Multi-level µ-Finite Element Analysis of Human Bone Structures
Methods: Studied bone strength changes within multi-bone, multi-muscle leg system under an isometric...
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Methods: Methods: • Studied bone strength changes within multi-bone, multi- Studied bone strength changes within multi-bone, multi- muscle leg system under an isometric exercise with a muscle leg system under an isometric exercise with a known net force between foot & fixed plate. known net force between foot & fixed plate. • A computational model was developed to determine: A computational model was developed to determine: • Individual Muscle Forces Individual Muscle Forces • Statically indeterminate system: Statically indeterminate system: • Gradient-based optimization methods used [2] Gradient-based optimization methods used [2] • Goal: Minimize sum of squares of muscle stresses Goal: Minimize sum of squares of muscle stresses • Distribution of Effects of Applied Forces within Femur Distribution of Effects of Applied Forces within Femur Bone Bone • Finite Element Analysis: Initially circular hollow Finite Element Analysis: Initially circular hollow cylinder cylinder • Muscle forces directly applied Muscle forces directly applied • External reaction forces applied External reaction forces applied • Strain Energy Density calculated for surface nodes Strain Energy Density calculated for surface nodes • Changes to the Surface Profile of the Femur Bone Changes to the Surface Profile of the Femur Bone • Radial movement of surface nodes based on SED Radial movement of surface nodes based on SED variation variation • Gradientless optimization methods used [3] Gradientless optimization methods used [3] • Goal: Uniformity of SED over each circumferential Goal: Uniformity of SED over each circumferential surface surface Modeling Changes in Whole Bone Strength Due to Muscle-Generated Loads Modeling Changes in Whole Bone Strength Due to Muscle-Generated Loads Catherine S. Florio, Catherine S. Florio, Doctoral Candidate Doctoral Candidate Department of Mechanical and Industrial Engineering, NCE, NJIT Department of Mechanical and Industrial Engineering, NCE, NJIT Introduction/Relevance: Introduction/Relevance: • The ability to predict changes in whole bone is strength The ability to predict changes in whole bone is strength important in mitigation of “bone loss” due to aging, important in mitigation of “bone loss” due to aging, limited mobility, or reduced gravity limited mobility, or reduced gravity • Bone strength is directly related to the bone’s Bone strength is directly related to the bone’s mechanical environment mechanical environment • Individual muscle forces + external gravitational and Individual muscle forces + external gravitational and impact forces impact forces • Muscle forces > external forces Muscle forces > external forces • Bone strength is modified by bone density and bone Bone strength is modified by bone density and bone geometry geometry • Strength changes due to geometric variations > due to Strength changes due to geometric variations > due to density variations density variations • A model to simulate bone strength changes should A model to simulate bone strength changes should accurately predict: accurately predict: • Individual muscle forces acting on bone Individual muscle forces acting on bone • Shape changes due to material accretion or removal on bone Shape changes due to material accretion or removal on bone surfaces surfaces Results: Results: Conclusions/Innovation: Conclusions/Innovation: • Coupled model based on optimization methods allows for determination of: Coupled model based on optimization methods allows for determination of: • Individual muscle forces generated on bones within whole limb system Individual muscle forces generated on bones within whole limb system • Improved bone “design” for more uniform surface SED = stronger bone Improved bone “design” for more uniform surface SED = stronger bone • Data obtained from the model can: Data obtained from the model can: • Quantitatively compare the effects of various loading schemes on bone Quantitatively compare the effects of various loading schemes on bone shape and strength at defined locations shape and strength at defined locations • Target specific regions for improved strength Target specific regions for improved strength References: References: [1] Wells & Evans. 