Keywords
Abstract
Table of Contents
List of Figures
List of Equations
List of Diagrams
List of Tables
List of Matlab Programs
List of Abbreviations
List of Papers and Posters
Declaration
Acknowledgements
1. Chapter 1 Introduction
1.1. The focus of the thesis
1.2. Research gap in articular cartilage computational modelling associated research
1.1. Current experimental studies of articular cartilage
1.2. Some main factors governing the deformation of articular cartilage
1.2. Numerical modelling of cartilage and related simulations
1.3. The gap in research
1.3. Significance and benefits
1.1. Articular cartilage degeneration and diseases
1.2. Significance and contribution to knowledge of this research
1.1. The virtual cartilage concept
1.2. Contribution to knowledge
Summary
2. Chapter 2 Articular cartilage and Cellular Automata approach
2.2. Constituents of articular cartilage
2.3. Fluid in cartilage
2.2. Osmosis, osmotic pressure and osmotic unit
2.1. Osmosis and osmotic pressure
2.2. The osmotic pressure in articular cartilage
2.1. Osmotic pressure at macro-scale level
2.2. Osmotic pressure at micro-scale level
2.3. Osmotic units in cartilage
2.3. Cellular automata, the Margolous neighbourhood and partitioning rule
2.4. Mechanics of the Margolus partitioning rule
3. Chapter 3 The conceptual in-silico structural model of articular cartilage
3.1. New conceptual idealization of cartilage structure for computational analysis
3.2. Margolus neighbourhood application to cartilage modelling
3.1. Physical model of the cartilage structure
3.2. The conceptual microscale load-bearing unit of articular cartilage
3.3. Osmotic units and the Margolus neighbourhood
3.3. Simulation of deformation with the in-silico model
3.4. Virtual clay simulation
4. Chapter 4 Determination of cartilage matrix components
The three major Components of cartilage
Histology
Image processing
Volume rendering
4.1. Introduction of proteoglycan
4.2. Material and method
4.4. Calculation of quantities from images using ImageJ
4.7. Optical Density Imaging
4.8. Converting into unit of (g/cm3)
4.4. Summary of proteoglycans quantification results
4.2. Collagen quantification
4.1. Introduction of collagen
4.2. Method and apparatus
4.1. An example for calculating collagen concentration from absorbance values
4.2. The results of all experiments
4.4. Summary of collagen quantification results
4.3. Quantification of water content
4.4. Determination of the thickness
4.5. Calculating osmotic pressure and collagen meshwork stress for articular cartilage
4.2. Stress on collagen component
Summary
5. Chapter 5 Deformable cellular automata of articular cartilage
5.1. Protocol for creating Voxel and implementing Cellular Automata
5.2. Setting up the voxels
5.1. Setting up the values of collagen, proteoglycans and water for each cell
5.2. Visualization of the change of the thicknesses during the deformation process
5.1. Collecting the real sample for 3D laser scanning
5.2. Create the base of the object
5.3. Creating the grid
5.4. Mapping the volume
6. Chapter 6 Implementation of forms of the Margolus neighbourhood rules with Matlab I
The set of rules
6.1. Applying virtual clay model for articular cartilage matrix
6.2. The set of rules using in the model of articular cartilage
6.2. The rules for the threshold condition
6.3. The moving plate rules
6.4. The One-Zero altering Rules
6.5. The Active-Inactive cell rules
6.6. Boundary conditions
II Structure of Matlab program in the thesis
6.3. Creating blocks on odd grid
6.1. Two-Dimension blocks (2D blocks)
6.2. Three-Dimension blocks (3D blocks)
6.4. Creating blocks on even grid
6.1. Two-Dimension blocks (2D blocks)
6.2. Three-Dimension blocks
6.5. The main algorithm for the main program
6.6. Description for Matlab codes
6.2. Preliminary calculation, volume of each voxel
6.3. Setting up Threshold
6.2. Modelling the special areas
6.1. Surface of cartilage
6.2. The bottom of the model
6.3. The area of loading
6.5. The cells next to the indenter
6.3. Modelling the boundary conditions
6.4. Setting up moving plate
6.5. Creating odd grid
6.1. Module subprogram “Odd_step_active” (Making 2D odd grid)
6.1. Numbering the blocks
6.2. Finding the active blocks in the odd grid
6.2. The module subprogram “CombineLayer” (Making 3D odd grid)
6. Calculating the quantities of active cells in active blocks
6.7. Calculating water movement based on the transition rule
6.8. Updating the results as input data for the next step
6.9. Working on the even steps
6.txt file
7. Chapter 7 Results and validation
7.1. The graphs obtained from the models
7.3. Comments
8. Chapter 8 Discussion
References
Appendixes (all appendixes are stored in the CD)
Appendix 1 New approach for articular cartilage and expected outcomes
Appendix 2 Numerical techniques and applications to cartilage modelling
Appendix 3 Introduction of some common neighbourhoods
Appendix 4 The consolidation of articular cartilage
Appendix 5.1 Main program for mode 1
Appendix 6.2 Main program for mode 2
Appendix 6.3 Sub program odd_step_active
Appendix 6.4 Sub program even_step_active
Appendix 6.5 Sub program CombineLayer
Appendix 6.6 Sub program odd_step_computation
Appendix 6.7 Sub program even_step_computation
Appendix 6.8 Sub program GeneralRules
Appendix 7 The graphs
Appendix 8.1 Water_layer
Appendix 8.2 Collagen_layer
Appendix 8.1 Map_Rule_1_vs_3
Appendix 8.2 Pressure_Rule_1_vs_3
Appendix 8.1 Water_BC_1D_vs_3D
Appendix 9 Scenario 1_Matlab program
Appendix 10 Matlab program (changing λ at boundary/ies)
Appendix 11 Scenario 2
