BONE FRACTURE & HEALING Lecture 9

Transcription

1 BONE FRACTURE & HEALING Lecture 9 Presented by Paul Wong, PhD AMME4981/9981 Semester 1, 2016 The University of Sydney Slide 1

2 Mechanical Responses of Bone Biomaterial mechanics Failure Body kinematics Biomaterial responses 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 The University of Sydney Slide 2

3 MECHANICAL BEHAVIOUR OF BONE The University of Sydney Slide 3

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 type Compressive strength (MPa) Tensile strength (MPa) Shear strength (MPa) Density (g/cm 3 ) Cortical bone Trabecular bone Dentin Enamel The University of Sydney Slide 4

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 5

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 6

7 Viscoelastic Behaviour of Bone The University of Sydney Slide 7

8 Viscoelastic Behaviour of Bone The Young s modulus of trabecular bone can be related to strain rate E = E static dε dt 0.06 Lab tests typically conducted at strain rates between 0.01 and s -1 For typical impact injuries (e.g. falls, vehicular accidents): ε! = 10s 1 The University of Sydney Slide 8

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 9

10 Mechanical Models Maxwell Kelvin-Voigt Standard Serial Parallel Hybrid E d d d s h E 0! δ =! δ! s + δ d δ = δ s + δ d δ!! σ σ! ε = + E η f! = + k f c f = k δ c! s + δ (same displacement) σ = Eε + ηε! E! σ + σ η = EE η ε + ( E + )ε! 0 E0 The University of Sydney Slide 10

11 TYPES OF FRACTURE The University of Sydney Slide 11

12 Classification The University of Sydney Slide 12

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 13

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 14

15 Example Acute Trauma The University of Sydney Slide 15

16 Example Acute Trauma G Gross The University of Sydney Slide 16

17 Example Acute Trauma The University of Sydney Slide 17

18 Example Acute Trauma The University of Sydney Slide 18

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 19

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 20

21 Fracture Risk Factor of risk Φ = Applied Load Failure Load 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 The University of Sydney Slide 21

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 22

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 23

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 24

25 FRACTURE MODELLING The University of Sydney Slide 25

26 Bone Damage Oblique cracks (compression) The University of Sydney Longitudinal and transverse cracks (tension) Interlamellar separation (torsion) Slide 26

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 27

28 Griffith s Theory s a s For a thin rectangular plate with a crack perpendicular to the load: G = πσ' a E 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 G " = πσ & ' a E s f is the applied stress beyond which the material will fail If G G c, the crack will begin to propagate The University of Sydney Slide 28

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 K I = σ π a Fracture toughness: Takes different values when measured under plane stress and plane strain Can be related to Griffith s energy terms Plane stress: EG c K c = EG c Plane strain: Kc = 2 1 ν The University of Sydney Slide 29

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 K I = Yσ π a Y is a function of crack length and sheet width, given by: Y a W = π a sec W a s s W The University of Sydney Slide 30

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 31

32 Cyclic Loading Total strain includes several components ε = ε + ε + ε + ε total elastic plastic visco damage Cannot distinguish roles of elasticity, plasticity, viscosity or damage in a monotonic test to failure Need to test using cyclic loading The University of Sydney Slide 32

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 33

34 Stress-strain Relationship Bone Mechanics Handbook, 2003 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 The University of Sydney Slide 34

35 Bone Damage Oblique cracks (compression) The University of Sydney Longitudinal and transverse cracks (tension) Interlamellar separation (torsion) Slide 35

36 Damage Modelling P A P A D da n da D D ( x,n) n D = da da n DAMAGE COEFFICIENT D = Total damage area Total cross - sectional area A A Scalar variable used to quantify degree of damage 0 D 1 D = 0: no damage D = 1: rupture Local damage coefficient based on location (x) and direction vector of cross-section (n): = D The University of Sydney Slide 36

37 Damage Modelling ACCOUNTING FOR DAMAGE IN MECHANICAL BEHAVIOUR Property Defining equation Comments Elongation Apparent stiffness Δ = PL ( A A )E ( A A ) P E = D = ( 1 D) E Δ L D A L Note reduction in effective cross-sectional area Modulus of damaged material reduced by factor (1 D) Yield loading ( A A ) PY = σ Y = σ ( 1 D)A Y D σ Y is yield strength of undamaged material Damage could also be regarded as reducing yield strength by (1 D) The University of Sydney Slide 37

38 Damage Modelling EFFECT ON MECHANICAL PROPERTIES Property Defining equation Comments Young s modulus Stress-strain relationship 0 E = E 1 ( D) 0 σ = E ( 1 D)ε E 0 = undamaged Young s modulus From Hooke s Law Similar arguments can be made for other properties Plasticity Viscoelasticity Hardness However, D is not constant and increases over time, producing non-linear behaviour The University of Sydney Slide 38

39 Damage Evolution Kachanov s power law model (1986): D! = B ( σ ) eff N = σ apparent σ B = D 1 σ ref N apparent ( 1 D) N B or σ ref, 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 The University of Sydney Slide 39

40 Damage Evolution Krajcinovic s model (J Biomech 20:779, 1987) D = Kε Describes damage as a linear function of strain Fondrk s model (PhD dissertation, 1989) D! 1 D = B ε ( σ ) apparent N 1 D σ = ε σ apparent ref N Davy and Jepsen s fatigue model (2003) D! = B ( σ ) n apparent Simple power law relationship between damage rate and apparent stress (not effective stress) amplitude The University of Sydney Slide 40

41 Damage Evolution Zysset and Curnier s model (J Biomech 29:1549, 1996)! = d α! 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 The University of Sydney Slide 41

42 HEALING The University of Sydney Slide 42

43 Stages of Healing Circumferential lamellae Concentric lamellae Interstitial lamellae Osteon Periosteum Blood vessels in central (Haversian) canal Blood vessel in Volkmann s canal The University of Sydney Slide 43

44 Stages of Healing Restoration of original tissue structure, with mechanical properties equal to those before the fracture Stabilisation Mechanical stabilisation of fracture fragments, either through optimal reduction and fragment apposition, or callus formation Bone union Callus differentiation and remodelling, or direct haversian remodelling Haversianremodelling Growth of osteons to maximise bone strength Overlap between phases (i.e. not sequential) The University of Sydney Slide 44

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 45

46 Stabilisation via Callus Formation Bone fragments Spongy bone (internal callus) Cartilage (external callus) Fracture hematoma New bone Periosteum Internal callus External callus Martini et al. 2015, Fundamentals of Anatomy & Physiology, 10th ed. The University of Sydney Slide 46

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 47

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 48

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 49

50 Remodelling Tissues within callus are continuously remodelled Fracture hematoma Granulation tissue Cartilage Woven bone Lamellar bone 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 The University of Sydney Slide 50

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 51

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 52

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 53

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 54

55 Internal Fixation REALIGNING A BROKEN ARM The University of Sydney Slide 55

56 Future Techniques REPAIR OF LONG-BONE DEFECTS The University of Sydney Slide 56

57 Future Techniques REPAIR OF LONG-BONE DEFECTS Melissa Knothe Tate, et al. (2007). Testing of a new one-stage bonetransport 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 57

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 58

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 pm: Computer quiz in N216 (undergrads only) 3-5pm: Paper quiz in MTR 1 The University of Sydney Slide 59