Load Deformation Curve: Elastic and Plastic Regions

• Load deformation curve illustrates a material's response to load.
• Two main regions of the load deformation curve include, elastic and plastic

Elastic Region

• Characterized by a linear stage.
• Deformation in the elastic region is not permanent.

Plastic Region

• Characterized by a non-linear stage.

• Deformation in the plastic region is permanent.

• The yield point separates the elastic and plastic regions.

• Ultimate load represents the highest load that a structure can bear before failure occurs.

• Ultimate deformation occurs when the bone or material loses structural integrity.

• Stiffness is the resistance to deformation under loading.

• Stiffer materials exhibit less deformation under load.

• Energy to failure is the total energy required to break a bone or material.

• The stress-strain curve normalizes load and deformation.

• The stress-strain curve describes the material properties.

• The stress-strain curve functionally looks identical to the load-deformation curve

Material Properties

• Stress is the load normalized into pressure.
• Strain is the deformation normalized as a percentage of the material's total length.

Modulus of Elasticity

• Also known as Young's Modulus (E).
• E = Stress/Strain
• Structural properties are compared to material properties when assessing bone strength and load post-fluoride consumption in rats.
  • There is a decrease in strength.
  • A minimal change in load is observed.

Force Application

• Force can be applied in various ways, including fatigue, direction, linear vs. rotational/torsional, and speed.
• Exposure to stress can occur through repetition.
• Constant stress can result in increased repetition
  • Leading to permanent micro-strain
  • Leading to increased deformation
• Standardizing the strain of a material can reduce stress.

Direction of Load

• Materials can be isotropic or anisotropic depending on load direction.
• Isotropic material properties are the same in every direction and are non-orientation dependent.
• Anisotropic material properties vary by the direction of the load and are orientation dependent.

Cortical Bone Strength

• Cortical bone strength is 200-250MPa in compression.
• 150MPa in tension with longitudinal orientation.
• 50MPa in tension with transverse orientation.
• Shear stress is present in the torsion of long bones.
• Torsional stress is measured as T (tau).
  • T = Tr/J, where T = Torque/force, R = radius, and J = polar moment of inertia.
• J describes how well a structure can resist torsion relative to its shape.

Speed and Material Properties

• Bone properties are strain/rate dependent.
• Bones become more brittle but stronger as loading rates increase.
• Bone failure depends on both the direction and rate of loading.

Viscoelasticity

• Measurement of a fluid's resisitance to change shape
• Viscosity occurs due to internal friction between molecules, which opposes the development of velocity differences within a fluid.
• Purely viscous liquid will resist strain in a linear manner as stress is applied over time.
• A purely elastic solid will deform readily when stress is applied and then return to its original form when stress is removed.
  • Behavior is not affected by rate of loading.

Viscoelastic Materials

• Human tissues are viscoelastic.
• Their mechanical behavior in response to loading is attributable in part to the behavior of the fluid component and in part to the behavior of the solid compartment.
  • Strain energy is stored in the material as potential energy, and some energy is dissipated as heat.
• This creates interesting properties.
• A hysteresis loop is created because the loading path does not adhere to the unloading path.
  • If strain was limited to the elastic region, the curve will return to 0.
  • If plastic strain occurred, the curve will be offset to the right.
• Creep occurs when stress is constant but strain increases over time.
• Stress-relaxation occurs when strain is constant, but stress decreases over time.

Bone Matrix

• Bone matrix constitutes are, inorganic and organic components.
• Can be organized as cortical and trabecular bones.
• How organization facilitates the functions of the bones.

Inorganic Component

• Bone tissue is about 65% hydroxyapatite.
• Stores/contains 99% of the body's calcium.
• Provides bitterness and compressive strength.

Organic Component

• Bone tissue comprises roughly 33% collagen.
• Provides flexibility, ductility, and tensile strength.
• Insufficient organic component can lead to brittle bones.
• Bone cells account for 2% of bone.

Bone Cells

• Osteoblasts
  • Create new bone matrix
  • Smaller cells that lie on the surface of bone
• Osteocytes
  • Maintain the bone matrix
  • Sit in lacunae in the matrix
• Osteoclasts
  • Large multinucleate cells
  • Breakdown bone matrix
  • Sit down in resorption bays

Cartilage Functions

• Withstand and distribute applied loads to protect underlying bone from high contact stresses.
• Allow relative motion of articulating surfaces with low friction and minimal surface wear

Cartilage Structures

• 10% chondrocytes
• 90% extracellular matrix
• H20
• Collagen type 2
• Proteoglycan aggregates
• Absence of blood vessels and lymphatics
• Innervation

Mechanical Properties

• Cartilage can be explained by a two phase model with two components including, fluid phase and solid phase
• Fluid phase:
  • the hydrostatic pressure in the interstitial fluid supports the initial compressive load
• Solid phase:
  • proteoglycans and collagen ii interaction

Biomechanics of Bone

• Mechanisms in which bone changes shape:
  • Growth
  • Modelling
  • Remodeling

Bone formation/ossification

• Endochondral ossification:
  • From hyaline cartilage
  • Ossification centers and long bones
• Intramembranous ossification:
  • From mesenchymal cells
  • Flat and irregular bones

