7.2 Mechanical properties of cortical bone

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@OpenStaxAnatomy2020 Ch. 6

Bone density peaks at about 30 years of age. Women lose bone mass more rapidly than men.

(slide credit: @OpenStaxAnatomy2020 Ch. 6)

Porosity is present in both cortical and trabecular bone
Define volume fraction (\(V_f\)) as the volume of actual bone tissue to the bulk volume
Cortical 70-95%
Trabecular 5-60%
Extremes are the young adult and elderly

Density is strongly dependent on porosity and volume fraction
It is also a primary indicator of bone strength and stiffness
Apparent density is mass per bulk volume
Common measure of apparent density include:
- Hydrated
- De-hydrated
- De-organified
Tissue density is mass per volume of actual bone tissue (2.0g/cc)
- Importantly, this volume excludes vascular pore spaces

The volume fraction, tissue density, and apparent density are related by \[\rho_{\mathrm{app}} = \rho_{\mathrm{tiss}} V_f\]
Apparent densities
- Cortical – \(\approx\) 1.85 g/cc
- Trabecular – 0.10-0.50 g/cc
Trabecular density decreases about 2% per decade after skeletal maturity
Note also the cortical bone wall thickness decreases as you age

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Mineral content is also important for mechanical properties
It is measured after heating bone to 700C for 24 hours (de-organification and drying)
Content increases during skeletal growth and remains fairly constant thereafter

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Average values

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Regressions with age

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Hypothesis is that the fractional fatigue lives sum together and predict failure
\(\displaystyle\sum_{i=1}^n \frac{N_i}{N_{Fi}} = 1\)
- Where there are \(n\) different load levels
Works well in most brittle metals (implants!)
Not validated for bone!!!
In bone, common assumption to replace stress with strain
- Account for various levels of porosity, etc (also reduces variability in the test data)
What about bone remodeling?

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De-vitalized bone exhibits creep
- Resistance better in compression then tension
- Difficult to test in-vivo response
Metals creep – may/may not be significant for ortho

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