Biomechanics of bones

1Bone Formation and Mechanical PropertiesProf. Dr. Blent MzrakBAU International University-Batumi 12ContentsIntroductionThe Skeleton SystemTypes of the BonesComposition of BonesFunctions of BonesBone Biomechanics23Introduction Bone tissue, or osseous tissue, - a type of connective tissue used in forming bones. Bones protect the vital organs and help support the body. Bone is composed mainly of collagen, or ossein, fibers, and bone cells called osteocytes. There are two types of bone tissue, referred to as cortical bone and cancellous bone.

The human skeletal system is primarily composed of two types of skeletal tissue, bones and cartilage. Bones provide the framework for the human body and help protect internal organs from trauma.34The Skeleton System

299 bones (baby), 209 bones (adults) 4 basic shapes

They also aid in red blood cell production, store minerals, and support movement. Cartilage keeps the bones connected, helps them move, and prevents friction damage at the ends of joined bones. It provides flexible support and shaping in external structures like the nose and ears as well as internal structures, such as the wind pipe.The skeletal system includes all the bones of the body plus joints where they attach to each other. Skeleton system protects internal organs and provides a framework, allows standing upright and moving. Skeleton system stores minerals that a body needs to function properly and produce blood cells.The skeletal system is made up 206 different bones which come in 4 basic shapes. 45Types of the Bones4 basic shapes: Long bones (femur)

Long bonesare characterized by a shaft, thediaphysis, that is much longer than it is wide. They are made up mostly ofcompact bone, with lesser amounts ofmarrow, located within themedullary cavity, andspongy bone. Most bones of thelimbs, including those of thefingersand toes, are long bones.56Types of the Bones4 basic shapes: Short bones (wrist, ankle)

Short bonesare roughlycube-shaped, and have only a thin layer of compact bone surrounding a spongy interior. The bones of the wrist and ankle are short bones.67Types of the Bones4 basic shapes: Flat bones (skull, scapula)

Flat bonesare thin and generally curved, with two parallel layers of compact bones sandwiching a layer of spongy bone. Most of the bones of theskullare flat bones.78Types of the Bones4 basic shapes: Irregular bones (vertebrae)

Irregular bonesdo not fit into the above categories. They consist of thin layers of compact bone surrounding a spongy interior. By the name, their shapes are irregular and complicated. Often this irregular shape is due to their many centers of ossification or because they contain bony sinuses. The bones of thespine,Pelvis, and some bones of the skull are irregular bones.

89Composition of Bones

The majority of bone is made of the bone matrix. It is composed primarily of inorganichydroxyapatiteand organiccollagen. Bone is formed by the hardening of this matrix around entrapped cells. When these cells become entrapped from osteoblasts they become osteocytes.It is much less dense and comparatively weaker than cortical bone tissue, cancellous tissue serves an important purpose. There are two kinds of bone marrow. Red bone marrow is almost completely made up of specialized cells that make the majority of the body's red and white blood cells, and platelets. 910Functions of Bones

This image shows trabecular bone structure in the lower spine of a young adult compared to an osteoporotic elderly adult. When a child is born, all of the bone marrow in his body is typically red bone marrow.As a person grows older, more and more red bone marrow is replaced by yellow bone marrow, which is made mostly of fat. During times of extreme starvation, the body will use these fat stores, and, in some cases, the yellow marrow can change back into red marrow if needed. Roughly half of all marrow in an adult's body is yellow.

1011Mechanical properties of boneRelativelyhard;Lightweight;Composite material;highcompressive strengthof about 170MPa(1800kgf/cm);poortensile strengthof 104121MPa;very lowshear stressstrength (51.6MPa).

