Applications of numerical methods in biomechanics

Abstract

Numerical methods are used in biomechanics like many other branches of engineering. In this study some examples from literature for the use of finite element and finite volume methods have been presented. The literature survey was kept broad in order to cover a wide range of examples. The most common numerical methods used in biomechanics applications are finite element and finite volume methods therefore some examples of these applications are presented as follows: Finite element method : Development of 3D finite element models (FEM) of femurs representing their behaviour before and after the application of hip prostheses; determination of the stresses occurring at joint discs under 3D static forces; 3D FEA of lower jaw joint; estimation of design parameters of an implant used for acetabular joints by means of nonlinear FEA; the FEA of the wear and heating mechanisms involved with the metal implants used in hip joints; development of FE model for the C4–C5 segment of vertebrae that form the spinal cord and the analysis of the injuries that occur when subjected to an impact; determination of the endurance level of vertebra with defects by means of computerized tomography and FEA; comparison of test and nonlinear FEA results for the lumbar vertebrae (L12) under compression; the simulation of the biomechanical reaction shown by the lumbosacral spinal unit (L1–S1) under physiological forces and boundary conditions; the simulation of the deformation occurring in the brain during a craniotomic surgery; FEA of cornea; FE simulation of the laceration of the cornea for astigmatism treatment; investigation of the biomechanical response of dental implants and the skeletal system in the vicinity under the influence of static and harmonic forces by means of FEA; life analysis of ceramic coatings on teeth under cyclic occlusion forces; ballistic simulation of a bullet penetrating the lower jaw of a boar and other similar studies were given. Finite volume method : Studies such as the calculation of the hydrodynamic forces for an arm without a hand; the computational fluid dynamics (CFD) analysis of the blood flowing in the vertebral arteries; enhancement of stent designs via CFD simulations; development of 3D CFD models of stents placed to coroner artery and investigation of the irregularities caused in the flow of blood for four different stent designs; investigation of aerosol deposition in lungs due to respiration, etc. were given. In this study some examples of FEM and CFD in biomechanics were given as applications of numerical methods in this field. It was observed that in these studies the models used were usually generated from BT and MR images. Also the analyses were generally accompanied by experimental studies for verification. In this compiling study examples of the application of numerical methods in the field of biomechanics were taken from the literature. The analyses were usually tried to be verified with experiments so as to set examples for further studies. By means of the use of numerical methods in biomechanics that is recently becoming more important, many illnesses may be investigated and new treatment methods may be developed.