Statistical factorial analysis on the material property sensitivity of the mechanical responses of the C4–C6 under compression, anterior and posterior shear

Finite element analysis of the cervical spine: dynamic characteristics and material property sensitivity study

The study aimed to investigate the dynamic characteristics of the cervical spine and determine the effect of the material properties of the cervical spinal components on it. A finite element model of the head-cervical spine was developed based on CT scan data, and the first six orders of modes (e.g. flexion-extension, lateral bending, and vertical, etc.) were verified by experimental and simulation studies. The material sensitivity study was conducted by varying elasticity modulus of cervical hard tissues (cortical bone, cancellous bone, endplates, and posterior elements) and soft tissues (intervertebral disc and ligaments). The results showed that increasing the elastic modulus of ligaments by 4 times increased the natural frequency by 77%, while increasing that of cancellous bone by 4 times only increased the natural frequency by 6%. In the axial mode, the cervical spine had not only axial deformation but also anterior-posterior deformation, with the largest deformation located at the intervertebral disc C6-C7. Decreasing the elastic modulus of a component in soft tissues by 80% increased modal displacement by up to 62%. The material properties of the intervertebral discs and ligaments had opposite effects on the modal displacement and deformation of the cervical spine. Low cervical discs were more susceptible to injury in a vertical vibration environment. Cervical spine dynamics were more sensitive to soft tissue material properties than to hard tissue material properties. Disc degeneration could reduce the range of vibratory motion of the cervical spine, thereby reducing the ability of the cervical spine to cushion head impacts.

Impact of extracellular matrix and collagen network properties on the cervical intervertebral disc response to physiological loads: A parametric study

Current intervertebral disc finite element models are hard to validate since they describe multi-physical phenomena and contain a huge number of material properties. This work aims to simplify numerical validation/identification studies by prioritizing the sensitivity of intervertebral disc behavior to mechanical properties. A 3D fiber-reinforced hyperelastic model of a C6-C7 intervertebral disc is used to carry out the parametric study. 10 parameters describing the extracellular matrix and the collagen network behaviors are included in the parametric study. The influence of varying these parameters on the disc response is estimated during physiological movements of the head, including compression, lateral bending, flexion, and axial rotation. The obtained results highlight the high sensitivity of the disc behavior to the stiffness of the annulus fibrosus extracellular matrix for all the studied loads with a relative increase in the disc apparent stiffness by 67% for compression and by 57% for axial rotation when the annulus stiffness increases from 0.4 to 2 MPa. It is also shown that varying collagen network orientation, stiffness, and stiffening in the studied configuration range have a noticeable effect on rotational motions with a relative apparent stiffness difference reaching 6.8%, 10%, and 22%, respectively, in lateral bending. However, the collagen orientation does not affect disc response to axial load.

In-vitro Biomechanics of the Cervical Spine: a Systematic Review

In-vitro testing has been conducted to provide a comprehensive understanding of the biomechanics of the cervical spine. This has allowed a characterization of the stability of the spine as influenced by the intrinsic properties of its tissue constituents and the severity of degeneration or injury. This also enables the pre-clinical estimation of spinal implant functionality and the success of operative procedures. The purpose of this review paper was to compile methodologies and results from various studies addressing spinal kinematics in pre- and post-operative conditions so that they could be compared. The reviewed literature was evaluated to provide suggestions for a better approach for future studies, to reduce the uncertainties and facilitate comparisons among various results. The overview is presented in a way to inform various disciplines, such as experimental testing, design development, and clinical treatment. The biomechanical characteristics of the cervical spine, mainly the segmental range of motion (ROM), intradiscal pressure (IDP), and facet joint load (FJL), have been assessed by testing functional spinal units (FSUs). The relative effects of pathologies including disc degeneration, muscle dysfunction, and ligamentous transection have been studied by imposing on the specimen complex load scenarios imitating physiological conditions. The biomechanical response is strongly influenced by specimen type, test condition, and the different types of implants utilized in the different experimental groups.

