The process of adaptive bone remodeling can be described mathematically and simulated in a computer model, integrated with the finite element method. The main focus of this thesis is the implementation of a bone remodeling algorithm in MATLAB and ANSYS on the basis of FEM. The strain energy density is used as mechanical stimulus. The cortical and trabecular bone are described as continuous materials with variable density. This thesis can be divided into four main parts. The first part is due to the material properties of cortical and trabecular bone. The second part is about the remodeling theory and gives an historical review of the developed numerical approaches up to now. The implementation of the remodeling algorithm in ANSYS and MATLAB as well as its validation is topic of part three. In last main part, the algorithm is applied to a 2D FE-model of a human proximal femur.
Table of Contents
1 Introduction
1.1 Motivation
1.2 Aim
2 Bone as Material
2.1 Composition of Bone
2.2 Difference between Cortical and Cancellous Bone
2.3 Material Properties of Bone Tissue
2.3.1 Cortical Bone Tissue
2.3.2 Cancellous Bone Tissue
3 Bone Remodeling - From Nature to Model
3.1 Remodeling Theory
3.1.1 Difference between Modeling and Remodeling
3.1.2 The Remodeling Process
3.1.3 Types of Remodeling
3.2 Theories from the Beginning up to now
3.2.1 Mechanically Excited Bone Adaption Theories (1865 -1920)
3.2.2 Bone Adaptation: General Relationships of Mechanics to Bone Physiology (1920 - 1970)
3.2.3 Bone Adaptation: Experimental Study of Mechanically Mediated Bone (1970 - 1984)
3.2.4 Theories of Bone Adaptation: Numerical Simulations (1985 to present)
4 Simulation of Remodeling
4.1 Implementation of Optimization Algorithm
4.1.1 Reference System
4.1.2 Optimization Part
4.2 Results
4.2.1 Reference System 1
4.2.2 Reference System 2
4.2.3 Convergence behavior
5 Applications
5.1 Modeling of Human Proximal Femur
5.1.1 Load Definitions
5.1.2 Initial Configuration and Boundary Conditions
5.2 Results
5.2.1 Proximal Femur with Stepwise Adaptation Function
5.2.2 Proximal Femur with Linear Adaptation Function
5.2.3 Convergence
6 Discussion
6.1 Approach
6.2 Details of Algorithm
6.2.1 Building the Model
6.2.2 Development of Bone Structure
6.2.3 Convergence Behavior
6.3 Conclusion and Outlook
A Implementation in MATLAB and ANSYS
A.1 MATLAB main file run.m
A.2 ANSYS macro
A.3 MATLAB function dr.m
B Basic Anatomic Terminology
Research Objectives and Themes
The primary aim of this thesis is to implement an easy-to-use and extendable numerical algorithm to simulate the bone remodeling process driven by mechanical stimuli. The research focuses on the internal structural changes of bone in response to variations in its mechanical environment, utilizing Finite Element Method (FEM) software (ANSYS) and MATLAB for control and processing.
- Implementation of bone remodeling algorithms in MATLAB and ANSYS.
- Analysis of bone as a continuous material with variable density.
- Utilization of strain energy density (SED) as the primary mechanical stimulus.
- Comparison of stepwise and linear adaptation functions.
- Application of the algorithm to a 2D FE-model of a human proximal femur.
Excerpt from the Book
1.1 Motivation
Bone is a living material which has its main function in building the skeleton and therefore enabling locomotion and protection of the organism. It is subjected to permanent and transient loads caused by the daily active or special events like accidents. In contrast to inert materials from standard mechanics, this tissue is able to react adaptively to its environment. Aside from skeletal growth and fracture healing, which are of temporary character, the internal bone structure is maintained and adapted continuously. This process is termed remodeling .
Within this process microdamage is removed, leading to an increase of the fatigue life of bone tissue. Furthermore, the structural adaptation to changes in the mechanical environment plays an important role in conjunction with implants and prostheses. In fact, latest developments of such devices have been analyzed numerically in order to predict the long-term reaction of the tissue to this impact.
Osteoporosis, nowadays a widespread bone disease, underlies similar concepts as the remodeling process. Due to the enormous social damage caused by such diseases on one side and failure of implants and prostheses on the other side, an advance in the understanding and computer simulation of remodeling is of great importance.
Summary of Chapters
1 Introduction: Discusses the biological significance of bone remodeling and establishes the motivation and primary aim of the thesis.
2 Bone as Material: Describes the composition of bone and distinguishes between the mechanical properties of cortical and cancellous bone types.
3 Bone Remodeling - From Nature to Model: Outlines the theoretical biological background of remodeling and provides a historical overview of numerical simulation approaches.
4 Simulation of Remodeling: Details the numerical implementation of the optimization algorithm using MATLAB and ANSYS, including convergence criteria.
5 Applications: Demonstrates the algorithm's application to a proximal femur model with various initial configurations and adaptation functions.
6 Discussion: Evaluates the approach, details the algorithm's behavior, and provides concluding remarks alongside potential future outlooks.
Keywords
Bone remodeling, finite element method, strain energy density, mechanical stimulus, cortical bone, cancellous bone, MATLAB, ANSYS, proximal femur, osteoporosis, adaptation functions, computer simulation, structural optimization, biomechanics, bone density.
Frequently Asked Questions
What is the core focus of this research?
The research focuses on the numerical simulation of adaptive bone remodeling, specifically how bone tissue structurally changes in response to mechanical load changes.
Which fields of study are involved?
The study integrates biomechanics, computational mechanics, and bone physiology.
What is the main objective of this thesis?
The goal is to develop an easy-to-use numerical algorithm that simulates bone remodeling based on mechanical strain energy density.
Which software tools were used for implementation?
The study uses ANSYS for the finite element calculation part and MATLAB to control the remodeling process and algorithm logic.
What does the main body cover?
It covers material properties of bone, historical and modern remodeling theories, the mathematical algorithm implementation, and simulations applied to the proximal femur.
What are the essential keywords for this work?
Bone remodeling, finite element method, strain energy density, and mechanical stimulus are among the most critical.
How is the mechanical stimulus defined?
The mechanical stimulus is defined as the strain energy density, which acts as the signal for bone formation, resorption, or maintenance in the model.
How does the algorithm handle the "lazy zone"?
The lazy zone is implemented as a threshold (Ω) where no significant bone remodeling occurs, preventing continuous changes when the strain energy is within a homeostatic range.
- Quote paper
- M.Sc.(TUM) Dipl.-Ing.(FH) Martin Groß (Author), 2006, Finite Element Analysis of Bone Remodeling. Implementation of a Remodeling Algorithm in MATLAB and ANSYS, Munich, GRIN Verlag, https://www.hausarbeiten.de/document/113199
