A feasibility study on the acceleration and upscaling of bone ingrowth simulation
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Transcript of A feasibility study on the acceleration and upscaling of bone ingrowth simulation
A feasibility study on the acceleration and upscaling of bone ingrowth simulationAn 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 KhoeDelft Technical University
Faculty of Biomedical Engineering – Tissue Biomechanics & ImplantsDate: June 30th
, 2009
Introduction• Uncemented Shoulder Implant
• Total Shoulder Arthroplasty• Osteoarthritis, rheumatoid arthritis• Porous surface in which bone can
grow to ensure fixation of the implant
• Cemented implant– Immediate fixation– Tissue necrosis– Cement fracture
Introduction• Finite Element Modelling of uncemented
implants – 2 approaches
• How to transfer knowledge from the detailed model to the larger (macroscopic) model?
Andreykiv, 2006 Folgado, 2009
Recommendations
Original Bone Ingrowth model
Contents
Model Optimizations
Options
Results
Code Optimization
Possibilities
Results
Computational Homogenization
Theory
Implementation
Results
Introduction
Summary & Conclusions
The original bone ingrowth model
The original bone ingrowth modelGeneral Overview
• Coupled Simulation• Prendergast tissue differentiation model for the
production of bone, cartilage and fibrous tissueMecha
nical Model
Biophysical
Stimulus
Biological
Model
Material Properti
es
General Overview Mechanical Model Biophysical Stimulus Biological Model Numerical Implementation
The Original Bone Ingrowth ModelMechanical Model
• Biological Tissue response– Non-linear– History dependent– Viscoelastic
• Biphasic Model– 80% is made up of fluid– Solid & Fluid component
General Overview Mechanical Model Biophysical Stimulus Biological Model Numerical Implementation
The Original Bone Ingrowth ModelMechanical Model
• Solid (3 displacements)– Neo-Hookean Hyperelastic Material
model• Fluid (pressure)
– Mass balance
0
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pvdtdp
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General Overview Mechanical Model Biophysical Stimulus Biological Model Numerical Implementation
The Original Bone Ingrowth ModelBiophysical Stimulus
• Input for the biological model• Determines the preference of the
formation of bone, cartilage of fibrous tissue
• Based on maximal shear strain and fluid velocity
baS
General Overview Mechanical Model Biophysical Stimulus Biological Model Numerical Implementation
The Original Bone Ingrowth Model Biological Model
• Diffusion – Mesenchymal stem cells– Fibroblast
• Cell Proliferation• Cell Differentiation• Tissue Production• Tissue Degradation• As a function of the biophysical stimulus
General Overview Mechanical Model Biophysical Stimulus Biological Model Numerical Implementation
The Original Bone Ingrowth Model Biological Model
Mesenchymal Cells
Osteoblast Cells
Chondrocyte Cells
Fibroblast Cells
Bone
Fibrous Tissue
Cartilage
Differentiation
Proliferation
Tissue production
General Overview Mechanical Model Biophysical Stimulus Biological Model Numerical Implementation
The Original Bone Ingrowth Model Numerical Implementation
• Implemented in subroutines of MSC Marc• Non Linear equations requires an iterative
solver
General Overview Mechanical Model Biophysical Stimulus Biological Model Numerical Implementation
force
displacement
force
displacement
The Original Bone Ingrowth Model Numerical Implementation & Results
• Loading based on the results of animal experiments– applied displacement in the first week, – average force over the remaining days
• Result: Tissue Evolution & Micromotions• Total simulation length 28 days• Computation time: ~200.000 sec
(2 days and 7 hours)
General Overview Mechanical Model Biophysical Stimulus Biological Model Numerical Implementation
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Results of the Bone Ingrowth Simulation
BoneCartilageFibrous TissueMicromotions
Time [Days]
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actio
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omoti
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µm]
Model Optimization
Model OptimizationPossibilities for model simplification (1)
• Investigate the necessity of the biphasic model
<Weighted Fluid Velocity Weighted Shear Strain
baS
Potential Simplifications(1) Results: Removing the fluid phase Results: Linearized Biological Model Results: 1D Diffusion
Model OptimizationPossibilities for model simplification (2)
• Linearization of the biological model
• Acceptable approximation?
Potential Simplifications(2) Results: Removing the fluid phase Results: Linearized Biological Model Results: 1D Diffusion
Model OptimizationPossibilities for model simplification (3)
• 1-D Diffusion approximation
Potential Simplifications(3) Results: Removing the fluid phase Results: Linearized Biological Model Results: 1D Diffusion
Model OptimizationResults – Removal of Fluid phase
• Fluid phase is essential for correct calculations• Increased fibrous tissue production• Reduced bone & cartilage production
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Effect of removing the fluid phase
Bone - OriginalBone - NoFluidCartilage - OriginalCartilage - NoFluidFibrous Tissue - OriginalFibrous Tissue - NoFluid
Day nr.
