Patient specific finite volume modeling for intraosseous PMMA cement flow simulation in vertebral cancellous bone

PATIENT SPECIFIC FINITE VOLUME MODELING FOR INTRAOSSEOUS PMMA CEMENT FLOW SIMULATION IN VERTEBRAL CANCELLOUS BONE JEREMY TEO CHOON MENG A THESIS SUBMITTED FOR THE DEGREE OF DOCTORATE OF PHILOSOPHY DEPARTMENT OF DIAGNOSTIC RADIOLOGY NATIONAL UNIVERSITY OF SINGAPORE 2007 SUMMARY Diagnostic radiologists or orthopaedic surgeons practicing percutaneous vertebroplasty inject viscous polymethylmethacrylate bone cement into fractured vertebrae increasing the strength and stiffness of the vertebrae as the biocompatible polymer hardens. The volume and spatial distribution of bone cement is currently determined empirically. Even cement viscosity is altered to suit the working style of the surgeon or radiologist. As with all surgical procedures, risks are implicated and it manifests in the form of cement leakage and the subsequent fracture of adjacent vertebrae. Reduction in the volume of bone cement injected has been theorized to reduce the risk of leakage as well as subsequent fractures. However, volume reduction may also reduce the effectiveness of the percutaneous vertebroplasty procedure. Ex vivo biomechanical tests have been used to investigate ideal cement volume and distribution. Results are still inconclusive, as the number of parameters involved requires substantial number of specimens, in order to be statistically significant. Computational biomechanics offers an attractive alternative solution. Computational models of the vertebra can be re-used to evaluate surgical parameters, eliminating considerations inherent to specimen variation. However, current models for percutaneous vertebroplasty are inadequate for in-depth research and are also restricted to post-procedure stress/strain analysis. Intraosseous flow visualization is not possible and cement distributions are generic and idealized in these models. An improved finite volume meshing platform, using patient clinical computed tomography datasets as input, have been developed to provide better computational models. Also in this dissertation, through experimental means, models describing a relationship between CT Hounsfield units, vertebral cancellous bone permeability ) and the viscosity – time behaviour of SimplexP® ( polymethylmethacrylate bone cement (# (t ) = 0.09e1.8t ("& ) !0.21t + 0.4 ) were determined. These mathematical models were used as inputs for the computational simulation. Their parameters could be altered subsequently, when more accurate models are developed. Percutaneous vertebroplasty simulation was performed on cadaver lumbar vertebrae specimens, which were clinically imaged both before and after bone cement injection, using computed tomography. Image datasets before percutaneous vertebroplasty were used to generate finite volume models and simulations were performed according to actual procedural parameters. Based on the comparison of bone cement filled areas in the post procedural image datasets and results from simulation, 67.6% of the final bone cement spatial distribution could be predicted. Unfortunately, as with all finite volume modeling, computational resources were the main limitation in this dissertation. Clinical computed tomography datasets had to be re-sampled to a lower resolution such that the finite volume mesh generated would have a computationally reasonable number of elements. This also resulted in an averaging of the CT attenuation and therefore permeability values, which was probably detrimental to detailed modeling. The accuracy of the mathematical models derived in this dissertation needs to be further tested experimentally as the number of specimens was limited for economic or logistic reasons. However, it represents a good starting ground for future work on computational modeling of intraosseous PMMA bone cement flow. The robust nature of the modeling and simulation framework developed through this dissertation allows these improvements to be made more readily. In the future, finite volume meshes could eventually be generated from higher resolution clinical CT datasets as greater computational resources become available. ACKNOWLEDGMENTS My greatest appreciation and thanks to my supervisors Prof. Wang Shih Chang and Prof. Teoh Swee Hin, for imparting knowledge, culturing my research instinct and training of the mind. They have made my stay as their Ph.D candidate at the National University of Singapore thoroughly fulfilling and fun at the same time. My parents, Thank you for your prayers and for believing in me. My brothers, nothing is impossible. Si-hoe Kuanming, Andy Png, Bina Rai, my fellow lab mates and friends from Biomat Center, NUSSTEP, Department of Diagnostic Radiology and Department of Orthopedic Surgery. You have all helped me in this journey in your own special way. It does not end here, this is just the beginning. Finally my dearest wife Joyce, thank you for your undying love, understanding and for not letting me quit on myself. TABLE OF CONTENTS LIST OF TABLES . xv LIST OF FIGURES . xvii LIST OF SYMBOLS xxi Introduction . 1.1 Motivation 1.2 Research Scope and Objectives . 1.3 Overview of Dissertation Literature Review 2.1 Introduction 2.2 Anatomical Planes and Directions . 2.3 Computed Tomography 10 2.3.1 Clinical CT Imaging . 10 2.3.2 Description of Pixels and Voxels 11 2.3.3 CT Intensity and Bone Density . 12 2.3.4 Micro CT Imaging and Microarchitecture . 14 2.4 Basic Anatomy of the Human Spine and Vertebra . 15 2.4.1 The Vertebrae and its Components . 17 2.4.2 Internal structure of the vertebral body . 18 2.4.3 Vertebral Venous Plexus 19 2.4.4 Intervertebral Disc 20 2.4.5 Motion Segment . 21 2.5 Osteoporosis and Fractures of the Vertebra . 21 vii 2.5.1 Osteoporosis of the Vertebral Body 22 2.5.2 Vertebral Compression Fractures 24 2.6 Percutaneous Vertebroplasty . 26 2.6.1 History . 26 2.6.2 Indications for Vertebroplasty 27 2.6.3 Percutaneous Vertebroplasty Procedure 27 2.6.4 Complications during Vertebroplasty . 33 PMMA Cement Extravastion . 33 Adjacent Vertebral Failure . 40 2.7 Reducing Complications through Biomechanical Evaluation 42 2.7.1 Clinical Dilemma . 42 2.7.2 Post-Vertebroplasty Biomechanics . 43 Effects of Varying PMMA Cement Volume . 44 Effects of Varying PMMA Spatial Distribution 46 2.7.3 Computational Biomechanics for Vertebroplasty Research . 