Lumbar spine finite element model for healthy subjects: development and validation

Finite element (FE) method is a proven powerful and efficient tool to study the biomechanics of the human lumbar spine. However, due to the large inter-subject variability of geometries and material properties in human lumbar spines, concerns existed on the accuracy and predictive power of one single deterministic FE model with one set of spinal geometry and material properties. It was confirmed that the combined predictions (median or mean value) of several distinct FE models can be used as an improved prediction of behavior of human lumbar spine under identical loading and boundary conditions. In light of this improved prediction, five FE models (L1-L5 spinal levels) of the human lumbar spine were developed based on five healthy living subjects with identical modeling method. The five models were extensively validated through experimental and computational results in the literature. Mesh convergence and material sensitivity analysis were also conducted. We have shown that the results from the five FE models developed in this paper were consistent with the experimental data and simulation results from the existing literature. The validated modeling method introduced in this study can be used in modeling dysfunctional lumber spines such as disc degeneration and scoliosis in future work.     

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.     

Effect of lumbar fasciae on the stability of the lower lumbar spine

The biomechanical effect of tensioning the lumbar fasciae (LF) on the stability of the spine during sagittal plane motion was analysed using a validated finite element model of the normal lumbosacral spine (L4-S1). To apply the tension in the LF along the direction of the fibres, a local coordinate was allocated using dummy rigid beam elements that originated from the spinous process. Up to 10 Nm of flexion and 7.5 Nm of extension moment was applied with and without 20 N of lateral tension in the LF. A follower load of 400 N was additionally applied along the curvature of the spine. To identify how the magnitude of LF tension related to the stability of the spine, the tensioning on the fasciae was increased up to 40 N with an interval of 10 N under 7.5 Nm of flexion/extension moment. A fascial tension of 20 N produced a 59% decrease in angular motion at 2.5 Nm of flexion moment while there was a 12.3% decrease at 10 Nm in the L5-S1 segment. Its decrement was 53 and 9.6% at 2.5 Nm and 10 Nm, respectively, in the L4-L5 segment. Anterior translation was reduced by 12.1 and 39.0% at the L4-L5 and L5-S1 segments under 10 Nm of flexion moment, respectively. The flexion stiffness shows an almost linear increment with the increase in fascial tension. The results of this study showed that the effect of the LF on the stability of the spine is significant.     

The development of an EMG-assisted model to assess spine loading during whole-body free-dynamic lifting

Low back disorders (LBDs) are the most common and costly occupationally-related compensable conditions facing employers today. Over the years several biomechanical assessment models have been developed that intended to assess the load profile imposed upon the spine during lifting and, thus, intended to facilitate the control of LBD risk in the workplace. Many of these biomechanical models have evolved based upon assumptions about how the trunk musculature respond to loads imposed upon the body during lifting. However, few of these models have been able to accurately predict the co-contraction of the trunk musculature which has been shown to have a major influence on the development of spinal loads. Thus, our understanding of how the spine is loaded under realistic dynamic lifting conditions has been deficient. A biologically-assisted or EMG-assisted model has been developed in our laboratory over the past 15 years which endeavours to overcome these traditional problems. The model has been assessed in the sagittal, coronal, and torsional planes of the body. The model development and performance will be reviewed as well as the benefits for controlling occupationally-related LBDs.     

A novel approach to evaluate abdominal coactivities for optimal spinal stability and compression force in lifting

A novel optimisation algorithm is developed to predict coactivity of abdominal muscles while accounting for both trunk stability via the lowest buckling load (P _cr) and tissue loading via the axial compression (F _c). A nonlinear multi-joint kinematics-driven model of the spine along with the response surface methodology are used to establish empirical expressions for P _cr and F _c as functions of abdominal muscle coactivities and external load magnitude during lifting in upright standing posture. A two-component objective function involving F _c and P _cr is defined. Due to opposite demands, abdominal coactivities that simultaneously maximise P _cr and minimise F _c cannot exist. Optimal solutions are thus identified while striking a compromise between requirements on trunk stability and risk of injury. The oblique muscles are found most efficient as compared with the rectus abdominus. Results indicate that higher abdominal coactivities should be avoided during heavier lifting tasks as they reduce stability margin while increasing spinal loads.     

