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.     

Increases of calcium and magnesium and decrease of iron in human posterior longitudinal ligaments of the cervical spine with aging

To elucidate compositional changes of ligaments with aging, the authors investigated age-related changes of elements in the posterior longitudinal ligaments (PLLs) by inductively coupled plasma—atomic emission spectrometry. After the ordinary dissection, PLLs were resected from the subjects ranging in age from 65 to 95 yr. The PLLs of the cervical spine were resected between the fourth and fifth cervical vertebrae, the PLLs of the thoracic spine between the fifth and seventh thoracic vertebrae, and the PLLs of the lumbar spine between the second and third lumbar vertebrae. Calcium and magnesium increased progressively with aging in the PLLs of the cervical spine, but they did not increase with aging in the PLLs of the thoracic and lumbar spine. In contrast, iron decreased gradually with aging in the PLLs of the cervical spine. Regarding the relationships among elements, significant correlations were found among the contents of calcium, phosphorus, magnesium, and sodium in the PLLs of the cervical spine.     

A model for studies of mechanical interactions between the human spine and rib cage

A three-dimensional mathematical model useful for studies of the mechanics of the human skeletal thorax is described. To construct this model, rib cage elements are incorporated into a previously reported model of the thoracolumbar spine. The vertebrae and bony portions of the ribs and sternum are idealized as rigid bodies. The behavior of the discs, ligaments and costal cartilages are modelled by deformable elements. Appropriate geometric and stiffness property data are assigned to the elements of the model. In constructing the model, it was found that the mechanical response of the costo-vertebral joint is strongly influenced by articulation geometry. Although rigid bodies were used to model calcified portions of the ribs, the model predicted rib cage deformations in close agreement with those measured experimentally. These studies indicate that the rigid body motion of calcified portions of the rib makes a major contribution to the deformation of the rib cage in response to certain types of loadings. Quantitative results are also reported on the roles the rib cage plays in bending responses of the spine, the lateral stability of the spine, and the production and correction of several scoliotic deformities.     

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 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.     

Intervertebral reaction force prediction using an enhanced assembly of OpenSim models

OpenSim offers a valuable approach to investigating otherwise difficult to assess yet important biomechanical parameters such as joint reaction forces. Although the range of available models in the public repository is continually increasing, there currently exists no OpenSim model for the computation of intervertebral joint reactions during flexion and lifting tasks. The current work combines and improves elements of existing models to develop an enhanced model of the upper body and lumbar spine. Models of the upper body with extremities, neck and head were combined with an improved version of a lumbar spine from the model repository. Translational motion was enabled for each lumbar vertebrae with six controllable degrees of freedom. Motion segment stiffness was implemented at lumbar levels and mass properties were assigned throughout the model. Moreover, body coordinate frames of the spine were modified to allow straightforward variation of sagittal alignment and to simplify interpretation of results. Evaluation of model predictions for level L1–L2, L3–L4 and L4–L5 in various postures of forward flexion and moderate lifting (8 kg) revealed an agreement within 10% to experimental studies and model-based computational analyses. However, in an extended posture or during lifting of heavier loads (20 kg), computed joint reactions differed substantially from reported in vivo measures using instrumented implants. We conclude that agreement between the model and available experimental data was good in view of limitations of both the model and the validation datasets. The presented model is useful in that it permits computation of realistic lumbar spine joint reaction forces during flexion and moderate lifting tasks. The model and corresponding documentation are now available in the online OpenSim repository.     

A three-dimensional model of the human cervical spine for impact simulation

A three-dimensional analytical model of the cervical spine is described. The cervical vertebrae and the head are modeled as rigid bodies which are interconnected by deformable elements representing the intervertebral disks, facet joints, ligaments and muscles. A special pentahedral continuum element for representing the articular facets is described which effectively maintains stability of the cervical spine in both lateral and frontal plane accelerations, which is very difficult with multi-spring models of the facets. A simplified representation is used for the spine and body below the level of T1. The neck musculature is modeled by over 100 muscle elements representing 22 major muscle groups in the neck. The model has been validated for frontal and sideways impact accelerations by simulating published experimental data. Results are also presented to show the effects of the stretch reflex response on the dynamics of the head and neck under moderate acceleration.     

Quantitative comparison of ligament formulation and pre-strain in finite element analysis of the human lumbar spine

Data has been published that quantifies the nonlinear, anisotropic material behaviour and pre-strain behaviour of the anterior longitudinal, supraspinous (SSL), and interspinous ligaments of the human lumbar spine. Additionally, data has been published on localized material properties of the SSL. These results have been incrementally incorporated into a previously validated finite element model of the human lumbar spine. Results suggest that the effects of increased ligament model fidelity on bone strain energy were moderate and the effects on disc pressure were slight, and do not justify a change in modelling strategy for most clinical applications. There were significant effects on the ligament stresses of the ligaments that were directly modified, suggesting that these phenomena should be included in FE models where ligament stresses are the desired metric.     