Bone growth

• Mesenchymal stem cells
  • These are stem cells of embryonic connective tissue.
  • Differentiate into osteoprogenitor cells on the periosteal and endosteal surfaces of bones.
• Osteoprogenitor cells
  • Derived from mesenchyme stem cells and give rise to osteoblasts.
• Osteoblasts
  • Can both, become trapped within the osteoid as they are making it to became osteocytes.
  • Or remain on the surface of the bone as bone-lining cells after the osteoid has been made.
• Bone-lining cells
  • Derived from osteoblasts, regulate the movement of calcium into and out of bone.
  • May activate osteoclasts and help maintain osteocytes.
• Osteocytes
  • Maintain bone.
  • Monitor and maintain the bone matrix
• Osteoclasts
  • Derived from a lineage of white blood cells, notably monocyte progenitor cells, which differentiate into osteoclasts.
• Skeletal development begins in utero and continues for about 25 years.
  • Bone number increases.
  • Mineralization increases.
  • Bone size increases.
  • Bone proportions change.
  • Patterns and magnitudes of forces change.
• Bone modelling
  • Bone grown in length
  • Bone diameter increases in response to longitudinal length.
  • The diaphyseal cross-section therefore increases.
  • The medullary cavity also increases.
  • Some components of the original bone are still present.
• Bone strained
  • Bone has not changed in size but shape.
  • The entire diaphyseal cross-section has shifted.
  • Almost all original bone has been removed.

Haversian System Formation

• Osteon creation
  1. .Osteoclasts form a cutting bone
  2. Osteoblasts narrows the bone by filling in from the perimeter
  3. Reversal zone is where resorption and formation are coupled together
  4. Multiple layers of lamellae bone forms the ring structure
  5. Once central canal is formed, osteoblasts converts to osteocytes
  6. Endosteal cells line the canal completing a new osteon
• Process takes 4 months to complete
• Remodeling in trabecular bone
  • The Trabecular struts have similar diameters to secondary osteons.
  • Surface remodeling occurs instead.
  • Osteoclasts dig a trench and than osteoblasts start to refill the resorption cavity.
• Osteopetrosis
  • Rare disease when bone resorption is defective.
  • Bone can be laid down but than not remodeled.
  • Bones become extremely dense and solid, often without a medullary center forming properly.

Physical Activity and the Skeleton

• Wolff's Law
  • Bone will change in mass and geometry to meet the physical demands placed upon it.
• Mechanostat theory
  • An extension of the ideas proposed by Wolff in which bone adapts to function mechanically as required by detecting and responding to mechanical loads.
• Frost's Mechanostat Concept
  • Trivial loading
  • Physiological loading zone
  • Overload zone
  • Pathological overload

Biomechanics of Bone

• Adaptation in bone: Loss
  • Microgravity and bedrest:
  • Microgravity is detrimental to bones
    • 4 month to 6 month exposure
    • 4% decrease in cortical thickness
    • 15% increase in cortical porosity
    • Total BMD does not recover post flight
    • Weightbearing bones are most impacted
  • Clinical practice
    • 6 weeks no weight bearing post surgery
    • 34.8 + or - 7.7 years
    • Changes occur in both cortical and trabecular bone
    • Material lost present at 6 weeks
    • -4% loss in stress across 6 weeks
    • Loss can persist despite the return of weight bearing

Bone

• To get back bone, use:
  • A simple contraption that loads a bone
  • Repetitive bone loading can increase bone parameters
  • Not all loading is equal
  • Increased frequency, spaced with short breaks
• Getting bone back by:
  • Not if but how we load it
  • Combinations of exercise interventions are effective
  • Resistance and high rate of loading
  • Whole body vibrations
• Bone Failure - Acute Loading
  • Acute fractures increase exponentially with age
  • With safey factor implying that bomes are built not only withstand forces, but also to have extra capacity to withstand extra force - safety factor.
  • With amount of bone.
• When safety factor is reached
  • Acute fracture occurs when external force is greater than what the bone can withstand.
  • Resulting fracture is dependent on the vector of the force

Fatigue Loading

• Applies to most materials
  • Repeated loading of a specimen as stresses lower than failure stress, can cause fracture
  • Progressive degradation in stiffness under repetitive load
  • Repetitive loading results in microdamage
• Mitigating Fatigue Loading
  • In two ways
  • Intracortical remodeling can be targeted to repair microdamage
    • Mechanotransduction plays a role in identifying where bone repair needs to occur. A secondary osteon of new bone is created in place of damaged bone
  • Bone can resist propagation of the crack/damage
    • Various structures assist with this
      • Voids
      • Lamellae (layers of bone)
      • Collagen fibrils
      • Cement lines

Fatigue Loading

• Concerns the trabecular bone
  • Trabecular bone is more elastic
    • Compression to 85% of the original height, 96% of original height is regained, indicating that this strain of 0.15 has created some permanent damage, but also the recovery is relatively good
  • Cortical bone would likely fracture under 2% strain
• Types of Fractures:
  • Transverse
    • Complete fractures that transverse the bone perpendicular to the axis of the bone
    • They usually are caused by tensile or bending forces, or a forceful impact
    • The bone breaks at a 90 degree angle to the long axis of the bone
  • Comminuted
    • More than 2 bone components are created
    • Very high rate of loading
    • Soft tissues are minimally damaged, bone displacement is minimal
  • Stress
    • Occurs due to a mismatch of bone strength and chronic mechanical stress
    • Low energy repetitive event
  • Greenstick
    • Partial thickness fracture where only the cortex and periosteum are interrupted
    • Common in long bones with falling on an outstretched hand
    • Approx 5.3% pediatric fractures are greenstick
    • Most common under 10 years old
    • Unique fracture that requires compliant bones
• Ageing of the Skeleton
  • Osteopenia
    • Low bone mass
  • Osteoporosis
    • Bone mineral density of young adult average
• Ageing of Trabecular Bone
  • Bones undergo a constant state of remodeling
  • Adaptive remodeling
    • There is preferential resorption of unloaded trabecular and maintenance of loaded trabeculae
  • Metabolic remodeling
    • There is uniform thinning and perforation of the trabeculae with age, as this process is age influenced
  • Microdamage remodeling
    • There is preferential remodeling of damaged trabeculae, some may be resorbed completely