Open Access

Quantitative Computed Tomography (QCT) derived Bone Mineral Density (BMD) in finite element studies: a review of the literature

Journal of Experimental Orthopaedics20163:36

https://doi.org/10.1186/s40634-016-0072-2

Received: 30 September 2016

Accepted: 30 November 2016

Published: 9 December 2016

Abstract

Background

Finite element modeling of human bone provides a powerful tool to evaluate a wide variety of outcomes in a highly repeatable and parametric manner. These models are most often derived from computed tomography data, with mechanical properties related to bone mineral density (BMD) from the x-ray energy attenuation provided from this data. To increase accuracy, many researchers report the use of quantitative computed tomography (QCT), in which a calibration phantom is used during image acquisition to improve the estimation of BMD. Since model accuracy is dependent on the methods used in the calculation of BMD and density-mechanical property relationships, it is important to use relationships developed for the same anatomical location and using the same scanner settings, as these may impact model accuracy. The purpose of this literature review is to report the relationships used in the conversion of QCT equivalent density measures to ash, apparent, and/or tissue densities in recent finite element (FE) studies used in common density-modulus relationships. For studies reporting experimental validation, the validation metrics and results are presented.

Results

Of the studies reviewed, 29% reported the use of a dipotassium phosphate (K2HPO4) phantom, 47% a hydroxyapatite (HA) phantom, 13% did not report phantom type, 7% reported use of both K2HPO4 and HA phantoms, and 4% alternate phantom types. Scanner type and/or settings were omitted or partially reported in 31% of studies. The majority of studies used densitometric and/or density-modulus relationships derived from different anatomical locations scanned in different scanners with different scanner settings. The methods used to derive various densitometric relationships are reported and recommendations are provided toward the standardization of reporting metrics.

Conclusions

This review assessed the current state of QCT-based FE modeling with use of clinical scanners. It was found that previously developed densitometric relationships vary by anatomical location, scanner type and settings. Reporting of all parameters used when referring to previously developed relationships, or in the development of new relationships, may increase the accuracy and repeatability of future FE models.

Keywords

QCTBone densityFinite element analysisMechanical properties

Background

Accurate characterization of the properties of bone in finite element (FE) studies, including accurate local bone density (Schileo et al. 2008; Synek et al. 2015), is essential to improve the accuracy of existing continuum-level FE modeling techniques (Schileo et al. 2008). Uncalibrated clinical CT images are limited to voxel information in the form of x-ray absorption coefficients, using the Hounsfield (HU) scale, with air (−1000 HU) and water (0 HU) as references. For high atomic number materials, quantitative computed tomography (QCT) provides local densitometric measurements in volumetric bone mineral density (vBMD) (Engelke et al. 2013). This allows for accurate regional variations in BMD to be mapped in subsequent continuum-level finite element models (FEMs). The accuracy and characterization of using calibration phantoms has been well established over the past two decades (Faulkner et al. 1993; Keyak et al. 1994; Les et al. 1994; Schileo et al. 2008).

Calibrated vBMD or quantitative equivalent CT density (ρQCT) is calculated by measuring the CT scanner’s response to the phantom’s calibrated regions. Typical calibration phantoms contain rods with varying concentrations of calcium hydroxyapatite (HA) (Engelke et al. 2013; Poelert et al. 2013), or are calibrated using liquid dipotassium phosphate (K2HPO4), and provide equivalent density in units of mgHA/cm3HA) or \( {\mathrm{mg}}_{{\mathrm{K}}_2\mathrm{H}\mathrm{P}{\mathrm{O}}_4}/{\mathrm{cm}}^3\left({\uprho}_{{\mathrm{K}}_2\mathrm{H}\mathrm{P}{\mathrm{O}}_4}\right) \)(Keyak et al. 1994; Les et al. 1994). These imaging based density methods have been related to physical methods, such as ash density (ash mass divided by bulk sample volume), and apparent density (wet mass divided by bulk sample volume) by use of CT scan energy specific (linear) relationships (Fig. 1) (Faulkner et al. 1993; Giambini et al. 2015).
Fig. 1

Ash and QCT equivalent density (a: dipotassium phosphate; b: calcium hydroxyapatite) relationships used in reviewed studies. Relationships from: a (Keyak et al. 1994) – 140 kVp, 70 mA; b (Les et al. 1994) – 140 kVp, 30 mA; c Unknown – used in (Eberle et al. 2013a, b); d (Keyak et al. 2005) – 80 kVp, 280 mAs

To account for the lack of cancellous bone geometry due to the clinical CT resolution, continuum-level FEMs use spatial variations of BMD related to mechanical properties in order to achieve physiologic accuracy. In the development of these FEMs, two relationships are required to convert raw CT x-ray attenuation data to bone mechanical properties. The first densitometric relationship relates raw CT attenuation to BMD (ρ = a*HU + b) (ρQCT if phantom calibrated), and the second mechanical property relationship, relates BMD to bone mechanical properties. To develop the second relationship, most studies use relationships developed using physical specimens and have found continuous functions and power relationships best fit experimental data (E = αρβ), where E is the Young’s Modulus, α and β are experimentally derived parameters, and ρ is the bone density (Helgason et al. 2008). Alternatively, relationships may be piecewise functions that represent experimentally derived relationships for cancellous and cortical bone separately. Density-modulus relationships for cancellous and cortical bone are determined by the experimental method in which they are derived. Small bone sample are typically mechanically tested to derive the desired relationships. Many of these studies test cancellous samples and cortical samples separately (instead of whole bones), and therefore derive separate equations for each bone type (Rice et al. 1988; Schaffler and Burr 1988). Due to the experimental testing of physical specimens, these equations use physical BMD measures such as ash, apparent, or tissue density; and therefore when using QCT derived equivalent density (ρQCT), conversions between QCT, ash (ρash), apparent (ρapp), and tissue densities (ρtissue) are required for accurate FEM development.

