European Journal of Radiology 83 (2014) e36–e42

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European Journal of Radiology journal homepage: www.elsevier.com/locate/ejrad

Prediction of bone strength by ␮CT and MDCT-based finite-element-models: How much spatial resolution is needed? Jan S. Bauer a,b,c,∗,1 , Irina Sidorenko c,1 , Dirk Mueller d , Thomas Baum a,b,c , Ahi Sema Issever b,e , Felix Eckstein f , Ernst J. Rummeny a , Thomas M. Link b , Christoph W. Raeth c a

Department of Radiology, Technische Universität München, Munich, Germany Department of Radiology, University of California, San Francisco, CA, United States c Max Planck Institute for Extraterrestrial Physics, Garching, Germany d Department of Radiology, Universität Köln, Germany e Department of Radiology, Charite, Berlin, Germany f Institute of Anatomy and Musculoskeletal Research, Paracelsus Medical University, Salzburg, Austria b

a r t i c l e

i n f o

Article history: Received 30 October 2012 Received in revised form 17 October 2013 Accepted 22 October 2013 Keywords: X-ray microtomography Multidetector computed tomography Finite element analysis Bone Spine Osteoporosis

a b s t r a c t Objectives: Finite-element-models (FEM) are a promising technology to predict bone strength and fracture risk. Usually, the highest spatial resolution technically available is used, but this requires excessive computation time and memory in numerical simulations of large volumes. Thus, FEM were compared at decreasing resolutions with respect to local strain distribution and prediction of failure load to (1) validate MDCT-based FEM and to (2) optimize spatial resolution to save computation time. Materials and methods: 20 cylindrical trabecular bone specimens (diameter 12 mm, length 15–20 mm) were harvested from elderly formalin-fixed human thoracic spines. All specimens were examined by micro-CT (isotropic resolution 30 ␮m) and whole-body multi-row-detector computed tomography (MDCT, 250 ␮m × 250 ␮m × 500 ␮m). The resolution of all datasets was lowered in eight steps to ∼2000 ␮m × 2000 ␮m × 500 ␮m and FEM were calculated at all resolutions. Failure load was determined by biomechanical testing. Probability density functions of local micro-strains were compared in all datasets and correlations between FEM-based and biomechanically measured failure loads were determined. Results: The distribution of local micro-strains was similar for micro-CT and MDCT at comparable resolutions and showed a shift toward higher average values with decreasing resolution, corresponding to the increasing apparent trabecular thickness. Small micro-strains (εeff < 0.005) could be calculated down to 250 ␮m × 250 ␮m × 500 ␮m. Biomechanically determined failure load showed significant correlations with all FEM, up to r = 0.85 and did not significantly change with lower resolution but decreased with high thresholds, due to loss of trabecular connectivity. Conclusion: When choosing connectivity-preserving thresholds, both micro-CT- and MDCT-based finiteelement-models well predicted failure load and still accurately revealed the distribution of local microstrains in spatial resolutions, available in vivo (250 ␮m × 250 ␮m × 500 ␮m), that thus seemed to be the optimal compromise between high accuracy and low computation time. © 2013 Elsevier Ireland Ltd. All rights reserved.

1. Introduction Bone mineral density (BMD) is the most widely accepted method for the assessment of fracture risk in osteoporosis [1],

∗ Corresponding author at: Institut für Radiologie, Abteilung für Neuroradiologie Technische Universität München, Ismaninger Str. 22, 81675 München, Germany. Tel.: +49 8941402626. E-mail address: [email protected] (J.S. Bauer). 1 Both authors share 1st authorship. 0720-048X/$ – see front matter © 2013 Elsevier Ireland Ltd. All rights reserved. http://dx.doi.org/10.1016/j.ejrad.2013.10.024

however, shortcomings of this method are well known, as the majority of patients with insufficiency fractures have non-osteoporotic BMD [2]. The WHO thus changed their recommendations and introduced a questionnaire for fracture risk prediction (FRAX), where BMD is just an optional parameter [3]. On the other hand, it is still debatable if parameters of bone microstructure better predict bone quality and fracture risk than BMD [4]. Many different parameters of trabecular and cortical architecture have been established, however in most studies finite-elementmodels (FEM) correlated best with bone strength [5–8]. Excellent results have been achieved in high-resolution datasets of small

