ME 518 - Lecture 3
Hard Tissues
Topics
- Consist of cortical bone, trabecular bone, and
marrow
- Distribution of each depends on anatomical location
- Long bones (See Figure 1)-
- Tubular in shape
- Length of bone greater than breadth
- Some long bones may actually be short
- Consist of a shaft and two enlarged, curved ends
- Shaft of bone consists of cortical bone surrounding medullary
cavity (filled with marrow) - diaphysis
- Ends of bone consist of cortical shell of bone surrounding
trabecular bone
- Examples:
- Femur (thigh)
- Tibia and fibula (calf)
- Humerus (upper arm)
- Radius and ulna (lower arm)
- After birth, longitudinal growth of long bones occurs in two
regions
- Epiphysis -
- Highly trabecular region at most proximal and distal ends
of long bone
- Metaphysis -
- Highly trabecular region at proximal and distal end of diaphysis
- The epiphysis and methaphysis are separated by epiphyseal
cartilage plate (growth plate) that ossifies when growth
has stopped
- Throughout life, radial growth can occur at two surfaces
- Periosteum -
- Outer surface of bone, through which blood supply reaches
the bone
- Endosteum -
- Inner surface of bone, in contact with medullary canal
- Bone can be deposited or resorbed at these two surfaces
- Resorbtion can occur in any region of the bone, typically
followed by deposition of bone in the same region -- termed remodeling
- Short bones (See Figure 2A)-
- Cuboidal in shape
- Consist of cortical shell with inner trabecular core
- Exist only in the wrist and foot
- Flat bones (See Figure 2B)-
- Consist of two plates of cortical bone with trabecular tissue
in between
- Generally curved rather than flat
- Examples:
- Calvaria (top of skull)
- Sternum (breast bone)
- Scapula (shoulder blade)
- Ribs
- Irregular bones (See Figure 2B)-
- Various shapes
- Composition depends on bone
- Examples:
- Facial bones
- Vertebrae (bones of spine)
- Consist of thin cortical shell surrounding trabecular core
- Combination of:
- Mineral phase (69 wt%):
- Majority is hydroxyapatite [HA] (calcium phosphate)
- Also citrate, carbonate, fluoride, and hydroxyl ions
- Organic phase (22 wt%)
- Collagen (90-96 wt%)
- Cellular components (osteoclasts, osteoblasts,
osteocytes)
- Water (9 wt%)
- Hydroxyapatite crystals form slender needles in the
collagen fiber matrix
- The resulting mineral containing fibrils form lamellar
sheets
- Also known as compact bone
- Two types of cortical bone based on their microstructure
- Woven bone - forms de novo (does not
need previous hard tissue or cartilage)
- Found in fetuses and children up to age 4
- Located at the growth plate
- Main function in adulthood is skeletal repair and defense
- Found when rapid bone growth occurs as a result of disease
or trauma
- Forms callus around fracture site
- Collagen fibers randomly oriented at the tissue level and
loosely packed
- Loose packing results in generally reduced density (not due
to low mineralization per fiber)
- Lamellar bone - requires substrate on
which to form
- Forms where bone has previously not existed
- Lamellae of mineral impregnated collagen fibers arranged in
cricular rings around the inner (endosteal) and outer (periosteal)
circumference of a whole bone
- Three types of cortical bone exist based on the arrangelment
of the lamellar bone (See Figure 4)
- Circumferential lamellar bone
- Layers of lamellae form circular rings around the inner (endosteal)
and outer (periosteal) surfaces of a whole bone
- Primary osteonal bone
- Forms where bone has previously not existed
- Composed of a vascular channel, surrounding concentric lamellae,
and associated bone cells (osteocytes)
- Each set of the above comprises a single osteon
- Up to 20 collagen and mineral based lamellae spiral helically
around each vascular channel
- Lamellae adjacent to vascular channels serve as storage space
for exchangable calcium ions
- Secondary osteonal bone
- Osteonal bone is also called haversian bone
- Forms as a result of resorption of existing bone and deposition
of new bone
- Larger vascular channel and more lamellae than primary osteons
- Each osteon is separated from the surrounding extraosteonal
bone matrix by a cement line, unlike primary osteons which
have no cement lines
- Secondary osteons are approximately 200 to 300 µm in
diameter in adult human bone
- Components form a hierarchy in organization (See Figure 3)
- Cortical Macrostructure
- Osteons and circumferential lamellae are alligned predominantly