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Potential Simplifications Results: Removing the fluid phase Results: Linearized Biological Model Results: 1D Diffusion
Model OptimizationResults – Linear Biological Model
• Results of linear biological model do not match non linear model
• No more fibrous tissue production• Overestimate bone production• Reasonable cartilage estimate
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 290
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Effect of a linear Biological model
Bone - OriginalBone - LinearBIOCartilage - OriginalCartilage - LinearBIOFibrous Tissue - OriginalFibrous Tissue - LinearBIO
Day nr.
Tiss
ue fr
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Mesenchymal Cells
Osteoblast Cells
Chondrocyte Cells
Fibroblast Cells
Bone
Fibrous Tissue Cartilage
Differentiation
Proliferation
Production
Tissue production
Potential Simplifications Results: Removing the fluid phase Results: Linearized Biological Model Results: 1D Diffusion
Model OptimizationResults – 1D diffusion
• Simulations failed– 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.
Potential Simplifications Results: Removing the fluid phase Results: Linearized Biological Model Results: 1D Diffusion
Code Optimizations
Code OptimizationsPotential for increasing speed
• Culprit: Disk operations• Example: Reading the stimuli.dat file • Reduce waiting times• Reduce number
of disk operationsSend command to open
stimulus.dat file. Is file in free for use?
Read element number and stimulus value.
Is file operation complete?
Yes
NoWait 1 second
START
Wait 1 secondNo
Yes
Is this the last record in stimuli.dat
Yes
Close file and go to next record
Close file and continue subroutine
No
Potential Optimizations Results:MINISLEEP Results:Batchwrites
Code OptimizationsMinisleep
• Reduce waiting time• FORTRAN limits the waiting period to 1 sec• Write the MINISLEEP
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time
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Comparison of timings
Iteration nr
OriginalMINISLEEP(1)MINISLEEP(10)MINISLEEP(250)
20%
Potential Optimizations Results:MINISLEEP Results:Batchwrites
Code OptimizationsBatchwrites
• Reduce the number of disk writes.• Store all variables in memory and write at the
end of an iteration• Keep in mind data sharing
• Reduction of 65% in computation time
Potential Optimizations Results:MINISLEEP Results:Batchwrites
Computational Homogenization
Computational HomogenizationTheory (1)
• Exploit periodicity to bridging the gap• Microscopic level Macroscopic level
Global Idea Deformation Tensor Localisation Upscale Stresses Macroscpoic Tangent Implementation Results
• Macroscopic deformation• Microscopic deformations / microfluctuations
Computational HomogenizationTheory (2)
deformedundeformed
wXxxdXd M
F
Global Idea Deformation Tensor Localisation Upscale Stresses Macroscpoic Tangent Implementation Results
Computational HomogenizationTheory (3) - Localisation
• Translation between microscopic and macroscopic deformation tensor
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Global Idea Deformation Tensor Localisation Upscale Stresses Macroscpoic Tangent Implementation Results
Computational HomogenizationTheory (4) – Stresses
• Hill-Mandel condition• Work conjugated couple:
– Deformation tensor & 1st Piola-Kirchhoff stress
mM WW
00 0
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dXpM
P
Global Idea Deformation Tensor Localisation Upscale Stresses Macroscpoic Tangent Implementation Results
Computational HomogenizationTheory (4) – Macroscopic tangent
• Tangent describes how small variations affect the stresses in the system
• Numerical differentiation• Very cumbersome method, but Miehe (1996)
developed a more efficient method.
Global Idea Deformation Tensor Localisation Upscale Stresses Macroscpoic Tangent Implementation Results
Computational HomogenizationImplementation in MSC Marc
• Macroscopic Model– Loading– Deformation tensor– Macroscopic tangent
• Microscopic Model– Periodic Boundary
Conditions– Upscale stresses
Global Idea Deformation Tensor Localisation Upscale Stresses Macroscpoic Tangent Implementation Results
Computational HomogenizationResults / Issues
• CH implementation requires a lot a additional computing time– Computational overhead in the numerical
differentiation scheme• Application of loading
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Effect of different loading
Bone - OriginalBone - TopLoadedCartilage - OriginalCartilage - TopLoadedFibrous Tissue - OriginalFibrous Tissue - TopLoaded
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Global Idea Deformation Tensor Localisation Upscale Stresses Macroscpoic Tangent Implementation Results
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 & Conclusions Recommendations Questions
Recommendationsalternatives for upscaling results
• How to 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 & Conclusions Recommendations Questions
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Summary & Conclusions Recommendations Questions
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