Basic Biomechanics & Biomaterials for Orthopaedic p Surgeons g Tariq Nayfeh, M.D./Ph.D. Outline Introduction Basic Definitions Joint Mechanics Mechanics of Materials Bending Theory Biomaterials Why Study Biomechanics and Biomaterials To Pass Exams? Basic Definitions Statics S i is i the h study d off forces f on bodies at rest Dynamics is the study of the motion of bodies and the forces that produce the motion Basic Definitions Kinematics is the study of motion in terms of displacement, velocity, and acceleration with reference to the cause of the motion Kinesiology is the the study of human movement and motion Principle Quantities • This area is actually a low yield area for time spent studying and the number of questions asked Biomechanics is the science of the action of forces, internal or external on the living body. Basic Quantities • Length • Time • Mass So Why Study It? Derived Quantities The basis of all implants and devices we use The basis for most trauma we see • Velocity (length/time) The basis for most of our interventions • Acceleration (length/time2) • Force (mass length/time2) 1 Scalars and Vectors Free Body Diagrams Scalar quantities have magnitude but no direction. • Time, speed (not velocity), mass, volume Vector quantities have magnitude and direction. The forces acting on a body may be identified by isolating that body part as a free body diagram • Velocity, Force, Acceleration Beer and Johnston, “Mechanics of Materials” Example Free Body Diagrams Vectors A vector can be resolved into its individual components Vectors can be added to form a new vector by adding their components or graphically by the parallelogram method Fy F Fx Basic Laws of Mechanics Newton’s Laws Moments A moment (torque) is the rotational effect of a force about a point. F M = d M=Fxd First Law: An object at rest will remain at rest and an object in motion will continue in motion with a constant velocity y unless it experiences a net externall fforce • Inertia is the tendency of an object to either remain at rest or to maintain uniform motion in a straight line • The weight of a body is a vector quantity that is equal to the force of gravity acting on it 2 Basic Laws of Mechanics Newton’s Laws By combining the first and second laws: For equilibrium to occur the sum of the forces and moments must be equal to zero F 0 Basic Laws of Mechanics Newton’s Laws Third Law: Joint Mechanics Joints are stabilized by the action of the muscles, ligaments and bony structures. The muscles are located at a distance from the joint Muscle action produce moments about the joint center Joint Mechanics For every action there is an equal and opposite reaction. Joint reaction forces occur at the joint center These reaction forces can be greater than the weight of the body segment or the entire body Joint Mechanics How do joints maintain stability? What produces joint movement? Joint Mechanics When the muscle and joint reaction forces are balanced equilibrium occurs and the body segments do not accelerate When there is an imbalance of forces acceleration (or deceleration) of the body segment occurs 3 Illustrative Problem F x 0 y 0 F W=20 N B R G W 0 R B 15 20 R B 35 G= 15 N M 0 B 3 G 15 W 30 0 Illustrative Problem If the person bends forward Lw = 25 cm Lp = 40 cm Mspine = 450x0.25+200x0.4 Mspine =192.5 Nm 20 30 15 15 B 275 N 3 R 240 N Illustrative Problem Hip Reaction forces in single leg stance Nordin and Frankel, “Basic Biomechanics of the Musculoskeletal System” Forces across the hip and knee Hip joint contact forces • Single leg stance – 2 to 3 x BW • Walking - 3 x BW • Stairs, Stairs running - 5 to 7 x BW Knee Tibiofemoral forces • Rising from a chair – 4 x BW • Walking – 3 x BW • Stairs Ascent – 6 to 7 x BW • Stair Descent – 7 to 8 x BW Buckwalter, et al. “Orthopaedic Basic Science” Illustrative Problem This person is trying to lift a 20 kg object. The force from the upper extremities is 450 N Mechanics of Materials In order to understand how materials behave we need to define some basic quantities. The estimated moment arm of the upper extremities is Lw = 2cm The estimated moment arm of the weight is Lp= 30 cm. Mspine = 450x0.02 + 200 x0.30 Mspine = 69 Nm 4 In pure tension or compression Stress Stress is the intensity of internal force. Normal stress are perpendicular p p to the surface Shear stress are parallel F A Beer and Johnston, “Mechanics