Detroit Medical Center - Biomech2

8/13/2019 Detroit Medical Center - Biomech2

1/61

Concepts in OrthopaedicBiomechanics

Basic Science LecturesDepartment of Orthopaedic Surgery

Detroit Medical Center

Michele J. Grimm, Ph.D.Director of Orthopaedic Biomechanics


2/61

Mechanical Concepts -- Friction

Friction -- Resistance generated between two objects when

one slides over the other

Friction results in a force parallel and opposite to the

direction of motion of an object

Direction of

motionDirection of

friction force


3/61

Mechanical Concepts -- Friction

Dependent upon the normalforce between the objects

and the coefficient of

friction for the two objects

Fk = µ

k *N

Every pair of materials

will have a different

coefficient of friction

Coefficient of friction isdependent on the surface

roughness of the objects and

the molecular interactions

between the surfaces

W

N

F

Fk

W = mass*gravity N = W Fk = µk*N F > Fk to move block

W = mass*gravity N = W*cosf Fk = µk*N F > Fk to move object F

W

N f

Fk


4/61

Question 21

In the Figure, if the coefficient of friction between the 10

kg box and the floor is 0.2, in order for the box to slide the

horizontal force component FH must exceed

(1) 2 kg

(2) 10 kg

(3) 50 kg

(4) FV

(5) F

F

10 kg


5/61

Question 21

In the Figure, if the coefficient of friction between the 10

kg box and the floor is 0.2, in order for the box to slide the

horizontal force component FH must exceed

(1) 2 kg

(2) 10 kg

(3) 50 kg

(4) FV

(5) F


6/61

Question 22

A cervical traction device is applied to the skull of a

patient as shown in the figure. Assume that the head

weighs 100 N and the coefficient of friction between the

back of the head and the bed is 0.2. What is the minimum

weight required in order to provide force at the cervicalspine?

(1) 10 N

(2) 20 N

(3) 55 N

(4) 100 N

(5) 200 N


7/61

Question 23

A cervical traction device is applied to the skull of a

patient as shown in the figure. Assume that the head

weighs 100 N and the coefficient of friction between the

back of the head and the bed is 0.2. What is the minimum

weight required in order to provide force at the cervicalspine?

(1) 10 N

(2) 20 N

(3) 55 N

(4) 100 N

(5) 200 N


8/61

Mechanical Concepts -- Lubrication

Lubrication -- use of a material of low friction coefficient

between the two surfaces to reduce the frictional force

between the two materials

Often lubricants are a fluid (oil, water, synovial fluid), butmay also be a powder such as graphite

Lubricant acts to form a layer between the surface

irregularities of the materials, adheres to both surfaces, and

aids in slip between the surfaces


9/61

Mechanical Concepts -- Lubrication

Boundary layer lubrication fills the valleys and coats the

peaks of the material surfaces, but still allows contact

between the opposing materials

Fluid film lubrication occurs when relative motion between

the surfaces is at a high enough velocity for the surfaces no

longer to be in contact

Ex: Tires hydroplaning on wet streets


10/61

Lubrication of Joints

Low coefficient of friction between cartilage surfaces is due tofluid-film lubrication

Synovial fluid -- static loads (no motion)

Cartilagenous exudate (water) from loading of cartilage in

cyclical manner Osteoarthritis results in increased water content in the articular

cartilage causing

Increased cartilage permeability which results in poor fluid-

film generation for lubricationDecreased tissue stiffness which alter the normal load-

carriage mechanisms

Both mechanisms result in accelerated wear and further break-

down of the articular cartilage


11/61

Mechanical Concepts -- Wear

Wear is defined as the removal of the surface material bymechanical action

Adhesive wear occurs due to the sliding contact of two rough

surfaces

Examples includemetal on metal

bone on bone

Abrasive wear occurs due to the sliding contact of a rough

surface on a softer material Examples include

stainless steel on polyethylene (femoral head implant on

acetabular component)