Experimentally derived density-modulus relationships are site-specific (Morgan et al. 2003; Schileo et al. 2008), and are also affected by the quality and pathology of the bone, with density being a function of the CT scanner settings (Faulkner et al. 1993). Therefore, the purpose of this literature review is to report i) the relationships used in the conversion of QCT equivalent density (ρQCT) measures to ash (ρash), apparent (ρapp), and/or tissue densities (ρtissue) in recent FE studies, and ii) the combined densitometric and density-modulus relationships impact on FEM accuracy.

Methods

The specific relationships used in the conversion of QCT (K2HPO4 or HA) to physical density (ash, apparent, or tissue) in current FE studies were reviewed. The search was limited to FE studies of human bone published after January 1st, 2010, reporting clinical scanner image acquisition with use of a calibration phantom. Studies reporting only HR-pQCT or micro-CT scanner image acquisition were omitted. Literature searches included the search terms “finite element analysis, FE, or finite element” with combinations of “quantitative computed tomography,” “QCT,” and “bone.” Included articles represented a variety of calibration phantom types, anatomical locations, CT scanner settings, and density relationships and density-modulus relationships. Each article was carefully reviewed by one of two independent reviewers (NKK & JMR), and characterized based on anatomical location, density calibration type and manufacturer, scanner, and scanner settings. Articles not reporting any of the above were included as long as they clearly defined use of a calibration phantom with a clinical scanner. All articles were secondly reviewed by a single author (NKK) for completeness, and to extract specific densitometric and density-modulus relationships reported in each study. At this stage, references reported for densitometric and density-modulus relationships were checked and collected. Discrepancies between reported relationships and accurate relationships were noted, and corrected, if possible. Validation metrics and results are included for studies comparing experimental to FEM results.

The number of studies reporting each phantom type (Dipotassium Phosphate (K2HPO4), Hydroxyapatite (HA), both, other, or not reported), were determined along with manufacturer of the phantom. Of the studies reviewed, four relationships were noted (ash density from K2HPO4 density, ash density from HA density, ash density from CT number, or apparent density from CT number). Studies using these relationships were collected and plotted (Figs. 1 and 2). Density-modulus relationships were tabulated (Table 1), but not reviewed in detail, as this is beyond the scope of this review, and many are summarized in detail in the review by Helgason et al. (2008).
Fig. 2

Apparent and ash density to CT number relationships reported by reviewed studies. Peak tube voltage and phantom type are reported when available. The relationship ρash = 0.6ρapp is assumed (Schileo et al. 2008)

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

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

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

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

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

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)

Densitometric measurements

Ash density

Ash density (ρash) is a measure typically taken on small bone samples, which are used to determine density-modulus relationships mechanically tested as a continuum (Les et al. 1994). It is calculated as the ash mass divided by bulk sample volume. In the method described by Les et al. (1994), physical measurements were taken on cylindrical bone samples to determine the total sample volume. The sample was ashed in a muffle furnace at 800 °C for 24 h, and weighed to determine the ash mass and the ash density is calculated by dividing by the sample volume.

A similar study tested the effect of ashing temperature on sample mass. Öhman et al. (2007) found that ashing their samples at a temperature of 650 °C for 24 h in a muffle furnace, produced little variation in measured ash mass, compared to increased furnace temperature. Temperatures between 600 and 650 °C, produced significant variation in sample mass. Although the original method described by Les et al. (1994) is still most commonly used, more accurate methods of initial volume measurement, such as micro-CT, or laser scanning may be employed.

Apparent density

Bone apparent density (ρapp) is calculated as the wet mass of a bone tissue sample divided by the total sample volume. To determine wet mass, Galante et al. (1970) first washed samples to remove marrow, immersed samples in distilled water, and degassed under vacuum. Samples were then removed from water, centrifuged for 15 min at 8000 × g and suspended from an analytical balance for submerged mass. Samples were removed and blotted dry and weighed in air for wet mass. Similarly, Keyak et al. (1994) measured bone cubes by first defatting samples in an 8 and 16 h ethyl alcohol bath, followed by an 8 and 16 h ethyl ether bath. Samples dried for 24 h at room temperature and were weighed for dry mass. The cubes were rehydrated under vacuum in water for 24 h, centrifuged at 750 × g for 15 min, and weighed for hydrated mass. Sample apparent density was then calculated with the known cube volume.

Tissue density

The tissue density (ρtissue) also uses the wet mass of the sample; however, as the name suggests, tissue density is a measure of the physical bone tissue (excluding pores) (Galante et al. 1970). It is calculated by dividing the wet mass by the volume of bone tissue. To determine the volume of bone tissue Galante et al. (1970) calculated the difference between the wet and submerged mass.

Radiological (mineral equivalent) density

Radiological, or mineral equivalent (K2HPO4 or HA) density (\( {\uprho}_{{\mathrm{K}}_2\mathrm{H}\mathrm{P}{\mathrm{O}}_4} \), ρHA, or ρQCT) is calculated by sampling the average CT number (HU) value of all voxels within a region of interest of the known calibration phantom sample rods. The radiographic density of the rods can be estimated using the calibration parameters supplied by the phantom manufacturer, and simple linear regression calculations (Les et al. 1994; Schileo et al. 2008). The QCT calibration can be completed on an entire volume, or by individual CT image.