of Materials” The plane of maximum shear is at 45 degrees to the axis of loading!! Strain Strain (Engineering): Relative measure of the deformation (six components) of a body as a result of loading. L L Can be normal or shear AO/ASIF **A relative quantity with no units. Often expressed as a percent Beer and Johnston, “Mechanics of Materials” Depending on how you “slice” the material you can get combinations of stress and sheer Beer and Johnston, “Mechanics of Materials” AO/ASIF 5 Shear strain Usually expressed as an angle radians Hoop Stress As humans age, the diameter of their bones increase, but the thickness decreases… We will see later that this change is not bad for ordinary human activity. It matters most when we as surgeons intervene. Material Testing In order to characterize how materials behave we have to create standardize methods to test them and document the behavior. behavior In the US the ASTM standards are the most widely used In Europe the most widely used is the ISO standards Beer and Johnston, “Mechanics of Materials” “Hoop” stress Hoop stress is the stress in a direction perpendicular to the axis of an item ***As the thickness of the item decreases the hoop stress increases*** Why is this important? Materials Testing Materials of standardized sizes and shapes are placed in testing machines and loaded following standardized protocols p pr t pr 2 2t 1 Beer and Johnston, “Mechanics of Materials” 6 Stress-Strain Curves Standardized curves used to help quantify how a material will respond to a given load. AO/ASIF Quantities Derived from Stress-Strain Curves Yield Strength: The stress level at which a material begins to deform plastically Ultimate Strength: The stress level at which a material fails Modulus of Elasticity: The linear slope of the materials elastic stress-strain behavior. Ductility: The deformation to failure Toughness: Energy to failure (the area under the stress strain curve) Elastic vs. Plastic Behavior AO/ASIF Types of failure Ductile Brittle Elasticity vs. ductility and strength All of these materials have the same modulus of elasticity But they have different toughness, ductility and strength. AO/ASIF Beer and Johnston, “Mechanics of Materials” 7 Force-deformation curves for materials having various combinations of structural properties Force-Displacement Curves Similar to stress-strain curves Not a material property, instead a measure of how the entire structure behaves Depends on • Material • Geometry Force-Displacement Curves Beer and Johnston, “Mechanics of Materials” Stiffness L Buckwalter, et al. “Orthopaedic Basic Science” Question Unloaded: A=cross section area E=Young’s E Young s modulus of elasticity The linear relationship between an applied stress and the resultant deformation defines a material's •1- modulus of elasticity. •2- brittleness. •3- yield strength. •4- ultimate strength. •5- toughness. F u Longitudinal stiffness Sax = EA L F = SEA ax u = Saxu L If the question was changed to applied force, instead of applied stress. The answer would change to stiffness. 8 Bending of Beams Most bones and orthopaedic implants are subjected to axial, bending, and torsion loading Most failures M f il occur secondary d to bending and torsion compressio on tension M eccentric load compressio on tension centric load Linear bending theory eccentric load compressio on tension Bending Theory Definitions Neutral Axis: The location where a beam experiences zero stress (this is a theoretical axis and can actually be located outside of the structure) Moment of Inertia: The geometric property of a beam/s cross section that determines the beams stiffness • There is a bending and a torsion moment of inertia (we will limit our discussion to bending) Lo w s t res s High stress 9 Relative bending resistance Bending Resistance The resistance of a beam to bending is directly proportional to its moment of inertia The moment of inertia depends on its cross sectional area and shape Solid rod 1 Flat beam 3.5 I beam edge on 6 I beam flat 0.6 Hollow cylinder 5.3 Identical size of cross sectional area Gozna et al. 1982 Bending resistance solid cylinder = / 64 · diam4 Bending resistance of a hollow cylinder = / 64 · (outer diam4 – inner diam4) or for thin shells = / 8 · diam3 · shell thickness When the diameter of a spinal instrumentation rod is increased from 4 mm to 5 mm, the rod's ability to resist