Skeleton Physics PDF

Physics of the Skeleton How strong are our bones? How efficient is the design of the skeleton, and what are the limits of the loads that we can apply to it? The Skeletal System The Skeletal System Parts of the skeletal system Bones (skeleton) Joints Cartilages Ligaments (bone to bone)(tendon=bone to...

Physics of the Skeleton How strong are our bones? How efficient is the design of the skeleton, and what are the limits of the loads that we can apply to it? The Skeletal System The Skeletal System Parts of the skeletal system Bones (skeleton) Joints Cartilages Ligaments (bone to bone)(tendon=bone to muscle) The Skeletal System Skeleton comes from a Greek word meaning dried up body. Bone appears dead and dried up, but it is not! Bone is living tissue Functions of Bones Support of the body (framework) Protection of soft organs Serve as levers (with help from muscles) Storage of minerals and fats (calcium) Blood cell formation Bones of the Human Body Two basic types of bone tissue ( according to cross sectional category) Compact bone Dense/hard Spongy bone (Cancellous) Many open spaces Decrease wt of bone/contain red bone marrow Classification of Bones (according to external or outside shape) Long bones Typically longer than wide Have a shaft with heads at both ends Contain mostly compact bone Found in legs and arms Examples: Femur, humerus Classification of Bones Short bones Generally cube-shape and small Contain mostly spongy bone Found in wrist, ankles, and toes Examples: Carpals, tarsals Classification of Bones Flat bones Thin and flattened Usually curved Cover organs/provide surface for lg. muscle Thin layers of compact bone around a layer of spongy bone Examples: Skull, ribs, sternum Irregular bone (vertebra) Classification of Bones on the Basis of Shape Sphenoid bone Talus Ulna Scapula Vertebra Sternum Radius Long Capitate (carpal) bone Short Flat Irregular Did you know? Bones are alive, growing and changing like the rest of your body! A baby’s body has about 300 bones at birth The adult human body has only 206 bones! What Are Bones Made Of? Periosteum: the outer surface of the bone; a thin, dense membrane that contains nerves and blood vessels that nourish the bone! Compact: this is the next layer; it is very smooth and very hard. It is the part you see when you look at a skeleton! Cancellous: Many layers within the compact bone; these look like sponges! Not as hard as compact bone, but it is still very hard. In many bones, the cancellous bone protects the innermost part of the bone, the bone marrow. It is sort of like a thick jelly, and its job is to make blood cells. What are some of the most recognized bones? Skull Ball & socket joint (shoulder) Fixed joint (parieto—temporal) Vertebra Sternum Rib Humerous Radius Ulna Pelvis Femur Hinge joint (knee) Fibula Tibia ⚫ Bone as a living tissue  Blood supply and nerve Osteocytes  Cells that maintain the bone in a healthy condition  2% of the volume of bone  Poor blood supply  osteocytes die  bone dies  loss of its strength  Aseptic necrosis: bone cells in the hip die  artificial joint  Bone remodeling by specialized bone cells    years   Osteoclasts destroy the bone by about 0.5 g of calcium each day Osteoblasts build the bone by about 0.5 g of calcium each day Bones have about 1000 g of calcium  new skeleton in every seven equivalently Osteoblasts dominate until 35 to 40 years old Osteoporosis: porous bones in older women, Fig. 3.4(c)  fractures Aseptic necrosis is a bone condition that results from poor blood supply to an area of bone, causing localized bone death. This is a serious condition because the dead areas of bone do not function normally, are weakened, and can collapse. Aseptic necrosis is also referred to as avascular necrosis or osteonecrosis. Fig. (3-4) 3.1 What is Bone Made of?  Composition of compact bone: Table 3.1  Large percentage of calcium with heavier nucleus  high x-ray absorption (Fig. 3.2(  Bone = collagen + bone mineral + water  Collagen  Collagen which is the major organic fraction, 40% of the weight of solid bone and 60% of its volume  Collagen remainder: flexible and bends easily, large tensile strength (Fig. 3.3)  Produced by osteoblastic cells  Bone mineral :inorganic component 60% of weight 40% of its volume  Bone mineral remainder: fragile, can be crushed with fingers  Formed on the collagen  Made up of calcium hydroxyapatite Ca10 (PO4 )6 (OH)2  Very large surface area of 4105 m2  rapid interaction with chemicals in the blood and other body fluids  Spongy or cancellous bones (trabecular bones)  