Module 2 Flashcards
Viscoelasticity
Visco -> fluid -> resistance to flow
Elastic -> solid -> return to original shape
Stress-Strain relationship of viscoelastic materials
For viscoelastic materials, stress-strain relationship is time dependent (not just dependent on strain as for elastic materials).
- CREEP BEHAVIOUR (CONSTANT LOADS): Increasing deformation (Strain) for a constant load (stress) as t -> infinity
- STRESS-RELAXATION BEHAVIOUR (CONSTANT DEFORMATION): Decreasing load impact (stress) under constant deformation (strain) as t -> infinity
- HYSTERESIS LOOP: representation of the change in loading/unloading of viscoelastic materials and this can be quantified by energy displaced.
Viscoelastic models
SPRINGS represent instant elastic deformation
DASHPOT demonstrates resistance with the deformation rate proportional to stress
- Maxwell (spring and dashpot in series)
- Kelvin - Voigt (spring and dashpot in parallel)
- SLS (combination)
Cortical Bone - Composition and Microstructure
- hard dense outer ‘coating’ of bone
- hierarchal structure starts with collagen fibrils progressing to third level lamellar, Haversian, laminar and woven structures.
- osteocytes lie in the lacunae (between lamellae) and blood vessels lie in the Haversian canals.
- osteocytes respond to mechanical strain and to send signals of bone formation or bone resorption to the bone surface (mechanotransduction), both to modify their microenvironment, and to regulate both local and systemic mineral homeostasis.
- 80% total bone mass - due to <30% (volume fraction of 0.7) porosity compared with trabecular bone
Cortical Bone - Material Properties
- Transversely isotropic - properties the same about transverse axis (x-y), but unique about z axis (longitudinal)
- Stronger in compression than tension, and in longitudinal direction than transverse.
- small amount of deformation in bone allows bone to absorb energy, giving ‘ductility’ or toughness property (still brittle, hence fractures, stiff for motion and load transmission).
- mechanical properties vary with loading rate and magnitude (viscoelastic).
- also vary due to age, gender, diesease ie. strength reduced by 2% per decade (apparent density reduced by 2% per decade too), ultimate strain reduced by 10% per decade.
Trabecular Bone - Composition and Microstructure
- ‘spongy’ layer underneath cortical bone
- structural hierarchy finishes predominantly with Haversian structure with some lamellae.
- this characterises its approx. 80% porosity hence why trabecular bone only accounts for approx. 20% total bone mass.
Trabecular Bone - Material Properties
Porosity characterises low apparent density
- stress-strain curves depend on apparent density
- varied nature of porosity means strength and stiffness can vary by two orders of magnitude in the same anatomical region
Similarly (variation) anisotropic (modulus & strength can vary 8 times).
Analysis complicated by variation (aligned oblique to anatomic axis)
Yield strains appear to be isotropic
Bone Creep, Failure and Fatigue
Creep refers to the development of residual strains when bone is loaded beyond the yield point. As such, the Young’s modulus is reduced when loaded beyond the yield point and this implies a reduction in strength ie. Fatigue.
Failure occurs when the maximum principal strain (or stress, dependent on which criteria used) of the element exceeds the maximum allowable on-axis uniaxial strain. This is importantly becomes identifiable for bone as complex strains for any state of loading can be converted to principal strains which are then independent of apparent density - the limiting microstructure parameter of bone.
Muscle - Composition and Microstructure
- Three levels of structural hierarchy
1. Whole muscle organ encased by epimysium
2. Fascicle encased by perimysium
3. Muscle fibre encased by endomysium - Muscle fibres consist of sarcomeres, repeated chains of this fundamental sub-unit is called a myofibril.
- Sarcomeres consist of thin and thick filaments
- THIN: Actin double stranded helix, tropomyosin within the groove of the actin helix and troponin at regular intervals
- THICK: Myosin molecules bundled together (long tail and large head) - arranged in a regular hexagonal lattice and switch polarity at m-line.
Muscle - Mechanical properties
- provide the active torque about skeletal joints
- (via) sliding filament theory: thick and thin filaments slide and overlap via cross bridge cylce (myosin head binds to actin)
- STRENGTH of contraction force determined by amount of OVERLAP (length): total tension (isometric test) – passive force (relaxed muscle’s resistance to external lengthening (elastic tension)) = active force (cross-bridge cycling)
- SPEED (velocity) of contraction determined by RATE of cross-bridge cycling.
- For large loads, muscle contracts slower, allowing more time for cross bridge connections -> more force.
- For smaller loads, muscle contracts more quickly as less force is required therefore less time for cross-bridge connection is needed.
Intervertebral Disc - Composition and Microstructure
- 23 intervertebral discs connect the vertebral bodies
- NUCLEUS PULPOSIS: 50% of IVD volume, a fluid-like viscous gel (70-90% water, proteoglycans and a random collagen (II) network). Creates swelling pressure similar to cartilage by PGs attracting H2O, resistance provided by annulus fibrosis:
- ANNULUS FIBROSIS: 20-25 lamallae of collagen (I), with collagen content highest toward outer layers, fibres cross hatch +/- 30-35 degrees. Connected to vertebral body by cartilaginous end plate:
- CARTILAGINOUS ENDPLATE: hyaline cartilage approx 0.6mm thick.
Intervertebral Disc - Mechanical Properties
- Allow limited relative motion b/w bones, transmit compressive load in spine.
- similar poroelastic behaviour to cartilage.
- similar non-linear elastic behaviour to tendons and ligaments
- similar to an inflated tyre supporting a car: pulposis pressurised, contained by tension in the annulus
- Annulus Fibrosis: specific collagen orientation optimised for maximum strength and stiffness; resisting hoop and axial stresses, generates osmotic pressure and gives load bearing properties. Strongest in A-P direction to support anterior bending.
- Viscoelastic - important for prolonged static loading-instantaneous response followed by creep, experiences reverse behaviour in unloading, but doesnt return to due to fluid loss.
Ligament - Composition and Microstructure
- 70-80% collagen (I), 1-15% elastin, 1-3% proteoglycan
- Fascicles are not necessarily aligned with the main structure. This is important because it allows ligaments to offer their stability, as well as kinematic freedom of joints.
Ligament - Mechanical Properties
- Connect bone to bone - joint stabiliser
- crimped nature of collagen acts viscously (resistance)
- elastin has elastic ability to quickly return to shape
- Pre-conditioning: toe region sees large strains only producing small stresses due to less aligned collagen fibres (crimp). Subtle viscoelasticity -> time dependency -> strain rate dependency (as E increase, K increases)
- Creep
- Stress-relaxation
- As viscoelasticity is only subtle, hookean laws apply once all collagen fibres are elongated/recruited.
Articular Cartilage - Composition and Microstructure
- heterogeneous -> 3 phases
1. EXTRACELLULAR MATRIC PHASE: Collagen (II) fibrils entrap proteoglycan aggregates that swell in water. regulated by chondrocytes and chondrons (mechanobiology)
2. FLUID PHASE: critical to mechanical behaviour,
due to swelling and flow of water in and out of the cartilage matrix due to porosity of the surface layer.
3. IONIC PHASE: Carboxyl (COO-) and sulphate (SO3-) ions maintain electroneutrality with Ca2+ and Na+, trapping H2O -> hydrogel with resilience and stress distribution properties - highly organised and distinct zonal structure implies specific zonal functions
