- Email: [email protected]
X-ray imaging characterization of femoral bones in aging mice with osteopetrotic disorder
Micron 71 (2015) 14–21
Contents lists available at ScienceDirect
Micron journal homepage: www.elsevier.com/locate/micron
X-ray imaging characterization of femoral bones in aging mice with osteopetrotic disorder Shu-Ju Tu a,∗ , Hong-Wen Huang b , Wei-Jeng Chang b a b
Department of Medical Imaging and Radiological Sciences, College of Medicine, Chang Gung University, Kwei-Shan, Tao-Yuan 333, Taiwan National Laboratory Animal Center, National Applied Research Laboratories, Nan-Kang, Taipei 115, Taiwan
a r t i c l e
i n f o
Article history: Received 19 September 2014 Received in revised form 3 December 2014 Accepted 22 December 2014 Available online 3 January 2015 Keywords: Micro CT Trabecular bone Cortical bone Femur Bone mineral density Biomechanical strength
a b s t r a c t Aging mice with a rare osteopetrotic disorder in which the entire space of femoral bones are filled with trabecular bones are used as our research platform. A complete study is conducted with a micro computed tomography (CT) system to characterize the bone abnormality. Technical assessment of femoral bones includes geometric structure, biomechanical strength, bone mineral density (BMD), and bone mineral content (BMC). Normal aging mice of similar ages are included for comparisons. In our imaging work, we model the trabecular bone as a cylindrical rod and new quantitative which are not previously discussed are developed for advanced analysis, including trabecular segment length, trabecular segment radius, connecting node number, and distribution of trabecular segment radius. We then identified a geometric characteristic in which there are local maximums (0.0049, 0.0119, and 0.0147 mm) in the structure of trabecular segment radius. Our calculations show 343% higher in percent trabecular bone volume at distal-metaphysis; 38% higher in cortical thickness at mid-diaphysis; 11% higher in cortical cross-sectional moment of inertia at mid-diaphysis; 42% higher in cortical thickness at femur neck; 26% higher in cortical cross-sectional moment of inertia at femur neck; 31% and 395% higher in trabecular BMD and BMC at distal-metaphysis; 17% and 27% higher in cortical BMD and BMC at distal-metaphysis; 9% and 53% higher in cortical BMD and BMC at mid-diaphysis; 25% and 64% higher in cortical BMD and BMC at femur neck. Our new quantitative parameters and findings may be extended to evaluate the treatment response for other similar bone disorders. © 2015 Elsevier Ltd. All rights reserved.
1. Introduction Bones are critical organs for protection and supporting of interior organs. Bones and muscles are integrated components of our musculoskeletal system for essential functions of biomechanical performance. Contrast to the commonly observed disorder of osteoporosis in the aging population or postmenopausal females, a rare condition of skeletal defect with deposition of excessive calcification to bones such as osteopetrosis may be developed (Bilezikian et al., 2008; Greenspan, 1991). As a consequence, bones may grow abnormal with exceptionally high density (Greenspan, 1991). At our main facility of small animals, we observed incidents of massive calcification in femoral bones in the aging population of BALB/c mice in our quality control process. Among these rare and
∗ Corresponding author at: Department of Medical Imaging and Radiological Sciences, College of Medicine, Chang Gung University, Wen-Hua 1st Road, Kwei-Shan, Tao-Yuan 333, Taiwan. Tel.: +886 3 2118800; fax: +886 3 2118700. E-mail address: [email protected] (S.-J. Tu). http://dx.doi.org/10.1016/j.micron.2014.12.007 0968-4328/© 2015 Elsevier Ltd. All rights reserved.
abnormal aging mice, we observed three mice with exceptionally high-density of trabecular bones in the proximal and distal metaphysis sites. Particularly, the entire space of diaphysis is filled with high-density of trabecular bones. Similar findings are not reported and discussed in the previous literature. In clinical settings, dual-energy X-ray absorptiometry (DXA) is the major imaging examination of bone mineral density (BMD) and bone mineral content (BMC) (Blake et al., 1992; Laskey, 1996). However, the image acquired from DXA is a 2D X-ray radiograph. Essential characteristics of 3D geometric structure in trabecular and cortical bones are not able to be identified in DXA. In recent advancement of imaging technology, images of spatial resolution for X-ray based micro computed tomography (CT) are significantly improved to the scale of micrometers (Holdsworth and Thornton, 2002; Ritman, 2011). In addition, images of micro CT are truly volumetric and isotropic. BMD and structure of trabecular bones are rapidly declined in aging mice. In general, trabecular bones in femoral bones are normally found at the proximal and distal metaphysis (Bilezikian et al., 2008). Typically, mid-diaphysis of a femur bone is filled entirely
S.-J. Tu et al. / Micron 71 (2015) 14–21
with bone marrow and empty with trabecular bones (Bilezikian et al., 2008). To characterize the abnormality of femoral bones in these aging mice which are rarely observed, a complete study with a micro CT scanning system is performed to evaluate the associated geometric structure, biomechanical strength, BMD, and BMC for their femoral bones. Normal BLAB/c mice of similar ages are included for comparisons. In particular, we also developed quantitative parameters which are not discussed in previous literature such as trabecular segment number and connecting node number for advanced analysis.
2. Materials and methods The ages of mice with an abnormal condition in femoral bones are 12, 17 and 20 months, while the corresponding normal aging BALB/c mice of similar ages are 12 months (n = 3). The strain type of our mice is BALB/c. Femoral bones were removed after euthanasia, freed from muscle and other soft tissues, and then fixed in the paraformaldehyde solution as the imaging specimen prior to the micro CT scanning. Animal care and experimental procedures were approved by the Institutional Animal Care and Use Committee of Chang Gung University (ID: CGU12-147) and National Laboratory Animal Center (ID: IACUC2011001 and IACUC2013001). We first acquire X-ray radiographic images for the entire femoral bone to show the global structures of cortical and trabecular bones at anatomical sites of proximal-metaphysis, diaphysis, distal-metaphysis, and femoral neck for the abnormal and normal aging mice. The radiography allows us to easily compare the bone structures between abnormal and normal aging mice. The images were acquired with both low X-ray energy of 30 kV and high energy of 100 kV. X-ray photons were transmitted through the specimen samples and received by a high-resolution detector made by a charge-coupled device (Bushberg et al., 2011; Laskey, 1996). The micro CT imaging system (SkyScan 1076, Bruker micro CT, Belgium) is a commercial scanning instrument in which the X-ray tube and detector are housed in the same radiation-shield unit. Xray beam is collimated as a cone beam system. The cone angle is less than 5 angular degrees. A charge-coupled device of high resolution with 11 million pixels and high quantum efficiency is installed as the detector. The distance between the X-ray tube and detector is 17.0 cm. Volumetric images with spatial resolution of 9.0 m were obtained by a high-speed program based on the FDK reconstruction algorithm (Feldkamp et al., 1984; Tu et al., 2006). The animal couch is made of carbon fiber material. Fixed specimens of femoral bones were scanned with hardware settings of 50 kV and 360 projections. An aluminum filter of 0.5 mm thickness was placed at the exit window for optimal contrast. We used a standard phantom set (QRM-microCT-HA, QRM GmbH, Moehrendorf, Germany) for calculations of BMD in mg-HA/cm3 and BMC in mg-HA (Barbour et al., 2010; Kalender, 2006). In this work, we used anatomical sites of femoral bones for image assessment of trabecular and cortical bones. For the image analysis of distal-metaphysis, we first identified the growth plate as the geometric reference. A total length of 2.0 mm is then delineated as the region of interest (Bouxsein et al., 2010; Glatt et al., 2007). The distance between the region of interest and the growth plate is 0.5 mm (Bouxsein et al., 2010; Glatt et al., 2007). We delineated a length of 0.5 mm at the mid-point between the growth plate and trochanteric forssa of the femoral bone along the straight longaxis direction for analysis of mid-diaphysis (Barbour et al., 2010; Bouxsein et al., 2010). For biomechanical strength assessment of cortical bones in femur neck, images of micro CT are first rotated to the upright position. Then the central rotation axis was determined by the formula of center-of-mass. The region of interest
15
with length of 0.1 mm along the straight long-axis was delineated (Hartog, 1987; Young et al., 2011b). CTAn (CT-Analyzer, Bruker microCT, Belgium), Avizo (Visualization Sciences Group, Massachusetts, USA), and ImageJ (National Institute of Health, Maryland, USA) were used for the delineation of regions of interest and subsequent image analysis. The following parameters are obtained from CTAn: total tissue volume, bone volume, percent bone volume, trabecular separation, trabecular number, and fractal dimension. The following parameters are obtained by Avizo: trabecular segment number, trabecular segment number density, mean trabecular segment radius, mean trabecular segment length, connecting node number, and connecting number density (Bilezikian et al., 2008; Bouxsein et al., 2010; Glatt et al., 2007; Qiu et al., 2010). ImageJ was used for parameters of structural model index and surface area to volume ratio. In this work, trabecular bones are considered as a geometric structure which is interconnected by trabecular segments. A trabecular segment is modeled mathematically as a cylindrical rod. A connecting node is defined as the location in which different trabecular segments are connected. For technical assessment of cortical bones at mid-diaphysis and femur neck, we used BMD, BMC, and the following parameters: total cross-sectional area, cortical cross-sectional area, cortical cross-sectional area fraction, cortical outer radius, cortical inner radius, cortical thickness, cross-sectional moment of inertia, rotational moment of inertia, sectional modulus, and buckling ratio (Hartog, 1987; Young et al., 2011b). These parameters are related to the biomechanical strength and may be used to evaluate the fracture risk of femoral bones. Results are presented as the format of mean ± standard error. The t-test is performed with Excel. The p-value is used to determine whether a difference of two groups is statistically significant. We use the convention that a result is significantly different when the p-value is less than 0.05.
