Identification of a lumped-parameter model of the intervertebral joint from experimental data

Through predictive simulations, multibody models can aid the treatment of spinal pathologies by identifying optimal surgical procedures. Critical to achieving accurate predictions is the definition of the intervertebral joint. The joint pose is often defined by virtual palpation. Intervertebral joint stiffnesses are either derived from literature, or specimen-specific stiffnesses are calculated with optimisation methods. This study tested the feasibility of an optimisation method for determining the specimen-specific stiffnesses and investigated the influence of the assigned joint pose on the subject-specific estimated stiffness. Furthermore, the influence of the joint pose and the stiffness on the accuracy of the predicted motion was investigated. A computed tomography based model of a lumbar spine segment was created. Joints were defined from virtually palpated landmarks sampled with a Latin Hypercube technique from a possible Cartesian space. An optimisation method was used to determine specimen-specific stiffnesses for 500 models. A two-factor analysis was performed by running forward dynamic simulations for ten different stiffnesses for each successfully optimised model. The optimisations calculated a large range of stiffnesses, indicating the optimised specimen-specific stiffnesses were highly sensitive to the assigned joint pose and related uncertainties. A limited number of combinations of optimised joint stiffnesses and joint poses could accurately predict the kinematics. The two-factor analysis indicated that, for the ranges explored, the joint pose definition was more important than the stiffness. To obtain kinematic prediction errors below 1 mm and 1° and suitable specimen-specific stiffnesses the precision of virtually palpated landmarks for joint definition should be better than 2.9 mm.

The strain distribution in the lumbar anterior longitudinal ligament is affected by the loading condition and bony features: An in vitro full-field analysis

The role of the ligaments is fundamental in determining the spine biomechanics in physiological and pathological conditions. The anterior longitudinal ligament (ALL) is fundamental in constraining motions especially in the sagittal plane. The ALL also confines the intervertebral discs, preventing herniation. The specific contribution of the ALL has indirectly been investigated in the past as a part of whole spine segments where the structural flexibility was measured. The mechanical properties of isolated ALL have been measured as well. The strain distribution in the ALL has never been measured under pseudo-physiological conditions, as part of multi-vertebra spine segments. This would help elucidate the biomechanical function of the ALL. The aim of this study was to investigate in depth the biomechanical function of the ALL in front of the lumbar vertebrae and of the intervertebral disc. Five lumbar cadaveric spine specimens were subjected to different loading scenarios (flexion-extension, lateral bending, axial torsion) using a state-of-the-art spine tester. The full-field strain distribution on the anterior surface was measured using digital image correlation (DIC) adapted and validated for application to spine segments. The measured strain maps were highly inhomogeneous: the ALL was generally more strained in front of the discs than in front of the vertebrae, with some locally higher strains both imputable to ligament fibers and related to local bony defects. The strain distributions were significantly different among the loading configurations, but also between opposite directions of loading (flexion vs. extension, right vs. left lateral bending, clockwise vs. counterclockwise torsion). This study allowed for the first time to assess the biomechanical behaviour of the anterior longitudinal ligament for the different loading of the spine. We were able to identify both the average trends, and the local effects related to osteophytes, a key feature indicative of spine degeneration.

METHODS FOR THE CHARACTERIZATION OF THE LONG-TERM MECHANICAL PERFORMANCE OF CEMENTS FOR VERTEBROPLASTY AND KYPHOPLASTY: CRITICAL REVIEW AND SUGGESTIONS FOR TEST METHODS

There is a growing interest towards bone cements for use in vertebroplasty and kyphoplasty, as such spine procedures are becoming more and more common. Such cements feature different compositions, including both traditional acrylic cements and resorbable and bioactive materials. Due to the different compositions and intended use, the mechanical requirements of cements for spinal applications differ from those of traditional cements used in joint replacement. Because of the great clinical implications, it is very important to assess their long-term mechanical competence in terms of fatigue strength and creep. This paper aims at offering a critical overview of the methods currently adopted for such mechanical tests. The existing international standards and guidelines and the literature were searched for publications relevant to fatigue and creep of cements for vertebroplasty and kyphoplasty. While standard methods are available for traditional bone cements in general, no standard indicates specific methods or acceptance criteria for fatigue and creep of cements for vertebroplasty and kyphoplasty. Similarly, a large number of papers were published on cements for joint replacements, but only few cover fatigue and creep of cements for vertebroplasty and kyphoplasty. Furthermore, the literature was analyzed to provide some indications of tests parameters and acceptance criteria (number of cycles, duration in time, stress levels, acceptable amount of creep) for possible tests specifically relevant to cements for spinal applications.