Results

Of the 55 studies that met the inclusion criteria and were included, 29% reported the use of a K2HPO4 phantom, 47% an HA phantom, 13% did not report phantom type, 7% reported use of both K2HPO4 and HA phantoms, and 4% alternate phantom types. The most commonly reported K2HPO4 phantom was the Mindways Software phantom, and the most commonly reported HA phantom was the Image Analysis phantom. The most common densitometric relationship between ash density and QCT equivalent density was that developed by Les et al. (1994) (13% of studies). Of all studies, 35% report density-modulus relationships based on ash density, and 18% report ash density directly equivalent to QCT density (K2HPO4 or HA). Of the studies included as part of this review, 24% report density-modulus relationships determined either from micro-CT bone volume/total volume (μCTBV/TV), or relate modulus directly to QCT density, through experimental validation (Zeinali et al. 2010; Christiansen et al. 2011; Unnikrishnan and Morgan 2011; Dall’Ara et al. 2012, 2013; Wang et al. 2012; Anez-Bustillos et al. 2013; Kersh et al. 2013; Unnikrishnan et al. 2013; Luisier et al. 2014; Lu et al. 2014b; Carballido-gamio et al. 2015; Synek et al. 2015). Scanner type and/or settings were omitted or only partially reported in 31% of studies. Studies involving the femur were most prevalent (37), followed by the spine (14), scapula (3), tibia (3), radius (1), knee (1), and humerus (1).

Of the studies reporting density-modulus relationships and experimental validation metrics, those with the lowest mean %-difference, lowest relative error, or correlations greater than 90% (R2 > 0.90), 5 used relationships based on ash density (Dragomir-Daescu et al. 2011; Trabelsi et al. 2011; Trabelsi and Yosibash 2011; Ruess et al. 2012; Hambli and Allaoui 2013), 3 based on K2HPO4 calibrated density (Zeinali et al. 2010; Eberle et al. 2013a, b), and 1 based on apparent density (Edwards et al. 2013).

Discussion

When creating continuum-level finite element models with heterogeneous material distributions, BMD must first be extracted from scan data, and then a density-modulus relationship applied. From the studies reviewed, it is difficult to quantify and isolate the effect of chosen densitometric relationships on experimental versus computational model error because reported results are the combination of two relationships (densitometric and density-modulus). It was therefore the goal of this review to provide the current state of QCT in FE modeling, and provide the most common methods used in the conversion of densitometric measures. When assessing the accuracy of density-modulus relationships developed in previous studies, and comparing experimental to computational results, replication of the density measure and/or accurate conversion between density measures is necessary to reduce inaccuracies and error.

The majority of articles included in this review were studies involving the femur. The hip represents one of the most widely studied joints, and as such, many of the densitometric and density-modulus relationships have been developed using femur specimens. Computational models using femur developed densitometric and density-modulus relationships have shown excellent agreement between experimental models and FEMs (Table 1). This is not the case with other bones/joints that lack relationships specific to each specific anatomical location, or use equations that have been developed using femurs, or femur specimens. Differences between the femur and other bones may reduce the effectiveness of translating these relationships for use in other bones/joints, especially those that exhibit drastically different loading conditions, or mineralization patterns.

A large number of the studies reviewed reported relationships between QCT derived density and ash or apparent density derived in previous studies (Table 1 & Figs. 1 and 2). Ash density was used as equivalent to QCT density in 18% of studies. Schileo et al. (2008) showed that although linearly correlated (R2 = 0.997), ash and QCT density are not equivalent. When using densitometric relationships developed in previous studies, it is important to note that the relationships may be a function of the scanner settings and protocol, as well as the anatomical location and pathology of the bone (Faulkner et al. 1993; Kopperdahl et al. 2002; Schileo et al. 2008; Giambini et al. 2015). All these factors may increase the error when then using previously developed bone density-modulus relationships. Giambini et al. (2015) found that reconstruction kernel, as well as tube voltage, had a significant effect on cortical and cancellous QCT derived CT number (HU). This may indicate that even for scans performed on the same scanner, when scanner settings are altered, there may be significant variations in measured CT number, and consequently, material property assignment.

Direct comparison of QCT derived bone density to modulus has the potential to decrease this error, and may improve the accuracy of subject-specific FE models (Kopperdahl et al. 2002). This method minimizes error arising from densitometric conversion, variations in BMD by anatomical location and pathology of bone, and allows for subject-specific material mapping, and density-modulus relationship development. The desired outcome of the FE model should also be noted in choosing a density measure, as BMD corresponds mainly to ultimate strength or modulus, due to its lack of dependence on bone size.

When modeling bone with use of clinical resolution CT, partial volume effects must be taken into account, as well as the averaging of CT lattice vertices in the generated mesh (Taddei et al. 2004). Micro-CT model generation allows for these effects to be minimized, and for the generation of material assignment based on bone volume and mineral density (Dall’Ara et al. 2011; Zysset et al. 2015). However, the clinical availability and feasibility (Poelert et al. 2013), as well as size restrictions and dose of micro-CT limit its use with patient populations, and with larger bones and joints. Giambini et al. (2015) suggest using dual-energy CT to isolate bone from non-bone constituents within the matrix. This method can be implemented on standard clinical CT scanners and provides an interesting framework for future clinical-based FE studies; however, may be less desirable to patient populations due to increased dose requirements.