along the axis of a long bone and according to stress alignment
in bones with less dominant axes
- Also known as cancellous bone or spongy bone
- Structural matrix of bony plates, beams, and struts with marrow
in intervening spaces (See Figure 5)
- Structure of beams and struts depends on location and loading
situation
- Trabecular struts typically 150-300 µm in diameter
- Form a three-dimensional lattice structure with optimized
strength to weight ratio in healthy bone
- Microstructure of Trabecular Bone
- Trabeculae formed from lamellar bone (See Figure 4)
- Macrostructure of Trabecular Bone
- Dependent on anatomic location
- Generally develops in response to loading situation at site
- Vertebrae (See Figure 5)
- Young adults: Vertical plates and horizontal struts
- Older adults: Vertical beams and horizontal struts
- Femoral Neck (See Figure 6)
- Trabeculae form tensile and compressive bands which are directed
along the force trajectories experienced by the femoral neck
- Femoral-Tibial Joint (Knee)
- Trabeculae aligned along direction of long bones, with connecting
horizontal struts
- Trabecular macrostructure can be defined in terms of quantities
such as
- Predominant orientation
- Mean trabecular plate separation
- Mean trabecular thickness
- Trabecular density
- Connectivity
- Multiphasic structure consisting of 4 basic materials plus
the gingiva (gums) and alveolar bone of the jaw
(See Figure 7)
- Enamel:
- 97% calcium phosphate salts in the form of large HA crystals
- Hardest substance in the body
- Dentin:
- Similar distribution of collagen and matrix to cortical bone
- Properties similar to cortical bone
- Pulp:
- Marrow-like substance through which blood supply is provided
to dentin -- also contains nerve cells and thin collagenous fibres
- Cementum:
- Coarsely fibred bone-like substance that does not contain
canaliculi, Haversian systems, or blood vessels
| Young's Modulus [GPa]
| Shear Modulus [GPa] | Compressive Strength [MPa]
| Tensile Strength [MPa] |
Shear Strength [MPa] | Density [g/cm3]
|
| Cortical Bone | 4 - 27
| 2 - 9 | 10 - 160
| 45 - 175 | 50 - 70
| 1.8 - 2.2 |
| Trabecular Bone | 1 - 11
| | 7 - 180*
| | | 1.5 - 1.9
|
| Enamel | 13.8
| 6 - 10 | 140 - 280
| 40 - 275 | 10 - 140
| 1.9 |
| Dentin | 20 - 84
| 29 | 95 - 386
| 30 - 35 | 6
| 2.2 |
* Estimated based on regression of strength versus structural
density
References: Park and Lake; Cowin; Duck
- Properties of tissues vary between individuals and with anatomic
location
- Material properties are significantly affected by the degree
of mineralization (and therefore density) of the bone
- The density of bone is not an intrinsic property and can change
with time
- Mineral stores within the bone can change dependent on physiological
demand
- Pathological processes can affect the degree of mineralization
- In normal, healthy bone, the range of bone mineralization
is small
- Cortical bone
- Cortical bone is anisotropic
- Typically modelled as orthotropic or transversely isotropic
- Longitudinal direction (along axis of osteons) has highest
mechanical properties
- Weaker and lower modulus in radial and transverse directions
- Cortical bone is weaker in tension and shear than in compression
- Trabecular bone
- Continuing debate over whether trabecular bone is merely porous
cortical bone or whether an intrinsic material difference exists
in the bony material
- Current trend is that trabecular material properties are less
than those of cortical bone
- Difficult to test individual trabeculae to determine conclusively
- Structural properties include
- Mechanical properties of tissue
- Structural density (or apparent density)
- Equal to the the mass of the bony material per unit volume
of tissue (including marrow or marrow space)
- Measures of trabecular structure as listed above
- Material and structural properties of blocks of cortical bone,
dentin, and enamel tissue considered equal due to compact structure
- Material and structural properties of trabecular bone differ
significantly
- Material properties are defined for trabeculae alone
- Structural properties are defined for tissue including bone
and marrow
- Trabecular bone is anisotropic, with degree of anisotropy
varying between anatomic location
- Properties (other than density) are thus directionally dependent
- Properties vary greatly between individuals and anatomic locations
- Measured mechanical properties for trabecular tissue are in
the following range
- For trabecular tissue, compressive strength has been found
