• 1 Preliminaries
    • 1.1 Preface
  • 2 Syllabus
    • 2.0.1 Teaching team
    • 2.1 Schedule
    • 2.2 Catalog Description
    • 2.3 Prerequisites
    • 2.4 Textbook/Suggested Resources
    • 2.5 Reference materials:
    • 2.6 Course topics
    • 2.7 Course Objective
    • 2.8 Learning Outcomes
    • 2.9 Method of instruction:
    • 2.10 Grading Standard
      • 2.10.1 Major graded items
    • 2.11 Assignments and communication
      • 2.11.1 Expectations on student conduct for assignments and assessments
    • 2.12 Academic integrity
    • 2.13 Attendance, illness, and absences
  • 3 Introduction
    • 3.1 Course Introduction
      • 3.1.1 Introductions
      • 3.1.2 Objectives
      • 3.1.3 Project
      • 3.1.4 Almost-weekly anatomy quiz (Method TBD)
    • 3.2 Conceptual Overview of Orthopaedic Biomechanics
      • 3.2.1 The human body as a machine
  • 4 Musculoskeletal Anatomy
    • 4.1 Body level concepts
      • 4.1.1 Gross and Microscopic Anatomy
    • 4.2 Levels of Structural Organization of the Human Body
      • 4.2.1 Organ Systems of the Human Body
    • 4.3 Anatomical Terms
      • 4.3.1 Directional Terms Applied to the Human Body
      • 4.3.2 Planes of the Body
      • 4.3.3 Relative reference terms
      • 4.3.4 Terms of action
    • 4.4 Principal functions of the musculoskeletal system
      • 4.4.1 Hematopoiesis
      • 4.4.2 Elements of the Human Body
      • 4.4.3 Protection of the vital organs
      • 4.4.4 Support and motion
    • 4.5 Principal anatomical structures examined to this course
    • 4.6 Bones
      • 4.6.1 Major boney structures examined in this course
      • 4.6.2 Bone tissue types
      • 4.6.3 Long bone
      • 4.6.4 Anatomy of a Long Bone
      • 4.6.5 Periosteum and Endosteum
      • 4.6.6 Anatomy of a Flat Bone
      • 4.6.7 Bone Features
    • 4.7 Joints
      • 4.7.1 Structural classification of joints
      • 4.7.2 Synovial joints
      • 4.7.3 Ball and socket
      • 4.7.4 Bi-condylar joints
      • 4.7.5 Bi-condylar joints
      • 4.7.6 Multiple bone joints
      • 4.7.7 Multiple bone joints
    • 4.8 Soft Tissue
      • 4.8.1 Soft Tissue
      • 4.8.2 Muscle
      • 4.8.3 Muscle groups
      • 4.8.4 Tendons and ligaments
      • 4.8.5 Articular cartilage
      • 4.8.6
    • 4.9 Critical joints discussed in this course
      • 4.9.1 The hip
      • 4.9.2 The knee
      • 4.9.3 Spine
      • 4.9.4 Anterior portion of the intervertebral joint
      • 4.9.5 Vertebral attachments
    • 4.10 Fracture
      • 4.10.1 WARNING: Traumatic video coming
      • 4.10.2 Fracture
    • 4.11 Arthritis
      • 4.11.1 Arthritis
      • 4.11.2 Soft tissue damage
      • 4.11.3 Repair
    • 4.12 Visualizing orthopaedic structures
      • 4.12.1 X-Ray of a Hand
      • 4.12.2 Computed Tomography Scan
      • 4.12.3 Magnetic Resonance Imaging
      • 4.12.4 Ultrasound
      • 4.12.5 Ultrasound in orthpaedics
      • 4.12.6 Positron emission tomography
    • 4.13 Summary
      • 4.13.1 Objective
  • 5 Basic biomechanics
    • 5.1 Forces, moments, and equilibrium
      • 5.1.1 Forces
      • 5.1.2 Moments
      • 5.1.3 Equilibrium
    • 5.2 “Mathematical tools” in biomechanics
      • 5.2.1 Vectors and scalars
      • 5.2.2 Relationship between vectors and scalars
      • 5.2.3 Rigid body and flexible body assumptions
    • 5.3 Review of Stress and strain
      • 5.3.1 Normal stress
      • 5.3.2 Shear stress
      • 5.3.3 Stresses on arbitrary planes
      • 5.3.4 Stress
    • 5.4 Strain
      • 5.4.1 Normal strain
      • 5.4.2 Shear strain
      • 5.4.3 Strain
      • 5.4.4 A chain of relationships in biomechanics
    • 5.5 Deformation and stiffness
      • 5.5.1 Skeletal structures and types of load
      • 5.5.2 Stiffness
      • 5.5.3 Structural properties
    • 5.6 Material properties
      • 5.6.1 Stress \(\Longleftrightarrow\) Strain
      • 5.6.2 Stress \(\Longleftrightarrow\) Strain
    • 5.7 Energy and its relation to material response
      • 5.7.1 Elastic-plastic behavior
      • 5.7.2 Elastic-plastic behavior
      • 5.7.3 Bone density and the elastic modulus
