# Table 1 Summary of Calibration Phantom, Densitometric and Modulus Relationships, Scanner and Scanner Settings

Author, Year Anatomical Location Phantom Type Phantom Manufacturer Densitometric Relationship (g/cm3) Density-Modulus Relationship (MPa) Validation Measure Experimental vs. FEM (Metric Value(s)) Scanner Peak Voltage (kVp) Tube Current (mA)/Time Product (mAs) Voxel Dimensions (mm)
(Tarala et al. 2011) Femur HA Image Analysis ρHA = ρash NR Displacement NR NR NR NR
CLS Stem R2 = 0.95
EPOCH Stem R2 = 0.88
(Cong et al. 2011) Femur K2HPO4 Mindways ρash = $${\uprho}_{{\mathrm{K}}_2\mathrm{H}\mathrm{P}{\mathrm{O}}_4}$$ = −0.009 + 0.0007 HU
ρashapp = 0.6a
Axial Stiffness Somatom Definition, Siemens 120 216 mAs 0.40 × 0.45 × 0.45
E = 14664ρash 1.49 R2(y = x) = −1.40
E = 10500ρash 2.29 R2(y = x) = −4.97
E = 17546ρash 3 R2(y = x) = −6.93
E = 8050ρash 1.16 R2(y = x) = 0.50
E = 15000e -4.91e-2.63ρash R2(y = x) =0.71
E = 20000e ^ -5.19e-2.10ρash R2(y = x) = 0.69
E = 55000e ^ -5.40e-2.63ρash R2(y = x) = 0.69
(Dragomir-Daescu et al. 2011) Femur K2HPO4 Mindways ρash = $${\uprho}_{{\mathrm{K}}_2\mathrm{H}\mathrm{P}{\mathrm{O}}_4}$$ = −9*10−3 + 7* 10−4*HU
ρashapp = 0.6a
E = 14664ρash 1.49 Axial Stiffness Somatom Definition, Siemens 120 216 mAs 0.40 × 0.30 to 0.45
R2 = 0.87
R2 = 0.93
(Keyak et al. 2011) Femur HA Image Analysis NR NR NR NR 120 140 mAs NR
(Trabelsi and Yosibash 2011) Femur K2HPO4 NR ρash = 1.22$${\uprho}_{{\mathrm{K}}_2\mathrm{H}\mathrm{P}{\mathrm{O}}_4}$$ + 0.0523b Ecort = 10200ρash 2.01
Etrab = 5307ρash + 469
Strain NR NR NR NR
R2 = 0.982 empirical
R2 = 0.939 MM-based
(Trabelsi et al. 2011) Femur K2HPO4 Mindways ρash = 1.22$${\uprho}_{{\mathrm{K}}_2\mathrm{H}\mathrm{P}{\mathrm{O}}_4}$$ + 0.0523b Ecort = 10200ρash 2.01
Etrab = 5307ρash + 469
Displacement Lightspeed VCT, GE Healthcare 120 90 mAs 1.0 × 0.488 to 0.547
R2 = 0.871
Strain
R2 = 0.951
Axial Stiffness
R2 = 0.619
(Amin et al. 2011) Femur European Spine Phantom NA NR NR NE Lightspeed QX/i, GE Healthcare NR NR 2.5 × 0.74 × 0.74
(Op Den Buijs and Dragomir-Daescu 2011) Femur K2HPO4 Mindways ρash = $${\uprho}_{{\mathrm{K}}_2\mathrm{H}\mathrm{P}{\mathrm{O}}_4}$$ = 7.0*10−4HUc E = 29800ρash 1.56 Axial Stiffness Somatom Definition, Siemens 120 216 mA 0.40 × 0.29 to 0.41
R2 = 0.76
Strength
R2 = 0.71
(Koivumäki et al. 2012a) Femur HA Osteo ρash = ρHA E = 10095ρash Fracture Load Sensation 16, Siemens 120 100 mAs 0.75 × 0.25 × 0.25
R2 = 0.87
(Shim et al. 2012) Femur NR NR NR E = 6750.3ρash 2.01 NE NR NR NR NR
(Gong et al. 2012) Femur HA Image Analysis ρHA to ρapp and converted to ρash d – Equation NR E = 0.001 for
ρash = 0
E = 33900ρash 2.20 for
0 < ρash < 0.27
E = 5307ρash + 469 for
0.27 < ρash < 0.60