3. Results To show the projection view of full-structure for the entire femoral bones in both groups of aging mice, we used the X-ray imaging technique of both 30 and 100 kV energies to build the twodimensional digital radiographs as shown in Fig. 1A–D. Trabecular bones fill up the spaces of proximal-metaphysis, distal-metaphysis, and entire diaphysis in abnormal mice as shown in Fig. 1A and B, while trabecular bones are nearly invisible in normal aging mice as shown in Fig. 1C and D. In particular, the mid-diaphysis region is empty with trabecular bones in normal aging mice, while trabecular bones are densely populated in abnormal aging mice. A series of volumetric images acquired from the micro CT projections is reconstructed for femoral bones of abnormal and normal aging mice as shown in Fig. 2A–C. Different viewing planes from the coronal, axial, and sagittal directions are respectively shown (Bushberg et al., 2011; Kalender, 2006). The interior space of femoral bone is filled up with the trabecular bones in the abnormal aging mice and empty in the normal aging mice. 3D images obtained by the computer processing technique of surface rendering for the abnormal and normal aging mice at the distal-metaphysis and mid-diaphysis are shown in Fig. 3A–D (Rubin et al., 1994; Vos et al., 2003). Trabecular bones of abnormal aging mice fill up the entire space of distal-metaphysis and mid-diaphysis as shown in Fig. 3A and B, while trabecular bones are empty in the normal aging mice as shown in Fig. 3C and D. Quantitative assessment of micro-structure for trabecular bones at distal-metaphysis are listed in Table 1. The total tissue volume in mm3 is reduced to 11.47% in abnormal aging mice with normal aging mice as the baseline reference; bone volume in mm3 is
16
S.-J. Tu et al. / Micron 71 (2015) 14–21
Fig. 1. (A) A typical 2D radiography of femoral bone obtained by a 30 kVp X-ray imaging for abnormal aging mice. As shown with arrows, trabecular bones fill the entire space at diaphysis and distal-metaphysis. (B) A typical 2D radiography of femoral bone obtained by a 100 kVp X-ray imaging for abnormal aging mice. As shown with arrows, trabecular bones fill the entire space at diaphysis and distal-metaphysis. (C) A typical 2D radiography of femoral bone obtained by a 30 kVp X-ray imaging for normal aging mice. Trabecular bones are nearly empty as shown. (D) A typical 2D radiography of femoral bone obtained by a 100 kVp X-ray imaging for normal aging mice. Trabecular bones are nearly empty as shown.
increased to 287.82%; percent bone volume is increased to 343.36%; trabecular separation in mm is reduced to 78.61%; trabecular number in mm−1 is increased to 318.09%; fractal dimension is increased to 10.69%; structural model index is reduced to 6.14%; trabecular segment number is increased to 749.96%; trabecular segment number density in mm−3 is increased to 814.83%; mean trabecular segment radius in mm is increased to 98.56%; mean trabecular segment length in mm is decreased to 36.47%; connecting node number is increased to 796.94%; connecting node number density is increased to 865.95%; surface area to volume ratio is reduced to 33.68%. Calculations of percentage changes are based on the ratio of quantity difference between abnormal and normal aging mice as the numerator and the quantity of normal aging mice as the denominator.
Table 1 also shows similar assessment of micro-structure for trabecular bones of abnormal mice at mid-diaphysis. Similar to that at distal-metaphysis, trabecular bones are observed to be densely populated. Results are not shown for the normal aging mice as trabecular bones are not observed at mid-diaphysis. In the anatomy of long bones, diaphysis is located at the midsection and is composed of compact cortical bones, bone marrow, and soft adipose tissue (Bilezikian et al., 2008). Interior space of diaphysis in general is not housed with trabecular bones. In particular at the age of older than 12 months, number of trabecular bones is declined significantly. However, a large density of trabecular bones is still observed at distal-metaphysis and mid-diaphysis in abnormal mice. Cortical bones are responsible for daily performance of biomechanical function. As listed in Table 2, we use parameters
Table 1 Micro CT assessment of trabecular bones at distal-metaphysis and mid-diaphysis for aging mice of abnormal and normal groups. Quantitative analysis includes parameters derived from the geometric micro-structure of trabecular bones, BMD, and BMC. Quantitative parameters
Total tissue volume (mm3 )
Trabecular @ distal-metaphysis 4.27 ± 0.27 Normal mice 3.78 ± 0.24 Abnormal mice Trabecular @ mid-diaphysis 1.06 ± 0.09 Abnormal mice Quantitative parameters
Bone volume (mm3 )
Percent bone volume (%)
Trabecular separation (mm)
Trabecular number (mm−1 )
Fractal dimension
Structural model index
Trabecular segment number
0.28 ± 0.03 1.11 ± 0.15
6.77 ± 0.93 30.02 ± 5.51
0.64 ± 0.06 0.13 ± 0.01
1.01 ± 0.15 4.22 ± 0.52
2.01 ± 0.02 2.23 ± 0.06
1.72 ± 0.11 1.61 ± 0.27
386 ± 41 3283 ± 398
0.36 ± 0.15
32.06 ± 11.34
0.15 ± 0.03
3.73 ± 1.03
2.12 ± 0.13
1.66 ± 0.54
806 ± 84
Trabecular segment number density (mm−3 )
Trabecular @ distal-metaphysis 345 ± 47 Normal mice 3158 ± 603 Abnormal mice Trabecular @ mid-diaphysis 757 ± 61 Abnormal mice
Mean trabecular segment radius (mm)
Mean trabecular segment length (mm)
Connecting node number
Connecting node density (mm−3 )
Surface area to volume ratio (mm−1 )
BMD (mgHA/cm3 )
BMC (mg-HA)
0.015 ± 0.001 0.029 ± 0.001
0.18 ± 0.05 0.11 ± 0.01
217 ± 27 1946 ± 233
193 ± 29 1872 ± 356
90 ± 3 59 ± 6
562 ± 26 738 ± 86
0.16 ± 0.02 0.79 ± 0.04
0.029 ± 0.001
0.12 ± 0.01
471 ± 46
442 ± 31
60 ± 17
939 ± 93
0.33 ± 0.13
S.-J. Tu et al. / Micron 71 (2015) 14–21
17
Fig. 2. (A) Typical images obtained from micro CT scanning for abnormal aging mice (left) and normal aging mice (right) from the coronal viewing plane. The interior space of the femoral bone is filled with the trabecular bones for abnormal aging mice (left) and is nearly empty for normal aging mice (right). (B) Typical images obtained from micro CT scanning for abnormal aging mice (left) and normal aging mice (right) from the axial viewing plane at mid-diaphysis. The interior space of the femoral bone is filled with the trabecular bones for abnormal aging mice (left) and is nearly empty for normal aging mice (right). (C) Typical images obtained from micro CT scanning for abnormal aging mice (left) and normal aging mice (right) from the sagittal viewing plane. The interior space of the femoral bone is filled with the trabecular bones for abnormal aging mice (left) and is nearly empty for normal aging mice (right).