      • 5.7.4 Energy and energy dissipation
      • 5.7.5 Energy and energy dissipation
      • 5.7.6 Toughness: brittle vs ductile
      • 5.7.7 Strength vs toughness
      • 5.7.8 Strength vs fatigue strength
    • 5.8 Properties of bone
      • 5.8.1 Mechanics of bone: anisotropy
      • 5.8.2 Types of bone fracture
      • 5.8.3 Types of bone fracture
      • 5.8.4 Types of bone fracture
      • 5.8.5 Types of bone fracture
      • 5.8.6 Types of bone fracture
    • 5.9 Geometric properties
      • 5.9.1 Properties of a cross section
      • 5.9.2 Properties of a cross section
      • 5.9.3 Properties of a cross section
      • 5.9.4 Properties of a cross section
      • 5.9.5 Implications for a fracture callus
      • 5.9.6 Stiffness as a function of healing time
      • 5.9.7 IM Nail Diameter
      • 5.9.8 Slotting
      • 5.9.9 Mechanics of bone: viscoelasticity
      • 5.9.10 Credits
  • 6 Link dynamic models
    • 6.1 Basic concepts
      • 6.1.1 Viewpoints for analysis of biomechanical systems
      • 6.1.2 Typical elements in a rigid body model
      • 6.1.3 Engineering perspective – simple joints
      • 6.1.4 Engineering perspective – complex joints
      • 6.1.5 Kinematics
      • 6.1.6 Modeling of muscle/tendon/ligament
      • 6.1.7 Muscle/tendon model
      • 6.1.8 Ligaments and capsules
      • 6.1.9 Mechanical response of ligaments
      • 6.1.10 Application of Link Dynamics Models
      • 6.1.11 Three types of solution are available for any problem
    • 6.2 Static analysis of the skeletal system
      • 6.2.1 Static analysis
    • 6.3 Computation of reaction forces
      • 6.3.1 Equilibrium revisited
      • 6.3.2 Force diagrams, statically equivalent forces, and “free body diagrams”
      • 6.3.3 Force diagrams, statically equivalent forces, and “free body diagrams”
      • 6.3.4 Force diagrams, statically equivalent forces, and “free body diagrams”
      • 6.3.5 Force diagrams, statically equivalent forces, and “free body diagrams”
      • 6.3.6 Force diagrams, statically equivalent forces, and “free body diagrams”
      • 6.3.7 The problem of redundancy (a mathematical problem)
      • 6.3.8 Additional examples of static analysis
      • 6.3.9 Indeterminance
      • 6.3.10 Example–rigid link analysis of body segments
      • 6.3.11
      • 6.3.12
      • 6.3.13 The Joint Force Distribution Problem
      • 6.3.14 Auxiliary conditions
      • 6.3.15 Optimization Technique
    • 6.4 The musculoskeletal dynamics problem
      • 6.4.1 Methods to solve the dynamics problem
      • 6.4.2 Body segment mass and geometric properties
      • 6.4.3 Anthropometric Data
    • 6.5 Anthropometry
      • 6.5.1 Proportionality Constants
    • 6.6 Sources of Anthropometric Data
    • 6.7 Deficiencies And Shortcomings Of Anthropometric Data
    • 6.8 Specific Examples Of Deficiencies
      • 6.8.1 Mathematical models for mass properties
      • 6.8.2 Muscle and ligament forces
      • 6.8.3 Lines of action
      • 6.8.4 Muscles cross joints
      • 6.8.5 Efficient use of muscles
    • 6.9 Joint stability
      • 6.9.1 Idealized stability in synovial joints
      • 6.9.2 Mechanisms for maintaining joint stability
      • 6.9.3 Range of healthy joint contact forces
  • 7 Mechanical Descriptions of Tissue
    • 7.1 Introduction
      • 7.1.1 The “material properties” of the musculoskeletal tissues
      • 7.1.2 Challenges in biological material testing
      • 7.1.3 Composition of bone
      • 7.1.4 Collagen
      • 7.1.5 Bone is a hierarchical composite material
      • 7.1.6 Lowest hierarchical level
      • 7.1.7 Highest hierarchical level
      • 7.1.8 Highest hierarchical level, diaphysis
      • 7.1.9 Cortical bone
      • 7.1.10 Damage detection
      • 7.1.11 Trabecular architecture
      • 7.1.12 Differences between cortical and trabecular bone
      • 7.1.13 Elastic anisotropy
      • 7.1.14 Thought experiment: isotropic material
      • 7.1.15 Uniform rectangular block pulled on both ends
      • 7.1.16 Isotropic constitutive behavior
      • 7.1.17 Is this how all materials behave?