This review is not to suggest that previously developed models using mechanical testing, and physical density measurements are obsolete or suboptimal, but rather to provide the current state of QCT-based FE modeling, and to suggest that considerations in density mapping be carefully explored before model generation – in particular when using previously developed relationships. In subject-specific modeling, it is important to use empirical density-modulus relationships developed for the same anatomical site in order to increase model accuracy (Zadpoor and Weinans 2015). In using previously developed density-modulus relationships, comparing ash to apparent density, Schileo et al. (2008) determined a conversion factor of ρashapp = 0.6 be used for both cortical and cancellous bone, to avoid over- or under-estimation of density. This equation was the most commonly used conversion between the two density measures in the studies reviewed, with most studies reporting previously determined density-modulus relationships using ash density. While this conversion provides one value for cortical and cancellous bone, the authors report that this conversion was determined using human femur specimens, and that similar conversions should be developed for alternate anatomical locations, as the structural mineralization of the tissue is dependent on anatomical location and pathology of the bone (Schileo et al. 2008).

The limitations of this study are that an in-depth evaluation of the specific effect of densitometric conversions of FEM outcomes, and specifics of the density-modulus relationships are not discussed. The combination of these two relationships as a requirement for FEM development means they are not mutually exclusive and the effect of one without the other is therefore difficult to assess. We have provided experimental versus FEM validation metrics to allow for the combination of the two relationships to be assessed based on the type of study (Table 1). Specifics regarding the density-modulus relationships are compared and contrasted in the review by Helgason et al. (2008).

The lack of reported scanning parameters used in QCT-based FE studies has been previously stated (Giambini et al. 2015). Many of the studies included in this review lack one or all of phantom type and manufacturer, density and modulus relationships, as well as scanner type and scanner settings (Table 1). Since the combination of these parameters may alter calculated density and subsequent elastic modulus, we suggest that standardized reporting (see Table 1) should be included in future QCT-based FE studies to facilitate comparison with previous findings, and to ensure that methods are repeatable. This has the potential to improve the accuracy of future FE models. When assessing uncertainty in mechanical property assignments in FE models, Laz et al. (2007) provides an excellent framework, which should be incorporated into both experimental and clinical FE models.

Conclusions

This review assessed the current state of QCT-based FE modeling with use of clinical scanners. It was found that previously developed relationships vary by anatomical location, scanner type and settings. Reporting of all parameters used when referring to previously developed relationships, or in the development of new relationships, may increase the accuracy and repeatability of future FE models. Furthermore, the specific image processing steps in the conversion of raw attenuation data should be included whenever using QCT methods.

Declarations

Acknowledgments

Nikolas Knowles and Jacob Reeves are supported in part by the Natural Sciences and Engineering Research Council of Canada, and in part by Transdisciplinary Bone and Joint Training Awards from the Collaborative Training Program in Musculoskeletal Health Research at the University of Western Ontario.

Funding

This work was supported in part by a Bone and Joint Institute Catalyst Grant, a Lawson Health Research Institute Internal Research Fund Grant, and the Natural Sciences and Engineering Research Council of Canada.

Authors’ contributions

NK reviewed studies, collected and summarized data, and wrote manuscript. JR reviewed studies, collected data, and edited manuscript. LF edited manuscript. All authors read and approved the final manuscript.

Authors’ information

NK is currently completing his PhD at the University of Western Ontario, with research focusing on computational methods in biomechanics of the shoulder. His Masters research focused on quantifying bone density and morphological variations of the glenoid due to osteoarthritis. Previous and future research has made use of computed tomography data using the principles associated with clinical (and currently micro) CT for use in computational modeling. JR is completing his PhD at the University of Western Ontario. His research focuses on the humerus and aims to characterize bone density variations throughout the bone in order to optimize implant fixation and support. LF is an Assistant Professor at the University of Western Ontario with researching spanning a vast number of disciplines. Much of his previous work has focused on the development of joint motion simulators for the analysis of cadaveric specimens and to assess the resulting kinematics of surgical procedures. More recently, his research has focused on implementing surgical mechatronics and computational methods in upper limb research.

Competing interests

The authors declare that they have no competing interests.

Ethics approval

Not applicable.

Open AccessThis article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.

Authors’ Affiliations

(1)
Graduate Program in Biomedical Engineering, The University of Western Ontario
(2)
Roth|McFarlane Hand and Upper Limb Centre, Surgical Mechatronics Laboratory, St. Josephs Health Care
(3)
Collaborative Training Program in Musculoskeletal Health Research, and Bone and Joint Institute, The University of Western Ontario
(4)
Department of Mechanical and Materials Engineering, The University of Western Ontario

