:بيومكانيك رشد و نمو استخوان انسان

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Bone Structural support of the body Connective tissue that has the potential to repair

and regenerate Comprised of a rigid matrix of calcium salts

deposited around protein fibers

Minerals provide rigidity

Proteins provide elasticity and strength

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Bone Tissue Mineral: ~50% of bone weight, provides stiffness and cmpressive strength (primarily calcium compounds) Collagen: ~ 25% of bone weight, provides tensile strength and stiffness Water: ~25% of bone weight, provides compressive strength and helps maintains bone health Ground Substance: ~1% of bone weight, increases elastic capabilities

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There are 2 types of bones: compact bone and spongy bone. 1. Compact Bone: Is a solid bone that at microscopic level has a concentric ring structure. It is made of bone cells called osteoblasts. These cells are growing within a material that is called a bone matrix. The bone matrix is made of 70% inorganic salts such as calcium phosphate and 30% protein called collagen. The calcium salts give the bone strength while the protein gives it flexibility. Blood vessels as well as nerve fibres are within the bone. 2. Spongy Bone: irregular openwork of thin plates of bone. It is also known as trabecular or cancellous bone. The mineral deposits are arranged as a system of struts. Bone marrow fills the spaces between the plates. The marrow cavity is the space within the diaphysis that also contains marrow.

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Inside view of cavities within spongy bone. They are filled with red bone marrow.

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Functions Osseous tissue performs numerous functions including: Directly: Support for muscles, organs, and soft tissues. Leverage and movement. Protection of vital organs, e.g., the heart. (Note: not all vital organs are protected by bones, e.g., the intestines.) Calcium phosphate storage. Indirectly: Hemopoiesis - formation of blood cells by the bone marrow interspersed within the spongy bone.

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سیستم اسکلتی مرکزی یا حموری

The axial skeleton consists of the 80 bones along the central axis of the human body. It is composed of six parts; the human skull, the ossicles of the middle ear, the hyoid bone of the throat, the rib cage, sternum and the vertebral column. The axial skeleton and the appendicular skeleton together form the complete skeleton.

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سیستم اسکلتی خارجی یا زائده ای

The Appendicular skeleton is composed of 126 bones in the human body. The word appendicular is the adjective of the noun appendage, which itself means a part that is joined to something larger. Functionally it is involved in locomotion (Lower limbs) of the axial skeleton and manipulation of objects in the environment (Upper limbs).

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Shape Long, short, flat, and irregular

Long bones are cylindrical and “hollow” to achieve

strength and minimize weight www.sirinet.net/ ~jgjohnso/skeleton.html

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1. Long bone

a. Longer than wide

b. Shaft with two ends

c. Mostly compact

d. Bones of limbs

2. Short bone

a. Cube-like

b. Mostly spongy

c. Sesamoid—

bones embedded in tendon

i. Patella

3. Flat bone

a. Spongy bone embedded

within parallel layers

of thin compact bone

4. Irregular bone

a. Vertebrae and hip bones

b. Complicated shapes

c. Mostly spongy with a

thin covering of compact

bone

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Bone Physiology. Courtesy Gray's Anatomy 35th edit Longman Edinburgh 1973

Cancellous Bone

Cortical Bone

Osteon

Periosteum

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Microstructure of the Bone

(a) (b) (c)

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Microstructure of Bone (Cont’d)

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Two architectures (classified by porosity) also relate to function: 1. Cortical (compact) bone is 5-30% porous 2. Cancellous (trabecular or spongy) bone is 30-90% porous Bone strength and stiffness are influenced by bone architecture

Bone Architecture

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Composition of Bone: Cells

Osteocytes

Osteoblasts

Osteoclasts

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Osteocyte: a bone cell Osteoblasts: specialized bone cells that form new bone tissue Osteoclasts: specialized bone cells that resorb existing bone tissue Under normal circumstances, activity of these cells is balanced

