Investigation of femoral neck instability in elderly osteoporotic women using finite element analysis

INVESTIGATION OF FEMORAL NECK INSTABILITY IN ELDERLY OSTEOPOROTIC WOMEN USING FINITE ELEMENT ANALYSIS D ANITHA (B.Eng (Hons.), NUS) A THESIS SUBMITTED FOR THE DEGREE OF MASTER OF ENGINEERING DEPARTMENT OF BIOMEDICAL ENGINEERING NATIONAL UNIVERSITY OF SINGAPORE 2013 DECLARATION I hereby declare that the thesis is my original work and it has been written by me in its entirety I have duly acknowledged all the sources of information which have been used in the thesis This thesis has also not been submitted for any degree in any university previously D Anitha 19 November 2013 th ii Acknowledgements This work would not have been possible without the continuous guidance and encouragements of my supervisor, Dr Taeyong Lee I would like to extend my gratitude for his belief in me during the course of my Masters Without his support in allowing me to attend workshops and courses to update my skills and knowledge, and bringing me to international conferences, I would not have been able to attain the confidence to finish this course successfully I would also like to thank Dr Kwang Joon Kim and Dr Sung-Kil Lim for their collaboration with this project as they provided the resources needed for this project to proceed I would also like to thank Abhishek Vishwanath Rammohan S for teaching me and guiding me during the initial phase of this project I would also like to thank my lab members (past and current) who have helped me along the way, Aly Chan, Jeeva Lavanya Lakshmi, Teoh Jee Chin, Padmalosini Maruthappan, Chen Xiuli, Yang Xiao and Saara Afzal Finally I would like to express my loving gratitude to my partner, Navindraram Naidu for accompanying me through this phase of life with continuous support and belief that I will excel I also would like to thank my father who has morally and financially supported me these two years and friends and family who have supported me along the way iii Table of Contents DECLARATION .ii Acknowledgements iii Summary vii List of Publications ix List of Tables x List of Figures xi List of Symbols and Abbreviations used xvi INTRODUCTION 1.1 Motivation and Background 1.2 Study Hypothesis 1.3 Objectives 1.3.1 Specific Aim 1.3.2 Specific Aim 1.4 Overview of the dissertation LITERATURE REVIEW 2.1 Bone Geometry 2.1.1 Background 2.1.2 Bone remodelling 2.1.3 Aging 2.1.4 Osteoporosis 11 2.1.5 Commonly Studied Parameters 14 2.1.6 Buckling Ratio 15 2.2 Bone Strength 17 2.2.1 Background 17 2.2.2 Factors of bone strength 17 2.2.2.1 Role of material properties 17 iv 2.2.2.2 Role of microarchitecture 18 2.2.2.3 Role of bone geometry 19 2.2.3 Mechanical behaviour of bone 19 2.2.3.1 Viscoelasticity 20 2.2.3.2 Fatigue 21 2.3 Biomechanics of Age-related Hip Fractures 21 2.3.1 Proximal Femur Fractures 23 2.3.1.1 Influence of Loading Rates during Sideways Falls 23 2.3.1.2 Influence of Impact Direction during Sideways Falls 24 2.4 Finite Element Analysis 25 2.4.1 Background 25 2.4.2 Assignment of Material Properties 26 2.4.3 Application of Boundary Conditions 30 NUMERICAL M ODELLING OF THE FEMUR 34 3.1 Background 34 3.2 Segmentation and 3D Generation 34 3.3 Meshing 36 3.4 Elastic Material Properties 38 3.5 Inelastic Material Properties 39 3.6 Convergence Study 40 3.7 Advantages and Disadvantages 42 LOCAL OSTEOPOROSIS – A RETROSPECTIVE S TUDY 45 4.1 Materials & Methods 45 4.1.1 Study Subjects 45 4.1.2 QCT measurements 45 4.1.3 FE analysis 47 4.2 Results 49 v 4.2.1 Summary of Key Findings 49 4.2.2 Key findings in detail 50 4.3 Discussion 54 TRIADIC RELATIONSHIP BETWEEN BMD, BR & FCR – A CORRELATIONAL S TUDY 59 5.1 Materials & Methods 59 5.1.1 Study Subjects 59 5.1.2 QCT measurements 59 5.1.3 FE analysis 60 5.1.4 Plotting Triadic Relationship 61 5.1.5 Statistical Analysis 61 5.2 Results 62 5.2.1 Summary of Key Findings 62 5.2.2 Key findings in detail 63 5.3 Discussion 70 CONCLUSION 74 6.1 Strengths & Limitations 74 6.2 Future work 75 REFERENCES 77 Appendix Implications of local osteoporosis on the efficacy of antiresorptive drug treatment: a 3-year follow-up finite element study in risedronate-treated women 89 Appendix Improving stability of locking compression plates through a design modification: a computational investigation 98 Appendix Matlab code to generate triadic surface plots 107 vi Summary Hip fracture amongst the elderly is a growing concern especially with improvements in living standards and increasing lifespan Currently, bone mineral density (BMD) is used by rule of thumb in the diagnosis of osteoporosis It is well-established that the specificity and sensitivity of BMD is low in predicting fractures and that the link between BMD and bone strength remains unclear Nevertheless, it is utilized as an approximate indication of bone quality due to ease of acquirement Almost half of total hip fractures result from those without osteoporosis Therefore, firstly, local osteoporosis, rather than generalized osteoporosis, was examined By observing the local buckling ratio (BR) in the femoral neck (FN) in ten risedronate-treated subjects over three years, this work discovered that subjects with improved fracture loads, as predicted