1. Biomechanics
Class 6: HSSP MIT

2. Topics Part 1: Part 2: Forces Free Body Diagram Bone mechanics
Small forces
Atomic Force Microscopy

3. Definition
Study of forces on and movement of living organisms and their components
Microscopic mechanics: muscle cells, proteins (collagen), cells
Macroscopic mechanics: muscles, bones, whole body

4. What are applications of biomechanics?
Orthopedics: replacement of knee joints and bones with artificial ones
Can metal joints withstand a load and distribute the force the same way that natural joints can?
Preventing sports injuries (correct postures that reduce stress/impact on the body)
Diseases: muscular dystrophy, osteoporosis

5. Force (F) Definition: push or pull on an object
Force is a vector: has magnitude and direction
F = mass x acceleration (SI unit= kg·m/s2=Newton)
Types of Forces:
Contact forces: applied force, friction, tension, compression
Non-contact forces: gravity, electric, magnetic

6. Newton’s Three Laws of Motion
1. Inertia: An object with no net force acting on it tends to remain as it is (be at rest or move at same velocity)
2. Force is mass x acceleration.
3. For every action, there is an equal and opposite reaction.

7. Free body diagram
Body (or part) removed from interconnected parts, so that the forces on the body can be studied
The center of gravity, and draw the forces to point toward or away from the center
Designate one direction to be positive and the other to be negative.
For an object at constant v or v=0, the sum of the net forces on the object should be zero.
Ftable=m·g y x
Fgravity= -m·g

8. Example of a Free Body Diagram
Fwood post
Fgravity
Σ Fy = Fwood post- Fgravity =0 (net force)

9. Bone Biomechanics

10. Structure of bone

11. Structure of Bone
Osteons: cylindrical fibers along length of compact bone

12. Bone Composition Bone as a Composite Material
Bone is a composite (like CFRP) of collagen (Cn) and hydroxyapatite (HA). Cn is rather like a polymer material (except that it comes in fibres,); HA is very like a reinforcing ceramic (in the form of elongated crystals). The photo shows the Cn fibres without the HA
Sheets of composite material (lamellae) are stacked together (very like CFRP construction methods). Fibre orientation may vary from sheet to sheet, and the sheets may be flat or curved.
Slide from:

13. Biomechanics terms Load: force applied to an object(Newtons)
Stress: force per unit area (Newtons/meter2)
Strain: change in length divided by original length
Elastic modulus: ratio of the stress divided by strain
Deformation: change in shape of the object due to applied load
Loading rate: speed at which the stress is repeatedly applied

14. Stress (σ) It’s an intensive property (independent of size/area)
For a normal force:
Tensile stress: stress vectors point out from the object
Compressive stress: force vectors point into the object
Unit=Newton/m2=Pascal
σtension
A (area)
tension
σ compression
A (area)
compression

15. Stresses on Bone

16. Strain (ε) ΔL=change in length L0=original length
Strain is a ratio of the change in length for a given applied stress (dimensionless number).
A metal rod has a strain γ=0.02 for an applied stress. Determine the change in length if the original length was 2 meters.

17. Strain Problem

18. Measuring Stiffness of Bone

19. Relationship b/w Stress and Strain
Stiffness is the ratio of the stress over the strain.
UTS= ultimate tensile stress that object can withstand w/o change in cross-sectional area
Failure:
Elastic
Slide from:

20. Elasticity Elasticity is a measure of stiffness of a material.
The greater the elasticity, the stiffer the material
Young’s modulus (γ) is the ratio of the tensile stress of the strain.
Table of Young’s modulus values:

21. Anisotropic behavior
Anisotropic: stiffness (Young’s modulus) of bone changes according to the direction of the applied load

22. Bone stiffness adapts to load
Bone strength adapts to forces applied to it
Loss of mineralization occurs with decrease in loading
1 month in space = 1% loss in bone density
17 weeks of bedrest= ~10% loss in bone density

23. Bone is constantly remodeled
Overtime, bone becomes weaker: micro-fractures occur with lamellae (layers within osteon)
Bone is constantly being rebuilt (collagen is re-deposited and minerals are embedded)
Osteoblasts are cells that rebuild bone.
Osteoclasts break down bone.

24. Osteoporosis Bone Strength (stiffness decreases with age)

25. Atomic force microscopy

26. AFM Can measure forces at the nano-scale (10^-9 Newtons)
Measure stiffness of cells, proteins
Can resolve the image of nano-sized objects

27. AFM device AFM measures the force b/w the tip (probe) and the surface
Components:
Cantilever
Laser beam
photodetector
Surface for scanning

28. Probe & Tip
Cantilever probe: um in width
Tip: 4 um depth

29. Using AFM to measure forces
Hooke’s Law
Δx: displacement
K: spring constant
F=-k·Δx

30. Using AFM to image objects
Contact mode
Using the tip to resolve small objects
Nano-sized DNA

31. Contact-mode AFM (Imaging)

32. Objects to measure
Calibration: Record the height of the deflection (h).
Dime (mm)
Nickel (mm)
3 objects to scan across & measure:
Paper clip
Cylindrical object
candy

33. Resources Physics tutorial:
2l2b.cfm
Human walking patterns: ml