Table 2 Micro CT assessment of cortical bones at mid-diaphysis and femur neck for aging mice of abnormal and normal groups. Quantitative analysis includes parameters derived from the geometric structure of cortical bones, biomechanical strength, BMD, and BMC. Quantitative parameters Cortical @ mid-diaphysis Normal mice Abnormal mice Cortical @ femur neck Normal mice Abnormal mice Quantitative parameters
Cortical @ mid-diaphysis Normal mice Abnormal mice Cortical @ femur neck Normal mice Abnormal mice
Total cross sectional area (mm2 )
Cortical cross sectional area (mm2 )
Cortical cross sectional area fraction
Cortical outer radius (mm)
Cortical inner radius (mm)
Cortical thickness (mm)
2.97 ± 0.08 3.03 ± 0.23
0.87 ± 0.11 1.18 ± 0.16
0.29 ± 0.03 0.38 ± 0.02
0.97 ± 0.01 0.98 ± 0.03
0.81 ± 0.02 0.76 ± 0.02
0.15 ± 0.02 0.21 ± 0.02
0.64 ± 0.04 0.71 ± 0.01
0.54 ± 0.02 0.69 ± 0.01
0.84 ± 0.04 0.97 ± 0.01
0.45 ± 0.01 0.47 ± 0.02
0.17 ± 0.02 0.08 ± 0.01
0.27 ± 0.01 0.39 ± 0.02
Cortical cross sectional moment of inertia (mm4 )
Rotational moment of inertia (mg mm2 )
Sectional modulus (mm3 )
Buckling ratio
BMD (mgHA/cm3 )
BMC (mg-HA)
0.35 ± 0.04 0.46 ± 0.09
839 ± 127 1168 ± 138
0.36 ± 0.04 0.47 ± 0.08
6.42 ± 0.78 4.63 ± 0.37
1181 ± 38 1282 ± 94
1.50 ± 0.14 2.30 ± 0.37
0.032 ± 0.002 0.040 ± 0.002
57.99 ± 5.93 92.48 ± 3.96
0.070 ± 0.009 0.085 ± 0.002
1.64 ± 0.16 1.20 ± 0.02
908 ± 40 1139 ± 65
4.39 ± 0.03 7.22 ± 0.39
18
S.-J. Tu et al. / Micron 71 (2015) 14–21
Fig. 3. (A) A typical 3D image processed by the computer technique of surface rendering for the femoral bone of abnormal aging mice at distal-metaphysis. The trabecular bones are in blue and cortical in gray. Notice that he trabecular bones are densely populated. (B) A typical 3D image processed by the computer technique of surface rendering for the femoral bone of abnormal aging mice at mid-diaphysis. The trabecular bones are in blue and cortical in gray. Notice that the trabecular bones are densely populated. (C) A typical 3D image processed by the computer technique of surface rendering for the femoral bone of normal aging mice at distal-metaphysis. The trabecular bones are in blue and cortical in gray. Notice that he trabecular bones are sparsely populated. (D) A typical 3D image processed by the computer technique of surface rendering for the femoral bone of normal aging mice at mid-diaphysis. The cortical bones are in gray. Notice that the interior space is empty with trabecular bones. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of the article.)
responsible for biomechanical strength to characterize the cortical bones (Hartog, 1987; Young et al., 2011a,b). For cortical bones at mid-diaphysis, the change of total cross-sectional area in mm2 is little; cortical cross-sectional area in mm2 is increased to 35.64%; fraction of cortical cross-sectional area is increased to 32.03%; the change of outer radius of cortical bone in mm is little; inner radius of cortical bone in mm is decreased to 6.14%; cortical bone thickness in mm is increased to 37.92%; cross-sectional moment of inertia in mm4 is increased to 11.60%; rotational moment of inertia
in mg mm2 is increased to 39.27%; sectional modulus in mm3 is increased to 30.33%; buckling ratio is decreased to 27.82%. The quantitative parameters of cortical bones for the femur neck are listed in Table 2. The total cross-sectional area in mm2 is increased to 11.28% in abnormal aging mice; cortical crosssectional area in mm2 is increased to 28.11%; fraction of cortical cross-sectional area is increased to 14.56%; outer radius of cortical bone in mm is increased to 5.60%; inner radius of cortical bone in mm is decreased to 53.04%; cortical bone thickness is increased
S.-J. Tu et al. / Micron 71 (2015) 14–21 250
Probability density funcon
200
150 Normal aging mice Abnormal aging mice
100
50
0 0.00
0.02
0.04
0.06
Trabecular segment radius (mm)
Fig. 4. Distributions of trabecular segment radius for abnormal and normal aging mice. The curves are normalized and areas are integrated to 1. The distributions show that the range of trabecular radius is distributed between 0.00 and 0.07 mm. There are several peaks of local maximums in which the first is 0.0049 mm; second 0.0119; and third 0.0147 mm.
to 42.4%; cross-sectional moment of inertia is increased to 26.49%; rotational moment of inertia is increased to 59.47%; sectional modulus is increased to 20.43%; buckling ratio decreased to 26.76%. Tables 1 and 2 list BMD in mg-HA/cm3 and BMC in mg-HA for trabecular and cortical bones at distal-metaphysis, mid-diaphysis, and neck. It is shown that BMD and BMC of abnormal aging mice are 31.13% and 395.09% higher than normal aging mice for trabecular bones at distal-metaphysis; 8.59% and 52.76% higher for cortical bones at mid-diaphysis; 25.55% and 64.22% higher for cortical bones at femur neck. The distributions of trabecular segment radius in mm at distalmetaphysis of abnormal and normal aging mice are shown in Fig. 4. The distribution curves are normalized and the areas under curves are integrated to 1 as required by the probability theory (Bushberg et al., 2011). The characteristics of the distributions show that there are several peaks or local maximums in which the first peak is located at 0.0049 mm; the second at 0.0119 mm; and the third at 0.0147 mm. The largest population occurs at the first peak of 0.0049 mm for both groups. It is shown that a majority population of trabecular segment radius is located at the first three peaks in normal aging mice, while the rest of the population in which the trabecular segment radius is larger than 0.0147 mm is relatively small. Contrast to the characteristics of trabecular segment radius in the normal aging mice, there remains a relatively large population in which the trabecular segment radius is thicker than 0.0147 mm in abnormal aging mice. Our distribution analysis suggests that the average trabecular segment radius is thicker in abnormal aging mice than the normal aging mice due to the fact that the relative weighting of the population in the thicker radiuses is bigger in abnormal aging mice. Our numerical calculations show that mean trabecular segment radius is increased from 0.0151 mm of normal aging mice to 0.0300 mm of abnormal aging mice, an increase of 98.56%, as shown in Table 1. The specific shape for the distribution of trabecular segment radius shows essential characterization of trabecular segment thickness and may be used further for advanced studies of trabecular bones. 4. Discussion In general, bone quality or bone strength is determined by essential factors like BMD and BMC (Malluche et al., 2013). In our work, quantitative parameters which are derived from
19
micro-structure and biomechanical strength are extended to characterize bone quality (Malluche et al., 2013). In particular, the subsequent fracture risk of femoral bones may be evaluated by parameters of biomechanical strength obtained from technical assessment of cortical bones. In the investigation, we used quantitative parameters such as percent bone volume and trabecular separation to characterize micro-structure of trabecular bones at distal-metaphysis and mid-diaphysis; parameters of biomechanical strength such as cross-sectional moment of inertia and sectional modulus for fracture risk assessment at mid-diaphysis and femur neck. In particular, we applied the computer algorithm of distance mapping to develop a mathematical model in which the trabecular bone is modeled as a cylindrical rod mathematically to study quantitative parameters which are not discussed in the previous literature such as the radius of trabecular segment and number of connecting node. A standard phantom set is used for calculations of BMD in mg-HA/cm3 and BMC in mg-HA (Kalender, 2006). We used a gray scale of 16-bit and Hounsfield units to reconstruct pixels in micro CT images (Bushberg et al., 2011; Kalender, 2011). Hounsfield unit of water is calibrated as the baseline reference. In imaging physics, Hounsfield units of a material are corresponding to the linear attenuation coefficient, relative electron density, and physical density. Also Hounsfield units represent the interaction mechanism between matters and X-ray photons, including photoelectric and Compton scatter effect (Bushberg et al., 2011). It is essential to use an optimal setting of imaging parameters, including hardware and software, to produce best image quality. In this work, we used the fact of physics principles that bones are relatively hard tissues than the surrounding soft tissues. Therefore, X-ray energy of 50 kVp is used for optimal image contrast to increase the accuracy of bone segmentation; spatial resolution of 9 m for reduction of image artifact and partial volume effect; software option of beam hardening correction for cupping artifact reduction (Kalender, 2006; Marxen et al., 2004). In biology, the skeleton disorder of bone with extremely high density such as osteopetrosis is often characterized by radical development of osteoblasts and unbalanced functions between osteoclasts and osteoblasts (Bilezikian et al., 2008). In our study, the assessment of micro-structure shows that trabecular bones at distal-metaphysis and mid-diaphysis grow densely populated in abnormal aging mice. Findings are supported by Figs. 1–3 in which X-ray radiographies, micro CT images, and image processing of surface rendering are presented, along with Tables 1 and 2 in which structural parameters are quantified. In particular, trabecular bones fill up 32.06% of mid-diaphysis space in abnormal aging mice, while the space of mid-diaphysis is empty with trabecular bones in normal aging mice. Our image analysis of abnormal aging mice suggests that the micro-structure of trabecular bones between the anatomical sites of distal-metaphysis and mid-diaphysis is similar. However, calculations of trabecular BMD show a difference of 939.57 vs. 738.21 mg-HA/cm3 at mid-diaphysis vs. distal-metaphysis; an increase of 27.27% when the distal-metaphysis site is used as the baseline reference. BMD measures BMC per unit volume. It then suggests that an exceeding amount of 27.27% in BMC deposition per unit volume at mid-diaphysis than distal-metaphysis. The consequence of higher BMD in mid-diaphysis for abnormal aging mice may be due to the different biological mechanism or functional dynamics between osteoblasts and osteoclasts at mid-diaphysis and distal-metaphysis. The ratio of surface area to volume is an important index in biology and has been applied to quantify cells with particular shape and bone morphology (Qiu et al., 2010; Rosenberg and Ramus, 1984; Yin et al., 2013). In our analysis, the quantity of surface area to volume ratio characterizes the amount of surface area per unit volume