a bending moment is increased by approximately what percent? •1- 10% •2- 25% •3- 50% •4- 100% •5- 300% R1 64 d14 64 4 4 5 d 24 64 64 4 4 R2 R1 5 4 625 256 1.44 100% 4 R1 256 4 R2 4 850Kg. 800Kg. 60Kg. 20Kg. The bending stiffness of a half pin is proportional to one half the radius of the pin to what power? • 2 • 3 • 4 • One third • One fourth Bone-implant composite AO/ASIF 10 Tension band principle Example of tension bands A properly done tension band shifts the neutral axis to the surface of the beam so that compression occurs across the entire cross section torque shear Example of tension bands Mechanical Properties of Materials Isotropy • Material properties do not depend on direction • Steel • Aluminum Anisotropy • Material properties depend on the direction of loading • • • • Bone Tendons Ligaments Cement 11 Anisotropy Bone is an anisotropic material Hence failure depends on load direction and loading type Bending forces in the long bones most commonly result in what type of fracture pattern? •1- Short oblique •2- Transverse with butterfly •3- Linear shear of 45° •4- Spiral •5- Segmental What type of loading is most likely to cause a pure spiral fracture? •1- Crush •2- Bending •3- Tensile •4- Compression •5- Torsion Buckwalter, et al. “Orthopaedic Basic Science” Bone Mechanics Cortical bone is weakest in directions that cause tensile stresses. In the transverse direction the bone is acting as a brittle material AO/ASIF Three-point bending produces a predominantly transverse fracture because 1. 2. 3. 4 4. a compression crack begins at the fulcrum. bone is weaker in tension than in compression. bone is weaker in compression than in tension. the forces are equally resolved between tension and compression. 5. the forces are resolved into pure tension. Bending forces in the long bones most commonly result in what type of fracture pattern? •1- Short oblique •2- Transverse with butterfly •3- Linear shear of 45° •4- Spiral •5- Segmental What type of loading is most likely to cause a pure spiral fracture? •1- Crush •2- Bending •3- Tensile •4- Compression •5- Torsion 12 Clinical Example A 27-year-old patient sustains the closed femoral fracture shown. This fracture pattern is most likely the result of which of the following f forces? ? 1. Pure torsion 2. Pure bending 3. Pure compression 4. Four-point bending 5. Torsion plus bending Why are Long Bones Hollow? For the same total cross sectional area a hollow tube has higher bending and torsional resistance than a solid tube Most bones are loaded in bending and torsion Bone responds to Wolfe’s law and tries to maximize the bone density where stress is highest and minimize it where stress is lowest The thinner a bone is the easier it is for nutrients to reach the osteocytes Less energy is required to maintain the bone Clinical Question Case 1: A 75 year old female with osteoporosis falls and sustains a supracondylar femur fracture. The patient undergoes ORIF with a locked supracondylar plate. plate She is allowed to increase her weight bearing to full weight bearing at 6 weeks. Two weeks later she presents with increasing pain, swelling and can not bear weight. Case 2: A 75 year old female with osteoporosis falls and sustains an intertrochanteric hip fracture. She undergoes ORIF with an intramedulary device and is allowed to weight bear as tolerated the next day. Her fracture goes on to heal without complications. Clinical Example Case 3: An 83 year old male with multiple medical problems presents with severe right hip pain and the h inability i bili to b bear weight. He had undergone a revision of his right total hip 10 years ago to a cementless stem. Clinical Case Why did the patient in Case 2 do well while the patient’s in Case 1 and Case 3 have their implants fail? 13 Fatigue Fatigue Life Fatigue testing is done using the same type of samples and machines that are used to create stress-strain curves. However, the samples p are loaded cyclically y y to failure. The goal of testing is to determine how many loading cycles at a given load a material can withstand before failing. In a fatigue test, the maximum stress under which the material will not fail, regardless of how many loading cycles are applied, is defined as •1- endurance limit. •2- failure stress. •3 critical stress. •3stress •4- yield stress. •5- elastic limit. **The failure stress levels are not the same as the yield stress and ultimate stress.