      • 7.1.18 Origin of anisotropic behavior in bone
      • 7.1.19 Principal material coordinate system
      • 7.1.20 Anisotropic behavior
      • 7.1.21 Anisotropic behavior
      • 7.1.22 Elastic constants
      • 7.1.23 For isotropic material:
      • 7.1.24 Lamé constants
      • 7.1.25 Other material descriptions
      • 7.1.26 Cortical bone is well described as transversely isotropic
      • 7.1.27 Transversely isotropic
      • 7.1.28 Have we covered it all?
    • 7.2 Mechanical properties of cortical bone
      • 7.2.1 Asymmetric stiffness and strength
      • 7.2.2 Asymmetric stiffness and strength
      • 7.2.3 Stiffness and strength with age
      • 7.2.4 Graph Showing Relationship Between Age and Bone Mass
      • 7.2.5 Volume fraction
      • 7.2.6 Bone density
      • 7.2.7 Relationship between bone density and volume fraction
      • 7.2.8 Heterogeneity and variability
      • 7.2.9 Mineral content
      • 7.2.10 Heterogeneity and variability
      • 7.2.11 Density and strength
      • 7.2.12 Fatigue
      • 7.2.13 Minor’s rule for fatigue
      • 7.2.14 Creep
      • 7.2.15 Creep
      • 7.2.16 Plasticity and micro-structural damage
      • 7.2.17 Strain rate sensitivity
    • 7.3 Mechanical properties of trabecular bone
      • 7.3.1 Trabecular bone behavior and large variability
      • 7.3.2 Trabecular bone apparent density
      • 7.3.3 Trabecular bone crush strength and age
      • 7.3.4 Trabecular bone yield asymmetry
      • 7.3.5 Trabecular bone yield anisotropy
      • 7.3.6 Fatigue of trabecular bone
      • 7.3.7 Post-yield damage of trabecular bone
      • 7.3.8 Failure prediction
  • 8 Cartilage biomechanics
    • 8.1 Cartilage: Anatomy, Function, Biology, Biomechanics, Injury, And Surgical Treatment
      • 8.1.1 What do you know about cartilage?
      • 8.1.2 Why is this topic important to engineers?
    • 8.2 Primary Functions of Articular Cartilage
    • 8.3 Types of Cartilage
      • 8.3.1 Cartilage sub-types
      • 8.3.2 Hyaline Cartilage and Synovial Joints
      • 8.3.3 Articular cartilage
      • 8.3.4 Friction at articular surfaces
      • 8.3.5 Exercise and cartilage wear (literature example)
      • 8.3.6 Fibrocartilage - enthesis
      • 8.3.7 Sidebar - Tendon healing (and its relationship to fibrocartilage)
      • 8.3.8 Perichondrium
    • 8.4 Articular cartilage composition, microstructure
      • 8.4.1 Chondrocytes
      • 8.4.2 Chondrocyte Distribution in Articular Cartilage
      • 8.4.3 Articular cartilage zones
      • 8.4.4 Organization of Cartilage
      • 8.4.5 Slightly simplified view of Extracellular (porous) matrix
      • 8.4.6 Collagen
      • 8.4.7 Collagen
      • 8.4.8 Collagen Structure
      • 8.4.9 Structure and Arrangement of Collagen in Articular Cartilage
      • 8.4.10 Strength of Collagen
      • 8.4.11 Proteoglycans
      • 8.4.12 Proteoglycan Aggregate
      • 8.4.13 Water, ions
      • 8.4.14 In summary:
    • 8.5 Biomechanical Loading of Articular Cartilage
      • 8.5.1 Viscoelasticity
      • 8.5.2 Impact of arrangement of collagen on mechanical properties
    • 8.6 Mechanical properties
      • 8.6.1 Material Properties of Articular Cartilage
      • 8.6.2 Uniaxial tensile test
      • 8.6.3 Equilibrium stress-strain behavior
