Is there any advantage of using stand-alone cages? A numerical approach

Background: Segment fusion using interbody cages supplemented with pedicle screw fixation is the most common surgery for the treatment of low back pain. However, there is still much controversy regarding the use of cages in a stand-alone fashion. The goal of this work is to numerically compare the influence that each surgery has on lumbar biomechanics. Methods: A non-linear FE model of the whole lumbar spine was developed to compare between two types of cages (OLYS and NEOLIF) with and without supplementary fixation. The motion of the whole spine was analysed and the biomechanical environment of the adjacent segments to the operated one was studied. Moreover, the risk of subsidence of the cages was qualitatively evaluated. Results: A great ROM reduction occurred when supplementary fixation was used. This stiffening increased the stresses at the adjacent levels. It might be hypothesised that the overloading of these segments could be related with the clinically observed adjacent disc degeneration. Meanwhile, the stand-alone cages allowed for a wider movement, and therefore, the influence of the surgery on adjacent discs was much lower. Regarding the risk of subsidence, the contact pressure magnitude was similar for both intervertebral cage designs and near the value of the maximum tolerable pressure of the endplates. Conclusions: A minimally invasive posterior insertion of an intervertebral cage (OLYS or NEOLIF) was compared using a stand-alone design or adding supplementary fixation. The outcomes of these two techniques were compared, and although stand-alone cage may diminish the risk of disease progression to the adjacent discs, the spinal movement in this case could compromise the vertebral fusion and might present a higher risk of cage subsidence

Stand-alone lumbar cage subsidence: A biomechanical sensitivity study of cage design and placement.

Background and objective: Spinal degeneration and instability are commonly treated with interbody fusion cages either alone or supplemented with posterior instrumentation with the aim to immobilise the segment and restore intervertebral height. The purpose of this work is to establish a tool which may help to understand the effects of intervertebral cage design and placement on the biomechanical response of a patient-specific model to help reducing post-surgical complications such as subsidence and segment instability. Methods: A 3D lumbar functional spinal unit (FSU) finite element model was created and a parametric model of an interbody cage was designed and introduced in the FSU. A Drucker–Prager Cap plasticity formulation was used to predict plastic strains and bone failure in the vertebrae. The effect of varying cage size, cross-sectional area, apparent stiffness and positioning was evaluated under 500 N preload followed by 7.5 Nm multidirectional rotation and the results were compared with the intact model. Results: The most influential cage parameters on the FSU were size, curvature congruence with the endplates and cage placement. Segmental stiffness was higher when increasing the cross-sectional cage area in all loading directions and when the cage was anteriorly placed in all directions but extension. In general, the facet joint forces were reduced by increasing segmental stiffness. However, these forces were higher than in the intact model in most of the cases due to the displacement of the instantaneous centre of rotation. The highest plastic deformations took place at the caudal vertebra under flexion and increased for cages with greater stiffness. Thus, wider cages and a more anteriorly placement would increase the volume of failed bone and, therefore, the risk of subsidence. Conclusions: Cage geometry plays a crucial role in the success of lumbar surgery. General considerations such as larger cages may be applied as a guideline, but parameters such as curvature or cage placement should be determined for each specific patient. This model provides a proof-of-concept of a tool for the preoperative evaluation of lumbar surgical outcomes

Numerical simulations of bone remodelling and formation following nucleotomy

Nucleotomy is the gold standard treatment for disc herniation and has proven ability to restore stability by creating a bony bridge without any additional fixation. However, the evolution of mineral density in the extant and new bone after nucleotomy and fixation techniques has to date not been investigated in detail. The main goal of this study is to determine possible mechanisms that may trigger the bone remodelling and formation processes. With that purpose, a finite element model of the L4–L5 spinal segment was used. Bone mineral density (BMD), new tissue composition, and endplate deflection were determined as indicators of lumbar fusion. A bone-remodelling algorithm and a tissue-healing algorithm, both mechanically driven, were implemented to predict vertebral bone alterations and fusion patterns after nucleotomy, internal fixation, and anterior plate placement. When considering an intact disc height, neither nucleotomy nor internal fixation were able to provide the necessary stability to promote bony fusion. However, when 75% of the disc height was considered, bone fusion was predicted for both techniques. By contrast, an anterior plate allowed bone fusion at all disc heights. A 50% disc-height reduction led to osteophyte formation in all cases. Changes in the intervertebral disc tissue caused BMD alterations in the endplates. From this observations it can be drawn that fusion may be self-induced by controlling the mechanical stabilisation without the need of additional fixation. The amount of tissue to be removed to achieve this stabilisation remains to be determined