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specimens [9–11], but FEM have also successfully been calculated for whole bones with low spatial resolution [12–16]. During recent years, advances in high resolution imaging modalities were at least as groundbreaking as the image post processing procedures like FEM [17]. The introduction of high-resolution peripheral quantitative computed tomography (HR-pQCT) allowed visualizing trabecular structure in vivo [18]. Simultaneously, whole body multi-row detector computed tomography (MDCT) improved regarding scan time and spatial resolution [19]. Although the spatial resolution is lower in MDCT as compared to HR-pQCT (about 250 ␮m × 250 ␮m × 500 ␮m vs. 82 ␮m isotropic), MDCT has the advantages of being widely available and capable to visualize trabecular structure also in the spine and proximal femur. These represent the primary sites of interest regarding osteoporotic fractures, and thus should be investigated to analyze fracture risk [20,21]. To optimize FEM of the spine and proximal femur, image acquisition and post-processing have to be aligned to achieve optimal results. While usually the highest resolution available was used for micro FEM, limitations exist regarding available calculation time and memory in particular for large bones. Additionally, radiation dose matters in whole body MDCT and significantly increases with increasing resolution. Thus, continuum FEM were used in QCT datasets of lower resolution of the proximal femur and the spine [15,16]. However little data is available regarding the transition zone between HR-pQCT data (82 ␮m isotropic resolution) and QCT data (400 ␮m × 400 ␮m × 3000 ␮m resolution). The purpose of this study was to (1) validate MDCT-based FEM and to (2) determine the optimal spatial resolution for MDCT-based FEM in regard to short computation time and accurately revealing local strain distributions. Thus, we compared FEM based on CT datasets with decreasing spatial resolution regarding their ability to (1) reveal the distribution of micro-strains within the trabecular bone structure and (2) predict the biomechanically tested failure load. This was done for both ␮CT and MDCT datasets with different threshold settings and simulated decreased spatial resolution; in MDCT, continuum FEM were additionally calculated to account for the lower spatial resolution.

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Fig. 1. Example demonstrating the effect of the different spatial resolution regimes on the visualization of one trabecular bone specimen. Shown are binarized ␮CT (upper row) and MDCT (lower row) datasets. In case of the ␮CT, only a part of each slice is displayed; spatial resolution decreases from 30 ␮m (left, original resolution) to 60 ␮m, 120 ␮m and 240 ␮m voxel size (virtually degraded resolution). In MDCT, spatial resolution starts with 100 ␮m pixel size (left, interpolated original resolution) and decreases to 250 ␮m, 500 ␮m and 800 ␮m. With lower resolution, thin trabecular structures are lost due to partial volume effects. Note the artificial increase in BV/TV, as thresholds were chosen to preserve connectivity.

resolution protocol was used, which is also applied clinically for high spatial resolution bone studies, e.g. to visualize the inner ear. This protocol had a collimation and a table feed of 0.5 mm and a reconstruction index of 0.3 mm. A kVp of 120 was used with 100 mAs. The image matrix was 512 × 512 pixels at a field of view of 50 mm. A high spatial resolution kernel was applied (U90u) to reconstruct axial images of the specimens, resulting in an maximum in-plane spatial resolution of 0.22 mm × 0.22 mm (determined at 10 of the modulation-transfer-function). Additionally, all specimens were imaged with a Computed Microtomography System (␮CT). It is considered to be the gold standard for visualizing the true trabecular structure. ␮CT was carried out on a SCANCO ␮CT20 (Scanco Medical AG, Basserdorf, Switzerland). A spatial resolution of 30 ␮m × 30 ␮m × 30 ␮m was obtained with an imaging time of about 4 h per specimen. Due to technical constrains, only the central part of the specimens was imaged, with a segmented volume of 8 mm in diameter and 7.8 mm in length.