bone on cartilage


12/61


Wear results in particulate debris which can cause an

inflammatory response and may affect implant behavior

The amount of wear that occurs depends on

The coefficient of friction between two surfaces

The hardness of the two surfaces The normal force between the surfaces

The contact area between the surfaces

Increased friction will result in increased wear due to the

greater shear force at the contact surface


13/61


Greater contact area between the surfaces

increases the area over which wear occurs


14/61

Question 23

The wear rate of a polyethylene acetabular total hip

component is most dependent on the

(1) Femoral neck offset

(2) Femoral head diameter

(3) Component position

(4) Acetabular component backing

(5) Acetabular component fixation technique


15/61

Question 23

The wear rate of a polyethylene acetabular total hip

component is most dependent on the

(1) Femoral neck offset

(2) Femoral head diameter

(3) Component position

(4) Acetabular component backing

(5) Acetabular component fixation technique


16/61

Material vs. Structural Properties

A structure is comprised of one or more materials Behavior of a structure depends not only on the mechanical

properties of the material (aka material properties), but on

Dimensions: thickness, width, length

Manner of supporting load

Type: uniaxial, biaxial, bending, torsion

Configuration: column, eccentric column, end or center-

loaded beam

Orientation of load with respect to geometry

Shape

Structures develop different combinations of tensile,

compressive, and shear stresses in various loading conditions


17/61

Structures

Basic structural shapes include

Beam - Two dimensions are smaller

than other one

Plate - One dimension is smaller thanother two

Rod - Solid cylinder

Tube - Hollow cylinder

Cable - Supports tensile stress only Sphere

Arch


18/61

Loading Conditions -- Column Loading

Load axis lies along center of vertical rod or cylinder acting as a

column or support

Compression (or tension) distributed evenly across horizontal

cross-section

Shear stress develops on planes at 45 degree angles to axis of

loading


19/61

Loading Conditions -- Torsion Caused by twisting force on two

ends of rod or cylinder

Develops shear stress along long

and short axes of cylinder

Tensile and compressive stresses

develop at angles of 45 degrees tolong axis

Bones undergo torsional loading

during internal and external

rotation Torsional failure may occur in

incidents such as a twisting fall

when skiing


20/61

Loading Conditions -- Bending Caused by uniaxial loading of a curved structure or eccentric

loading of a straight beam

As a beam bends under an applied load, one surface becomes

convex and one becomes concave

Tensile stress develops on convex surface

Compressive stress develops on concave surface

Stresses are maximum at surfaces and become zero at neutral

plane

Bones have slight curvature and thus experience bending under

normal conditions

Neutral Axis, Stress = 0

Region of Tensile Stress

Region of Compressive Stress


21/61

Loading Conditions

Eccentric Column Loading

Common in skeleton

Load is applied off center

In addition to direct compression,

additional compression and tension

due to bending

Can be seen as bending with an

additional compressive force

Loading of femoral neck an

example of eccentric column

loading


22/61

Unixaxial Loading

Strength and stiffness are proportional to the cross-sectional area of

the structure

Examining the simple uniaxial loading condition allows us to see the

effect of geometry when material properties are constant

Case 1:

Ligaments of equal length and different diameters, A and 2A,under the same force rupture at the same deformation (D)

Stiffness of ligament 2A will be twice that of ligament A

Force required to cause deformation (D) which results in

rupture for ligament 2A will be twice that of ligament A

2A

A

Load

Deformation


23/61

Uniaxial Loading

Case 2: Ligaments of equal diameters and different lengths, L and

2L, under the same force will rupture at different

deformations

Stiffness of ligament 2L will be half that of ligament LDeformation at rupture for ligament 2L will be twice

that of ligament L

Force at rupture, and therefore strength, will be equal for

the two ligaments

Load

Deformation

2LL


24/61

Moments

A Rotational Moment is produced by a force out of line

with the axis of a structure

The moment is equal to the product of the force and the

distance from the point of force application to the

center of rotation of the structure

M = F*L

L

F


25/61

Equilibrium

For an object to be at rest, or in equilibrium, the followingrules apply

The sum of forces and moments must equal zero:

Forces act through the center of mass of an object

Moments tend to rotate an object about its center ofmass (or about a fixed rotational point, such as a pin or

joint) and are caused by off axis forces

Forces and moments must be treated separately in

determining equilibrium conditionsA B A B A B

A + B = R

Ac = Bd

Rc d


26/61

Bending

Bending Rigidity: load required to produce a unit deflection of a beam

Increases with increasing beam dimension which resists the

bending [R a thickness3]

Decreases with increasing "working length" of beam [R a

(1/length)3]

Increases with redistribution of material away from neutral axis

This distribution of material is defined by the cross-sectional

moment of inertia (Ixx)


