Ch. 3 - Bone Mechanics

Question 1

What is the aim of mechanobiology and why can it be helpful to understand?

Answer 1

Mechanobiology aims to discover how mechanical forces modulate morphological and structural fitness of the skeletal tissues. Bone is remodelling itself constantly in response to the external mechanical environment. An understanding of how mechanical forces regulate bone adaptation can lead to improved:

• implants
• fracture treatment
• drug development for bone disease

Question 2

Describe the molecular structure of bone.

Answer 2

1. Helical protein chain consisting of amino acids connected by peptide bonds
2. Collagen molecule is made up of 3 of these protein chains
3. Collagen fibril is made up of collagen molecules arranged in parallel in a regular 1/4 stagger arrangement

Question 3

Describe the hierarchical composition of bone and its corresponding dimensions.

Answer 3

1. Mineralised collagen fibril (0.1 microns)
2. Lamellar (stacked thin sheets) + Woven (block of randomly oriented) (10 microns)
3. Primary lamellar (concentric lamellar rings), Haversian, Laminar, Woven (500 microns)
4. Trabecular, Cortical (>1000 microns)

Question 4

Define the term volume fraction.

Answer 4

Volume fraction is the ratio of volume of actual bone tissue to bulk volume of the sample.

Question 5

How does the porosity of cortical bone compare to that of trabecular bone?

Answer 5

Cortical bone has P<30%

Trabecular bone has P<60%

Question 6

Define the term tissue density. How is it different from apparent density?

Answer 6

Tissue density is the ratio of mass to volume of actual bone tissue, not including vascular porosity. Apparent density is the ratio of mass of bone tissue to bulk volume of the sample, including volume associated with vascular pore spaces.

Question 7

Define ash density and describe how it is obtained.

Answer 7

Ash density is used to describe the degree of mineralisation and can be obtained when bone is deorganified by heating it in a furnace for 24 hrs. at 700C, thereby removing all water and organic material.

Question 8

Define anisotropic.

Answer 8

Having different properties in different directions (e.g. biological materials - bone, wood)

Question 9

Define isotropic.

Answer 9

Having the same properties in all directions (e.g. engineered materials - metal, plastic)

Question 10

Define orthotropic.

Answer 10

Material behaviour can be described by 3 axes (x,y,z); used to describe anisotropy of bone

Question 11

Define transverse isotropic.

Answer 11

Material properties are the same about any one axis.

Question 12

What are the main material properties of cortical bone?

Answer 12

1. Transversely isotropic bc of osteon microstructure
2. Stronger in longitudinal direction than in radial directions
3. Stronger in compression than in tension
4. Heterogenous
5. Cortical porosity varies btw men and women at different ages
6. When loaded beyond yield point, then unloaded, permanent residual strains develop and Young’s modulus is reduced
7. Viscoelastic material - modulus and strength increase as the strain rate increases
8. Age and disease decrease strength 2% per decade, while ultimate strain decreases 10% per decade

Question 13

What is the most important parameter used to describe the microstructure of trabecular bone? Why?

Answer 13

Apparent density. Because porosity here plays a role.

Question 14

How come trabecular bone is anisotropic if the structure is initially random?

Answer 14

If the material structure is initially random, we may think the material ends up being isotropic. However, tissue is most frequently loaded in certain directions and reinforced in those directions, leading to anisotropy.

Question 15

What does the porous nature of trabecular bone mean in terms of how much compression it can withstand?

Answer 15

In compression we can get larger deformations without reaching catastrophic failure. At very large deformations we compact the structure - changing its density and so increasing its strength!

Question 16

Could you use average values to describe the mechanical properties of trabecular bone? Why or why not?

Answer 16

No, because of the large variation in apparent density. Instead, we perform mechanical experiments and derive structural property relations by relating results to microstructural parameters.

Question 17

How and why do strength and strain of trabecular bone change with time?

Answer 17

Both architecture and apparent density are related to age, resulting in a large age-related reduction in strength. However, yield strain is remarkably constant, even across sites. (Here we can use average values!)

Question 18

When specifying the modulus of trabecular bone, which other factors must also be specified? Why do these factors affect the modulus?

Answer 18

• Species
• Anatomic site
• Age
• Loading direction
• Disease state
  These factor may affect remodelling activity.

Question 19

Would you use Von Mises criteria to predict failure in trabecular bone? Why or why not?

Answer 19

No. Although it is one of the easiest criteria, it is not suitable. Trabecular bone has high tension-compression asymmetry. Shear stresses in trabecular bone are too high to use Von Mises.

Question 20

Would you use Principle Strains to predict failure in trabecular bone? Why or why not? How?

Answer 20

Yes, because this method is independent of apparent density and isotropic. You start with a general strain tensor, which depends on the frame of reference used. You then find the orientation of the ref. frame for which diagonal elements are non-zero. Finally, you find the eigenvalues and corresponding eigenvectors.
Strains for any state of loading are converted to principal strains; whether these exceed the max. allowable on-axis uniaxial strains, failure is assumed to occur.

Question 21

On a tissue (local) level, how to trabecular and cortical bone properties compare to each other?

Answer 21

Modulus of trabecular < Modulus of cortical

Trabecular is less mineralised than cortical and has a slightly different structure.

Question 22

Provide 2 techniques to evaluate microstructural bone tissue properties.

Answer 22

1. Nanoindentation - specimen is polished and diamond tip is brought to its surface. Contact mechanics used to determine its elastic modulus and hardness.
2. Ion beam - ion beam is used to erode surface of the specimen.

Question 23

What mechanical environment do these cells need to activate bone remodelling? Provide 2 possible cues.

Answer 23

1. Microfracture disrupting communication between cells

2. Shear stress imposed by fluid flow through cannaliculi are senses by mechanoreceptors.

Question 24

How can we model structural anisotropy?

Answer 24

Use the general form of the elastic constitutive relation (think: Hooke’s Law)
sigma = c x epsilon

Question 25

Machining of specimens along anatomical axes can lead to “off-axis” samples that are not aligned with the principle material coordinate system. How can we treat the data to simplify the analysis?

Answer 25

We can rotate the stress and strain tensors using the following steps to extend the eqns from an on-axis case to a general off-axis case:

1. Rotate from lab frame to material frame
2. Apply constitutive equations (these are ALWAYS applied in the material frame
3. Rotate stress and strains back to lab frame

Question 26

Describe the ARF sequence in bone.

Answer 26

1. Activation - of bone lining cells, takes 3 days, monocytes differentiate into pre-osteoclasts
2. Resorption - osteoclasts attach to free bone surface, form tight seal, start dissolving material by secreting acid, 30 days
3. Formation - MSCs differentiate into preosteoblasts, organize into groups, become active osteoblasts, they lay down osteoid which mineralised over time, 90 days

Question 27

State the 3 different regions of elastic bone deformation.

Answer 27

1. Disuse (low strain levels)
2. Adapted state (bone optimally loaded, homeostasis, bone resorption = bone formation)
3. Overload (large strain levels)