Biomechanical modeling of posterior instrumentation of the scoliotic spine

Scoliosis is a three-dimensional deformation of the spine that can be treated by vertebral fusion using surgical instrumentation. However, the optimal configuration of instrumentation remains controversial. Simulating the surgical maneuvers with personalized biomechanical models may provide an analytical tool to determine instrumentation configuration during the pre-operative planning. Finite element models used in surgical simulations display convergence difficulties as a result of discontinuities and stiffness differences between elements. A kinetic model using flexible mechanisms has been developed to address this problem, and this study presents its use in the simulation of Cotrel-Dubousset Horizon surgical maneuvers. The model of the spine is composed of rigid bodies corresponding to the thoracic and lumbar vertebrae, and flexible elements representing the intervertebral structures. The model was personalized to the geometry of three scoliotic patients (with a thoracic Cobb angle of 45 degrees, 49 degrees and 39 degrees ). Binary joints and kinematic constraints were used to represent the rod-implant-vertebra joints. The correction procedure was simulated using three steps: (1) Translation of hooks and screws on the first rod; (2) 90 degrees rod rotation; (3) Hooks and screws look-up on the rod. After the simulation, slight differences of 0-6 degrees were found for the thoracic spine scoliosis and the kyphosis, and of 1-8 degrees for the axial rotation of the apical vertebra and for the orientation of the plane of maximum deformity, compared to the real post-operative shape of the patient. Reaction loads at the vertebra-implant link were mostly below 1000 N, while reaction loads at the boundary conditions (representing the overall action of the surgeon) were in the range 7-470 N and maximum torque applied to the rod was 1.8 Nm. This kinetic modeling approach using flexible mechanisms provided a realistic representation of the surgical maneuvers. It may offer a tool to predict spinal geometry correction and assist in the pre-operative planning of surgical instrumentation of the scoliotic spine.     

The effect of passive vertebral rotation on pressure in the nucleus pulposus

To study the immediate effects of axial rotation on the intervertebral disc, six pig cadaver lumbar functional spinal units were exposed to rotations of up to 2 degrees, while disc height and intradiscal pressure were measured. The results showed that rotary movements are capable of causing an immediate increase in disc height and drop in nucleus pressure. However, the long-term effects were opposite in direction.     

Patient-specific finite element model of the spine and spinal cord to assess the neurological impact of scoliosis correction: preliminary application on two cases with and without intraoperative neurological complications

Scoliosis is a 3D deformation of the spine and rib cage. For severe cases, surgery with spine instrumentation is required to restore a balanced spine curvature. This surgical procedure may represent a neurological risk for the patient, especially during corrective maneuvers. This study aimed to computationally simulate the surgical instrumentation maneuvers on a patient-specific biomechanical model of the spine and spinal cord to assess and predict potential damage to the spinal cord and spinal nerves. A detailed finite element model (FEM) of the spine and spinal cord of a healthy subject was used as reference geometry. The FEM was personalized to the geometry of the patient using a 3D biplanar radiographic reconstruction technique and 3D dual kriging. Step by step surgical instrumentation maneuvers were simulated in order to assess the neurological risk associated to each maneuver. The surgical simulation methodology implemented was divided into two parts. First, a global multi-body simulation was used to extract the 3D displacement of six vertebral landmarks, which were then introduced as boundary conditions into the personalized FEM in order to reproduce the surgical procedure. The results of the FEM simulation for two cases were compared to published values on spinal cord neurological functional threshold. The efficiency of the reported method was checked considering one patient with neurological complications detected during surgery and one control patient. This comparison study showed that the patient-specific hybrid model reproduced successfully the biomechanics of neurological injury during scoliosis correction maneuvers.     

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.     

Assessment of non-invasive intervertebral motion measurements in the lumbar spine

This study compared the accuracy of new, FDA-approved, image-analysis software to conventional radiographic assessment techniques for the measurement of intervertebral motion. Six adult human cadaveric lumbar spines (L1-S1) were individually mounted in a custom Plexiglas device and electromagnetic sensors were rigidly mounted to the spinous processes of L3, L4, and L5. Lateral radiographs of the spines in neutral, full flexion, and full extension were digitized and analyzed both using the software and manually by three orthopedic surgeons. Compared to intervertebral rotations determined from the electromagnetic device, the errors in rotations reported by the software and surgeons were 0.47+/-0.24 degrees and 2.16+/-0.78 degrees , respectively. Rotations measured by the surgeons were significantly less accurate and more variable than that of the software (p<0.05).     

