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Courant 08
Bone basics
Bonemeasurementand modeling
BoneFEAsoftware
Conclusion
Finite Element Analysis of Human BoneModels
D. Bindel
Courant Institute for Mathematical SciencesNew York University
Biomath Lunch Seminar, 1 Apr 2008
Courant 08
Bone basics
Bonemeasurementand modeling
BoneFEAsoftware
Conclusion
Outline
1 Bone basics
2 Bone measurement and modeling
3 BoneFEA software
4 Conclusion
Courant 08
Bone basics
Bonemeasurementand modeling
BoneFEAsoftware
Conclusion
Outline
1 Bone basics
2 Bone measurement and modeling
3 BoneFEA software
4 Conclusion
Courant 08
Bone basics
Bonemeasurementand modeling
BoneFEAsoftware
Conclusion
Why study bones?
Osteoporosis: 44M Americans, $17B / year> 55% of over 50 have osteoporosis or low bone mass350K hip fractures / year; over $10B / yearA quarter of hip fracture patients die within a year... and we’re getting older
Courant 08
Bone basics
Bonemeasurementand modeling
BoneFEAsoftware
Conclusion
Bone basics: macrostructure
Courant 08
Bone basics
Bonemeasurementand modeling
BoneFEAsoftware
Conclusion
Bone basics: microstructure
Courant 08
Bone basics
Bonemeasurementand modeling
BoneFEAsoftware
Conclusion
Bone basics: microstructure
Courant 08
Bone basics
Bonemeasurementand modeling
BoneFEAsoftware
Conclusion
Bone basics: trabecular microstructure
Courant 08
Bone basics
Bonemeasurementand modeling
BoneFEAsoftware
Conclusion
Bone basics: trabecular microstructure
(Scans from 23 and 85 year old females)
Courant 08
Bone basics
Bonemeasurementand modeling
BoneFEAsoftware
Conclusion
Bone basics: orientation and remodeling
Courant 08
Bone basics
Bonemeasurementand modeling
BoneFEAsoftware
Conclusion
Why study bones?
... because bone is a fascinating material!
Structurally complicated across length scalesStructure adapts to loads and changes over timeinhomogeneous, anisotropic, asymmetric, oftennonlinear
Courant 08
Bone basics
Bonemeasurementand modeling
BoneFEAsoftware
Conclusion
Outline
1 Bone basics
2 Bone measurement and modeling
3 BoneFEA software
4 Conclusion
Courant 08
Bone basics
Bonemeasurementand modeling
BoneFEAsoftware
Conclusion
Bone measurement
Diagnostic for osteoporosis: T-scores from DXAOrdinary microscopy on extracted coresQCT software: density profile, about 3 mm scaleMicro-CT and micro-MRI: O(10 micron)
Courant 08
Bone basics
Bonemeasurementand modeling
BoneFEAsoftware
Conclusion
Micro-FE bone modeling
One vertebrate = 57M+ elements at 40 microns
Courant 08
Bone basics
Bonemeasurementand modeling
BoneFEAsoftware
Conclusion
Whole bone modeling
Density only weakly predicts strengthWanted: Good effective constitutive relation
Courant 08
Bone basics
Bonemeasurementand modeling
BoneFEAsoftware
Conclusion
Difficulties
Bone is:Variable over time and between individualsInhomogeneous and anisotropicDifferent in tension and compression
Courant 08
Bone basics
Bonemeasurementand modeling
BoneFEAsoftware
Conclusion
Yielding and nonlinearity
Example difficulty:Trabecular network has beam and plate elementsSmall macro strains yield much larger micro strainsSmall-scale geometric nonlinearity a significant effect
Courant 08
Bone basics
Bonemeasurementand modeling
BoneFEAsoftware
Conclusion
Yielding and nonlinearity
Courant 08
Bone basics
Bonemeasurementand modeling
BoneFEAsoftware
Conclusion
An approach
Micro-CT structure scans for orientationUse orientation indices + density to approximatematerial parametersProceed phenomenologically
Courant 08
Bone basics
Bonemeasurementand modeling
BoneFEAsoftware
Conclusion
Outline
1 Bone basics
2 Bone measurement and modeling
3 BoneFEA software
4 Conclusion
Courant 08
Bone basics
Bonemeasurementand modeling
BoneFEAsoftware
Conclusion
Diagnostic toolchain
Micro-CT scan data from patientInference of material propertiesConstruction of coarse FE model (voxels)Simulation under loadingOutput of stress fields, displacements, etc.
Courant 08
Bone basics
Bonemeasurementand modeling
BoneFEAsoftware
Conclusion
BoneFEA
Standard displacement-based finite element codeElastic and plastic material models (includinganisotropy and asymmetric yield surfaces)High-level: incremental load control loop,Newton-Krylov solvers with line search for nonlinearsystemsLibrary of (fairly simple) preconditioners; default is atwo-level geometric multigrid preconditioner
Courant 08
Bone basics
Bonemeasurementand modeling
BoneFEAsoftware
Conclusion
Example analysis loop
mesh:rigid(mesh:numnp()-1, {z=’min’},function()return ’uuuuuu’, 0, 0, bound_disp
end)
pc = simple_msm_pc(mesh,20)mesh:set_cg{M=pc, tol=1e-6, max_iter=1000}for j=1,n dobound_disp = 0.2*jmesh:step()mesh:newton{max_iter=6, Rtol=1e-4}
end
Courant 08
Bone basics
Bonemeasurementand modeling
BoneFEAsoftware
Conclusion
Example analyses
Courant 08
Bone basics
Bonemeasurementand modeling
BoneFEAsoftware
Conclusion
Outline
1 Bone basics
2 Bone measurement and modeling
3 BoneFEA software
4 Conclusion
Courant 08
Bone basics
Bonemeasurementand modeling
BoneFEAsoftware
Conclusion
Conclusion
Bones are interesting as well as important!Initial BoneFEA work done, in use by ON DiagnosticsPossible follow-up work for diagnostic toolPlenty of interesting research directions
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