2. Materials and methods 2.3. Image analysis 2.1. Specimens Twenty cylindrical trabecular bone specimens (diameter 12 mm, length 15–20 mm) were harvested from the eighth thoracic vertebra of formalin-fixed human thoracic spines. The donors had dedicated their body for educational and research purposes to the Institute of Anatomy in Munich prior to death, in line with German legislative requirements. They had a mean age ± standard deviation (SD) of 82 ± 9 years (range 65–100 years; 11 females, 9 males). To exclude donors with metastatic bone disease and hematological or metabolic bone disorders others than osteoporosis, biopsies were taken from the iliac crest and examined histologically as well as radiographs were obtained from the whole spine. Fractures were classified semi-quantitatively using the spinal fracture index (SFI) [22]. Fractured vertebrae were excluded. Specimens were degassed for at least 24 h prior to imaging. Until completion of all imaging procedures, specimens were stored in formalin solution, to avoid air artifacts. The time between fixation and imaging was 27 ± 2 months, the time between imaging and biomechanical testing was 11 ± 0 months. 2.2. Imaging MDCT images were obtained with a 4-row multi-detector CT (“Volume Zoom”, Siemens, Erlangen, Germany). A high spatial

To separate trabecular bone from bone marrow, a fixed global threshold was used. In ␮CT images, a threshold equal to 22% of the maximal gray value was used to extract the mineralized bone phase. This setting best represented the trabecular structure in previous studies [23]. In MDCT images the threshold was calibrated with a reference phantom (Osteo Phantom, Siemens), placed below the specimens. As determined by correlations of BV/TV (calculated from MDCT images) with BMD (r = 0.93) and experimentally determined failure load Lexp (r = 0.76) the best threshold for extraction of bone tissue was th = 70 mg/cm3 hydroxyapatite. However, for further analysis, all calculations were performed with four different threshold settings of th = 0 mg/cm3 , 70 mg/cm3 , 140 mg/cm3 and 210 mg/cm3 . All thresholds overestimated mean BV/TV as compared to micro-CT values, in particular both thresholds ≤70 mg/cm3 , however higher thresholds destroyed the connectivity of the trabecular network and thus decreased correlation coefficients with BMD and Lexp . All MDCT images were segmented manually for all further evaluations. Spatial resolution of all ␮CT and MDCT datasets was degraded stepwise by decreasing the imaging matrix as shown in Table 1 and Fig. 1. In case of ␮CT, eight additional datasets were generated, with spatial resolutions ranging from 30 ␮m × 30 ␮m × 30 ␮m (original), via 240 ␮m × 240 ␮m × 480 ␮m (corresponding to the MDCT resolution) down to 1920 ␮m × 1920 ␮m × 480 ␮m.

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Table 1 Mean values ± standard deviation of ␮CT- and MDCT-based FEM. For comparison, biomechanically measured failure load Lexp = 119 ± 65 N. ␮CT Resolution (␮m3 )

Image size (px)

LFEM  ± SD (N)

30 × 30 × 30 60 × 60 × 60 120 × 120 × 120 240 × 240 × 240 240 × 240 × 480 480 × 480 × 480 720 × 720 × 480 960 × 960 × 480 1920 × 1920 × 480

256 × 256 × 256 128 × 128 × 128 64 × 64 × 64 32 × 32 × 32 32 × 32 × 16 16 × 16 × 16 11 × 11 × 16 8 × 8 × 16 4 × 4 × 16

118 ± 117 ± 123 ± 120 ± 118 ± 118 ± 115 ± 113 ± –b

a b

42 39 34 23 17 11 11 11

MDCT

th = 70 mg/cm3

Resolution (␮m3 )

