Introduction to Analysis of strain and strain in Human bone

1. Analysis of and strain in human bone 1 By Nabapallab Deka Structural Engineering Civil Engineering Department NIT Silchar

2. Organic Components (e.g. collagen) Inorganic Components (e.g., calcium and phosphate) 65-70% (dry wt) H 2 O (25-30%) one of the body’s hardest structures viscoelastic ductile brittle Biomechanical Characteristics of Bone 25-30% (dry wt)

3. Strength and Stiffness of Bone Tissue It is evaluated using relationship between applied load and amount of deformation which is represented by LOAD - DEFORMATION CURVE Bone Tissue Characteristics Anisotropic Viscoelastic Elastic Plastic

4. Properties of Bone An organic material, bone can often be considered in the same way as man-made engineering materials. Factors affecting properties include: Age Gender Location in the body Temperature Mineral content Amount of water present Disease, e.g. osteoporosis.

5. Stress = Force/Area Strain = Change in Length or Angle/original dimension Note: Stress-Strain curve is a normalized Load-Deformation Curve

6. elastic region plastic region fracture/failure Stress (Load) Strain (Deformation) D stress D strain Elastic & Plastic responses

7. Elastic Biomaterials (Bone) Elastic/Plastic characteristics Brittle material fails before permanent deformation Ductile material deforms greatly before failure Bone exhibits both properties Load/deformation curves deformation (length) load ductile material elastic limit bone brittle material

8. Anisotropic response behavior of bone is dependent on direction of applied load Bone is strongest along long axis - Why?

9. fracture fracture fast slow Load deformation Visco -elastic Response Behavior of bone is dependent on rate at which load is applied. Bone will fracture sooner when load applied slowly

10. Compression Tension Shear Torsion Bending Mechanical Loading of Bone

11. Vertebral fractures cervical fractures spine loaded through head e.g ., football, diving, gymnastics once “spearing” was outlawed in football the number of cervical injuries declined dramatically. 2. lumbar fractures weight lifters, linemen, or gymnasts spine is loaded in hyperlordotic (aka swayback) position. Compressive Loading

12. Tensile Loading Main source of tensile load is muscle. T ension can stimulate tissue growth F racture due to tensile loading is usually an avulsion, other injuries include sprains, strains, inflammation, bony deposits. W hen the tibial tuberosity experiences excessive loads from quadriceps muscle group develop ,the condition is known as Osgood- Schlatter’s disease

13. Shear Forces It is created by the application of compressive, tensile or a combination of these loads.

14. Usually a 3- or 4-point force application Bending Forces

15. Torsional Forces Caused by a twisting force produces shear, tensile, and compressive loads tensile and compressive loads are at an angle spiral fracture can develop from this load

16. Modulus Bone can be considered to consist primarily of collagen fibres and an inorganic matrix, and so on a simple level it can be analysed as a fibre composite. The Young’s Modulus of aligned fibre composites can be calculated using the Rule of Mixtures and the Inverse Rule of Mixtures for loading parallel and perpendicular to the fibres respectively.

17. Young’s Modulus measurement

18. Observations For the transverse direction, the composite model closely agrees with experimental values. However, in the longitudinal direction the difference is large. A better approximation would be to model it as a two level composite. Actual values of Young’s Modulus are given below

19. Tensile and Compressive Strength There is a large variation in measured values of both the tensile and compressive strength of bone. Different bones in the body need to support different forces, so there is a large variation in strength between them. Additionally, age is an important factor, with strength often decreasing as a person gets older.

20. Elasticity Bone mineral is a ceramic material and exhibits normal Hook’s elastic behaviour, i.e. a linear stress-strain relationship. In contrast, collagen is a polymer that exhibits a J-shaped stress-strain curve. Typical stress-strain curves for compact bone, tested in tension or compression in the wet condition, are approximately a straight line. Bone generally has a maximum total elongation of only 0.5 - 3%, and therefore is classified as a brittle rather than a ductile solid.

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