Sensitivity of the properties of the graduated compression stocking and soft tissues on the lower limb-stocking interfacial pressure using the orthogonal simulation test

Graduated compression stocking (GCS) plays an important role in the treatment of venous disease in the lower limb. However, the effect of the variation in the mechanical properties of the GCS and the soft tissues on the treatment of the venous disease in the lower limb remains unclear. The aim of the present study was to investigate the influence of the material properties of the GCS and soft tissues on the lower limb-stocking interfacial pressure using the orthogonal simulation test. A three-dimensional finite element (FE) model of the lower limb was established using the MRI dataset of a 40-year-old volunteer. The bones, the skin, the veins and the skeletal muscles were reconstructed in the FE model. The FE model of the GCS was generated using the information provided by the manufacturer. Then the parameter sensitivity analysis was performed using a two-step orthogonal simulation test. The first-step orthogonal test showed that the variation in the Young's modulus in the wale direction of the GCS induced a change of 0.37 mmHg in the lower limb-stocking interfacial pressure in the ankle section. The second-step orthogonal test showed that the variations in the Young's modulus in the wale direction of the GCS in the knee section induced the changes of 0.05 mmHg, 0.15 mmHg and 0.60 mmHg in the interfacial pressure in the ankle, the calf and the knee, respectively. In conclusion, the Young's modulus in the wale direction of the GCS and the Poisson's ratio of the GCS are the parameters significantly influencing the lower limb-stocking interfacial pressure. The interfacial pressure in the ankle is not sensitive to the Young's modulus in the wale direction of the GCS in the knee section. However, the interfacial pressures in the calf and knee are sensitive to the Young's modulus in the wale direction of the GCS in the knee section. These data provide important information for the design of GCS.

Load-Sharing and Kinematics of the Human Cervical Spine Under Multi-Axial Transverse Shear Loading: Combined Experimental and Computational Investigation

The cervical spine experiences shear forces during everyday activities and injurious events yet there is a paucity of biomechanical data characterizing the cervical spine under shear loading. This study aimed to (1) characterize load transmission paths and kinematics of the subaxial cervical spine under shear loading, and (2) assess a contemporary finite element cervical spine model using this data. Subaxial functional spinal units (FSUs) were subjected to anterior, posterior, and lateral shear forces (200 N) applied with and without superimposed axial compression preload (200 N) while monitoring spine kinematics. Load transmission paths were identified using strain gauges on the anterior vertebral body and lateral masses and a disc pressure sensor. Experimental conditions were simulated with cervical spine finite element model FSUs (GHBMC M50 version 5.0). The mean kinematics, vertebral strains, and disc pressures were compared to experimental results. The shear force-displacement response typically demonstrated a toe region followed by a linear response, with higher stiffness in anterior shear relative to lateral and posterior shear. Compressive axial preload decreased posterior and lateral shear stiffness and increased initial anterior shear stiffness. Load transmission patterns and kinematics suggest the facet joints play a key role in limiting anterior shear while the disc governs motion in posterior shear. The main cervical spine shear responses and trends are faithfully predicted by the GHBMC cervical spine model. These basic cervical spine biomechanics and the computational model can provide insight into mechanisms for facet dislocation in high severity impacts, and tissue distraction in low severity impacts.

Surgical Design Optimization of Proximal Junctional Kyphosis

Purpose

The objective of this study was to construct a procedural planning tool to optimize the proximal junction angle (PJA) to prevent postoperative proximal junctional kyphosis (PJK) for each scoliosis patient.

Methods

Twelve patients (9 patients without PJK and 3 patients with PJK) who have been followed up for at least 2 years after surgery were included. After calculating the loading force on the cephalad intervertebral disc of upper instrumented vertebra of each patient, the finite-element method (FEM) was performed to calculate the stress of each element. The stress information was summarized into the difference value before and after operation in different regions of interest. A two-layer fully connected neural network method was applied to model the relationship between the stress information and the risk of PJK. Leave-one-out cross-validation and sensitivity analysis were implemented to assess the accuracy and stability of the trained model. The optimal PJA was predicted based on the learned model by optimization algorithm.