The effect of degenerative morphological changes of the intervertebral disc on the lumbar spine biomechanics: a poroelastic finite element investigation

Intervertebral disc degeneration involves changes in the spinal anatomical structures. The mechanical relevance of the following changes was investigated: disc height, endplate sclerosis, disc water content, permeability and depressurisation. A poroelastic nonlinear finite element model of the L4–L5 human spine segments was employed. Loads represented a daily cycle (500 N compression combined with flexion–extension motion for 16 h followed by 200 N compression for 8 h). In non-degenerative conditions, the model predicted a diurnal axial displacement of 1.32 mm and a peak intradiscal pressure of 0.47 MPa. Axial displacement, facet force and range of motion in flexion–extension are decreased by decreasing disc height. By decreasing the initial water content, axial displacement, facet force and fluid loss were all reduced. Endplate sclerosis did not have a significant influence on the calculated results. Depressurisation determined an increase of the disc effective stress, possibly inducing failure. Degenerative instability was not calculated in any simulations.     

Sensitivity of lumbar spine response to follower load and flexion moment: finite element study

The follower load (FL) combined with moments is commonly used to approximate flexed/extended posture of the lumbar spine in absence of muscles in biomechanical studies. There is a lack of consensus as to what magnitudes simulate better the physiological conditions. Considering the in-vivo measured values of the intradiscal pressure (IDP), intervertebral rotations (IVRs) and the disc loads, sensitivity of these spinal responses to different FL and flexion moment magnitudes was investigated using a 3D nonlinear finite element (FE) model of ligamentous lumbosacral spine. Optimal magnitudes of FL and moment that minimize deviation of the model predictions from in-vivo data were determined. Results revealed that the spinal parameters i.e. the IVRs, disc moment, and the increase in disc force and moment from neutral to flexed posture were more sensitive to moment magnitude than FL magnitude in case of flexion. The disc force and IDP were more sensitive to the FL magnitude than moment magnitude. The optimal ranges of FL and flexion moment magnitudes were 900–1100 N and 9.9–11.2 Nm, respectively. The FL magnitude had reverse effect on the IDP and disc force. Thus, magnitude for FL or flexion that minimizes the deviation of all the spinal parameters together from the in-vivo data can vary. To obtain reasonable compromise between the IDP and disc force, our findings recommend that FL of low magnitude must be combined with flexion moment of high intensity and vice versa.     

Parametric convergence sensitivity and validation of a finite element model of the human lumbar spine

The primary objective of this study was to generate a finite element model of the human lumbar spine (L1–L5), verify mesh convergence for each tissue constituent and perform an extensive validation using both kinematic/kinetic and stress/strain data. Mesh refinement was accomplished via convergence of strain energy density (SED) predictions for each spinal tissue. The converged model was validated based on range of motion, intradiscal pressure, facet force transmission, anterolateral cortical bone strain and anterior longitudinal ligament deformation predictions. Changes in mesh resolution had the biggest impact on SED predictions under axial rotation loading. Nonlinearity of the moment-rotation curves was accurately simulated and the model predictions on the aforementioned parameters were in good agreement with experimental data. The validated and converged model will be utilised to study the effects of degeneration on the lumbar spine biomechanics, as well as to investigate the mechanical underpinning of the contemporary treatment strategies.     

Pedicle screw-based posterior dynamic stabilisation of the lumbar spine: in vitro cadaver investigation and a finite element study

Pedicle screw-based dynamic constructs either benefit from a dynamic (flexible) interconnecting rod or a dynamic (hinged) screw. Both types of systems have been reported in the literature. However, reports where the dynamic system is composed of two dynamic components, i.e. a dynamic (hinged) screw and a dynamic rod, are sparse. In this study, the biomechanical characteristics of a novel pedicle screw-based dynamic stabilisation system were investigated and compared with equivalent rigid and semi-rigid systems using in vitro testing and finite element modelling analysis. All stabilisation systems restored stability after decompression. A significant decrease in the range of motion was observed for the rigid system in all loadings. In the semi-rigid construct the range of motion was significantly less than the intact in extension, lateral bending and axial rotation loadings. There were no significant differences in motion between the intact spine and the spine treated with the dynamic system (P>0.05). The peak stress in screws was decreased when the stabilisation construct was equipped with dynamic rod and/or dynamic screws.     

Implementation and validation of probabilistic models of the anterior longitudinal ligament and posterior longitudinal ligament of the cervical spine

The objective of this investigation was to develop probabilistic finite element (FE) models of the anterior longitudinal ligament (ALL) and posterior longitudinal ligament (PLL) of the cervical spine that incorporate the natural variability of biological specimens. In addition to the model development, a rigorous validation methodology was developed to quantify model performance. Experimental data for the geometry and dynamic properties of the ALL and PLL were used to create probabilistic FE models capable of predicting not only the mean dynamic relaxation response but also the observed experimental variation of that response. The probabilistic FE model uses a quasilinear viscoelastic material constitutive model to capture the time-dependent behaviour of the ligaments. The probabilistic analysis approach yields a statistical distribution for the model-predicted response at each time point rather than a single deterministic quantity (e.g. ligament force) and that response can be statistically compared to experimental data for validation. A quantitative metric that compares the cumulative distribution functions of the experimental data and model response is computed for both the ALL and PLL throughout the time histories and is used to quantify model performance.     