27/61

Bending

Working Length: length of structure subjected to bending

In internal fixation, it is the length between the two

main points where bone may experience discontinuities

in bending or torsional moments

For example -- fracture surfaces

L


28/61

Bending Bending Strength of a structure: maximum bending load

that can be sustained The bending strength is proportional to the ratio c/Ixx

c is the distance from the neutral axis to the surface

of the structure

Ixx is the moment of inertia

Limit to the increase in strength with moment of inertia

reached when the material is too thin to support the

load and begins to buckle


29/61

Question 24

In the analysis of mechanical forces, a moment is caused

by:

(1) The product of a mass and its velocity

(2) Two equal, parallel forces of opposite sense

(3) Two equal, parallel forces of the same sense

(4) A force acting at a distance from a point

(5) A system of concurrent forces acting on a free body

of equilibrium


30/61

Question 24

In the analysis of mechanical forces, a moment is caused

by:

(1) The product of a mass and its velocity

(2) Two equal, parallel forces of opposite sense

(3) Two equal, parallel forces of the same sense

(4) A force acting at a distance from a point

(5) A system of concurrent forces acting on a free body

of equilibrium


31/61

Torsion

Torsional Rigidity: torque required to produce a unit angular

twist of a structure

Decreases with increasing working length

Increases with increasing structural radius (R a r 4) through

the polar moment of inertia (J)

For rectangular cross-sections, rigidity is related to the

dimensions of the circle which can fit within the cross-

section


32/61

Torsion

A cylinder with a slot or cut on one side will have a greatly

reduced torsional rigidity

Reduced by a factor of 5 to 10

Width of cut relatively unimportant

Torsional Strength: maximum torque that can be sustained

Most efficient shape for bending and torsion is a

cylindrical tube because it provides an equivilent area

moment about all axes


33/61

Question 25

A set mass of material is most resistant to both torsion and

bending when it is shaped like a:

(1) A cylinder

(2) A solid rod

(3) A flat beam

(4) An I-beam

(5) An elliptical beam


34/61

Question 25

A set mass of material is most resistant to both torsion and

bending when it is shaped like a:

(1) A cylinder

(2) A solid rod

(3) A flat beam

(4) An I-beam

(5) An elliptical beam


35/61

Stress Concentrations

A structure first begins to yield, exhibiting permanent

deformation, and then fails at the point where the highest

stress is experienced

In almost all structures, except axially loaded columns or

cubes, there is some variation in stress over the structure

due to the geometry and mode of loading

Thus for a beam in bending, the maximum stresses

occur at the surfaces perpendicular to the direction of

loading


36/61

Stress Concentrations

Any discontinuities in a structure will produce stressconcentrations

Examples: notches, holes, sharp angles, grooves, or other

sharp transitions in structure

Increases stress at location by 2 to 4 times and creates a highstress gradient

In most cases, failure will initiate at the stress-concentrating

defect. The exception is if the defect exists in a region of low

stress in a structure under nonuniform stress. Stress defects in orthopaedic structures can be the result of

surgical intervensions, such as bone graft removal or the

insertion of bone screws, or the development of structural

defects such as result from metastatic cancer


37/61

Stress Distribution

In a composite structure, stresses

and displacements will be

distributed among the component

materials dependent upon their

material properties

Structures in parallel

Displacement will be constant for

two components

Stress in each component will

depend on its elastic modulus:higher modulus --> higher stress

Load distribution depends on

stress and component area

fraction


38/61

Stress Distribution Structures in series

Stress will be constant for two components

Displacement will depend on each

component's elastic modulus

Higher modulus --> lower strain

Same principles apply for all modes of

loading

Failure of the composite will occur when

stress in one component reaches its ultimate

strength

Failure in one area reduces the area

supporting the load

Stress increases in remaining regions -->

potential failure


39/61

Loading of Bone

Bone material is strongest in compression, intermediately

strong in tension, and weakest in shear

Strength also depends on orientation of trabeculae or osteons

with respect to the load

Pure Tensile Loading:

Primarily due to muscle action

Tensile fractures relatively uncommon, strict tension on a

bone will typically result in dislocation of a joint

Most tension fractures are avulsions of muscle origins or

insertions or occur in sesmoid bones


40/61

Loading of Bone Pure Compressive Loading:

Compression fractures occur primarily in trabecular bone

Cause is ususally traumatic impact or excessive muscle forces

or a severe reduction in mechanical properties, such as in

osteoporosis

Cracks propagate through lamina and trabecular structure is

crushed

Resistance of bone to tensile or compressive fracture is

dependent on:

