Prediction of the elastic modulus of the trabecular bone based on X-ray computed tomography

International audienceThis work aims to estimate the apparent Young's modulus of real human trabecular bones using a numerical micro-macro approach. Cylindrical specimens of trabecular bone were extracted from human femur heads, cleaned and scanned using a SkyScan-1072 micro-computed tomography system. 3D volumetric tetrahedral grids were generated from the exploitation of the reconstructed images using original meshing techniques. Numerical compressive tests were simulated, assuming isotropic tissue Young's modulus for all elements. The large size of the volumes implies grids with a high number of nodes, which required the use of a large number of parallel processors in order to perform the finite element calculations. Numerical Young's moduli varied between 1300 MPa and 1600 MPa, with a good agreement with experiments

Computationally-Optimized Bone Mechanical Modeling from High-Resolution Structural Images

Image-based mechanical modeling of the complex micro-structure of human bone has shown promise as a non-invasive method for characterizing bone strength and fracture risk in vivo. In particular, elastic moduli obtained from image-derived micro-finite element (μFE) simulations have been shown to correlate well with results obtained by mechanical testing of cadaveric bone. However, most existing large-scale finite-element simulation programs require significant computing resources, which hamper their use in common laboratory and clinical environments. In this work, we theoretically derive and computationally evaluate the resources needed to perform such simulations (in terms of computer memory and computation time), which are dependent on the number of finite elements in the image-derived bone model. A detailed description of our approach is provided, which is specifically optimized for μFE modeling of the complex three-dimensional architecture of trabecular bone. Our implementation includes domain decomposition for parallel computing, a novel stopping criterion, and a system for speeding up convergence by pre-iterating on coarser grids. The performance of the system is demonstrated on a dual quad-core Xeon 3.16 GHz CPUs equipped with 40 GB of RAM. Models of distal tibia derived from 3D in-vivo MR images in a patient comprising 200,000 elements required less than 30 seconds to converge (and 40 MB RAM). To illustrate the system's potential for large-scale μFE simulations, axial stiffness was estimated from high-resolution micro-CT images of a voxel array of 90 million elements comprising the human proximal femur in seven hours CPU time. In conclusion, the system described should enable image-based finite-element bone simulations in practical computation times on high-end desktop computers with applications to laboratory studies and clinical imaging

Mechanical competence of bone-implant systems can accurately be determined by image-based micro-finite element analyses

The precise failure mechanisms of bone implants are still incompletely understood. Micro-computed tomography in combination with finite element analysis appears to be a potent methodology to determine the mechanical stability of bone-implant constructs. To assess this microstructural finite element (μFE) analysis approach, pull-out tests were designed and conducted on ten sheep vertebral bodies into which orthopedic screws were inserted.μFE models of the same bone-implant constructs were then built and solved, using a large-scale linear FE-solver.μFE calculated pull-out strength correlated highly with the experimentally measured pull-out strength (r 2= 0.87) thereby statistically supporting theμFE approach. These results suggest that bone-implant constructs can be analyzed usingμFE in a detailed and unprecedented way. This could potentially facilitate the development of future implant designs leading to novel and improved fracture fixation method

Biomechanics

Biomechanics is a vast discipline within the field of Biomedical Engineering. It explores the underlying mechanics of how biological and physiological systems move. It encompasses important clinical applications to address questions related to medicine using engineering mechanics principles. Biomechanics includes interdisciplinary concepts from engineers, physicians, therapists, biologists, physicists, and mathematicians. Through their collaborative efforts, biomechanics research is ever changing and expanding, explaining new mechanisms and principles for dynamic human systems. Biomechanics is used to describe how the human body moves, walks, and breathes, in addition to how it responds to injury and rehabilitation. Advanced biomechanical modeling methods, such as inverse dynamics, finite element analysis, and musculoskeletal modeling are used to simulate and investigate human situations in regard to movement and injury. Biomechanical technologies are progressing to answer contemporary medical questions. The future of biomechanics is dependent on interdisciplinary research efforts and the education of tomorrow’s scientists

The dune-subgrid module and some applications

We present an extension module for the Dune system. This module, called dune-subgrid, allows to mark elements of another Dune hierarchical grid. The set of marked elements can then be accessed as a Dune grid in its own right. dune-subgrid is free software and is available for download (External Dune Modules: www.​dune-project.​org/​downloadext.​html). We describe the functionality and use of dune-subgrid, comment on its implementation, and give two example applications. First, we show how dune-subgrid can be used for micro-FE simulations of trabecular bone. Then we present an algorithm that allows to use exact residuals for the adaptive solution of the spatial problems of time-discretized evolution equations

SOLID-SHELL FINITE ELEMENT MODELS FOR EXPLICIT SIMULATIONS OF CRACK PROPAGATION IN THIN STRUCTURES

Crack propagation in thin shell structures due to cutting is conveniently simulated using explicit finite element approaches, in view of the high nonlinearity of the problem. Solidshell elements are usually preferred for the discretization in the presence of complex material behavior and degradation phenomena such as delamination, since they allow for a correct representation of the thickness geometry. However, in solid-shell elements the small thickness leads to a very high maximum eigenfrequency, which imply very small stable time-steps. A new selective mass scaling technique is proposed to increase the time-step size without affecting accuracy. New ”directional” cohesive interface elements are used in conjunction with selective mass scaling to account for the interaction with a sharp blade in cutting processes of thin ductile shells