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 ρash/ρapp = 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 ρash/ρapp = 0.6a | E = 14664ρash 1.49 | Axial Stiffness | Somatom Definition, Siemens | 120 | 216 mAs | 0.40 × 0.30 to 0.45 |
R2 = 0.87 | ||||||||||
Ultimate Load | ||||||||||
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 ρash/ρapp = 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 | ||||||||||
Failure Load | ||||||||||
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 | ||||||||||
Failure Load | ||||||||||
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 | ||||||||||
Failure Load | ||||||||||
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 ρapp/ρHA = 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 |