by finite-element (FE) analysis, were associated with lower local BR and vice versa Secondly, by incorporating geometric and structural predictors, the simultaneous dependence of critical fracture load (Fcr) on BR and BMD using triad graphic representations was proven superior over dyadic relationships The BR, which quantifies the distribution of cortical bone, was chosen as the geometric predictor Three-dimensional (3D) models of the left proximal femurs were generated and local BR values at 30 intervals were obtained from FN slices by measuring the respective mean cortical thickness (CTh) and mean outer radius (Ro) Following geometric analysis, structural strength was examined with FE analysis where Fcr were acquired from sideways fall load simulations BR and Fcr measurements in relation to FN BMD in elderly female patients in a 3-year follow-up study were analysed graphically In the first part of this work, subjects were classified in three groups according to the change in Fcr; adequate (+20%), inadequate (-22%) and indefinite drug treatments (-2%) A common striking feature was that lower and higher ranges of local BR values (baseline year) were found for adequate (min=2.14, max=8.04) and inadequate (min=1.72, max=11.38) drug treatment groups respectively Subjects in the inadequate drug treatment group exhibited high local BR at the supero-anterior and supero-posterior regions These high vii local BR values coincided with FE-predicted critical strain regions Whereas, subjects from the adequate drug treatment group showed significantly reduced strain regions The superiority of coupling geometry (BR) with structure (Fcr) over BMD measurements alone by monitoring local osteoporosis was illustrated In the second part of this work, in all three triadic representation plots (baseline, mid and final year), high Fcr values were found at the leftmost upper quadrant containing high BMD and low BR values Quantitatively, the average maximum Fcr value was accompanied by a relatively higher BMD (75.5%) and lower BR (14.5%) than that of the average minimum Fcr value The dependence of structural strength on both the spatial distribution and amount of bone mass was illustrated These observations provide new insight into the etiology of hip fractures and cannot be achieved with dyadic relationships We conclude that the use of a triadic relationship can be relevant clinically to complement the diagnosis and monitoring of osteoporosis Key Words: Bone Mineral Density; Prediction of Hip Fracture; Finite Element Analysis; Osteoporosis; Bone Strength; Buckling Ratio viii List of Publications This dissertation is based on the following original publications: I Anitha D, Kim KJ, Lim SK, Lee T Implications of local osteoporosis on the efficacy of anti-resorptive drug treatment: A 3-year follow-up finiteelement study in risedronate-treated women, Osteoporosis International, In Press, 2013 (Appendix 1) II Anitha D, Kim KJ, Lim SK, Lee T Understanding osteoporosis-related femoral neck fractures using triad graphic representations, Medical Engineering and Physics, Submitted, 2013 Publications not included in this dissertation: III Anitha D, DasDe S, Khong KS, Doshi HK, Lee T Improving LCP stability through a design modification: A computational investigation Computer Methods in Biomechanics and Biomedical Engineering, In Press, 2013 (Appendix 2) ix List of Tables Table No Description Page Table Material Relations used to determine density, elastic 29 modulus and Poisson’s ratio Table Boundary conditions and parameters analysed in FE 32 studies Table Mean geometrical properties, FN BMD and Fcr of subjects (n=10) classified according to increase (adequate drug treatment), decrease (inadequate drug 50 treatment) or negligible change (indefinite drug treatment) in Fcr (Anitha et al., 2013) (With kind permission from Springer Science and Business Media) Table Mean (SD) values of various parameters are shown by 65 year and for the pooled dataset Table Spearman’s rank Correlation Coefficients between 66 Various Predictors pooled over 3-years (n =78) Table Lowest and highest Fcr values obtained x 67 93 94 95 96 97 Appendix Improving stability of locking compression plates through a design modification: a computational investigation 98 99 100 101 102 103 104 105 106 Appendix Matlab code to generate triadic surface plots %start of matlab code clear all colormap(jet) title('2009'); xlabel BMD; ylabel BR; zlabel Fcr; view(90,90); load BMD2008.mat load BR2008.mat load Fcr2008.mat load BMD2009.mat load BR2009.mat load Fcr2009.mat load BMD2010.mat load BR2010.mat load Fcr2010.mat figure(3); x3min = min(x3); y3min = min(y3); x3max = max(x3); y3max = max(y3); x3res=20; y3res=20; figure(1); x1min = min(x1); y1min = min(y1); x1max = max(x1); y1max = max(y1); x3v = linspace(x3min, x3max, x3res); y3v = linspace(y3min, y3max, y3res); [X3interp,Y3interp] = meshgrid(x3v,y3v); Z3interp = griddata(x3,y3,z3,X3interp,Y3interp); x1res=20; y1res=20; surf(X3interp,Y3interp,Z3interp, 'EdgeColor', 'none') colormap(jet) title('2010'); xlabel BMD; ylabel BR; zlabel Fcr; view(90,90); x1v = linspace(x1min, x1max, x1res); y1v = linspace(y1min, y1max, y1res); [X1interp,Y1interp] = meshgrid(x1v,y1v); Z1interp = griddata(x1,y1,z1,X1interp,Y1interp); surf(X1interp,Y1interp,Z1interp, 'EdgeColor', 'none') colormap(jet) title('2008'); xlabel BMD; ylabel BR; zlabel Fcr; view(90,90); %end of matlab code figure(2); x2min = min(x2); y2min = min(y2); x2max = max(x2); y2max = max(y2); x2res=20; y2res=20; x2v = linspace(x2min, x2max, x2res); y2v = linspace(y2min, y2max, y2res); [X2interp,Y2interp] = meshgrid(x2v,y2v); Z2interp = griddata(x2,y2,z2,X2interp,Y2interp); surf(X2interp,Y2interp,Z2interp, 'EdgeColor', 'none') 107 [...]