E = 10200ρash 2.01 for
ρash > 0.60
NE Lightspeed 16, GE Healthcare 80 280 mA 2.5 × 0.9375 × 0.9375
(Tomaszewski et al. 2012) Femur HA NR ρash = 0.0633 + 0.887ρHA e NR but referenced NE NR NR NR NR
(Keaveny et al. 2012) Femur K2HPO4 Mindways NR NR but referenced NE NR 80 280 mAs 3.0 × 0.78 to 0.94 × 0.78 to 0.94
(Koivumäki et al. 2012b) Femur HA Osteo NR NR Cortical Fracture Load Sensation 16, Siemens 120 100 mAs 0.75 × 0.25 × 0.25
R2 = 0.73
(Ruess et al. 2012) Femur NR NR $${\uprho}_{{\mathrm{K}}_2\mathrm{H}\mathrm{P}{\mathrm{O}}_4}$$ = 10−3(0.793)HU
ρash = 1.22$${\uprho}_{{\mathrm{K}}_2\mathrm{H}\mathrm{P}{\mathrm{O}}_4}$$ + 0.0523b
Ecort = 10200ρash 2.01
Etrab = 5307ρash + 469
Strain Brilliance 64, Phillips 120 250 mAs 1.25 × 0.195 × 0.195
R2 = 0.918–0.981 See paper for specifics by method
(Eberle et al. 2013a) Femur K2HPO4 Mindways ρash = 1.22$${\uprho}_{{\mathrm{K}}_2\mathrm{H}\mathrm{P}{\mathrm{O}}_4}$$ + 0.0523b
ρHA = 1.15$${\uprho}_{{\mathrm{K}}_2\mathrm{H}\mathrm{P}{\mathrm{O}}_4}$$ - 0.0073f
ρash = 0.8772ρHA + 0.0789
ρapp = 1.58 ρash + 0.00011
Strain Lightspeed VCT, GE Healthcare 120 90 mAs 1.0 × 0.547 × 0.547 OR 1.0 × 0.488 × 0.488
E = 10200ρash 2.01 Bland-Altman (mean) −9%
E = 6850ρapp 1.49 Bland-Altman (mean) −10.6%
E = 15100$${\uprho}_{{\mathrm{K}}_2\mathrm{H}\mathrm{P}{\mathrm{O}}_4}^{2.225}$$ Bland-Altman (mean) −7.9%
Displacement
E = 10200ρash 2.01 Bland-Altman (mean) −20.9%
E = 6850ρapp 1.49 Bland-Altman (mean) −22.9%
E = 15100$${\uprho}_{{\mathrm{K}}_2\mathrm{H}\mathrm{P}{\mathrm{O}}_4}^{2.225}$$ Bland-Altman (mean) 1.6%
Axial Stiffness
E = 10200ρash 2.01 Bland-Altman (mean) 15.8%
E = 6850ρapp 1.49 Bland-Altman (mean) 22.6%
E = 15100$${\uprho}_{{\mathrm{K}}_2\mathrm{H}\mathrm{P}{\mathrm{O}}_4}^{2.225}$$ Bland-Altman (mean) −9.6%
(Eberle et al. 2013b) Femur K2HPO4 Mindways ρash = 1.22$${\uprho}_{{\mathrm{K}}_2\mathrm{H}\mathrm{P}{\mathrm{O}}_4}$$ + 0.0523b
ρHA = 1.15$${\uprho}_{{\mathrm{K}}_2\mathrm{H}\mathrm{P}{\mathrm{O}}_4}$$ - 0.0073f
ρash = 0.8772ρHA +0.0789
ρapp = 1.58 ρash + 0.00011
Strain Lightspeed VCT, GE Healthcare 120 90 mAs 1.0 × 0.547 × 0.547 OR 1.0 × 0.488 × 0.488
E = 12486$${\uprho}_{{\mathrm{K}}_2\mathrm{H}\mathrm{P}{\mathrm{O}}_4}^{1.16}$$ Relative Error (mean) 5%
E = 8346ρapp 1.50 Relative Error (mean) −28%
E = 8050ρash 1.16 Relative Error (mean) 18%
E = 25000e^ -5.40e-2.10ρash Relative Error (mean) −16%
E = 6850ρapp 1.49 Relative Error (mean) −12%
Displacement
E = 12486 $${\uprho}_{{\mathrm{K}}_2\mathrm{H}\mathrm{P}{\mathrm{O}}_4}^{1.16}$$ Relative Error (mean) −10%
E = 8346ρapp 1.50 Relative Error (mean) −40%
E = 8050ρash 1.16 Relative Error (mean) 3%
E = 25000e-5.40e-2.10ρash Relative Error (mean) −29%
E = 6850ρapp 1.49 Relative Error (mean) −26%
