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Finite Element Analysis of Human BoneModels

D. Bindel

Courant Institute for Mathematical SciencesNew York University

Biomath Lunch Seminar, 1 Apr 2008

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Outline

1 Bone basics

2 Bone measurement and modeling

3 BoneFEA software

4 Conclusion

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Bone basics

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Outline

1 Bone basics

2 Bone measurement and modeling

3 BoneFEA software

4 Conclusion

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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

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Bone basics: macrostructure

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Bone basics: microstructure

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Bone basics: microstructure

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Bone basics: trabecular microstructure

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Bone basics: trabecular microstructure

(Scans from 23 and 85 year old females)

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Bone basics: orientation and remodeling

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Why study bones?

... because bone is a fascinating material!

Structurally complicated across length scalesStructure adapts to loads and changes over timeinhomogeneous, anisotropic, asymmetric, oftennonlinear

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Bone basics

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Outline

1 Bone basics

2 Bone measurement and modeling

3 BoneFEA software

4 Conclusion

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Bone basics

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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)

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Micro-FE bone modeling

One vertebrate = 57M+ elements at 40 microns

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Whole bone modeling

Density only weakly predicts strengthWanted: Good effective constitutive relation

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Difficulties

Bone is:Variable over time and between individualsInhomogeneous and anisotropicDifferent in tension and compression

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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

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Yielding and nonlinearity

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An approach

Micro-CT structure scans for orientationUse orientation indices + density to approximatematerial parametersProceed phenomenologically

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Outline

1 Bone basics

2 Bone measurement and modeling

3 BoneFEA software

4 Conclusion

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Diagnostic toolchain

Micro-CT scan data from patientInference of material propertiesConstruction of coarse FE model (voxels)Simulation under loadingOutput of stress fields, displacements, etc.

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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

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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

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Example analyses

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Bone basics

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Outline

1 Bone basics

2 Bone measurement and modeling

3 BoneFEA software

4 Conclusion

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Bone basics

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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