      • 8.6.4 Intrinsic compressive properties
      • 8.6.5 Intrinsic compressive properties
      • 8.6.6 Intrinsic compressive properties
      • 8.6.7 “Creep” manifestation in cartilage confined compression tests
      • 8.6.8 Intrinsic compressive properties
      • 8.6.9 Water content and compressive modulus
      • 8.6.10 Pure Shear
      • 8.6.11 Shear
      • 8.6.12 Shear: collagen and modulus
      • 8.6.13 Shear Stress
      • 8.6.14 Stress relaxation
      • 8.6.15 Compression and permeability (of cartilage plug)
      • 8.6.16 Creep and stress relaxation
      • 8.6.17 Permeability
      • 8.6.18 Cartilage - putting it together
      • 8.6.19 Clinical Correlate
      • 8.6.20 Clinical Correlate
      • 8.6.21 Clinical Correlate
      • 8.6.22 Clinical correlates
    • 8.7 Surgical repair options
      • 8.7.1 Microfracture - 2 years
      • 8.7.2 Microfracture - 2 years
      • 8.7.3 Microfracture FAQ
      • 8.7.4 Autologous Osteochondral Transplantation
      • 8.7.5 Fresh frozen allograph
      • 8.7.6 Evidence based medicine
      • 8.7.7 Future directions in cartilage repair
      • 8.7.8 Chondral scaffolds
      • 8.7.9 Scaffold methods
      • 8.7.10 Osteochondral scaffolds
      • 8.7.11 Biologics
    • 8.8 Lubrication of Articular Cartilage
      • 8.8.1 Joint Lubrication
      • 8.8.2 Lubrication Processes for Articular Cartilage
      • 8.8.3 Boundary Lubrication (dominant for low loads)
      • 8.8.4 Boundary Lubrication (dominant for low loads)
      • 8.8.5 Lubrication Processes for Articular Cartilage
      • 8.8.6 Fluid-film Lubrication
      • 8.8.7 Lubrication Processes for Articular Cartilage
      • 8.8.8 Hydrodynamic Lubrication
      • 8.8.9 Schematic of Hydrodynamic Lubrication
      • 8.8.10 Schematic of Hydrodynamic Lubrication
      • 8.8.11 Lubrication Processes for Articular Cartilage
      • 8.8.12 Squeeze-film Lubrication
      • 8.8.13 Schematic of Squeeze-film Lubrication
      • 8.8.14 Schematic of Squeeze-film Lubrication
      • 8.8.15 Articular Cartilage Asperities and Lubrication
      • 8.8.16 Asperities in Articular Cartilage
      • 8.8.17 Lubrication Processes for Articular Cartilage
      • 8.8.18 Modes of Mixed Lubrication
      • 8.8.19 Modes of Mixed Lubrication
      • 8.8.20 Modes of Mixed Lubrication
      • 8.8.21 Variation of Lubrication Processes for Articular Cartilage
      • 8.8.22 Comparison of Hydrodynamic and Squeeze-film Lubrication under Rigid and Elastodynamic Conditions
      • 8.8.23 Elastohydrodynamic Lubrication
      • 8.8.24 Dynamic Relationship between Vertical Load and Hip Joint Lubrication
      • 8.8.25 Dynamic Relationship between Vertical Load and Hip Joint Lubrication
    • 8.9 Two Types of Wear of Articular Cartilage
      • 8.9.1 Potential Methods for Articular Cartilage Degeneration
    • 8.10 Articular Surface of Cartilage
      • 8.10.1
    • 8.11 Cartilage Mechanics
      • 8.11.1 Mechanotransduction
      • 8.11.2 Mechanotransduction in soft tissue
  • 9 Ligaments and tendon mechanics (Bartel Chapter 4)
    • 9.0.1 Summary: tendon and ligament composition and microstructure
    • 9.0.2 Length scales in tendon and ligament
    • 9.0.3
    • 9.0.4 Typical stress-strain in tendon and ligament
    • 9.0.5 Be careful!