Stiffness (N/mm)
E = 12486 $${\uprho}_{{\mathrm{K}}_2\mathrm{H}\mathrm{P}{\mathrm{O}}_4}^{1.16}$$ Relative Error (mean) 6%
E = 8346ρapp 1.50 Relative Error (mean) 56%
E = 8050ρash 1.16 Relative Error (mean) −6%
E = 25000e-5.40e-2.10ρash Relative Error (mean) 31%
E = 6850ρapp 1.49 Relative Error (mean) 28%
(Haider et al. 2013) Femur K2HPO4 Mindways ρash = 0.00106$${\uprho}_{{\mathrm{K}}_2\mathrm{H}\mathrm{P}{\mathrm{O}}_4}$$ + 0.0389g
ρashapp = 0.6b
E = 6850ρapp 1.49 NE NR NR NR 0.5 × 0.49 × 0.49
(Dall’Ara et al. 2012) Femur HA QMR BMD to BV/TV from μCT Relation to BV/TV – Equation NR Axial Stiffness Brilliance 64, Phillips 120 100 mAs 1.0 × 0.33 × 0.33
Stance: R2 = 0.449 Side: R2 = 0.869
(Nishiyama et al. 2013) Femur HA B-MAS200 ρash = ρHA E = 10500ρash 2.29 Axial Stiffness Discovery CT750HD, GE Healthcare 120 60 mAs 0.625 × 0.439 × 0.439
R2 = 0.89
R2 = 0.81
(Kersh et al. 2013) Femur HA NR BV/TV = 9.3BMD + 3 from μCTh NR NE Brilliance 64, Phillips 120 100 mA 0.60 × 0.36 × 0.36
(Keyak et al. 2013) Femur HA Image Analysis ρash = 0.0633 + 0.887ρHA i Etrab = 14900ρash 1.86 NE Sensation 4, Siemens 120 140 mAs NR
(Hambli and Allaoui 2013) Femur HA Osteo ρHA = 6.932*10−4HU - 5.68*10−4
ρash = 1.22$${\uprho}_{{\mathrm{K}}_2\mathrm{H}\mathrm{P}{\mathrm{O}}_4}$$ + 0.0523b
E = 33900ρash 2.20 for
0 < ρash < 0.27
E = 5307ρash + 469 for
0.27 < ρash < 0.60
E = 10200ρash 2.01 for ρash > 0.60
Fracture Load Somatom Plus 4, Siemens 120 160 mAs 0.70 × 0.25 × 0.25
R2 = 0.943
(Carballido-Gamio et al. 2013) Femur Both Mindways & Image Analysis NR NR NE Sensation, Siemens NR NR 2.5 × 0.74 × 0.74 & 1.0 × 0.98 × 0.98
(Nishiyama et al. 2014) Femur Both Mindways &
B-MAS200
ρash = ρHA E = 10500ρash 2.29 NE Somatom Cardiac 64, Siemens 120 250 mAs 0.50 × 0.625 × 0.625
(Luisier et al. 2014) Femur HA QMR BMD to BV/TV from μCTj Eo = 6614 Ultimate Force Brilliance 64, Phillips 120 100 mA 1.0 × 0.33 × 0.33
Stance: R2 = 0.797 Side: R2 = 0.842
(Enns-Bray et al. 2014) Femur NR NR ρash = ρQCT E3 = 10500ρash 2.29
See paper for anisotropic modulus
Axial Stiffness Discovery CT750HD, GE Healthcare 120 60 mAs 0.625 × 0.625 × 0.625
Anisotropic: R2 = 0.783 Isotropic: R2 = 0.792
Ultimate Strength
Anisotropic: R2 = 0.355 Isotropic: R2 = 0.350
(Anez-Bustillos et al. 2013) Femur HA Image Analysis NR Experimentally derived Axial Rigidity ACQSim, Phillips 120 220 mA 3.0 × 0.9375 × 0.9375
R2 = 0.82
Bending Rigidity
R2 = 0.86
R2 = 0.89
(Mirzaei et al. 2014) Femur K2HPO4 Mindways ρash = 1.22$${\uprho}_{{\mathrm{K}}_2\mathrm{H}\mathrm{P}{\mathrm{O}}_4}$$ + 0.0526b E = 33900ρash 2.20 for
0 < ρash < 0.27
E = 5307ρash + 469 for
0.27 < ρash < 0.60
E = 10200ρash 2.01 for ρash > 0.60