48 Finite Volume Method and Finite Element Method 49 Current Finite Element Mesh for Vertebroplasty 51 2.8 Finite element Modeling Techniques 55 2.8.1 Automatic Meshing Technique . 55 2.8.2 Automatic Voxel-Based Meshing Technique 56 2.8.3 Adopted Finite Element Modeling Technique . 60 2.8.4 Other Finite Element Modeling Considerations 62 2.9 Permeability of Cancellous Bone 62 2.9.1 Permeability and Darcy’s Law 62 2.9.2 Direct Perfusion Testing . 64 2.9.3 Inference of permeability from Porosity . 65 1.1.1 Inference of permeability from Porosity . 66 viii 2.9.4 Increasing Vertebral Cancellous Bone Permeability Data . 69 2.10 Rheology of Polymethylmethacrylate Cement . 70 2.10.1 Viscosity and PMMA Bone Cement . 70 2.10.2 Rheometers 73 2.10.3 Viscosity Behavior of PMMA bone cement 74 Permeability of Vertebral Cancellous Bone 78 3.1 Introduction 78 3.1.1 Permeability of Bone 78 3.1.2 Microarchitectural Phases on Compression . 78 3.1.3 Cancellous Bone Orientation Convention . 80 3.1.4 Anisotropy of Cancellous Bone and Specimen Orientation for Permeability Testing 80 3.1.5 Measurement of Cancellous Bone Permeability 82 3.1.6 Cancellous Bone Microarchitectural Parameters . 84 3.2 Materials and Methods 85 3.2.1 Cancellous Bone Permeability Testing at Various Compressive States . 85 Experimental Overview . 85 Extraction of Cancellous Bone Specimens . 86 Custom Permeameter Setup . 87 Permeability Measurement with Custom Permeameter . 88 MicroCT Imaging and Microarchitectural Analysis of Cancellous Bone 90 Mechanical Compression of Cancellous Bone Specimens 91 3.3 Results 93 3.3.1 Microarchitecture and Permeability Results of Vertebral Cancellous Bone specimens at Each Compressed Phase . 93 3.3.2 Predicting Permeability of Vertebral Cancellous Bone using Porosity 99 3.3.3 Anisotropy of Permeability in Vertebral Cancellous Bone .103 ix 3.3.4 Microarchitectural Parameters that Influences Permeability of Intact Vertebral Cancellous Bone Specimens 105 3.3.5 Improving Prediction Model Using Microarchitectural Parameters and Multivariable Linear Regression Analyses .106 3.4 Discussion .108 3.4.1 Change in Permeability and Microarchitecture Parameters with Compression .108 3.4.2 Microarchitectural Parameters that affect Permeability of Intact Vertebral Cancellous Bone 111 3.4.3 Models for Predicting Permeability of Cancellous Bone 112 3.4.4 Permeability – Porosity Model based on Pooled Literature Results 113 3.5 Inferring Permeability from Clinical CT Data 115 3.6 Limitations 118 3.7 Conclusion .121 Rheological Study on SimplexP® PMMA Cement .123 4.1 Introduction .123 4.2 Materials and Methods .124 4.2.1 Rheological Testing of PMMA Bone Cement 124 Rotational Rheometer .124 Preparation and Loading of PMMA Cement .125 Testing Conditions Subjected to PMMA Cement Samples 126 4.3 Results .127 4.3.1 Shear stress vs. shear rate data of SimplexP® PMMA Cement at liquid monomer to powder ratio of 1.0ml/g .127 4.3.2 Flow Index as a Function of Time .130 4.3.3 Consistency Index as a Function of Time 131 4.3.4 Viscosity (!) as a Function of Time (t) 132 4.3.5 Comparison of Models for SimplexP® PMMA bone Cement at Different Liquid monomer to Powder Ratio .134 x 4.3.6 Environmental Effects on Rheological and Mechanical Properties of SimplexP® PMMA cement 135 Change in Rheological Behaviour due to Environmental Effects .135 Changes in Mechanical Behaviour 137 4.4 Discussion .138 4.4.1 Rheological Testing .138 4.4.2 Viscosity Changes due to Modification of Monomer – Powder Ratio 139 Viscosity Changes due to Radiopacifiers .140 4.4.3 Environmental Effects on Rheological and Mechanical Properties of SimplexP® PMMA cement 142 Change in Rheological Behaviour .142 Changes in Mechanical Behaviour 142 4.5 Limitations 143 4.6 Conclusion .145 Mesh Generation for Patient Specific Vertebral Body 146 5.1 Introduction .146 5.2 Materials and Methods .147 5.2.1 Segmentation of CT Dataset 147 5.2.2 Automated Modeling for Intraosseous Flow Simulation 148 Generating the Vertebral Body Finite Volume Mesh .148 Grouping of Finite Volumes for Automatic Permeabilty Assignment 150 Smoothening of the Voxel-based Mesh .151 Clinical Decisions .154 Modifications to FE Mesh .154 Direct Implementation into Simulation 157 Overview of Developed Finite Element Meshing Process .157 5.2.3 Initial Test .159 xi Graph of Permeability vs. Porosity - Literature Values for Vertebral Cancellous Bone 1.0E-06 Longitudinal Specimen y = 6E-16e Permeability, k (m2 ) Transverse Specimen k = 5E-11e 1.0E-07 19.78! R = 0.77 7.09 ! R = 0.56 1.0E-08 longitudinal 1.0E-09 0.70 0.75 0.80 0.85 0.90 transverse 0.95 1.00 Porosity, ! ( ) Graph of Permeability vs. Porosity – Literature Values from Baroud et al. (2003) and Naumen et al. (1999) 233 Relationship between permeability and porosity based on experimental results obtained from human calcaneous cancellous bone and using linseed oil as an infiltrating fluid. Relationship between permeability and volume fraction based on experimental results obtained from human verterbra, human femur and bovine tibial cancellous bone and using water as an infiltrating fluid. Grimm et al. 1997 Naumen et al., 1999 Relationship between permeability and porosity based on experimental results obtained from bovine femur cancellous bone and using water as an infiltrating fluid. Kohles et al, 2001 Relationship between permeability and porosity based on experimental results obtained from porcine femur cancellous bone and using saline as an infiltrating fluid. Hui et al., 1996 234 Appendix F. Hounsfield Unit and Porosity of Porcine Cancellous Bone Hounsfield Unit Porosity 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 560 416 738 681 612 645 699 475 505 598 486 472 716 682 665 586 372 377 343 457 299 405 495 368 407 389 401 337 219 235 264 289 0.70 0.86 0.72 0.73 0.67 0.72 0.73 0.79 0.77 0.77 0.71 0.80 0.72 0.71 0.71 0.85 0.86 0.83 0.82 0.81 0.87 0.83 0.78 0.83 0.82 0.80 0.81 0.82 0.88 0.86 0.87 0.85 32 porcine cancellous bone specimens were excised longitudinally and transversely and aligned accordingly onto the CT scanner bed. The alignment was such that it coincides with the alignment, similar to that a normal patient. The Siemens Somatom Sensation 64 CT scanner at the National University Hospital, Singapore was used for this imaging. X-ray voltage and ampere of 120kVp and 240mA were used respectively. Graph of HU vs. Porosity 850 Hounsfield Unit,HU ( ) Specimen 750 650 550 450 350 250 HU = -2116.2! + 2147.5 R = 0.72 150 0.55 0.75 Porosity, ! ( ) 0.95 Now, Hounsfield Units (HU) values from CT images can be converted to bone porosity (!) using the above equation. 