Relative strength of cortical and trabecular components

Fraction of cross-sectional area of each component

If ultimate strength is exceeded in either component, failure

will generally occur


41/61

Loading of Bone

Bending

Many bones loaded in eccentric column mode which

induces bending

Bending fractures may result from

Normal modes of loading at increased forces

Jumping from a height

End loaded (cantilever) beam loading

Stopping fall with hand resulting in radial/ulnar

fractureThree-point bending

Bumper injuries

"Boot top" skiing fractures


42/61

Loading of Bone Bending

Fracture typically initiates on the tension surface and

then propagates medially

As long bone cross-sections are asymmetrical, the

rigidity and stress generated will not be the same for all

directions of bending

Torsion

Produces high shear and tensile stresses resulting in

spiral fractures

Fracture will occur at the level of lowest polar moment

of inertia

Typically mid-region of diaphysis


43/61

Loading of Bone -- Stress Concentrations

A hole in the cortex of a bone, with a size of to 20% of the

diameter of the bone, has the following effects

Reduces bending strength by 50 percent if located on

tensile surface

Reduces torsional strength by 50 percent and energy

absorption capacity by 75 percent if located at junction

of mid and distal tibia

Whether hole is empty or filled with a screw appears to

make little difference in effect on strength

Remodeling of bone or early filling of holes with new

bone tends to eliminate stress concentrations


44/61


45/61

Question 26

Cortical bone exhibits its greatest strength when subjected

to:

(1) Tension

(2) Torsion

(3) Bending

(4) Pure shear

(5) Compression


46/61

Question 26

Cortical bone exhibits its greatest strength when subjected

to:

(1) Tension

(2) Torsion

(3) Bending

(4) Pure shear

(5) Compression


47/61

Torsion and Bending of the Spine

Torsion applied to the spine is transmitted between the

vertebrae primarily through the facet joints, which are

compressed on one side and pulled apart on the other

If the torsional force is great enough, bony breakage

occurs on the compression side and ligaments ruptureon the tensile side

When the spine is flexed

The interspinous ligaments, ligamenum flavum, and

posteriour longitudinal ligaments on the posterior sideare in tension

The disc and vertebral body are compressed on the

anterior, concave side


48/61

Torsion and Bending of the Spine

Possible protection mechanisms for an intervertebral discA. If the posterior ligaments are stiffer than the disc, the

amount of deformation in forward flexion depends more on

the geometry of the posterior elements than on the disc. High

compressive stresses are prevented in the disc.

B. Contraction of the most posterior aspect of the muscles

tends to compress the posterior elements and stretch the

anterior elements. Stresses on the spine due to bending are

reduced.

C. If a strong contraction of abdominal muscles exists, the

abdominal cavity can support some of the weight of the

upper body because lateral deformation of the abdomen is

prevented. The load the spine must bear is decreased.


49/61

Internal Fixation Devices and

Mechanical Considerations -- Screws

To minimize stress concentrations at the bone-

screw interface (when no plate is used) screws

should be countersunk to reduce sharp angleinteractions

To reduce bending of the screw, which can

damage both the screw and the bone

Screws should be inserted perpendicular tothe bone or plate surface

Screw-plate junction should be rounded

Internal Fi ation De ices and


50/61

Internal Fixation Devices and

Mechanical Considerations -- Plates

Plates are designed for several different applications Thick plates are designed to facilitate primary bone healing

Thin plates are designed to allow physiological load bearing

following healing

A thick plate will have 5 to 10 times the rigidity of a thin one

In design, the effect of screw holes, and the resultant stress

concentrations, must be considered

A uniform cross-section must be obtained, including at screw-

plate interfaces, in order to eliminate stress-concentrationinduced weaknesses

I t l Fi ti D i d M h i l


51/61

Internal Fixation Devices and Mechanical

Considerations -- Bone-Plate Structures

Bending RigidityA bone-plate structure is 100 times more rigid if the plate is

placed on the side of the bone that experiences tension

during bending rather than compression

A fractured bone can withstand compressive loading, butnot tensile loading

If the bending axis is at right angles to the plate, the rigidity

is between the above two conditions, with the load falling

much more on the screwsA two plate system, oriented at 90 degrees to each other, is

insensitive to the plane or direction of bending and is more

rigid than a single plate in its optimum orientation


52/61


53/61

Question 27

A 23-year old man who sustains a transverse tibial mid-shaft

fracture undergoes internal fixation of the fracture with a

stainless steel plate and screws. One screw hole of the six-hole

plate is left open because it is located over the fracture site.