** Fatigue Fatigue testing generated fatigue life curves. Fatigue Endurance Limit – The stress level below which a material does not fail (usually must last greater than 10 million cycles) Bone Fatigue Bone has no in vitro endurance limit! In vivo bone heals If bone fails to heal when subjected to cyclic loads we get stress fractures Fatigue life – The number of cycles that a material can withstand at a given stress level Fatigue Life Clinical Examples In Case 1 above the patient was allowed to weight bear before her fracture healed. In this case the stress from walking on the bone resulted in rapid failure with relatively few cycles. Endurance Limit 14 At higher rates of loading, bone absorbs more energy prior to failure because Case 3 The applied stress to the small diameter implant again resulted in fatigue failure of the stem Stress Concentration When a structural member contains a discontinuity, such as a hole or a sudden change in cross section, high localized stresses may occur near the discontinuity. 1. the modulus of elasticity decreases. 2. bone is anisotropic. 3. bone is viscoelastic. 4. bone deforms plastically. 5. bone is stronger in compression than in tension. Viscoelasticity Viscoelasticty is a term used to describe materials that demonstrate time-dependant behavior to loading. • Visco is derived from viscocity (fluid like) • Elastic come from elasticity (solid like) Most normal temperature metals are elastic Most biologic materials (bone, tendon, ligaments), glass, polymers, and metals at high temperature exhibit viscoelastic behavior Beer and Johnston, “Mechanics of Materials” Stress Concentration The highest stress concentration occurs near a sharp point y max n 1 2 a p Viscoelasticity A simple model for an elastic material is a simple spring in which instantaneous displacement occurs to an applied load. load The energy of displacement is stored as potential energy and recovered when the load is removed. Buckwalter, et al. “Orthopaedic Basic Science” 15 Viscoelasticity Viscous behavior can be modeled as a dashpot (shock absorber). Deflection occurs in response to the rate of force application At higher rates of loading, bone absorbs more energy prior to failure because •1- the modulus of elasticity decreases. •2- bone is anisotropic. •3- bone is viscoelastic. •4- bone deforms plastically. •5- bone is stronger in compression than in tension. In this case the energy produced from loading is dissipated as heat. Buckwalter, et al. “Orthopaedic Basic Science” Viscoelasticity Viscoelastic Behavior is modeled as a combination of elastic and viscous materials. The change in strain of a material under a constant load that occurs with time is defined as •1- creep. •2- relaxation. Time •3- energy dissipation. •4- plastic deformation. •5- elastic deformation. The energy from loading is partially stored and partially dissipated Buckwalter, et al. “Orthopaedic Basic Science” Stress Relaxation The biomechanical properties of ligaments and bone demonstate 1. a time-dependent behavior. 2. a rate-independent t i d d tb behavior. h i 3. a straight-line load-deformation behavior. 4. modeling with linear elastic-spring elements. 5. similar stress-stretch curves. Stress relaxation is the decrease of stress with time under constant strain. Time 16 Examples of Materials Used for Implants Stress Shielding Wolff’s law “If you don’t use it, you lose it!” Stress shielding occurs when an implant carries most of the stress and effectively unloads the bone Examples are the proximal femur with an ingrown implant and loss of bone under a plate. Assume the plate is stainless steel with E=190 GPa Stress Shielding Assume the bone is all cortical bone with E=17 GPa Which of the following properties is most commonly associated with titanium alloy implants when compared with cobalt-chromium alloys? Both the bone and the plate must deform the same •1- Lower elastic modulus •2- Lower corrosive resistance •3- Better wear characteristics P F A P Fp Fb E p Ess p Eb b b 190 p b 10 b 17 Eb Ep P •4- Lower notch sensitivity •5- Greater hardness P Ap p Ab b (10 Ap Ab ) b b •ELASTIC MODULUS cancellous bone polyethylene PMMA (bone cement) cortical bone titanium alloy stainless steel cobalt-chromium alloy •ULTIMATE TENSILE STRENGTH cancellous bone polyethylene PMMA (bone cement) cortical bone stainless steel titanium