to be linearly related to Young's modulus (Goldstein)
- Young's modulus, for a given direction of testing, can be
related to the apparent density (pa) of the material
by a power-law relationship with n ranging from about 1 to 3 depending
on the trabecular structure (Gibson and Ashby)
- The contribution of the trabecular and cortical components
of whole bone to overall structural strength will vary with anatomical
location
- Variable amounts of cortical and trabecular bone are present
at every site
- In highly trabecular sites, the trabecular bone can be presumed
to provide a substantial portion of the mechanical integrity of
the structure
- In the femoral neck, bending strength was reduced by approximately
40 percent when the trabecular bone was removed
- In vertebral bodies, removal of the cortical shell was determined
to reduce the compressive strength by about 10 percent
- In both cases, the contribution of trabecular bone to overall
strength is greater than what would be proportional to its mass
or mineral density
- The mechanical properties of both cortical and trabecular
bone have been found to vary with strain rate
- Young's modulus of trabecular tissue is estimated to have
the following relationship with strain rate
- Cortical bone has also been seen to exhibit a creep fracture
response
- Laboratory tests typically conducted at strain rates of 0.01
to 0.001 sec-1, quasi-static
- Impact injuries (falls, vehicular accidents) typically involve
strain rates 10 sec-1
- At higher strain rates, bone has a higher ultimate strength
but fractures at a lower strain (See Figure 8)
- The viscoelastic properties of bone are most likely due to
a combination of
- Simplifed model is taken to be a three element spring/dashpot
model (Figure 9)
- Bone thus behaves in the following manner (at relatively low
strain rates):
- Undergoes initial, immediate deformation with application
of stress
- Deformation will continue to an assymptotic limit if stress
is maintained
- When stress is removed, initial deformation will be regained
(within elastic limits) and additional viscous deformation will
gradually be regained (Figure 10)
- Compound bar with isostrain condition
- Bone acts as reinforced bar with collagen matrix and oriented
HA fibres
- In normally mineralized bone, HA and collagen occupy about
equal amounts of load-bearing volume (the water is not a load-bearing
component)
- Similar to a reinforced concrete beam (Figure 11)
- If the components are assumed to undergo the same strain,
then the fraction of the load borne by each when the fibres are
alligned with the loading direction can be estimated by:
- Total load is the sum of loads on each component
- s = P/A = Ee
- A is cross-sectional area, E is modulus
- Pm = Am*Em*em
and Pc = Ac*Ec*ec
- Since em = ec Pc = Pm
*(Ac*Ec/Am*Em)
- Therefore
- Pm = Pt*Am*Em/(Am*Em
+ Ac *Ec ) and
- Pc = Pt*Ac*Ec/(Am*Em
+ Ac*Ec)
- This model is likely to overestimate the load borne by the
HA "fibres" or crystals
- Two-phase model
- Bone acts a two-phase composite similar to fibreglass
- This type of material typically has a modulus intermediate
to the two components but a higher strength than either component
tested separately
- Fracture will occur if a crack, typically initiated in the
high modulus material, is able to propagate and run through the
whole structure
- HA crystals are so small that the occurrence of random flaws
is also small
- When cracks do occur they quickly enter the more ductile collagen
phase and energy is dissipated in deformation instead of crack
propagation
- Calculation of load borne by each phase is more complicated
in this model due to the possiblity of multiple orientations of
the collagen fibre/HA crystal compound within the structure
- Fatique microdamage occurs in bone just as it does in other
materials under cyclic loading
- Bone undergoes cyclic loading throughout life, with frequency,
duration, and load varying with time and between individuals
- Fatigue microdamage reduces a bone's elastic modulus
- The benefit of bone as a living structure is that it can repair
microdamage before it progresses to failure
- Some pathological processes interfere with this repair mechanism
which may be one cause of increased fracture occurance
- Stress fractures are most common, in healthy individuals,
in cases of both increased loading and increased number of cycles
over normal use and typically occur in a matter of hours
- Example: Forced marches in boot camp
