Incorporating ligament laxity in a finite element model for the upper cervical spine

Quantifying the Importance of Active Muscle Repositioning a Finite Element Neck Model in Flexion Using Kinematic, Kinetic, and Tissue-Level Responses

PURPOSE

Non-neutral neck positions are important initial conditions in impact scenarios, associated with a higher incidence of injury. Repositioning in finite element (FE) neck models is often achieved by applying external boundary conditions (BCs) to the head while constraining the first thoracic vertebra (T1). However, in vivo, neck muscles contract to achieve a desired head and neck position generating initial loads and deformations in the tissues. In the present study, a new muscle-based repositioning method was compared to traditional applied BCs using a contemporary FE neck model for forward head flexion of 30°.

METHODS

For the BC method, an external moment (2.6 Nm) was applied to the head with T1 fixed, while for the muscle-based method, the flexors and extensors were co-contracted under gravity loading to achieve the target flexion.

RESULTS

The kinematic response from muscle contraction was within 10% of the in vivo experimental data, while the BC method differed by 18%. The intervertebral disc forces from muscle contraction were agreeable with the literature (167 N compression, 12 N shear), while the BC methodology underpredicted the disc forces owing to the lack of spine compression. Correspondingly, the strains in the annulus fibrosus increased by an average of 60% across all levels due to muscle contraction compared to BC method.

CONCLUSION

The muscle repositioning method enhanced the kinetic response and subsequently led to differences in tissue-level responses compared to the conventional BC method. The improved kinematics and kinetics quantify the importance of repositioning FE neck models using active muscles to achieve non-neutral neck positions.

Spinal Cord Boundary Conditions Affect Brain Tissue Strains in Impact Simulations

Brain and spinal cord injuries have devastating consequences on quality of life but are challenging to assess experimentally due to the traumatic nature of such injuries. Finite element human body models (HBM) have been developed to investigate injury but are limited by a lack of biofidelic spinal cord implementation. In many HBM, brain models terminate with a fixed boundary condition at the brain stem. The goals of this study were to implement a comprehensive representation of the spinal cord into a contemporary head and neck HBM, and quantify the effect of the spinal cord on brain deformation during simulated impacts. Spinal cord tissue geometries were developed, based on 3D medical imaging and literature data, meshed, and implemented into the GHBMC 50th percentile male model. The model was evaluated in frontal, lateral, rear, and oblique impact conditions, and the resulting maximum principal strains in the brain tissue were compared, with and without the spinal cord. A new cumulative strain curve metric was proposed to quantify brain strain distribution. Presence of the spinal cord increased brain tissue strains in all simulated cases, owing to a more compliant boundary condition, highlighting the importance of the spinal cord to assess brain response during impact.

Implications of range of motion requirements for the laxity of ligaments in a lumbar finite element model

Finite element models of the lumbar spine often adopt ligament properties from tensile tests without accounting for possible differences between testing and in situ initial ligament length. Such differences could result in laxities or preloads at the beginning of a simulation that would affect the ligament forces, tangent stiffness, and the posture at which they fail. In vivo and in vitro human experimental data reported laxities or preloads. However, laxities or preloads, which could also result from postural differences, are often neglected in simulation studies. This study proposes a numerical methodology to identify ranges of ligament laxities or preloads compatible with the selected tensile ligament properties, the model, and the range of motion (RoM) the model aims to simulate. The approach assumes that ligaments should remain in a safe elongation range for the complete RoM, and that each ligament should play a significant mechanical role in at least one load case. The methodology was applied to the functional spinal unit (FSU) models using the RoM from healthy subjects and ligament properties from the literature. Without laxity, some ligaments reached their elongation at failure within the RoM. Laxity ranges varied considerably (from -9.2 mm preload to 10.7 mm laxity) and flexion was the most critical load case to determine them. Their effect on the mobility response was also assessed. The effect on the mobility of a FSU was also assessed. While the proposed method cannot determine an exact laxity value, it is simple and it can be applied to any model to identify a plausible range of ligament initial length.

Biomechanical analysis of odontoid and transverse atlantal ligament in humans with ponticulus posticus variation under different loading conditions: Finite element study

PURPOSE

Ponticulus posticus (PP) is a variation of the bone bridge that appears in the first cervical vertebra and through which the vertebral artery passes. Odontoid fractures are common spinal bone fractures in older people. This study aims to investigate the effect of neck movements on the odontoid and transverse atlantal ligament (TAL) of people with PP variation from a biomechanical view.