20
S.-J. Tu et al. / Micron 71 (2015) 14–21
for trabecular bones. In particular, the dynamics of osteoblast and osteoclast cells may be correlated with the ratio of surface area to volume for trabecular bones. For objects with similar shape, the ratio of surface area to volume is inversely proportional to the geometric size of structure mathematically. Our calculations for trabecular bones at distal-metaphysis show a decrease of 33.68% in the ratio of surface area to volume in abnormal aging mice. Results of our ratio calculations of surface area to volume are strongly supported by the observations that trabecular bones are densely populated in abnormal aging mice, suggesting the measurement of surface area to volume ratio is a useful index for size quantification of trabecular bones. We also used the ratio of surface area to volume to characterize the cortical bones at mid-diaphysis and femur neck. It is shown that surface area to volume ratio is 25% lower at mid-diaphysis and 30% lower at femur neck in abnormal aging mice. It is then suggested that the geometric size of cortical bones at mid-diaphysis and femur neck is greater in abnormal aging mice than normal aging mice (Qiu et al., 2010; Yin et al., 2013). The finding may also suggest that the biomechanical movement of femur bones in abnormal aging mice is less agile due to the size of cortical bones is increased. In the biomechanical strength assessment of cortical bones at mid-diaphysis, our calculations of cross-sectional area and fraction of cortical bones show that cortical bones are thicker in abnormal than normal aging mice. In specific, the inner radius is reduced by 6.14%, while the outer radius remains similar to that of normal aging mice. The shrinkage of inner radius in abnormal aging mice suggested that the cortical bones at mid-diaphysis grow and expand toward the interior space of medullary cavity. As a consequence, the volume of medullary cavity is projected to be less space in abnormal aging mice than normal aging mice. Our further calculations confirm that the space of medullary cavity is indeed reduced by 37.59% in abnormal aging mice. In addition, the medullary cavity is further occupied by the densely populated trabecular bones as shown in Fig. 3B. In the femoral bone, diaphysis is composed mainly with exterior cortical bones and interior bone marrow (Bilezikian et al., 2008). Red blood cells are produced in the bone marrow space by the hematopoiesis process. As a consequence, the total number of red blood cells is projected to be affected by the volume of medullary cavity. A decrease in the number of red blood cells may result in an anemia disorder. Previous literature showed a positive correlation between osteopetrosis and anemia disorder (Fischer et al., 1991; Gamsu et al., 1961; Lees and Sautter, 1979; Saluja et al., 2009; Sreehari et al., 2011). Our quantitative study of abnormal aging mice suggests that the anemia disorder may be directly linked to the internal expansion of cortical bones at diaphysis. Bones are organs of supporting body frame and quality of cortical bones is critical to the performance of biomechanical functions. Our imaging assessment of cortical bones shows high BMD and BMC in abnormal aging mice; therefore, quality of mobility may be affected. In addition to BMD and BMC, biomechanical strength is an essential factor of cortical bone quality (Bouxsein et al., 2010). Cortical bones in nature are grown to minimize the fracture risk induced by the stress or strain from external forces of different directions. In particular, parameter of cross-sectional area is a geometry quantity of breaking resistance to an external force of axial compression; cross-sectional moment of inertia is a mechanical quantity for resistance to external tensile force; rotational moment of inertia for resistance to angular rotation and angular distortion; sectional modulus is a quantity for breaking risk assessment when suffered by a two-point bending force (Hartog, 1987; Young et al., 2011b). Our technical assessment of cortical bones for biomechanical strength shows that fracture risk by external forces to femur cortical bones may be lower in abnormal aging mice than normal aging mice at both mid-diaphysis and femur neck. Nevertheless, assessment of
bone fracture risk is a complex subject and some essential variables remain critical. They include total body weight, BMD, BMC, number of cortical pore, cortical porosity, and the placement of an external force (Mayhew et al., 2005). Our further works on the assessment of biomechanical strength for femoral bones include experimental measurements of different force models with an instrument such as a material testing system (Hsu et al., 2012). 5. Conclusions We used an imaging approach of micro CT to perform a quantitative study of bone quality in aging mice with osteopetrotic disorder. Bone quality was determined by parameters of BMD, geometric structure, and biomechanical strength. New parameters for bone characterization were developed. We presented radiographic images, micro CT images of different viewing planes, and 3D images for complete visual comparisons. The calculations of inner and outer radius of cortical bones at mid-diaphysis suggested that cortical bones grew thicker and expanded toward the direction of bone center. Parameters of biomechanical strength were used to evaluate bone fracture risk. Conceivably, our micro CT study may be extended to quantitative evaluation for other similar bone-related diseases. Acknowledgements This work was supported by research grants from Ministry of Science and Technology of Taiwan, Department of Research and Development at Chang Gung Memorial Hospital of Taiwan (CMRPD1C0671, CMRPD1C0672), and the Healthy Aging Research Center at Chang Gung University. References Barbour, K.E., Zmuda, J.M., Strotmeyer, E.S., Horwitz, M.J., Boudreau, R., Evans, R.W., Ensrud, K.E., Petit, M.A., Gordon, C.L., Cauley, J.A., 2010. Correlates of trabecular and cortical volumetric bone mineral density of the radius and tibia in older men: the osteoporotic fractures in men study. J. Bone Miner. Res. 25, 1017–1028. Bilezikian, J.P., Raisz, L.G., Martin, T.J., 2008. Principles of Bone Biology, third ed. Academic Press, Waltham, MA, USA. Blake, G.M., McKeeney, D.B., Chhaya, S.C., Ryan, P.J., Fogelman, I., 1992. Dual energy X-ray absorptiometry: the effects of beam hardening on bone density measurements. Med. Phys. 19, 459–465. Bouxsein, M.L., Boyd, S.K., Christiansen, B.A., Guldberg, R.E., Jepsen, K.J., Müller, R., 2010. Guidelines for assessment of bone microstructure in rodents using microcomputed tomography. J. Bone Miner. Res. 25, 1468–1486. Bushberg, J., Seibert, J., Leidholdt, E., Boone, J., 2011. The Essential Physics of Medical Imaging, third ed. Lippincott Williams & Wilkins, Philadelphia, PA, USA. Feldkamp, I.A., Davis, L.C., Kress, J.W., 1984. Practical cone-beam algorithm. J. Opt. Soc. Am. A: Opt. Image Sci. Vis. 1, 612–619. Fischer, A., Friedrich, W., Fasth, A., Blanche, S., Le Deist, F., Girault, D., Veber, F., Vossen, J., Lopez, M., Griscelli, C., Hirn, M., 1991. Reduction of graft failure by a monoclonal antibody (anti-LFA-1 CD11a) after HLA nonidentical bone marrow transplantation in children with immunodeficiencies, osteopetrosis, and Fanconi’s anemia: a European Group for Immunodeficiency/European Group for Bone Marrow Transplantation Report. Blood 77, 249–256. Gamsu, H., Lorber, J., Rendle-Short, J., 1961. Haemolytic anaemia in osteopetrosis. A report of two cases. Arch. Dis. Child. 36, 494–499. Glatt, V., Canalis, E., Stadmeyer, L., Bouxsein, M.L., 2007. Age-related changes in trabecular architecture differ in female and male C57BL/6J mice. J. Bone Miner. Res. 22, 1197–1207. Greenspan, A., 1991. Sclerosing bone dysplasias – a target-site approach. Skelet. Radiol. 20, 561–583. Hartog, J.P., 1987. Advanced strength of materials. Dover Publications, Mineola, NY, USA. Holdsworth, D.W., Thornton, M.M., 2002. Micro-CT in small animal and specimen imaging. Trends Biotechnol. 20, S34–S39. Hsu, J.T., Chen, Y.J., Tsai, M.T., Lan, H.H.C., Cheng, F.C., Chen, M.Y.C., Wang, S.P., 2012. Predicting cortical bone strength from DXA and dental cone-beam CT. PLoS ONE 7. Kalender, W., 2011. Computed Tomography: Fundamentals, System Technology, Image Quality, Applications, third ed. Publicis Corporate Publishing, Erlangen. Kalender, W.A., 2006. X-ray computed tomography. Phys. Med. Biol. 51, R29–R43. Laskey, M.A., 1996. Dual-energy X-ray absorptiometry and body composition. Nutrition 12, 45–51.