Load Somatom 64, Siemens 140 80 mAs 1.0 × 0.50 × 0.50
R2 = 0.809–0.886 See paper for specifics by method
(Arachchi et al. 2015) Femur HA NR NR NR NE Brilliance 64, Phillips & Somatom Plus 4, Siemens 140 206 mAs 2.0 × 0.29 × 0.29
(Kheirollahi and Luo 2015) Femur NR NR ρash = 0.04162 + 0.000854HU E = 10500ρash 2.29 NE NR NR NR NR
(Carballido-gamio et al. 2015) Femur Both Mindways & Image Analysis vBMD reported NR NE Lightspeed QX-I, Lightspeed VCT, Lightspeed 16, GE Healthcare & Biograph 16, Siemens NR NR 2.0 × 0.742 × 0.742 OR 2.5 × 0.938 × 0.938 OR 1.0 × 0.977 × 0.977
(Kaneko et al. 2015) Femur HA B-MAS200 ρash = ρHA NR NE Light Speed Ultra16, GE Healthcare 120 80 mA NR
(Varghese et al. 2011) Femur, Tibia, Humerus, Radius K2HPO4 Mindways NR NR Strain Lightspeed 16, GE Healthcare 80 200 mAs 0.625 × 0.625 × 0.625
R2 = 0.61–0.99 See paper for specifics by method
(Kopperdhal et al. 2014) Spine & Femur HA Image Analysis BMD related to HU NR NE Somatom Plus 4, Siemens 120 150 mAs Spine: 1.0 × 1.0 × 1.0
Femur: 1.5 × 1.5 × 1.5
(Kleerekoper et al. 2014) Spine & Femur NR NR NR NR NE NR NR NR NR
(Keaveny et al. 2014) Spine & Femur HA European Spine Phantom NR NR NE NR 120 Femur: 170 mAs
Spine: 100 mAs
NR
(Zeinali et al. 2010) Spine K2HPO4 Mindways BMD related to HU Ez = −34.7 + 3230$${\uprho}_{{\mathrm{K}}_2\mathrm{H}\mathrm{P}{\mathrm{O}}_4}$$
Ez = −2980$${\uprho}_{{\mathrm{K}}_2\mathrm{H}\mathrm{P}{\mathrm{O}}_4}$$ 1.05
$${\uprho}_{{\mathrm{K}}_2\mathrm{H}\mathrm{P}{\mathrm{O}}_4}$$ = 0.0527 g/cc
Ex = Ey = 0.333Ez
Strength Somatom Plus 64, Siemens 140 400 mA 1.0 × 0.25 × 0.25
Linear elastic–plastic: R2 = 0.937 Linear elastic-perfectly plastic: R2 = 0.855 Linear elastic: R2 = 0.831 Min. sectional: R2 = 0.863
(Tawara et al. 2010) Spine HA B-MAS200 ρapp = 0.0 (HU < −1)
ρapp = (0.733HU + 4.51)*10−3 (−1 ≤ HU)
E = 0.001 for
ρash = 0
E = 33900ρash 2.20 for
0 < ρash < 0.27
E = 5307ρash + 469 for
0.27 < ρash < 0.60
E = 10200ρash 2.01 for
ρash > 0.60
NE Hitachi 120 NR 1.0 × 0.39 × 0.39
(Unnikrishnan and Morgan 2011) Spine HA Image Analysis ρHA based Ezz = −34.7 + 3.230ρHA
Exx = Eyy = 0.333
NE Light Speed VCT, GE Healthcare 120 240 mA 0.625 × 0.31 × 0.31
(Christiansen et al. 2011) Spine HA Image Analysis ρHA based NR NE Light Speed Plus, GE Healthcare 120 100 to 360 mAs 2.5 × 0.68 × 0.68
(Imai 2011) Spine HA NR ρash = ρHA Ecort = 10000 NE Light Speed QX/i, GE Healthcare 120 360 mA 2.0 × 0.35 × 0.35
(Dall’Ara et al. 2012) Spine K2HPO4 Mindways BV/TV using the relationships
BV/TV = 0 for BMD < −100 BV/TV = 0.0942*BMD-0.0297 for −100 < BMD < 1061
BV/TV = 1061 for BMD >1061
E = 8780 Strength Brilliance 64, Pillips 120 100 mA 0.45 × 0.39 × 0.39
hFE: R2 = 0.79
hFE: R2 = 0.78
