A Fully Anisotropic Hierarchical Hybrid Cellular Automata Methodology to Simulate Bone Remodeling

Published on May 1, 2006
· DOI :10.2514/6.2006-1625
Charles L. Penninger6
Estimated H-index: 6
 , Neal M. Patel13
Estimated H-index: 13
 + 2 AuthorsAndres Tovar19
Estimated H-index: 19
Sources
Abstract
accommodate the hierarchical structure of bone. This hierarchical-HCA methodology utilizes communication between continuum level and tissue level models of bone to guide the remodeling process. The HCA algorithm utilizes the average apparent density of the tissue level structures to update the stiffness characteristics of the continuum model of bone. In this research, a method for calculating the local anisotropic properties of these structures is developed. This approach utilizes confined uni-axial strain tests, on each tissue level model, to numerically determine the structure's stiffness tensor. The objective of this work is to increase the fidelity and versatility of the hierarchical-HCA algorithm by assimilating the computed mechanical properties of the tissue level models. Preliminary analyses display improved efficiency and a more consistent material distribution when incorporating the anisotropic properties into this methodology.
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#1Andres TovarH-Index: 19
#1Andres TovarH-Index: 19
#2Glen L. NieburH-Index: 38
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Nov 1, 2000·Journal of Biomechanics2.71
#1Mette Bagge (DTU: Technical University of Denmark)H-Index: 1
Abstract The internal bone adaptation of the proximal femur is considered. A three-dimensional finite element model of the proximal femur is used. The bone remodeling in this work is numerically described by an evolutionary remodeling scheme with anisotropic material parameters and time-dependent loading. The memory of past loading is included in the model to account for the delay in the bone response from the load changes. The remodeling rate equation is derived from the structural optimization...
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Jun 1, 1997·Journal of Biomechanics2.71
#1Christopher R. Jacobs (PSU: Pennsylvania State University)H-Index: 63
#2Juan C. Simo (Stanford University)H-Index: 84
Last. Dennis R. Carter (Stanford University)H-Index: 92
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Abstract Over 100 years ago, Wolff hypothesized that cancellous bone altered both its apparent density and trabecular orientation in response to mechanical loads. A mathematical counterpart of this principle is derived by adding a remodeling rule for the rate-of-change of the full anisotropic stiffness tensor (all 21 independent terms) to the density rate-of-change rule adapted from an existing isotropic theory. As a result, anisotropy and density patterns develop such that the local stiffness t...
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Dec 1, 1996·Journal of Biomechanics2.71
#1B. van Rietbergen (Radboud University Nijmegen)H-Index: 12
#2A. Odgaard (Aarhus University Hospital)H-Index: 32
Last. Rik Huiskes (Radboud University Nijmegen)H-Index: 96
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A method is presented to find orthotropic elastic symmetries and constants directly from the elastic coefficients in the overall stiffness matrix of trabecular bone test specimens. Contrary to earlier developed techniques, this method does not require pure orthotropic behavior or additional fabric measurements. The method uses high-resolution computer reconstructions of trabecular bone specimens as input for large-scale FE-analyses to determine all the 21 elastic coefficients in the overall stif...
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Dec 1, 1992·Journal of Biomechanics2.71
#1Harrie Weinans (Radboud University Nijmegen)H-Index: 93
#2Rik Huiskes (Radboud University Nijmegen)H-Index: 96
Last. Henk J. Grootenboer (UT: University of Twente)H-Index: 25
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The process of adaptive bone remodeling can be described mathematically and simulated in a computer model, integrated with the finite element method. In the model discussed here, cortical and trabecular bone are described as continuous materials with variable density. The remodeling rule applied to simulate the remodeling process in each element individually is, in fact, an objective function for an optimization process, relative to the external load. Its purpose is to obtain a constant, preset ...
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Mar 1, 1992·Computational Mechanics4.01
#1Scott J. Hollister (UM: University of Michigan)H-Index: 77
#2Noboru Kikuchi (UM: University of Michigan)H-Index: 66
Abstraet. Composite material elastic behavior has been studied using many approaches, all of which are based on the concept of a Representative Volume Element (RVE). Most methods accurately estimate effective elastic properties when the ratio of the RVE size to the global structural dimensions, denoted here as ~/, goes to zero. However, many composites are loeally periodic with finite q. The purpose of this paper was to compare homogenization and standard mechanics RVE based analyses for periodi...
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Jan 1, 1991·Journal of Biomechanics2.71
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Last. Steven A. Goldstein (UM: University of Michigan)H-Index: 87
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Aha& strain. At this time, however, there is no generally accepted (or easily accomplished) technique for predicting the effect of microstructure on trabecular bone apparent stiffness and strength or estimating tissue level stress or strain. In this paper, a recently developed mechanics theory specifically designed to analyze microstructured materials, called the homogenization theory, is presented and applied to analyze trabecular bone mechanics. Using the homogenization theory it is possible t...
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Jan 1, 1987·Journal of Biomechanics2.71
#1Lance E. Lanyon (RVC: Royal Veterinary College)H-Index: 62
Abstract The skeleton consists of a series of elements with a variety of functions. In locations where shape or protection are of prime importance the bone's architecture is achieved during growth under direct genetic control. In locations where resistance to repetitive loading is important only the general form of the bone will be achieved as a result of growth alone, the remaining characteristics result from functional adaptation. This mechanism ensures that bone architecture is modelled and r...
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#1Rik Huiskes (Radboud University Nijmegen)H-Index: 96
#2Harrie Weinans (Radboud University Nijmegen)H-Index: 93
Last. T. J. J. H. Slooff (Radboud University Nijmegen)H-Index: 12
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The subject of this article is the development and application of computer-simulation methods to predict stress-related adaptive bone remodeling, in accordance with ‘Wolff's Law’. These models are based on the Finite Element Method (FEM) in combination with numerical formulations of adaptive bone-remodeling theories. In the adaptive remodeling models presented, the Strain Energy Density (SED) is used as a feed-back control variable to determine shape or bone density adaptations to alternative fu...
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