S.-J. Tu et al. / Micron 71 (2015) 14–21 Lees, G.E., Sautter, J.H., 1979. Anemia and osteopetrosis in a dog. J. Am. Vet. Med. Assoc. 175, 820–824. Malluche, H.H., Porter, D.S., Pienkowski, D., 2013. Evaluating bone quality in patients with chronic kidney disease. Nat. Rev. Nephrol. 9, 671–680. Marxen, M., Thornton, M.M., Chiarot, C.B., Klement, G., Koprivnikar, J., Sled, J.G., Henkelman, R.M., 2004. MicroCT scanner performance and considerations for vascular specimen imaging. Med. Phys. 31, 305–313. Mayhew, P.M., Thomas, C.D., Clement, J.G., Loveridge, N., Beck, T.J., Bonfield, W., Burgoyne, C.J., Reeve, J., 2005. Relation between age, femoral neck cortical stability, and hip fracture risk. Lancet 366, 129–135. Qiu, S., Rao, D.S., Palnitkar, S., Parfitt, A.M., 2010. Dependence of bone yield (volume of bone formed per unit of cement surface area) on resorption cavity size during osteonal remodeling in human rib: implications for osteoblast function and the pathogenesis of age-related bone loss. J. Bone Miner. Res. 25, 423–430. Ritman, E.L., 2011. Current status of developments and applications of micro-CT. Annu. Rev. Biomed. Eng. 13, 531–552. Rosenberg, G., Ramus, J., 1984. Uptake of inorganic nitrogen and seaweed surface area: volume ratios. Aquat. Bot. 19, 65–72. Rubin, G.D., Dake, M.D., Napel, S., Jeffrey Jr., R.B., McDonnell, C.H., Sommer, F.G., Wexler, L., Williams, D.M., 1994. Spiral CT of renal artery stenosis: comparison of three-dimensional rendering techniques. Radiology 190, 181–189.
21
Saluja, S., Bhandari, S., Aggarwal, S., Kapoor, S., 2009. Osteopetrosis: a rare cause of anemia – review of literature. Indian J. Pathol. Microbiol. 52, 363– 367. Sreehari, S., Naik, D.R., Eapen, M., 2011. Osteopetrosis: a rare cause of anemia. Hematol. Rev. 3, 1–2. Tu, S.J., Shaw, C.C., Chen, L., 2006. Noise simulation in cone beam CT imaging with parallel computing. Phys. Med. Biol. 51, 1283–1297. Vos, F.M., Van Gelder, R.E., Serlie, I.W.O., Florie, J., Nio, C.Y., Glas, A.S., Post, F.H., Truyen, R., Gerritsen, F.A., Stoker, J., 2003. Three-dimensional display modes for CT colonography: conventional 3D virtual colonoscopy versus unfolded cube projection. Radiology 228, 878–885. Yin, Z., Sadok, A., Sailem, H., McCarthy, A., Xia, X., Li, F., Garcia, M.A., Evans, L., Barr, A.R., Perrimon, N., Marshall, C.J., Wong, S.T.C., Bakal, C., 2013. A screen for morphological complexity identifies regulators of switch-like transitions between discrete cell shapes. Nat. Cell Biol. 15, 860–871. Young, H.D., Freedman, R.A., Ford, A.L., 2011a. University Physics with Modern Physics, 13th ed. Addison-Wesley Publishing Company, Reading, MA, USA. Young, W., Budynas, R., Sadegh, A., 2011b. Roark’s Formulas for Stress and Strain, eighth ed. McGraw-Hill Professional, New York, NY, USA.
Contents lists available at ScienceDirect
Micron journal homepage: www.elsevier.com/locate/micron
X-ray imaging characterization of femoral bones in aging mice with osteopetrotic disorder Shu-Ju Tu a,∗ , Hong-Wen Huang b , Wei-Jeng Chang b a b
Department of Medical Imaging and Radiological Sciences, College of Medicine, Chang Gung University, Kwei-Shan, Tao-Yuan 333, Taiwan National Laboratory Animal Center, National Applied Research Laboratories, Nan-Kang, Taipei 115, Taiwan
a r t i c l e
i n f o
Article history: Received 19 September 2014 Received in revised form 3 December 2014 Accepted 22 December 2014 Available online 3 January 2015 Keywords: Micro CT Trabecular bone Cortical bone Femur Bone mineral density Biomechanical strength
a b s t r a c t Aging mice with a rare osteopetrotic disorder in which the entire space of femoral bones are filled with trabecular bones are used as our research platform. A complete study is conducted with a micro computed tomography (CT) system to characterize the bone abnormality. Technical assessment of femoral bones includes geometric structure, biomechanical strength, bone mineral density (BMD), and bone mineral content (BMC). Normal aging mice of similar ages are included for comparisons. In our imaging work, we model the trabecular bone as a cylindrical rod and new quantitative which are not previously discussed are developed for advanced analysis, including trabecular segment length, trabecular segment radius, connecting node number, and distribution of trabecular segment radius. We then identified a geometric characteristic in which there are local maximums (0.0049, 0.0119, and 0.0147 mm) in the structure of trabecular segment radius. Our calculations show 343% higher in percent trabecular bone volume at distal-metaphysis; 38% higher in cortical thickness at mid-diaphysis; 11% higher in cortical cross-sectional moment of inertia at mid-diaphysis; 42% higher in cortical thickness at femur neck; 26% higher in cortical cross-sectional moment of inertia at femur neck; 31% and 395% higher in trabecular BMD and BMC at distal-metaphysis; 17% and 27% higher in cortical BMD and BMC at distal-metaphysis; 9% and 53% higher in cortical BMD and BMC at mid-diaphysis; 25% and 64% higher in cortical BMD and BMC at femur neck. Our new quantitative parameters and findings may be extended to evaluate the treatment response for other similar bone disorders. © 2015 Elsevier Ltd. All rights reserved.