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.     

A novel rapid prototyping and finite element method-based development of the patient-specific temporomandibular joint implant

Objective: The objective of this study was to fabricate a successful implant for temporomandibular joint (TMJ) disorder patients who could not be treated through conventional surgeries.

Methods: A custom-made implant was fabricated using rapid prototyping (RP) for the TMJ surgery. The stability of the metallic implant was validated using a finite element analysis.

Results: The results of finite elements were stable and the design of the TMJ implant was suitable as per the patient's need. The customised implant was made using a fused deposition modelling method of RP and a vertical machining centre. The implant has provided normal jaw function for over 2 years since surgery.

Conclusions: The approach utilised will be helpful in providing successful treatment to the deformed mandible and the mandible joints. This method allows to customise and to accurately fabricatie the implant. Advantages of this approach are that the physical model of the implant was tested for stability before the implantation, the surgeon can plan and rehearse the surgery in advance, it is a less invasive and less time-consuming surgical procedure.     

Smart platform for the analysis of cupula deformation caused by otoconia presence within SCCs

In this paper, we first briefly describe the mechanical model of cupula deformation with the appropriate analytical solution. Then, we present the numerical solution of the same problem and compare it with the analytical one. Besides, we provide another numerical solution based on the Finite Element Method procedure, in an effort to encompass a more realistic approach to the problem such as considering the real geometry of the SCCs and the obstruction of the fluid flow during head movement due to the presence of otoconia. As a result, we obtain fifty solutions for a head rotation angle in a range from 0° to 120°, taking into account that such a manoeuvre lasts exactly 3?seconds. In the end, we present a mobile client–server application for visualising the finite element solutions in a way that is convenient for the clinical practice.     

An upper bound computational model for investigation of fusion effects on adjacent segment biomechanics of the lumbar spine

Abstract

Prediction of the biomechanical effects of fusion surgery on adjacent segments is a challenge in computational biomechanics of the spine. In this study, a two-segment L3-L4-L5 computational model was developed to simulate the effects of spinal fusion on adjacent segment biomechanical responses under a follower load condition. The interaction between the degenerative segment (L4-5) and the adjacent segment (L3-4) was simulated using an equivalent follower spring. The spring stiffness was calibrated using a rigid fusion of a completely degenerated disc model at the L4-5 level, resulting in an upper bound response at the adjacent (L3-4) segment. The obtained upper bound equivalent follower spring was used to simulate the upper bound biomechanical responses of fusion of the disc with different degeneration grades. It was predicted that as the disc degeneration grade at the degenerative segment decreased, the effect on the adjacent segment responses decreased accordingly after fusion. The data indicated that the upper bound computational model can be a useful computational tool for evaluation of the interaction between segments and for investigation of the biomechanical mechanisms of adjacent segment degeneration after fusion.     

Multi-scale finite element modelling at the posterior lumbar vertebra: analysis of pedicle stresses due to pars fracture

Multi-scale finite element (FE) model is a cost-effective way to analyse stress response of micro-level structures to the changes in loading at macro-level. This study deals with the development of a multi-scale model of a human vertebra and stress changes in the pedicle at high resolution after a gross fracture at the posterior neural arch. Spondylolysis (pars fracture) is a painful condition occurring in the vertebral neural arch and common especially among the athletic young population. The fracture of the pars significantly alters load distribution and load transfer characteristics at the neural arch. Structural changes in the posterior vertebra due to the new loading patterns can trigger secondary complications. Clinical reports have shown the association of pedicle hypertrophy or pedicle fracture with unilateral pars fractures. However, the biomechanical consequences of pars fracture and its effect on the pedicle have never been studied in detail. Therefore, we prepared a multi-scale model of posterior vertebra with continuum laminar complex model combined with micro-FE model of a pedicle section. The results showed that stress at the contralateral pars and pedicle increased after unilateral pars fracture simulation. High-stress regions were found around the outer boundaries of the pedicle. This model and information are helpful in understanding the stress changes in the pedicle and can be used for adaptive remodelling studies.     