Lets talk about Mechanical properties.The primary tissue of bone is a relativelyhardand lightweightcomposite material. It is mostly made up of a composite material incorporating the mineralcalcium phosphatein the chemical arrangement termed calciumhydroxyl apatite(this is theosseous tissuethat gives bones their rigidity) and collagen, an elastic protein which improves fracture resistance. It has relatively highcompressive strengthof about 170MPa but poortensile strengthof up to 121MPaand very lowshear stressstrength (51.6MPa),meaning it resists pushing forces well, but not pulling or torsional forces. While bone is essentiallybrittle, it does have a significant degree ofelasticity, contributed chiefly bycollagen. All bones consist of living and dead cellsembedded in the mineralized organic matrix that makes up the osseous tissue.1112

Basic BiomechanicsMaterial PropertiesElastic-PlasticYield pointBrittle-DuctileToughnessIndependent of Shape!Structural PropertiesBending StiffnessTorsional StiffnessAxial StiffnessDepends on Shape and Material!1313Material Properties: fundamental behaviors of a substance independent of its geometry.Structural Properties: the ability of an object to resist bending under torsion, axial load, or bending is a function of its shape and distribution of material around the cross section.ForceDisplacementSlope Stiffness = Force/Displacement Force, Displacement & StiffnessBasic Biomechanics1414Force applied to a body causes a deformation. If one plots a graph of displacement due to the force applied to a material, the slope of the curve represent the materials stiffness.15

Basic BiomechanicsStress = Force/AreaStrain Change Height (L) / Original Height(L0)ForceAreaL1616Stress: is the force applied per unit area (F/A).STRESSTo have stretched or compressed the bone, a force had to be applied to it. The force per unit area is the stress, and is reported in Newtons per square meter, or Pascals. A Pascal is essentially the stress caused by the weight of one apple (0.1Kg) acting on a square meter tabletop. One million Pascals (1 MPa) is 10kg per cm2 of bone. Imagine the stress on your knee as you are standing. The force applied to your knee is your weight, acting upon the top of your tibia. Strain: is the change in a materials length due to an applied stress relative to its original length = L/ L0. 17

Stress = Force/Area Strain = Change in Length/Original Length (L/ L0) Elastic Modulus = Stress/StrainStress-Strain & Elastic ModulusBasic Biomechanics1818When a force is applied to any material, such as bone, it deforms. The amount of deformation in the material relative to its original length, is called strain. When a material is pushed together, the material shortens (compressive strain). When pulled, it gets longer (tensile strain). Shear strain arises when layers of a material slide against another, as might occur with torsion or bending.

If one graphs the resulting strain (L/ L0) due to the applied stress (F/A), the slope of the Stress-Strain curve is the Elastic Modulus.19

Elastic Modulus (GPa) of Common Materials in OrthopaedicsStainless Steel 200Titanium 100Cortical Bone 7-21Bone Cement 2.5-3.5Cancellous Bone 0.7-4.9UHMW-PE 1.4-4.2Basic Biomechanics2020Review the elastic modulus of common materials encountered in orthopaedic surgery relative to each other.Elastic DeformationPlastic DeformationEnergy

Energy AbsorbedForceDisplacementPlasticElasticBasic Biomechanics2121Elastic Deformation: In the elastic region, the relationship of displacement to the applied force in linear. In this region, the material returns to its resting state if the force is removed (elastic), like a rubber band.Stiffness: again, is the slope of the elastic portion of the force-displacement curve.Plastic Deformation: As more force is applied, the materials behavior becomes plastic, and permanent deformation occurs. The material will not return to its original state after the force is removed.Energy: The area under the curve represents energy absorbed into the material during the deformation process (work).22

Stiffness-FlexibilityYield PointFailure PointBrittle-DuctileToughness-WeaknessForceDisplacementPlasticElasticFailureYieldStiffnessBasic Biomechanics2323Stiffness: The steeper the slope, the stiffer the material. A material with a flat slope is flexible.Yield Point: the point on the force-displacement curve where the material changes from elastic to plastic deformation is the yield point.Failure Point: At some point the material will break; this point due is the materials Failure Point.Brittle: a material which experiences little plastic deformation before it fails is said to be brittle (glass for example).Ductile: if a material with a large plastic deformation region before it fails is said to be ductile (copper for example).Toughness: a material which can absorb more energy prior to failure (large area under the curve) is said to be tougher.Weakness: a material which can absorb little energy prior to failure (small area under the curve) is said to be weak.