235 Appendix G. Description of Microarchitectural Parameters Name: Tissue Volume Abbreviation: TV Units: mm3 Description: Total volume of the volume-of-interest (VOI), whose measurement is simply the total number of voxels of (solid and space) in the VOI times the voxel volume. The word “tissue” simply refers to the volume of interest. It does not mean any kind of recognition of any particular density range as biological tissue, soft, hard, or otherwise. Name: Bone Volume Abbreviation: BV Units: mm3 Description: Total volume of binarised objects within the VOI. Measured in both 2D and 3D. The measurement is simply the number of voxels of binarised solid objects in the VOI times the voxel volume. Name: Percent Bone Volume Abbreviation: BV/TV Units: % Description: The proportion of the VOI occupied by binarised solid objects. This parameter is only relevant if the studied volume is fully contained within a biphasic region of solid and space such as a trabecular bone region, and does not for example extend into or beyond the bounding cortical wall of bone. Name: Bone Surface Abbreviation: BS Units: mm2 Description: In 2D, the binarised object surface includes both, the crossectional slice perimeter measurements plus the vertical surfaces between solid and space. So in fact, it is an essentially 3d measurement based on a simple cubic voxel. The 3D measured surface is based on the faceted surface of the marching cubes volume model. In this dissertation we are concerned with the 3D measurement. Name: Bone Specific Surface Abbreviation: BS/BV Units: 1/mm Description: The ratio of binarised solid surface to volume measured as described above in both 2D and 3D within the VOI. Surface to volume ratio or “specific surface” is a useful basic parameter in characterising the complexity of structures and is the basis of model-dependent estimates of thickness. 236 Name: Bone Surface Density Abbreviation: BS/TV Units: 1/mm Description: The ratio of surface area to total volume measured as described above in both 2D and 3D within the VOI. Name: Trabecular thickness Abbreviation: Tb.Th Units: mm Description: With 3D image analysis by micro-CT a true 3D thickness can be measured which is model-independent. This is determined as an average of the local thickness at each voxel representing solid (or bone) (Ulrich et al. 1999). Local thickness for a point in solid is defined by Hildebrand and Ruegsegger (1997a) as the diameter of a sphere which fulfils two conditions: (a) the sphere encloses the point (but the point is not necessarily the centre of the sphere); (b) the sphere is entirely bounded within the solid surfaces. Histomorphometrists typically measure a single mean value of bone Tb.Th from a trabecular bone site. However a trabecular bone volume – or any complex biphasic object region – can also be characterised by a distribution of thicknesses. CT-analyser outputs a histogram of thicknesses with an interval of two pixels. Name: Trabecular Separation Abbreviation: Tb.Sp Units: mm Description: Trabecular separation is essentially the thickness of the spaces as defined by binarisation within the VOI. It can also be calculated directly in 3D by applying the surface area-based models as for thickness (Tb.Th). Name: Trabecular Number Abbreviation: Tb.N Units: 1/mm Description: Structure linear density or trabecular number implies the number of traversals across a trabecular or solid structure made per unit length on a linear path through a trabecular bone region. This parameter is measured in CT-analyser in 3D by application of equation below, and using a direct 3D measurement of thickness. Note that the optional stereology analysis (not included in this report) includes measurements of thickness, separation and number/linear density based on the mean intercept length (MIL) analysis which represents an alternative basis for these architectural measurements. Name: Trabecular Bone Pattern Factor Abbreviation: Tb.Pf Units: 1/mm Description: This is an index of connectivity of trabecular bone, which was developed and defined by Hahn et al. (1992). It was applied by these authors to 2D images of trabecular bone, and calculates an index of relative convexity or concavity of the total bone surface, on the principle that concavity indicates connectivity, and convexity indicates isolated disconnected structures (struts). Tb.Pf is calculated in 3D by comparing area 237 and perimeter (or volume and surface, respectively) of binarised solid before and after an image dilation. It is defined: Where P and A are solid area and perimeter, and the subscript numbers and indicate before and after image dilation. Where structural / trabecular connectedness results in enclosed marrow spaces, then dilation of trabecular surfaces will contract the perimeter. By contrast, open ends or nodes will have their perimeter expanded by surface dilation. As a result, lower Tb.Pf signifies better connected trabecular lattices while higher Tb.Pf means a more disconnected trabecular structure. A prevalence of enclosed cavities and concave surfaces can push Tb.Pf to negative values – as with the structure model index (SMI) – see below. Name: Structure Model Index Abbreviation: SMI Units: none Description: Structure model index indicates the relative prevalence of rods and plates in a 3D structure such as cancellous bone. SMI involves a measurement of surface convexity. This parameter is of importance in osteoporosis of trabecular bone which is characterised by a transition from plate-like to rod-like architecture. An ideal plate, cylinder and sphere have SMI values of 0, and respectively. The calculation of SMI is based on dilation of the 3D voxel model. This artificially adds one voxel thickness to all binarised object surfaces (Hildebrand et al. 1997b). This is also the basis of the Tb.Pf parameter (see above) which explains why changes in both parameters correlate very closely with each other. SMI is derived as follows: Where, S is the object surface area before dilation and S’ is the change in surface area caused by dilation. V is the initial, undilated object volume. It should be noted that concave surfaces of enclosed cavities represent negative convexity to the SMI parameter, since dilation of an enclosed space will reduce surface area causing S’ to be negative. Therefore regions of bone containing a prevalence of enclosed cavities – such as regions with relative volume above 50% – can have negative SMI values. As a consequence, the SMI parameter is sensitive to relative volume, and this can accentuate differences between experimental groups in the measured SMI value. 