Biomechanics: Material Mechanics of Biological Tissues Notes

Biomechanics is mechanics applied to biology to understand living systems.
It helps understand organism function, predict changes due to alterations, and propose artificial interventions.
Early contributors include Galileo Galilei, William Harvey, Robert Hooke, Isaac Newton, Leonhard Euler, and Thomas Young.

Characterizing biological materials involves methods similar to testing industrial materials, but with considerations for:
- Small sample sizes
- Maintaining viability
- Non-homogeneity
Common methods include:
- Ostwald viscometer: Measures fluid viscosity using the formula $\eta = \frac{\pi R^4}{8Q} \frac{dp}{dL}$ , where $\eta$ is viscosity, $\frac{dp}{dL}$ is the pressure gradient, $Q$ is the volume rate of flow, and $R$ is the tube radius.
- Cone-plate rheometer: Measures flow behavior.
- Commercial testing machines: Used for solid materials, with non-contact methods to overcome limitations due to tissue heterogeneity.

Different tissues have different functions and behaviors depending on their structures.

Bone operates in a small strain range and behaves linearly with strain, but is anisotropic.
Bone is a composite of collagen and hydroxyapatite, with:
- Apatite crystals providing compressive strength (Young’s modulus ~165GPa).
- Collagen contributing to flexibility (tangent modulus ~1.24GPa).
- Femur Young's Modulus ~18GPa.
Bone stress can be analyzed similarly to engineering structural analysis.
Dry bone fails at ~0.4% strain, while wet bone fails at ~1.2% strain.
For uniaxial loading below the proportional limit, Hooke’s law applies: $\sigma = E \varepsilon$ , where $\sigma$ is stress, $E$ is Young’s modulus, and $\varepsilon$ is strain.

Tensile strength is derived from collagen, which has a triple helix structure.
When stretched, the wavy course (crimp) of fibers decreases.
Load-elongation curve has three parts:
- "Toe" region (O to A)
- Linear part (A to B)
- Maximum load at point C
Elastic stiffness is the slope of the linear portion, tan(⍺), on the load-elongation curve.
Stress relaxation occurs when tendons/ligaments are held at a constant length after being loaded.
Preconditioning involves cyclic loading and unloading until a steady state is achieved.

Experimental testing of whole organs can be complex, costly, and difficult to replicate.
Computational models (in silico analysis) can represent joints and biological systems.