Biomedical and physiological foundations of Bone Tensile Elastic Modulus.
Bone is a complex, hierarchical, anisotropic composite biomaterial composed of mineralized collagen fibrils (hydroxyapatite crystals embedded in a type-I collagen matrix) organized into osteons (Haversian systems) in cortical compact bone. In biomechanical engineering and orthopaedic implant design, characterizing the mechanical stiffness and yield behavior of bone is critical for predicting fracture risk, modeling joint contact forces, and avoiding stress shielding in femoral hip prostheses. Under physiological tensile loading along the longitudinal axis of long bones (such as the human or bovine femur and tibia), cortical bone displays linear elastic behavior at small strains (typically ε < 0.007 or 7000 microstrain) before yielding into plastic deformation and microcracking. According to Hooke's law for linear orthotropic continuum elasticity, the uniaxial stress-strain relation along the osteon orientation is given by σ = E_L · ε, where E_L is the longitudinal Young's modulus (typically 15 to 20 GPa for mature Haversian cortical bone). In this laboratory investigation, standardized dog-bone cortical bone specimens milled along the femoral diaphysis are maintained in hydrated physiological saline at 37.0 °C and loaded in uniaxial tension using a servohydraulic materials testing system equipped with a high-resolution laser extensometer to accurately determine Young's modulus E.
Viva voce questions & analytical theory
Why is cortical bone mechanically anisotropic?
Cortical bone consists of longitudinally aligned cylindrical osteons surrounded by cement lines; it is significantly stiffer and stronger in tension and compression along its longitudinal axis (E ≈ 17–18 GPa) than in the transverse radial or circumferential directions (E ≈ 10–12 GPa).
How does specimen hydration influence the mechanical properties of bone?
Dehydration removes water bound within the collagen fibrils and hydroxyapatite crystal lattice, drastically increasing apparent stiffness and brittleness while decreasing ultimate strain to failure and fracture toughness by up to 50%.
What is the phenomenon of stress shielding in orthopaedic joint replacement?
When a metallic implant (e.g., cobalt-chromium or titanium, E = 110–210 GPa) is implanted into bone (E ≈ 18 GPa), the much stiffer metal carries the majority of the physiological load. Deprived of normal mechanical stress, surrounding bone undergoes osteoclast-mediated resorption according to Wolff's Law.
What is the distinction between cortical (compact) bone and trabecular (cancellous) bone?
Cortical bone is dense (porosity 5–10%) and forms the outer structural shell of bones, providing high stiffness and bending resistance, whereas trabecular bone is a porous cellular lattice (porosity 70–90%) found at epiphyses that absorbs impact energy and houses marrow.
Why must strain rate be strictly controlled during bone biomechanical testing?
Bone is a viscoelastic material whose apparent elastic modulus, yield stress, and ultimate strength increase with higher strain rates due to viscous fluid flow within canaliculi and time-dependent collagen fibril deformation.
How does aging and osteoporosis alter the cortical bone tensile stress-strain curve?
Aging and osteoporosis increase cortical porosity, widen Haversian canals, accumulate advanced glycation end-products (AGEs) in collagen, and reduce mineral density, causing significant reductions in elastic modulus, yield strength, and work to fracture.
Experimental precautions and patient safety
- Keep specimens continuously submerged in phosphate buffered saline; surface drying alters mechanical compliance within minutes.
- Ensure perfect axial alignment between upper and lower grips to prevent spurious bending moments from corrupting tensile strain.
- Verify that strain rate remains within the quasi-static regime (0.001 s⁻¹) to avoid viscoelastic rate-hardening artifacts.
- Do not exceed 7.0 mstrain to ensure testing remains strictly within the linear elastic, non-damaging reversible regime.
Theoretical assumptions & biological limits
- The linear elastic Hookean model applies strictly to small strains (ε < 0.006); post-yield microcracking requires continuum damage mechanics.
- Assumes homogeneous continuum stress distribution, neglecting microscopic stress concentrations around individual Haversian canals.
- Modulus value is specific to the diaphyseal longitudinal orientation; transverse and shear moduli require separate directional testing.
- Testing is performed at room or 37 °C saline in vitro; living bone exhibits active cellular repair and remodeling not captured in vitro.