A model-based approach for estimation of changes in lumbar segmental kinematics associated with alterations in trunk muscle forces

The kinematics information from imaging, if combined with optimization-based biomechanical models, may provide a unique platform for personalized assessment of trunk muscle forces (TMFs). Such a method, however, is feasible only if differences in lumbar spine kinematics due to differences in TMFs can be captured by the current imaging techniques. A finite element model of the spine within an optimization procedure was used to estimate segmental kinematics of lumbar spine associated with five different sets of TMFs. Each set of TMFs was associated with a hypothetical trunk neuromuscular strategy that optimized one aspect of lower back biomechanics. For each set of TMFs, the segmental kinematics of lumbar spine was estimated for a single static trunk flexed posture involving, respectively, 40° and 10° of thoracic and pelvic rotations. Minimum changes in the angular and translational deformations of a motion segment with alterations in TMFs ranged from 0° to 0.7° and 0 mm to 0.04 mm, respectively. Maximum changes in the angular and translational deformations of a motion segment with alterations in TMFs ranged from 2.4° to 7.6° and 0.11 mm to 0.39 mm, respectively. The differences in kinematics of lumbar segments between each combination of two sets of TMFs in 97% of cases for angular deformation and 55% of cases for translational deformation were within the reported accuracy of current imaging techniques. Therefore, it might be possible to use image-based kinematics of lumbar segments along with computational modeling for personalized assessment of TMFs.     

Computational biomechanics of a lumbar motion segment in pure and combined shear loads

Anterior shear has been implicated as a risk factor in spinal injuries. A 3D nonlinear poroelastic finite element model study of a lumbar motion segment L4-L5 was performed to predict the temporal shear response under various single and combined shear loads. Effects of nucleotomy and facetectomy as well as changes in the posture and facet gap distance were analyzed as well.     

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.     

Representation of passive spinal element contributions to in vitro flexion-extension using a polynomial model: illustration using the porcine lumbar spine

A polynomial modeling approach was developed to describe the contribution of individual passive spinal elements to the lumbar spinal motion segment flexion-extension motion. Flexion-extension moment-angle curves from porcine lumbar spines tested using a robotic testing system were described using sixth-order polynomials; the polynomials describing different dissection conditions were subtracted to describe the contribution of individual spinal elements to the motion segment flexion-extension properties. This modeling approach is a powerful and straightforward method for representing the mechanics of individual spinal tissues in biomechanical models and could easily be expanded to incorporate other features such as axial load.     

Finite element lumbar spine facet contact parameter predictions are affected by the cartilage thickness distribution and initial joint gap size

Current finite element modeling techniques utilize geometrically inaccurate cartilage distribution representations in the lumbar spine. We hypothesize that this shortcoming severely limits the predictive fidelity of these simulations. Specifically, it is unclear how these anatomically inaccurate cartilage representations alter range of motion and facet contact predictions. In the current study, cadaveric vertebrae were serially sectioned, and images were taken of each slice in order to identify the osteochondral interface and the articulating surface. A series of custom-written algorithms were utilized in order to quantify each facet joint's three-dimensional cartilage distribution using a previously developed methodology. These vertebrae-dependent thickness cartilage distributions were implemented on an L1 through L5 lumbar spine finite element model. Moments were applied in three principal planes of motion, and range of motion and facet contact predictions from the variable thickness and constant thickness distribution models were determined. Initial facet gap thickness dimensions were also parameterized. The data indicate that the mean and maximum cartilage thickness increased inferiorly from L1 to L5, with an overall mean thickness value of 0.57 mm. Cartilage distribution and initial facet joint gap thickness had little influence on the lumbar range of motion in any direction, whereas the mean contact pressure, total contact force, and total contact area predictions were altered considerably. The data indicate that range of motion predictions alone are insufficient to establish model validation intended to predict mechanical contact parameters. These data also emphasize the need for the careful consideration of the initial facet joint gap thickness with respect to the spinal condition being studied.     