    • 9.0.6 Typical Whole Ligament Structural Properties (mean ± SD)
    • 9.0.7 On the next few slides
    • 9.0.8 Other simple models
    • 9.0.9 Strain rate sensitivity of tendon fascicles
    • 9.0.10 Summary of strain rate sensitivity
    • 9.0.11 Hypothesized relationship between failure mode vs. age
    • 9.0.12 Remodeling
    • 9.0.13 Time dependence and creep
    • 9.1 Intervertebral Disc
      • 9.1.1 Composition
      • 9.1.2 Other facts
      • 9.1.3 Mechanics
      • 9.1.4 Herniated, or slipped, disc
  • 10 Muscle mechanics
    • 10.0.1
    • 10.1 Meniscus
      • 10.1.1 Contact mechanics
      • 10.1.2 Meniscus
      • 10.1.3 Meniscus repair
  • 11 Arthroplasty
    • 11.1 Total Hip
    • 11.2 Biomechanics of Total Hip Arthroplasticity (Jastifer)
    • 11.3
    • 11.4
    • 11.5
    • 11.6
    • 11.7
    • 11.8 Total Knee
    • 11.9 Biomechanics of knee Arthroplasty (Jastifer)
    • 11.10
    • 11.11
    • 11.12
    • 11.13
    • 11.14
    • 11.15
    • 11.16
    • 11.17
    • 11.18
    • 11.19
    • 11.20
    • 11.21
  • 12 Tendon and Ligament: Anatomy, Function and Mechanics
    • 12.1
  • 13 Tendon and Ligament Mechanics (Jastifer)
    • 13.1
    • 13.2
    • 13.3
    • 13.4
    • 13.5
    • 13.6
    • 13.7
    • 13.8
    • 13.9
    • 13.10
    • 13.11
    • 13.12
    • 13.13
  • 14 Muscle Mechanics (Jastifer)
    • 14.1
      • 14.1.1
      • 14.1.2 Muscle Tissue
      • 14.1.3 Dense Connective Tissue
    • 14.2
    • 14.3
    • 14.4
    • 14.5
    • 14.6
      • 14.6.1 Muscle Slides Bartel
  • 15 Structural Analysis
  • 16 Beam Bending
    • 16.1 Beams in ortho
    • 16.2 Observations of beam physical deflection
    • 16.3 Definition of a beam
    • 16.4 Kinematics of an Euler-Bernoulli beam
      • 16.4.1 Assumed Euler-Bernoulli beam bending kinematics
      • 16.4.2 Strain in a beam
      • 16.4.3 Stress in a beam
    • 16.5 Beam loads
      • 16.5.1 Axial load in a beam
      • 16.5.2 Definitions
      • 16.5.3 Choice of coordinate system
    • 16.6
      • 16.6.1 Bending moments about \(x\)
      • 16.6.2 Bending moments about \(y\)
    • 16.7 Differential equations of static equilibrium
      • 16.7.1 Axial static equilbrium
      • 16.7.2 Bending static equilibrium
    • 16.8 Summary of beam equations
    • 16.9 Example: Uniform beam
      • 16.9.1 With uniform loading
      • 16.9.2 With uniform loading
      • 16.9.3 Caution!!!
      • 16.9.4 Contact Relationship Between Components
    • 16.10 Bartel Chapter 5 Structural Analysis of Musculoskeletal Systems: Beam Theory
  • 17 Torsion of solid shafts
    • 17.1 Torsion of uniform bars (shafts)
    • 17.2 Torsion boundary condition
    • 17.3 Integration of torque
      • 17.3.1 Notes
      • 17.3.2 Summary of key equations
      • 17.3.3 Examples
    • 17.4 Advanced Structural Analysis of Musculoskeletal Systems
      • 17.4.1 Torsion
      • 17.4.2 Contact stress analysis
  • 18 Finite elements
    • 18.1 Intro by example: spring elements
      • 18.1.1 Consider adding a second spring to the system
      • 18.1.2 Note: this process can also be accomplished through other methods such a through variational principles
    • 18.2 Brief summary of FEA
    • 18.3 Example of discretization
    • 18.4 Comments on the matrices
    • 18.5 Interpolation functions
    • 18.6 1D Truss Element
      • 18.6.1 Natural coordinate system
    • 18.7 Boundary conditions
      • 18.7.1 Elimination method
      • 18.7.2 Example: elimination method with symbols
      • 18.7.3 Example: elimination method with no applied force
      • 18.7.4 Example: elimination method with applied force
      • 18.7.5 Example: elimination method via partitioning with applied force
      • 18.7.6 Example: Penalty approach
      • 18.7.7 Problems with the penalty approarch
    • 18.8 Quadratic shape functions for bar elements
    • 18.9 Temperature effects
    • 18.10 2D Isoparametric elements and numerical integration
      • 18.10.1 2D Quad Element
    • 18.11 Numerical integration
  • 19 Bartel Chapter 7 Bone Implant Systems
    • 19.0.1 Implant materials
    • 19.0.2 Fracture fixation devices
    • 19.0.3 Joint replacement (Guest Lecture)