1. Introduction Bones are critical organs for protection and supporting of interior organs. Bones and muscles are integrated components of our musculoskeletal system for essential functions of biomechanical performance. Contrast to the commonly observed disorder of osteoporosis in the aging population or postmenopausal females, a rare condition of skeletal defect with deposition of excessive calcification to bones such as osteopetrosis may be developed (Bilezikian et al., 2008; Greenspan, 1991). As a consequence, bones may grow abnormal with exceptionally high density (Greenspan, 1991). At our main facility of small animals, we observed incidents of massive calcification in femoral bones in the aging population of BALB/c mice in our quality control process. Among these rare and
∗ Corresponding author at: Department of Medical Imaging and Radiological Sciences, College of Medicine, Chang Gung University, Wen-Hua 1st Road, Kwei-Shan, Tao-Yuan 333, Taiwan. Tel.: +886 3 2118800; fax: +886 3 2118700. E-mail address: [email protected] (S.-J. Tu). http://dx.doi.org/10.1016/j.micron.2014.12.007 0968-4328/© 2015 Elsevier Ltd. All rights reserved.
abnormal aging mice, we observed three mice with exceptionally high-density of trabecular bones in the proximal and distal metaphysis sites. Particularly, the entire space of diaphysis is filled with high-density of trabecular bones. Similar findings are not reported and discussed in the previous literature. In clinical settings, dual-energy X-ray absorptiometry (DXA) is the major imaging examination of bone mineral density (BMD) and bone mineral content (BMC) (Blake et al., 1992; Laskey, 1996). However, the image acquired from DXA is a 2D X-ray radiograph. Essential characteristics of 3D geometric structure in trabecular and cortical bones are not able to be identified in DXA. In recent advancement of imaging technology, images of spatial resolution for X-ray based micro computed tomography (CT) are significantly improved to the scale of micrometers (Holdsworth and Thornton, 2002; Ritman, 2011). In addition, images of micro CT are truly volumetric and isotropic. BMD and structure of trabecular bones are rapidly declined in aging mice. In general, trabecular bones in femoral bones are normally found at the proximal and distal metaphysis (Bilezikian et al., 2008). Typically, mid-diaphysis of a femur bone is filled entirely
S.-J. Tu et al. / Micron 71 (2015) 14–21
with bone marrow and empty with trabecular bones (Bilezikian et al., 2008). To characterize the abnormality of femoral bones in these aging mice which are rarely observed, a complete study with a micro CT scanning system is performed to evaluate the associated geometric structure, biomechanical strength, BMD, and BMC for their femoral bones. Normal BLAB/c mice of similar ages are included for comparisons. In particular, we also developed quantitative parameters which are not discussed in previous literature such as trabecular segment number and connecting node number for advanced analysis.
2. Materials and methods The ages of mice with an abnormal condition in femoral bones are 12, 17 and 20 months, while the corresponding normal aging BALB/c mice of similar ages are 12 months (n = 3). The strain type of our mice is BALB/c. Femoral bones were removed after euthanasia, freed from muscle and other soft tissues, and then fixed in the paraformaldehyde solution as the imaging specimen prior to the micro CT scanning. Animal care and experimental procedures were approved by the Institutional Animal Care and Use Committee of Chang Gung University (ID: CGU12-147) and National Laboratory Animal Center (ID: IACUC2011001 and IACUC2013001). We first acquire X-ray radiographic images for the entire femoral bone to show the global structures of cortical and trabecular bones at anatomical sites of proximal-metaphysis, diaphysis, distal-metaphysis, and femoral neck for the abnormal and normal aging mice. The radiography allows us to easily compare the bone structures between abnormal and normal aging mice. The images were acquired with both low X-ray energy of 30 kV and high energy of 100 kV. X-ray photons were transmitted through the specimen samples and received by a high-resolution detector made by a charge-coupled device (Bushberg et al., 2011; Laskey, 1996). The micro CT imaging system (SkyScan 1076, Bruker micro CT, Belgium) is a commercial scanning instrument in which the X-ray tube and detector are housed in the same radiation-shield unit. Xray beam is collimated as a cone beam system. The cone angle is less than 5 angular degrees. A charge-coupled device of high resolution with 11 million pixels and high quantum efficiency is installed as the detector. The distance between the X-ray tube and detector is 17.0 cm. Volumetric images with spatial resolution of 9.0 m were obtained by a high-speed program based on the FDK reconstruction algorithm (Feldkamp et al., 1984; Tu et al., 2006). The animal couch is made of carbon fiber material. Fixed specimens of femoral bones were scanned with hardware settings of 50 kV and 360 projections. An aluminum filter of 0.5 mm thickness was placed at the exit window for optimal contrast. We used a standard phantom set (QRM-microCT-HA, QRM GmbH, Moehrendorf, Germany) for calculations of BMD in mg-HA/cm3 and BMC in mg-HA (Barbour et al., 2010; Kalender, 2006). In this work, we used anatomical sites of femoral bones for image assessment of trabecular and cortical bones. For the image analysis of distal-metaphysis, we first identified the growth plate as the geometric reference. A total length of 2.0 mm is then delineated as the region of interest (Bouxsein et al., 2010; Glatt et al., 2007). The distance between the region of interest and the growth plate is 0.5 mm (Bouxsein et al., 2010; Glatt et al., 2007). We delineated a length of 0.5 mm at the mid-point between the growth plate and trochanteric forssa of the femoral bone along the straight longaxis direction for analysis of mid-diaphysis (Barbour et al., 2010; Bouxsein et al., 2010). For biomechanical strength assessment of cortical bones in femur neck, images of micro CT are first rotated to the upright position. Then the central rotation axis was determined by the formula of center-of-mass. The region of interest
15
with length of 0.1 mm along the straight long-axis was delineated (Hartog, 1987; Young et al., 2011b). CTAn (CT-Analyzer, Bruker microCT, Belgium), Avizo (Visualization Sciences Group, Massachusetts, USA), and ImageJ (National Institute of Health, Maryland, USA) were used for the delineation of regions of interest and subsequent image analysis. The following parameters are obtained from CTAn: total tissue volume, bone volume, percent bone volume, trabecular separation, trabecular number, and fractal dimension. The following parameters are obtained by Avizo: trabecular segment number, trabecular segment number density, mean trabecular segment radius, mean trabecular segment length, connecting node number, and connecting number density (Bilezikian et al., 2008; Bouxsein et al., 2010; Glatt et al., 2007; Qiu et al., 2010). ImageJ was used for parameters of structural model index and surface area to volume ratio. In this work, trabecular bones are considered as a geometric structure which is interconnected by trabecular segments. A trabecular segment is modeled mathematically as a cylindrical rod. A connecting node is defined as the location in which different trabecular segments are connected. For technical assessment of cortical bones at mid-diaphysis and femur neck, we used BMD, BMC, and the following parameters: total cross-sectional area, cortical cross-sectional area, cortical cross-sectional area fraction, cortical outer radius, cortical inner radius, cortical thickness, cross-sectional moment of inertia, rotational moment of inertia, sectional modulus, and buckling ratio (Hartog, 1987; Young et al., 2011b). These parameters are related to the biomechanical strength and may be used to evaluate the fracture risk of femoral bones. Results are presented as the format of mean ± standard error. The t-test is performed with Excel. The p-value is used to determine whether a difference of two groups is statistically significant. We use the convention that a result is significantly different when the p-value is less than 0.05.
3. Results To show the projection view of full-structure for the entire femoral bones in both groups of aging mice, we used the X-ray imaging technique of both 30 and 100 kV energies to build the twodimensional digital radiographs as shown in Fig. 1A–D. Trabecular bones fill up the spaces of proximal-metaphysis, distal-metaphysis, and entire diaphysis in abnormal mice as shown in Fig. 1A and B, while trabecular bones are nearly invisible in normal aging mice as shown in Fig. 1C and D. In particular, the mid-diaphysis region is empty with trabecular bones in normal aging mice, while trabecular bones are densely populated in abnormal aging mice. A series of volumetric images acquired from the micro CT projections is reconstructed for femoral bones of abnormal and normal aging mice as shown in Fig. 2A–C. Different viewing planes from the coronal, axial, and sagittal directions are respectively shown (Bushberg et al., 2011; Kalender, 2006). The interior space of femoral bone is filled up with the trabecular bones in the abnormal aging mice and empty in the normal aging mice. 3D images obtained by the computer processing technique of surface rendering for the abnormal and normal aging mice at the distal-metaphysis and mid-diaphysis are shown in Fig. 3A–D (Rubin et al., 1994; Vos et al., 2003). Trabecular bones of abnormal aging mice fill up the entire space of distal-metaphysis and mid-diaphysis as shown in Fig. 3A and B, while trabecular bones are empty in the normal aging mice as shown in Fig. 3C and D. Quantitative assessment of micro-structure for trabecular bones at distal-metaphysis are listed in Table 1. The total tissue volume in mm3 is reduced to 11.47% in abnormal aging mice with normal aging mice as the baseline reference; bone volume in mm3 is
16
S.-J. Tu et al. / Micron 71 (2015) 14–21
Fig. 1. (A) A typical 2D radiography of femoral bone obtained by a 30 kVp X-ray imaging for abnormal aging mice. As shown with arrows, trabecular bones fill the entire space at diaphysis and distal-metaphysis. (B) A typical 2D radiography of femoral bone obtained by a 100 kVp X-ray imaging for abnormal aging mice. As shown with arrows, trabecular bones fill the entire space at diaphysis and distal-metaphysis. (C) A typical 2D radiography of femoral bone obtained by a 30 kVp X-ray imaging for normal aging mice. Trabecular bones are nearly empty as shown. (D) A typical 2D radiography of femoral bone obtained by a 100 kVp X-ray imaging for normal aging mice. Trabecular bones are nearly empty as shown.