1987. [1] Wells & Evans. 1987. Hum Mov Sci Hum Mov Sci 6:349-72 [2] Crowninshield & Brand. 1981. 6:349-72 [2] Crowninshield & Brand. 1981. J J Biomech Biomech 14:793-801 14:793-801 [3] Heller et al. 1999. [3] Heller et al. 1999. J Strain Analysis J Strain Analysis 34:326-36 [4] Luo. 2010. 34:326-36 [4] Luo. 2010. Int J Numer Meth Biomed Int J Numer Meth Biomed Engng. Engng. 26:1077-86. 26:1077-86. [5] ANSYS FLUENT User’s Guide. Nov. 2010. Release 13.0. Chapter 12. 631-4. [6] [5] ANSYS FLUENT User’s Guide. Nov. 2010. Release 13.0. Chapter 12. 631-4. [6] Florio & Narh. 2011. Florio & Narh. 2011. Simulation Simulation 87: 313-33. 87: 313-33. NJIT GSA Research Day November 9, 2011 NJIT GSA Research Day November 9, 2011 This work was partially supported by an Amelia Earhart Fellowship from the Zonta International Foundation This work was partially supported by an Amelia Earhart Fellowship from the Zonta International Foundation i SurfAvg i i SurfAvg SED SED G SED G G i i = Growth at node i = Growth at node i i i = Growth rate node i = Growth rate node i SED = SED = Strain Strain Energy Energy Density Density Number Number Muscle Name Muscle Name 1 Tibialis Tibialis Anterior Anterior 2 Soleus Soleus 3 Gastrocnemius Gastrocnemius 4 Vastii Vastii 5 Rectus Rectus Femoris Femoris 6 Short Head Short Head Biceps Biceps Femoris Femoris 7 Long Head Long Head Biceps Biceps Femoris Femoris 8 Iliacus Iliacus 9 Gluteus Gluteus Maximus Maximus Typical Applied Typical Applied Joint Moment Joint Moment Typical Typical Region of Region of Applied Applied Muscle Muscle Force Force Hip Joint Hip Joint Moment Moment Knee Joint Knee Joint Moment Moment Muscle Forces Muscle Forces Acting Near Acting Near Hip Hip Muscle Forces Muscle Forces Acting Near Acting Near Knee Knee Based on experimental study in [1] Based on experimental study in [1] System System Boundary Boundary Torso Fixed Torso Fixed to Table to Table Radial Variation Radial Variation of Load Direction of Load Direction Rigid, Fixed Plate Rigid, Fixed Plate Net Resultant Net Resultant Force Force 1 2 3 4 5 6 7 8 9 Femur Femur Strength Strength Studied Studied Femur Femur Tib i a Tib i a Foot Foot Initial Initial Cross Cross Section Section Final Cross Section Final Cross Section at 45% Length from at 45% Length from Knee Knee Final Final Geometry Geometry Approache Approache s a s a Typical Typical Long Long Bone: Bone: Wider at Wider at Ends and Ends and Narrower Narrower in Mid- in Mid- Shaft Shaft TYPICAL DATA OBTAINED TYPICAL DATA OBTAINED Comparison of Comparison of Polar Moments Polar Moments of Inertia (m of Inertia (m 4 4 ) ) Displacement Displacement Distribution Distribution FEA Whole Leg System FEA Whole Leg System – – One Load Application One Load Application Iteration from [6] Iteration from [6] 0.0E+00 1.0E -08 2.0E -08 3.0E -08 4.0E -08 5.0E -08 6.0E -08 7.0E -08 8.0E -08 O riginal Final 6% 6% Improvement Improvement Ratio of Nodal SED to Ratio of Nodal SED to Surface Averaged SED at X=Y, Surface Averaged SED at X=Y, Convergence Convergence Surface Averaged Strain Surface Averaged Strain Energy Density Energy Density 0 2000 4000 6000 8000 10000 12000 0 100 200 300 400 500 600 Iteration SED (Pa) O uterSurface InnerSurface 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0 100 200 300 400 500 600 Iteration SED (i)/SED SurfA vg O uterSurface InnerSurface 0.0E+00 1.0E-05 2.0E-05 3.0E-05 4.0E-05 5.0E-05 6.0E-05 7.0E-05 8.0E-05 9.0E-05 1.0E-04 0 100 200 300 400 500 600 Iteration C onvergence M easure O uterSurface InnerSurface
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Transcript of Methods: Studied bone strength changes within multi-bone, multi-muscle leg system under an isometric...