Chronic low back pain patients walk with locally altered spinal kinematics

Various studies have reported alterations of spinal kinematics in patients with chronic low back pain (CLBP) during gait. However, while recent findings stressed the importance of multi-segment analysis, most of prior gait studies modelled the lumbar spine as one segment, when it was not the entire trunk that was considered as a single segment. Therefore, there is a need for comprehensive multi-segment research that could improve our understanding of CLBP pathomechanism and thus possibly contribute to better care for CLBP. This study aimed at characterizing the angle patterns at the lower lumbar (LLS), upper lumbar (ULS), lower thoracic (LTS) and upper thoracic (UTS) joints in the three anatomical planes and at comparing CLBP patients and asymptomatic subjects. Spinal kinematics of 11 CLBP patients and 11 controls was measured using a marker-based motion capture system and described according to a previously proposed multi-segment biomechanical model. Characteristic patterns were observed at the UTS, LTS and ULS joints in the transverse plane and at the UTS, ULS and LLS joints in the frontal plane. CLBP patients walked with smaller frontal-plane LLS range of motion than controls. The results also suggested that patients had more asymmetrical LTS motion in the transverse plane. In conclusion, this work extended prior literature by showing specific CLBP-related alterations in multi-segment spinal kinematics during gait. Further research is necessary to understand the factors influencing kinematics alterations and how treatment strategies might improve motor behaviour in CLBP patients.     

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.     

The role of the facet capsular ligament in providing spinal stability

Abstract

Low back pain (LBP) is the most common type of pain in America, and spinal instability is a primary cause. The facet capsular ligament (FCL) encloses the articulating joints of the spine and is of particular interest due to its high innervation – as instability ensues, high stretch values likely are a cause of this pain. Therefore, this work investigated the FCL's role in providing stability to the lumbar spine. A previously validated finite element model of the L4-L5 spinal motion segment was used to simulate pure moment bending in multiple planes. FCL failure was simulated and the following outcome measures were calculated: helical axes of motion, range of motion (ROM), bending stiffness, facet joint space, and FCL stretch. ROM increased, bending stiffness decreased, and altered helical axis patterns were observed with the removal of the FCL. Additionally, a large increase in FCL stretch was measured with diminished FCL mechanical competency, providing support that the FCL plays an important role in spinal stability.     

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.     

Study on effect of graded facetectomy on change in lumbar motion segment torsional flexibility using three-dimensional continuum contact representation for facet joints

Facet joints provide rigidity to the lumbar motion segment and thus protect the disk, particularly against torsional injury. A surgical procedure that fully or partially removes the facet joints (facetectomy) will decrease the mechanical stiffness of the motion segment, and potentially place the disk at risk of injury. Analytical models can be used to understand the effect of facet joints on motion segment stability. Using a facet joint model that represents the contact area as contact between two surfaces rather than as point contact, it was concluded that a substantial sudden change in rotational motion, due to applied torsion moment, was observed after 75 percent of any one of the facet joints was removed. Applied torsional moment loading produced coupled extension motion in the intact motion segment. This coupled motion also experienced a large change following complete unilateral facetectomy. Clinically, the present study showed that surgical intervention in the form of unilateral or bilateral total facetectomy might require fusion to reduce the primary torsion motion.     

In vitro analysis of kinematics and elastostatics of the human rib cage during thoracic spinal movement for the validation of numerical models

Neither kinematic nor stiffness properties of the rib cage during thoracic spinal motion were investigated in previous studies, while being essential for the accurate validation of numerical models of the whole thorax. The aim of this in vitro study therefore was to quantify the kinematics and elastostatics of the human rib cage under defined boundary conditions. Eight fresh frozen human thoracic spine specimens (C7-L1, median age 55 years, ranging from 40 to 60 years) including entire rib cages were loaded quasi-statically in flexion/extension, lateral bending, and axial rotation using pure moments of 5 Nm. Relative motions of ribs, thoracic vertebrae, and sternal structures as well as strains on the ribs were measured using optical motion tracking of 150 reflective markers per specimen, while specimens were loaded displacement-controlled with a constant rate of 1°/s for 3.5 cycles. The third full cycle was used to determine relative angles and strains at full loading of the spine for all motion directions. Largest relative angles were found in the main loading directions with only small motions at the mid-thoracic levels. Highest strains of the intercostal spaces were detected in the anterior section of the lowest fourth of the rib cage, showing compressions and elongations of more than 10% in all spinal motion planes. Elastostatic rib deformation was generally less than 1%. Rib-sternum relative motions exhibited complex motion patterns, overall showing relative angles below 2°. The results indicate that rib cage structures are not macroscopically deformed during spinal motion, but exhibit characteristic reproducible kinematics patterns.     