Found at the ends of long bones  Weaker than compact bones  Stress: force per unit area,  = F /A  Tension: pulling it apart  Compression: pushing it together  I beam: support beam with a less amount of material, Fig. 3.5(b)  Hollow cylinder: maximum strength with a less amount of material for forces from any direction, Fig. 3.5(c)  Strain: fractional change in length due to stress,  = L / L  Hooke’s law:  = Y  , stress-strain diagram in Fig. 3.7  Young’s modulus, Y=  /  = LF/A∆L : Table 3.2 and Example 3.1  Femur (Fig. 3.4)  Hollow cylinder  Compact bone of the shaft of the femur is thickest in the center to prevent buckling  Trabecular pattern at the ends Fig. 3.6  Strength with a less amount of material than compact bone for compressive forces  Absorb more energy when large forces are involved (walking, running, and jumping) Weak for bending stresses that occur mostly in the center of long bone  Mechanical properties of bone  Combination of two materials (bone mineral and collagen)  As strong as granite in compression  25 times stronger that granite under tention  Density of compact bone  About 1.9 g/cm3 (1.9 times as dense as water)  Constant throughout life even in old age  In old age, the bone becomes more porous and thinner (Fig. 3.4)  reduced strength  Ultimate tensile stress: 120 N/mm2 or 17,000 lb/in2  Forces on the bone and safety factor  Running  four times the body weight on the hip bone when the heel strikes the ground  Normal walking  two times the body weight on the hip bone when the heel strikes the ground  Stiff-legged landing  about 1.42105 N or 32,000 lb  215 N/mm2 (31,000 lb/in2) for each tibia with 3.3 cm2 in area at the ankle  may result in a fracture if the force is applied for enough time  Viscoelasticity: withstand a large force for a short period  Safety factor  10 times the maximum expected force in most engineering design  Ultimate compressive stress of compact bone = 170 N/mm2 (Table 3.2)  midshaft of the femur with cross-sectional area of 3.3 cm2 can withstand about 5.7104 N or 6 tons  Fractures  Shear stress, Fig. 3.9(a)  shear or spiral fracture, compound fracture, easy to be infected  Tensile stress, Fig. 3.9 (c): bone has a smaller ultimate stress for tension than compression (Table 3.2)  Repair requires immobilization  metal prosthetic hip joints, pins, nails, etc (Fig. 3.10)  Electrical stimulation provides faster healing Increase of temperature leads to a reduction in the bone’s ability to absorb part of the load applied to it, resulting in a reduction in stress in general. loss of water in the collagen phase decreases the toughness of bone, whereas loss of water associated with the mineral phase decreases both bone strength and toughness. Bone is anisotropic - its modulus is dependent upon the direction of loading. Bone is weakest in shear, then tension, then compression. Bone is viscoelastic: its force-deformation characteristics are dependent upon the rate of loading 3.3 Lubrication of Bone Joints  Boosted lubrication  Rough articular cartilage traps some of the synovial fluid (lubricant), Fig. 3.11  Stress  lubricating material is squeezed into the joint from the articular cartilage  No stress  articular cartilage pulls back lubricating material into its holes  Viscosity of synovial fluid: large shear stress  decreased viscosity  better lubricant  Coefficient of friction of a joint (Fig. 3.12)  Independent of the load from 89 to 890 N (20 to 200 lb)  Fat in the cartilage helps to reduce the friction  For healthy joints, the coefficient of friction is less than 0.01 (0.03 for steel blade on ice)  Without synovial fluid, the coefficient of friction increases 3.4 Measurement of Bone Mineral in the Body  In vivo versus in vitro  Mass of bone mineral  Determines strength of bone  Decreases slowly, 1 to 2% per year  Osteoporosis: lower bone mineral mass  Problems in measuring bone mineral mass using conventional xray (Fig. 3.13)  X-ray beam has many different energies and x-ray absorption by calcium changes with x-ray energy  X-ray scattering Dual-energy X-ray absorptiometry (DXA, or DEXA) is a means of measuring bone mineral density (BMD) using spectral imaging. Two Xray beams, with different energy levels, are aimed at the patient's bones. When soft tissue absorption is subtracted out, the bone mineral density (BMD) can be determined from the absorption of each beam by bone. Dual-energy X-ray absorptiometry is the most widely used and most thoroughly studied bone density measurement technology.The DXA scan is typically used to diagnose and follow osteoporosis.