Methods:Methods:•Studied bone strength changes within multi-bone, multi-muscle leg system Studied bone strength changes within multi-bone, multi-muscle leg system under an isometric exercise with a known net force between foot & fixed plate.under an isometric exercise with a known net force between foot & fixed plate.
•A computational model was developed to determine:A computational model was developed to determine:•Individual Muscle ForcesIndividual Muscle Forces
•Statically indeterminate system: Statically indeterminate system: •Gradient-based optimization methods used [2]Gradient-based optimization methods used [2]
•Goal: Minimize sum of squares of muscle stressesGoal: Minimize sum of squares of muscle stresses•Distribution of Effects of Applied Forces within Femur BoneDistribution of Effects of Applied Forces within Femur Bone
•Finite Element Analysis: Initially circular hollow cylinderFinite Element Analysis: Initially circular hollow cylinder•Muscle forces directly appliedMuscle forces directly applied•External reaction forces appliedExternal reaction forces applied•Strain Energy Density calculated for surface nodesStrain Energy Density calculated for surface nodes
•Changes to the Surface Profile of the Femur BoneChanges to the Surface Profile of the Femur Bone•Radial movement of surface nodes based on SED variationRadial movement of surface nodes based on SED variation
•Gradientless optimization methods used [3]Gradientless optimization methods used [3]•Goal: Uniformity of SED over each circumferential surfaceGoal: Uniformity of SED over each circumferential surface
•Surface node smoothing based on SED gradient [4]Surface node smoothing based on SED gradient [4]•Interior node “spring smoothing” [5]Interior node “spring smoothing” [5]
•Geometric Properties at Specific LocationsGeometric Properties at Specific Locations•Cross Sectional Areas, Wall Thicknesses, Moments of Inertia (Ixx, Iyy, Ixy, J)Cross Sectional Areas, Wall Thicknesses, Moments of Inertia (Ixx, Iyy, Ixy, J)
Modeling Changes in Whole Bone Strength Due to Muscle-Generated LoadsModeling Changes in Whole Bone Strength Due to Muscle-Generated LoadsCatherine S. Florio,Catherine S. Florio, Doctoral CandidateDoctoral Candidate
Department of Mechanical and Industrial Engineering, NCE, NJITDepartment of Mechanical and Industrial Engineering, NCE, NJIT
Introduction/Relevance: Introduction/Relevance: •The ability to predict changes in whole bone is strength important in The ability to predict changes in whole bone is strength important in mitigation of “bone loss” due to aging, limited mobility, or reduced gravity mitigation of “bone loss” due to aging, limited mobility, or reduced gravity •Bone strength is directly related to the bone’s mechanical environmentBone strength is directly related to the bone’s mechanical environment
•Individual muscle forces + external gravitational and impact forcesIndividual muscle forces + external gravitational and impact forces•Muscle forces > external forcesMuscle forces > external forces
•Bone strength is modified by bone density and bone geometryBone strength is modified by bone density and bone geometry•Strength changes due to geometric variations > due to density variationsStrength changes due to geometric variations > due to density variations
•A model to simulate bone strength changes should accurately predict:A model to simulate bone strength changes should accurately predict:•Individual muscle forces acting on boneIndividual muscle forces acting on bone•Shape changes due to material accretion or removal on bone surfacesShape changes due to material accretion or removal on bone surfaces
Results:Results:
Conclusions/Innovation:Conclusions/Innovation:•Coupled model based on optimization methods allows for determination of:Coupled model based on optimization methods allows for determination of:
•Individual muscle forces generated on bones within whole limb systemIndividual muscle forces generated on bones within whole limb system•Improved bone “design” for more uniform surface SED = stronger boneImproved bone “design” for more uniform surface SED = stronger bone
•Data obtained from the model can:Data obtained from the model can:•Quantitatively compare the effects of various loading schemes on bone Quantitatively compare the effects of various loading schemes on bone shape and strength at defined locationsshape and strength at defined locations•Target specific regions for improved strengthTarget specific regions for improved strength
References:References:[1] Wells & Evans. 1987. [1] Wells & Evans. 1987. Hum Mov Sci Hum Mov Sci 6:349-72 [2] Crowninshield & Brand. 1981. 6:349-72 [2] Crowninshield & Brand. 1981. J Biomech J Biomech 14:793-801 14:793-801 [3] Heller et al. 1999. [3] Heller et al. 1999. J Strain Analysis J Strain Analysis 34:326-36 [4] Luo. 2010. 34:326-36 [4] Luo. 2010. Int J Numer Meth Biomed Engng. Int J Numer Meth Biomed Engng. 26:1077-86.26:1077-86.[5] ANSYS FLUENT User’s Guide. Nov. 2010. Release 13.0. Chapter 12. 631-4. [6] Florio & Narh. 2011. [5] ANSYS FLUENT User’s Guide. Nov. 2010. Release 13.0. Chapter 12. 631-4. [6] Florio & Narh. 2011. Simulation Simulation 87: 313-33. 87: 313-33.
