Disc mechanical characteristics : construction of a finite element mathematical model, first results

Computational mechanics is an invaluable tool to analyze biomechanical systems, either in healthy or degenerative conditions, and to improve our understanding on the events that can trigger trauma or diseases, to design new medical devices to restore working conditions, or even to point out treatment techniques. Numerical methods in general, and the Finite Elements Analysis (FEA) in particular, if properly built and used, can allow an inside view, a rigorous analysis and a qualitative study of any assumption, frequently too much difficult or even impossible to achieve with any in-vivo or in-vitro experimental technique. An Intervertebral Disc (IVD) is a functionally-oriented construction of several soft tissues, supporting a wide range of dynamic and static loads that generate complex stress fields, which experimental study and understanding of its biomechanical behavior is of an enormous complexity. On the one hand, human’s in-vivo study is almost impossible – due to the high degree of uncertainty in applied loads, geometric variability of individuals, complex surrounding musculoskeletal interactions, the role played by electro-chemical phenomena like osmolarity, etc – and post-mortem studies hardly provides accurate information to allow a clear and precise characterization and transposition to in-vivo biomechanics. On the other hand, due to that intrinsic complexity of the IVD, an accurate biomechanical model cannot easily be achieved. It is rather a step-by-step task where, although there are still many open questions, an important effort is being done to bring to the FEA the multi-physics behavior, and the complex interactions between them, in order to accurately model the IVD’s constitutive performance. This work is focused in the most relevant issues and phenomena that shall be taken into account in the development of an accurate biomechanical FEA model of the IVD, either in healthy or degenerated states

Pair formation in two electron correlated chains

We study two correlated electrons in a nearest neighbour tight- binding chain, with both on site and nearest neighbour interaction. Both the cases of parallel and antiparallel spins are considered. In addition to the free electron band for two electrons, there are correlated bands with positive or negative energy, depending on wheather the interaction parameters are repulsive or attractive. Electrons form bound states, with amplitudes that decay exponentially with separation. Conditions for such states to be filled at low temperatures are discussed.Comment: To appear in J. Phys: Condens. Matter 15 (2003

3D reconstruction of a spinal motion segment from 2D medical images: objective quantification of the geometric accuracy of the FE mesh generation procedure

The Finite Element (FE) Analysis is an essential tool to study the biomechanical behaviour of the spine, and particularly of the intervertebral disc (IVD). The 3D reconstruction of a patient-oriented IVD has numerous obstacles. Difficulties arise mainly due to the complexity and dimensions of the IVD’s constituent structures. The lack of detailed data in conventional imaging techniques causes further problems in the IVD finite element mesh generation and analysis. The accuracy of the FE computation increases if the geometry of model resembles, for instance, the natural smoothness of real anatomical structure. Accounting to this, the main idea of this work is to evaluate the impact of the reconstruction parameters by comparing the final 3D geometrical reconstruction by finite elements with an initial well-defined geometry of a given anatomical structure, and to develop the procedures for the 3D mesh generation from 2D medical imaging

Dynamic instabilities in resonant tunneling induced by a magnetic field

We show that the addition of a magnetic field parallel to the current induces self sustained intrinsic current oscillations in an asymmetric double barrier structure. The oscillations are attributed to the nonlinear dynamic coupling of the current to the charge trapped in the well, and the effect of the external field over the local density of states across the system. Our results show that the system bifurcates as the field is increased, and may transit to chaos at large enough fields.Comment: 4 pages, 3 figures, accepted in Phys. Rev. Letter

Optimized FE mesh generation based on medical imaging and on a user-defined spatial refinement gradient. Application to a motion segment

In general, the starting point for the 3D geometrical modelling by finite elements of an anatomical structure is the generation of a 3D voxel-based geometrical model, obtained after denoising, smoothing and segmentation of a set of 2D medical images. The accuracy of the FE computation increases if the geometry of model resembles, for instance, the natural smoothness of real anatomical structure. Usually, the lack of detailed data in conventional imaging techniques causes further problems in the IVD finite element mesh generation and analysis. Difficulties arise mainly due to the complexity and the dimension of the IVD constituent structures and the lower resolution of medical imaging. After the 3D voxelized model has been defined, a specific isotropic tetrahedral FE meshing procedure is applied and, generally, a too dense and highly refined FE mesh is obtained. Therefore, it is necessary to decrease its size by diminishing the total number of nodes and elements while maintaining both geometrical accuracy and a physically compatible FE mesh refinement. Generally, after this procedure, the smaller elements are located at the internal and external boundaries, while larger elements are located inside the FE mesh. However, this is not always acceptable. There may be situations where this accuracy may be required simultaneously in structures outside and inside the FE mesh. In a motion segment, the FE mesh should be more refined at the IVD and coarser at the vertebrae (nearly incompressible medium). On the other hand, since the annulus fibrosus (AF) is a stiff ring-shaped structure made up of concentric lamellae [1], an optimized FE mesh should be more refined at the annulus fibrosus than at the nucleus pulposus (NP)The aims of this study are: - to study the impact of medical imaging resolution in the FE mesh accuracy; - to develop a refinement gradient, where in this case the elements should be smaller in the outer annulus (where lamellae are denser and combined) than the ones in the inner annulus (less dense lamellae)