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A feasibility study on the acceleration and upscaling of bone ingrowth simulation

A feasibility study on the acceleration and upscaling of bone ingrowth simulation. An investigation into the feasibility of applying a homogenization scheme to bone ingrowth model as well other options of accelerating the bone ingrowth model developed by A. Andreykiv. .

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A feasibility study on the acceleration and upscaling of bone ingrowth simulation

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  1. A feasibility study on the acceleration and upscaling of bone ingrowth simulation An investigation into the feasibility of applying a homogenization scheme to bone ingrowth model as well other options of accelerating the bone ingrowth model developed by A. Andreykiv. MSc colloquium by Yoeng Sin Khoe Delft Technical University Faculty of Biomedical Engineering– Tissue Biomechanics & Implants • Date: June 30th, 2009

  2. Introduction • UncementedShoulderImplant • Total ShoulderArthroplasty • Osteoarthritis, rheumatoidarthritis • Poroussurface in whichbonecangrow to ensurefixation of the implant • Cementedimplant • Immediatefixation • Tissue necrosis • Cement fracture

  3. Introduction • Finite Element Modelling of uncementedimplants – 2 approaches • How to transfer knowledgefrom the detailed model to the larger (macroscopic) model? Andreykiv, 2006 Folgado, 2009

  4. Recommendations • Original Bone Ingrowth model • Introduction • Summary & Conclusions Contents

  5. The originalbone ingrowth model

  6. The originalbone ingrowth modelGeneral Overview • Coupled Simulation • Prendergast tissue differentiation model for the production of bone, cartilage and fibrous tissue General OverviewMechanical Model Biophysical Stimulus Biological Model NumericalImplementation

  7. The Original Bone Ingrowth ModelMechanical Model • Biological Tissue response • Non-linear • Historydependent • Viscoelastic • Biphasic Model • 80% is made up of fluid • Solid & Fluid component General OverviewMechanical Model Biophysical Stimulus Biological Model NumericalImplementation

  8. The Original Bone Ingrowth ModelMechanical Model • Solid (3 displacements) • Neo-Hookean Hyperelastic Materialmodel • Fluid (pressure) • Massbalance General OverviewMechanical Model Biophysical Stimulus Biological Model NumericalImplementation

  9. The Original Bone Ingrowth ModelBiophysical Stimulus • Input for the biological model • Determines the preference of the formation of bone, cartilage of fibrous tissue • Basedonmaximalshearstrain and fluidvelocity General OverviewMechanical Model Biophysical Stimulus Biological Model NumericalImplementation

  10. The Original Bone Ingrowth Model Biological Model • Diffusion • Mesenchymal stem cells • Fibroblast • CellProliferation • CellDifferentiation • Tissue Production • Tissue Degradation • As a function of the biophysical stimulus General OverviewMechanical Model Biophysical Stimulus Biological Model NumericalImplementation

  11. Differentiation Proliferation Tissue production Mesenchymal Cells Fibroblast Cells Chondrocyte Cells Osteoblast Cells Fibrous Tissue Cartilage Bone The Original Bone Ingrowth Model Biological Model General OverviewMechanical Model Biophysical Stimulus Biological Model NumericalImplementation

  12. The Original Bone Ingrowth Model NumericalImplementation • Implemented in subroutines of MSC Marc • Non Linearequationsrequiresaniterative solver force force displacement displacement General OverviewMechanical Model Biophysical Stimulus Biological Model NumericalImplementation

  13. The Original Bone Ingrowth Model NumericalImplementation & Results • Loadingbasedon the results of animalexperiments • applied displacement in the first week, • average force over the remainingdays • Result: Tissue Evolution & Micromotions • Total simulationlength 28 days • Computation time: ~200.000 sec (2 days and 7 hours) General OverviewMechanical Model Biophysical Stimulus Biological Model NumericalImplementation

  14. Model Optimization

  15. Model OptimizationPossibilitiesfor model simplification (1) • Investigate the necessity of the biphasic model < Weighted Fluid Velocity Weighted Shear Strain PotentialSimplifications(1)Results: Removingthe fluidphaseResults: LinearizedBiological Model Results: 1D Diffusion

  16. Model OptimizationPossibilitiesfor model simplification (2) • Linearization of the biologicalmodel • Acceptableapproximation? PotentialSimplifications(2)Results: Removingthe fluidphaseResults: LinearizedBiological Model Results: 1D Diffusion

  17. Model OptimizationPossibilitiesfor model simplification(3) • 1-D Diffusion approximation PotentialSimplifications(3)Results: Removingthe fluidphaseResults: LinearizedBiological Model Results: 1D Diffusion

  18. Model OptimizationResults – Removal of Fluidphase • Fluidphase is essentialfor correct calculations • Increasedfibrous tissue production • Reducedbone & cartilageproduction PotentialSimplificationsResults: Removingthe fluidphaseResults: LinearizedBiological Model Results: 1D Diffusion