Image size x–y (px)

LFEM  ± SD (N)

100 × 100 × 300a

512 × 512

118 ± 17

250 × 250 × 500 500 × 500 × 500 800 × 800 × 500 1000 × 1000 × 500 2000 × 2000 × 500

200 × 200 100 × 100 60 × 60 50 × 50 25 × 25

115 115 115 113 113

± ± ± ± ±

17 15 22 35 54

Interpolated resolution; spatial resolution at MTF 10 : 220 ␮m × 220 ␮m × 500 ␮m. Too few voxels for valid calculations.

In case of MDCT, five additional datasets were generated, ranging from 250 ␮m × 250 ␮m × 500 ␮m down to 2000 ␮m × 2000 ␮m × 500 ␮m. FEM were calculated for all original and degraded datasets as described below. For comparison, two standard parameters were obtained additionally: BV/TV was calculated as the number of bone voxels divided by the number of total voxels of the segmented specimen. Bone mineral density (BMD) was measured in a reformatted, 1 cm thick slice in the center of the specimen, using the calibration phantom to convert the measured Houndsfield units in mg hydroxyapatite per cm3 .

calculated from the strain energy density U normalized on Young’s modulus Y0 of the tissue: U = 1/2(xx εxx + yy εyy + zz εzz ) + xy εxy + xz εxz + yz εyz . The values of the effective strain for each voxel were compiled in the probability density function (pdf): P(εeff ) = prob(εeff ∈ [εeff , εeff + εeff ]). For a correlation analysis with respect to MCS we use the failure load LFEM : LFEM = Fr · kc estimated by scaling of the total reaction force at the top face At :

2.4. FEM calculations For assessing biomechanical strength of bone specimens we applied linear elastic Finite Element Model (FEM) by converting each voxel of original and degraded images into equally sized and oriented brick elements [24,25]. Material properties were chosen to be isotropic and elastic with Young’s modulus Y0 = 10 GPa and Poisson’s ratio  = 0.3. Dirichlet boundary conditions were set to simulate a high friction compressive test in the uniaxial direction (denoted as z axis) with constant strain ε0 = 1% prescribed on the top surface. From discrete nodal displacements calculated by FEM strain and stress components εij and  ij (i, j = x, y, z) were recovered at any point of the structure and voxel values were obtained by averaging over eight Gauss points in the interior of an individual element [26]. Effective strain was used as a measure of tissue deformation (Fig. 2):

 εeff =

2U , Y0



Fr =

t zz dAt

with the linear factor kc . The factor was calculated according to the critical value method [27] as a ratio of two parameters: assumed critical volume Vc and amount of bone tissue, which exceed some critical value of the effective strain εc , as calculated by FEM: kc =

Nvox i=1

Vc H(εeff − εc )

Here Nvox is number of voxels composing the observed structure and H(x) is Heaviside step function. Thus, failure load LFEM depends both on the global value of the reaction force Fr and the distribution of local elastic deformations in the trabecular bone network P(εeff ). The estimation of the failure load depends on two assumptions: relative amount of bone tissue Vc /TV and critical value of deformation expressed as εc . In order to optimize the absolute value of the failure load one can vary these two parameters. Another parameter affecting the value of the failure load estimated by FEM is BV/TV of the bone structure after binarization: overestimation of BV/TV leads to an overestimation of failure load LFEM . In the present work

Fig. 2. 3D rendering of ␮CT samples with high (A) and low (B) failure load. Local effective strain is color-coded: blue (small) to purple (high).