A Constitutive Model for the Annulus of Human Intervertebral Disc: Implications for Developing a Degeneration Model and Its Influence on Lumbar Spine Functioning

The study of the mechanical properties of the annulus fibrosus of the intervertebral discs is significant to the study on the diseases of lumbar intervertebral discs in terms of both theoretical modelling and clinical application value. The annulus fibrosus tissue of the human intervertebral disc (IVD) has a very distinctive structure and behaviour. It consists of a solid porous matrix, saturated with water, which mainly contains proteoglycan and collagen fibres network. In this work a mathematical model for a fibred reinforced material including the osmotic pressure contribution was developed. This behaviour was implemented in a finite element (FE) model and numerical characterization and validation, based on experimental results, were carried out for the normal annulus tissue. The characterization of the model for a degenerated annulus was performed, and this was capable of reproducing the increase of stiffness and the reduction of its nonlinear material response and of its hydrophilic nature. Finally, this model was used to reproduce the degeneration of the L4L5 disc in a complete finite element lumbar spine model proving that a single level degeneration modifies the motion patterns and the loading of the segments above and below the degenerated disc

Linearly scaling direct method for accurately inverting sparse banded matrices

In many problems in Computational Physics and Chemistry, one finds a special kind of sparse matrices, termed "banded matrices". These matrices, which are defined as having non-zero entries only within a given distance from the main diagonal, need often to be inverted in order to solve the associated linear system of equations. In this work, we introduce a new O(n) algorithm for solving such a system, being n X n the size of the matrix. We produce the analytical recursive expressions that allow to directly obtain the solution, as well as the pseudocode for its computer implementation. Moreover, we review the different options for possibly parallelizing the method, we describe the extension to deal with matrices that are banded plus a small number of non-zero entries outside the band, and we use the same ideas to produce a method for obtaining the full inverse matrix. Finally, we show that the New Algorithm is competitive, both in accuracy and in numerical efficiency, when compared to a standard method based in Gaussian elimination. We do this using sets of large random banded matrices, as well as the ones that appear when one tries to solve the 1D Poisson equation by finite differences.Comment: 24 pages, 5 figures, submitted to J. Comp. Phy

A Quantum-mechanical Approach for Constrained Macromolecular Chains

Many approaches to three-dimensional constrained macromolecular chains at thermal equilibrium, at about room temperatures, are based upon constrained Classical Hamiltonian Dynamics (cCHDa). Quantum-mechanical approaches (QMa) have also been treated by different researchers for decades. QMa address a fundamental issue (constraints versus the uncertainty principle) and are versatile: they also yield classical descriptions (which may not coincide with those from cCHDa, although they may agree for certain relevant quantities). Open issues include whether QMa have enough practical consequences which differ from and/or improve those from cCHDa. We shall treat cCHDa briefly and deal with QMa, by outlining old approaches and focusing on recent ones.Comment: Expands review published in The European Physical Journal (Special Topics) Vol. 200, pp. 225-258 (2011

Labor Market 'Rigidity' and the Success of Economic Reforms Across More Than 100 Countries

This paper shows that labor market policies and institutions have an impact on the effectiveness of economic reform programs. Countries with relatively 'rigid' labor markets experienced deeper recessions before adjustment and slower recoveries afterwards. Minimum wages and mandatory benefits are not detrimental to growth, but the relative size of organized labor, in government and overall, appear to be crucial. Labor market rigidity thus seems to be relevant for political reasons, more than for economic reasons. These findings suggest that insufficient attention has been paid to vocal groups who stand to lose from economic reforms.Labor market rigidity, economic reforms,