The feasibility of modal testing for measurement of the dynamic characteristics of goat vertebral motion segments

Structural vibration testing might be a promising method to study the mechanical properties of spinal motion segments as an alternative to imaging and spinal manipulation techniques. Structural vibration testing is a non-destructive measurement technique that measures the response of a system to an applied vibration as a function of frequency, and allows determination of modal parameters such as resonance frequencies (ratio between stiffness and mass), vibration modes (pattern of motion) and damping. The objective of this study was to determine if structural vibration testing can reveal the resonance frequencies that correspond to the mode shapes flexion-extension, lateroflexion and axial rotation of lumbar motion segments, and to establish whether resonance frequencies can discriminate specific structural alterations of the motion segment. Therefore, a shaker was used to vibrate the upper vertebra of 16 goat lumbar motion segments, while the response was obtained from accelerometers on the transverse and spinous processes and the anterior side of the upper vertebra. Measurements were performed in three conditions: intact, after dissection of the ligaments and after puncturing the annulus fibrosus. The results showed clear resonance peaks for flexion-extension, lateral bending and axial rotation for all segments. Dissection of the ligaments did not affect the resonance frequencies, but puncturing the annulus reduced the resonance frequency of axial rotation. These results indicate that vibration testing can be utilised to assess the modal parameters of lumbar motion segments, and might eventually be used to study the mechanical properties of spinal motion segments in vivo.     

A multibody modelling approach to determine load sharing between passive elements of the lumbar spine

The human spinal segment is an inherently complex structure, a combination of flexible and semi-rigid articulating elements stabilised by seven principal ligaments. An understanding of how mechanical loading is shared among these passive elements of the segment is required to estimate tissue failure stresses. A 3D rigid body model of the complete lumbar spine has been developed to facilitate the prediction of load sharing across the passive elements. In contrast to previous multibody models, this model includes a non-linear, six degrees of freedom intervertebral disc, facet bony articulations and all spinal ligaments. Predictions of segmental kinematics and facet joint forces, in response to pure moment loading (flexion-extension), were compared to published in vitro data. On inclusion of detailed representation of the disc and facets, the multibody model fully captures the non-linear flexibility response of the spinal segment, i.e. coupled motions and a mobile instantaneous centre of rotation. Predicted facet joint forces corresponded well with reported values. For the loading case considered, the model predicted that the ligaments are the main stabilising elements within the physiological motion range; however, the disc resists a greater proportion of the applied load as the spine is fully flexed. In extension, the facets and capsular ligaments provide the principal resistance. Overall patterns of load distribution to the spinal ligaments are in agreement with previous predictions; however, the current model highlights the important role of the intraspinous ligament in flexion and the potentially high risk of failure. Several important refinements to the multibody modelling of the passive elements of the spine have been described, and such an enhanced passive model can be easily integrated into a full musculoskeletal model for the prediction of spinal loading for a variety of daily activities.     

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.     

Spinal stiffness increases with axial load: another stabilizing consequence of muscle action.

This paper addresses the role of lumbar spinal motion segment stiffness in spinal stability. The stability of the lumbar spine was modelled with loadings of 30 Nm or 60 Nm efforts about each of the three principal axes, together with the partial body weight above the lumbar spine. Two assumptions about motion segment stiffness were made: first the stiffness was represented by an 'equivalent beam' with constant stiffness properties; second the stiffness was updated based on the motion segment axial loading using a relationship determined experimentally from human lumbar spinal specimens tested with 0, 250 and 500 N of axial compressive preload. Two physiologically plausible muscle activation strategies were used in turn for calculating the muscle forces required for equilibrium. Stability analyses provided estimates of the minimum muscle stiffness required for stability. These critical muscle stiffness values decreased when preload effects were used in estimating spinal stiffness in all cases of loadings and muscle activation strategies, indicating that stability increased. These analytical findings emphasize that the spinal stiffness (as well as muscular stiffness) is important in maintaining spinal stability, and that the stiffness-increasing effect of 'preloading' should be taken into account in stability analyses.     