Impact of material and morphological parameters on the mechanical response of the lumbar spine – A finite element sensitivity study

Finite element models are frequently used to study lumbar spinal biomechanics. Deterministic models are used to reflect a certain configuration, including the means of geometrical and material properties, while probabilistic models account for the inherent variability in the population. Because model parameters are generally uncertain, their predictive power is frequently questioned. In the present study, we determined the sensitivities of spinal forces and motions to material parameters of intervertebral discs, vertebrae, and ligaments and to lumbar morphology. We performed 1200 model simulations using a generic model of the human lumbar spine loaded under pure moments. Coefficients of determination and of variation were determined for all parameter and response combinations. Material properties of the vertebrae displayed the least impact on results, whereas those of the discs and morphology impacted most. The most affected results were the axial compression forces in the vertebral body and in several ligaments during flexion and the facet-joint forces during extension. Intervertebral rotations were considerably affected only when several parameters were varied simultaneously. Results can be used to decide which model parameters require careful consideration in deterministic models and which parameters might be omitted in probabilistic studies. Findings allow quantitative estimation of a model׳s precision.     

Model-guided derivation of lumbar vertebral kinematics in vivo reveals the difference between external marker-defined and internal segmental rotations

This study investigated whether the external marker-defined spine inter-segmental rotation is different from the internal vertebral rotation, and explored how to estimate the latter from limited surface measurement. A kinematic model was first created to elucidate analytically the relation between the external and internal rotations. A novel approach guided by the model was proposed for deriving vertebral centers of rotation (CORs) from measured planar trajectories of skin-surface markers. The approach involved a recursive procedure for establishing local (anatomical) coordinate systems, and an optimization routine that identified the maximum-likelihood circles best fitting the marker trajectories in local coordinate systems. An experiment with 10 subjects (5 males and 5 females) was conducted to test the approach along with the model. Skin-surface markers were strategically placed over individual spinous processes and other body landmarks, and recorded by an opto-electronic system while sagittally symmetric load-lifting movements were being performed. For the majority (89%) of measured motions, the COR locations for lumbar vertebrae (L2-L5) were derived successfully: solutions resulting from the optimization routine met a convergence criterion governed by the model, and were in agreement with existing data from radiographic or cadaveric studies. Empirical results confirmed the differences between the external marker-defined inter-segmental motions and corresponding internal vertebral rotations (1.1-5.8 degrees on average, all statistically significant). The study demonstrated the necessity and viability of quantifying internal vertebral kinematics when utilizing non-invasive marker-based measurement for spine-related clinical diagnosis and biomechanical modeling.     

A method for the intravital measurement of interspinous kinematics.

A novel non-radiographic technique for objectively quantifying quasi-static or dynamic intervertebral motion of a spinal motion segment in vivo in human subjects is presented here. The intervertebral motion device (IMD) is an instrumented linkage transducer system which can continuously measure over time two-dimensional sagittal plane rigid-body motion. Three custom-built omega-shaped displacement transducers are utilized. The IMD is rigidly fixed to the spinous processes of the lumbar motion segment by means of two intraosseous pins. Knowing the mechanoelectrical behavior and geometric configuration of the IMD, the relative spatial motion between the vertebral bodies can be resolved into sagittal rotation, axial translation, and anterior-posterior shear translation. Static calibrations of the IMD in the ranges of +/- 4 degrees rotation and +/- 4 mm translation determined the absolute maximum errors to be 0.2 degree and 0.07 mm for rotation and translation measurements, respectively, with corresponding variances of 0.1 degrees and 0.03 mm. For use in the vibration environment, negligible motion artifact content was detected in the IMD output signals when excited at discrete frequencies of 5.0 and 8.0 Hz. The first natural frequency of the IMD, specific for this design, was measured at 16.25 Hz. This technique may be used to study in vivo the spinal kinematics in healthy lumbar motion segments and in patients suspected of having segmental instability, and can perhaps be of clinical diagnostic significance.     