Firm fixation is obtained when two screws are placed proximal

to the fracture and three screws are placed distal to the fracture.Six weeks later, the plate fails at the open screw hole due to:

(1) Failure to bone graft that fracture.

(2) Delayed union due to stress shielding the bone.

(3) Stress concentration at the open screw hole.

(4) Use of a stainless plate rather than a titanium plate.

(5) A difference in torsional stiffness between the proximal

and distal halves of the plate.


54/61

Question 27

A 23-year old man who sustains a transverse tibial mid-shaft

fracture undergoes internal fixation of the fracture with a

stainless steel plate and screws. One screw hole of the six-hole

plate is left open because it is located over the fracture site.

Firm fixation is obtained when two screws are placed proximal

to the fracture and three screws are placed distal to the fracture.Six weeks later, the plate fails at the open screw hole due to:

(1) Failure to bone graft that fracture.

(2) Delayed union due to stress shielding the bone.

(3) Stress concentration at the open screw hole.

(4) Use of a stainless plate rather than a titanium plate.

(5) A difference in torsional stiffness between the proximal

and distal halves of the plate.


55/61

Response of Tissues to Load -- Bone

Wolff's Law -- Living bone adapts dependent upon the

stress or strain acting on the tissue

There is an “ideal” loading situation for each bone

which maintains normal bone mass

When additional force is applied, bone is deposited to

reduce the stress

When force is removed, bone is resorbed as it no longer

is needed to distribute the force

These changes occur over time, not instantaneously

When designing an implant or fixator, the ideal is to

maintain the same loading conditions for the bone


56/61

Response of Tissues to Load -- Joints

Mechanism of effect of immobilization (removal of load) onligaments and tendons is unknown

Immobilization tends to make joints "stiffer" in flexion and

extension

Require greater force to move joint Possibly due to:

Adhesions of articular tissue

Pannus formation

Capsular contractions - increased pressure

Ligament shortenings

Tensile properties of joints affected differently than "motion

properties"

Effect of Immobilization on Bone Ligament


57/61

Effect of Immobilization on Bone-Ligament-

Bone Structure -- Tensile Properties

Strength and energy absorbed to failure reduced

significantly for joint

Elastic modulus of ligaments reduced significantly

Ligament modulus dominates deformation as it is much

less than that of bone and components are in series

Significant weakening of bone-ligament junction

Failure ususally the result of an avulsion injury

Joint may take up to 1 year to regain normal propertiesafter 8 weeks of immobilization

Ligament properties seem to recover quickly

Bone-ligament junction recovers more slowly


58/61

Question 28

After six weeks of immobilization of the knee, the tensile load-deformation curves (structural properties) of the bone-ligament-

bone complex and the stress-strain curves (mechanical

properties) of the knee ligament substance will be:

(1) Unchanged

(2) Significantly softened with no change in load at failure

and tensile strength

(3) Significantly stiffened with no change in load at failure


(4) Significantly softened with decreased load at failure and

tensile strength

(5) Significantly stiffened with decreased load at failure and

tensile strength


59/61

Question 28

After six weeks of immobilization of the knee, the tensile load-

deformation curves (structural properties) of the bone-ligament-

bone complex and the stress-strain curves (mechanical

properties) of the knee ligament substance will be:

(1) Unchanged

(2) Significantly softened with no change in load at failure


(3) Significantly stiffened with no change in load at failure


(4) Significantly softened with decreased load at failure and

tensile strength

(5) Significantly stiffened with decreased load at failure and

tensile strength


60/61

Stress Shielding in Bone

Metallic implants with high elastic moduli typically used

in bone repair and joint replacement

Design of implant or fixation devices often creates parallel

structures

Femoral implant

Bone plate

Metal will bear larger portion of stress than bone, stress in

bone is reduced below normal levels

(1) Reduction in stress results in resorption of bone

(2) Reduction in bone cross-sectional area causes

further reduction in percent of stress borne by bone

(3) Results in further resorption


61/61

Stress Shielding in Bone

Therefore:

Don't want stiffest bone plate or implant possible, even

though these may be stronger as well

Must consider methods to transfer more stress to the

bone

Porous coatings

Press-fits

Collared prostheses

Less rigid prosthesis or plate to allow for greater

stresses in bone

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