238 Appendix H. Permeability and Microarhictecture Results Intact Cancellous Bone time taken (s) time taken (s) time taken (s) average time taken (s) Hydraulic Conductivity, K (m/s) permeability, k (m2) Porosity, ! () Bone surface density, BS/TV (mm-1) Trabecular pattern factor , Tb.Pf (mm-1) Structure model index, SMI () Trabecular thickness, Tb.Th (mm) Trabecular number, Tb.N (mm-1) Trabecular separation, Tb.Sp (mm) mm mm dtube2/dperm2 () Diameter of Falling Head Tube, dtube : 1.90E-02 Diameter of Permeameter Tube, dperm : 6.00E-03 ln h0/h () m m Length, L (m) 5.3E-02 2.00E-03 Specimen No. Initial Height, h0: End Height, h: 10 11 12 13 14 15 16 17 18 19 20 6.955E-03 6.740E-03 6.835E-03 6.784E-03 6.704E-03 6.187E-03 6.245E-03 6.088E-03 6.108E-03 6.210E-03 6.389E-03 6.355E-03 6.498E-03 6.431E-03 6.415E-03 6.290E-03 6.517E-03 6.363E-03 6.273E-03 3.277 3.277 3.277 3.277 3.277 3.277 3.277 3.277 3.277 3.277 3.277 3.277 3.277 3.277 3.277 3.277 3.277 3.277 3.277 10.028 10.028 10.028 10.028 10.028 10.028 10.028 10.028 10.028 10.028 10.028 10.028 10.028 10.028 10.028 10.028 10.028 10.028 10.028 9.69 9.01 9.11 9.05 8.81 10.18 9.82 8.36 9.11 8.81 10.23 10.00 9.43 9.55 10.55 9.88 11.17 10.43 10.24 9.43 8.88 9.69 8.95 9.56 10.11 9.63 8.69 8.82 9.17 10.59 10.00 9.62 9.95 10.18 9.43 11.00 9.37 10.06 10.05 8.81 9.76 9.17 8.88 10.05 9.63 8.49 9.00 9.18 10.17 10.06 10.00 10.00 10.24 9.63 10.88 9.82 10.05 9.723 8.900 9.520 9.057 9.083 10.113 9.693 8.513 8.977 9.053 10.330 10.020 9.683 9.833 10.323 9.647 11.017 9.873 10.117 2.35E-02 2.49E-02 2.36E-02 2.46E-02 2.43E-02 2.01E-02 2.12E-02 2.35E-02 2.24E-02 2.25E-02 2.03E-02 2.08E-02 2.21E-02 2.15E-02 2.04E-02 2.14E-02 1.94E-02 2.12E-02 2.04E-02 2.40E-09 2.54E-09 2.41E-09 2.51E-09 2.47E-09 2.05E-09 2.16E-09 2.40E-09 2.28E-09 2.30E-09 2.07E-09 2.13E-09 2.25E-09 2.19E-09 2.08E-09 2.18E-09 1.98E-09 2.16E-09 2.08E-09 0.86 0.88 0.87 0.93 0.88 0.88 0.88 0.90 0.89 0.89 0.85 0.89 0.88 0.87 0.87 0.89 0.87 0.88 0.88 3.17 3.10 2.99 2.26 2.69 2.86 2.85 2.55 2.61 2.64 3.32 2.54 2.74 2.79 2.97 2.57 3.04 2.85 2.78 2.81 3.52 3.43 7.02 4.85 3.65 3.36 5.58 4.73 5.17 2.45 5.19 4.14 4.62 2.81 4.40 3.26 4.71 3.91 1.04 1.10 1.14 1.54 1.49 1.20 1.14 1.60 1.44 1.54 0.94 1.51 1.34 1.51 1.04 1.38 1.14 1.44 1.23 0.14 0.13 0.14 0.11 0.15 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.15 0.16 0.14 0.14 0.14 0.14 0.13 1.02 0.97 0.94 0.64 0.79 0.89 0.90 0.75 0.79 0.78 1.07 0.76 0.84 0.82 0.94 0.79 0.95 0.86 0.87 0.66 0.67 0.69 0.75 0.70 0.70 0.72 0.70 0.71 0.69 0.65 0.72 0.73 0.67 0.72 0.72 0.68 0.67 0.74 239 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 75 77 79 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 6.367E-03 6.251E-03 6.552E-03 6.130E-03 5.780E-03 6.420E-03 6.139E-03 5.822E-03 6.157E-03 6.247E-03 6.280E-03 6.305E-03 6.348E-03 6.369E-03 6.424E-03 6.397E-03 5.416E-03 6.808E-03 5.987E-03 5.970E-03 5.987E-03 5.983E-03 6.001E-03 5.995E-03 6.003E-03 6.004E-03 5.849E-03 5.855E-03 5.820E-03 5.962E-03 5.959E-03 5.900E-03 5.923E-03 6.225E-03 6.169E-03 6.124E-03 6.024E-03 5.984E-03 6.043E-03 3.277 3.277 3.277 3.277 3.277 3.277 3.277 3.277 3.277 3.277 3.277 3.277 3.277 3.277 3.277 3.277 3.277 3.277 3.277 3.277 3.277 3.277 3.277 3.277 3.277 3.277 3.277 3.277 3.277 3.277 3.277 3.277 3.277 3.277 3.277 3.277 3.277 3.277 3.277 10.028 10.028 10.028 10.028 10.028 10.028 10.028 10.028 10.028 10.028 10.028 10.028 10.028 10.028 10.028 10.028 10.028 10.028 10.028 10.028 10.028 10.028 10.028 10.028 10.028 10.028 10.028 10.028 10.028 10.028 10.028 10.028 10.028 10.028 10.028 10.028 10.028 10.028 10.028 10.23 10.00 10.37 10.43 10.62 9.81 10.05 9.82 9.36 10.29 11.12 10.11 10.23 9.88 10.17 11.05 10.95 10.23 8.55 8.75 8.67 9.07 8.56 9.87 10.12 9.81 8.40 8.93 8.63 9.37 10.32 9.75 9.50 10.76 9.89 9.25 9.97 9.31 9.63 10.11 10.24 10.88 10.11 10.11 10.06 9.95 10.30 10.37 10.17 11.49 10.06 10.18 9.88 10.43 10.49 11.25 10.81 8.83 8.68 8.56 8.71 8.55 9.68 10.26 9.87 8.02 9.07 8.75 9.25 10.33 9.56 9.80 10.89 9.93 9.30 9.86 9.38 9.51 10.06 10.24 10.94 10.11 10.43 10.11 10.11 10.11 10.56 10.24 11.37 10.18 10.17 10 11 10.56 10.43 10.88 10.89 8.75 8.50 9.00 8.98 8.43 9.68 10.25 10.05 8.36 8.99 8.61 8.94 10.25 9.56 9.62 10.61 9.87 9.49 9.81 9.55 9.45 10.133 10.160 10.730 10.217 10.387 9.993 10.037 10.077 10.097 10.233 11.327 10.117 10.193 9.880 10.387 10.657 11.027 10.643 8.710 8.643 8.743 8.920 8.513 9.743 10.210 9.910 8.260 8.997 8.663 9.187 10.300 9.623 9.640 10.753 9.897 9.347 9.880 9.413 9.530 2.06E-02 2.02E-02 2.01E-02 1.97E-02 1.83E-02 2.11E-02 2.01E-02 1.90E-02 2.00E-02 2.01E-02 1.82E-02 2.05E-02 2.05E-02 2.12E-02 2.03E-02 1.97E-02 1.61E-02 2.10E-02 2.26E-02 2.27E-02 2.25E-02 2.20E-02 2.32E-02 2.02E-02 1.93E-02 1.99E-02 2.33E-02 2.14E-02 2.21E-02 2.13E-02 1.90E-02 2.01E-02 2.02E-02 1.90E-02 2.05E-02 2.15E-02 2.00E-02 2.09E-02 2.08E-02 240 2.11E-09 2.06E-09 2.05E-09 2.01E-09 1.86E-09 2.15E-09 2.05E-09 1.94E-09 2.04E-09 2.05E-09 1.86E-09 2.09E-09 2.09E-09 2.16E-09 2.07E-09 2.01E-09 1.65E-09 2.14E-09 2.30E-09 2.31E-09 2.29E-09 2.25E-09 2.36E-09 2.06E-09 1.97E-09 2.03E-09 2.37E-09 2.18E-09 2.25E-09 2.17E-09 1.94E-09 2.05E-09 2.06E-09 1.94E-09 2.09E-09 2.20E-09 2.04E-09 2.13E-09 2.12E-09 0.88 0.89 0.85 0.88 0.86 0.89 0.86 0.90 0.88 0.86 0.86 0.86 0.88 0.88 0.89 0.88 0.84 0.87 0.82 0.83 0.82 0.82 0.82 0.81 0.79 0.81 0.85 0.82 0.84 0.83 0.80 0.82 0.81 0.78 0.80 0.83 0.82 0.84 0.79 2.89 2.64 3.27 2.75 3.26 2.40 2.95 2.30 2.61 3.14 3.18 2.94 2.87 2.77 2.66 2.79 3.54 2.94 3.37 3.25 3.41 3.37 3.45 3.42 3.76 3.59 2.86 3.35 3.06 3.28 3.57 3.13 3.53 3.80 3.58 3.06 3.44 3.00 3.66 4.56 4.83 2.78 4.92 3.16 4.59 3.91 4.84 3.00 3.18 2.49 3.93 4.56 4.47 4.22 4.79 2.54 4.15 1.81 2.86 2.61 2.23 2.39 2.22 1.80 2.22 3.29 2.74 3.18 2.54 2.26 2.70 2.10 0.97 1.80 2.00 1.97 2.95 1.05 