Results

The mean prediction accuracy was 83.3% for all these cases, and the area under the curve (AUC) of prediction was 0.889. And the output variance of this model was less than 5% when the important factor values were perturbed in a range of 5%.

Conclusion

Our approach integrated biomechanics and machine learning to support the surgical decision. For a new individual, the risk of PJK and optimal PJA can be simultaneously predicted based on the learned model.

Impact of material properties of intervertebral disc on dynamic response of the human lumbar spine to vertical vibration: a finite element sensitivity study

This study aimed to determine the effect of variations in material properties of the intervertebral disc on dynamic response of the human lumbar spine to vertical vibration using a finite element model of the lumbar L1-S1 motion segment. The present material sensitivity study was conducted by varying elastic moduli for annulus ground substance (AGS), annulus fibers (AF), and nucleus pulposus (NP) in the disc. Transient dynamic analysis was performed initially on the model with basic material property under a sinusoidal vertical vibration load. Subsequently, the same analysis was done for each of the three disc components corresponding to high and low material property cases. The computed results were plotted as a function of time and compared. The AGS property displayed a larger impact on vertebral axial displacement and von Mises stress in AGS, and the AF property displayed a larger impact on disc bulge. In contrast, the NP property had little effect on all the response parameters. Additionally, the intradiscal pressure was found to be not sensitive to any of the disc properties. These findings may be helpful in adoption of appropriate material parameters for the intervertebral disc in finite element model of the lumbar spine used for vibration analysis. Graphical abstract Material property sensitivity analysis on vibration characteristics of the human lumbar spine.

Analysis of Uncertainty and Variability in Finite Element Computational Models for Biomedical Engineering: Characterization and Propagation

Computational modeling has become a powerful tool in biomedical engineering thanks to its potential to simulate coupled systems. However, real parameters are usually not accurately known, and variability is inherent in living organisms. To cope with this, probabilistic tools, statistical analysis and stochastic approaches have been used. This article aims to review the analysis of uncertainty and variability in the context of finite element modeling in biomedical engineering. Characterization techniques and propagation methods are presented, as well as examples of their applications in biomedical finite element simulations. Uncertainty propagation methods, both non-intrusive and intrusive, are described. Finally, pros and cons of the different approaches and their use in the scientific community are presented. This leads us to identify future directions for research and methodological development of uncertainty modeling in biomedical engineering.

Simulated effects of head movement on contact pressures between headforms and N95 filtering facepiece respirators-part 1: headform model and validation

In a respirator fit test, a subject is required to perform a series of exercises that include moving the head up and down and rotating the head left and right. These head movements could affect respirator sealing properties during the fit test and consequently affect fit factors. In a model-based system, it is desirable to have similar capability to predict newly designed respirators. In our previous work, finite element modeling (FEM)-based contact simulation between a headform and a filtering facepiece respirator was carried out. However, the headform was assumed to be static or fixed. This paper presents the first part of a series study on the effect of headform movement on contact pressures-a new headform with the capability to move down (flexion), up (extension), and rotate left and right-and validation. The newly developed headforms were validated for movement by comparing the simulated cervical vertebrae rotation angles with experimental results from the literature.

Computational Biomechanical Modeling of Scoliotic Spine: Challenges and Opportunities

BACKGROUND

Biomechanical computer models of the spine have important roles in the treatment and correction of scoliosis by providing predictive information for surgeons and other clinicians.

OBJECTIVES

This article reviews computational models of intact and scoliotic spine and its components; vertebra, intervertebral disc, ligament, facet joints, and muscle. Several spine models, developed using multi-body modelling and finite element modelling schemes, and their pros and cons are discussed.

CONCLUSIONS

The review reveals that scoliosis modelling is performed for 3 main applications: 1) brace simulation; 2) analysis of surgical correction technique; and 3) patient positioning before surgical instrumentation. The models provide predictive information for a priori choice of brace configurations and mechanically effective surgical correction techniques and the expected degree of correction. However, they have many shortcomings: for instance, they do not fully reproduce the active behaviour of the spine and the models' properties are not personalized.

