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Table 1 Equations proposed by Keyak, Carter, Keller, and Keller for vertebra

From: Finite element analysis of the femoral diaphysis of fresh-frozen cadavers with computed tomography and mechanical testing

  Young’s modulus (E: MPa) Yield stress (σ: MPa)
Keyak E = 0.001 (ρ = 0) σ = 1.0 × 1020 (ρ 0.2)
E = 33,900 ρ2.20 (0 < ρ 0.27)
E = 5307 ρ + 469 (0.27 < ρ < 0.6)
E = 10,200 ρ2.01 (0.6 ρ)
σ = 137 ρ1.88 (0.2 < ρ < 0.317), σ = 114ρ1.72 (0.317 ρ)
Carter E = 0.001 (ρ = 0) σ = 1.0 × 1020 (ρ 0.2)
E = 3790(0.01)0.05 ρ (ρ < 0) σ = 68(0.01)0.06 ρ2 (0.2 < ρ)
Keller E = 0.001 (ρ = 0) σ = 1.0 × 1020 (ρ 0.2)
E = 10,500 ρ2.51 (ρ < 0) σ = 117 ρ1.93 (0.2 < ρ)
Keller for vertebra E = 0.001 (ρ = 0) σ = 1.0 × 1020 (ρ 0.2)
E = 1890 ρ1.92 (ρ < 0) σ = 284 ρ2.27 (0.2 < ρ)
  1. E Young’s modulus (MPa), σ yield stress (MPa), ρ ash density (g/cm3)