1.42 1.47 1.01 1.50 1.07 1.48 1.35 1.50 1.07 1.10 0.94 1.36 1.44 1.40 1.31 1.43 0.97 1.33 1.02 1.27 1.24 1.10 1.11 1.13 1.04 1.08 1.32 1.27 1.32 1.14 1.32 1.43 1.22 0.97 1.19 1.18 1.13 1.37 0.97 0.14 0.14 0.14 0.14 0.13 0.15 0.15 0.15 0.14 0.14 0.14 0.15 0.14 0.14 0.14 0.14 0.14 0.14 0.17 0.17 0.17 0.17 0.16 0.18 0.18 0.16 0.17 0.18 0.17 0.17 0.19 0.20 0.18 0.18 0.18 0.18 0.17 0.18 0.18 0.87 0.79 1.03 0.81 1.03 0.71 0.89 0.67 0.82 0.99 1.03 0.89 0.85 0.83 0.82 0.84 1.13 0.89 1.07 0.99 1.05 1.06 1.09 1.06 1.19 1.13 0.87 1.02 0.94 1.02 1.08 0.92 1.09 1.20 1.11 0.96 1.07 0.92 1.17 0.66 0.72 0.69 0.72 0.68 0.81 0.64 0.80 0.80 0.69 0.69 0.68 0.67 0.70 0.76 0.69 0.58 0.65 0.66 0.62 0.59 0.62 0.59 0.60 0.54 0.57 0.71 0.60 0.65 0.62 0.56 0.66 0.57 0.59 0.58 0.66 0.61 0.67 0.58 Transverse 1.99E-09 2.03E-09 1.92E-09 2.17E-09 1.89E-09 1.94E-09 2.50E-09 2.04E-09 1.99E-09 2.11E-09 1.85E-09 2.48E-09 2.14E-09 0.76 0.78 0.80 0.83 0.79 0.82 0.84 0.79 0.80 0.78 0.80 0.87 0.88 4.10 3.73 3.66 2.80 3.77 3.26 2.85 3.63 3.33 3.63 2.99 2.11 2.84 0.70 1.05 1.14 2.38 1.53 2.25 2.25 1.45 1.07 0.44 1.92 2.67 4.07 1.00 1.03 0.97 1.40 1.13 1.22 1.24 1.12 0.97 0.82 1.52 1.38 1.29 0.18 0.18 0.18 0.20 0.18 0.18 0.18 0.19 0.19 0.18 0.22 0.20 0.14 1.29 1.18 1.17 0.87 1.17 1.02 0.89 1.12 1.07 1.18 0.89 0.65 0.87 0.52 0.57 0.62 0.74 0.55 0.64 0.73 0.59 0.65 0.60 0.69 0.94 0.70 SD Mean SD Mean SD 1.82E-03 2.08E-02 1.65E-03 2.09E-02 1.73E-03 1.86E-10 2.12E-09 1.69E-10 2.13E-09 1.77E-10 0.02 0.81 0.02 0.85 0.04 0.28 3.36 0.38 3.09 0.42 1.00 2.02 0.72 3.10 1.35 0.20 1.17 0.16 1.24 0.19 0.01 0.18 0.01 0.16 0.02 0.11 1.05 0.13 0.95 0.15 0.05 0.63 0.08 0.67 0.07 Trabecular separation, Tb.Sp (mm) Longitudinal 1.95E-02 1.99E-02 1.88E-02 2.13E-02 1.85E-02 1.90E-02 2.46E-02 2.00E-02 1.95E-02 2.07E-02 1.81E-02 2.43E-02 2.09E-02 Trabecular number, Tb.N (mm-1) Pool 10.143 9.953 10.503 9.253 10.663 10.350 8.827 10.940 11.230 10.767 10.997 8.163 Mean Trabecular thickness, Tb.Th (mm) 10.00 10.00 10.38 9.25 10.43 10.43 8.69 11.01 11.13 10.75 10.93 8.19 Structure model index, SMI () 10.19 9.87 10.63 9.38 10.82 10.31 8.87 10.93 11.37 10.74 11.06 8.06 Trabecular pattern factor , Tb.Pf (mm-1) 10.24 9.99 10.50 9.13 10.74 10.31 8.92 10.88 11.19 10.81 11.00 8.24 Bone surface density, BS/TV (mm-1) 10.028 10.028 10.028 10.028 10.028 10.028 10.028 10.028 10.028 10.028 10.028 10.028 Porosity, ! () 3.277 3.277 3.277 3.277 3.277 3.277 3.277 3.277 3.277 3.277 3.277 3.277 permeability, k (m2) 6.030E-03 6.020E-03 6.012E-03 5.993E-03 6.012E-03 5.997E-03 6.595E-03 6.665E-03 6.673E-03 6.776E-03 6.059E-03 6.035E-03 Hydraulic Conductivity, K (m/s) 57 58 59 60 61 62 63 64 65 69 70 72 241 Plateau Cancellous Bone time taken (s) time taken (s) average time taken (s) Hydraulic Conductivity, K (m/s) permeability, k (m2) Porosity, ! () Bone surface density, BS/TV (mm-1) Trabecular pattern factor , Tb.Pf (mm-1) Structure model index, SMI () Trabecular thickness, Tb.Th (mm) Trabecular number, Tb.N (mm-1) Trabecular separation, Tb.Sp (mm) mm mm time taken (s) 1.90E-02 6.00E-03 dtube2/dperm2 () Diameter of Falling Head Tube, dtube : Diameter of Permeameter Tube, dperm: ln h0/h () m m Length, L (m) 5.3E-02 2.00E-03 Specimen No. Initial Height, h0: End Height, h: 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 5.410E-03 6.600E-03 6.420E-03 6.390E-03 6.440E-03 5.840E-03 5.850E-03 5.860E-03 5.760E-03 5.770E-03 6.110E-03 5.870E-03 6.190E-03 5.840E-03 6.050E-03 5.880E-03 6.210E-03 5.950E-03 5.760E-03 5.960E-03 5.850E-03 6.250E-03 5.750E-03 3.277 3.277 3.277 3.277 3.277 3.277 3.277 3.277 3.277 3.277 3.277 3.277 3.277 3.277 3.277 3.277 3.277 3.277 3.277 3.277 3.277 3.277 3.277 10.028 10.028 10.028 10.028 10.028 10.028 10.028 10.028 10.028 10.028 10.028 10.028 10.028 10.028 10.028 10.028 10.028 10.028 10.028 10.028 10.028 10.028 10.028 12.33 12.52 13.42 14.23 14.43 14.08 13.02 12.69 13.58 13.86 15.60 13.17 13.47 13.33 13.36 13.01 15.30 15.36 14.33 14.01 14.26 14.62 15.36 12.30 12.80 13.28 14.45 13.70 13.95 12.80 12.98 13.24 13.77 16.02 13.67 14.08 14.01 12.44 12.80 14.73 14.39 12.89 13.60 13.86 13.86 15.09 12.17 13.11 13.36 13.90 14.13 13.86 12.77 13.80 13.17 13.39 15.56 14.19 13.74 13.39 13.57 12.72 15.20 14.62 14.71 13.39 13.93 13.93 14.76 12.27 12.81 13.35 14.19 14.09 13.96 12.86 13.16 13.33 13.67 15.73 13.68 13.76 13.58 13.12 12.84 15.08 14.79 13.98 13.67 14.02 14.14 15.07 1.45E-02 1.69E-02 1.58E-02 1.48E-02 1.50E-02 1.37E-02 1.49E-02 1.46E-02 1.42E-02 1.39E-02 1.28E-02 1.41E-02 1.48E-02 1.41E-02 1.51E-02 1.50E-02 1.35E-02 1.32E-02 1.35E-02 1.43E-02 1.37E-02 1.45E-02 1.25E-02 1.48E-09 1.73E-09 1.61E-09 1.51E-09 1.53E-09 1.40E-09 1.52E-09 1.49E-09 1.45E-09 1.41E-09 1.30E-09 1.44E-09 1.51E-09 1.44E-09 1.54E-09 1.53E-09 1.38E-09 1.35E-09 1.38E-09 1.46E-09 1.40E-09 1.48E-09 1.28E-09 0.79 0.82 0.81 0.81 0.84 0.83 0.83 0.86 0.85 0.84 0.80 0.85 0.83 0.82 0.82 0.84 0.81 0.82 0.83 0.82 0.84 0.79 0.82 3.67 3.30 3.59 3.59 3.09 3.21 3.18 2.88 2.94 3.11 3.66 2.90 3.03 3.15 3.23 2.86 3.41 3.29 3.11 3.28 2.99 3.51 3.16 0.99 1.60 1.19 1.19 2.81 1.80 1.53 3.46 2.83 2.88 0.50 3.18 2.18 2.74 1.09 2.70 1.48 2.47 1.77 2.40 2.87 0.99 2.58 1.04 1.08 1.03 1.03 1.43 1.16 1.07 1.51 1.38 1.41 0.86 1.44 1.27 1.48 1.00 1.39 1.08 1.34 1.12 1.36 1.43 0.95 1.39 0.18 0.17 0.17 0.17 0.18 0.17 0.17 0.17 0.17 0.17 0.17 0.17 0.18 0.19 0.18 0.18 0.18 0.18 0.18 0.19 0.18 0.19 0.19 1.17 1.05 1.14 1.14 0.92 1.01 1.01 0.86 0.90 0.93 1.20 0.88 0.93 0.93 1.04 0.88 1.08 1.00 0.98 0.99 0.90 1.11 0.94 0.56 0.63 0.59 0.59 0.63 0.63 0.66 0.65 0.65 0.62 0.59 0.65 0.69 0.62 0.66 0.68 0.62 0.60 0.67 0.60 0.65 0.63 0.69 242 25 26 27 28 29 30 31 32 33 34 35 75 77 79 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 5.540E-03 6.110E-03 5.760E-03 5.440E-03 5.850E-03 5.910E-03 6.060E-03 5.850E-03 5.980E-03 6.060E-03 6.130E-03 6.020E-03 5.200E-03 6.410E-03 4.940E-03 5.407E-03 5.783E-03 5.827E-03 5.714E-03 5.827E-03 5.913E-03 5.762E-03 5.320E-03 5.701E-03 5.609E-03 5.632E-03 5.846E-03 5.588E-03 5.810E-03 5.715E-03 5.529E-03 5.368E-03 5.647E-03 5.584E-03 5.875E-03 5.746E-03 5.924E-03 5.921E-03 5.671E-03 3.277 3.277 3.277 3.277 3.277 3.277 3.277 3.277 3.277 3.277 3.277 3.277 3.277 3.277 3.277 3.277 3.277 3.277 3.277 3.277 3.277 3.277 3.277 3.277 3.277 3.277 3.277 3.277 3.277 3.277 3.277 3.277 3.277 3.277 3.277 3.277 3.277 3.277 3.277 10.028 10.028 10.028 10.028 10.028 10.028 10.028 