INFLUENCE OF THE CONSTITUTIVE MATERIAL BEHAVIOR MODEL ASSIGNED TO THE ANNULUS FIBROSUS AND THE NUCLEUS PULPOSUS ON THE BIOMECHANICAL PERFORMANCE OF A MODEL OF THE CERVICAL SPINE: A FINITE ELEMENT ANALYSIS STUDY

One feature of the literature on finite element analysis of models of cervical spine segment(s) is that an assortment of constitutive models has been used for the elastic behavior of the annulus fibrosus (AF) and the nucleus pulposus (NF). The extent to which the model assigned to each of these tissues affects the values of the biomechanical parameters of interest of the model is lacking. This issue was the subject of the present study. We used a three-dimensional solid model of the C4–C6 motion segment units (which comprised the vertebral bodies, the bony posterior elements (transverse processes, pedicles, laminae, spinous processes, and facet joints), the intervertebral discs (IVDs), the endplates, and the five major ligaments) and eight combinations of constitutive models. It was found that (1) the influence of the constitutive material models used depended on the tissue considered, with some, such as the posterior endplate of C5 and the cancellous bone of C6, showing marked sensitivity, while others, such as the cancellous bone of C4 and the cortical bone of C5, were moderately affected; and (2) the biomechanical performance of the spine model is more sensitive to the material behavior model used for the AF than it is to that used for the NF. These results suggest that experimental and computational efforts expended in obtaining the most appropriate constitutive model for the elastic behavior of the two parts of the IVD, in particular the AF, are justified.

Sensitivity studies of pediatric material properties on juvenile lumbar spine responses using finite element analysis

The objective of the study was to determine the sensitivity of material properties of the juvenile spine to its external and internal responses using a finite element model under compression, and flexion-extension bending moments. The methodology included exercising the 8-year-old juvenile lumbar spine using parametric procedures. The model included the vertebral centrum, growth plates, laminae, pedicles, transverse processes and spinous processes; disc annulus and nucleus; and various ligaments. The sensitivity analysis was conducted by varying the modulus of elasticity for various components. The first simulation was done using mean material properties. Additional simulations were done for each component corresponding to low and high material property variations. External displacement/rotation and internal stress-strain responses were determined under compression and flexion-extension bending. Results indicated that, under compression, disc properties were more sensitive than bone properties, implying an elevated role of the disc under this mode. Under flexion-extension moments, ligament properties were more dominant than the other components, suggesting that various ligaments of the juvenile spine play a key role in modulating bending behaviors. Changes in the growth plate stress associated with ligament properties explained the importance of the growth plate in the pediatric spine with potential implications in progressive deformities.

Biomechanical changes of the lumbar segment after total disc replacement : charite(r), prodisc(r) and maverick(r) using finite element model study

OBJECTIVE

The purpose of this study was to analyze the biomechanical effects of three different constrained types of an artificial disc on the implanted and adjacent segments in the lumbar spine using a finite element model (FEM).

METHODS

The created intact model was validated by comparing the flexion-extension response without pre-load with the corresponding results obtained from the published experimental studies. The validated intact lumbar model was tested after implantation of three artificial discs at L4-5. Each implanted model was subjected to a combination of 400 N follower load and 5 Nm of flexion/extension moments. ABAQUS version 6.5 (ABAQUS Inc., Providence, RI, USA) and FEMAP version 8.20 (Electronic Data Systems Corp., Plano, TX, USA) were used for meshing and analysis of geometry of the intact and implanted models.

RESULTS

Under the flexion load, the intersegmental rotation angles of all the implanted models were similar to that of the intact model, but under the extension load, the values were greater than that of the intact model. The facet contact loads of three implanted models were greater than the loads observed with the intact model.

