<0.01). Half of the stiffness terms were greater at L4-5 than L2-3 at higher preloads. The linearized stiffness matrices at each preload magnitude were expressed as an equivalent structure consisting of a truss and a beam with a rigid posterior offset, whose geometrical properties varied with preload. These stiffness properties can be used in structural analyses of the lumbar spine.     

Translational constraint influences dynamic spinal canal occlusion of the thoracic spine: an in vitro experimental study

Mechanical constraints to spine motion can arise in a variety of real-world situations such as when shoulder belts prevent anterior translation of the thorax during automotive collisions. The effect of such constraint on spinal column-spinal cord interaction during injury remains unknown. The purpose of the present study was to compare maximal dynamic spinal canal occlusion, measured via a specialized transducer, in cadaveric upper thoracic spine specimens under a variety of anterior-posterior constraint conditions. Four injury models were produced using 24 cadaveric spine specimens (T1-T4). Incremental compressive trauma was applied under constrained (i.e. blocked anterior-posterior translation) flexion-compression, pure-compression and extension-compression, and under unconstrained (i.e. free anterior-posterior translation) flexion-compression. All displacements were applied at 500 mm/s. For all three constrained trauma groups, complete transducer occlusion occurred between 20 and 30 mm of compressive displacement. The extension-compression caused transducer occlusion significantly less than the other constrained models (p < 0.022) at 20 mm compression. For unconstrained flexion-compression, a compression of up to 50 mm resulted in a mean of 26% transducer occlusion. The constrained pure-compression tests led to burst fracture with significant body height loss at T2. The constrained flexion-compression and extension-compression tests caused fracture-dislocation injury at the T2-T3 level. Constrained trauma clearly led to more spinal canal occlusion than the unconstrained in these models, and more severe injury to the spinal column. The results add to our understanding of the effect of column injury pattern on spinal cord injury. This information has clear implications for the design of injury prevention devices.     

Can generic knee joint models improve the measurement of osteoarthritic knee kinematics during squatting activity?

Knee joint kinematics derived from multi-body optimisation (MBO) still requires evaluation. The objective of this study was to corroborate model-derived kinematics of osteoarthritic knees obtained using four generic knee joint models used in musculoskeletal modelling – spherical, hinge, degree-of-freedom coupling curves and parallel mechanism – against reference knee kinematics measured by stereo-radiography. Root mean square errors ranged from 0.7° to 23.4° for knee rotations and from 0.6 to 9.0 mm for knee displacements. Model-derived knee kinematics computed from generic knee joint models was inaccurate. Future developments and experiments should improve the reliability of osteoarthritic knee models in MBO and musculoskeletal modelling.     

Multi-body optimization with subject-specific knee models: performance at high knee flexion angles

When estimating knee kinematics from skin markers and stereophotogrammetry, multi-body optimization (MBO) has provided promising results for reducing soft tissue artefacts (STA), but can still be improved. The goal of this study was to assess the performance of MBO with subject-specific knee models at high knee flexion angles (up to 110°) against knee joint kinematics measured by magnetic resonance imaging. Eight subjects were recruited. MBO with subject-specific knee models was more effective in compensating STA compared to no kinematic and spherical constraints, in particular for joint displacements. Moreover, it seems to be more reliable over large ranges of knee flexion angle. The ranges of root mean square errors for knee rotations/displacements were 3.0°–9.2°/1.3–3.5 mm for subject-specific knee models, 6.8°–8.7°/6.0–12.4 mm without kinematic constraint and 7.1°–9.8°/4.9–12.5 mm for spherical constraints.     

Verification of predicted specimen-specific natural and implanted patellofemoral kinematics during simulated deep knee bend

Verified computational models represent an efficient method for studying the relationship between articular geometry, soft-tissue constraint, and patellofemoral (PF) mechanics. The current study was performed to evaluate an explicit finite element (FE) modeling approach for predicting PF kinematics in the natural and implanted knee. Experimental three-dimensional kinematic data were collected on four healthy cadaver specimens in their natural state and after total knee replacement in the Kansas knee simulator during a simulated deep knee bend activity. Specimen-specific FE models were created from medical images and CAD implant geometry, and included soft-tissue structures representing medial–lateral PF ligaments and the quadriceps tendon. Measured quadriceps loads and prescribed tibiofemoral kinematics were used to predict dynamic kinematics of an isolated PF joint between 10° and 110° femoral flexion. Model sensitivity analyses were performed to determine the effect of rigid or deformable patellar representations and perturbed PF ligament mechanical properties (pre-tension and stiffness) on model predictions and computational efficiency.Predicted PF kinematics from the deformable analyses showed average root mean square (RMS) differences for the natural and implanted states of less than 3.1° and 1.7 mm for all rotations and translations. Kinematic predictions with rigid bodies increased average RMS values slightly to 3.7° and 1.9 mm with a five-fold decrease in computational time. Two-fold increases and decreases in PF ligament initial strain and linear stiffness were found to most adversely affect kinematic predictions for flexion, internal–external tilt and inferior–superior translation in both natural and implanted states. The verified models could be used to further investigate the effects of component alignment or soft-tissue variability on natural and implant PF mechanics.     