10.028 10.028 10.028 10.028 10.028 10.028 10.028 10.028 10.028 10.028 10.028 10.028 10.028 10.028 10.028 10.028 10.028 10.028 10.028 10.028 10.028 10.028 10.028 10.028 10.028 10.028 10.028 10.028 10.028 10.028 10.028 10.028 15.46 15.99 15.82 16.18 15.42 17.36 16.45 16.64 16.36 15.70 17.89 15.54 17.11 15.42 10.3 10 9.68 9.49 9.99 10.18 10.68 10.06 9.43 9.81 9.51 10 10.24 9.88 10.68 12.44 10.81 9.93 10.23 9.99 11.56 11.13 10.63 10.93 10.27 16.01 15.95 15.95 15.70 16.22 16.95 17.23 16.30 16.54 16.01 16.45 16.48 17.67 15.36 10.43 9.74 9.82 9.51 9.24 10.2 10.7 10.24 9.57 9.87 9.43 9.83 10.44 9.87 10.25 12.63 10.82 10.12 10.49 10 11.5 11 10.62 10.99 10.06 16.39 15.23 15.17 15.16 15.65 16.68 16.57 16.81 15.23 15.92 16.09 15.92 17.95 15.45 10.49 9.74 9.94 9.49 9.93 10.32 10.74 10.3 9.57 10 9.31 9.93 10.2 10.01 9.94 12.62 10.83 10.06 10.72 10.19 11.62 11.12 10.57 11.12 10.12 15.95 15.72 15.65 15.68 15.76 17.00 16.75 16.58 16.04 15.88 16.81 15.98 17.58 15.41 10.41 9.83 9.81 9.50 9.72 10.23 10.71 10.20 9.52 9.89 9.42 9.92 10.29 9.92 10.29 12.56 10.82 10.04 10.48 10.06 11.56 11.08 10.61 11.01 10.15 1.14E-02 1.28E-02 1.21E-02 1.14E-02 1.22E-02 1.14E-02 1.19E-02 1.16E-02 1.22E-02 1.25E-02 1.20E-02 1.24E-02 9.72E-03 1.37E-02 1.56E-02 1.81E-02 1.94E-02 2.02E-02 1.93E-02 1.87E-02 1.81E-02 1.86E-02 1.84E-02 1.89E-02 1.96E-02 1.87E-02 1.87E-02 1.85E-02 1.86E-02 1.49E-02 1.68E-02 1.76E-02 1.77E-02 1.82E-02 1.67E-02 1.70E-02 1.84E-02 1.77E-02 1.84E-02 243 1.16E-09 1.30E-09 1.23E-09 1.16E-09 1.24E-09 1.17E-09 1.21E-09 1.18E-09 1.25E-09 1.28E-09 1.22E-09 1.26E-09 9.91E-10 1.39E-09 1.59E-09 1.84E-09 1.97E-09 2.06E-09 1.97E-09 1.91E-09 1.85E-09 1.89E-09 1.87E-09 1.93E-09 2.00E-09 1.90E-09 1.90E-09 1.89E-09 1.89E-09 1.52E-09 1.71E-09 1.79E-09 1.81E-09 1.86E-09 1.70E-09 1.74E-09 1.87E-09 1.80E-09 1.87E-09 0.80 0.85 0.81 0.86 0.84 0.80 0.80 0.81 0.82 0.82 0.83 0.82 0.76 0.81 0.77 0.79 0.81 0.81 0.81 0.81 0.79 0.80 0.83 0.79 0.82 0.82 0.80 0.81 0.81 0.77 0.79 0.79 0.80 0.81 0.77 0.76 0.79 0.80 0.81 3.50 2.67 3.32 2.62 2.81 3.38 3.37 3.26 3.29 3.17 3.03 3.23 4.02 3.30 4.07 3.87 3.53 3.58 3.73 3.55 3.81 3.83 3.24 3.74 3.43 3.46 3.62 3.27 3.55 4.06 3.71 3.80 3.64 3.60 3.93 4.10 3.68 3.65 3.11 0.99 2.80 1.95 3.20 1.63 1.27 0.55 2.12 2.60 2.41 2.20 2.58 0.40 2.16 0.77 1.85 2.39 2.10 2.02 2.21 1.69 1.93 3.35 2.39 2.77 2.30 2.24 2.71 2.17 0.53 1.35 1.52 1.62 2.77 0.95 1.10 1.47 1.41 2.18 0.97 1.48 1.32 1.60 1.12 1.06 0.86 1.33 1.40 1.34 1.30 1.35 0.89 1.31 0.87 1.16 1.20 1.11 1.07 1.13 1.01 1.05 1.36 1.26 1.27 1.13 1.16 1.33 1.09 0.77 1.00 1.07 0.95 1.27 0.87 0.91 0.95 0.87 1.20 0.18 0.20 0.19 0.18 0.18 0.18 0.18 0.19 0.18 0.19 0.18 0.18 0.18 0.19 0.17 0.18 0.17 0.17 0.16 0.17 0.17 0.17 0.17 0.19 0.18 0.17 0.18 0.19 0.18 0.18 0.18 0.18 0.17 0.18 0.18 0.18 0.18 0.17 0.19 1.12 0.79 1.00 0.77 0.90 1.07 1.10 0.99 0.98 0.96 0.93 0.97 1.29 0.99 1.29 1.18 1.09 1.13 1.17 1.10 1.20 1.21 0.97 1.13 1.05 1.07 1.10 0.97 1.10 1.30 1.15 1.17 1.14 1.10 1.25 1.29 1.16 1.17 0.98 0.61 0.74 0.58 0.74 0.74 0.66 0.67 0.63 0.60 0.64 0.69 0.62 0.53 0.59 0.56 0.55 0.58 0.59 0.57 0.58 0.54 0.56 0.63 0.54 0.59 0.60 0.56 0.64 0.58 0.57 0.58 0.57 0.58 0.56 0.55 0.52 0.58 0.60 0.68 0.79 0.81 0.81 0.79 0.82 0.77 0.80 0.83 0.821 0.020 0.799 0.017 0.811 3.94 3.43 3.45 3.79 3.25 3.92 2.98 2.80 3.219 0.289 3.609 0.309 3.403 1.69 2.25 1.95 1.59 1.58 0.22 1.52 2.31 2.002 0.828 1.846 0.671 1.929 1.06 1.13 1.14 1.04 0.93 0.68 1.18 1.22 1.232 0.205 1.074 0.160 1.157 0.17 0.17 0.18 0.18 0.17 0.18 0.22 0.20 0.180 0.008 0.179 0.010 0.179 1.22 1.08 1.07 1.17 1.05 1.28 0.90 0.87 0.996 0.112 1.125 0.107 1.057 0.54 0.60 0.64 0.57 0.66 0.56 0.70 0.77 0.638 0.047 0.591 0.052 0.616 2.81E-03 2.87E-10 0.022 0.355 0.757 0.200 0.009 0.127 0.054 Trabecular separation, Tb.Sp (mm) Transverse 1.79E-09 2.04E-09 2.14E-09 1.95E-09 2.02E-09 1.92E-09 1.88E-09 1.74E-09 1.37E-09 1.53E-10 1.87E-09 1.28E-10 1.60E-09 Trabecular number, Tb.N (mm-1) Longitudinal 1.75E-02 2.00E-02 2.10E-02 1.91E-02 1.98E-02 1.88E-02 1.85E-02 1.71E-02 1.34E-02 1.50E-03 1.83E-02 1.25E-03 1.57E-02 Trabecular thickness, Tb.Th (mm) 10.87 10.85 9.74 9.70 9.76 9.82 11.24 10.96 11.01 10.77 10.76 10.73 10.5 10.48 8.82 8.86 Pool Structure model index, SMI () 10.75 9.68 9.62 10.76 10.88 10.81 10.57 8.94 Trabecular pattern factor , Tb.Pf (mm-1) 10.93 9.67 10.07 10.88 10.43 10.62 10.37 8.81 Bone surface density, BS/TV (mm-1) 10.028 10.028 10.028 10.028 10.028 10.028 10.028 10.028 Porosity, ! () 3.277 3.277 3.277 3.277 3.277 3.277 3.277 3.277 permeability, k (m2) 5.782E-03 5.899E-03 6.275E-03 6.375E-03 6.499E-03 6.147E-03 5.884E-03 4.609E-03 Hydraulic Conductivity, K (m/s) 61 62 63 64 65 69 70 72 244 Densified Cancellous Bone time taken (s) time taken (s) time taken (s) average time taken (s) Hydraulic Conductivity, K (m/s) permeability, k (m2) Porosity, ! () Bone surface density, BS/TV (mm-1) Trabecular pattern factor , Tb.Pf (mm-1) Structure model index, SMI () Trabecular thickness, Tb.Th (mm) Trabecular number, Tb.N (mm-1) Trabecular separation, Tb.Sp (mm) mm mm dtube2/dperm2 () Diameter of Falling Head Tube, dtube : 1.90E-02 Diameter of Permeameter Tube, dperm : 6.00E-03 ln h0/h () m m Length, L (m) 5.3E-02 2.00E-03 Specimen No. Initial Height, h0: End Height, h: 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 5.88E-03 5.08E-03 5.30E-03 5.23E-03 4.95E-03 4.45E-03 5.00E-03 4.60E-03 5.45E-03 4.45E-03 5.13E-03 5.37E-03 4.32E-03 5.86E-03 4.75E-03 4.70E-03 5.49E-03 4.56E-03 5.23E-03 5.11E-03 4.90E-03 6.06E-03 4.18E-03 3.277 3.277 3.277 3.277 3.277 3.277 3.277 3.277 3.277 3.277 3.277 3.277 3.277 3.277 3.277 3.277 3.277 3.277 3.277 3.277 3.277 3.277 3.277 10.028 10.028 10.028 10.028 10.028 10.028 10.028 10.028 10.028 10.028 10.028 10.028 10.028 10.028 10.028 10.028 10.028 10.028 10.028 10.028 10.028 10.028 10.028 10.65 10.22 9.17 10.40 9.51 11.41 10.14 8.49 9.30 11.00 11.85 9.18 11.18 10.67 10.93 10.58 9.60 10.98 9.34 10.05 8.83 10.30 9.46 10.78 10.57 9.77 10.96 9.85 9.60 9.42 9.96 9.46 11.63 12.70 9.74 10.02 10.48 10.50 10.41 10.49 10.44 9.88 10.12 9.15 10.80 10.27 10.65 9.54 9.72 10.88 10.05 10.69 11.97 9.68 9.41 10.85 12.16 9.93 10.02 10.15 10.12 10.21 10.15 10.38 9.82 9.42 9.15 10.63 9.95 10.693 10.110 9.553 10.747 9.803 10.567 10.510 9.377 9.390 11.160 12.237 9.617 10.407 10.433 10.517 10.400 10.080 10.600 9.680 9.863 9.043 10.577 9.893 1.81E-02 1.65E-02 1.82E-02 