    • 19.0.4 Joint replacement (Dr. Gustafson)
    • 19.0.5 Implant systems
  • 20 Bartel Chapter 8 Fracture Fixation Devices materials were covered by Drs. Jaster and Geeslin
    • 20.1
    • 20.2
  • 21 Bartel Chapter 9 Total Hip Replacement
    • 21.1
    • 21.2
    • 21.3
    • 21.4
  • 22 Bartel Chapter 10: Total Knee Replacement
    • 22.1
    • 22.2
    • 22.3
  • 23 Bartel Chapter 11: Articulating Surfaces
    • 23.1
    • 23.2
    • 23.3 The shoulder
    • 23.4 Covering of the humeral head
    • 23.5 Key anatomy
    • 23.6 Humeral Head
    • 23.7 Stability
    • 23.8 Hierarchy of stability mechanisms
    • 23.9 Passive elements in gleno-humeral stability
    • 23.10 Bony elements
    • 23.11 Scapular inclination
    • 23.12 Labrum, Capsule, and Articular Surface
      • 23.12.1 The visoelastic piston model
    • 23.13 Piston in a vacuum
    • 23.14 Capillary attraction
    • 23.15
    • 23.16 The reinforcing ligamentous structures
    • 23.17 Inferior gleno-humeral ligament
    • 23.18 Middle gleno-humeral ligament
    • 23.19 Superior gleno-humeral ligament and the coracohumeral ligament
    • 23.20 Dynamic elements in gleno-humeral stability
    • 23.21 Rotator cuff
    • 23.22 The overall function of the dynamic stabilizers
    • 23.23 Abduction
    • 23.24 Adduction
    • 23.25 Flexion
    • 23.26 Extension
    • 23.27 Internal rotation
    • 23.28 External roation
    • 23.29 Summary
    • 23.30 Mobility
    • 23.31 Gleno-humeral movement
    • 23.32 Scapulo-thoracic movment
    • 23.33 Forces observed at the gleno-humeral joint
    • 23.34 The position of the upper limb
    • 23.35
    • 23.36 Demonstration
    • 23.37 Muscles
  • 24 Primer on Statistics
  • 25 Probability Distributions
    • 25.1 Introduction
    • 25.2 Question for this lecture?
    • 25.3 Sleepy?
    • 25.4 Random variables
    • 25.5 Types of probability distribution
    • 25.6 Normal distribution
    • 25.7 Normal (Gaussian) distribution
      • 25.7.1 Histogram and idealized probability density function
    • 25.8 Normal (Gaussian) distribution
    • 25.9 Normal (Gaussian) distribution
      • 25.9.1 Histogram and idealized probability density function
    • 25.10 Normal (Gaussian) distribution
    • 25.11 Bi-modal distributions
    • 25.12 Non-parametric distribution
    • 25.13 Assumptions regarding distribution of continuous variables
    • 25.14 Categorical distributions
    • 25.15 Bathtub Curve
  • 26 The Foundations of Statistic Analysis
    • 26.1 Populations and samples
    • 26.2 Populations and samples
    • 26.3 Populations and samples
    • 26.4 Inference
    • 26.5 Inference, hypothesis testing
    • 26.6 Confidence intervals
      • 26.6.1 Confidence interval
    • 26.7 10 Sample sets of 5 samples
    • 26.8 10 Sample sets of 5 samples
    • 26.9 10 Sample sets of 10 samples
    • 26.10 10 Sample sets of 20 samples
    • 26.11 10 Sample sets of 100 samples
    • 26.12 10 Sample sets of 1000 samples
    • 26.13 Confidence intervals
    • 26.14 Inference, hypothesis testing
    • 26.15 Measurement and Bias
    • 26.16 Bias
    • 26.17 Example: Do most smurfs like ice cream?
      • 26.17.1 Bias can be introduced by good intentions
    • 26.18 Example: Do most smurfs like ice cream?
      • 26.18.1 Bias can be introduced by good intentions
    • 26.19 Example: Do most smurfs like ice cream?
      • 26.19.1 Bias can be introduced by good intentions
    • 26.20 Example: Do most smurfs like ice cream?
      • 26.20.1 Bias can be introduced by good intentions
    • 26.21 Measurement and Instruments
      • 26.21.1 Accuracy vs precision
    • 26.22 Measurements
    • 26.23 Measurements
    • 26.24 Sensitivity and specificity
    • 26.25 Sensitivity and specificity
      • 26.25.1 TSA and Airport Security
    • 26.26 Sensitivity and specificity
      • 26.26.1 TSA and Airport Security
    • 26.27 Sensitivity and specificity
      • 26.27.1 TSA and Airport Security
    • 26.28 Dependency, correlation, and causation
    • 26.29 Dependency, correlation, and causation
    • 26.30 Hypothesis Testing
    • 26.31 Is there a real difference in the means?
