1. The University of SydneySlide 1 Biomechanical Modelling of Musculoskeletal Systems Presented by Phillip Tran AMME4981/9981 Semester 1, 2015 Lecture 5

2. The University of SydneySlide 2 The Musculoskeletal System

3. The University of SydneySlide 3 The Musculoskeletal System Skeletal System Provides support, structure, and protection Made up of: –Bones –Ligaments –Cartilage –Joints Muscular System Provides movement Made up of: –Muscles –Tendons

4. The University of SydneySlide 4 Bones Cortical/Compact bone –Hard, dense bone Cancellous/Spongy bone –Trabeculae align along lines of stress –Contains red marrow in spaces Medullary Cavity –Contains yellow marrow

5. The University of SydneySlide 5 Synovial Joints Articular Cartilage –Act as spongy cushions to absorb compressive forces Joint Cavity –Space that contains synovial fluid Articular Capsule –Synovial membrane secretes synovial fluid –Fibrous layer holds the joint together Synovial Fluid –Reduces friction between cartilage Ligaments –Reinforce the entire structure

6. The University of SydneySlide 6 Tendons and Ligaments Tendons –Dense connective tissue that attach muscles to bones –Made up of collagen fibres that are aligned along the length of the tendon –Transfers pulling force of the muscle to the attached bone Ligaments –Connect one bone to another –Provides stabilisation

7. The University of SydneySlide 7 Skeletal Muscles Muscle Contraction –Concentric: muscle shortens –Isometric: no change in length –Eccentric: muscle extends Force of Muscle Contraction –Number of muscle fibres recruited –Size of fibres –Frequency of stimulation –Degree of muscle stretch

8. The University of SydneySlide 8 Anatomical Position and Planes Anatomical Position –Arms at side with palms facing forward –Legs straight and together with feet flat on the ground –Movements of the body are described in relation to this position Anatomical Planes –Coronal (front/back) –Sagittal (left/right) –Transverse (top/bottom)

9. The University of SydneySlide 9 Anatomical Directions

10. The University of SydneySlide 10 Movement Flexion/ExtensionAbduction/Adduction

11. The University of SydneySlide 11 Movement RotationSupination/PronationDorsi/Plantarflexion

12. The University of SydneySlide 12 Biomechanical Modelling

13. The University of SydneySlide 13 Solving a Mechanical Problem –Forces are applied to a body –Geometry is known –Finding the internal stresses –Finding the resultant motion

14. The University of SydneySlide 14 Solving a Mechanical Problem Known Forces F Equations of MotionDouble Integration ∬ Displacement r Forces (known) Motion (unknown)

15. The University of SydneySlide 15 Solving a Biomechanical Problem Internal Forces –Active muscles –Reactions at joints –Reactions at ligaments External Forces –Inertial forces due to acceleration of a segment –Load applied directly to a body segment External force Internal force

16. The University of SydneySlide 16 Solving a Biomechanical Problem Known Displacement r Double DifferentiationEquations of MotionForces F Internal Forces (unknown) Motion (known) External Forces (known)

17. The University of SydneySlide 17 Direct/Inverse Problems Direct Problems (Mechanical) Using known forces to determine movement –Requires accurate measurements of the geometry –Requires knowledge of external forces Inverse Problems (Biomechanical) Using known movements to determine the internal forces: –Requires full description of the movement (displacement, velocity, acceleration) –Requires accurate measurements of anthropometry (measurement of the human body) –Requires knowledge of external forces

18. The University of SydneySlide 18 Movement: Motion Tracking

19. The University of SydneySlide 19 Movement: Motion Tracking

20. The University of SydneySlide 20 Movement: Trajectories of Motion

21. The University of SydneySlide 21 Movement: Trajectories of Motion

22. The University of SydneySlide 22 Measuring Movement

23. The University of SydneySlide 23 Types of Motion

24. The University of SydneySlide 24 Anthropometry Measurement of the human body –Segment length –Segment mass –Position of centre of gravity –Density

25. The University of SydneySlide 25 Anthropometry Body SegmentLength (% of height) Distance of centre of mass from distal joint (% of limb) Mass (% of body mass) Head9.450.05.7 Neck4.51.3 Thorax+Abdomen25.030.3 Upper Arm18.043.62.6 Forearm26.043.01.9 Hand50.60.7 Pelvis9.414.0 Thigh31.543.312.8 Shank23.043.35.1 Foot16.050.01.3

