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Biomechanics of Bone 柴惠敏 台灣大學 物理治療學系
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主要參考書 Nordin, M. & Frankel V.H., Basic Biomechanics of the Musculoskeletal System, 3rd ed. Philadelphia, PA, Lea & Febiger. pp Nigg B.M. & Herzog W., Biomechanics of the Musculo-Skeletal System. New York, John Wiley & Sons. pp.64-85 Biomechnics is a discipline of science, newly developed and in the process of becoming established.
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Biomechanics of Bone Basic Concepts
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Bones in Human Body Vertebral Column Cranium Face Auditory Ossicles
Name Number Vertebral Column Cranium Face Auditory Ossicles Hyoid Bone, Sternum, and Ribs Upper Extremities Lower Extremities 26 8 14 6 64 62 Total
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Functions of Skeletal System
Mechanical functions to protect internal organs to provide rigid kinematic links To provide attachment sites for muscles to facilitate muscle action and body movement Physiological functions to produce blood cells (hematopoiesis) to maintain calcium metabolism (mineral homeostasis) Biomechnics is a discipline of science, newly developed and in the process of becoming established.
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Strucutres of Long Bone -- Based on Position
diaphysis: from primary ossification center epiphysis: from secondary ossification center metaphysis: growth plate diaphysis metaphysis epiphysis Although the bones vary considerably in size and shape, they are similar in structure and development.
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Structure of Bone -- Based on Pososity
cortical bone (compact bone) solid and dense material comprising the walls of diaphyses 5-30% of porosity thickness depending on mechanical demands cancellous bone (spongy bone) at epiphyses, flat bones, short bones, etc. 30-90% of porosity Although the bones vary considerably in size and shape, they are similar in structure and development.
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Bone Modelling and Remodelling
the process by which bone mass is increased Remodelling the process by which bone mass adapts, by change its size, shape, and structure, to the mechanical demands placed upon it
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Wolff’s Law Wolff, 1870: static stress model Bone is Revised:
deposited where needed resorbed where not needed Revised: Bone modelling and remodelling occurs in response to the mechanical demands placed upon it.
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Biomechanics of Bone Basic Concepts Mechanical Properties
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Strength-Stress Curve
strain stress elastic region plastic region failure point yield point energy stored ultimate
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Bone Strength ultimate stress the bone can sustain before failure
failure point in the stress-strain curve ultimate strain the bone can sustain before failure energy the bone can store before failure size of the area under the entire curve
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Bone Stiffness slope of the stress-strain curve in the elastic region
plastic region xi yi stiffness = yi / xi
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Elastic Modulus for a linearly elastic structure
Ratio of stress to strain E = / where E: N/m2 or Pa (N/m2 or Pa) = F / A (%) = L / L0
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Stiffness: metal >> glass > bone
strain stress Metal Bone Glass
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Anisotropic Behavior of Bone
mechanical properties change when loaded in different directions L o n g Transv 60 30 strain stress Adapted from Nordin & Frankel, 1989
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Biomechanics of Bone Basic Concepts Mechanical Properties of Bone
Bone Behaviors Under Various Loads
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Tension = Tensile load Failure under tensile loads
debonds at the cement lines pulls out of the osteons occurs in bones with large cancellous bone =
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Compression = Compressive load Failure under compressive loads
oblique cracking of the osteons occurs in bones with weak structure or those with strong muscle co-contraction =
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Shear Shear load =
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Ultimate Stress of Cortical Bone Testes in Various Loads
Adapted from Reilly & Burstein, 1975
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Bending = Bending load Failure under bending loads tension
three-point bending: point of the middle force four-point bending: weakest point = tension neutral axis compression
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Types of Bending Loads Three-Point Bending Four-Point Bending point at
weakest point point at middle force
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Torsion = Torsion load Failure under torsion loads neutral axis
shear tensile compressive stresses = neutral axis
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Combined Stresses in Torsion Loading
shear tension compression
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Biomechanics of Bone Basic Concepts Mechanical Properties of Bone
Bone Behaviors Under Various Loads Factors Affecting Bone Strength and Stiffness Gravity Muscle activity Strain rate dependency Repetition of loading Bone geometry Immobilization Aging of bone Artificial defects
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Effect of Gravity Positive correlation between body weight and bone mass Decreased bone mass in the weight bearing joints of astronauts
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Bending Load on Femoral Neck
BW GT FH tension compression tension compression
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Effect of Muscle Activity
Contraction of muscle alters stress distribution in the bone muscle relaxed GT FH GM muscle contracted
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Strain Rate Dependency
when loads are applied at higher rate within the physiological limit, the bone becomes stiffer sustains a higher load to failure stores more energy before failure strain stress 0.1/s 0.01/s 0.001/s 300/s 1500/s
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Energy Released At Fracture
when a bone fractures, the stored energy is released. single bone crack for a low-energy fracture comminution of bone for a higher-energy fracture severe destruction of bone before failure
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× Repetition of Loading
Stress fracture may occur when repeated application of a load of low magnitude march fracture spondylolithesis repetition stress injury × less more high low
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Effect of Bone Geometry
I = mr2 r1 r1 < r I1 < I2 r2
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Artificial Defects stress raiser: defect length < bone diameter
the stresses concentrating around the defect marked weakening effect under torsion load e.g. drilling a whole or inserting a screw open section defect: defect length > bone diameter
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Effect of Open Section Defect
strain stress close section open section
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Effect of Immobilzation
strain stress immobilized normal
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Aging of Bone thinner walls of the trabeculae in cancellous bone
marked reduction in the amount of cancellous bone decrease in the diameter and thickness of the cortex strain stress Old Young
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Biomechanics of Bone Basic Concepts Mechanical Properties of Bone
Factors Affecting Bone Strength and Stiffness Failure of Bone Definition Possible causes
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Possible Causes of Bone Failure
Excessive acting forces Unfavorable acting moments Small bone dimension Excessive repetition of force application
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