    • 26.32 Null and alternative hypotheses
    • 26.33 Probability of data, given the null hypothesis
    • 26.34 Error types
    • 26.35 Type I error rate (\(α\))
      • 26.35.1 False positives
    • 26.36 Type II error rate (\(β\))
      • 26.36.1 False negatives
    • 26.37 p-value, power and sample size
    • 26.38 Power analysis
      • 26.38.1 a priori power analysis
    • 26.39 Power analysis
      • 26.39.1 Post-hoc power analysis
    • 26.40 Implications of power analysis
    • 26.41 Implications of power analysis
    • 26.42 Types of statistics and statistical tests
      • 26.42.1 Descriptive statistics
    • 26.43 One-variable and descriptive statistics
    • 26.44 Two-variable statistics
    • 26.45 Two-variable statistics
    • 26.46 Recommended methods from expertconsultbook.com
    • 26.47 Clinical Study Types
    • 26.48 Experimental versus observational studies
    • 26.49 Randomized controlled trial
    • 26.50 Observational studies
    • 26.51 Prospective observational studies
    • 26.52 Retrospective observational studies
    • 26.53 Strength of the evidence
    • 26.54 Hints for reading the literature
  • 27 Examples of power analysis calculations using R
    • 27.1 T-Test
    • 27.2 Arguments to pwr.t.test:
    • 27.3 One sided vs two sided
    • 27.4 One sided vs two sided
    • 27.5 Examples
    • 27.6 Examples
    • 27.7 T-Test
    • 27.8 Power for an anova
      • 27.8.1 (Multiple groups, continous outcomes)
    • 27.9 Arguments:
    • 27.10 Examples
  • 28 Sizing based on initial data – look a ficticious data
    • 28.1 Alternative methods for the same result
    • 28.2 Anova test compares more than two groups
    • 28.3 Max value of between.var if only 10 can be tested.
    • 28.4 Group variance if only 10 or 20 can be tested
    • 28.5 Power if only 10 or 20 can be tested.
    • 28.6 Example for biomechanical testing of surgical suturing technique
    • 28.7
    • 28.8
    • 28.9
    • 28.10
    • 28.11
    • 28.12
    • 28.13
    • 28.14 Chi-square test – Test two categorical variables (chisq.test, table)
    • 28.15 Tests for Normality
    • 28.16 Example, tests for normality, large sample
    • 28.17 Histogram
    • 28.18 QQ Norm
    • 28.19 Example, test for normality, small sample
    • 28.20 Histogram
    • 28.21 QQ Norm
    • 28.22 Example, test for normality, medium sample
    • 28.23 Histogram
    • 28.24 QQ Norm
  • 29 Sample survivorships study
    • 29.1 Number of mortalities requiring suspension and likelihood of case 1 (mortalities were random at suspension) and case 2 (mortalities were random at minimum survivorship) given the assumed survivorship.
  • 30 Appendix
    • 30.1 Generalized Linear Models – Compare continuous outcomes that are functions of catorical variables. (glm)
    • 30.2 Correlation compares to continous variables (cor.test, lm)
    • 30.3 Anova
      • 30.3.1 Post-hoc Tukey
    • 30.4 Compute Tukey Honest Significant Differences –
  • 31 OpenStax slides
    • 31.1 OpenStax chapter 1 images
      • 31.1.1 Metabolism
      • 31.1.2 Dorsal and Ventral Body Cavities
    • 31.2 OpenStax chapter 2 images
    • 31.3 OpenStax chapter 3 images
      • 31.3.1 Mitochondrion
      • 31.3.2 Multinucleate Muscle Cell
      • 31.3.3 Pathways in Calcium Homeostasis
    • 31.4 OpenStax chapter 4 images
      • 31.4.1 The Neuron
      • 31.4.2 Nervous Tissue
      • 31.4.3 Tissue Healing (Skin)
    • 31.5 OpenStax chapter 6 images
      • 31.5.1 Arm Brace
      • 31.5.2 Head of Femur Showing Red and Yellow Marrow
      • 31.5.3 Classifications of Bones
      • 31.5.4 Bone Cells