A six-degree-of-freedom acoustic transducer for rotation and translation measurements across the knee

An acoustic transducer design to measure the relative translations and rotations across the knee with no mechanical coupling between the tibia and femur is presented. Platforms attached to femoral and tibial tracking fixtures hold acoustic sources and receivers, respectively. The distance from each source to each receiver is measured by the acoustic transit time and the translations and rotations across the knee joint are computed. For rotations less than 30 deg around the expected operating position, the resolution of the transducer is 0.3 deg; for translations less than 1.5 cm around the expected operating position, the resolution is 0.03 cm. Theoretical error analysis using a Monte Carlo method shows that the uncertainty in the measurement depends on the relative position of the sources and receivers. The analysis predicts the worst case resolution of the transducer as 0.09 cm in translation and 0.6 deg in rotation when the receiver platform is translated 8.0 cm parallel to the source platform. The transducer and fixturing system are demonstrated on a cadaver specimen for applied anterior force and applied internal-external rotation. Errors due to (soft tissue) motion of the transducer relative to the bone during in vivo measurements are assessed on the cadaver specimen. For internal-external rotation the error due to soft tissue motion is a maximum of 0.5 cm in translation and 1.8 deg in rotation. For applied anterior force the error due to soft tissue motion is a maximum of 0.16 cm in translation and 2.7 deg in rotation.     

Analysis of the interaction between vertebral lateral deviation and axial rotation in scoliosis

There is a lack of clear biomechanical analyses to explain the interaction of the lateral and axial deformity of the spine in idiopathic scoliosis. A finite element model which represented an isolated ligamentous spine with realistic elastic properties and idealized geometry was used to analyse this interaction. Three variations of this model were used to investigate two different hypotheses about the etiology of scoliosis and to define the forces required to produce a scoliosis deformity. The first hypothesis is that coupling within a motion segment produces the interaction between lateral deviation and axial rotation. The second hypothesis is that posterior tethering by soft tissues in the growing spine produces the observed interaction. Modeling of both hypotheses failed to produce the clinically observed pattern of interaction. Therefore, to find which biomechanical forces were required to produce an idealized scoliosis, prescribed displacements were applied to the model. Production of a double curve scoliosis of 10 degrees Cobb angles required lateral forces on the order of 20 N acting 40 mm anterior to the vertebral body centers. There do not appear to be any anatomic structures capable of producing such forces. Therefore, it seems unlikely that scoliosis deformity can be explained in terms of forces acting on the spine, and understanding of its origins may come from examination of other mechanisms such as asymmetric thoracic growth, or asymmetric vertebral development.     

Are coupled rotations in the lumbar spine largely due to the osseo-ligamentous anatomy?--a modeling study

Prior studies have found that primary rotations in the lumbar spine are accompanied by coupled out-of-plane rotations. However, it is not clear whether these accompanying rotations are primarily due to passive (discs, ligaments and facet joints) or active (muscles) spinal anatomy. The aim of this study was to use a finite element (FE) model of the lumbar spine to predict three-dimensional coupled rotations between the lumbar vertebrae, due to passive spinal structures alone. The FE model was subjected to physiologically observed whole lumbar spine rotations about in vivo centres of rotation. Model predictions were validated by comparison of intra-discal pressures and primary rotations with in vivo measurements and these showed close agreement. Predicted coupled rotations matched in vivo measurements for all primary motions except lateral bending. We suggest that coupled rotations accompanying primary motions in the sagittal (flexion/extension) and transverse (axial rotation) planes are primarily due to passive spinal structures. For lateral bending the muscles most likely play a key role in the coupled rotation of the spine.     

Combined measurement and modeling of specimen-specific knee mechanics for healthy and ACL-deficient conditions

Quantifying the mechanical environment at the knee is crucial for developing successful rehabilitation and surgical protocols. Computational models have been developed to complement in vitro studies, but are typically created to represent healthy conditions, and may not be useful in modeling pathology and repair. Thus, the objective of this study was to create finite element (FE) models of the natural knee, including specimen-specific tibiofemoral (TF) and patellofemoral (PF) soft tissue structures, and to evaluate joint mechanics in intact and ACL-deficient conditions. Simulated gait in a whole joint knee simulator was performed on two cadaveric specimens in an intact state and subsequently repeated following ACL resection. Simulated gait was performed using motor-actuated quadriceps, and loads at the hip and ankle. Specimen-specific FE models of these experiments were developed in both intact and ACL-deficient states. Model simulations compared kinematics and loading of the experimental TF and PF joints, with average RMS differences [max] of 3.0° [8.2°] and 2.1° [8.4°] in rotations, and 1.7 [3.0] and 2.5 [5.1] mm in translations, for intact and ACL-deficient states, respectively. The timing of peak quadriceps force during stance and swing phase of gait was accurately replicated within 2° of knee flexion and with an average error of 16.7% across specimens and pathology. Ligament recruitment patterns were unique in each specimen; recruitment variability was likely influenced by variations in ligament attachment locations. ACL resections demonstrated contrasting joint mechanics in the two specimens with altered knee motion shown in one specimen (up to 5 mm anterior tibial translation) while increased TF joint loading was shown in the other (up to 400 N).     

The finite displacements vector's method: an application to the scoliotic spine

This paper presents a vectorial method to directly obtain the components of the screw displacement between two positions of a body in a three-dimensional space (position of the helical axis of motion, rotation around this axis and translation along it). This method can be applied either to the case of a bone, moving with respect to the reference frame, or to the case of the relative motion of a joint; it gives exact formulae even if the displacements are finite; it generalizes the results (already published) obtained for finite displacements in the plane. The involved computation is easy, and the use of this method deals with only a small magnification of experimental errors. The technique of a screw displacement is applied to the vertebral segments of a scoliolic spine. The necessary data is taken from a couple of in-vivo X-rays. The goals of this study are: first, to describe the shape of the spine at each step of its evolution and second, to quantify the evolution in time of any segment of the spine between two states.