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The University of Sydney Slide 1
BONE FRACTURE & HEALING
Presented byPaul Wong, PhDAMME4981/9981Semester 1, 2016
Lecture 9
The University of Sydney Slide 2
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
The University of Sydney Slide 3
MECHANICAL BEHAVIOUR OF BONE
The University of Sydney Slide 4
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
The University of Sydney Slide 5
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
The University of Sydney Slide 6
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 University of Sydney Slide 7
Viscoelastic Behaviour of Bone
The University of Sydney Slide 8
Viscoelastic Behaviour of Bone
– 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 −=!
The University of Sydney Slide 9
Viscoelastic Behaviour of Bone
– 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
The University of Sydney Slide 10
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
++=
+
The University of Sydney Slide 11
TYPES OF FRACTURE
The University of Sydney Slide 12
Classification
The University of Sydney Slide 13
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
The University of Sydney Slide 14
Classification
BY SEVERITY– Greenstick – incomplete
fracture– Simple – single fracture line
through bone– Comminuted – multitude of
bony fragments– Open / Compound – bone
penetrates skin
The University of Sydney Slide 15
Example – Acute Trauma
The University of Sydney Slide 16
Example – Acute Trauma
G Gross
The University of Sydney Slide 17
Example – Acute Trauma
The University of Sydney Slide 18
Example – Acute Trauma
The University of Sydney Slide 19
Example – Acute Trauma
– “Don’t worry about me, I’ll be OK. You guys go win this thing.”
~ Kevin Ware
The University of Sydney Slide 20
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
The University of Sydney Slide 21
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
The University of Sydney Slide 22
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
The University of Sydney Slide 23
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
The University of Sydney Slide 24
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?
The University of Sydney Slide 25
FRACTURE MODELLING
The University of Sydney Slide 26
Bone Damage
Oblique cracks (compression)
Longitudinal and transverse cracks
(tension)
Interlamellarseparation(torsion)
The University of Sydney Slide 27
Fracture Mechanics
Mode I– Tension– Opening
Mode II– In plane shear– Sliding
Mode III– Out of plane shear– Tearing
The University of Sydney Slide 28
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
The University of Sydney Slide 29
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:
The University of Sydney Slide 30
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
The University of Sydney Slide 31
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
The University of Sydney Slide 32
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 +++=
The University of Sydney Slide 33
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
The University of Sydney Slide 34
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
The University of Sydney Slide 35
Bone Damage
Oblique cracks (compression)
Longitudinal and transverse cracks
(tension)
Interlamellarseparation(torsion)
The University of Sydney Slide 36
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,
The University of Sydney Slide 37
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
The University of Sydney Slide 38
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
The University of Sydney Slide 39
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!
The University of Sydney Slide 40
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=!
The University of Sydney Slide 41
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
The University of Sydney Slide 42
HEALING
The University of Sydney Slide 43
Stages of Healing
PeriosteumCircumferentiallamellae
Concentriclamellae
Interstitiallamellae
Blood vessel inVolkmann’s canal
Osteon
Blood vesselsin central
(Haversian) canal
The University of Sydney Slide 44
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
The University of Sydney Slide 45
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
The University of Sydney Slide 46
Stabilisation via Callus Formation
Fracturehematoma
Bonefragments
New bone
Periosteum
Spongy bone(internal callus)
Cartilage(external callus)
Internalcallus
Externalcallus
Martini et al. 2015, Fundamentals of Anatomy & Physiology, 10th ed.
The University of Sydney Slide 47
Stabilisation via Callus Formation
– 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
The University of Sydney Slide 48
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
The University of Sydney Slide 49
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
The University of Sydney Slide 50
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
The University of Sydney Slide 51
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.
The University of Sydney Slide 52
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
The University of Sydney Slide 53
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
The University of Sydney Slide 54
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
The University of Sydney Slide 55
Internal Fixation
REALIGNING A BROKEN ARM
The University of Sydney Slide 56
Future Techniques
REPAIR OF LONG-BONE DEFECTS
The University of Sydney Slide 57
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)
The University of Sydney Slide 58
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
The University of Sydney Slide 59
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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