  19. Model OptimizationResults – LinearBiological Model • Results of linearbiological model do not match non linear model • No more fibrous tissue production • Overestimateboneproduction • Reasonablecartilageestimate Differentiation Proliferation Production Tissue production Mesenchymal Cells Fibroblast Cells Chondrocyte Cells PotentialSimplificationsResults: Removingthe fluidphaseResults: LinearizedBiological Model Results: 1D Diffusion Osteoblast Cells Fibrous Tissue Cartilage Bone

  20. Model OptimizationResults – 1D diffusion • Simulationsfailed • Non-Positive definite stiffness matrix • Snap back behaviour? Causing the Newton-Raphson method to fail? • Perhaps an arc length method can improve the results • Potentially gained simulation time is marginal • A estimated decrease of 200 seconds over the complete simulations. PotentialSimplificationsResults: Removingthe fluidphaseResults: LinearizedBiological Model Results: 1D Diffusion

  21. Code Optimizations

  22. START Send command to open stimulus.dat file. Is file in free for use? Wait 1 second No Yes Read element number and stimulus value.Is file operation complete? Close file and go to next record Wait 1 second No Yes Is this the last record in stimuli.dat No Yes Close file and continue subroutine Code OptimizationsPotentialforincreasing speed • Culprit: Disk operations • Example: Reading the stimuli.dat file • Reducewaitingtimes • Reducenumberof disk operations PotentialOptimizationsResults:MINISLEEP Results:Batchwrites

  23. Code OptimizationsMinisleep • Reducewaiting time • FORTRAN limits the waitingperiod to 1 sec • Write the MINISLEEP 20% PotentialOptimizationsResults:MINISLEEPResults:Batchwrites

  24. Code OptimizationsBatchwrites • Reduce the number of disk writes. • Store all variables in memory and write at the end of aniteration • Keep in mind data sharing • Reduction of 65% in computation time PotentialOptimizationsResults:MINISLEEP Results:Batchwrites

  25. ComputationalHomogenization

  26. ComputationalHomogenizationTheory (1) • Exploitperiodicity to bridging the gap • Microscopic level Macroscopic level Global IdeaDeformationTensorLocalisationUpscaleStressesMacroscpoic Tangent ImplementationResults

  27. ComputationalHomogenizationTheory (2) • Macroscopicdeformation • Microscopicdeformations / microfluctuations undeformed deformed Global IdeaDeformationTensorLocalisationUpscaleStressesMacroscpoic Tangent ImplementationResults

  28. ComputationalHomogenizationTheory (3) - Localisation • Translationbetweenmicroscopic and macroscopicdeformationtensor Global IdeaDeformationTensorLocalisationUpscaleStressesMacroscpoic Tangent ImplementationResults

  29. ComputationalHomogenizationTheory (4) – Stresses • Hill-Mandelcondition • Workconjugatedcouple: • Deformationtensor & 1st Piola-Kirchhoff stress Global IdeaDeformationTensorLocalisationUpscaleStressesMacroscpoic Tangent ImplementationResults

  30. ComputationalHomogenizationTheory (4) – Macroscopic tangent • Tangent describeshowsmallvariations affect the stresses in the system • Numericaldifferentiation • Verycumbersomemethod, but Miehe (1996) developed a more efficientmethod. Global IdeaDeformationTensorLocalisationUpscaleStressesMacroscpoic TangentImplementationResults

  31. ComputationalHomogenizationImplementation in MSC Marc • Macroscopic Model • Loading • Deformationtensor • Macroscopic tangent • Microscopic Model • PeriodicBoundaryConditions • Upscalestresses Global IdeaDeformationTensorLocalisationUpscaleStressesMacroscpoic Tangent ImplementationResults

  32. ComputationalHomogenizationResults / Issues • CH implementationrequires a lot a additionalcomputing time • Computational overhead in the numericaldifferentiationscheme • Application of loading Global IdeaDeformationTensorLocalisationUpscaleStressesMacroscpoic Tangent ImplementationResults

  33. Summary & Conclusions • Sections of the constitutive equations that are responsible for long calculations cannot be neglected • Fluid phase, non-linear biological model, diffusion • Acceleration of the simulation was obtained by efficiently directing disk activity. • Computational Homogenization increases simulation time and cannot account for specific loading Summary & ConclusionsRecommendationsQuestions

  34. Recommendationsalternativesfor upscaling results • Howto bridge the gap? • Use the model to investigate time to fixation under different loadings • Use a larger model to asses post-surgery micromotions • Develop an element that adapts the stiffness in order to ensure that at the time to fixation the micromotions are reduced to zero. Summary & ConclusionsRecommendationsQuestions

  35. Questions? ? ? ? ? Questions? ? ? ? ? ? ? ? Summary & ConclusionsRecommendationsQuestions

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