Biomechanics of Bone 柴惠敏 台灣大學 物理治療學系

主要參考書 Nordin, M. & Frankel V.H., 2001. Basic Biomechanics of the Musculoskeletal System, 3rd ed. Philadelphia, PA, Lea & Febiger. pp. 26-58 Nigg B.M. & Herzog W., 1999. 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.

Biomechanics of Bone Basic Concepts

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 206

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.

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.

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.

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

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.

Biomechanics of Bone Basic Concepts Mechanical Properties

Strength-Stress Curve strain stress elastic region plastic region failure point yield point energy stored ultimate

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

Bone Stiffness slope of the stress-strain curve in the elastic region plastic region xi yi stiffness = yi / xi

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

Stiffness: metal >> glass > bone strain stress Metal Bone Glass

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

Biomechanics of Bone Basic Concepts Mechanical Properties of Bone Bone Behaviors Under Various Loads

Tension =  Tensile load Failure under tensile loads debonds at the cement lines pulls out of the osteons occurs in bones with large cancellous bone = 

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 = 

Shear Shear load = 

Ultimate Stress of Cortical Bone Testes in Various Loads Adapted from Reilly & Burstein, 1975

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

Types of Bending Loads Three-Point Bending Four-Point Bending point at weakest point point at middle force

Torsion =  Torsion load Failure under torsion loads neutral axis shear  tensile  compressive stresses =  neutral axis

Combined Stresses in Torsion Loading shear tension compression

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

Effect of Gravity Positive correlation between body weight and bone mass Decreased bone mass in the weight bearing joints of astronauts

Bending Load on Femoral Neck BW GT FH tension compression tension compression

Effect of Muscle Activity Contraction of muscle alters stress distribution in the bone muscle relaxed GT FH GM muscle contracted

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

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

× 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

Effect of Bone Geometry I = mr2 r1 r1 < r2 I1 < I2 r2

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

Effect of Open Section Defect strain stress close section open section

Effect of Immobilzation strain stress immobilized normal

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

Biomechanics of Bone Basic Concepts Mechanical Properties of Bone Factors Affecting Bone Strength and Stiffness Failure of Bone Definition Possible causes

Possible Causes of Bone Failure Excessive acting forces Unfavorable acting moments Small bone dimension Excessive repetition of force application