Q: How is the bone S-N curve (fatigue life) determined?

Cortical bone fatigue life follows the S-N relation σ_a = σ_f(2N)^b (σ_f ≈ 150 MPa, b ≈ −0.07). At stress amplitude 60 MPa, the fatigue limit (N → ∞) is approached; at 120 MPa, N ≈ 10⁴ cycles. During walking, strain amplitude is about 1000–2000 με, and bone remodeling-based self-repair competes with fatigue damage accumulation.

Q: What is the relationship between osteoporosis T-score and bone strength?

The T-score is the WHO bone mineral density (BMD) assessment index: ≥ −1.0 is normal, −1.0 to −2.5 is osteopenia, and ≤ −2.5 is osteoporosis. For every 10% decrease in BMD, fracture risk approximately doubles. Elastic modulus scales as ρ² and strength scales as ρ², so lower T-scores lead to rapidly declining strength and stiffness.

Q: How can this tool be used in implant design?

This tool is applicable in the design of fracture fixation plates, intramedullary nails, and hip stem prostheses for evaluating residual host bone strength and stress shielding effects. It serves as a hand-calculation tool before FEM simulation for cross-sectional properties (I, J), stress, and safety factor estimation. For implants in osteoporotic patients, T-score-adjusted strength reduction must be considered; screw pullout force also decreases proportionally with BMD.

Question 1

What are typical Young's modulus and strength values for cortical bone?

Accepted Answer

Cortical bone Young's modulus is approximately 17 GPa longitudinally (12 GPa transversely), compressive strength ~170 MPa, tensile strength ~130 MPa, shear strength ~65 MPa, and fatigue limit at 10⁷ cycles ~60 MPa. These values decrease significantly with osteoporosis (T-score < −2.5).

Question 2

How is the bone S-N curve (fatigue life) determined?

Accepted Answer

Cortical bone fatigue life follows the S-N relation σ_a = σ_f(2N)^b (σ_f ≈ 150 MPa, b ≈ −0.07). At stress amplitude 60 MPa, the fatigue limit (N → ∞) is approached; at 120 MPa, N ≈ 10⁴ cycles. During walking, strain amplitude is about 1000–2000 με, and bone remodeling-based self-repair competes with fatigue damage accumulation.

Question 3

What is the relationship between osteoporosis T-score and bone strength?

Accepted Answer

The T-score is the WHO bone mineral density (BMD) assessment index: ≥ −1.0 is normal, −1.0 to −2.5 is osteopenia, and ≤ −2.5 is osteoporosis. For every 10% decrease in BMD, fracture risk approximately doubles. Elastic modulus scales as ρ² and strength scales as ρ², so lower T-scores lead to rapidly declining strength and stiffness.

Question 4

How can this tool be used in implant design?

Accepted Answer

This tool is applicable in the design of fracture fixation plates, intramedullary nails, and hip stem prostheses for evaluating residual host bone strength and stress shielding effects. It serves as a hand-calculation tool before FEM simulation for cross-sectional properties (I, J), stress, and safety factor estimation. For implants in osteoporotic patients, T-score-adjusted strength reduction must be considered; screw pullout force also decreases proportionally with BMD.

Bone Fracture Risk, Bone Strength & Fatigue Calculator

Governing Equations