24

FlexibleDuctile ToughStrong

FlexibleBrittleStrongFlexibleDuctileWeakFlexibleBrittleWeakStrainStress2525Bone tissue is a type of connective tissue used in forming bones. As I said Bones protect the vital organs and help support the body. It is composed mainly of collagen, or ossein, fibers, and bone cells called osteocytes. There are two types of bone tissue, referred to as cortical bone and cancellous bone. Cortical bone is also known as compact or dense bone, and most of a body's bones are made from this kind of bone. It is very strong and dense, and it makes up the hard exterior of a bone. Its surface is smooth and white, and covered by a thin membrane referred to as the periosteum, which holds capillaries and also gives tendons and muscles something to attach to. There are two types of cortical bone tissue as well, known as lamellar and woven bone. Lamellar is very strong and made from organized layers of ossein fibers. Most of the bones in an adult's body are made of lamellar bone. Woven bone is made very quickly by the cells called osteoblasts, and it is much weaker than lamellar. The ossein fibers that make up this type of tissue are typically arranged in an unorganized pattern, and it is usually made to help repair a fracture until it can be replaced by stronger material. Purposes of cortical bone include protection, support, and storage of minerals. Because this tissue is so strong, it is what protects vital organs and helps support the weight of the body. As I said Minerals that the body needs, like calcium, are also stored in cortical bone until the body has a need for them. Cancellous bone is also referred to as trabecular bone, and commonly referred to as spongy bone. This is the weaker of the two types of bone tissue. It resembles a sponge, and can usually be found inside bones, surrounded by cortical tissue, and at joints at the end of long bones.

Elastic Biomaterials (Bone)Elastic/Plastic characteristics

Brittle material fails before permanent deformation

Ductile material deforms greatly before failure

Bone exhibits both propertiesLoad/deformation curvesdeformation (length)loadductile materialelasticlimitbonebrittle material26Basic BiomechanicsLoad to FailureContinuous application of force until the material breaks (failure point at the ultimate load).Common mode of failure of bone and reported in the implant literature.Fatigue FailureCyclical sub-threshold loading may result in failure due to fatigue.Common mode of failure of orthopaedic implants and fracture fixation constructs.2727Compare the two types of failure:Load to Failure: Continuous application of force until the material breaks (failure point at the ultimate load). Bone usually fractures by load to failure.Fatigue Failure: Cyclical sub-threshold loading may result in failure due to fatigue.Load to failure testing often reported in the orthopaedic literature: however, clinically, failure fracture fixation constructs or implants often due to fatigue failure.

Basic BiomechanicsAnisotropicMechanical properties dependent upon direction of loadingViscoelasticStress-Strain character dependent upon rate of applied strain (time dependent).

Material properties of bones:2828Anisotropic: some materials (bone) have different mechanical properties dependent upon the type of load applied (transverse, longitudinal, shear).Viscoelastic: many biological materials to include bone reveal different stress-strain curves depending upon the speed at which the force is applied.Load and ResponseStressforce per unit areaStraindeformation amount of deformation divided by original lengthBone Stress-Strain RelationshipStrain (deformation)Stress (load)Elastic RegionFractureThresholdPlastic RegionBone BiomechanicsBone is anisotropic - its modulus is dependent upon the direction of loading.Bone is weakest in shear, then tension, then compression.Ultimate Stress at Failure Cortical BoneCompression < 212 N/m2Tension< 146 N/m2Shear< 82 N/m23131Bone is anisotropic - its modulus is dependent upon the direction of loading. Bone is weakest in shear, then tension, then compression. This can help us understand the fracture produced (failure) from various mechanisms (applied loads).Review the values of the Ultimate Stress at Failure of cortical bone based upon the different direction of loading for cortical bone.Anisotropic response behavior of bone is dependent on direction of applied loadBone is strongest alonglong axis - Why?