      • 31.5.5 Diagram of Compact Bone
      • 31.5.6 Diagram of Spongy Bone
      • 31.5.7 Paget’s Disease
      • 31.5.8 Diagram of Blood and Nerve Supply to Bone
      • 31.5.9 Intramembranous Ossification
      • 31.5.10 Endochondral Ossification
      • 31.5.11 Longitudinal Bone Growth
      • 31.5.12 Progression from Epiphyseal Plate to Epiphyseal Line
      • 31.5.13 Types of Fractures
      • 31.5.14 Stages in Fracture Repair
      • 31.5.15 Synthesis of Vitamin D
    • 31.6 OpenStax chapter 6 images
      • 31.6.1 Lateral View of the Human Skull
      • 31.6.2 Axial and Appendicular Skeleton
      • 31.6.3 Parts of the Skull
      • 31.6.4 Anterior View of Skull
      • 31.6.5 Lateral View of Skull
      • 31.6.6 Cranial Fossae
      • 31.6.7 Temporal Bone
      • 31.6.8 External and Internal Views of Base of Skull
      • 31.6.9 Posterior View of Skull
      • 31.6.10 Sphenoid Bone
      • 31.6.11 Sagittal Section of Skull
      • 31.6.12 Ethmoid Bone
      • 31.6.13 Lateral Wall of Nasal Cavity
      • 31.6.14 Maxillary Bone
      • 31.6.15 Isolated Mandible
      • 31.6.16 Bones of the Orbit
      • 31.6.17 Nasal Septum
      • 31.6.18 Paranasal Sinuses
      • 31.6.19 Hyoid Bone
      • 31.6.20 Vertebral Column
      • 31.6.21 Abnormal Curvatures of the Vertebral Column
      • 31.6.22 Osteoporosis
      • 31.6.23 Parts of a Typical Vertebra
      • 31.6.24 Intervertebral Disc
      • 31.6.25 Cervical Vertebrae
      • 31.6.26 Thoracic Vertebrae
      • 31.6.27 Rib Articulation in Thoracic Vertebrae
      • 31.6.28 Lumbar Vertebrae
      • 31.6.29 Sacrum and Coccyx
      • 31.6.30 Herniated Intervertebral Disc
      • 31.6.31 Ligaments of Vertebral Column
      • 31.6.32 Thoracic Cage
      • 31.6.33 Newborn Skull
    • 31.7 OpenStax chapter 8 images: The Appendicular Skeleton
      • 31.7.1 Dancer
      • 31.7.2 Axial and Appendicular Skeletons
      • 31.7.3 Pectoral Girdle
      • 31.7.4 Scapula
      • 31.7.5 Humerus and Elbow Joint
      • 31.7.6 Ulna and Radius
      • 31.7.7 Bones of the Wrist and Hand
      • 31.7.8 Bones of the Hand
      • 31.7.9 Carpal Tunnel
      • 31.7.10 Hand During Gripping
      • 31.7.11 Fractures of the Humerus and Radius
      • 31.7.12 Pelvis
      • 31.7.13 The Hip Bone
      • 31.7.14 Ligaments of the Pelvis
      • 31.7.15 Male and Female Pelvis
      • 31.7.16 Femur and Patella
      • 31.7.17 The Q-Angle
      • 31.7.18 Tibia and Fibula
      • 31.7.19 Bones of the Foot
      • 31.7.20 Embryo at Seven Weeks
      • 31.7.21 Clubfoot
  • 32 OpenStax chapter 8 images: Joints
    • 32.1 Introduction
      • 32.1.1 Girl Kayaking
    • 32.2 Types of joints
      • 32.2.1 Suture Joints of Skull
      • 32.2.2 Intervertebral Disc
      • 32.2.3 Multiaxial Joint
      • 32.2.4 Fibrous Joints
      • 32.2.5 The Newborn Skull
      • 32.2.6 Cartiliginous Joints
      • 32.2.7 Subtypes of synovial joints
      • 32.2.8 Bursae
      • 32.2.9 Types of Synovial Joints
      • 32.2.10 Osteoarthritis of a synovial joint
    • 32.3 Movements of the Body
      • 32.3.1 Movements of the Body
    • 32.4 Joints in and around the head
      • 32.4.1 Atlantoaxial Joint
      • 32.4.2 Temporomandibular Joint
    • 32.5 Appendicular joints (of interest to this course)
      • 32.5.1 Glenohumeral Joint (Shoulder)
      • 32.5.2 Elbow Joint
      • 32.5.3 Hip Joint
      • 32.5.4 Knee Joint
      • 32.5.5 Knee Injury
      • 32.5.6 Ankle Joint
  • 33 Miscellaneous
    • 33.1 Differential equations of static equilibrium
      • 33.1.1 Axial static equilbrium

ME5200 - Orthopaedic Biomechanics

6 Link dynamic models