METHOD

C1, C2, and C3 vertebrae of the occipital bone were analyzed using the finite element method (FEM). In this study, solid models were created with the help of normal (N), incomplete (IC), and asymmetric complete (AC) PP tomography images. The necessary elements for the models were assigned, and the material properties were defined for the elements. As boundary conditions, models were fixed from the C3 vertebra, and 74 N loading was applied from the occipital bone. Stress and deformation values in the odontoid and transverse atlantal ligament were obtained by applying 1.8 Nm moment in flexion, extension, bending, and axial rotation directions.

RESULTS

The stress and deformation values of all three models in odontoid and TAL were obtained, and numerical results were evaluated. In all models, stress and deformation values were obtained in decreasing order in rotation, bending, extension, and flexion movements. The highest stress and strain values were obtained in AC and the lowest values were obtained in N. In all movements of the three models, the stress and deformation values obtained in the TAL were lower than in the odontoid.

CONCLUSION

The greatest stresses and deformations obtained in spines (AC) with PP were found in the odontoid. This may help explain the pathogenesis of odontoid fractures in older people. First, this study explains the mechanism of the formation of neck trauma in people with PP and the need for a more careful evaluation of the direction of impact. Secondly, the study reveals that the rotational motion of the neck independent of PP has more negative effects on the odontoid.

Design of personalized scoliosis braces based on differentiable biomechanics—Synthetic study

This work describes a computational methodology for the design of braces for adolescent idiopathic scoliosis. The proposed methodology relies on a personalized simulation model of the patient’s trunk, and automatically searches for the brace geometry that optimizes the trade-off between clinical improvement and patient comfort. To do this, we introduce a formulation of differentiable biomechanics of the patient’s trunk, the brace, and their interaction. We design a simulation model that is differentiable with respect to both the deformation state and the brace design parameters, and we show how this differentiable model is used for the efficient update of brace design parameters within a numerical optimization algorithm. To evaluate the proposed methodology, we have obtained trunk models with personalized geometry for five patients of adolescent idiopathic scoliosis, and we have designed Boston-type braces. In a simulation setting, the designed braces improve clinical metrics by 45% on average, under acceptable comfort conditions. In the future, the methodology can be extended beyond synthetic validation, and tested with physical braces on the actual patients.

Scoliosis assessment tools to reduce follow-up X-rays

Purpose

Clinical examinations of scoliosis often includes X-rays. Regular clinical monitoring is recommended in particular at young age, because of the high risk of progression during periods of rapid growth. Supplementary methods free of ionizing radiation thus could help to reduce the potential risk of ionizing radiation related health problems.

Methods

Twelve 3D scan images from female and male patients with different types and severities of spinal deformations were analysed using body scanner image analysis tools. The scan images were captured with a 3D body scanner, which used an infrared sensor and a video camera. To calculate and compare with the patient's specific spinal deformations, simulations based on finite elements methods were performed on biomechanical models of ribcage and spinal column.

Results

The methods and parameters presented here are in good agreement with corresponding X-rays, used for comparison. High correlation coefficients of ‖ρ _s ‖ ≥ 0.87 between Cobb angle and lateral deviation, as well as between Cobb angle and rotation of the vertebrae, indicate that the parameters could provide supplementary informations in the assessment of spinal deformations. So-called apex angles, in addition introduced to relate the results of the present method with Cobb angles, show strong correlations of ‖ρ _s ‖ ≥ 0.68 and thus could be used for comparison in later follow-up examinations.

Conclusion

The user-friendly 3D body scanner image analysis tools enable orthopaedic specialists to simulate, visualize and inspect patient's specific spinal deformations. The method is intended to provide supplementary information in complement to the Cobb angle for the assessment of spinal deformations in clinical daily routine and might have the potential to reduce X-rays in follow-up examinations.

The Translational Potential of this article

The study presents a new method, based on 3D body scanner images and biomechanical modelling, that has the potential to reduce X-rays when monitoring scoliosis especially in young patients.