(Wang et al. 2012) Spine HA Image Analysis vBMD based NR Strength NR 120 150 mAs NR
R2 = 0.85
(Unnikrishnan et al. 2013) Spine HA Image Analysis BMD related to HU Ez = −34.7 + 3230ρHA
Ez = −2980ρHA 1.05
ρHA = 0.0527 g/cc Ex = Ey = 0.333Ez
NE Light Speed VCT, GE Healthcare 120 240 mA 0.625 × 0.3125 × 0.3125
(Lu et al. 2014a) Spine Both Mindways & QRM NR NR NE Sensation 64, Siemens 120 360 mAs 0.60 × 0.32 × 0.32 OR 0.30 × 0.18 × 0.18
(Matsuura et al. 2014) Spine K2HPO4 Mindways ρash = $${\uprho}_{{\mathrm{K}}_2\mathrm{H}\mathrm{P}{\mathrm{O}}_4}$$ ρash = 0: E = 0.001
ρash > 0: E = 1890 ρash 1.92
Fracture Load Somatom Definition, Siemens 120 210 mA 0.40 × 0.30 × 0.30
R2 = 0.78
Axial Stiffness
R2 = 0.39
(Lu et al. 2014b) Spine HA QMR BMD related to HU Ez = 2980(ρHA/1000)1.05 for ρHA < 52.7 [mgHA/cc]
Ez = = −34.7 + 3230ρHA for ρHA > 52.7 [mgHA/cc]
NE Mx8000, Phillips 90 & 120 100 & 150 mAs 1.3 × 0.30 × 0.30
(Campoli et al. 2014) Scapula NR NR ρapp = HU + 0.00039 E = 6850ρapp 1.49 NE Somatom Definition, Siemens NR NR 0.6 × 0.6 × 0.6
(Pomwenger et al. 2014) Scapula NR NR ρapp = 1.1187*10−3*HUk assumed ρapp = 0 no bone & ρapp = 1.8 for bone E = 1049.45ρapp 2
ρapp < 0.35
E = 3000ρapp 3
ρapp > 0.35
NE NR NR NR NR
(Hermida et al. 2014) Scapula K2HPO4 Mindways NR Ecort = 20000 NE NR NR NR NR
(Edwards et al. 2013) Tibia HA QRM ρHA = BMD
ρappHA = 0.626
E3 = 6570ρapp 1.37
Emin = 0.01
E1 = 0.574E3
E2 = 0.577E3
Rotation Stiffness Brightspeed, GE Healthcare 120 200 mA 0.625 × 0.352 × 0.352
R2 = 0.920
Ultimate Strength
R2 = 0.753
(Nazemi et al. 2015) Tibia K2HPO4 Mindways ρash = 0.55 ρapp g
ρash = 0.597ρdry g
ρreal = 1.8 g/ccl
ρapp = ρreal*BV/TV
BMD = 0.904ρash - 0.0321g
ρash = 1.06*BMD + 0.0389g
Axial Stiffness Aquilion 64, Tobisha 120 150 mAs 0.5 × 0.5 × 0.5
E = 15520ρapp 1.93 R2 = 0.75
E = 6570ρapp 1.37 R2 = 0.65
E = 33200ρash 2.2 R2 = 0.70
E = 4778ρapp 1.99 R2 = 0.69
E = 3311ρdry 1.66 R2 = 0.67
E = 3890ρdry 2 R2 = 0.69
E = 6310(BV/TV)2.1 R2 = 0.70
(McErlain et al. 2011) Knee SB3 Gamex NR NR NE Multistar, Siemens 90 40 mAs NR
(Synek et al. 2015) Radius NR NR BMD to BV/TV from μCT Multiple – Refer to paper Axial Stiffness Discovery CT750HD. GE Healthcare 140 260 mA 0.63 × 0.20 × 0.20
Isotropic-Homogeneous R2 = 0.500
Isotropic-Heterogeneous R2 = 0.816
Orthotropic-Heterogeneous R2 = 0.807
1. HA Hydroxyapatite, K 2 HPO 4 Dipotassium Phosphate, NR Not Reported, BMD Bone Mineral Density, BV/TV Bone Volume/Total Volume, NE No Experimental; a (Schileo et al. 2008); b (Les et al. 1994); c (Suzuki et al. 1991); d (Keyak et al. 1997); e (Keyak et al. 2005); (Faulkner et al. 1993); g (Keyak et al. 1994); h (Dall’Ara et al. 2011); I (Keyak et al. 2005); j (Pahr and Zysset 2009); k (Gupta and Dan 2004); l (Carter and Hayes 1977)