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we evaluated the performance of the FEM by means of two criteria: (i) comparison of mean values and (ii) linear correlation analysis of experimentally measured Lexp and estimated from the FEM LFEM failure loads. To compute LFEM we fixed Vc /TV and varied the critical value of the effective strain εc in order to satisfy both criteria. Mean values of the estimated failure load LFEM were calculated for Vc /TV = 1%, but for different values of εc . Depending on BV/TV of the binarized structure, the critical value εc varied from 0.0074 to 0.0084 for MDCT images and from 0.0098 to 0.0135 for ␮CT images. Such an approach for estimation of the failure load enables to compare results of FEM generated from image obtained by different scanning techniques, which provide quite different value of BV/TV for the same bone specimen. In case of the MDCT datasets, we additionally calculated continuous FEM, prescribing local material property. Elastic modulus Yi for each voxel of the structure was simulated as power law of normalized intensity with p = 1, 2 or 3 [28]: Yi = Y0

  p i 

.

Two models were considered: (i) continuous material model in which a material matrix is applied for the whole CT image without separation of bone mineral tissue and bone marrow; and (ii) bone material model in which a threshold intensity value is used to separate bone mineral compartment from bone marrow and the material matrix is applied to the bone tissue only. 2.5. Biomechanical testing After ␮CT and MDCT measurements, all bone samples were cut to a length of 12 mm with parallel surfaces using a saw microtome (Leica Microsystems, Wetzlar, Germany). The samples were re-hydrated and tested using a servo hydraulic testing machine (Zwick 1445, Ulm, Germany) with a load cell of 1.5 kN. The samples were loaded to 5 mm compression at a velocity of 5 mm/min [29]. Force and displacement were recorded. Failure load was identified from the first maximum value of the force–displacement curve. 2.6. Statistical analysis Absolute values were expressed in mean and standard deviation, as a Kolmogorov–Smirnov-analysis revealed no significant difference from a normal distribution. Correlations between FEMbased and biomechanically measured failure loads LFEM and Lexp were calculated using Pearson’ correlation coefficients. Differences between correlation coefficients were assessed using a Fisher-ZTransformation. Values were considered significant when p < 0.05. The agreement between FEM-based and biomechanically measured failure loads was assessed using Bland–Altman plots. 3. Results The biomechanically determined failure load Lexp of the specimen ranged from 25 N to 243 N with a mean value of Lexp  = 119 ± 65 N. Average BMD was 107 ± 41 mg/cm3 and average BV/TV 0.088 ± 0.028 calculated from the high-resolution (30 ␮m isotropic) ␮CT images. Both BV/TV estimated from ␮CT images and BMD significantly correlated with biomechanically determined Lexp , with rbv/tv = 0.70 and rBMD = 0.75. By applying FEM to original and coarser MDCT and ␮CT images (Fig. 1) we obtained local distributions of effective strain εeff (Fig. 2), which were compiled in a probability density function P(εeff ) (Fig. 3). From comparison of the ␮CT- and MDCT images (Fig. 1) one can observe that decreasing of the spatial resolution leads to an increase of the BV/TV of the specimen. This trend cannot