Finite element simulation of spinal deformities correction by in situ contouring technique

Biomechanical models have been proposed in order to simulate the surgical correction of spinal deformities. With these models, different surgical correction techniques have been examined: distraction and rod rotation. The purpose of this study was to simulate another surgical correction technique: the in situ contouring technique. In this way, a comprehensive three-dimensional Finite Element (FE) model with patient-specific geometry and patient-specific mechanical properties was used. The simulation of the surgery took into account elasto-plastic behavior of the rod and multiple moments loading and unloading representing the surgical maneuvers. The simulations of two clinical cases of hyperkyphosis and scoliosis were coherent with the surgeon's experience. Moreover, the results of simulation were compared to post-operative 3D measurements. The mean differences were under 5 degrees for vertebral rotations and 5 mm for spinal lines. These simulations open the way for future predictive tools for surgical planning.     

Evaluation of Euler's angles with a least squares method for the study of lumbar spine motion

To analyse intervertebral movements, methods with a high level of accuracy are required. Stereoradiographic methods have been used for a number of years to describe intervertebral movements, but their major problem is to identify the same anatomical landmarks, not only on the pair of radiographs used for three-dimensional reconstruction, but also on all the pairs used to analyse the displacements. To minimize the errors due to the incorrect identification of anatomical landmarks, a least squares method to resolve the parameters of Euler's angles was validated by means of measurements made on a spine obtained from a cadaver. The accuracy of this method varied between 0.69° and 0.71° in rotation and between 0.28 mm and 0.77 mm in translation. In addition, this method significantly corrected the position of the anatomical landmarks. Euler's angles, used with a least squares estimate, can provide accurate and precise results.     

Finite Element Analysis of a New Pedicle Screw-Plate System for Minimally Invasive Transforaminal Lumbar Interbody Fusion

Purpose

Minimally invasive transforaminal lumbar interbody fusion (MI-TLIF) is increasingly popular for the surgical treatment of degenerative lumbar disc diseases. The constructs intended for segmental stability are varied in MI-TLIF. We adopted finite element (FE) analysis to compare the stability after different construct fixations using interbody cage with posterior pedicle screw-rod or pedicle screw-plate instrumentation system.

Methods

A L3–S1 FE model was modified to simulate decompression and fusion at L4–L5 segment. Fixation modes included unilateral plate (UP), unilateral rod (UR), bilateral plate (BP), bilateral rod (BR) and UP+UR fixation. The inferior surface of the S1 vertebra remained immobilized throughout the load simulation, and a bending moment of 7.5 Nm with 400N pre-load was applied on the L3 vertebra to recreate flexion, extension, lateral bending, and axial rotation. Range of motion (ROM) and Von Mises stress were evaluated for intact and instrumentation models in all loading planes.

Results

All reconstructive conditions displayed decreased motion at L4–L5. The pedicle screw-plate system offered equal ROM to pedicle screw-rod system in unilateral or bilateral fixation modes respectively. Pedicle screw stresses for plate system were 2.2 times greater than those for rod system in left lateral bending under unilateral fixation. Stresses for plate were 3.1 times greater than those for rod in right axial rotation under bilateral fixation. Stresses on intervertebral graft for plate system were similar to rod system in unilateral and bilateral fixation modes respectively. Increased ROM and posterior instrumentation stresses were observed in all loading modes with unilateral fixation compared with bilateral fixation in both systems.

Conclusions

Transforaminal lumbar interbody fusion augmentation with pedicle screw-plate system fixation increases fusion construct stability equally to the pedicle screw-rod system. Increased posterior instrumentation stresses are observed in all loading modes with plate fixation, and bilateral fixation could reduce stress concentration.     

Effect of the intra-abdominal pressure and the center of segmental body mass on the lumbar spine mechanics - a computational parametric study