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.     

Finite element investigation of the loading rate effect on the spinal load-sharing changes under impact conditions

Sudden deceleration and frontal/rear impact configurations involve rapid movements that can cause spinal injuries. This study aimed to investigate the rotation rate effect on the L2–L3 motion segment load-sharing and to identify which spinal structure is at risk of failure and at what rotation velocity the failure may initiate?Five degrees of sagittal rotations at different rates were applied in a detailed finite-element model to analyze the responses of the soft tissues and the bony structures until possible fractures. The structural response was markedly different under the highest velocity that caused high peaks of stresses in the segment compared to the intermediate and low velocities. Under flexion, the stress was concentrated at the upper pedicle region of L2 and fractures were firstly initiated in this region and then in the lower endplate of L2. Under extension, maximum stress was located in the lower pedicle region of L2 and fractures started in the left facet joint, then they expanded in the lower endplate and in the pedicle region of L2. No rupture has resulted at the lower or intermediate velocities. The intradiscal pressure was higher under flexion and decreased when the endplate was fractured, while the contact forces were greater under extension and decreased when the facet surface was cracked. The highest ligaments stresses were obtained under flexion and did not reach the rupture values. The endplate, pedicle and facet surface represented the potential sites of bone fracture. Results showed that spinal injuries can result at sagittal rotation velocity exceeding 0.5°/ms.     

Geometry strongly influences the response of numerical models of the lumbar spine--a probabilistic finite element analysis

Typical FE models of the human lumbar spine consider a single, fixed geometry. Such models cannot account for potential effects of the natural variability of the spine's geometry. In this study, we performed a probabilistic uncertainty and sensitivity analysis of a fully parameterized, geometrically simplified model of the L3-L4 segment. We examined the impact of the uncertainty in all 40 geometry parameters, estimated lower and upper bounds for the required sample size and determined the most important geometry parameters. The natural variability of the spine's geometry indeed strongly affects intradiscal pressure, range of motion and facet joint contact forces. Deriving generalized statements from fixed-geometry models as well as transferring those results to different cases thus can easily lead to wrong conclusions and should only be performed with extreme caution. We recommend a sample size of ≈ 100 to obtain reasonable accurate point estimates and a sufficient overview of the remaining uncertainties. Yet, only few parameters, especially those determining the disc geometry (disc height, end-plate width and depth) and the facets' position (intra-articular space, pedicle length, facet angles), proved to be truly important. Accurate measurement and modeling of those structures should therefore be prioritized.     

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.     

Cervical spine morphology and ligament property variations: A finite element study of their influence on sagittal bending characteristics

Cervical spine finite element models reported in biomechanical literature usually represent a static morphology. Not considering morphology as a model parameter limits the predictive capabilities for applications in personalized medicine, a growing trend in modern clinical practice. The objective of the study was to investigate the influence of variations in spinal morphology on the flexion-extension responses, utilizing mesh-morphing-based parametrization and metamodel-based sensitivity analysis. A C5-C6 segment was used as the baseline model. Variations of intervertebral disc height, facet joint slope, facet joint articular processes height, vertebral body anterior-posterior depth, and segment size were parametrized. In addition, material property variations of ligaments were considered for sensitivity analysis. The influence of these variations on vertebral rotation and forces in the ligaments were analyzed. The disc height, segmental size, and body depth were found to be the most influential (in the cited order) morphology variations; while among the ligament material property variations, capsular ligament and ligamentum flavum influenced vertebral rotation the most. Changes in disc height influenced forces in the posterior ligaments, indicating that changes in the anterior load-bearing column of the spine could have consequences on the posterior column. A method to identify influential morphology variations is presented in this work, which will help automation efforts in modeling to focus on variations that matter. This study underscores the importance of incorporating influential morphology parameters, easily obtained through computed tomography/magnetic resonance images, to better predict subject-specific biomechanical responses for applications in personalized medicine.     