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be decreased by thresholding: high values of threshold parameters decrease connectivity of the structure, which is important for calculation of bone strength by FEM. In our artificial decrease of image resolution we followed this observed tendency and did not compensate this increase of BV/TV. This approach enabled us to compare local distributions of the effective strain of the same structure represented in different spatial resolutions and obtained with different scanning techniques. The probability distribution of local stresses P(εeff ) strongly depended on the bone volume fraction BV/TV and demonstrated the same typical pattern for datasets with different spatial resolution (Figs. 1 and 3). In case of MDCT, mean BV/TV varied according to the threshold value, separating trabeculae from bone marrow. Investigating the distribution of simulated elastic deformations within the specimens, similar characteristics were found in both ␮CT- and MDCT-based FEM (Fig. 3). For bone specimens with BV/TV < 0.2, the P(εeff )-spectrum demonstrated high peak values in the region of micro deformations (εeff < 0.002). Increasing the bone fraction decreased the peak value in the region of small deformations and specimens with 0.2 < BV/TV < 0.4 showed flatter distributions. Specimens with high BV/TV > 0.4 had increased number of voxels with moderate elastic deformation (εeff ≈ 0.007). This tendency was typical for all structures, binarized from MDCT and ␮CT image and independent of spatial resolution. In both MDCT and ␮CT small and moderate micro-strains (εeff < 0.01) showed largest heterogeneity among the specimens. In the small inlay plots in Fig. 3 the correlation coefficients rFEM between experimental Lexp and estimated LFEM failure load were displayed as a function of critical effective strain εc = εeff . Structures with BV/TV < 0.3 showed good correlations between Lexp and LFEM for critical effective strain εc > 0.01, which means that such rarefied structures had many thin overstressed trabecular elements. With increasing BV/TV, values of critical strain for the optimal correlation decreased, because less thin trabeculae are present in the structure and large local deformations become uncommon in the bone network. For structures with BV/TV > 0.4 high correlations were also observed for very small εc < 0.005, which means that the total reaction force Fr itself correlates very well with Lexp without additional correction by assessment of the overstressed tissue. These tendencies are typical for all FEM, generated from images with different resolutions both for ␮CT and MDCT scanning techniques. Lexp showed significant correlations with all FEM (Table 2) up to rFEM = 0.75 and rFEM = 0.84 for the 8 mm-diameter ␮CT-datasets and the 12 mmdiameter MDCT-datasets, respectively. For comparison, correlation coefficients of two standard characteristics BV/TV and BMD were rbv/tv = 0.70 and rBMD = 0.75, respectively. Degrading the resolution did not significantly change correlation in MDCT and ␮CT-based FEM. However, there was a trend to lower correlation coefficients, for a spatial resolution less than 500 ␮m isotropic. This trend could also be observed for ␮CT data in the Bland–Altman plots, in particular in more osteoporotic specimens (see Fig.4 in suppl. data) The Bland–Altman plots also showed that most values were between ±1.96 standard deviations, independent of scanner and spatial resolution. A minimal increase of correlation coefficients in coarsened ␮CTs could be an evidence that some thin trabecular elements and their connectivity disappeared during the image reconstruction process. The clear advantage of the MDCT images over ␮CT aroused due to the much larger scanning volume of the bone specimens. By only including the central 8 mm of the MDCT-dataset in the FEM, like in case of ␮CT, correlation with Lexp decreased to r = 0.68, regardless of the resolution. In MDCT, continuum FEM were calculated using the voxel gray levels to define local material properties of the tissue. In case of a continuous material model without threshold, low correlations were found between FEM and Lexp (rMCS < 0.63) for all resolutions. In contrast, the bone material model with a threshold of th = 70 mg/cm3 , including material properties of bone tissue only, showed a slight

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Fig. 3. Probability density function of effective strain for ␮CT (left, middle) and MDCT (right) datasets with decreasing resolution. Specimens from donors with Leff < Leff  are plotted in red, from donors with Leff > Leff  in blue. Thresholds were chosen to preserve connectivity (left column, right column, th = 70 mg/cm3 ) and to preserve BV/TV (middle column). The small inlays give the correlation of the failure load LFEM calculated by FEM with Leff for the each εeff taken as critical value εc .

improvement of correlations with MSC in case of cubic power law (th c p3, r = 0.85, Table 2). 4. Discussion Micro-CT- and MDCT-based Finite-Element Models could equally predict failure load of trabecular bone of elderly subjects in this in vitro study. A spatial resolution of

250 ␮m × 250 ␮m × 500 ␮m was optimal for MDCT-based FEM in regard to short computation time and accurately revealing local strain distributions, as it was still sufficient to also reveal small micro-strains, an important determinant in fracture prediction. Every quantitative data analysis has to be adapted and optimized for the data being analyzed. To predict bone strength, FEM has successfully been adjusted both for small bone cubes and for large bones [10–16]. These settings involve two completely

