BONE FRACTURE & HEALING - University of...

The University of Sydney Slide 1

BONE FRACTURE & HEALING

Presented byPaul Wong, PhDAMME4981/9981Semester 1, 2016

Lecture 9


Mechanical Responses of Bone

– Previously…– Internal loading from

kinematics– Constitutive models and

relationships– Physiological responses to

mechanical stimuli(e.g. bone remodelling)

– This week– What happens when bone

fails?– The healing process

Bodykinematics

Biomaterial mechanics

Biomaterial responses

Failure


MECHANICAL BEHAVIOUR OF BONE


Strength of Hard Tissues

– Intrinsic factors– Natural variations between

and within individuals– Anatomical location, function,

loading environment and history, individual health (genetics, age, diet, etc.)

– Extrinsic factors– Measurement technique– Specimen treatment

(freshly excised, frozen, preserved, etc.)

Tissue typeCompressive

strength (MPa)Tensile strength

(MPa)Shear strength

(MPa)Density(g/cm3)

Cortical bone 10-160 45-175 50-70 1.8-2.2

Trabecular bone 7-180 0.1-66 1-17 1.5-1.9

Dentin 140-280 40-275 10-140 1.9

Enamel 95-386 30-35 6 2.2


Viscoelasticity

– Stress-strain behaviour can be time-dependent

– Elastic component– Viscous component

(depends on strain rate)– During a loading cycle:

– Viscoelastic materials exhibit hysteresis (energy dissipation), with energy loss given by area of loop

– Purely elastic materials do not– Viscoplastic materials develop

permanent strain


Viscoelastic Behaviour of Bone

– The mechanical properties of both cortical and trabecular bone (as well as other biological tissues) vary with strain rate

– This viscoelasticity is due to their composite structure– Collagen– Bone mineral (hydroxyapatite)– Bone cells– Bone marrow



– The Young’s modulus of trabecular bone can be related to strain rate

– Lab tests typically conducted at strain rates between 0.01 and 0.001 s-1

– For typical impact injuries (e.g. falls, vehicular accidents):

06.0

static dtdεEE ⎟⎠

⎞⎜⎝

⎛=

110sε −=!



– Differences in behaviour under quasi-static conditions and high strain rates can be quite large

– At higher strain rates, bone has a higher ultimate strength, but can fracture at a lower strain

– Cortical bone exhibits a creep fracture response

Guedes RM, Simoes JA, Morais JL, J Biomechanics 39:49-60, 2006


Maxwell Kelvin-Voigt Standard

Serial Parallel Hybrid

Mechanical Models

dsdd

ds δδδ +=

ds δδδ !!! +=cf

kf+=!

!δ

ησσ

ε +=E!

!

δδ !ckf s +=

εηεσ !+= E

(same displacement)

E0

E

h

( )εεη

ση

σ

!

!

00 EEEE

E

++=

+


TYPES OF FRACTURE


Classification


Classification

BY SHAPE– Transverse – perpendicular to long axis

of bone– Oblique – at an angle to axis– Spiral – runs around axis of bone;

produced by shear stresses spread along length of bone


Classification

BY SEVERITY– Greenstick – incomplete

fracture– Simple – single fracture line

through bone– Comminuted – multitude of

bony fragments– Open / Compound – bone

penetrates skin


Example – Acute Trauma



G Gross



– “Don’t worry about me, I’ll be OK. You guys go win this thing.”