1.60E-02 1.66E-02 1.38E-02 1.56E-02 1.61E-02 1.91E-02 1.31E-02 1.38E-02 1.83E-02 1.37E-02 1.84E-02 1.48E-02 1.48E-02 1.79E-02 1.41E-02 1.77E-02 1.70E-02 1.78E-02 1.88E-02 1.39E-02 1.84E-09 1.68E-09 1.86E-09 1.63E-09 1.69E-09 1.41E-09 1.59E-09 1.64E-09 1.95E-09 1.34E-09 1.41E-09 1.87E-09 1.39E-09 1.88E-09 1.51E-09 1.51E-09 1.83E-09 1.44E-09 1.81E-09 1.74E-09 1.82E-09 1.92E-09 1.41E-09 0.75 0.73 0.81 0.73 0.77 0.75 0.77 0.81 0.82 0.77 0.71 0.81 0.75 0.80 0.77 0.81 0.75 0.75 0.79 0.78 0.81 0.75 0.75 4.35 4.72 3.73 4.82 4.18 4.44 4.05 3.78 3.53 4.26 5.02 3.56 4.34 3.57 3.85 3.51 4.35 4.60 3.81 4.05 3.61 4.27 4.25 0.15 -1.38 2.17 -1.10 0.51 -0.51 0.09 2.43 2.61 0.96 -1.51 1.41 -0.44 0.99 0.05 1.48 -0.06 0.36 1.37 1.77 2.07 0.56 -0.68 1.00 0.79 1.37 0.80 1.18 0.95 0.96 1.46 1.44 1.25 0.68 1.28 1.02 1.04 1.16 1.29 0.91 1.11 1.16 1.35 1.41 1.01 0.95 0.18 0.18 0.17 0.18 0.19 0.19 0.18 0.17 0.18 0.18 0.18 0.18 0.19 0.18 0.20 0.18 0.18 0.18 0.17 0.18 0.18 0.19 0.19 1.36 1.48 1.11 1.50 1.24 1.36 1.26 1.11 1.05 1.25 1.60 1.06 1.32 1.12 1.13 1.06 1.36 1.37 1.18 1.20 1.07 1.32 1.28 0.49 0.47 0.56 0.46 0.51 0.51 0.57 0.55 0.58 0.47 0.44 0.65 0.52 0.62 0.56 0.60 0.53 0.49 0.56 0.53 0.58 0.53 0.53 245 25 26 27 28 29 30 31 32 33 34 35 75 77 79 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 5.29E-03 4.47E-03 4.61E-03 5.04E-03 5.04E-03 5.62E-03 5.85E-03 5.55E-03 4.93E-03 5.03E-03 4.89E-03 4.78E-03 4.27E-03 5.48E-03 0.004292 0.00508 0.004914 0.005444 0.005038 0.005142 0.005108 0.004954 0.0053 0.005322 0.004968 0.00568 0.00541 0.00504 0.004994 0.005436 0.005152 0.005212 0.005338 0.005424 0.005114 0.005244 0.006468 0.005446 3.277 3.277 3.277 3.277 3.277 3.277 3.277 3.277 3.277 3.277 3.277 3.277 3.277 3.277 3.277 3.277 3.277 3.277 3.277 3.277 3.277 3.277 3.277 3.277 3.277 3.277 3.277 3.277 3.277 3.277 3.277 3.277 3.277 3.277 3.277 3.277 3.277 3.277 10.028 10.028 10.028 10.028 10.028 10.028 10.028 10.028 10.028 10.028 10.028 10.028 10.028 10.028 10.028 10.028 10.028 10.028 10.028 10.028 10.028 10.028 10.028 10.028 10.028 10.028 10.028 10.028 10.028 10.028 10.028 10.028 10.028 10.028 10.028 10.028 10.028 10.028 9.96 9.64 9.91 9.54 10.04 9.50 10.07 10.98 10.64 9.85 9.91 10.48 10.71 9.26 12.31 10.52 11.26 10.2 11.12 10.99 13.62 13.3 10.68 12.06 9.94 11.5 11.56 10.94 12.81 14 12.19 11.51 12.5 11.37 13.56 15.26 11.58 14.14 10.10 10.98 9.47 9.42 9.54 9.76 10.32 10.96 10.69 10.34 10.36 10.26 10.80 9.86 12.57 10.56 11.2 10.24 11.01 10.89 13.7 13.37 10.43 12.12 10.12 11.5 11.77 10.81 12.57 14.25 12.06 11.5 12.37 11.44 13.56 15.38 11.49 14.31 9.73 10.03 9.73 9.06 9.40 9.70 9.68 10.04 10.12 9.78 10.24 10.21 10.66 9.480 12.38 10.31 11.39 10.19 11.19 10.87 13.63 13.44 10.74 12.13 10 11.69 11.7 10.93 12.68 14.55 12.12 11.21 12.44 11.37 13.32 15.63 11.75 14.55 9.930 10.217 9.703 9.340 9.660 9.653 10.023 10.660 10.483 9.990 10.170 10.317 10.723 9.533 12.420 10.463 11.283 10.210 11.107 10.917 13.650 13.370 10.617 12.103 10.020 11.563 11.677 10.893 12.687 14.267 12.123 11.407 12.437 11.393 13.480 15.423 11.607 14.333 1.75E-02 1.44E-02 1.56E-02 1.77E-02 1.71E-02 1.91E-02 1.92E-02 1.71E-02 1.54E-02 1.65E-02 1.58E-02 1.52E-02 1.31E-02 1.89E-02 5.68E-03 7.98E-03 7.16E-03 8.76E-03 7.45E-03 7.74E-03 6.15E-03 6.09E-03 8.20E-03 7.23E-03 8.15E-03 8.07E-03 7.61E-03 7.60E-03 6.47E-03 6.26E-03 6.98E-03 7.51E-03 7.05E-03 7.82E-03 6.23E-03 5.59E-03 9.16E-03 6.24E-03 246 1.79E-09 1.47E-09 1.59E-09 1.81E-09 1.75E-09 1.95E-09 1.96E-09 1.74E-09 1.57E-09 1.69E-09 1.61E-09 1.55E-09 1.33E-09 1.93E-09 5.79E-10 8.13E-10 7.30E-10 8.93E-10 7.60E-10 7.89E-10 6.27E-10 6.21E-10 8.36E-10 7.37E-10 8.31E-10 8.23E-10 7.76E-10 7.75E-10 6.60E-10 6.38E-10 7.12E-10 7.66E-10 7.19E-10 7.98E-10 6.36E-10 5.70E-10 9.34E-10 6.37E-10 0.78 0.78 0.76 0.85 0.80 0.78 0.79 0.78 0.77 0.78 0.79 0.77 0.70 0.77 0.50 0.59 0.55 0.59 0.57 0.55 0.47 0.52 0.65 0.55 0.61 0.61 0.54 0.57 0.56 0.48 0.54 0.63 0.61 0.65 0.51 0.46 0.62 0.54 3.87 3.90 4.14 2.86 3.59 3.98 3.66 3.95 4.21 4.03 3.92 4.23 5.17 4.16 7.12 6.51 6.88 6.85 7.11 6.90 7.23 7.22 6.05 6.66 6.37 6.36 6.88 6.57 7.03 6.98 6.76 6.14 6.72 6.28 7.08 7.31 6.13 7.10 0.99 1.09 0.69 3.42 1.12 0.89 0.47 1.63 1.17 1.66 1.06 -0.21 -1.43 0.98 -8.94 -5.15 -6.21 -4.80 -5.67 -6.10 -9.49 -7.64 -1.93 -6.18 -3.78 -4.08 -6.49 -5.05 -5.96 -10.17 -7.03 -3.84 -4.67 -1.60 -8.67 -10.24 -3.58 -6.62 1.02 1.29 1.24 1.57 1.15 1.10 0.90 1.32 1.25 1.29 1.12 1.05 0.74 1.18 -0.74 0.11 -0.06 0.10 0.02 -0.09 -0.93 -0.53 0.67 -0.09 0.36 0.21 -0.20 0.17 -0.17 -1.22 -0.29 0.34 0.20 0.73 -0.69 -1.09 0.25 -0.31 0.18 0.19 0.19 0.18 0.18 0.18 0.18 0.19 0.19 0.18 0.18 0.18 0.18 0.19 0.22 0.20 0.21 0.19 0.19 0.21 0.23 0.20 0.19 0.22 0.21 0.19 0.21 0.22 0.20 0.23 0.21 0.20 0.19 0.19 0.21 0.23 0.20 0.20 1.22 1.14 1.22 0.83 1.11 1.23 1.18 1.17 1.23 1.20 1.20 1.28 1.62 1.25 2.31 2.02 2.15 2.15 2.22 2.17 2.35 2.34 1.83 2.08 1.97 1.99 2.17 2.00 2.23 2.31 2.13 1.91 2.10 1.92 2.30 2.38 1.92 2.29 0.57 0.56 0.51 0.68 0.62 0.55 0.65 0.53 0.50 0.54 0.55 0.52 0.43 0.49 0.25 0.30 0.28 0.29 0.28 0.28 0.23 0.27 0.35 0.27 0.31 0.31 0.27 0.29 0.27 0.25 0.28 0.35 0.30 0.32 0.25 0.23 0.35 0.26 0.64 0.54 0.59 0.62 0.48 0.58 0.48 0.55 0.74 0.77 0.03 0.57 0.06 0.68 0.11 5.58 6.98 6.51 6.10 7.05 6.45 7.03 5.86 4.16 4.06 0.46 6.60 0.62 5.26 1.39 -2.20 -6.77 -4.02 -3.19 -8.49 -4.45 -9.27 -4.93 0.82 0.73 1.15 -5.65 2.61 -2.28 3.76 0.62 -0.30 0.23 0.40 -0.73 0.08 -1.00 0.20 1.09 1.13 0.21 -0.08 0.55 0.56 0.73 0.20 0.21 0.20 0.20 0.23 0.20 0.22 0.25 0.20 0.18 0.01 0.21 0.01 0.19 0.02 1.75 2.22 2.04 1.90 2.27 2.06 2.32 1.80 1.28 1.23 0.16 2.09 0.23 1.64 0.47 0.37 0.26 0.30 0.34 0.24 0.31 0.25 0.31 0.51 0.54 0.06 0.30 0.05 0.42 0.13 Trabecular separation, Tb.Sp (mm) Transverse 9.40E-10 7.89E-10 8.44E-10 9.33E-10 7.16E-10 7.41E-10 6.68E-10 8.06E-10 1.01E-09 1.67E-09 1.91E-10 7.61E-10 1.09E-10 1.24E-09 4.85E-10 Trabecular number, Tb.N (mm-1) Longitudinal 9.22E-03 7.73E-03 8.28E-03 9.15E-03 7.02E-03 7.26E-03 6.55E-03 7.91E-03 9.86E-03 1.64E-02 1.87E-03 7.46E-03 1.07E-03 1.22E-02 4.76E-03 Trabecular thickness, Tb.Th (mm) 9.98 10.020 11.7 11.523 10.62 10.390 10.25 10.227 13.18 12.977 13.57 13.707 13.87 13.737 11.38 11.357 9.01 9.050 Pool Structure model index, SMI ( ) 9.93 11.44 10.37 10.37 12.93 13.8 13.65 11.25 9.24 Trabecular pattern factor , Tb.Pf (mm-1) 10.15 11.43 10.18 10.06 12.82 13.75 13.69 11.44 8.9 Bone surface density, BS/TV (mm-1) 10.028 10.028 