Enhancing the Biofidelity of an Upper Cervical Spine Finite Element Model within the Physiologic Range of Motion and Its Effect On the Full Ligamentous Neck Model Response

Contemporary finite element neck models are developed in a neutral posture; however, evaluation of injury risk for out-of-position impacts requires neck model repositioning to non-neutral postures, with much of the motion occurring in the upper cervical spine (UCS). Current neck models demonstrate a limitation in predicting the intervertebral motions within the UCS within the range of motion (ROM), while recent studies have highlighted the importance of including the tissue strains resulting from repositioning FE neck models to predict injury risk. In the current study, the ligamentous cervical spine from a contemporary neck model (GHBMC M50 v4.5) was evaluated in flexion, extension and axial rotation by applying moments from 0 to 1.5 Nm in 0.5 Nm increments, as reported in experimental studies and corresponding to the physiologic loading of the UCS. Enhancements to the UCS model were identified, including the C0-C1 joint-space and alar ligament orientation. Following geometric enhancements, an analysis was undertaken to determine the UCS ligament laxities, using a sensitivity study followed by an optimization study. The ligament laxities were optimized to UCS-level experimental data from the literature. The mean percent difference between UCS model response and experimental data improved from 55% to 23% with enhancements. The enhanced UCS model was integrated with a ligamentous cervical spine (LS) model and assessed with independent experimental data. The mean percent difference between the LS model and the experimental data improved from 46% to 35% with the integration of the enhanced UCS model.

Biomechanical Morphing for Personalized Fitting of Scoliotic Torso Skeleton Models

The use of patient-specific biomechanical models offers many opportunities in the treatment of adolescent idiopathic scoliosis, such as the design of personalized braces. The first step in the development of these patient-specific models is to fit the geometry of the torso skeleton to the patient’s anatomy. However, existing methods rely on high-quality imaging data. The exposure to radiation of these methods limits their applicability for regular monitoring of patients. We present a method to fit personalized models of the torso skeleton that takes as input biplanar low-dose radiographs. The method morphs a template to fit annotated points on visible portions of the spine, and it relies on a default biomechanical model of the torso for regularization and robust fitting of hardly visible parts of the torso skeleton, such as the rib cage. The proposed method provides an accurate and robust solution to obtain personalized models of the torso skeleton, which can be adopted as part of regular management of scoliosis patients. We have evaluated the method on ten young patients who participated in our study. We have analyzed and compared clinical metrics on the spine and the full torso skeleton, and we have found that the accuracy of the method is at least comparable to other methods that require more demanding imaging methods, while it offers superior robustness to artifacts such as interpenetration of ribs. Normal-dose X-rays were available for one of the patients, and for the other nine we acquired low-dose X-rays, allowing us to validate that the accuracy of the method persisted under less invasive imaging modalities.

Sensitivity of the Cervical Disc Loads, Translations, Intradiscal Pressure, and Muscle Activity Due to Segmental Mass, Disc Stiffness, and Muscle Strength in an Upright Neutral Posture

Musculoskeletal disorders of the cervical spine have increased considerably in recent times. To understand the effects of various biomechanical factors, quantifying the differences in disc loads, motion, and muscle force/activity is necessary. The kinematic, kinetic, or muscle response may vary in a neutral posture due to interindividual differences in segmental mass, cervical disc stiffness, and muscle strength. Therefore, our study aimed to develop an inverse dynamic model of the cervical spine, estimate the differences in disc loads, translations, intradiscal pressure, and muscle force/activity in a neutral posture and compare these results with data available in the literature. A head–neck complex with nine segments (head, C1–T1) was developed with joints having three rotational and three translational degrees of freedom, 517 nonlinear ligament fibers, and 258 muscle fascicles. A sensitivity analysis was performed to calculate the effect of segmental mass (5th to 95th percentile), translational disc stiffness (0.5–1.5), and muscle strength (0.5–1.5) on the cervical disc loads (C2–C3 to C7–T1), disc translations, intradiscal pressure, and muscle force/activity in a neutral posture. In addition, two axial external load conditions (0 and 40 N) were also considered on the head. The estimated intradiscal pressures (0.2–0.56 MPa) at 0 N axial load were comparable to in vivo measurements found in the literature, whereas at 40 N, the values were 0.39–0.93 MPa. With increased segmental mass (5th to 95th), the disc loads, translations, and muscle forces/activities increased to 69% at 0 N and 34% at 40 N axial load. With increased disc stiffness (0.5–1.5), the maximum differences in axial (<1%) and shear loads (4%) were trivial; however, the translations were reduced by 67%, whereas the differences in individual muscle group forces/activities varied largely. With increased muscle strength (0.5–1.5), the muscle activity decreased by 200%. For 40 vs. 0 N, the differences in disc loads, translations, and muscle forces/activities were in the range of 52–129%. Significant differences were estimated in disc loads, translations, and muscle force/activity in the normal population, which could help distinguish between normal and pathological cervical spine conditions.