Bone Cells

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Controlling Factors

Hormones

Estrogen

Testosterone

Cytokines

Growth factors,

Interleukins (1, 6, and 11),

Transforming growth factor-b

Tumor necrosis factor-a

of osteoclasts and osteoblasts

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Macrophage

Phagocytose invading pathogens

Cell alters shape to surround bacteria or debris

Process: Chemotaxis, adherence, phagosome formation, phagolysosome formation

Secrete Interleukin-1

(IL-1)

Involved in bone resorption

Controlling Factors of osteoclasts and osteoblasts

http://saints.css.edu/bio/schroeder/macrophage.html http://academic.brooklyn.cuny.edu/biology/bio4fv/page/phago.htm http://www.allsciencestuff.com/mbiology/research/osteoporosis

Bacterium

Nuclei

Ingested bacterium

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Composition of Bone: Matrix

Cortical/ Compact

Bone

Cancellous/

Trabecular/ Spongy

Bone

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Cortical Cancellous

Physical Description

Dense protective shell Rigid lattice designed for strength; Interstices are filled with marrow

Location

Around all bones, beneath periosteum; Primarily in the shafts of long bones

In vertebrae, flat bones (e.g. pelvis) and the ends of long bones

% of Skeletal Mass

80% 20%

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Cortical Cancellous First Level Structure

Osteons Trabeculae

Porosity 5-10% 50-90%

Circulation Slow circulation of nutrients and waste

Haversian system allows diffusion of nutrients and waste between blood vessels and cells; Cells are close to the blood supply in lacunae

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Cortical Cancellous Strength Withstand greater stress Withstand greater strain

Direction of Strength

Bending and torsion, e.g. in the middle of

long bones

Compression; Young’s modulus is much greater

in the longitudinal direction

Stiffness Higher Lower

Fracture Point

Strain>2% Strain>75%

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Properties of Cortical and Cancellous Bones

Load Type Elastic modulus (109N/m2)

Ultimate stress (106N/m2)

Bone Type Cortical Cancellous Cortical Cancellous

Tension 11-19 ~0.2-5 107-146 ~3-20

Compression 15-20 0.1-3 156-212 1.5–50

Shear 73-82 6.6+/-1.6

http://www.orthoteers.co.uk/Nrujp~ij33lm/Orthbonemech.htm 40

Bone Remodeling

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Bone deposition

Bone resorption

Bone Remodeling Bone structural integrity is continually maintained by

remodeling

Osteoclasts and osteoblasts assemble into Basic Multicellular Units (BMUs)

Bone is completely remodeled in approximately 3 years

Amount of old bone removed equals new bone formed

http://www.elixirindustry.com/resource/osteoporosis/jilka.htm 43

Basic Multicellular Units “The Basic Multicellular Unit (BMU) is a

wandering team of cells that dissolves a pit in the bone surface and then fills it with new bone.”

http://uwcme.org/site/courses/legacy/bonephys/physiology.php

BMUs are discrete temporary anatomic structures organized as functional unit

Osteoclasts remove old bone, then osteoblasts synthesize new bone

old bone is replaced by new bone in quantized packets

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BMU Remodeling Sequence

Activation

Resorption

Reversal

Quiescence

Formation & Mineralization

www.ifcc.org/ejifcc/ vol13no4/130401004n.htm

Osteocytes

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Schematic diagram of the Davy and Hart model

for bone remodelling

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The cell-biology based model of Davy and Hart expresses functional dependence of bone remodelling on the strain field, based on cell activity. The load applied to the bone together with geometric and material properties determine the local strain. Strain is detected by a transducer which generates the strain remodelling potential (SRP). This signal is modulated by genetic, hormonal and metabolic factors, generating the remodelling potential which regulates the recruitment rate and the activity of osteoblasts and osteoclasts, stimulating bone formation and bone resorption. The balance between bone deposition and bone resorption determines the net bone remodelling. remodelling modifies bone geometric and material properties through a feedback loop.