32Bone Anisotropytensioncompressiontrabecularcorticalsheartensioncompression020010050150Maximum Stress (MPa)From: Biomechanics of the Musculo-skeletal System, Nigg and Herzog33#Bone BiomechanicsBone is viscoelastic: its force-deformation characteristics are dependent upon the rate of loading.Trabecular bone becomes stiffer in compression the faster it is loaded.3434Bone is viscoelastic, the force-deformation curve will be different for different rates of loading.Trabecular bone becomes stiffer in compression the faster it is loaded. It is hypothesized that at high rates of loading the marrow elements do not have time to be push out, and act like a fluid filled shock absorber.fracturefracturefastslowLoaddeformationViscoelastic Response behavior of bone is dependent on rate load is appliedBone will fracture soonerwhen load applied slowly35#Wolffs LawEach change in the form and function of a bone or only its function is followed by certain definitive changes in its internal architecture, and secondary changes equally definitive in its external compliance, in accordance to the mathematics law36Wolffs Law (simplified)Theprinciplethateverychangeintheformandthefunctionofaboneorinthefunctionofthebonealone,leadstochangesinitsinternalarchitectureandinitsexternalform37Wolffs Law (further simplified)Bone in a healthy person or animal will adapt to the loads under which it is placed38

3940

Bone MechanicsBone DensitySubtle density changes greatly changes strength and elastic modulusDensity changesNormal agingDiseaseUseDisuseCortical BoneTrabecular BoneFigure from: Browner et al: Skeletal Trauma 2nd Ed. Saunders, 1998.4141Bone, as a living material, can experience changes in its density. Subtle density changes can have great effects upon the material properties of the bone. Graph shows a marked change in the stress/strain curve of trabecular bone when its density is decreased by a factor of 3. These changes occur with normal aging, disease, use and disuse.42

Basic BiomechanicsBendingAxial LoadingTensionCompressionTorsion

Bending Compression Torsion4343These bending, torsion, tensile and compressive forces are applied to bones, and if excessive, may lead to fracture.Fracture Mechanics

Figure from: Browner et al: Skeletal Trauma 2nd Ed, Saunders, 1998.4444The nature of the applied force is often evident by the nature of the fracture.Tension TransverseBending - Butterfly Compression - Oblique Torsion - Spiral

Vertebral fracturescervical fracturesspine loaded through heade.g., football, diving, gymnastics once spearing was outlawed in football the number of cervical injuries declined dramatically.2. lumbar fracturesweight lifters, linemen, or gymnastsspine is loaded in hyperlordotic (aka swayback) position.Compressive Loading4546

47

48

49

Fracture MechanicsBending load:Compression strength greater than tensile strengthFails in tension

Figure from: Tencer. Biomechanics in Orthopaedic Trauma, Lippincott, 1994.5050As the bone is subjected to a bending load, one side is placed under compression, the other is placed under tension. Since the bones compressive strength is greater than its tensile strength, the bone fails first on the tension side.51

52

53

54

55

Fracture MechanicsTorsionThe diagonal in the direction of the applied force is in tension cracks perpendicular to this tension diagonalSpiral fracture 45 to the long axisFigures from: Tencer. Biomechanics in Orthopaedic Trauma, Lippincott, 1994.5656TORSION: The diagonal in the direction of the applied force is in tension cracks perpendicular to this tension diagonalSpiral fracture 45 to the long axis.57

58

Fracture MechanicsCombined bending & axial loadOblique fractureButterfly fragment

Figure from: Tencer. Biomechanics in Orthopaedic Trauma, Lippincott, 1994.5959Combined bending & axial loads result in oblique fractures or those with a butterfly fragment.60ConclusionStress-Strain-Strength properties;Elastic Deformation Analyses;Plastic Deformation Analyses;Hardness of the parts;Resistance of bones.

60