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Table 2 Pearson correlation coefficients (rLexp ) of ␮CT- and MDCT-based FEM with biomechanically measured MCS. In case of the binary model, two different threshold settings are given (th = 0 and 70 mg/cm3 ), in case of the bone material model, p1 and p3 represent two different settings of the power law. ␮CT

MDCT

Resolution (␮m3 )

Image size (px)

30 × 30 × 30 60 × 60 × 60 120 × 120 × 120 240 × 240 × 240 240 × 240 × 480 480 × 480 × 480 720 × 720 × 480 960 × 960 × 480 1920 × 1920 × 480

256 × 256 × 256 128 × 128 × 128 64 × 64 × 64 32 × 32 × 32 32 × 32 × 16 16 × 16 × 16 11 × 11 × 16 8 × 8 × 16 4 × 4 × 16

a b

RLexp 0.707 0.731 0.749 0.750 0.702 0.658 0.600 0.603 –b

Resolution (␮m3 )

Binary model

Continuum model

Image size x–y (px)

RLexp th = 0 mg/cm3

RLexp th = 70 mg/cm3

RLexp p1

RLexp p3

100 × 100 × 300a

512 × 512

0.824

0.812

0.820

0.832

250 × 250 × 500 500 × 500 × 500 800 × 800 × 500 1000 × 1000 × 500 2000 × 2000 × 500

200 × 200 100 × 100 60 × 60 50 × 50 25 × 25

0.704 0.795 0.743 0.807 0.637

0.827 0.834 0.819 0.812 0.748

0.835 0.840 0.822 0.812 0.747

0.850 0.847 0.823 0.813 0.747

Interpolated resolution; spatial resolution at MTF 50 : 250 ␮m × 250 ␮m × 500 ␮m. Too few voxels for valid calculations.

different spatial resolution regimes, both with different advantages and disadvantages. However, with the advancement of both scanner and computer capabilities, both high and low resolution scenarios start fusing together. In this context, this is – to our best knowledge – the first study to systematically analyze the effect of spatial resolution in this “transition zone” in direct comparison of high-resolution ␮CT and whole-body MDCT. Historically, FEM of trabecular bone were calculated for highresolution, binarized datasets using a distinct mesh to represent the structure [9]. This method was first developed in ␮CT datasets of small in vitro bone specimens, but can easily be transferred to HR-pQCT scans, where single trabeculae are visualized in vivo [18]. This matches with one study where small inaccuracies in results of non-linear FEM occurred in voxel sizes greater than 120 ␮m only [30]. Other data suggested a similar dependency on spatial resolution: Maloul et al. artifcially coarsened ␮CT data of facial bone, and concluded that variations in geometry were not the major cause of changes in micro-strains, but rather the material property assignment that was dependent on the ␮CT intensity and thus highly dependent on partial volume effects [31]. To account for these partial volume effects, continuum FEM have been developed, that use the CT density information to define local material properties [15,16]. Of note, in our setting with voxel sizes smaller than 500 ␮m, the continuum FEM showed only a minimal increase in correlation with Lexp , if the appropriate CT-threshold was applied. Without threshold, even lower correlations were found between FEM and MCS for all resolutions, which is consistent with earlier conclusions that for loading with strain rate less than 10 per second bone marrow does not influence the mechanical strength of trabecular bone (29). This might be different at lower resolutions that are typically used in QCT studies [21]. In whole bones, best results have been obtained when not only considering tissue density but also anisotropy (fabric tensor) of the trabecular network, that can be obtained from CT data [12,16,32]. Additionally, boundary conditions change, as the cortex has a different mechanical behavior as compared to trabecular bone [13,33]. Thus, several studies demonstrated the necessity of the definition of anisotropy and a definitive cortical shell, which goes beyond the CT density information [12,15,16]. This adequate definition of material properties together with an appropriate CT threshold turned out to be more important than the mesh size of the FEM [34]. Most investigators focused on the correlation with Lexp , neglecting the distribution of micro-strains. In contrast, Eswaran et al. described in their coarsened continuum-model of vertebral bodies similar major load paths but different distributions of minimalstrains at 960 ␮m isotropic resolution [15]. This is a very interesting finding, as Sidorenko et al. recently mentioned the importance of small micro-strains for the prediction of tissue failure [5]. We analyzed the distribution of micro-strains as their probability