Biomechanical characterisation of ovine spinal facet joint cartilage

The spinal facet joints are known to be an important component in the kinematics and the load transmission of the spine. The articular cartilage in the facet joint is prone to degenerative changes which lead to back pain and treatments for the condition have had limited long term success. There is currently a lack of information on the basic biomechanical properties of the facet joint cartilage which is needed to develop tissue substitution or regenerative interventions. In the present study, the thickness and biphasic properties of ovine facet cartilage were determined using a combination of indentation tests and computational modelling. The equilibrium biphasic Young's modulus and permeability were derived to be 0.76±0.35 MPa and 1.61±1.10×10^?15 m⁴/(Ns) respectively, which were within the range of cartilage properties characterised from the human synovial joints. The average thickness of the ovine facet cartilage was 0.52±0.10 mm, which was measured using a needle indentation test. These properties could potentially be used for the development of substitution or tissue engineering interventions and for computational modelling of the facet joint. Furthermore, the developed method to characterise the facet cartilage could be used for other animals or human donors.     

Numerical analysis of the influence of nucleus pulposus removal on the biomechanical behavior of a lumbar motion segment

Nucleus replacement was deemed to have therapeutic potential for patients with intervertebral disc herniation. However, whether a patient would benefit from nucleus replacement is technically unclear. This study aimed to investigate the influence of nucleus pulposus (NP) removal on the biomechanical behavior of a lumbar motion segment and to further explore a computational method of biomechanical characteristics of NP removal, which can evaluate the mechanical stability of pulposus replacement. We, respectively, reconstructed three types of models for a mildly herniated disc and three types of models for a severely herniated disc based on a L4–L5 segment finite element model with computed tomography image data from a healthy adult. First, the NP was removed from the herniated disc models, and the biomechanical behavior of NP removal was simulated. Second, the NP cavities were filled with an experimental material (Poisson's ratio = 0.3; elastic modulus = 3 MPa), and the biomechanical behavior of pulposus replacement was simulated. The simulations were carried out under the five loadings of axial compression, flexion, lateral bending, extension, and axial rotation. The changes of the four biomechanical characteristics, i.e. the rotation degree, the maximum stress in the annulus fibrosus (AF), joint facet contact forces, and the maximum disc deformation, were computed for all models. Experimental results showed that the rotation range, the maximum AF stress, and joint facet contact forces increased, and the maximum disc deformation decreased after NP removal, while they changed in the opposite way after the nucleus cavities were filled with the experimental material.     

Investigation of impact loading rate effects on the ligamentous cervical spinal load-partitioning using finite element model of functional spinal unit C2–C3

The cervical spine functions as a complex mechanism that responds to sudden loading in a unique manner, due to intricate structural features and kinematics. The spinal load-sharing under pure compression and sagittal flexion/extension at two different impact rates were compared using a bio-fidelic finite element (FE) model of the ligamentous cervical functional spinal unit (FSU) C2–C3. This model was developed using a comprehensive and realistic geometry of spinal components and material laws that include strain rate dependency, bone fracture, and ligament failure. The range of motion, contact pressure in facet joints, failure forces in ligaments were compared to experimental findings. The model demonstrated that resistance of spinal components to impact load is dependent on loading rate and direction. For the loads applied, stress increased with loading rate in all spinal components, and was concentrated in the outer intervertebral disc (IVD), regions of ligaments to bone attachment, and in the cancellous bone of the facet joints. The highest stress in ligaments was found in capsular ligament (CL) in all cases. Intradiscal pressure (IDP) in the nucleus was affected by loading rate change. It increased under compression/flexion but decreased under extension. Contact pressure in the facet joints showed less variation under compression, but increased significantly under flexion/extension particularly under extension. Cancellous bone of the facet joints region was the only component fractured and fracture occurred under extension at both rates. The cervical ligaments were the primary load-bearing component followed by the IVD, endplates and cancellous bone; however, the latter was the most vulnerable to extension as it fractured at low energy impact.