CONCLUSION

Under the flexion load, three types of the implanted model at the L4-5 level showed the intersegmental rotation angle similar to the one measured with the intact model. Under the extension load, all of the artificial disc implanted models demonstrated an increased extension rotational angle at the operated level (L4-5), resulting in an increase under the facet contact load when compared with the adjacent segments. The increased facet load may lead to facet degeneration.

An interactive multiblock approach to meshing the spine

Finite element (FE) analysis is a useful tool to study spine biomechanics as a complement to laboratory-driven experimental studies. Although individualized models have the potential to yield clinically relevant results, the demands associated with modeling the geometric complexity of the spine often limit its utility. Existing spine FE models share similar characteristics and are often based on similar assumptions, but vary in geometric fidelity due to the mesh generation techniques that were used. Using existing multiblock techniques, we propose mesh generation methods that ease the effort and reduce the time required to create subject-specific allhexahedral finite element models of the spine. We have demonstrated the meshing techniques by creating a C4-C5 functional spinal unit and validated it by comparing the resultant motions and vertebral strains with data reported in the literature.

Effect of geometrical uncertainty on cemented hip implant structural integrity

A large number of parameters such as material properties, geometry, and structural strength are involved in the design and analysis of cemented hip implants. Uncertainties in these parameters have a potential to compromise the structural performance and lifetime of implants. Statistical analyses are well suited to investigating this type of problem as they can estimate the influence of these uncertainties on the incidence of failure. Recent investigations have focused on the effect of uncertainty in cement properties and loading condition on the integrity of the construct. The present study hypothesizes that geometrical uncertainties will play a role in cement mantle failure. Finite element input parameters were simulated as random variables and different modes of failure were investigated using a response surface method (RSM). The magnitude of random von Mises stresses varied up to 8 MPa, compared with a maximum nominal value of 2.38 MPa. Results obtained using RSM are shown to match well with a benchmark direct Monte Carlo simulation method. The resulting probability that the maximum cement stress will exceed the nominal stress is 62%. The load and the bone and prosthesis geometries were found to be the parameters most likely to influence the magnitude of the cement stresses and therefore to contribute most to the probability of failure.

Material Property Sensitivity Analysis on Resonant Frequency Characteristics of the Human Spine

The aim of this study is to investigate the effect of material property changes in the spinal components on the resonant frequency characteristics of the human spine. Several investigations have reported the material property sensitivity of human spine under static loading conditions, but less research has been devoted to the material property sensitivity of spinal biomechanical characteristics under a vibration environment. A detailed three-dimensional finite element model of the human spine, T12– pelvis, was built and used to predict the influence of material property variation on the resonant frequencies of the human spine. The simulation results reveal that material properties of spinal components have obvious influences on the dynamic characteristics of the spine. The annulus ground substance is the dominant component affecting the vertical resonant frequencies of the spine. The percentage change of the resonant frequency relative to the basic condition was more than 20% if Young’s modulus of disc annulus is less than 1.5 MPa. The vertical resonant frequency may also decrease if Poisson’s ratio of nucleus pulposus of intervertebral disc decreases.

Viscoelastic finite element analysis of the cervical intervertebral discs in conjunction with a multi-body dynamic model of the human head and neck

This article presents the effects of the frontal and rear-end impact loadings on the cervical spine components by using a multi-body dynamic model of the head and neck, and a viscoelastic finite element (FE) model of the six cervical intervertebral discs. A three-dimensional multi-body model of the human head and neck is used to simulate 15 g frontal and 8.5 g rear-end impacts. The load history at each intervertebral joint from the predictions of the multi-body model is used as dynamic loading boundary conditions for the FE model of the intervertebral discs. The results from the multi-body model simulations, such as the intervertebral disc loadings in the form of compressive, tensile, and shear forces and moments, and from the FE analysis such as the von Mises stresses in the intervertebral discs are analysed. This study shows that the proposed approach that uses dynamic loading conditions from the multi-body model as input to the FE model has the potential to investigate the kinetics and the kinematics of the cervical spine and its components together with the biomechanical response of the intervertebral discs under the complex dynamic loading history.