Porcine models in spinal research: calibration and comparative finite element analysis of various configurations during flexion-extension

This study was conducted to develop and calibrate a detailed 3-dimensional finite element model of the porcine lumbar spine and to compare this model with various configurations in flexion and extension. Computed tomography scans obtained from the L4-L5 lumbar segment of a Landrace x Large White pig were used to generate a solid volume. The various passive components were characterized by using a step-by-step calibration procedure in which the material properties of the anatomic structures were modified to match the corresponding in vitro data set-points retrieved from the literature. The range of motion of the totally assembled intact model was assessed under a 10-Nm flexion-extension moment and compared with data from a bilateral complete and hemifacetectomy configuration. In addition, the results from our porcine model were compared with published data regarding range of motion in a human finite element model in order to predict the configuration of the porcine model that most closely represented the human spine. Both the intact and hemifacetectomy configurations of the porcine model were comparable to the human spine. However, qualitative analysis of the instantaneous axis of rotation revealed a dissimilarity between the intact porcine model and human spine behavior, indicating the hemifacetectomy configuration of the porcine model as the most appropriate for spinal instrumentation studies. The present 3-dimensional finite element porcine model offers an additional tool to improve understanding of the biomechanics of the porcine spine and to decrease the expense of spinal research.     

A finite element model of the L4-L5 spinal motion segment: biomechanical compatibility of an interspinous device

The biomechanical compatibility of an interspinous device, used for the "dynamic stabilization" of a diseased spinal motion segment, was investigated. The behaviour of an implant made of titanium based alloy (Ti6Al4V) and that of an implant made of a super-elastic alloy (Ni-Ti) have been compared. The assessment of the biomechanical compatibility was achieved by means of the finite element method, in which suitable constitutive laws have been adopted for the annulus fibrosus and for the metal alloys. The model was aimed at simulating the healthy, the nucleotomized and the treated L4-L5 lumbar segment, subjected to compressive force and flexion-extension as well as lateral flexion moments. The computational model has shown that both the implants were able to achieve their main design purpose, which is to diminish the forces acting on the apophyseal joints. Nevertheless, the Ni-Ti implant has shown a more physiological flexural stiffness with respect to the Ti6Al4V implant, which exhibited an excessive stiffness and permanent strains (plastic strains), even under physiological loads. The computational models presented in this paper seems to be a promising tool able to predict the effectiveness of a biomedical device and to select the materials to be used for the implant manufacturing, within an engineering approach to the clinical problem of the spinal diseases.     

Automated muscle wrapping using finite element contact detection

Realistic muscle path representation is essential to musculoskeletal modeling of joint function. Algorithms predicting these muscle paths typically rely on a labor intensive predefinition of via points or underlying geometries to guide wrapping for given joint positions. While muscle wrapping using anatomically precise three-dimensional (3D) finite element (FE) models of bone and muscle has been achieved, computational expense and pre-processing associated with this approach exclude its use in applications such as subject-specific modeling. With the intention of combining advantageous features of both approaches, an intermediate technique relying on contact detection capabilities of commercial FE packages is presented. We applied the approach to the glenohumeral joint, and validated the method by comparison against existing experimental data. Individual muscles were modeled as a straight series of deformable beam elements and bones as anatomically precise 3D rigid bodies. Only the attachment locations and a default orientation of the undeformed muscle segment were pre-defined. The joint was then oriented in a static position of interest. The muscle segment free end was then moved along the shortest Euclidean path to its origin on the scapula, wrapping the muscle along bone surfaces by relying on software contact detection. After wrapping for a given position, the resulting moment arm was computed as the perpendicular distance from the line of action vector to the humeral head center of rotation.This approach reasonably predicted muscle length and moment arm for 27 muscle segments when compared to experimental measurements over a wide range of shoulder motion. Artificial via points or underlying contact geometries were avoided, contact detection and multiobject wrapping on the bone surfaces were automatic, and low computational cost permitted wrapping of individual muscles within seconds on a standard desktop PC. These advantages may be valuable for both general and subject-specific musculoskeletal modeling.     

Validation of single-segment and three-segment spinal models used to represent lumbar flexion

Changes in spinal posture between the erect and flexed positions were calculated using angular measurements from lateral photographs and radiographs of ten adult male subjects. For photographic measurements, the thoracolumbar vertebral column was modelled as either a single segment or as three segments. In the three-segment model, there was a non-significant correlation between the decrease in lumbar concavity and intervertebral motion. In addition, there was a non-significant negative correlation between the increase in thoracic convexity and lumbar motion determined radiographically. In the single-segment model, the decrease in angulation between the thoracolumbar spine and pelvis was a good representation of lumbar spine flexion as determined by the mean lumbar intervertebral angular change. Therefore, modelling the thoracolumbar vertebral column as a single segment allowed better estimation of lumbar intervertebral angular change during flexion than a three-segment model. The results indicate that large range dynamic motion of the lumbar vertebral column can be represented using photographic analysis of the positions of three easily identified anatomical landmarks: the anterior superior iliac spine, posterior superior iliac spine and the spinous process of the first thoracic vertebra.     