References

  1. Amin S, Kopperdhal DL, Melton LJ et al (2011) Association of hip strength estimates by finite-element analysis with fractures in women and men. J Bone Miner Res 26:1593–1600. doi:10.1002/jbmr.347 View ArticlePubMedPubMed CentralGoogle Scholar
  2. Anez-Bustillos L, Derikx LC, Verdonschot N et al (2013) Finite element analysis and CT-based structural rigidity analysis to assess failure load in bones with simulated lytic defects. Bone 58:160–167. doi:10.1016/j.bone.2013.10.009 View ArticlePubMedPubMed CentralGoogle Scholar
  3. Arachchi S, Pitto RP, Anderson IA, Shim VB (2015) Analyzing bone remodeling patterns after total hip arthroplasty using quantitative computed tomography and patient-specific 3D computational models. Quant Imaging Med Surg 5:575–582. doi:10.3978/j.issn.2223-4292.2015.08.03 PubMedPubMed CentralGoogle Scholar
  4. Campoli G, Bolsterlee B, van der Helm F et al (2014) Effects of densitometry, material mapping and load estimation uncertainties on the accuracy of patient-specific finite-element models of the scapula. J R Soc Interface 11:20131146. doi:10.1098/rsif.2013.1146 View ArticlePubMedPubMed CentralGoogle Scholar
  5. Carballido-Gamio J, Harnish R, Saeed I et al (2013) Structural patterns of the proximal femur in relation to age and hip fracture risk in women. Bone 57:290–299. doi:10.1016/j.bone.2013.08.017 View ArticlePubMedGoogle Scholar
  6. Carballido-gamio J, Bonaretti S, Saeed I et al (2015) Automatic multi-parametric quantification of the proximal femur with quantitative computed tomography. Quant Imaging Med Surg 5:552–568. doi:10.3978/j.issn.2223-4292.2015.08.02 PubMedPubMed CentralGoogle Scholar
  7. Carter D, Hayes W (1977) The compressive behavior of bone as a two-phase porous structure. J Bone Jt Surg 59(7):954–962View ArticleGoogle Scholar
  8. Christiansen BA, Kopperdahl DL, Kiel DP et al (2011) Mechanical contributions of the cortical and trabecular compartments contribute to differences in age-related changes in vertebral body strength in men and women assessed by QCT-based finite element analysis. J Bone Miner Res 26:974–983. doi:10.1002/jbmr.287 View ArticlePubMedPubMed CentralGoogle Scholar
  9. Cong A, Den Buijs JO, Dragomir-daescu D (2011) Medical engineering & physics in situ parameter identification of optimal density – elastic modulus relationships in subject-specific finite element models of the proximal femur. Med Eng Phys 33:164–173. doi:10.1016/j.medengphy.2010.09.018 View ArticlePubMedGoogle Scholar
  10. Dall’Ara E, Varga P, Pahr D, Zysset P (2011) A calibration methodology of QCT BMD for human vertebral body with registered micro-CT images. Med Phys 38:2602–2608. doi:10.1118/1.3582946 View ArticlePubMedGoogle Scholar
  11. Dall’Ara E, Pahr D, Varga P et al (2012) QCT-based finite element models predict human vertebral strength in vitro significantly better than simulated DEXA. Osteoporos Int 23:563–572. doi:10.1007/s00198-011-1568-3 View ArticlePubMedGoogle Scholar
  12. Dall’Ara E, Luisier B, Schmidt R et al (2013) A nonlinear QCT-based finite element model validation study for the human femur tested in two configurations in vitro. Bone 52:27–38. doi:10.1016/j.bone.2012.09.006 View ArticlePubMedGoogle Scholar
  13. Dragomir-Daescu D, Op Den Buijs J, McEligot S et al (2011) Robust QCT/FEA models of proximal femur stiffness and fracture load during a sideways fall on the hip. Ann Biomed Eng 39:742–755. doi:10.1007/s10439-010-0196-y View ArticlePubMedGoogle Scholar
  14. Eberle S, Göttlinger M, Augat P (2013a) An investigation to determine if a single validated density – elasticity relationship can be used for subject specific finite element analyses of human long bones. Med Eng Phys 35:875–883. doi:10.1016/j.medengphy.2012.08.022 View ArticlePubMedGoogle Scholar
  15. Eberle S, Göttlinger M, Augat P (2013b) Individual density-elasticity relationships improve accuracy of subject-specific finite element models of human femurs. J Biomech 46:2152–2157. doi:10.1016/j.jbiomech.2013.06.035 View ArticlePubMedGoogle Scholar
  16. Edwards WB, Schnitzer TJ, Troy KL (2013) Torsional stiffness and strength of the proximal tibia are better predicted by finite element models than DXA or QCT. J Biomech 46:1655–1662. doi:10.1016/j.jbiomech.2013.04.016 View ArticlePubMedPubMed CentralGoogle Scholar
  17. Engelke K, Libanati C, Fuerst T et al (2013) Advanced CT based in vivo methods for the assessment of bone density, structure, and strength. Curr Osteoporos Rep 11:246–255. doi:10.1007/s11914-013-0147-2 View ArticlePubMedGoogle Scholar
  18. Enns-Bray WS, Owoc JS, Nishiyama KK, Boyd SK (2014) Mapping anisotropy of the proximal femur for enhanced image based finite element analysis. J Biomech 47:3272–3278. doi:10.1016/j.jbiomech.2014.08.020 View ArticlePubMedGoogle Scholar
  19. Faulkner KG, Gluer CC, Grampp S, Genant HK (1993) Cross-calibration of liquid and solid QCT calibration standards: corrections to the UCSF normative data. Osteoporos Int 3:36–42. doi:10.1007/BF01623175 View ArticlePubMedGoogle Scholar
