effect of bone shaft geometry in its bending

8/8/2019 Effect of Bone Shaft Geometry in Its Bending

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Effect of Bone Shaft Geometry

in its Bending

Presented by

Naveen Meena 07010326Shailendra kumar Meena 07010346

Group no. B03


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IntroductionThe determination of the internal stress field induced in the

human femur under the action of forces is of significant

importance both for the localization of the more severely

loaded areas from which fractures would initiate and for

the efficient design of implants and joint replacements.


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Femury The femur is the largest, longest, and strongest bone of the

human skeleton

y It is a hollow cylindrical shaft filled with bone marrow.

y Its rounded, smooth head fits into a socket in the pelvis called

the acetabulum to form the hip joint .

y The head of the femur is joined to the bone shaft by a narrow

piece of bone known as the neck of the femur.

y The lower end of the femur hinges with the tibia (shinbone) to

form the knee joint.


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Femur


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L

iterature surveyy Previously used methods for stress analysis :

Direct Methods

Brittle coating

o First applied to the femur by Kiintscher who used a

melted colophonium as coating .

o After applying the forces in testing machine they

observed the deformation patterns formed by cracks on

the coating .


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Photoelastic coatingso Used for a full-field determination of surface strains in

two- or three-dimensional bodies

o Applied to the human femur by Rabischong and Avri,

Leduc and Blaimont and Wagner.


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Strain gauges

o Provides a point-by-point method for the

determination of surface strains of bodies.o Due to technological problems strain gauges were

inadequate to monitor strains for long periods inliving bones


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Indirect Methodsy These methods necessitate the construction of a model from the

actual femur, hence called indirect

Beam Theory

o Introdued by Koch to study the stress distribution in human femur.

o Simulated the femur as a two-dimensional beam.

o Only accurate for long beams of constant cross-section.

o Unknown errors are therefore created when this method is applied

to the femur.


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Photoelasticity

o Milch used a two-dimensional and homogeneous model

of the femur and obtained the isochromatic fringe patterns

when the model was subjected to forces.

o From the pattern of isochromatics he established a close

resemblance between the lines of stress and the known

trabecular arrangement of the bone

o Two dimensional models are only partially valid.


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Finite element analysis

y Brekelmans et al. simulated the femur as a two-

dimensional member consisting of a homogeneous,

isotropic elastic material.

y The loading consisted either of one concentrated load,

or of two concentrated loads, with the second load

representing muscle forces.

y In these analyses the problem is considered as a two-

dimensional one.


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Objective

o Previous studies were mostly confined to Two

Dimensional models which were not accurate enough.

o Hence our objective is to analyse the state of stress and

deformation and to predict the zone of frequent fracture in

a femur bone using 3 D model by finite element method.


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3D Stress Analysis of

Femur

y The femur is one of the most highly loaded bones of the

human body

y Shape of the femur is asymmetric and curved in all three

planes, 2 D model seems only partially valid

y A three-dimensional model has been used in this study of

stress analysis.

y Finite element stress analysis methods allow the solution of

three dimensional problems involving complex shapes.


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Problem solving steps

y Assumptions :

1) Bone is made of linear, homogenous, solid, isotropic

material with predefined elastic properties.2) Sideways force on epiphysis is negligible.

3) Distal part is flat and fixed.

4) One legged stance.

5) Two forces viz. joint reaction force and force due to

abductor muscles are only considered and forces due to

other muscle groups which are not well defined are

neglected in our study.


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3D Cad Model (SolidWorks)y 3D CAD model was developed in cad drawing software

SOLIDWORKS using real dimensions of femur

y The bone is made solid volume instead of being hollow in

real.

y Exported to simulation software ANSYS 11.0 for its stress

analysis.


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Stress AnalysisMaterial Parameters

y

Bone is assumed to be a linear, isotropic andhomogeneous material .

y Elastic constants and other mechanical properties .

1) Youngs modulus (E) = 17 GPa = 17*109 Pa

2) Poissons ratio () = 0.33


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Loads on Femur

y Assumed a 70 kg person on one foot on the ground

orientation.

yThe forces taken into account are:

1) Joint reaction force on the femur head due to pelvis (R)

2) Abductor muscles force which acts at 700 from the

horizontal as shown in figure (F)

3) Weight of the body (W)

4) Normal force (N)


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y Person is stationary, the horizontal and vertical

components of the forces and the total torque are all

equal to zero.


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yAfter solving these equations

F = 1.6W R = 2.4W

y The angle is

tan( ) =RH/RV

= 0.23 radian

1) Joint reaction force at 130 to the vertical, R = 2.4*70*9.8 =

1646 N

2) Abductor muscle force at 700 to the horizontal, F=1100 N


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Finite Element stress Analysis

yAnalysis of intact femur in one legged position has

been done in ANSYS 11.0

y Imported CAD model is meshed using element

SOLID45which is triangular in shape.

y Forces are applied on the meshed bone restrained

from moving at distal part at defined positions.


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y NODE 27: on femur neck

Joint reaction force, R= 1646N

Rx

= R cos(130) = 1603.8 N

Rz = R sin(130) = -370.2 N z

Ry= R sin(30) = 86.14 N x


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y

NODE 390 : on top of greater trochanterAbductor muscle force,F= 1100 N

Fz =Fcos(700) = 376.2 N

Fx =F

sin(700

)= -1033.66 NFy=Fsin(3

0)= 57.56 N


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R

esults and analysisDeformation

y The maximum deformation of bone is found to be at the

point of application of joint reaction force i.e. MX point in

figure.

y As we move from femur head to the distal part, the values

of deformation (total sum) found to be decreasing linearlyas shown in figure.

y Maximum deformation = 4.63 mm at femur head


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5 Variation of total deformation in femur with distance from point of application of forces5 Variation of total deformation in femur with distance from point of application of forces5 Variation of total deformation in femur with distance from point of application of forces5 Variation of total deformation in femur with distance from point of application of forces

Variation of total deformation in femur with distance from point

of application of forces


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Von Mises Stressesy Maximum stresses were observed at upper shaft position and

femur neck where the areas are lesser as compared to other

parts of the bone. MX point in the figure is the point of

maximum stress in the femur bone.

y Lateral surface of the shaft observed the tensile stresses

whereas compressive stresses occurred at medial surface.

y Maximum stress = 8.8 MPa at upper lateral shaft.


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Variation of stresses with distance from point ofapplication of forces


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Conclusiony A linear finite element analysis of the proximal femur was

performed.

y The maximum displacement magnitude occurs within the

femoral head where the hip contact force is applied.

y The maximum fracture risk in the cortex seems to be on the

upper part of the diaphysis and on the femoral neck where the

maximum stress concentration occurs.


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Futur rky In the above study, stress analysis in human femur has been

done using 3D finite element technique.

y In the future we will be developing the mathematical model

for the femur bone to study the effects of bone geometry and

bone density on the stresses developed on the application of

the forces of varying magnitude .


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Thank You

effect of bone shaft geometry in its bending

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