- The load at failure of a whole bone will depend on:
- Failure generally occurs due to tensile or shear loading (Figure 12)
- There is a always a bending moment on bones loaded physiologically
inducing both compressive and tensile forces
- Failure in bending begins on the tensile surface of the bone
- Failure due to shear results in a spiral fracture of the bone
- Exception is crush fractures (at sites like the vertebrae)
- Failure is actually a result of successive bending-induced
fractures of the trabeculae and finally bending of the cortical
shell
- Failure of bone in vivo under impact is also dependent on
the energy absorbed by the surrounding soft tissue
- Bone is a living tissue which is constantly undergoing modeling
and remodeling
- In 1892, Wolff presented the first evidence that bone remodels
in response to mechanical forces acting upon it
- The trabecular bone structure of the femoral neck follows
the principal stress trajectories at that location (See Figure 13)
- Further evidence that bone remodeling is stress or strain
dependent
- Bone is lost as a result of extended immobilization or time
in a zero-gravity environment
- Centrifuge, hypergravity experiments on rats resulted in increased
bone mass
- A bone graft from the tibia used to replace a metacarpal remodels
to resemble the original bone structure
- Bone in the anterior and posterior aspects of the femur is
weaker and less stiff than that of the medial and lateral aspects
- Corresponds to amount of stress at each location due to natural
bending
- In pigs, the increased strain on the radius noted after removal
of the ulna was gradually reduced to normal levels by an increase
in radial diameter
- There is continued debate on two general areas of this phenomena
- #1: What is the driving force behind remodeling?
- #2: What is the mechanism by which mechanical data is transferred
to the bone cells to produce remodeling?
- Hypotheses on point #1:
- Time averaged strain over a threshold limit acts as the stimulus
for bone remodeling, with a goal of maintaining an "ideal"
level of strain at every location
- Disruption of communication channels (through canaliculi)
between the periostem and the internal osteocytes result in bone
hypertrophy
- Fatigue induced micro-cracks are necessary to trigger any
bone remodeling which will result in a change of bone mass
- Increased strain rate, which often parallels increases in
strain levels, is the stimulus behind increased bone deposition
- Hypotheses on point #2:
- Bone is a piezolectric material which generates electrical
signals in response to (dynamic) mechanical loading. These electrical
signals then trigger the bone cells to control remodeling.
- Mechanical deformation results in changes in fluid flow within
bone canals and pores. The fluid flow stimulates bone cells (osteocytes
or osteoblasts) in one of the following ways:
- (1) Changes in the fluid-induced shear stress observed by
cells
- (2) Changes in the hydrostatic pressure observed by the cells
- (3) Changes in cell deformation/strain caused by fluid flow
past cells
- (4) Electrokinetic phenomena (streaming potential) induced
when fluid flows past the charged surface of bone and bone cells
- These mechanisms may act individually, or most likely cooperatively,
to induce a remodeling response in bone cells
- General phenomenological theories regarding bone remodeling
- The objective of bone remodeling, with changes in bone mass,
is to minimize the flexural deformity of the bone through a drift
in the mass of bone towards the concavity created by the bending.
(See Figure 12)
- Cyclic loading is required to induce bone apposition -- both
to maintain and to increase bone mass.
- A number of bone remodeling theories have been included in
finite element models in an attempt to see which produces the
most natural type of bone remodeling
- Very possibly a combination of mechanisms which result in
the overall remodeling behavior of bone in response to mechanical
loading (or lack thereof)
The "ideal" level of stress or strain must be site dependent
to allow for the fact that minimally loaded bones, such as the
calvaria (top of skull) and ossicles (inner ear bones) do not
atrophy
- In any case, the necessary strain to maintain bone or to cause
bone apposition is small
- Maintenance - 1000 to 3000 microstrain (e = 0.001 to 0.003)
- Bone apposition - microstrain > 3000 (e > 0.003)
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