  20. Galante J, Rostoker W, Ray RD (1970) Physical properties of trabecular bone. Calcif Tissue Res 5:236–246. doi:10.1007/BF02017552 View ArticlePubMedGoogle Scholar
  21. Giambini H, Dragomir-Daescu D, Huddleston PM et al (2015) The effect of quantitative computed tomography acquisition protocols on bone mineral density estimation. J Biomech Eng 137:1–6. doi:10.1115/1.4031572 View ArticleGoogle Scholar
  22. Gong H, Zhang M, Fan Y et al (2012) Relationships between femoral strength evaluated by nonlinear finite element analysis and BMD, material distribution and geometric morphology. Ann Biomed Eng 40:1575–1585. doi:10.1007/s10439-012-0514-7 View ArticlePubMedGoogle Scholar
  23. Gupta S, Dan P (2004) Bone geometry and mechanical properties of the human scapula using computed tomography data. Trends Biomater Artif Organs 17:61–70Google Scholar
  24. Haider IT, Speirs AD, Frei H (2013) Effect of boundary conditions, impact loading and hydraulic stiffening on femoral fracture strength. J Biomech 46:2115–2121. doi:10.1016/j.jbiomech.2013.07.004 View ArticlePubMedGoogle Scholar
  25. Hambli R, Allaoui S (2013) A robust 3D finite element simulation of human proximal femur progressive fracture under stance load with experimental validation. Ann Biomed Eng 41:2515–2527. doi:10.1007/s10439-013-0864-9 View ArticlePubMedGoogle Scholar
  26. Helgason B, Perilli E, Schileo E, Taddei F (2008) Mathematical relationships between bone density and mechanical properties: a literature review. Clin Biomech 23:135–146. doi:10.1016/j.clinbiomech.2007.08.024 View ArticleGoogle Scholar
  27. Hermida JC, Flores-Hernadez C, Hoenecke HR, D'Lima DD. Augmented wedge-shaped glenoid component for the correction of glenoid retroversion: a finite element analysis. Shoulder Elb Surg 23(3):347–354Google Scholar
  28. Imai K (2011) Vertebral fracture risk and alendronate effects on osteoporosis assessed by a computed tomography-based nonlinear finite element method. J Bone Miner Metab 29:645–651. doi:10.1007/s00774-011-0281-9 View ArticlePubMedGoogle Scholar
  29. Kaneko M, Ohnishi I, Bessho M et al (2015) Prediction of proximal femur strength by a quantitative computed tomography-based finite element method -creation of predicted strength data of the proximal femur according to age range in a normal population and analysis of risk factors for hip fracture-. Mod Rheumatol 26:151–155. doi:10.3109/14397595.2015.1046220 View ArticlePubMedGoogle Scholar
  30. Keaveny TM, McClung MR, Wan X et al (2012) Femoral strength in osteoporotic women treated with teriparatide or alendronate. Bone 50:165–170. doi:10.1016/j.bone.2011.10.002 View ArticlePubMedGoogle Scholar
  31. Keaveny TM, McClung MR, Genant HK et al (2014) Femoral and vertebral strength improvements in postmenopausal women with osteoporosis treated with denosumab. J Bone Miner Res 29:158–165. doi:10.1002/jbmr.2024 View ArticlePubMedGoogle Scholar
  32. Kersh ME, Zysset PK, Pahr DH et al (2013) Measurement of structural anisotropy in femoral trabecular bone using clinical-resolution CT images. J Biomech 46:2659–2666. doi:10.1016/j.jbiomech.2013.07.047 View ArticlePubMedGoogle Scholar
  33. Keyak JH, Lee IY, Skinner HB (1994) Correlations between orthogonal mechanical properties and density of trabecular bone: use of different densitometric measures. J Biomed Mat Res 28:1329–1336View ArticleGoogle Scholar
  34. Keyak JH, Rossi SA, Jones KA, Skinner HB (1997) Prediction of femoral fracture load using automated finite element modelling. J Biomech 31:125–133. doi:10.1016/S0021-9290(97)00123-1 View ArticleGoogle Scholar
  35. Keyak JH, Kaneko TS, Tehranzadeh J, Skinner HB (2005) Predicting proximal femoral strength using structural engineering models. Clin Orthop Relat Res 437:219–228. doi:10.1097/01.blo.0000164400.37905.22 View ArticleGoogle Scholar
  36. Keyak JH, Sigurdsson S, Karlsdottir G et al (2011) Male–female differences in the association between incident hip fracture and proximal femoral strength: a finite element analysis study. Bone 48:1239–1245. doi:10.1016/j.bone.2011.03.682 View ArticlePubMedPubMed CentralGoogle Scholar
  37. Keyak JH, Sigurdsson S, Karlsdottir GS et al (2013) Effect of finite element model loading condition on fracture risk assessment in men and women: The AGES-Reykjavik study. Bone 57:18–29. doi:10.1016/j.bone.2013.07.028 View ArticlePubMedPubMed CentralGoogle Scholar
  38. Kheirollahi H, Luo Y (2015) Assessment of Hip fracture risk using cross-section strain energy determined by QCT-based finite element modeling. Biomed Res Int. doi:10.1155/2015/413839 PubMedPubMed CentralGoogle Scholar
  39. Kleerekoper M, Greenspan SL, Lewiecki EM et al (2014) Assessing the effects of teriparatide treatment. J Bone Jt Surg 90:1–9. doi:10.1016/S0021-9355(14)74223-7 Google Scholar
  40. Koivumäki JEM, Thevenot J, Pulkkinen P et al (2012a) Ct-based fi nite element models can be used to estimate experimentally measured failure loads in the proximal femur. Bone 50:824–829. doi:10.1016/j.bone.2012.01.012 View ArticlePubMedGoogle Scholar
