Statistical Finite Element Modeling: Application To .
Statistical finite element modeling:application to orthopedic implant designSerena BonarettiGCB Students’ Symposium 2011
Bones Rigid organs that form the skeleton Functions:————— SupportMovementInternal organ protectionMineral reservoirBlood cell formationFunctional adaptation: “use it or lose it”2
Bone fracture It occurs when the bone cannotwithstand the applied force3
Bone fracture It occurs when the bone cannotwithstand the applied force Bone is genetically programmed toheal after fracture4
Bone fracture It occurs when the bone cannotwithstand the applied force Bone is genetically programmed toheal after fracture Plates restore bone anatomy andproduce stability that allowsphysiological exercise5
Plate fixationMinimal skin incision Reduction refinement Plate and screw insertion Plate g/modules/dlmat plates/dlmat plates en.htm6
Plate evaluation Population groups:— Sex, age, ethnicity, Population-based implant assessment? Creation of a statistical bone model that takesinto account bone shape and density variabilityin order to assess the biomechanical behaviorof the bone-implant coupling7
MethodSegmentedCT tion of a statistical bone model that takesStatistical bone model into account bone shape and density variabilityin order to assess the biomechanical behaviorof the bone-implant nFinite element simulationsMaterialpropertiesVolumemesh8
Statistical bone model Bones are conceived as samples in ahigh dimensional space Principal Component Analysis (PCA)projects bones in a lower dimensionalspace where bone shape and densityvariances are minimized 12n3 3Virtual bones are created samplingthe space using a Gaussian distributionin order to have a more dense andrationalized space219
Finite elementsimulations Mechanical property assignmentBone Mineral ComponentCT intensitiesρQCTComplete BoneρashImageρAsh (ρQCT 0.09)/1.14 ρash/ρapp 0.60calibration: ESP- EFPρappEE(GPa) 6.850 r app (g/cm3)1.49Schileo E. et al. An accurate estimation of bone density improves the accuracy ofsubject-specific finite element methods. J Biomech. 41, 2483-2491. 2008.Helgason B. et al. Mathematical relationship between bone density and mechanicalproperties: a literature review. Clin Biomech. 23, 135-146.2008.10
Preliminary results Tibia CT images: 43 Caucasian 47 Asian Statistical shape model— 2 modes represent 75% of variation— 13 new instances for each group FEM simulation———— 10-nodes tetrahedral meshBone: E 15.52ρ1.93 GPa, ν 0.3Implant: E 110 GPa, ν 0.3L 1600 N; tibia distal part constrainedBone-implant average distance higher for AsianStress in plates statistically higher for Asian (p 0.05)Asian0 mmCaucasian7 mm11
Conclusion Creation of a statistical bone model to assess the boneimplant coupling mechanical behavior Limitations— Dependence of the model on the training dataset— Linearity of PCA— Non-unique PCA parameter meaning Outlook— Patient-specific modeling— Orthopedic surgery planning12
Statistical finite element modeling:application to orthopedic implant designSerena BonarettiGCB Students’ Symposium 2011
Finite element simulations 10 CT intensities ρ QCT ρ ash ρ app E Image calibration: ESP -EFP Bone Mineral Component Complete Bone ρ Ash (ρ QCT 0.09)/1.14 ρ ash/ρ app 0.60 E(GPa) 6.850 (g/cm3) 1.49 r app Schileo E. et al. An accurate estimation of bone density improves the accuracy of subject-specific finite element methods.
Finite element analysis DNV GL AS 1.7 Finite element types All calculation methods described in this class guideline are based on linear finite element analysis of three dimensional structural models. The general types of finite elements to be used in the finite element analysis are given in Table 2. Table 2 Types of finite element Type of .
element type. This paper presents a comprehensive study of finite element modeling techniques for solder joint fatigue life prediction. Several guidelines are recommended to obtain consistent and accurate finite element results. Introduction Finite element method has been used for a long time to study the solder joint fatigue life in thermal .
3.2 Finite Element Equations 23 3.3 Stiffness Matrix of a Triangular Element 26 3.4 Assembly of the Global Equation System 27 3.5 Example of the Global Matrix Assembly 29 Problems 30 4 Finite Element Program 33 4.1 Object-oriented Approach to Finite Element Programming 33 4.2 Requirements for the Finite Element Application 34 4.2.1 Overall .
1 Overview of Finite Element Method 3 1.1 Basic Concept 3 1.2 Historical Background 3 1.3 General Applicability of the Method 7 1.4 Engineering Applications of the Finite Element Method 10 1.5 General Description of the Finite Element Method 10 1.6 Comparison of Finite Element Method with Other Methods of Analysis
Finite Element Method Partial Differential Equations arise in the mathematical modelling of many engineering problems Analytical solution or exact solution is very complicated Alternative: Numerical Solution – Finite element method, finite difference method, finite volume method, boundary element method, discrete element method, etc. 9
2.7 The solution of the finite element equation 35 2.8 Time for solution 37 2.9 The finite element software systems 37 2.9.1 Selection of the finite element softwaresystem 38 2.9.2 Training 38 2.9.3 LUSAS finite element system 39 CHAPTER 3: THEORETICAL PREDICTION OF THE DESIGN ANALYSIS OF THE HYDRAULIC PRESS MACHINE 3.1 Introduction 52
Figure 3.5. Baseline finite element mesh for C-141 analysis 3-8 Figure 3.6. Baseline finite element mesh for B-727 analysis 3-9 Figure 3.7. Baseline finite element mesh for F-15 analysis 3-9 Figure 3.8. Uniform bias finite element mesh for C-141 analysis 3-14 Figure 3.9. Uniform bias finite element mesh for B-727 analysis 3-15 Figure 3.10.
The Finite Element Method: Linear Static and Dynamic Finite Element Analysis by T. J. R. Hughes, Dover Publications, 2000 The Finite Element Method Vol. 2 Solid Mechanics by O.C. Zienkiewicz and R.L. Taylor, Oxford : Butterworth Heinemann, 2000 Institute of Structural Engineering Method of Finite Elements II 2
