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Research Papers

Three-Dimensional Local Measurements of Bone Strain and Displacement: Comparison of Three Digital Volume Correlation Approaches

[+] Author and Article Information
Marco Palanca

School of Engineering and Architecture,
University of Bologna,
Via Terracini 28,
Bologna 40131, Italy
e-mail: marco.palanca2@unibo.it

Gianluca Tozzi

School of Engineering,
University of Portsmouth,
Anglesea Building, Anglesea Road,
Portsmouth PO1 3DJ, UK
e-mail: gianluca.tozzi@port.ac.uk

Luca Cristofolini

School of Engineering and Architecture,
University of Bologna,
Viale Risorgimento 2,
Bologna 40136, Italy
e-mail: luca.cristofolini@unibo.it

Marco Viceconti

Department of Mechanical Engineering and
INSIGNEO Institute for In Silico Medicine,
University of Sheffield,
Sir Frederick Mappin Building,
Pam Liversidge Building,
Sheffield S1 3JD, UK
e-mail: m.viceconti@sheffield.ac.uk

Enrico Dall'Ara

Department of Mechanical Engineering and
INSIGNEO Institute for In Silico Medicine,
University of Sheffield,
Sir Frederick Mappin Building,
Pam Liversidge Building,
Sheffield S1 3JD, UK
e-mail: e.dallara@sheffield.ac.uk

1Corresponding author.

Manuscript received December 8, 2014; final manuscript received March 13, 2015; published online June 2, 2015. Assoc. Editor: Pasquale Vena.

J Biomech Eng 137(7), 071006 (Jul 01, 2015) (14 pages) Paper No: BIO-14-1612; doi: 10.1115/1.4030174 History: Received December 08, 2014; Revised March 13, 2015; Online June 02, 2015

Different digital volume correlation (DVC) approaches are currently available or under development for bone tissue micromechanics. The aim of this study was to compare accuracy and precision errors of three DVC approaches for a particular three-dimensional (3D) zero-strain condition. Trabecular and cortical bone specimens were repeatedly scanned with a micro-computed tomography (CT). The errors affecting computed displacements and strains were extracted for a known virtual translation, as well as for repeated scans. Three DVC strategies were tested: two local approaches, based on fast-Fourier-transform (DaVis-FFT) or direct-correlation (DaVis-DC), and a global approach based on elastic registration and a finite element (FE) solver (ShIRT-FE). Different computation subvolume sizes were tested. Much larger errors were found for the repeated scans than for the virtual translation test. For each algorithm, errors decreased asymptotically for larger subvolume sizes in the range explored. Considering this particular set of images, ShIRT-FE showed an overall better accuracy and precision (a few hundreds microstrain for a subvolume of 50 voxels). When the largest subvolume (50–52 voxels) was applied to cortical bone, the accuracy error obtained for repeated scans with ShIRT-FE was approximately half of that for the best local approach (DaVis-DC). The difference was lower (250 microstrain) in the case of trabecular bone. In terms of precision, the errors shown by DaVis-DC were closer to the ones computed by ShIRT-FE (differences of 131 microstrain and 157 microstrain for cortical and trabecular bone, respectively). The multipass computation available for DaVis software improved the accuracy and precision only for the DaVis-FFT in the virtual translation, particularly for trabecular bone. The better accuracy and precision of ShIRT-FE, followed by DaVis-DC, were obtained with a higher computational cost when compared to DaVis-FFT. The results underline the importance of performing a quantitative comparison of DVC methods on the same set of samples by using also repeated scans, other than virtual translation tests only. ShIRT-FE provides the most accurate and precise results for this set of images. However, both DaVis approaches show reasonable results for large nodal spacing, particularly for trabecular bone. Finally, this study highlights the importance of using sufficiently large subvolumes, in order to achieve better accuracy and precision.

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References

Figures

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Fig. 2

Description of the three DVC approaches for the determination of strain accuracy and precision. DaVis software enabled both FFT (DaVis-FFT) and DC (DaVis-DC) displacement calculation and strain was computed using a CFD scheme. A custom-written software (ShIRT) in combination with a FE solver was also tested.