Differences in 3D vs. 2D analysis in lumbar spinal fusion simulations

Lumbar interbody fusion is currently the gold standard in treating patients with disc degeneration or segmental instability. Despite it having been used for several decades, the non-union rate remains high. A failed fusion is frequently attributed to an inadequate mechanical environment after instrumentation. Finite element (FE) models can provide insights into the mechanics of the fusion process. Previous fusion simulations using FE models showed that the geometries and material of the cage can greatly influence the fusion outcome. However, these studies used axisymmetric models which lacked realistic spinal geometries. Therefore, different modeling approaches were evaluated to understand the bone-formation process.Three FE models of the lumbar motion segment (L4–L5) were developed: 2D, Sym-3D and Nonsym-3D. The fusion process based on existing mechano-regulation algorithms using the FE simulations to evaluate the mechanical environment was then integrated into these models. In addition, the influence of different lordotic angles (5, 10 and 15°) was investigated. The volume of newly formed bone, the axial stiffness of the whole segment and bone distribution inside and surrounding the cage were evaluated.In contrast to the Nonsym-3D, the 2D and Sym-3D models predicted excessive bone formation prior to bridging (peak values with 36 and 9% higher than in equilibrium, respectively). The 3D models predicted a more uniform bone distribution compared to the 2D model.The current results demonstrate the crucial role of the realistic 3D geometry of the lumbar motion segment in predicting bone formation after lumbar spinal fusion.     

Uncertainty analysis of material properties and morphology parameters in numerical models regarding the motion of lumbar vertebral segments

Abstract

The kinematics of a spinal motion segment is determined by the material properties of the soft-tissue and the morphology. The material properties can vary within subjects and between vertebral levels, leading to a wide possible range of motion of a spinal segment independently on its morphology. The goal of this numerical study was to identify the most influential material parameters concerning the kinematics of a spinal motion segment and their plausible ranges. Then, a method was tested to deduce the material properties automatically, based on a given ROM and morphology. A fully parametric finite element model of the morphology and material properties of a lumbar spinal motion segment was developed. The impact of uncertainty of twelve spinal material parameters, as well as the size of the gap between the articular surfaces of the facet joints was examined. The simulation results were compared to our own in vitro data. The flexibility of a lumbar segment was especially influenced by the properties of the anterior annulus region, the facet gap size and the interspinous ligament. The high degree of uncertainty in the material properties and facet gap size published in the literature can lead to a wide scatter in the motion of a spinal segment, with a range of 6°-17° in the intact condition in flexion/extension, from 5°-22° in lateral bending and from 3°-14° in axial rotation. Statistical analysis of the variability might help to estimate the sensitivity and total uncertainty propagated through biomechanical simulations, affecting the reliability of the predictions.     

Moderately degenerated lumbar motion segments: Are they truly unstable?

The two main load bearing tissues of the intervertebral disc are the nucleus pulposus and the annulus fibrosus. Both tissues are composed of the same basic components, but differ in their organization and relative amounts. With degeneration, the clear distinction between the two tissues disappears. The changes in biochemical content lead to changes in mechanical behaviour of the intervertebral disc. The aim of the current study was to investigate if well-documented moderate degeneration at the biochemical and fibre structure level leads to instability of the lumbar spine. By taking into account biochemical and ultrastructural changes to the extracellular matrix of degenerating discs, a set of constitutive material parameters were determined that described the individual tissue behaviour. These tissue biomechanical models were then used to simulate dynamic behaviour of the degenerated spinal motion segment, which showed instability in axial rotation, while a stabilizing effect in the other two principle bending directions. When a shear load was applied to the degenerated spinal motion segment, no sign of instability was found. This study found that reported changes to the nucleus pulposus and annulus fibrosus matrix during moderate degeneration lead to a more stable spinal motion segment and that such biomechanical considerations should be incorporated into the general pathophysiological understanding of disc degeneration and how its progress could affect low back pain and its treatments thereof.     

Measurement of a spinal motion segment stiffness matrix

The six-degrees-of-freedom elastic behavior of spinal motion segments can be approximated by a stiffness matrix. A method is described to measure this stiffness matrix directly with the motion segment held under physiological conditions of axial preload and in an isotonic fluid bath by measuring the forces and moments associated with each of the six orthogonal translations and rotations. The stiffness matrix was obtained from the load-displacement measurements by linear least squares assuming a symmetric matrix. Results from a pig lumbar spinal motion segment in an isotonic bath, with and without a 500 N axial preload, showed a large stiffening effect with axial preload.     