density function and found similar distributions in ␮CT and MDCT for spatial resolutions up to 250 ␮m × 250 ␮m × 500 ␮m only. In accordance to the study of Eswaran, small micro-strains were almost completely missing at resolutions of about 1000 ␮m [15]. Recently, Kim et al. showed that most trabecular bone parameters can be revealed by MRI wit a spatial resolution down to 230 ␮m, what is close to our results [35]. They also outlined the importance of preserving the tissue connectivity, what still was possible at resolution twice the trabecular diameter in their study. This underlines the differences in FEM based on resolutions below and beyond a level of about 250–500 ␮m; of note a level that corresponds well to the average trabecular separation and has been widely used for trabecular bone structure analysis [4,6–8]. These findings again demonstrate the complexity of the FEM, where simple results like average values and correlation coefficients have to be interpreted with care, as in our study, where differences in correlation coefficients between ␮CT and MDCT are partly due to a different scan volume. Also other new imaging modalities have successfully been used to calculate bone strength by FEM. A flat panel CT (XperCT) has successfully been applied at the cervical spine and the femur, while there was too much noise at the thoracic spine to achieve meaningful results [36]. MRI can also reveal high spatial resolutions and thus FEM have successfully been calculated; however good image quality is possible at the peripheral skeleton only and due to the artificial enhancement of the trabeculae correction factors have to be applied [37]. In summary, to date MDCT remains the most promising imaging modality when analyzing the spine [21]. Some limitations have to be considered in this study. First, correlations with biomechanically measured failure load Lexp were substantially lower compared to other studies. This may have different reasons: The specimens used in this study were formalinfixed, which may change the mechanical competence locally, not related to the hydroxyapatite density and thus not visible in CT images. Second, ␮CT datasets were available only for a part of the biomechanically tested specimens. Thus correlations with Lexp were lower in ␮CT as compared to MDCT; of note, by correcting for this effect and calculating FEM in the central part of the MDCT datasets only, correlations decreased to r ≤ 0.68 in MDCT. However, this does not change the probability density function of local microstrains, which best revealed resolution-related differences. We also did not use a phantom to simulate beam-hardening and scattering artifacts, thus image quality will be worse in a real in vivo setting. The systematic optimization of FEM with respect to image quality, related to noise, artifacts and radiation dose has to be the scope of future work and will be influenced by the evolving iterative CT reconstruction algorithms. For an in vivo application, the cortical shell of the bone will have to be considered as well; however as the thickness of the vertebral cortex is similar to the vertebral

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trabecular structures, similar dependencies on the spatial resolution may be expected. In conclusion, FEM of trabecular bone specimens of elderly subjects showed similar results for ␮CT and MDCT datasets. A spatial resolution of 250 ␮m × 250 ␮m × 500 ␮m was optimal for MDCTbased FEM in regard to short computation time and accurately revealing local strain distributions, in particular small microstrains, an important determinant in fracture prediction. This is encouraging for further studies, as such spatial resolutions are available in in vivo whole-body MDCT imaging. Conflict of interest

[14]

[15]

[16]

[17]

[18]

None.

[19]

Funding

[20]

Contract grant sponsor: Deutsche Forschungsgemeinschaft (DFG). Contract grant numbers: LO 730/3–1 and BA 4085/1–2. Appendix A. Supplementary data

[21]

[22] [23]

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Prediction of bone strength by μCT and MDCT-based finite-element-models: how much spatial resolution is needed?

Finite-element-models (FEM) are a promising technology to predict bone strength and fracture risk. Usually, the highest spatial resolution technically...
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