Mechanical Properties of Biological Tissue

• Mechanical properties of biological tissue can be described using strength and stiffness

• These two properties are shown graphically in this load × deformation curve

• Strength is related to the load, while stiffness (k) is the slope of the load × deformation curve

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The load × deformation curve The elastic region of the curve is between points A and B With initial loading bone can change shape (up to ~3% deformation) When deformation is < 3%, bone is more likely to return to its original shape after the load is removed (elastic deformation)

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The load × deformation curve The plastic region of the curve is between points B and C If loading continues beyond the yield point, plastic deformation is likely to occur The transition from the elastic to the plastic region is called the yield point

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The stress × strain curve

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Load Characteristics of Bone Load characteristics of a bone include:

Direction of the applied force Tension

Compression

Bending

Torsion

Shear

Magnitude of the load

Rate of load application

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Principal Mechanical Stresses (𝜎) • How might your bones be stressed in these ways? • Bones respond differently to different stress • What stress do you think your bone most effectively bears?

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Resistance to Stress Bone bears compressive stress most effectively and shear stress least effectively. How do you suppose we know this?

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Mechanical Testing Device

Note the various measures of strength 57

Sample Problem A bone sample is subjected to a stress of 80 KN. The cross sectional area is 1 cm2 (0.0001 m2) and Young’s Modulus is 70 GPa. What strain can be expected as a result of this stress?

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More stress × strain curves…ductile or brittle?

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Two Additional, Unique Mechanical

Characteristics of Bone

Anisotropic: bone responds differently depending on the direction of applied load. Stress × strain curves differ, depending on load direction. Viscoelastic: bone responds differently depending on rate of load application. Stress × strain curves differ, depending on rate of load application.

Comparison between the mechanical behavior of isotropic and anisotropic materials

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Material Properties Comparison* Material

Compressive Strength (MPa)

Modulus (GPa)

Cortical 10-160 4-27

Trabelcular 7-180 1-11

Concrete ~ 4 30

Steel 400-1500 200

Wood 100 13

Pink: http://www.engineeringtoolbox.com/24_417.html Yellow: http://www.brown.edu/Departments/EEB/EML/background/Background_Bone.htm Green: http://ttb.eng.wayne.edu/%7Egrimm/BME5370/Lect3Out.html#TrabecularBone

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*Variability of Properties Material properties listed may vary widely due to test

methods used to determine them

Variances of the following can effect results:

Orientation of sample

Bone and wood are elastically anistropic; steel is not

Condition of sample

Dry or wet with various liquids

Specifics of sample

Bone: age of donor, particular bone studied

Wood: species of tree

Steel/Concrete: preparation methods, components

http://silver.neep.wisc.edu/~lakes/BoneAniso.html 64

Ultimate strength (MPa) and ultimate strain (%) of cortical bone from the human femur as a function of age

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Cortical bone is an anisotropic material, meaning that its mechanical properties vary according to the direction of load. Cortical bone is often considered an orthotropic material. Orthotropic materials are a class of anisotropic materials characterized by three different Young's moduli E1, E2, E3 according to the direction of load, three shear moduli G12, G13, G23 and six Poisson's ratios ν12, ν13, ν23, ν21, ν31, ν32.

Average elastic constants of mandible bone in corpus and ramus

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Average elastic constants of corpus cortical bone in inferior, lingual and buccal zones

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Anisotropic Behavior of Bone

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Viscoelastic Behavior of Bone

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Three stress × strain curves for cortical bone (tension) at three different loading rates As loading rate increases, the modulus of elasticity and strength increases

قانون ولف

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Wolff’s Law

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Wolff’s Law (1892)

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Bone elements place or displace themselves in the direction of functional forces, and increase or decrease their mass to reflect the magnitude of those functional forces… In other words, bone adapts to increased use (physical activity) or disuse (bed rest) Mechanical properties of bone (strength and stiffness) that depend upon form (size, shape) can be altered in response to load