  41. Koivumäki JEM, Thevenot J, Pulkkinen P et al (2012b) Cortical bone finite element models in the estimation of experimentally measured failure loads in the proximal femur. Bone 51:737–740. doi:10.1016/j.bone.2012.06.026 View ArticlePubMedGoogle Scholar
  42. Kopperdahl DL, Morgan EF, Keaveny TM (2002) Quantitative computed tomography estimates of the mechanical properties of human vertebral trabecular bone. J Orthop Res 20:801–805. doi:10.1016/S0736-0266(01)00185-1 View ArticlePubMedGoogle Scholar
  43. Kopperdhal DL, Aspelund T, Hoffmann PF et al (2014) Assessment of incident spine and Hip fractures in women and men using FEA of CT scans. J Bone Miner Res 29:570–580. doi:10.1016/j.devcel.2010.12.007.Peroxiredoxin View ArticleGoogle Scholar
  44. Laz PJ, Stowe JQ, Baldwin MA et al (2007) Incorporating uncertainty in mechanical properties for finite element-based evaluation of bone mechanics. J Biomech 40:2831–2836. doi:10.1016/j.jbiomech.2007.03.013 View ArticlePubMedGoogle Scholar
  45. Les CM, Keyak J, Stover SM et al (1994) Estimation of material properties in the equine metacarpus with use of quantitative computed tomography. Jounral Orthop Res 12:822–833View ArticleGoogle Scholar
  46. Lu Y, Engelke K, Glueer C-C et al (2014a) The effect of in situ/in vitro threedimensional quantitative computed tomography image voxel size on the finite element model of human vertebral cancellous bone. Proc Inst Mech Eng Part H J Eng Med 228:1208–1213. doi:10.1177/0954411914558654 View ArticleGoogle Scholar
  47. Lu Y, Engelke K, Puschel K et al (2014b) Influence of 3D QCT scan protocol on the QCT-based finite element models of human vertebral cancellous bone. Med Eng Phys 36:1069–1073. doi:10.1016/j.medengphy.2014.05.001 View ArticlePubMedGoogle Scholar
  48. Luisier B, Dall’Ara E, Pahr DH (2014) Orthotropic HR-pQCT-based FE models improve strength predictions for stance but not for side-way fall loading compared to isotropic QCT-based FE models of human femurs. J Mech Behav Biomed Mater 32:287–299. doi:10.1016/j.jmbbm.2014.01.006 View ArticlePubMedGoogle Scholar
  49. Matsuura Y, Kuniyoshi K, Suzuki T et al (2014) Accuracy of specimen-specific nonlinear finite element analysis for evaluation of radial diaphysis strength in cadaver material. Comput Methods Biomech Biomed Engin 5842:1–7. doi:10.1080/10255842.2014.974579 Google Scholar
  50. McErlain DD, Milner JS, Ivanov TG et al (2011) Subchondral cysts create increased intra-osseous stress in early knee OA: a finite element analysis using simulated lesions. Bone 48:639–646. doi:10.1016/j.bone.2010.11.010 View ArticlePubMedGoogle Scholar
  51. Mirzaei M, Keshavarzian M, Naeini V (2014) Analysis of strength and failure pattern of human proximal femur using quantitative computed tomography (QCT)-based finite element method. Bone 64:108–114. doi:10.1016/j.bone.2014.04.007 View ArticlePubMedGoogle Scholar
  52. Morgan E, Bayraktar H, Keaveny T (2003) Trabecular bone modulus–density relationships depend on anatomic site. J Biomech 36(7):897–904View ArticlePubMedGoogle Scholar
  53. Nazemi SM, Amini M, Kontulainen SA et al (2015) Clinical Biomechanics Prediction of local proximal tibial subchondral bone structural stiffness using subject-specific finite element modeling : effect of selected density – modulus relationship. J Clin Biomech 30:703–712. doi:10.1016/j.clinbiomech.2015.05.002 View ArticleGoogle Scholar
  54. Nishiyama KK, Gilchrist S, Guy P et al (2013) Proximal femur bone strength estimated by a computationally fast finite element analysis in a sideways fall configuration. J Biomech 46:1231–1236. doi:10.1016/j.jbiomech.2013.02.025 View ArticlePubMedGoogle Scholar
  55. Nishiyama KK, Ito M, Harada A, Boyd SK (2014) Classification of women with and without hip fracture based on quantitative computed tomography and finite element analysis. Osteoporos Int 25:619–626. doi:10.1007/s00198-013-2459-6 View ArticlePubMedGoogle Scholar
  56. Öhman C, Baleani M, Perilli E et al (2007) Mechanical testing of cancellous bone from the femoral head: experimental errors due to off-axis measurements. J Biomech 40:2426–2433. doi:10.1016/j.jbiomech.2006.11.020 View ArticlePubMedGoogle Scholar
  57. Op Den Buijs J, Dragomir-Daescu D (2011) Validated finite element models of the proximal femur using two-dimensional projected geometry and bone density. Comput Methods Programs Biomed 104:168–174. doi:10.1016/j.cmpb.2010.11.008 View ArticlePubMedGoogle Scholar
  58. Pahr DH, Zysset PK (2009) A comparison of enhanced continuum FE with micro FE models of human vertebral bodies. J Biomech 42:455–462. doi:10.1016/j.jbiomech.2008.11.028 View ArticlePubMedGoogle Scholar
  59. Poelert S, Valstar E, Weinans H, Zadpoor AA (2013) Patient-specific finite element modeling of bones. Proc Inst Mech Eng Part H J Eng Med 227:464–478. doi:10.1177/0954411912467884 View ArticleGoogle Scholar
  60. Pomwenger W, Entacher K, Resch H, Schuller-Götzburg P (2014) Need for CT-based bone density modelling in finite element analysis of a shoulder arthroplasty revealed through a novel method for result analysis. Biomed Tech (Berl) 59:421–430. doi:10.1515/bmt-2013-0125 Google Scholar