Effect of the In Vitro Boundary Conditions on the Surface Strain Experienced by the Vertebral Body in the Elastic Regime

The vertebral strength and strain can be assessed in vitro by both using isolated vertebrae and sets of three adjacent vertebrae (the central one is loaded through the disks). Our goal was to elucidate if testing single-vertebra-specimens in the elastic regime provides different surface strains to three-vertebrae-segments. Twelve three-vertebrae sets were extracted from thoracolumbar human spines. To measure the principal strains, the central vertebra of each segment was prepared with eight strain-gauges. The sets were tested mechanically, allowing comparison of the surface strains between the two boundary conditions: first when the same vertebra was loaded through the disks (three-vertebrae-segment) and then with the endplates embedded in cement (single-vertebra). They were all subjected to four nondestructive tests (compression, traction, torsion clockwise, and counterclockwise). The magnitude of principal strains differed significantly between the two boundary conditions. For axial loading, the largest principal strains (along vertebral axis) were significantly higher when the same vertebra was tested isolated compared to the three-vertebrae-segment. Conversely, circumferential strains decreased significantly in the single vertebrae compared to the three-vertebrae-segment, with some variations exceeding 100% of the strain magnitude, including changes from tension to compression. For torsion, the differences between boundary conditions were smaller. This study shows that, in the elastic regime, when the vertebra is loaded through a cement pot, the surface strains differ from when it is loaded through the disks. Therefore, when single vertebrae are tested, surface strain should be taken with caution.

Application of digital volume correlation to study the efficacy of prophylactic vertebral augmentation

BACKGROUND

Prophylactic augmentation is meant to reinforce the vertebral body, but in some cases it is suspected to actually weaken it. Past studies only investigated structural failure and the surface strain distribution. To elucidate the failure mechanism of the augmented vertebra, more information is needed about the internal strain distribution. This study aims to measure, for the first time, the full-field three-dimensional strain distribution inside augmented vertebrae in the elastic regime and to failure.

METHODS

Eight porcine vertebrae were prophylactically-augmented using two augmentation materials. They were scanned with a micro-computed tomography scanner (38.8μm voxel resolution) while undeformed, and loaded at 5%, 10%, and 15% compressions. Internal strains (axial, antero-posterior and lateral-lateral components) were computed using digital volume correlation.

FINDINGS

For both augmentation materials, the highest strains were measured in the regions adjacent to the injected cement mass, whereas the cement-interdigitated-bone was less strained. While this was already visible in the elastic regime (5%), it was a predictor of the localization of failure, which became visible at higher degrees of compression (10% and 15%), when failure propagated across the trabecular bone. Localization of high strains and failure was consistent between specimens, but different between the cement types.

INTERPRETATION

This study indicated the potential of digital volume correlation in measuring the internal strain (elastic regime) and failure in augmented vertebrae. While the cement-interdigitated region becomes stiffer (less strained), the adjacent non-augmented trabecular bone is affected by the stress concentration induced by the cement mass. This approach can help establish better criteria to improve vertebroplasty.

A PRELIMINARY IN VITRO BIOMECHANICAL EVALUATION OF PROPHYLACTIC CEMENT AUGMENTATION OF THE THORACOLUMBAR VERTEBRAE

In this paper, the biomechanical effectiveness of prophylactic augmentation in preventing fracture was investigated. In vitro biomechanical tests were performed to assess which factors make prophylactic augmentation effective/ineffective in reducing fracture risk. Nondestructive and destructive in vitro tests were performed on isolated osteoporotic vertebrae. Five sets of three-adjacent-vertebrae were tested. The central vertebra of each triplet was tested in the natural condition (control) non-destructively (axial-compression, torsion) and destructively (axial-compression). The two adjacent vertebrae were first tested nondestructively (axial-compression, torsion) pre-augmentation; prophylactic augmentation (uni- or bi-pedicular access) was then performed delivering 5.04[Formula: see text]mL to 8.44[Formula: see text]mL of acrylic cement by means of a customized device; quality of augmentation was CT-assessed; the augmented vertebrae were re-tested nondestructively (axial-compression, torsion), and eventually loaded to failure (axial-compression). Vertebral stiffness was correlated with the first-failure, but not with ultimate failure. The force and work to ultimate failure in prophylactic-augmented vertebrae was consistently larger than in the controls. However, in some cases the first-failure force and work in the augmented vertebrae were lower than for the controls. To investigate the reasons for such unpredictable results, the correlation with augmentation quality was analyzed. Some augmentation parameters seemed more correlated with mechanical outcome (statistically not-significant due to the limited sample size): uni-pedicular access resulted in a single cement mass, which tended to increase the force and work to first- and ultimate failure. The specimens with the highest strength and toughness also had: at least 25% cement filling, cement mass shifted anteriorly, and cement-endplate contact. These findings seem to confirm that prophylactic augmentation may aid reducing the risk of fracture. However, inadequate augmentation may have detrimental consequences. This study suggests that, to improve the strength of the augmented vertebrae, more attention should be dedicated to the quality of augmentation in terms of amount and position of the injected cement.