Finite Element Analysis of Bone Remodeling. Implementation of a Remodeling Algorithm in MATLAB and ANSYS

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

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.