Simulation of the behaviour of the L1 vertebra for different material properties and loading conditions

Three-dimensional finite element models of the thoracolumbar junction (T12–L2) and isolated L1 vertebra were developed to investigate the role of material properties and loading conditions on vertebral stresses and strains to predict fracture risk. The geometry of the vertebrae was obtained from computed tomography images. The isolated vertebra model included an L1 vertebra loaded through polymethylmethacrylate plates located at the top and bottom of the vertebra, and the segment model included T12 to L2 vertebrae and seven ligaments, fibrous intervertebral discs and facet joints. Each model was examined with both homogeneous and spatially varying bone tissue properties. Stresses and strains were compared for uniform compression and flexion. Including material heterogeneity remarkably reduced the stiffness of the isolated L1 vertebra and increased the magnitudes of the minimum principal strains and stresses in the mid-transverse section. The stress and strain distributions further changed when physiological loading was applied to the L1 vertebra. In the segment models, including heterogeneous material properties increased the magnitude of the minimum principal strain by 158% in the centre of the mid-transverse section. Overall, the inclusion of heterogeneity and physiological loading increased the magnitude of the strains up to 346% in flexion and 273% in compression.     

The influence of different magnitudes and methods of applying preload on fusion and disc replacement constructs in the lumbar spine: a finite element analysis

In a finite element (FE) analysis of the lumbar spine, different preload application methods that are used in biomechanical studies may yield diverging results. To investigate how the biomechanical behaviour of a spinal implant is affected by the method of applying the preload, hybrid-controlled FE analysis was used to evaluate the biomechanical behaviour of the lumbar spine under different preload application methods. The FE models of anterior lumbar interbody fusion (ALIF) and artificial disc replacement (ADR) were tested under three different loading conditions: a 150 N pressure preload (PP) and 150 and 400 N follower loads (FLs). This study analysed the resulting range of motion (ROM), facet contact force (FCF), inlay contact pressure (ICP) and stress distribution of adjacent discs. The FE results indicated that the ROM of both surgical constructs was related to the preload application method and magnitude; differences in the ROM were within 7% for the ALIF model and 32% for the ADR model. Following the application of the FL and after increasing the FL magnitude, the FCF of the ADR model gradually increased, reaching 45% at the implanted level in torsion. The maximum ICP gradually decreased by 34.1% in torsion and 28.4% in lateral bending. This study concluded that the preload magnitude and application method affect the biomechanical behaviour of the lumbar spine. For the ADR, remarkable alteration was observed while increasing the FL magnitude, particularly in the ROM, FCF and ICP. However, for the ALIF, PP and FL methods had no remarkable alteration in terms of ROM and adjacent disc stress.     

Biomechanical analysis of the anterior cervical fusion

This paper presents a biomechanical analysis of the cervical C5–C6 functional spine unit before and after the anterior cervical discectomy and fusion. The aim of this work is to study the influence of the medical procedure and its instrumentation on range of motion and stress distribution. First, a three-dimensional finite element model of the lower cervical spine is obtained from computed tomography images using a pipeline of image processing, geometric modelling and mesh generation software. Then, a finite element study of parameters' influence on motion and a stress analysis at physiological and different post-operative scenarios were made for the basic movements of the cervical spine. It was confirmed that the results were very sensitive to intervertebral disc properties. The insertion of an anterior cervical plate influenced the stress distribution at the vertebral level as well as in the bone graft. Additionally, stress values in the graft decreased when it is used together with a cage.     

Analysis of the effect of design parameters and their interactions on the strength of dental restorations with endodontic posts,using finite element models and statistical analysis

Many previous studies, both in vitro and with model simulations, have been conducted in an attempt to reach a full understanding of how the different design parameters of an endodontically restored tooth affect its mechanical strength. However, differences in the experimental set-up or modelling conditions and the limited number of parameters studied in each case prevent us from obtaining clear conclusions about the real significance of each parameter. In this work, a new approach is proposed for this purpose based on the combination of a validated three-dimensional parametric biomechanical model of the restored tooth and statistical analysis using full factorial analysis of variance. A two-step approach with two virtual tests (with, respectively, 128 and 81 finite element models) was used in the present work to study the effect of several design parameters on the strength of a restored incisor, using full factorial designs. Within the limitations of this study, and for cases where the parameters are within the ranges that were tested, the conclusions indicate that the material of the post is the most significant factor as far as its strength is concerned, the use of a low Young's modulus being preferable for this component. Once the post material has been chosen, the geometry of the post is of less importance than the Young's modulus selected for the core or, especially, for the crown.