A study of the sensitivity of biomechanical models of the spine for scoliosis brace design

BACKGROUND AND OBJECTIVE

The development of biomechanical models of the torso and the spine opens the door to computational solutions for the design of braces for adolescent idiopathic scoliosis. However, the design of such biomechanical models faces several unknowns, such as the correct identification of relevant mechanical elements, or the required accuracy of model parameters. The objective of this study was to design a methodology for the identification of the aforementioned elements, with the purpose of creating personalized models suited for patient-specific brace design and the definition of parameter estimation criteria.

METHODS

We have developed a comprehensive model of the torso, including spine, ribcage and soft tissue, and we have developed computational tools for the analysis of the model parameters. With these tools, we perform an analysis of the model under typical loading conditions of scoliosis braces.

RESULTS

We present a complete sensitivity analysis of the models mechanical parameters and a comparison between a reference healthy subject and a subject suffering from scoliosis. Furthermore, we make a direct connection between error bounds on the deformation and tolerances for parameter estimation, which can guide the personalization of the model.

CONCLUSIONS

Not surprisingly, the stiffness parameters that govern the lateral deformation of the spine in the frontal plane are some of the most relevant parameters, and require careful modeling. More surprisingly, their relevance is on par with the correct parameterization of the soft tissue of the torso. For scoliosis patients, but not for healthy subjects, we observe that the axial rotation of the spine also requires careful modeling.

Biomechanical comparison of a C1 posterior arch clamp with C1 lateral mass screws in constructs for C1-C2 fusion

The aim of this experimental study was to assess the biomechanical performance of a novel C1 posterior arch (C1PA) clamp compared with C1 lateral mass (C1LM) screws in constructs used to treat atlantoaxial instability. These constructs had either C2 pedicle (C2P) screws or C2 translaminar (C2TL) screws. Eight fresh-frozen human cadaveric ligamentous spine specimens (C0-C3) were tested under six conditions: the intact state, the destabilized state after a simulated odontoid fracture, and when instrumented with four constructs (C1LM-C2P, C1LM-C2TL, C1PA-C2P, C1PA-C2TL). Each specimen was tested in a spinal loading simulator that separately applied axial rotation, flexion-extension and lateral bending. In each test condition, displacement controlled angular motion was applied in both directions at a speed of 2 deg/s until a resulting moment of 1.5 Nm was achieved. The measured ranges of motion (ROM) of the C1-C2 segments were compared for each test condition using nonparametric Friedman tests. The destabilized state had significantly more C1-C2 motion (p < 0.05) than the intact state in all cases, and all constructs greatly reduced this motion. C2 pedicle screw constructs that used the C1PA clamp had significantly less C1-C2 motion (p < 0.05) than those with C1LM screws in flexion-extension as well as axial rotation and no statistically significant difference was detected in lateral bending. C2 translaminar screw constructs that used the C1PA clamp had significantly less C1-C2 motion (p < 0.05) than those with C1LM screws in flexion-extension and no statistically significant difference was detected in axial rotation or in lateral bending. Data from the current study suggested that constructs using the novel C1PA clamp would provide as good, or improved, biomechanical stability to the C1-C2 segment compared with constructs using C1LM screws.

Multilevel Validation of a Male Neck Finite Element Model With Active Musculature

Computational models of the human neck have been developed to assess human response in impact scenarios; however, the assessment and validation of such models is often limited to a small number of experimental data sets despite being used to evaluate the efficacy of safety systems and potential for injury risk in motor vehicle collisions. In this study, a full neck model (NM) with active musculature was developed from previously validated motion segment models of the cervical spine. Tissue mechanical properties were implemented from experimental studies, and were not calibrated. The neck model was assessed with experimental studies at three levels of increasing complexity: ligamentous cervical spine in axial rotation, axial tension, frontal impact, and rear impact; postmortem human subject (PMHS) rear sled impact; and human volunteer frontal and lateral sled tests using an open-loop muscle control strategy. The neck model demonstrated good correlation with the experiments ranging from quasi-static to dynamic, assessed using kinematics, kinetics, and tissue-level response. The contributions of soft tissues, neck curvature, and muscle activation were associated with higher stiffness neck response, particularly for low severity frontal impact. Experiments presenting single-value data limited assessment of the model, while complete load history data and cross-correlation enabled improved evaluation of the model over the full loading history. Tissue-level metrics demonstrated higher variability and therefore lower correlation relative to gross kinematics, and also demonstrated a dependence on the local tissue geometry. Thus, it is critical to assess models at the gross kinematic and the tissue levels.