26. The University of SydneySlide 26 Anthropometry Body SegmentDensity (g/cm 3 )Mass moment at centre of mass per segment length (km·m 2 /m) Head 1.11 Neck 1.11 Thorax+Abdomen Upper Arm 1.070.322 Forearm 1.130.303 Hand 1.160.297 Pelvis Thigh 1.050.323 Shank 1.090.302 Foot 1.100.475

27. The University of SydneySlide 27 External Forces Gravitational Forces –Acting downward through the centre of mass of each segment Ground Reaction Forces –Distributed over an area –Assumed to be acting as a single force at the centre of pressure Externally Applied Forces –Restraining or accelerating force that acts outside the body –Mass being lifted

28. The University of SydneySlide 28 Biomechanical Modelling: Body Segments –Body segments can be modelled as rigid bodies –Free body diagrams can be drawn for each segment –Forces and moments acting at joint centres –Gravitational forces acting at the centres of mass –Accurate measurements are needed of: –Segment masses (m) –Location of centres of mass –Location of joint centres –Mass moment of inertia (I)

29. The University of SydneySlide 29 Biomechanical Modelling: Assumptions –Rigid body motion (deformation is small relative to overall motion) –Body segments interconnected at joints –Length of each body segment remains constant –Each body segment has a fixed mass located at its centre of mass –The location of each body segment’s centre of mass is fixed –Joints are considered to be hinge (2D) or ball and socket (3D) –The moment of inertia of each body segment about any point is constant during any movement

30. The University of SydneySlide 30 Examples

31. The University of SydneySlide 31 Arm Analysis: Part 1 A flexed arm is holding a ball of W b =20 N with a distance of 35 cm to the elbow centre. What is the force required in the biceps (B) if the forearm weighs W a =15 N and the centre of mass for the forearm is 15 cm from the elbow centre of rotation? Also find the reaction force at the elbow joint. Assume the forearm is in the horizontal position and the angle between the forearm and upper arm at the elbow is 100 degrees. The biceps tendon is inserted 3 cm from the elbow centre of the forearm, and at the proximal end of the upper arm, which is 30 cm in length.

32. The University of SydneySlide 32 Arm Analysis: Part 1 Free Body Diagram Using trig formulae: θ = 74.5°

33. The University of SydneySlide 33 Arm Analysis: Part 1

34. The University of SydneySlide 34 Arm Analysis: Part 2 The ball is lifted from the horizontal forearm position with an angular acceleration of α =2rad/s 2. Determine the additional force required by the bicep to provide this movement. The radius of the forearm is 4cm. Assume that the upper arm remains stationary.

35. The University of SydneySlide 35 Arm Analysis: Part 2

36. The University of SydneySlide 36 Summary –The skeletal and muscular systems work together to provide movement for the human body –The body can be modelled biomechanically –Inverse method to derive the internal muscle forces and joint reactions –Movement –Anthropometry –External forces

37. The University of SydneySlide 37 Joint Reaction Analysis A person stands statically on one foot. The ground reaction force R acts 4cm anterior to the ankle centre of rotation. The body mass is 60kg and the foot mass is 0.9kg. The centre of mass of the foot is 6cm from the centre of rotation. Determine the forces and moment in the ankle. Rotation Centre Mass Centre RyRy RxRx mg AxAx AyAy MAMA

38. The University of SydneySlide 38 Joint Reaction Analysis

39. The University of SydneySlide 39 Joint Reaction Analysis A person exercises his left shoulder rotators. Calculate the forces and moments exerted on his shoulder. F = 200 N a = 25 cm b = 30 cm y x z RjRj MjMj F A a b B C a b

40. The University of SydneySlide 40 Joint Reaction Analysis

41. The University of SydneySlide 41 Muscle Analysis A weight lifter raises a barbell to his chest. Determine the torque developed by the back and the hip extensor muscles (M j ) when the barbell is about knee height. Weight of barbell, W b = 1003N Mass of upper body, m u = 53.5kg a = 38cm, b = 32cm, d = 64cm I G = 7.43 kg·m 2, α = 8.7 rad/s 2 a Gx = 0.2 m/s 2, a Gy = -0.1 m/s 2 MjMj FjFj O y x 60° WbWb a mugmug b G d

42. The University of SydneySlide 42 Muscle Analysis