alloy cobalt-chromium alloy P (10 Ap Ab ) p 10 Elastic modulus and ultimate tensile strength of the most common orthopedic biomaterials, listed in order of increasing modulus or strength: P (10 Ap Ab ) Stainless Steel In a 77-year-old woman who underwent total hip arthroplasty 10 years ago. What is the predominant cause of the proximal femoral bone loss? 1. Stress shielding 2. Polyethylene debris-induced osteolysis 3. Senile osteoporosis 4. Modulus of elasticity of the femoral stem 5. Diffuse osteopenia Used for fracture fixation and spinal implants Most common is 316L Contains chromium, chromium nickel, nickel molybdenum The chromium forms an oxide layer on the out side of the implant that acts as a corrosion resistant layer and forms the “stainless” quality to it Strong material but can get stress or crevice corrosion with time • Caused by “cracking” the Cr-oxide layer with loading 17 Cobalt-Chromium Alloys Polymers Polymers are large molecules made from combinations of smaller molecules Consists mostly of cobalt with chromium added for corrosion resistance Like stainless steel the chromium forms a surface oxide layer Their mechanical and biologic properties depends on their micro and macro-structure Used for joint replacements, bearing surfaces and occasionally for fracture fixation devices A polymers molecular weight depends on the number of molecules in its chains Not all Co-Cr is the same and the mechanical properties are a function of which alloy is used and how the alloy is processed There are a number of different alloys used for implants depending on what type of manufacturing is used Titanium • Nylon, PMMA, Polyethylene Polymers One of the most biocompatible metals Very good corrosion resistance • Resistance is generated by a rapidly formed oxidized layer on its surface and this layer makes the titanium implant more corrosion resistant that Stainless steel or CoCr implants Most commonly used alloy is Ti-6Al-4V Ti 6Al 4V • 6% aluminum and 4% vanadium • Initially developed as a high strength to weight ratio material for aircraft Its modulus of elasticity is around half of that of stainless steel or CoCr, hence using titanium implants my reduce the stress sheilding Very notch sensitive – leads to crack formation and decreased fatigue life Not a good bearing surface in joint arthroplasty because it gets rough with time Buckwalter, et al. “Orthopaedic Basic Science” Ceramics Ceramics are materials are inorganic materials formed from metallic and nonmetallic materials held together by ionic and covalent bonds • Examples include silica, alumina, zirconia Mechanical properties are very process dependant and can vary from manufacturer to manufacturer • Ceramtec a few years ago changed a single step in their process of making femoral heads (they did not change the material) which resulted in fracture of the heads in vivo Ceramics are very stiff, very hard, demonstrate very little wear Can be very brittle Very biocompatible if manufactured to a high purity level Polyethylene Semi-crystalline polymer Basic momer is CH2 with a molecular weight of 28 It mechanical Its h i l and d wear properties ti depend on its molecular weight, structure, oxidation, cross linking, processing method, and sterilization **Not all polyethylene is the same** 18 Highly cross-linked ultra-high molecular weight polyethylene has what effect on tensile and fatigue strength when compared with ultra-high molecular weigth polyethylene? 1. Increased d tensile il and d ffatigue i strength h 2. Increased tensile strength and decreased fatigue strength 3. Decreased tensile and fatigue strength 4. Decreased tensile strength and no change in fatigue strength 5. No change in tensile or fatigue strength Crosslinking Crosslinking is done to create larger molecular polyethylene molecules that can theoretically be more wear resistant There are two common methods for crosslinking • Irradiation • Free radical generating chemical Crosslinking Crosslinking The major problem with crosslinking is that usually higher doses of radiation which produce the greatest amount of crosslinking also may cause a degradation in the materials mechanical properties. Specifically a decrease in fracture toughness h and d fatigue f i strength h and d life. lif Newer “versions” of highly crosslinked polyethylene are being released that are being treated by a combination of lower