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

2000

4000

6000

8000

10000

12000

0 100 200 300 400 500 600Iteration

SE

D (

Pa

)

Outer SurfaceInner Surface

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 600Iteration

SE

D(i

)/S

ED

Su

rfA

vg

Outer SurfaceInner Surface

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 600Iteration

Co

nv

erg

en

ce

Me

as

ure

Outer SurfaceInner Surface