Increased Bone Mineral Content

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Osteoblast Activity > Osteoclast Activity Degree of increase in bone density

directly proportional to the

magnitude of force application

Bones with increased density are

stronger and more resistant to

fractures

Increased Bone Mineral Content

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External loads, especially high-magnitude

loads, increase bone density:

Weight bearing loads…

Obesity…

Certain athletes: tennis

A tibia that was a fibula (Adrian and Cooper, 1989)

A construction worker (Ross, 1997)

Decreased Bone Mineral Content

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Osteoclast Activity > Osteoblast Activity Reduced loading on bone can lead to substantial demineralization: 17 weeks of bedrest has been shown to lead to 10.5 % reduction in bone density Bone that is less dense is not as strong or resistant to fracture

Trabecular structures in the calcaneus of a 24 year old

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Trabecular structures of vertebrae in a 36 year old woman

Trabecular structures of vertebrae in a 74 year old woman

Bone remodelling: effect of reduction (from A to B) and of intensification of strain (from B to A) on bone trabecules.

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Decreased Bone Mineral Content

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Decreased loading results in decreases in bone

mineral density

• Physical activity levels…

• Certain athletes: swimmers, cyclists…

Anything else?

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Decreased Bone Mineral Content

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Space related bone loss:

Amount of bone loss is

proportional to time spent

away from gravitational

field (~1% per month)

Countermeasures are

now being developed to

delay rate of bone loss

Countermeasures

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A study in the March issue of the Journal of Applied Physiology reported that a person in a “reclining bedrest” position experiences the same weightless environment that an astronaut’s body must adapt to while in space. Without any exercise, Peterson’s body is going through the same muscle atrophy and bone density loss endured during space travel. Astronauts can lose 1% to 2% of their leg’s bone density in just one month in space, said Englehaupt. That is a substantial effect, he added, and is equivalent to the bone density loss a postmenopausal woman has in one year on Earth. According to Englehaupt, astronauts also experience muscle atrophy in their legs from not having to support their own weight.

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Countermeasures

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Bed rest studies at the NASA Flight Analogs Research Unit at the University of Texas Medical Branch in Galveston, Texas utilize 6-degree head down tilt best rest to simulate the physiological deconditioning in muscle, bone and cardiovascular systems associated with spaceflight.

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Function of Bone Mechanical support

Hematopoiesis زنده خونسازي درموجود

Protection of vital structures

Mineral homeostasis

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Mechanical Support Provides strength and stiffness

Hollow cylinder: Strong and light

Have mechanisms for avoiding fatigue fracture

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Hematopoiesis Development of blood cells

• Occurs in the marrow of bone

These regions are mainly composed of trabecular bone

• (e.g. The iliac crest, vertebral body, proximal and distal femur)

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Protection of Vital Structures

Flat bones in the head protect the brain

Protects heart and lungs in chest

Vertebrae in the spine protect the spinal cord

and nerves

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Mineral Homeostasis Primary storehouse of calcium and

phosphorus

Trabecular bone are rapidly formed or

destroyed

In response to shifts in calcium stasis without

serious mechanical consequences

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Fatigue of Bone

Microstructural damage due to repeated loads below the bone’s ultimate strength

Occurs when muscles become fatigued and less able to counter-act loads during continuous strenuous physical activity

Results in Progressive loss of strength and stiffness

Cracks begin at discontinuities within the bone (e.g. haversian canals, lacunae)

Affected by the magnitude of the load, number of cycles, and frequency of loading

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Fatigue of Bone (Cont’) 3 Stages of fatigue fracture