increased to 287.82%; percent bone volume is increased to 343.36%; trabecular separation in mm is reduced to 78.61%; trabecular number in mm−1 is increased to 318.09%; fractal dimension is increased to 10.69%; structural model index is reduced to 6.14%; trabecular segment number is increased to 749.96%; trabecular segment number density in mm−3 is increased to 814.83%; mean trabecular segment radius in mm is increased to 98.56%; mean trabecular segment length in mm is decreased to 36.47%; connecting node number is increased to 796.94%; connecting node number density is increased to 865.95%; surface area to volume ratio is reduced to 33.68%. Calculations of percentage changes are based on the ratio of quantity difference between abnormal and normal aging mice as the numerator and the quantity of normal aging mice as the denominator.
Table 1 also shows similar assessment of micro-structure for trabecular bones of abnormal mice at mid-diaphysis. Similar to that at distal-metaphysis, trabecular bones are observed to be densely populated. Results are not shown for the normal aging mice as trabecular bones are not observed at mid-diaphysis. In the anatomy of long bones, diaphysis is located at the midsection and is composed of compact cortical bones, bone marrow, and soft adipose tissue (Bilezikian et al., 2008). Interior space of diaphysis in general is not housed with trabecular bones. In particular at the age of older than 12 months, number of trabecular bones is declined significantly. However, a large density of trabecular bones is still observed at distal-metaphysis and mid-diaphysis in abnormal mice. Cortical bones are responsible for daily performance of biomechanical function. As listed in Table 2, we use parameters
Table 1 Micro CT assessment of trabecular bones at distal-metaphysis and mid-diaphysis for aging mice of abnormal and normal groups. Quantitative analysis includes parameters derived from the geometric micro-structure of trabecular bones, BMD, and BMC. Quantitative parameters
Total tissue volume (mm3 )
Trabecular @ distal-metaphysis 4.27 ± 0.27 Normal mice 3.78 ± 0.24 Abnormal mice Trabecular @ mid-diaphysis 1.06 ± 0.09 Abnormal mice Quantitative parameters
Bone volume (mm3 )
Percent bone volume (%)
Trabecular separation (mm)
Trabecular number (mm−1 )
Fractal dimension
Structural model index
Trabecular segment number
0.28 ± 0.03 1.11 ± 0.15
6.77 ± 0.93 30.02 ± 5.51
0.64 ± 0.06 0.13 ± 0.01
1.01 ± 0.15 4.22 ± 0.52
2.01 ± 0.02 2.23 ± 0.06
1.72 ± 0.11 1.61 ± 0.27
386 ± 41 3283 ± 398
0.36 ± 0.15
32.06 ± 11.34
0.15 ± 0.03
3.73 ± 1.03
2.12 ± 0.13
1.66 ± 0.54
806 ± 84
Trabecular segment number density (mm−3 )
Trabecular @ distal-metaphysis 345 ± 47 Normal mice 3158 ± 603 Abnormal mice Trabecular @ mid-diaphysis 757 ± 61 Abnormal mice
Mean trabecular segment radius (mm)
Mean trabecular segment length (mm)
Connecting node number
Connecting node density (mm−3 )
Surface area to volume ratio (mm−1 )
BMD (mgHA/cm3 )
BMC (mg-HA)
0.015 ± 0.001 0.029 ± 0.001
0.18 ± 0.05 0.11 ± 0.01
217 ± 27 1946 ± 233
193 ± 29 1872 ± 356
90 ± 3 59 ± 6
562 ± 26 738 ± 86
0.16 ± 0.02 0.79 ± 0.04
0.029 ± 0.001
0.12 ± 0.01
471 ± 46
442 ± 31
60 ± 17
939 ± 93
0.33 ± 0.13
S.-J. Tu et al. / Micron 71 (2015) 14–21
17
Fig. 2. (A) Typical images obtained from micro CT scanning for abnormal aging mice (left) and normal aging mice (right) from the coronal viewing plane. The interior space of the femoral bone is filled with the trabecular bones for abnormal aging mice (left) and is nearly empty for normal aging mice (right). (B) Typical images obtained from micro CT scanning for abnormal aging mice (left) and normal aging mice (right) from the axial viewing plane at mid-diaphysis. The interior space of the femoral bone is filled with the trabecular bones for abnormal aging mice (left) and is nearly empty for normal aging mice (right). (C) Typical images obtained from micro CT scanning for abnormal aging mice (left) and normal aging mice (right) from the sagittal viewing plane. The interior space of the femoral bone is filled with the trabecular bones for abnormal aging mice (left) and is nearly empty for normal aging mice (right).
Table 2 Micro CT assessment of cortical bones at mid-diaphysis and femur neck for aging mice of abnormal and normal groups. Quantitative analysis includes parameters derived from the geometric structure of cortical bones, biomechanical strength, BMD, and BMC. Quantitative parameters Cortical @ mid-diaphysis Normal mice Abnormal mice Cortical @ femur neck Normal mice Abnormal mice Quantitative parameters
Cortical @ mid-diaphysis Normal mice Abnormal mice Cortical @ femur neck Normal mice Abnormal mice
Total cross sectional area (mm2 )
Cortical cross sectional area (mm2 )
Cortical cross sectional area fraction
Cortical outer radius (mm)
Cortical inner radius (mm)
Cortical thickness (mm)
2.97 ± 0.08 3.03 ± 0.23
0.87 ± 0.11 1.18 ± 0.16
0.29 ± 0.03 0.38 ± 0.02
0.97 ± 0.01 0.98 ± 0.03
0.81 ± 0.02 0.76 ± 0.02
0.15 ± 0.02 0.21 ± 0.02
0.64 ± 0.04 0.71 ± 0.01
0.54 ± 0.02 0.69 ± 0.01
0.84 ± 0.04 0.97 ± 0.01
0.45 ± 0.01 0.47 ± 0.02
0.17 ± 0.02 0.08 ± 0.01
0.27 ± 0.01 0.39 ± 0.02
Cortical cross sectional moment of inertia (mm4 )
Rotational moment of inertia (mg mm2 )
Sectional modulus (mm3 )
Buckling ratio
BMD (mgHA/cm3 )
BMC (mg-HA)
0.35 ± 0.04 0.46 ± 0.09
839 ± 127 1168 ± 138
0.36 ± 0.04 0.47 ± 0.08
6.42 ± 0.78 4.63 ± 0.37
1181 ± 38 1282 ± 94
1.50 ± 0.14 2.30 ± 0.37
0.032 ± 0.002 0.040 ± 0.002
57.99 ± 5.93 92.48 ± 3.96
0.070 ± 0.009 0.085 ± 0.002
1.64 ± 0.16 1.20 ± 0.02
908 ± 40 1139 ± 65
4.39 ± 0.03 7.22 ± 0.39
18
S.-J. Tu et al. / Micron 71 (2015) 14–21
Fig. 3. (A) A typical 3D image processed by the computer technique of surface rendering for the femoral bone of abnormal aging mice at distal-metaphysis. The trabecular bones are in blue and cortical in gray. Notice that he trabecular bones are densely populated. (B) A typical 3D image processed by the computer technique of surface rendering for the femoral bone of abnormal aging mice at mid-diaphysis. The trabecular bones are in blue and cortical in gray. Notice that the trabecular bones are densely populated. (C) A typical 3D image processed by the computer technique of surface rendering for the femoral bone of normal aging mice at distal-metaphysis. The trabecular bones are in blue and cortical in gray. Notice that he trabecular bones are sparsely populated. (D) A typical 3D image processed by the computer technique of surface rendering for the femoral bone of normal aging mice at mid-diaphysis. The cortical bones are in gray. Notice that the interior space is empty with trabecular bones. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of the article.)