Biomechanical implications of lumbar spinal ligament transection

Many lumbar spine surgeries either intentionally or inadvertently damage or transect spinal ligaments. The purpose of this work was to quantify the previously unknown biomechanical consequences of isolated spinal ligament transection on the remaining spinal ligaments (stress transfer), vertebrae (bone remodelling stimulus) and intervertebral discs (disc pressure) of the lumbar spine. A finite element model of the full lumbar spine was developed and validated against experimental data and tested in the primary modes of spinal motion in the intact condition. Once a ligament was removed, stress increased in the remaining spinal ligaments and changes occurred in vertebral strain energy, but disc pressure remained similar. All major biomechanical changes occurred at the same spinal level as the transected ligament, with minor changes at adjacent levels. This work demonstrates that iatrogenic damage to spinal ligaments disturbs the load sharing within the spinal ligament network and may induce significant clinically relevant changes in the spinal motion segment.     

Parametric finite element analysis of vertebral bodies affected by tumors

The vertebral column is the most frequent site of metastatic involvement of the skeleton. Due to the proximity to the spinal cord, from 5% to 10% of all cancer patients develop neurologic manifestations. As a consequence, fracture risk prediction has significant clinical importance. In this study, we model the metastatically involved vertebra so as to parametrically investigate the effects of tumor size, material properties and compressive loading rate on vertebral strength. A two-dimensional axisymmetric finite element model of a spinal motion segment consisting of the first lumbar vertebral body (no posterior elements) and adjacent intervertebral disc was developed to allow the inclusion of a centrally located tumor in the vertebral body. After evaluating elastic, mixed, and poroelastic formulations, we concluded that the poroelastic representation was most suitable for modeling the metastatically involved vertebra's response to compressive load. Maximum principal strains were used to localize regions of potential vertebral trabecular bone failure. Radial and axial vertebral body displacements were used as relative indicators of spinal canal encroachment and endplate failure. Increased tumor size and loading rate, and reduced trabecular bone density all elevated axial and radial displacements and maximum tensile strains. The results of this parametric study suggest that vertebral tumor size and bone density contribute significantly to a patients risk for vertebral fracture and should be incorporated in clinical assessment paradigms.     

A multibody modelling approach to determine load sharing between passive elements of the lumbar spine

The human spinal segment is an inherently complex structure, a combination of flexible and semi-rigid articulating elements stabilised by seven principal ligaments. An understanding of how mechanical loading is shared among these passive elements of the segment is required to estimate tissue failure stresses. A 3D rigid body model of the complete lumbar spine has been developed to facilitate the prediction of load sharing across the passive elements. In contrast to previous multibody models, this model includes a non-linear, six degrees of freedom intervertebral disc, facet bony articulations and all spinal ligaments. Predictions of segmental kinematics and facet joint forces, in response to pure moment loading (flexion–extension), were compared to published in vitro data. On inclusion of detailed representation of the disc and facets, the multibody model fully captures the non-linear flexibility response of the spinal segment, i.e. coupled motions and a mobile instantaneous centre of rotation. Predicted facet joint forces corresponded well with reported values. For the loading case considered, the model predicted that the ligaments are the main stabilising elements within the physiological motion range; however, the disc resists a greater proportion of the applied load as the spine is fully flexed. In extension, the facets and capsular ligaments provide the principal resistance. Overall patterns of load distribution to the spinal ligaments are in agreement with previous predictions; however, the current model highlights the important role of the intraspinous ligament in flexion and the potentially high risk of failure. Several important refinements to the multibody modelling of the passive elements of the spine have been described, and such an enhanced passive model can be easily integrated into a full musculoskeletal model for the prediction of spinal loading for a variety of daily activities.     

A continuous pure moment loading apparatus for biomechanical testing of multi-segment spine specimens

An apparatus is described that enables the application of continuous pure moment loads to multi-segment spine specimens. This loading apparatus allows continuous cycling of the spine between specified flexion and extension (or right and left lateral bending) maximum load endpoints. Using a six-degree-of-freedom load cell and three-dimensional optoelectronic stereophotogrammetry, characteristic displacement versus load hysteresis curves can be generated and analyzed for different spinal constructs of interest. Unlike quasi-static loading, the use of continuous loading permits the analysis of the spine's behaviour within the neutral zone. This information is of particular clinical significance given that the instability of a spinal segment is related to its flexibility within the neutral zone. Representative curves for the porcine lumbar spine in flexion-extension and lateral bending are presented to illustrate the capabilities of this system.     