Crack Initiation Discontinuities result in points of increased local stress where

micro cracks form Often bone remodeling repairs these cracks

Crack Growth (Propagation) If micro cracks are not repaired they grow until they encounter a

weaker material surface and change direction Often transverse growth is stopped when the crack turns from

perpendicular to parallel to the load

Final Fracture Occurs only when the fatigue process progresses faster than

the rate of remodeling

http://www.orthoteers.co.uk/Nrujp~ij33lm/Orthbonemech.htm

Simon, SR. Orthopaedic Basic Science. Ohio: American Academy of Orthopaedic Surgeons; 1994. 101

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Fatigue Curve

Probability of Injury

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Process to Fatigue Failure Road to Failure: Region 1

1. Crack initiation

2. Accumulation انباشتگي

3. Growth

Characteristics:

Matrix damage in regions of

High stress concentration

Low strength

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Relatively rapid loss of stiffness

Bear less load

Absorb more energy ( can sustain larger deflections)

Cracks develop rapidly

May stabilize quickly without much

propagation

Process to Fatigue Failure (cont’d)

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Process to Fatigue Failure (Cont’d)

Cracks occur first in regions of high strain

Accumulate with either

Increased number of cycles

Increased strain

Cracks develop perpendicular to the load axis

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Road to Failure: Region 2

1. Crack growth

2. Coalescenceبهم اميختگي ،

3. Delamination اليه اليه شدگيand debonding

Characteristics:

After a crack forms

Interlamellar tensile and shear stresses are generated at its tip

Tend to separate and shear lamellae at the fiber-matrix interface

Process to Fatigue Failure (cont’d)

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Secondary cracks may extend between lamellae in the

load direction

Cracks tend to grow parallel to the load

Delamination along the load axis

Elevated and probably unidirectional strain redistributions

Along the fibers parallel to the load axis

Process to Fatigue Failure (cont’d)

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Process to Fatigue Failure (Cont’d)

Road to Failure: Region 3

Stiffness declines rapidly

End of a material’s fatigue life

Fiber failure

Coalescence of accumulated damage

Crack propagation along interfaces

Rapid process

Ultimate failure of the structure

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Fatigue Theory During repeated efforts (as in running)

Muscles become unable to support during impact

Muscles do not absorb the shock

Load is transferred to the bone

As the loading surpasses the capacity of the bone to adapt

A fracture develops

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The End

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Activation Occurs when bone experiences micro damage or

mechanical stress, or at random

A BMU originates and travels along the bone surface

•Differentiated cells are recruited from stem cell

populations

Pre-osteoclasts merge to form multi-nucleated osteoclasts

http://uwcme.org/site/courses/legacy/bonephys/physiology.php 112

Bone Resorption Newly differentiated osteoclasts are activated and begin to

resorb bone

Minerals are dissolved and the matrix is digested by enzymes and hydrogen ions secreted by the osteoclastic cells

Move longitudinally on bone surface

This process is more rapid than formation, though it may last several days

http://uwcme.org/site/courses/legacy/bonephys/physiology.php http://www.britannica.com/ebc/article?tocId=41887

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Reversal Transition from osteoclastic to osteoblastic activity

Takes several days

Results in a cylindral space (tunnel) between the resorptive

region and the refilling region

Forms the cement line

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Bone Formation Following Resorption, osteoclasts are replaced by osteoblasts

around the periphery of the tunnel

Attracted by cytokines and growth factors

Active osteoblasts secrete and produce layers of osteoid, refilling the

tunnel

Osteoblasts do not completely refill the tunnel

Leaves a Haversian canal

•Contains capillaries to support the metabolism of the

BMU and bone matrix cells

•Carries calcium and phosphorus to and from the bone

http://uwcme.org/site/courses/legacy/bonephys/physiology.php 115

Mineralization When the osteoid is about 6 microns thick, it begins to

mineralize

Formation of the initial mineral deposits at multiple discrete

sites (initiation)

Mineral is deposited within and between the collagen fibers

This process, also, is regulated by the osteoclasts

Mineral maturation

Once the cavity is full the mineral crystals pack together,

increasing the density of the new bone

http://uwcme.org/site/courses/legacy/bonephys/physiology.php 116