  61. Rice J, Cowin S, Bowman J (1988) On the dependence of the elasticity and strength of cancellous bone on apparent density. J Biomech 21(2):155–168View ArticlePubMedGoogle Scholar
  62. Ruess M, Tal D, Trabelsi N et al (2012) The finite cell method for bone simulations: verification and validation. Biomech Model Mechanobiol 11:425–437. doi:10.1007/s10237-011-0322-2 View ArticlePubMedGoogle Scholar
  63. Schaffler M, Burr D (1988) Stiffness of compact bone: effects of porosity and density. J Biomech 21(1):13–16View ArticlePubMedGoogle Scholar
  64. Schileo E, Dall’Ara E, Taddei F (2008) An accurate estimation of bone density improves the accuracy of subject-specific finite element models. J Biomech 41(11):2483–2491View ArticlePubMedGoogle Scholar
  65. Shim VB, Pitto RP, Anderson IA (2012) Quantitative CT with finite element analysis: towards a predictive tool for bone remodelling around an uncemented tapered stem. Int Orthop 36:1363–1369. doi:10.1007/s00264-012-1513-x View ArticlePubMedPubMed CentralGoogle Scholar
  66. Suzuki S, Yamamuro T, Okumura H, Yamamoto I (1991) Quantitative computed tomography: comparative study using different scanners with two calibration phantoms. Br J Radiol 64:1001–1006. doi:10.1259/0007-1285-64-767-1001 View ArticlePubMedGoogle Scholar
  67. Synek A, Chevalier Y, Baumbach SF, Pahr DH (2015) The influence of bone density and anisotropy in finite element models of distal radius fracture osteosynthesis: evaluations and comparison to experiments. J Biomech 48:4116–4123. doi:10.1016/j.jbiomech.2015.10.012 View ArticlePubMedGoogle Scholar
  68. Taddei F, Pancanti A, Viceconti M (2004) An improved method for the automatic mapping of computed tomography numbers onto finite element models. Med Eng Phys 26:61–69. doi:10.1016/S1350-4533(03)00138-3 View ArticlePubMedGoogle Scholar
  69. Tarala M, Janssen D, Telka A et al (2011) Experimental versus computational analysis of micromotions at the implant-bone interface. Proc Inst Mech Eng H 225:8–15. doi:10.1243/09544119JEIM825 View ArticlePubMedGoogle Scholar
  70. Tawara D, Sakamoto J, Murakami H et al (2010) Mechanical evaluation by patient-specific finite element analyses demonstrates therapeutic effects for osteoporotic vertebrae. J Mech Behav Biomed Mater 3:31–40. doi:10.1016/j.jmbbm.2009.03.001 View ArticlePubMedGoogle Scholar
  71. Tomaszewski PK, van Diest M, Bulstra SK et al (2012) Numerical analysis of an osseointegrated prosthesis fixation with reduced bone failure risk and periprosthetic bone loss. J Biomech 45:1875–1880. doi:10.1016/j.jbiomech.2012.05.032 View ArticlePubMedGoogle Scholar
  72. Trabelsi N, Yosibash Z (2011) Patient-specific finite-element analyses of the proximal femur with orthotropic material properties validated by experiments. J Biomech Eng 133:061001. doi:10.1115/1.4004180 View ArticlePubMedGoogle Scholar
  73. Trabelsi N, Yosibash Z, Wutte C et al (2011) Patient-specific finite element analysis of the human femur-A double-blinded biomechanical validation. J Biomech 44:1666–1672. doi:10.1016/j.jbiomech.2011.03.024 View ArticlePubMedGoogle Scholar
  74. Unnikrishnan GU, Morgan EF (2011) A new material mapping procedure for quantitative computed tomography-based, continuum finite element analyses of the vertebra. J Biomech Eng 133:071001. doi:10.1115/1.4004190 View ArticlePubMedPubMed CentralGoogle Scholar
  75. Unnikrishnan GU, Barest GD, Berry DB et al (2013) Effect of specimen-specific anisotropic material properties in quantitative computed tomography-based finite element analysis of the vertebra. J Biomech Eng 135:101007–101011. doi:10.1115/1.4025179 View ArticlePubMedGoogle Scholar
  76. Varghese B, Short D, Penmetsa R et al (2011) Computed-tomography-based finite-element models of long bones can accurately capture strain response to bending and torsion. J Biomech 44:1374–1379. doi:10.1016/j.jbiomech.2010.12.028 View ArticlePubMedGoogle Scholar
  77. Wang X, Sanyal A, Cawthon PM et al (2012) Prediction of New clinical vertebral fractures in elderly men using finite element analysis of CT scans for the osteoporotic fractures in men (MrOS) research group. J Bone Min Res J Bone Min Res 27:808–816. doi:10.1002/jbmr.1539 View ArticleGoogle Scholar
  78. Zadpoor AA, Weinans H (2015) Patient-specific bone modeling and analysis: the role of integration and automation in clinical adoption. J Biomech 48:750–760. doi:10.1016/j.jbiomech.2014.12.018 View ArticlePubMedGoogle Scholar
  79. Zeinali A, Hashemi B, Akhlaghpoor S (2010) Noninvasive prediction of vertebral body compressive strength using nonlinear finite element method and an image based technique. Phys Medica 26:88–97. doi:10.1016/j.ejmp.2009.08.002 View ArticleGoogle Scholar
  80. Zysset P, Qin L, Lang T et al (2015) Clinical use of quantitative computed tomography-based finite element analysis of the hip and spine in the management of osteoporosis in adults: the 2015 ISCD official positions-part II. J Clin Densitom 18:359–392. doi:10.1016/j.jocd.2015.06.011 View ArticlePubMedGoogle Scholar

Copyright

© The Author(s). 2016