~ Kevin Ware


Fracture Mechanism

– Arises from fatigue induced microcracking, which then progresses to catastrophic failure– e.g. Progressive failure of trabeculae in vertebral bodies

– Failure occurs due to a single loading event– Lifting a heavy load, abnormal muscle loading, falling

– Most common in:– Wrist/forearm– Hip– Spine


Fracture Risk

– Factor of risk

– Used to estimate probability of failure

– Φ<<1: Unlikely to fracture– Φ>1: Fracture predicted

– Only count fractures occurring with trauma less than or equal to a fall from a standing position

– Fracture risk increases with age– Hormonal changes in both men

and women– Increased bone porosity– Decreased geometric

properties and fatigue resistance

– More frequent adverse loading events (e.g. falls) and lower energy absorption

LoadFailureLoadApplied

=Φ


Fracture Risk

– Depends on:– Inherent strength of bone

• Geometry• Material properties

– Applied load• Magnitude• Direction, rate and mode

of loading

Geometry

Material properties

Loads

Boundary conditions


Ongoing Research

– Chicken or egg?– Fractures occur as a result of a fall

• Accounts for 90% of cases• Fall induced loading on greater trochanter causes bone to fail

– Fractures occur before the fall• Accounts for 10% of cases• Patient-based evidence• Only 2% of falls result in fracture• In side-impact automotive crashes, loading of greater trochanter

causes fracture in the acetabulum, not the femoral neck


Ongoing Research

– What influences fall severity?– Height and weight of individual– Speed of fall– Presence/absence of active protective mechanisms

(e.g. outstretched arms)– Energy absorption of soft tissues– Direction and point of loading

– How can these parameters be controlled to prevent injury?


FRACTURE MODELLING


Bone Damage

Oblique cracks (compression)

Longitudinal and transverse cracks

(tension)

Interlamellarseparation(torsion)


Fracture Mechanics

Mode I– Tension– Opening

Mode II– In plane shear– Sliding

Mode III– Out of plane shear– Tearing


Griffith’s Theory

– For a thin rectangular plate with a crack perpendicular to the load:

– G is the strain energy release rate (rate at which energy is absorbed by growth of crack)

– σ is applied stress, etc.

– The critical strain energy release rate corresponds to failure

– sf is the applied stress beyond which the material will fail

– If G ≥ Gc, the crack will begin to propagate

as s

𝐺" =𝜋𝜎&'𝑎𝐸

𝐺 =𝜋𝜎'𝑎𝐸


Irwin’s Theory

– Modification of Griffith’s theory– Stress intensity replaced strain energy release rate– Fracture toughness replaced surface energy

– Stress intensity for the rectangular plate

– Fracture toughness:– Takes different values when measured under plane stress and plane

strain– Can be related to Griffith’s energy terms

aKI πσ=

cc EGK = 21 ν−= c

cEG

KPlane stress: Plane strain:


Irwin’s Theory

– Correction factor– The expression for stress intensity differs for geometries other than a

centre-cracked plate– Need to introduce a correction factor, Y, to account for geometry

– Y is a function of crack length and sheet width, given by:

aYKI πσ=

⎟⎠

⎞⎜⎝

⎛=⎟⎠

⎞⎜⎝

⎛Wa

WaY πsec

as s W


Monotonic Loading

– Inelastic behaviour due to loading– Flow processes create

irrecoverable strain– Damage via formation of cracks

or voids– Loss of material continuity– Degrades stiffness, as well as

other mechanical properties


Cyclic Loading

– Total strain includes several components

– Cannot distinguish roles of elasticity, plasticity, viscosity or damage in a monotonic test to failure

– Need to test using cyclic loading

damageviscoplasticelastictotal εεεεε +++=


Stress-strain Relationship

– Classic elastic-plastic behaviour– Unloading curve is parallel to

initial elastic curve– Continues until compressive

yielding occurs (not shown)

– Viscoelastic behaviour– Closed hysteresis loop– Relaxation to zero stress at

zero strain


Stress-strain Relationship

Figure (d):– Strained to ~1.1% at 1%/sec and

unloaded at same rate– Unloading curve crosses zero stress

at about 0.25% strain with slope ~2/3 the initial modulus

– Residual compressive stress of ~26 MPa at zero strain undergoes relaxation to ~15.7 MPa 15 seconds after loading

– At that point, the recovery rate is probably not zero, but is nearly undetectable over the last 5 seconds

Bone Mechanics Handbook, 2003


Bone Damage

Oblique cracks (compression)