NJIT GSA Research Day November 9, 2011NJIT GSA Research Day November 9, 2011 This work was partially supported by an Amelia Earhart Fellowship from the Zonta International FoundationThis work was partially supported by an Amelia Earhart Fellowship from the Zonta International Foundation
i SurfAvg
i iSurfAvg
SED SEDG
SED
GGii = Growth at node i = Growth at node i
ii = Growth rate node i = Growth rate node i
SED = Strain SED = Strain Energy DensityEnergy Density
NumberNumber Muscle NameMuscle Name
11 Tibialis AnteriorTibialis Anterior
22 SoleusSoleus
33 GastrocnemiusGastrocnemius
44 VastiiVastii
55 Rectus FemorisRectus Femoris
66Short Head Short Head
Biceps FemorisBiceps Femoris
77Long Head Long Head
Biceps FemorisBiceps Femoris
88 IliacusIliacus
99Gluteus Gluteus
MaximusMaximus
Typical Applied Typical Applied Joint MomentJoint Moment
Typical Typical Region of Region of Applied Applied Muscle Muscle ForceForce
Hip Joint MomentHip Joint Moment
Knee Joint MomentKnee Joint Moment
Muscle Forces Muscle Forces Acting Near HipActing Near Hip
Muscle Forces Muscle Forces Acting Near KneeActing Near Knee
Based on experimental study in [1]Based on experimental study in [1]
System System BoundaryBoundary
Torso Fixed to Torso Fixed to TableTable
Radial Variation of Radial Variation of Load DirectionLoad Direction
Rigid, Fixed PlateRigid, Fixed Plate
Net Resultant Net Resultant ForceForce
11
22
33
44
55 66
778899
Femur Femur Strength Strength StudiedStudied
Femur
Femur
TibiaTibia
FootFoot
Initial Cross Initial Cross SectionSection
Final Cross Section at Final Cross Section at 45% Length from Knee45% Length from Knee
Final Final GeometryGeometry
Approaches Approaches a Typical a Typical
Long Bone: Long Bone: Wider at Wider at
Ends and Ends and Narrower in Narrower in Mid-ShaftMid-Shaft
TYPICAL DATA OBTAINEDTYPICAL DATA OBTAINED
Comparison of Comparison of Polar Moments of Polar Moments of
Inertia (mInertia (m44))
Displacement Displacement DistributionDistribution
FEA Whole Leg System –FEA Whole Leg System –One Load Application One Load Application
Iteration from [6]Iteration from [6]
0.0E+00
1.0E-08
2.0E-08
3.0E-08
4.0E-08
5.0E-08
6.0E-08
7.0E-08
8.0E-08
Original Final
6% 6%
Improvement
Improvement
Ratio of Nodal SED to Surface Ratio of Nodal SED to Surface Averaged SED at X=Y, 45% LengthAveraged SED at X=Y, 45% Length
ConvergenceConvergenceSurface Averaged Strain Energy Surface Averaged Strain Energy DensityDensity
0
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0 100 200 300 400 500 600Iteration
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D (
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)
Outer SurfaceInner Surface
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D(i
)/S
ED
Su
rfA
vg
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0.0E+00
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9.0E-05
1.0E-04
0 100 200 300 400 500 600Iteration
Co
nv
erg
en
ce
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as
ure
Outer SurfaceInner Surface