Load-displacement properties of lower cervical spine motion segments

The load-displacement behavior of 35 fresh adult cervical spine motion segments was measured in compression, shear, flexion, extension, lateral bending and axial torsion tests. Motion segments were tested both intact and with posterior elements removed. Applied forces ranged to 73.6 N in compression and to 39 N in shear, while applied moments ranged to 2.16 Nm. For each mode of loading, principal and coupled motions were measured and stiffnesses were calculated. The effect of disc degeneration on motion segment stiffnesses and the moments required for motion segment failure were also measured. In compression, the stiffnesses of the cervical motion segments were similar to those of thoracic and lumbar motion segments. In other modes of loading, cervical stiffnesses were considerably smaller than thoracic or lumbar stiffnesses. Removal of the posterior elements decreased cervical motion segment stiffnesses by as much as 50%. Degenerated cervical discs were less stiff in compression and stiffer in shear than less degenerated discs, but in bending or axial torsion, no statistically significant differences were evident. Bending moments causing failure were an order of magnitude lower than those for lumbar segments.     

Between-session reliability of opto-electronic motion capture in measuring sagittal posture and 3-D ranges of motion of the thoracolumbar spine

This study evaluated between-session reliability of opto-electronic motion capture to measure trunk posture and three-dimensional ranges of motion (ROM). Nineteen healthy participants aged 24–74 years underwent spine curvature, pelvic tilt and trunk ROM measurements on two separate occasions. Rigid four-marker clusters were attached to the skin overlying seven spinous processes, plus single markers on pelvis landmarks. Rigid body rotations of spine marker clusters were calculated to determine neutral posture and ROM in flexion, extension, total lateral bending (left-right) and total axial rotation (left-right). Segmental spine ROM values were in line with previous reports using opto-electronic motion capture. Intraclass correlation coefficients (ICC) and standard error of measurement (SEM) were calculated as measures of between-session reliability and measurement error, respectively. Retroreflective markers showed fair to excellent between-session reliability to measure thoracic kyphosis, lumbar lordosis, and pelvic tilt (ICC = 0.82, 0.63, and 0.54, respectively). Thoracic and lumbar segments showed highest reliabilities in total axial rotation (ICC = 0.78) and flexion-extension (ICC = 0.77–0.79) ROM, respectively. Pelvic segment showed highest ICC values in flexion (ICC = 0.78) and total axial rotation (ICC = 0.81) trials. Furthermore, it was estimated that four or fewer repeated trials would provide good reliability for key ROM outcomes, including lumbar flexion, thoracic and lumbar lateral bending, and thoracic axial rotation. This demonstration of reliability is a necessary precursor to quantifying spine kinematics in clinical studies, including assessing changes due to clinical treatment or disease progression.     

Validation of vibration testing for the assessment of the mechanical properties of human lumbar motion segments

Experimental modal analysis is a non-destructive measurement technique, which applies low forces and small deformations to assess the integrity of a structure. It is therefore a promising method to study the mechanical properties of the spine in vivo. Previously, modal parameters successfully revealed artificially induced spinal injuries. The question remains however, whether experimental modal analysis can be applied successfully in human spinal segments with mechanical changes due to physiological processes. Since quasi-static mechanical testing is considered the "gold standard" for assessing intervertebral stiffness, the purpose of our study was to examine if the mechanical properties derived from vibration testing and quasi-static testing correlate. Six cadaver human spines (L1-L5) were loaded quasi-statically in bending and torsion, while an optical system measured the angular rotations of the individual motion segments. Subsequently, the polysegmental spines were divided into L2-L3 and L4-L5 segments and a shaker was used to vibrate the upper vertebra, while its response was obtained from accelerometers in anteroposterior and mediolateral directions. From the resulting frequency response function the eigenfrequencies (ratio between stiffness and mass) and vibration modes (pattern of motion) were determined. The vibration results showed clear eigenfrequencies for flexion-extension (mean 121.83Hz, SD 40.05Hz), lateroflexion (mean 132.17, SD 34.80Hz) and axial rotation (mean 236.17Hz, SD 81.45Hz). Furthermore, the correlation between static and dynamic tests was significant (r=0.73, p=0.01). In conclusion, the findings from this study show that experimental modal analysis is a valid method to assess the mechanical properties of human lumbar motion segments.