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Table 1 Current literature using HR-pQCT finite element (FE) modeling for uniaxial compression simulations in the older human bone; illustrating the type of FE model used, the elastic modulus (E) used in the model, the reported outcomes, and the sites measured per study. Literature is listed in chronological order by year

From: In vivo precision of three HR-pQCT-derived finite element models of the distal radius and tibia in postmenopausal women

Reference

FE Modela

Elastic modulus (E)

Outcomes reported

Site measured

Pistoia et al. Bone 2002; 30(6): 842–848.

STM

10 GPa

1. Failure Load (N)

Cadaver Radius

MacNeil et al. Med Eng and Phys 2007; 29: 1096–1105.

STM

10 GPa

1. Reaction Load (N)

2. Strain Energy Density

3. Average von Mises Stress (MPa)

Cadaver Radius (Cube Sample)

MacNeil et al. Med Eng and Phys 2008; 30: 792–799.b

STM

Calculatedc

1. Elastic Modulus (CV%RMS)b

2. Reaction Force (CV%RMS)b

3. Average von Mises Stress (CV%RMS)b

4. Strain Energy Density (CV%RMS)b

In vivo

Radius and Tibia

MacNeil et al. Bone 2008; 42: 1203–1213.

STM

E-BMD

6829 MPa

Eelement = 15004 × (ρ/1200 mg HA/cm3)1.7

1. Apparent Bone Strength (Ultimate Stress) (GPa)

In vivo

Radius

Boutroy et al. JBMR 2008; 23(3): 392–399.

DTM

Cortical: 20 GPa

Trabecular: 17.5 GPa

1. Stiffness (kN/mm)

2. % Load Carried by Each Tissued

3. Average von Mises Stress for each Tissued (MPa)

In vivo

Radius and Tibia

Mueller et al. Bone 2009; 44: 364–371.

STM

10 GPa

1. Strength (N)

2. Stiffness (N/mm)

Cadaver Radius

Dalzell et al. Osteoporos Int 2009; 20: 1683–1694.

STM

10 GPa

1. Stiffness (N/mm)

2. Failure Load (N)

In vivo

Radius and Tibia

Varga et al. J Biomech 2009; 42: 1726–1731.

DTM

Cortical: 16.5 GPa

Trabecular: 2974.0 MPa

1. Failure Load (N)

2. Stiffness (N/mm)

Cadaver Radius

Burghardt et al. JBMR 2010; 25(12): 2558–2571.

DTM

Cortical: 10 GPa

Trabecular: 10 GPa

1. Stiffness (N/mm)

2. Apparent Modulus (N/mm2)

3. Failure Load (N)

4. % Load Carried by Cortex

In vivo

Radius and Tibia

Vilayphiou et al. Bone 2010; 46: 1030–1037.

DTM

Cortical: 20 GPa

Trabecular: 17 GPa

1. Failure Load (N)

2. Stiffness (kN/mm)

3. % Load Carried by Each Tissued

4. Average von Mises stress for each Tissued (MPa)

In vivo

Radius and Tibia

Varga et al. Bone. 2010; 47: 982–988.

STM

15 GPa

1. Stiffness (kN.mm)

2. Failure Load (kN)

Cadaver Radius

Vilayphiou et al. JBMR 2011; 26(5): 965–973.

DTM

Cortical: 20 GPa

Trabecular: 17 GPa

1. Failure Load (N)

2. Stiffness (kN/mm)

3. % Load Carried by Each Tissued

4. Average von Mises stress for each Tissued (MPa)

In vivo

Radius and Tibia

Macdonald et al. JBMR 2011; 26(1): 50–62.

STM

6829 MPa

1. Stiffness (N/mm)

2. Apparent Bone Strength (Ultimate Stress) (MPa)

3. Failure Load (N)

4. % Strain Energy Carried by each Tissued

In vivo

Radius and Tibia

Varga et al. Biomech Model Mecahnobiol 2011; 10: 431–444.

DTM

Cortical: 15 GPa

Trabecular: 15 GPa

1. Stiffness (kN/mm)

2. Failure Load (kN)

3. Apparent Modulus (kN/mm2)

4. % Load Carried by each Tissued

Cadaver

Radius

Rizzoli et al. Osteoporos Int 2012; 23: 305–315.

DTM

E-BMD

Cortical: 20 GPa

Trabecular: 17 GPa

Eelement = 15004 × (ρ/900 mg HA/cm3)1.1

1. Failure Load (N)

2. Stiffness (kN/mm)

3. Average von Mises stress for each Tissued (MPa)

In vivo

Radius and Tibia

Nishiyama et al. Osteoprosis Int 2012; 24(5): 1733–1740

STM

6829 MPa

1. Apparent Bone Strength (Ultimate Stress) (MPa)

2. % Load Carried by each Tissued

In vivo

Radius and Tibia

Ellouz et al. Bone 2014; 63: 147–157

DTM

Cortical: 20 GPa

Trabecular: 17 GPa

1. Stiffness (kN/mm)

2. Average von Mises stress (MPa) for Each Tissued

3. % Load Carried by each Tissued

In vivo

Radius and Tibia

  1. a STM single tissue model, DTM dual tissue model, E-BMD scaled model based on bone mineral density
  2. bResults of this study only report long-term and short-term precision errors (CV%), outcome values not reported
  3. cElastic modulus (E) was calculated in this study based on the reaction force required to induce 1 % strain over the average area of the slices within the section
  4. d“Each tissue” refers separately to the cortical and trabecular tissues