Functional implications of variation in lumbar vertebral count among hominins

As early as the 1970s, Robinson defined lumbar vertebrae according to their zygapophyseal orientation. He identified six lumbar elements in fossil Sts 14 Australopithecus africanus, one more than is commonly present in modern humans. It is now generally inferred that the modal number of lumbar vertebrae for australopiths and early Homo was six, from which the mode of five in later Homo is derived. The two central questions this study investigates are (1) to what extent do differences in human lumbar vertebral count affect lordotic shape and lumbar function, and (2) what does lumbar number variation imply about lumbar spine function in early hominins? To address these questions, I first outline a biomechanical model of lumbar number effect on lordotic function. I then identify relevant morphological differences in the human modal and extra-modal variants, which I use to test the model. These tests permit evaluation of the human L6 variant as a model for reconstructing early hominin modal number and spine function. Application of the biomechanical model in reconstructing australopith/early Homo lumbar spines highlights shared principles of Euler column strength and sagittal spine flexibility among early and modern hominins. Within modern humans, the extra-modal L6 variant has an extended series of three cranially positioned kyphotic vertebrae and strongly oblique zygapophyseal facets at the last lumbar level. Although they share the same radius and length of lumbar curvature, the L6 variant differs functionally from the L5 mode in its expanded range of sagittal flexion/extension and enhanced resistance to shear. Given the modal number of six lumbar vertebrae in australopiths and early Homo, lumbar spine mobility and strength would have been key properties of vertebral function in early bipeds whose upper and lower body segments were coupled by close approximation of the thorax and iliac crests.     

Estimation of trunk muscle forces using the finite element method and in vivo loads measured by telemeterized internal spinal fixation devices.

Direct quantitative measurement of muscle forces is not possible. Forces in the trunk muscles were estimated for standing and flexion of the upper body using three-dimensional, nonlinear finite element models of the lumbar spine with and without an internal spinal fixation device. Muscle forces assumed were two pairs dorsally and one ventrally, each representing several muscles. Muscle forces in the model with internal fixators were varied in discrete steps until the implant loads calculated closely corresponded to those measured in a patient with an instrumented implant. The calculated angles between adjacent lumbar vertebrae were compared with corresponding values measured on X-ray films of a patient as well as with literature values and served as a second criterion for predicting muscle forces. For the model without an implant, the muscle forces of the first model were slightly varied until the lumbar spine shape and the intradiscal pressure were physiological. The abdomen was shown to have a considerable supporting function for flexion.     

A validated three-dimensional computational model of a human knee joint

This paper presents a three-dimensional finite element tibio-femoral joint model of a human knee that was validated using experimental data. The geometry of the joint model was obtained from magnetic resonance (MR) images of a cadaveric knee specimen. The same specimen was biomechanically tested using a robotic/universal force-moment sensor (UFS) system and knee kinematic data under anterior-posterior tibial loads (up to 100 N) were obtained. In the finite element model (FEM), cartilage was modeled as an elastic material, ligaments were represented as nonlinear elastic springs, and menisci were simulated by equivalent-resistance springs. Reference lengths (zero-load lengths) of the ligaments and stiffness of the meniscus springs were estimated using an optimization procedure that involved the minimization of the differences between the kinematics predicted by the model and those obtained experimentally. The joint kinematics and in-situ forces in the ligaments in response to axial tibial moments of up to 10 Nm were calculated using the model and were compared with published experimental data on knee specimens. It was also demonstrated that the equivalent-resistance springs representing the menisci are important for accurate calculation of knee kinematics. Thus, the methodology developed in this study can be a valuable tool for further analysis of knee joint function and could serve as a step toward the development of more advanced computational knee models.     

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.     

Finite element analysis of moment-rotation relationships for human cervical spine

A comprehensive, geometrically accurate, nonlinear C0-C7 FE model of head and cervical spine based on the actual geometry of a human cadaver specimen was developed. The motions of each cervical vertebral level under pure moment loading of 1.0 Nm applied incrementally on the skull to simulate the movements of the head and cervical spine under flexion, tension, axial rotation and lateral bending with the inferior surface of the C7 vertebral body fully constrained were analysed. The predicted range of motion (ROM) for each motion segment were computed and compared with published experimental data. The model predicted the nonlinear moment-rotation relationship of human cervical spine. Under the same loading magnitude, the model predicted the largest rotation in extension, followed by flexion and axial rotation, and least ROM in lateral bending. The upper cervical spines are more flexible than the lower cervical levels. The motions of the two uppermost motion segments account for half (or even higher) of the whole cervical spine motion under rotational loadings. The differences in the ROMs among the lower cervical spines (C3-C7) were relatively small. The FE predicted segmental motions effectively reflect the behavior of human cervical spine and were in agreement with the experimental data. The C0-C7 FE model offers potentials for biomedical and injury studies.     