Longitudinal and transverse cracks

(tension)

Interlamellarseparation(torsion)


Damage Modelling

DAMAGE COEFFICIENT

– Scalar variable used to quantify degree of damage–– D = 0: no damage– D = 1: rupture

– Local damage coefficient based on location (x) and direction vector of cross-section (n):

10 ≤≤ D

A

AD

P

P

dAn dAD

AAD D==

areasectional-crossTotalareadamageTotal

( ) n

nD

dAdAD =nx,


Damage Modelling

ACCOUNTING FOR DAMAGE IN MECHANICAL BEHAVIOUR

Property Defining equation Comments

Elongation Note reduction in effectivecross-sectional area

Apparent stiffness Modulus of damaged material reduced by factor (1 – D)

Yield loading σY is yield strength of undamaged material

Damage could also be regarded as reducing yield strength by (1 – D)

( )EAAPL

D−=Δ

( ) ( )LAED

LAAEP D ⋅−=

−= 1

Δ

( )( )AD

AAP

Y

DYY

−=

−=

1σ

σ


Damage Modelling

EFFECT ON MECHANICAL PROPERTIES

– Similar arguments can be made for other properties– Plasticity– Viscoelasticity– Hardness

– However, D is not constant and increases over time, producing non-linear behaviour

Property Defining equation Comments

Young’s modulus E0 = undamaged Young’s modulus

Stress-strain relationship From Hooke’s Law

( )DEE −= 10

( )εσ DE −= 10


Damage Evolution

– Kachanov’s power law model (1986):

– B or σref, and N are experimentally determined material parameters– Predicts damage accumulation at an accelerating rate for a constant

stress– Kachanov’s model tended to overestimate softening due to damage

accumulation compared to tensile loading experiments of human and bovine bones

( )( )

N

ref

apparentN

apparentNeff DD

BBD ⎟⎟⎠

⎞⎜⎜⎝

⎛

−=⎟⎟

⎠

⎞⎜⎜⎝

⎛

−==

11 σ

σσσ!


Damage Evolution

– Krajcinovic’s model (J Biomech 20:779, 1987)

– Describes damage as a linear function of strain– Fondrk’s model (PhD dissertation, 1989)

– Davy and Jepsen’s fatigue model (2003)

– Simple power law relationship between damage rate and apparent stress (not effective stress) amplitude

εKD =

( )N

ref

apparentNapparent

DDBD ⎟⎟

⎠

⎞

⎜⎜

⎝

⎛⎟⎠

⎞⎜⎝

⎛ −=⎥⎦

⎤⎢⎣

⎡ −=

σ

σ

εσ

ε11!

( )napparentBD σ=!


Damage Evolution

– Zysset and Curnier’s model (J Biomech 29:1549, 1996)

– Most general damage model to date in application to bone– Plastic flow and damage accumulation are intrinsically related– d is used deliberately to distinguish it from D, which was defined in a

more heuristic fashion– α is plastic strain

α!! =d


HEALING


Stages of Healing

PeriosteumCircumferentiallamellae

Concentriclamellae

Interstitiallamellae

Blood vessel inVolkmann’s canal

Osteon

Blood vesselsin central

(Haversian) canal


Stages of Healing

– Stabilisation – Mechanical stabilisation of fracture fragments, either through optimal reduction and fragment apposition, or callus formation

– Bone union – Callus differentiation and remodelling, or direct haversianremodelling

– Haversian remodelling – Growth of osteons to maximise bone strength– Overlap between phases (i.e. not sequential)

Restoration of original tissue structure,with mechanical properties equal

to those before the fracture


Stabilisation via Callus Formation

– Bone healing is ultimately a physiological process

– Surgical interventions merely serve to prevent mishealing

– Endosteal and periosteal calluses act to stabilise fracture fragments

1. Induction and proliferation of undifferentiated periosteal tissue

2. Differentiation of callus tissue into woven bone

3. Remodelling of woven bone into osteonal or lamellar bone



Fracturehematoma

Bonefragments

New bone

Periosteum

Spongy bone(internal callus)

Cartilage(external callus)

Internalcallus

Externalcallus

Martini et al. 2015, Fundamentals of Anatomy & Physiology, 10th ed.