dose radiation and post irradiation melting and or annealing. These processes are showing promise for low wear rates and small changes to the mechanical properties of the polyethylene Tribology The study of Friction, Lubrication, and Wear. Lewis, Biomaterials 22 (2001) 371-401 19 The natural joint Lubrication. Elements that influence the tribological function of a joint are: Lubrication reduces Wear reduces Friction The articular cartilage The synovial fluid And to a lesser extent the subcondral bone, capsule, soft tissues and ligaments. Friction Ability of a bearing to support a fluid film will inevitably influence the friction and wear of the bearing surfaces during articulation Lubrication modes “is the resistance to motion that is experienced whenever one solid body Slides over another” Boundary Lubrication Hydrodynamic Lubrication Hydrostatic Lubrication LOAD FRICTION FORCE DIRECTION OF MOTION STRIBECK CURVE Lubrication. “materials applied to the interface reducing friction and wear”. Coefficient of Friction (μ) BL ML FFL Sommerfeld Number (viscosity x sliding speed x radius / load) 20 Hydrodynamic Lubrication Boundary Lubrication Bearings are supported by a thin layer of fluid which is pulled into the bearing through viscous entrainment compressed entrainment, compressed, creating a sufficient hydrodynamic pressure to support load. h EHD h ~0.025μm - 2.5 μm High Friction and Wear Boundary Lubrication No pressure build up in the lubricant. Loading is 100% carried by the asperities i i iin the h contact area. The contact area is protected by absorbed molecules of the lubricant and / or a thin oxide layer. HD h >0.25μm Generation of fluid film As the ball rotates, fluid is drawn into the converging wedge and builds up a pressure which carries the load The characteristics for boundary lubrication is the absence of Hydrodynamic pressure. Fluid Film Lubrication Hydrodynamic Lubrication Pressure builds as speed increases. The surface asperities are completely separated by a lubricant film. No Friction or Wear The load and Hydrodynamic pressures are in equilibrium. 21 Hydrostatic Lubrication Clearance Bearings are supported on a thick film of fluid supplied from an external pressure source. P h P What is Radial Clearance? Artificial joint surfaces Metal / Ceramic bearing on UHMWPE do not benefit from fluid film lubrication they operate in a mixed fluid film regime. Unavoidable wear results at a rate of approximately 200µm of linear penetration per year giving a life expectancy of a 4mm thick cup about 20 years. M-on-M and Ceramic on Ceramic perform in a fluid film regime therefore the resultant wear rate is significantly reduced. Which of the following features improved fluid film lubrication in a metal-on-metal total hip arthroplasty? 1. 2. 3. 4. 5. Smaller diameter femoral head, a completely congruent fit between the socket and the head, and sufficient roughness to allow for some microseparation between the head and socket Smaller diameter femoral head, a slight clearance between the socket and the head, and no surface roughness Larger diameter femoral head, a completely congruent fit between the socket and the head, and minimal surface roughness Larger diameter femoral head, a slight clearance between the socket and the head, and minimal surface roughness Larger diameter femoral head, a slight Radius Cup R2 -- Radius Head R1 -= Radial Clearance -Clearance allows a fluid Is there an optimal clearance? No one clearance, it is a ratio to head diameter The bigger the head gets, the bigger the clearance gets We must consider manufacturing capabilities Nominal and Ranges etc… The lubricant fluid in Vivo V ti ht 22 Effect of clearance with bovine serum all tests to date Too tight and too high clearances may end up in high wear rates due to an increase in friction 0 Does reduced clearance make a difference? BOA Manchester 2004 McMinn presented early results of 20 controlled clearance cases implanted in 2004. Radiolucencies observed in superior acetabulum in 10% of the cases to date. Reduced Clearance bearings need further assessment. 24 hour Cobalt output in Regular and low clearance BHR£ Regular BHR vs Controlled Clearance BHR Urine Cobalt Output 90 80 Regular BHR Low Clearance BHR Urine Output µg/24hr 70 60 50 40 30 20 10 0 Pre Op 5 day 2 month 6 month 1 year 4 year 23
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