Personalised mechanical properties of scoliotic vertebrae determined in vivo using tomodensitometry

This in vivo study investigated the mechanical properties of apical scoliotic vertebrae using computed tomography (CT) and finite element (FE) meshing. CT examination was performed on seven scoliotic girls. FE meshing of each vertebral body allowed automatic mapping of the CT scan and the visualisation of the bone density distribution. Centroids and mass centres were compared to analyse the mechanical properties distribution. Compared to the centroid, the mass centre migrated into the concavity of the curvature. The three vertebrae of a same patient had the same body migration behaviour because they were located at the curvature apex. This observation was verified in the coronal plane, but not in the sagittal plane. These results represent new data over few geometrical analyses of scoliotic vertebrae. Same in vivo personalisation of mechanical properties should be performed on intervertebral discs or ligaments to personalise stiffness properties of the spine for the biomechanical modelling of human torso. Moreover, do this mechanical deformation of scoliotic vertebrae, that appears before the vertebral wedging, could be a predictive tool in scoliosis treatment?     

A computational model for dynamic analysis of the human gait

Biomechanical models are important tools in the study of human motion. This work proposes a computational model to analyse the dynamics of lower limb motion using a kinematic chain to represent the body segments and rotational joints linked by viscoelastic elements. The model uses anthropometric parameters, ground reaction forces and joint Cardan angles from subjects to analyse lower limb motion during the gait. The model allows evaluating these data in each body plane. Six healthy subjects walked on a treadmill to record the kinematic and kinetic data. In addition, anthropometric parameters were recorded to construct the model. The viscoelastic parameter values were fitted for the model joints (hip, knee and ankle). The proposed model demonstrated that manipulating the viscoelastic parameters between the body segments could fit the amplitudes and frequencies of motion. The data collected in this work have viscoelastic parameter values that follow a normal distribution, indicating that these values are directly related to the gait pattern. To validate the model, we used the values of the joint angles to perform a comparison between the model results and previously published data. The model results show a same pattern and range of values found in the literature for the human gait motion.     

A finite element model technique to determine the mechanical response of a lumbar spine segment under complex loads

This study presents a CT-based finite element model of the lumbar spine taking into account all function-related boundary conditions, such as anisotropy of mechanical properties, ligaments, contact elements, mesh size, etc. Through advanced mesh generation and employment of compound elements, the developed model is capable of assessing the mechanical response of the examined spine segment for complex loading conditions, thus providing valuable insight on stress development within the model and allowing the prediction of critical loading scenarios. The model was validated through a comparison of the calculated force-induced inclination/deformation and a correlation of these data to experimental values. The mechanical response of the examined functional spine segment was evaluated, and the effect of the loading scenario determined for both vertebral bodies as well as the connecting intervertebral disc.     

Lumbar posterior ligament involvement during extremely heavy lifts estimated from fluoroscopic measurements.

The mechanical role of the lumbar posterior ligaments during lifting tasks remains controversial. This study was designed to assess the ligament and disc contribution in resisting trunk flexion moment during extremely heavy lifts performed by national class powerlifters. Direct measurements of lumbar vertebrae kinematics in sagittal plane were obtained from videofluoroscopy utilizing multiple digitizing, correction for optical distortions and digital filtering. Four experienced powerlifters executed three trials, resulting in about 72 mA s of total radiation exposure. In the first trial, joint angles were measured when subjects fully flexed their spines to a point where the passive tissues resisted the flexor moment creating myoelectric silence in the extensor musculature. Next, two conventional deadlift style lifts were executed with the barbell load ranging from 183.7 to 210.9 kg. Four vertebral corners were digitized at a sampling rate of 30 Hz. The relative intervertebral joint angles, distance between the ligament attachment points, shearing and compressive displacements were calculated from a rigid body motion approach. Analysis revealed that except for one trial of one subject, they accomplished their lifts with an amount of lumbar flexion between 1.5 and 13 degrees less than they demonstrated during full flexion. Resultant ligament lengths at the beginning of the lifts ranged from 56.1 to 99.8% of their lengths when the trunk was fully flexed. It was concluded that ligaments did not strain sufficiently to contribute substantial resistance to the trunk flexion moment, relegating this responsibility to the musculature.