Análise mecânica da coluna lombar com ênfase nos esforços nos ligamentos

Abstract

This document describes simulations by the finite element method of the lumbar spine, including calculations of the principal stresses, nonlinear mechanical properties for bones and ligaments, and ligament representations considering natural contractions and geometries, verifying how the tensegrity structure principles contribute for the knowledge of its stability and the effect of discal prosthesis in its mobility. This nonlinear static study of the lumbar spine includes the construction of the computational geometric model representing the spine, definition of the boundary and contact conditions, definition of the mechanical properties, generation of finite element meshes, generation of the results, calculation of the rotations, comparison with the literature and verification of the stresses. The three-dimensional model mentioned represents from the first to the fifth lumbar vertebra, their ligaments and discs. The model was assembled without interferences and fixed in its base in all directions. Successive nonlinear studies were done, using bonded contact conditions, and contracting the anterior longitudinal, posterior longitudinal, flavum, interspinous, supraspinous and intertransverse ligaments by a thermal analogy, with the purpose of establishing the stresses observed in the natural lumbar spine before loading. After the definition of the initial configuration of balance, the finite element model was submitted to 10 Nm flexure and extension moments. In the study of discal prosthesis for the lumbar spine, the materials of the discs were changed to prosthetic material, maintaining the study type, the geometries, and the boundary and contact conditions. Meshes and results were generated to compare of angles and stresses between the natural and prosthetic spine models. The simulations of the health spine showed permanent tension in most of the ligaments, permanent compressions in the nucleus, and simultaneous compressions and tensions in the bones and annulus. The spine manifests evidences of tensegrity, forming compression islands named compressed complexes, inside an ocean of tension named tensioned complex and represented by the ligaments and neighboring structures. The substitution of the discs, for the linear elastic material, reduced the flexure and extension angles of the lumbar spine. Keywords: tensegrity structures; lumbar spine; geometric modeling; finite element method; prosthesis.