... expansion of bone and cortical thinning maintains the bone strength with aging (Martin & Correa, 2010) For the same aBMD, CTh reduces and radius of the tubular bone increases from A to C, maintaining or improving the bending strength as the mass is distributed further away from the neutral axis of the cross-section In other words, the area moment of inertia increases This is further explained by Figure... buckling of concern is local buckling also known as elastic instability (Mayhew et al., 2005) Figure 9 Schematic representation of local buckling, analogous to the bending of a thin-walled straw It is well-established that the age-related decline in BMD resulting in cortical thinning especially in osteoporotic patients is counteracted by subperiosteal expansion This is the body’s way of responding to... Hypothesis The principal aim of the study was to improve the diagnosis and monitoring of osteoporosis so as to consequently improve the prediction of hip fractures This was aimed to be done by examining non-invasive methods such as geometric analysis of radiological scans and structural analysis through FE analysis The penultimate aim is to complement engineering analysis with that of clinical diagnosis... understand the etiology of osteoporotic fractures Also, the engineering analysis tested in this work is aimed for simplicity without compromising on the efficacy of the analysis While improvement of the current diagnosis is the main aim, it is also aimed for a simple engineering analysis that medical personnel would be receptive to in the near future 2 A retrospective study (n=10 women) was first carried... (∆Ri) and from baseline to 63 final year, the rate of periosteal widening declined (15.8%) more drastically than the rate of endocortical widening (-10.7%), [C] a statistically significant correlation between Fcr and BMD ( = 0.74, p < 0.0001) obtained and [D] the rate of increase of Fcr was greater xiv in the final year (9.5%) across increasing BMD Figure 30 Yearly 3D surface plots of BMD, BR and Fcr... osteoporosis results in excessive bone resorption that is unmatched by an equal amount of bone formation Estrogen deficiency is one of the leading causes of osteoporosis in post-menopausal women This phenomenon results in the increase in the rate of remodelling, which results in less dense mineralized bone to replace the more dense bone This means that the bone loses its material stiffness since the mineral gives... does fail by local buckling, it is an important geometric parameter that deserves more attention There are two types of buckling; Euler buckling and local buckling Euler buckling is the folding of an unsupported rod or flat sheet under compressive loads while local buckling is the bending of a part of the crosssection of a structural member, analogous to the bending of a thin-walled straw (Fig 9) (Lee... and a consequent increase (48%) in local BR at the supero- 52 anterior region (30) for subject #5 was accurately predicted by FE analysis (Anitha et al., 2013) (With kind permission from Springer Science and Business Media) Figure 28 Plots of local BR against angle in the baseline and final years for the adequate ( Fcr), inadequate ( Fcr) and indefinite ( Fcr) drug treatment groups In the adequate... under-mineralized) or decrease (if bone is already fully mineralized) with increasing mineral content (Bouxsein, 2005) Trabecular bone microarchitecture can be described in terms of the number and orientation of the trabeculae, thickness of trabecular plates and rods, spacing of the trabeculae and degree of trabeculae interconnections, which ultimately determines the architecture and density of bone... for better characterization of bone properties Accompanied with normal aging, the proximal femur undergoes remodelling as compensation for declining mass so that its bending strength is maintained (Bouxsein, 2005) However, this redistribution to preserve bone strength reaches a threshold where excessive cortical thinning ultimately initiates These local changes in the femoral neck (FN) can be captured ... decline in BMD resulting in cortical thinning especially in osteoporotic patients is counteracted by subperiosteal expansion This is the body’s way of responding to loss in bone mass to maintain... then be useful for isolating the effects of individual factors, for example, of muscle activity or of regions of geometrical instability in the bone 24 2.4 Finite Element Analysis 2.4.1 Background... Load FE Finite Element FHD Femoral Head Diameter FN Femoral Neck FNAL Femoral Neck Axis Length FND Femoral Neck Diameter FSW Femoral Shaft Width xvi HAL Hip Axis Length HSA Hip Structural Analysis