10.028 10.028 10.028 10.028 10.028 10.028 10.028 Porosity, ! () 3.277 3.277 3.277 3.277 3.277 3.277 3.277 3.277 3.277 permeability, k (m2) 0.00562 0.005424 0.005236 0.005692 0.005544 0.00606 0.00548 0.005466 0.00543 Hydraulic Conductivity, K (m/s) 60 61 62 63 64 65 69 70 72 247 Appendix I. Centroid of Complex Solids A smoothening technique, developed by Camancho et al., [1997], was incorporated to smooth out the surface of the voxel-based finite element mesh generated. The technique required the centroid of elements representing bone or centroid of representing empty spaces, to be determined. The surface node is then moved towards this centroid. As each surface node is shared by only hexahedral elements, the complex solids is a combination of rectangular blocks, or cubes, attached in different combinations. To determine the centroid of a complex solid, it should be first broken down into a finite number of simpler shapes; each with a centroid that are easily determined. Subsequently, the spatial coordinates (x, y, z) of the centroid of the complex solids is determined by: "V C "V n Cx = n n xn "V C "V n ,Cy = n n n where n yn "V C "V n ,Cz = zn n n n n is the numbering ! of each simpler solid, Vn is the colume of solid n, Cxn is the perpendicular distance in the x direction from the yz plane to the centroid of solid n, Cyn is the perpendicular distance in the y direction from the xz plane to the centroid of solid n, and Czn is the perpendicular distance in the z direction from the xy plane to the centroid of solid n. e.g. x Surface If each voxel! cube is 2mm in length: node ni Cx1 = 1mm, CY1 = 1mm And Cz1 = 1mm !1 Cx2 = 1mm, Cy2 = 3mm And Cz2 = 1mm !c !2 y V1 = V2 = 8mm3 Cx = (8*1 + 8*1)/(8+8) = 1mm z Cy = (8*1 + 8*3)/(8+8) = 2mm Cz = (8*1 + 8*1)/(8+8) = 1mm 248 [...]...Introduction 159 Vertebral Body Geometry 159 Assigned Permeability Values of Vertebral Cancellous Bone 161 Assigned Rheological Model for PMMA Cement .162 Simulation of Intraosseous PMMA Bone Cement Flow Using CFX5.7.1 162 Exporting PMMA Distribution for Stress/Strain Analyses 163 5.3 Results .165 5.3.1 3D Spatial Distribution of PMMA Cement ... spatiatl distributions of PMMA bonec cement 168 Table 19 Needle tip position for experimental vertebroplasty 179 Table 20 Time-lapse images of intraosseous 3D PMMA bone cement distribution for bi-pedicular injection into the L1 and L2 vertebral bodies 183 Table 21 Time-lapse images of intraosseous 3D bone PMMA cement distribution for bi-pedicular injection into the L3 and L4 vertebral bodies ... it has been assumed that PMMA bone cement flow through porous cancellous bone is analogous to water flowing through soil Figure 2 Use of computational fluid dynamics (CFD) simulation for the study of groundwater flow in geosciences Computational fluid dynamics (CFD) employing Finite Volume Method (FVM) have been used to predict groundwater flow In all FVM simulations, a finite volume (FV) mesh must first... prediction of PMMA bone cement flow path as well as spatial distribution that can be used for post-vertebroplasty stress/strain analyses Similar to stress/strain analysis of augmented vertebral bodies, simulating intraosseous PMMA bone cement flow can adopt two approaches: (a) model the intricate microstructure of cancellous bone or (b) model the cancellous bone as a solid, with properties reflecting its... Water, cancellous bone and soft issue will have grayscale intensities between these extremes (Figure 5) On closer inspection of the cancellous bone region, it can be seen that a single intensity value is insufficient Cancellous bone varies in density and therefore its corresponding CT attenuation varies accordingly 13 Figure 5 Clinical CT intensity and vertebral cancellous bone The CT attenuation of vertebral. .. for persistently painful osteoporotic vertebral fractures The volume filled and spatial distribution of PMMA bone cement for each vertebra should have more science to it, instead of being an ‘art form’ 1.2 Research Scope and Objectives It is hypothesized that engineering computational fluid dynamics (CFD), employing the finite volume (FV) method, is capable of providing both patientspecific visualization... data at several time intervals, for SimplexP® PMMA bone cement mixed at liquid monomer to PMMA powder ratio of 1.0 ml/g .129 Figure 46 Graph of flow index vs time data, for SimplexP® PMMA bone cement mixed at liquid monomer to PMMA powder ratio of 1.0ml/g 131 Figure 47 Graph of Consistency index vs time data, for SimplexP® PMMA bone cement mixed at liquid monomer to PMMA powder ratio of... permeability of cancellous bone .85 Figure 32 Extraction of vertebral cancellous bone specimens 87 Figure 33 Schematic of custom falling head permeameter used for permeability measurement of vertebral cancellous bone specimens .89 Figure 34 Typical stress - strain curve for vertebral cancellous bone specimen under compression 91 Figure 35 Compression jig for cancellous bone specimens... http://www.spineuniverse.com 2.3 Computed Tomography Radiological imaging is a non-invasive method of obtaining internal information of a patient Amongst all the radiological imaging modalities, computed tomography (CT) imaging is best suited for bone imaging CT imaging is a computer-automated technique that combines transmission X-ray imaging with tomographical reconstruction Knowledge in this section... allhexahedral finite volume (FV) mesh 153 Figure 60 User interface for needle positioning and the export of needle coordinates 155 Figure 61 Creation of new CT dataset with selected needle placement 156 Figure 62 Implementation of a fluid with operator -specific parameters in CFX 5.7.1 157 Figure 63 Method of generating patient- specific finite volume (FV) mesh of the vertebral body from CT images for . PATIENT SPECIFIC FINITE VOLUME MODELING FOR INTRAOSSEOUS PMMA CEMENT FLOW SIMULATION IN VERTEBRAL CANCELLOUS BONE JEREMY TEO CHOON MENG A THESIS SUBMITTED FOR THE DEGREE. 161 Assigned Rheological Model for PMMA Cement 162 Simulation of Intraosseous PMMA Bone Cement Flow Using CFX5.7.1 162 Exporting PMMA Distribution for Stress/Strain Analyses 163 5.3 Results. images of intraosseous 3D PMMA bone cement distribution for bi-pedicular injection into the L1 and L2 vertebral bodies. 183 Table 21 Time-lapse images of intraosseous 3D bone PMMA cement distribution