Establishment and Finite Element Analysis of a Three-dimensional Dynamic Model of Upper Cervical Spine Instability

Objectives

To establish a dynamic three‐dimensional (3D) model of upper cervical spine instability and to analyze its biomechanical characteristics.

Methods

A 3D geometrical model was established after CT scanning of the upper cervical spine specimen. The ligament of the specimen was fatigued to establish the upper cervical spine‐instability model. A 100‐N preloaded stress was applied to the upper surface of the occipital bone, and then a 1.5‐Nm moment was applied in the occipital‐sagittal direction to simulate upper cervical spine flexion and extension. Subsequently, the 3D dynamic model was established based on trajectory data that were measured using a motion‐capture system. The stress on the main ligament and the relative motion angle of the joint were analyzed.

Results

The shape of the model grid was regular and the total number of its units was 627 000. After finite‐element analysis was conducted, results of the ligament stress and relative movement angle were obtained. After the upper cervical spine instability, the pressure of the alar ligament during the upper cervical spine extension was increased from 2.85 to 8.12 MPa. The pressure of the flavum ligament was increased during the upper‐cervical spine flexion, from 0.90 to 1.21 MPa. The pressure of the odontoid ligament was reduced during the upper cervical spine flexion and extension, from 10.46 to 6.67 MPa and 25.66 to 16.35 MPa, respectively. The pressure of the anterior longitudinal ligament and cruciate ligament was increased to a certain degree during upper cervical spine flexion and extension. The pressure of the anterior longitudinal ligament was increased during flexion and extension, from 7.70 to 10.10 MPa and 10.45 to 13.75 MPa, respectively. The pressure of the cruciate ligament was increased during flexion and extension, from 2.29 to 4.34 MPa and 2.32 to 4.40 MPa, respectively. In addition, after upper cervical spine instability, the articular‐surface relative‐movement angle of the atlanto‐occipital joint and atlanto‐axial joint had also changed. During upper cervical spine flexion, the angle of the atlanto‐occipital joint was increased from 3.49° to 5.51°, and the angle of the atlanto‐axial joint was increased from 8.84° to 13.70°. During upper cervical spine extension, the angle of the atlanto‐occipital joint was increased from 11.16° to 12.96°, and the angle of the atlanto‐axial joint was increased from 14.20° to 17.20°. Therefore, the movement angle of the atlanto‐axial joint was most obvious after induction of instability.

Conclusion

The 3D dynamic finite‐element model of the upper cervical spine can be used to analyze and summarize the relationship between the change of ligament stress and the degree of instability in cervical instability. Frequent or prolonged flexion activities are more likely to lead to instability of the upper cervical spine.

Musculoskeletal modeling of total ankle arthroplasty using force-dependent kinematics for predicting in vivo joint mechanics

In vivo load and motion in the ankle joint play a key role in the understanding of the failure mechanism and function outcomes of total ankle arthroplasty. However, a thorough understanding of the biomechanics of the ankle joint in daily activities is lacking. The objective of this study was to develop a novel lower extremity musculoskeletal multibody dynamics model with total ankle arthroplasty considering the 6 degrees of freedom of the ankle joint motions and the deformable contact mechanics of the implant, based on force-dependent kinematics method. A patient who underwent total ankle arthroplasty surgery was considered. The walking gait data of the patient was measured in a gait laboratory and used as the input for the patient-specific musculoskeletal modeling. The predictions from the musculoskeletal model of total ankle arthroplasty included dorsiflexion-plantar flexion, inversion-eversion, internal-external rotation, anterior-posterior translation, inferior-superior translation, and medial-lateral translation of the tibiotalar joint, the ankle contact forces, the muscle activations, and the ligament forces. The magnitudes and tendencies of the predicted results were all within reasonable ranges, as compared with the data available in the literature. The predicted peak total ankle contact force was 6.55 body weight. In addition, the peak contact forces of the lateral and medial compartments were 4.22 body weight and 2.59 body weight, respectively. This study provides a potential new platform for the design of a better ankle prosthesis, the improvement of the operation techniques of the clinicians, and the accelerated postoperative recovery of the patients.