Determination of physiological loads in human lumbar spine is critical for understanding the mechanisms of lumbar diseases and for designing surgical treatments. Computational models have been used widely to estimate the physiological loads of the spine during simulated functional activities. However, various assumptions on physiological factors such as the intra-abdominal pressure (IAP), centers of mass (COMs) of the upper body and lumbar segments, and vertebral centers of rotation (CORs) have been made in modeling techniques. Systematic knowledge of how these assumptions will affect the predicted spinal biomechanics is important for improving the simulation accuracy. In this paper, we developed a 3D subject-specific numerical model of the lumbosacral spine including T12 and 90 muscles. The effects of the IAP magnitude and COMs locations on the COR of each motion segment and on the joint/muscle forces were investigated using a global convergence optimization procedure when the subject was in a weight bearing standing position. The data indicated that the line connecting the CORs showed a smaller curvature than the lordosis of the lumbar spine in standing posture when the IAP was 0?kPa and the COMs were 10?mm anterior to the geometric center of the T12 vertebra. Increasing the IAP from 0 kPa to 10 kPa shifted the location of CORs toward the posterior direction (from 1.4?±?8.9 mm anterior to intervertebral disc (IVD) centers to 40.5?±?3.1 mm posterior to the IVD centers) and reduced the average joint force (from 0.78?±?0.11 Body weight (BW) to 0.31?±?0.07 BW) and overall muscle force (from 349.3?±?57.7 N to 221.5?±?84.2 N). Anterior movement of the COMs from -30 mm to 70 mm relative to the geometric center of T12 vertebra caused an anterior shift of the CORs (from 25.1?±?8.3 mm posterior to IVD centers to 7.8?±?6.2 mm anterior to IVD centers) and increases of average joint forces (from 0.78?±?0.1 BW to 0.93?±?0.1 BW) and muscle force (from 348.9?±?47.7 N to 452.9?±?58.6 N). Therefore, it is important to consider the IAP and correct COMs in order to accurately simulate human spine biomechanics. The method and results of this study could be useful for designing prevention strategies of spinal injuries and recurrences, and for enhancing rehabilitation efficiency.     

Direct measurement of intervertebral disc maximum shear strain in six degrees of freedom: motions that place disc tissue at risk of injury

Human intervertebral disc specimens were tested to determine the regions of largest maximum shear strain (MSS) experienced by disc tissues in each of three principal displacements and three rotations, and to identify the physiological rotations and displacements that may place the disc at greatest risk for large tissue strains and injury. Tearing of disc annulus may be initiated by large interlamellar shear strains. Nine human lumbar discs were tagged with radiographic markers on the endplates, disc periphery and with a grid of wires in the mid-transverse plane and subjected to each of the six principal displacements and rotations. Stereo-radiographs were taken in each position and digitized for reconstruction of the three-dimensional position of each marker. Maximum tissue shear strains were calculated from relative marker displacements and normalized by the input displacement or rotation. Lateral shear, compression, and lateral bending were the motions that produced the mean (95% confidence interval) largest mean MSS of 9.6 (0.7)%/mm, 9.0 (0.5)%/mm, and 5.8 (1.6)%/ degrees , respectively, and which occurred in the posterior, posterolateral and lateral peripheral regions of the disc. After taking into account the reported maximum physiological range of motion for each degree of freedom, motions producing the highest physiological MSS were lateral bending (57.8 (16.2)%) and flexion (38.3 (3.3)%), followed by lateral shear (14.4 (1.1)%) and compression (12.6 (0.7)%).     

An ImageJ-based tool for three-dimensional registration between different types of microscopic images

Three-dimensional (3D) registration (i.e., alignment) between two microscopic images is very helpful to study tissues that do not adhere to substrates, such as mouse embryos and organoids, which are often 3D rotated during imaging. However, there is no 3D registration tool easily accessible for experimental biologists. Here we developed an ImageJ-based tool which allows for 3D registration accompanied with both quantitative evaluation of the accuracy and reconstruction of 3D rotated images. In this tool, several landmarks are manually provided in two images to be aligned, and 3D rotation is computed so that the distances between the paired landmarks from the two images are minimized. By simultaneously providing multiple points (e.g., all nuclei in the regions of interest) other than the landmarks in the two images, the correspondence of each point between the two images, i.e., to which nucleus in one image a certain nucleus in another image corresponds, is quantitatively explored. Furthermore, 3D rotation is applied to one of the two images, resulting in reconstruction of 3D rotated images. We demonstrated that this tool successfully achieved 3D registration and reconstruction of images in mouse pre- and post-implantation embryos, where one image was obtained during live imaging and another image was obtained from fixed embryos after live imaging. This approach provides a versatile tool applicable for various tissues and species.     

Three-dimensional mathematical reconstruction of the spinal shape, based on active contours

To reduce the amount of radiographs needed for patients with a scoliosis, a radiation-free method based on topographic images of the back was developed. An active contour model simulating spinal stiffness has been applied to video rasterstereographic (VRS) data. The aim of the present study is (a) to evaluate the applicability of active contours to improve the accuracy and the reliability of the three-dimensional (3D) spinal midline reconstruction from back surface data and (b) to design a more robust method to detect the spinal midline. To evaluate the reliability and accuracy, the active contour-based method is compared to a conventional procedure, which has been specifically developed for scoliosis; both methods produce a 3D curve of the spinal midline. The frontal projections and surface rotations of these spinal midlines are compared; r.m.s. deviations of 0.9 mm between the frontal curves and 0.4 degrees between the surface rotations were obtained. Applying the active contour-based method does therefore not result in a substantial difference in accuracy to the conventional procedure. As a conclusion the active contour method is a valuable mathematical method that can accurately reconstruct the spinal midline based on back surface data. In addition, the method can be applied to various postures.     

