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Process Ofestimating the Material Properties of Human Heel Pad Sub- Layers Using Inverse Finite Element Analysis and Some Model

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Process Ofestimating the Material Properties of Human Heel Pad Sub- Layers Using Inverse Finite Element Analysis and Some Model PROCESS OF ESTIMATING THE MATERIAL PROPERTIES OF HUMAN HEEL PAD SUB- LAYERS USING INVERSE FINITE ELEMENT ANALYSIS AND SOME MODEL APPLICATIONS NAFISEH AHANCHIAN School of Health Sciences University of Salford, Salford, UK Submitted in Partial Fulfilment of the Requirements of the Degree of Doctor of Philosophy, December 2013 Table of Contents List of Tables .................................................................................................................................. vi List of Figures ............................................................................................................................... viii List of Charts ................................................................................................................................. xv Acknowledgements ...................................................................................................................... xvi Abstract ........................................................................................................................................ xvii 1. Chapter One: INTRODUCTION ........................................................................................... 1 2. Chapter Two: LITERATURE REVIEW ............................................................................... 6 2.1 THE HUMAN HEEL PAD .............................................................................................. 7 2.1.1 The Structure ............................................................................................................. 8 2.1.2 The Mechanical Properties ...................................................................................... 11 2.1.3 The Function ............................................................................................................ 15 2.1.4 Mechanism of Injuries ............................................................................................. 16 2.2 DIFFERENT METHODS TO OBTAIN THE HEEL PAD MATERIAL PROPERTIES… ....................................................................................................................... 18 2.3 USE OF INVERSE FEA IN DETERMINATION OF THE HUMAN HEEL PAD MATERIAL PROPERTIES ...................................................................................................... 32 2.3.1 Introduction to FEA ................................................................................................. 32 2.3.2 Using Inverse FEA to Study the Biomechanical Properties of the Human Heel Pad……. ................................................................................................................................. 35 2.4 APPLICATIONS OF FEA IN FOOTWEAR DESIGN ................................................. 51 2.5 AIMS AND OBJECTIVES ............................................................................................ 58 3. Chapter Three: DEVELOPMENT OF THE HEEL REGION GEOMETRY ................. 61 3.1 INTRODUCTION .......................................................................................................... 62 3.2 METHODS ..................................................................................................................... 63 3.2.1 Data Acquisition: Magnetic Resonance Imaging (MRI) ......................................... 63 3.2.2 Development of the Surface Geometries ................................................................. 66 3.2.2.1 Pre-processing of MRI Data ................................................................................ 67 3.2.2.2 Segmentation ....................................................................................................... 69 3.2.2.3 Repeatability of the Segmentation Procedure of the MRI Scans ......................... 82 3.2.3 Development of the Solid Geometries..................................................................... 84 3.2.3.1 The Solid Model of the Heel Region as a Single Layer Structure ....................... 85 3.2.3.2 Development of Solid Geometries of Different Tissue Layers in the Heel Region…. ............................................................................................................................ 89 3.3 RESULTS AND DISCUSSION ..................................................................................... 91 ii 3.4 CONCLUSIONS ............................................................................................................ 99 4. Chapter Four: INITIAL DEVELOPMENT OF THE FE MODEL OF THE HEEL REGION ..................................................................................................................................... 101 4.1 INTRODUCTION ........................................................................................................ 102 4.2 DEVELOPMENT OF THE FE MODEL ..................................................................... 102 4.2.1 CAD Geometry and Mesh Generation .................................................................. 102 4.2.2 Loading and Boundary Conditions of the Finite Element Model ......................... 112 4.2.3 Material Properties of the Finite Element Model .................................................. 114 4.2.3.1 Linear Elastic Material Models for Muscle and Plantar Fascia ......................... 114 4.2.3.2 Nonlinear Material Model for Macro-chamber, Micro-chamber and Skin ....... 117 4.3 PARAMETRIC STUDIES ........................................................................................... 120 4.3.1 Effect of Varying the Stiffness of the Muscle Tissue ............................................ 121 4.3.2 Effect of Varying the Stiffness of the Plantar Fascia ............................................ 123 4.3.3 Effect of Varying the Angle of Rotation of the Heel Model ................................. 124 4.4 CONCLUSIONS .......................................................................................................... 126 5. Chapter Five: EXPERIMENTAL ACQUISITION OF FORCE AND TISSUE DISPLACEMENT DATA ......................................................................................................... 129 5.1 INTRODUCTION ........................................................................................................ 130 5.2 METHODS ................................................................................................................... 131 5.2.1 Experimental Device ............................................................................................. 131 5.2.2 Foot Positioning ..................................................................................................... 133 5.2.3 Subjects Characteristics ......................................................................................... 134 5.2.4 Loading Protocol ................................................................................................... 134 5.2.5 Ultrasound Data Processing .................................................................................. 139 5.3 RESULTS AND DISCUSSION ................................................................................... 140 5.3.1 Slow Compression Tests ....................................................................................... 141 5.3.1.1 Selection of the Appropriate Low Displacement Rate ...................................... 141 5.3.1.2 Slow Compression Tests at 5mm/s to Determine the Hyperelastic Material Properties .......................................................................................................................... 142 5.3.2 Rapid Compression Tests ...................................................................................... 146 5.3.2.1 Rapid Compression Test at 225mm/s ................................................................ 146 5.3.2.2 Rapid Compression Test at 141mm/s ................................................................ 149 5.3.2.3 Rapid Compression Test under Sinusoidal Loading .......................................... 151 5.4 CONCLUSIONS .......................................................................................................... 152 iii 6. Chapter Six: INVERSE FINITE ELEMENT ANALYSIS .............................................. 154 6.1 INTRODUCTION ........................................................................................................ 155 6.2 METHODS ................................................................................................................... 156 6.2.1 Hyperelastic Material Properties ........................................................................... 156 6.2.1.1 Determination of the Hyperelastic Material Properties of the Macro-chamber Layer….. ........................................................................................................................... 159 6.2.1.2 Determination of the Hyperelastic Material Properties of the Micro-chamber Layer….. ........................................................................................................................... 161 6.2.1.3 Determination of the Final Hyperelastic Material Properties of the Macro- chamber, Micro-chamber and Skin Layers....................................................................... 163 6.2.2 Validation of the Hyperelastic FE Model .............................................................. 165 6.2.3 Viscoelastic Material Properties ............................................................................ 168 6.2.3.1 Determination of the Viscoelastic Material Properties of the Macro-chamber
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