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Fig. 1

Schematic of the two specimens obtained from a fresh bovine femur: a cylinder of cortical bone was extracted from the diaphysis (3 mm diameter, 20 mm height), and a cylinder of trabecular bone was extracted from the greater trochanter (8 mm diameter, 12 mm height). Each specimen was scanned twice (height of 9.323 mm). Identical VOI were extracted from each specimen. The displacements and strains were computed for such a zero-strain condition, both between scan1 and scan2, and by virtually displacing scan1.

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Fig. 3

Virtually-Moved-Test: trend of the accuracy (microstrain) for both cortical and trabecular specimen, as a function of the subvolume size (voxels). The accuracy of the three DVC approaches was first computed as a scalar, consistently with Ref. [8]. The trendline equation (power-law relation and R2) is also reported. *The subvolume was different for DaVis-DC. Refer to Table 1 for more details.

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Fig. 4

Virtually-Moved-Test: trend of the precision (microstrain) for both cortical and trabecular specimen, as a function of the subvolume size (voxels). The precision of the three DVC approaches was first computed as a scalar, consistently with Ref. [8]. The trendline equation (power-law relation and R2) is also reported. *The subvolume was different for DaVis-DC. Refer to Table 1 for more details.

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Fig. 5

Repeated-Scan-Test: trend of the accuracy (microstrain) for both cortical and trabecular specimen, as a function of the subvolume size (voxels). The accuracy of the three DVC approaches was first computed as a scalar, consistently with Ref. [8]. The trendline equation (power-law relation and R2) is also reported. *The subvolume was different for DaVis-DC. Refer to Table 1 for more details.

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Fig. 6

Repeated-Scan-Test: trend of the precision (microstrain) for both cortical and trabecular specimen, as a function of the subvolume size (voxels). The precision of the three DVC approaches was first computed as a scalar, consistently with Ref. [8]. The trendline equation (power-law relation and R2) is also reported. *The subvolume was different for DaVis-DC. Refer to Table 1 for more details.

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Fig. 7

Virtually-Moved-Test: analysis of the accuracy of the six components of strain (microstrain), in both cortical and trabecular specimen, for the largest subvolume size considered (50 voxels ShIRT and DaVis-FFT, 52 voxels DaVis-DC). The Z-axis represents the axis of rotation of the specimen during imaging in the micro-CT. The accuracy of the three DVC approaches was computed as the average of the absolute values of each component of strain. Different scales are used for the three computation approaches due to large differences in absolute values.

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Fig. 8

Virtually-Moved-Test: analysis of the precision of the six components of strain (microstrain), in both cortical and trabecular specimen, for the largest subvolume size considered (50 voxels ShIRT and DaVis-FFT, 52 voxels DaVis-DC). The Z-axis represents the axis of rotation of the specimen during imaging in the micro-CT. The precision of the three DVC approaches was computed as the SD of the absolute values of each component of strain. Different scales are used for the three computation approaches due to large differences in absolute values.

Grahic Jump Location
Fig. 9

Repeated-Scan-Test: analysis of the accuracy of the six components of strain (microstrain), in both cortical and trabecular specimen, for the largest subvolume size considered (50 voxels ShIRT and DaVis-FFT, 52 voxels DaVis-DC). The Z-axis represents the axis of rotation of the specimen during imaging in the micro-CT. The accuracy of the three DVC approaches was computed as the average of the absolute values of each component of strain. Different scales are used for the three computation approaches due to large differences in absolute values.

Grahic Jump Location
Fig. 10

Repeated-Scan-Test: analysis of the precision of the six components of strain (microstrain), in both cortical and trabecular specimen, for the largest subvolume size considered (50 voxels ShIRT and DaVis-FFT, 52 voxels DaVis-DC). The Z-axis represents the axis of rotation of the specimen during imaging in the micro-CT. The precision of the three DVC approaches was computed as the SD of the absolute values of each component of strain. Different scales are used for the three computation approaches due to large differences in absolute values.

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