– Opportunity windows for induction and proliferation are finite

– Suppressed by rigid fixation and excessive motion– Strength of callus increases with time over 5-28

days post-fracture– Callus strength

– Not easy to predict accurately, even with radiographic estimates of callus size

– Tensile strength appears to be related to transverse area of new bone uniting fracture fragments


Bone Union

– Formation of an intact, bony bridge between fragments– Can occur:

– With or without previous callus formation– With or without direct contact between bone fragments

– Contact healing– Osteons grow directly from one fragment to another– Does not require interposed lamellar bone

– Gap healing– Lamellar bone forms within fracture gap, with collagen fibres oriented

perpendicular to long axis of bone– Osteons grow through lamellar bone between fracture fragments


Bone Union

– Hindered when physiological conditions are less than ideal– Axial misalignment– Insufficient stabilisation– Excessive fracture gap (more than 1mm)

– Can lead to:– Non-osteonal healing– Hypertrophic non-union when fibrous tissue persists within callus


Remodelling

– Tissues within callus are continuously remodelled

– Biological trade-off between quick response and strength– Given time and ideal physiological conditions (including the reintroduction of

typical stress patterns), the fracture site should become effectively indistinguishable from the surrounding bone

Fracture hematoma

Granulation tissue Cartilage Woven

boneLamellar

bone


Reasons for Intervention

TO PREVENT MISALIGNED HEALING

– Fractured bones can shift at the discontinuity

– The body cannot realign bones by itself and will attempt to repair the fracture site via callus formation

– This causes the bones to rejoin in the misaligned state, leading to physical deformity, loss of function, pain, etc.


Reasons for Intervention

TO ALLOW COMPLETE HEALING

– Stage I: Bone fails through original fracture site with a low stiffness, soft tissue pattern

– Stage II: Bone fails through original fracture site with a high stiffness, hard tissue pattern

– Stage III: Bone fails partially through original fracture site and partially through previously intact bone with a hard tissue pattern

– Stage IV: Site of failure not related to original fracture


External Fixation

– External (transcutaneous) fixation devices aim to keep fractured bones stabilised and in alignment

– Can be adjusted to ensure bones remain in an optimal position while they are healing

– Commonly used in children, or when skin over fracture site has been damaged

– Care must be taken to avoid infection


Internal Fixation

– Allows early mobility and faster healing

– Unless the internal fixation causes problems, it is not necessary or desirable to remove it

– Excellent long term prognosis


Internal Fixation

REALIGNING A BROKEN ARM


Future Techniques

REPAIR OF LONG-BONE DEFECTS


Future Techniques

REPAIR OF LONG-BONE DEFECTS

Melissa Knothe Tate, et al. (2007). Testing of a new one-stage bone-transport surgical procedure exploiting the periosteum for the repair of

long-bone defects. Journal of Bone and Joint Surgery, vol. 89-A(2)


Summary

– Bone (and other biomaterials) exhibit viscoelastic behaviour, which is difficult to quantify

– Bones fail via fracture– Damage starts with microcracking, which weakens the bone– Cyclic loading tends to increase crack lengths– At some point (usually upon application of an unexpectedly heavy

load), the critical fracture toughness is exceeded– Healing is an endogenous physiological process– We can facilitate bone healing by providing additional stabilisation at the

point of fracture


Coming Up…

Week 11– Guest lecture by Jim Pierrepont (Optimised Ortho) on clinical applications of

modelling– Informal mentoring session (careers, life goals, balance, etc.) for those who

are interested

Week 12– 12-2pm: Computer quiz in N216 (undergrads only)– 3-5pm: Paper quiz in MTR 1

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