Optimised loads for the simulation of axial rotation in the lumbar spine

Simplified loading modes (pure moment, compressive force) are usually applied in the in vitro studies to simulate flexion-extension, lateral bending and axial rotation of the spine. The load magnitudes for axial rotation vary strongly in the literature. Therefore, the results of current investigations, e.g. intervertebral rotations, are hardly comparable and may involve unrealistic values. Thus, the question 'which in vitro applicable loading mode is the most realistic' remains open. A validated finite element model of the lumbar spine was employed in two sensitivity studies to estimate the ranges of results due to published load assumptions and to determine the input parameters (e.g. torsional moment), which mostly affect the spinal load and kinematics during axial rotation. In a subsequent optimisation study, the in vitro applicable loading mode was determined, which delivers results that fit best with available in vivo measurements. The calculated results varied widely for loads used in the literature with potential high deviations from in vivo measured values. The intradiscal pressure is mainly affected by the magnitude of the compressive force, while the torsional moment influences mainly the intervertebral rotations and facet joint forces. The best agreement with results measured in vivo were found for a compressive follower force of 720N and a pure moment of 5.5Nm applied to the unconstrained vertebra L1. The results reveal that in many studies the assumed loads do not realistically simulate axial rotation. The in vitro applicable simplified loads cannot perfectly mimic the in vivo situation. However, the optimised values lead to the best agreement with in vivo measured values. Their consequent application would lead to a better comparability of different investigations.     

Lumbar spine angles and intervertebral disc characteristics with end-range positions in three planes of motion in healthy people using upright MRI

Understanding changes in lumbar spine (LS) angles and intervertebral disc (IVD) behavior in end-range positions in healthy subjects can provide a basis for developing more specific LS models and comparing people with spine pathology. The purposes of this study are to quantify 3D LS angles and changes in IVD characteristics with end-range positions in 3 planes of motion using upright MRI in healthy people, and to determine which intervertebral segments contribute most in each plane of movement. Thirteen people (average age = 24.4 years, range 18–51 years; 9 females; BMI = 22.4 ± 1.8 kg/m²) with no history of low back pain were scanned in an upright MRI in standing, sitting flexion, sitting axial rotation (left, right), prone on elbows, prone extension, and standing lateral bending (left, right). Global and local intervertebral LS angles were measured. Anterior-posterior length of the IVD and location of the nucleus pulposus was measured. For the sagittal plane, lower LS segments contribute most to change in position, and the location of the nucleus pulposus migrated from a more posterior position in sitting flexion to a more anterior position in end-range extension. For lateral bending, the upper LS contributes most to end-range positions. Small degrees of intervertebral rotation (1–2°) across all levels were observed for axial plane positions. There were no systematic changes in IVD characteristics for axial or coronal plane positions.     

Three-dimensional static modeling of the lumbar spine

This paper presents three-dimensional static modeling of the human lumbar spine to be used in the formation of anatomically-correct movement patterns for a fully cable-actuated robotic lumbar spine which can mimic in vivo human lumbar spine movements to provide better hands-on training for medical students. The mathematical model incorporates five lumbar vertebrae between the first lumbar vertebra and the sacrum, with dimensions of an average adult human spine. The vertebrae are connected to each other by elastic elements, torsional springs and a spherical joint located at the inferoposterior corner in the mid-sagittal plane of the vertebral body. Elastic elements represent the ligaments that surround the facet joints and the torsional springs represent the collective effect of intervertebral disc which plays a major role in balancing torsional load during upper body motion and the remaining ligaments that support the spinal column. The elastic elements and torsional springs are considered to be nonlinear. The nonlinear stiffness constants for six motion types were solved using a multiobjective optimization technique. The quantitative comparison between the angles of rotations predicted by the proposed model and in the experimental data confirmed that the model yields angles of rotation close to the experimental data. The main contribution is that the new model can be used for all motions while the experimental data was only obtained at discrete measurement points.