responsible for biomechanical strength to characterize the cortical bones (Hartog, 1987; Young et al., 2011a,b). For cortical bones at mid-diaphysis, the change of total cross-sectional area in mm2 is little; cortical cross-sectional area in mm2 is increased to 35.64%; fraction of cortical cross-sectional area is increased to 32.03%; the change of outer radius of cortical bone in mm is little; inner radius of cortical bone in mm is decreased to 6.14%; cortical bone thickness in mm is increased to 37.92%; cross-sectional moment of inertia in mm4 is increased to 11.60%; rotational moment of inertia
in mg mm2 is increased to 39.27%; sectional modulus in mm3 is increased to 30.33%; buckling ratio is decreased to 27.82%. The quantitative parameters of cortical bones for the femur neck are listed in Table 2. The total cross-sectional area in mm2 is increased to 11.28% in abnormal aging mice; cortical crosssectional area in mm2 is increased to 28.11%; fraction of cortical cross-sectional area is increased to 14.56%; outer radius of cortical bone in mm is increased to 5.60%; inner radius of cortical bone in mm is decreased to 53.04%; cortical bone thickness is increased
S.-J. Tu et al. / Micron 71 (2015) 14–21 250
Probability density funcon
200
150 Normal aging mice Abnormal aging mice
100
50
0 0.00
0.02
0.04
0.06
Trabecular segment radius (mm)
Fig. 4. Distributions of trabecular segment radius for abnormal and normal aging mice. The curves are normalized and areas are integrated to 1. The distributions show that the range of trabecular radius is distributed between 0.00 and 0.07 mm. There are several peaks of local maximums in which the first is 0.0049 mm; second 0.0119; and third 0.0147 mm.
to 42.4%; cross-sectional moment of inertia is increased to 26.49%; rotational moment of inertia is increased to 59.47%; sectional modulus is increased to 20.43%; buckling ratio decreased to 26.76%. Tables 1 and 2 list BMD in mg-HA/cm3 and BMC in mg-HA for trabecular and cortical bones at distal-metaphysis, mid-diaphysis, and neck. It is shown that BMD and BMC of abnormal aging mice are 31.13% and 395.09% higher than normal aging mice for trabecular bones at distal-metaphysis; 8.59% and 52.76% higher for cortical bones at mid-diaphysis; 25.55% and 64.22% higher for cortical bones at femur neck. The distributions of trabecular segment radius in mm at distalmetaphysis of abnormal and normal aging mice are shown in Fig. 4. The distribution curves are normalized and the areas under curves are integrated to 1 as required by the probability theory (Bushberg et al., 2011). The characteristics of the distributions show that there are several peaks or local maximums in which the first peak is located at 0.0049 mm; the second at 0.0119 mm; and the third at 0.0147 mm. The largest population occurs at the first peak of 0.0049 mm for both groups. It is shown that a majority population of trabecular segment radius is located at the first three peaks in normal aging mice, while the rest of the population in which the trabecular segment radius is larger than 0.0147 mm is relatively small. Contrast to the characteristics of trabecular segment radius in the normal aging mice, there remains a relatively large population in which the trabecular segment radius is thicker than 0.0147 mm in abnormal aging mice. Our distribution analysis suggests that the average trabecular segment radius is thicker in abnormal aging mice than the normal aging mice due to the fact that the relative weighting of the population in the thicker radiuses is bigger in abnormal aging mice. Our numerical calculations show that mean trabecular segment radius is increased from 0.0151 mm of normal aging mice to 0.0300 mm of abnormal aging mice, an increase of 98.56%, as shown in Table 1. The specific shape for the distribution of trabecular segment radius shows essential characterization of trabecular segment thickness and may be used further for advanced studies of trabecular bones. 4. Discussion In general, bone quality or bone strength is determined by essential factors like BMD and BMC (Malluche et al., 2013). In our work, quantitative parameters which are derived from
19
micro-structure and biomechanical strength are extended to characterize bone quality (Malluche et al., 2013). In particular, the subsequent fracture risk of femoral bones may be evaluated by parameters of biomechanical strength obtained from technical assessment of cortical bones. In the investigation, we used quantitative parameters such as percent bone volume and trabecular separation to characterize micro-structure of trabecular bones at distal-metaphysis and mid-diaphysis; parameters of biomechanical strength such as cross-sectional moment of inertia and sectional modulus for fracture risk assessment at mid-diaphysis and femur neck. In particular, we applied the computer algorithm of distance mapping to develop a mathematical model in which the trabecular bone is modeled as a cylindrical rod mathematically to study quantitative parameters which are not discussed in the previous literature such as the radius of trabecular segment and number of connecting node. A standard phantom set is used for calculations of BMD in mg-HA/cm3 and BMC in mg-HA (Kalender, 2006). We used a gray scale of 16-bit and Hounsfield units to reconstruct pixels in micro CT images (Bushberg et al., 2011; Kalender, 2011). Hounsfield unit of water is calibrated as the baseline reference. In imaging physics, Hounsfield units of a material are corresponding to the linear attenuation coefficient, relative electron density, and physical density. Also Hounsfield units represent the interaction mechanism between matters and X-ray photons, including photoelectric and Compton scatter effect (Bushberg et al., 2011). It is essential to use an optimal setting of imaging parameters, including hardware and software, to produce best image quality. In this work, we used the fact of physics principles that bones are relatively hard tissues than the surrounding soft tissues. Therefore, X-ray energy of 50 kVp is used for optimal image contrast to increase the accuracy of bone segmentation; spatial resolution of 9 m for reduction of image artifact and partial volume effect; software option of beam hardening correction for cupping artifact reduction (Kalender, 2006; Marxen et al., 2004). In biology, the skeleton disorder of bone with extremely high density such as osteopetrosis is often characterized by radical development of osteoblasts and unbalanced functions between osteoclasts and osteoblasts (Bilezikian et al., 2008). In our study, the assessment of micro-structure shows that trabecular bones at distal-metaphysis and mid-diaphysis grow densely populated in abnormal aging mice. Findings are supported by Figs. 1–3 in which X-ray radiographies, micro CT images, and image processing of surface rendering are presented, along with Tables 1 and 2 in which structural parameters are quantified. In particular, trabecular bones fill up 32.06% of mid-diaphysis space in abnormal aging mice, while the space of mid-diaphysis is empty with trabecular bones in normal aging mice. Our image analysis of abnormal aging mice suggests that the micro-structure of trabecular bones between the anatomical sites of distal-metaphysis and mid-diaphysis is similar. However, calculations of trabecular BMD show a difference of 939.57 vs. 738.21 mg-HA/cm3 at mid-diaphysis vs. distal-metaphysis; an increase of 27.27% when the distal-metaphysis site is used as the baseline reference. BMD measures BMC per unit volume. It then suggests that an exceeding amount of 27.27% in BMC deposition per unit volume at mid-diaphysis than distal-metaphysis. The consequence of higher BMD in mid-diaphysis for abnormal aging mice may be due to the different biological mechanism or functional dynamics between osteoblasts and osteoclasts at mid-diaphysis and distal-metaphysis. The ratio of surface area to volume is an important index in biology and has been applied to quantify cells with particular shape and bone morphology (Qiu et al., 2010; Rosenberg and Ramus, 1984; Yin et al., 2013). In our analysis, the quantity of surface area to volume ratio characterizes the amount of surface area per unit volume
20
S.-J. Tu et al. / Micron 71 (2015) 14–21
for trabecular bones. In particular, the dynamics of osteoblast and osteoclast cells may be correlated with the ratio of surface area to volume for trabecular bones. For objects with similar shape, the ratio of surface area to volume is inversely proportional to the geometric size of structure mathematically. Our calculations for trabecular bones at distal-metaphysis show a decrease of 33.68% in the ratio of surface area to volume in abnormal aging mice. Results of our ratio calculations of surface area to volume are strongly supported by the observations that trabecular bones are densely populated in abnormal aging mice, suggesting the measurement of surface area to volume ratio is a useful index for size quantification of trabecular bones. We also used the ratio of surface area to volume to characterize the cortical bones at mid-diaphysis and femur neck. It is shown that surface area to volume ratio is 25% lower at mid-diaphysis and 30% lower at femur neck in abnormal aging mice. It is then suggested that the geometric size of cortical bones at mid-diaphysis and femur neck is greater in abnormal aging mice than normal aging mice (Qiu et al., 2010; Yin et al., 2013). The finding may also suggest that the biomechanical movement of femur bones in abnormal aging mice is less agile due to the size of cortical bones is increased. In the biomechanical strength assessment of cortical bones at mid-diaphysis, our calculations of cross-sectional area and fraction of cortical bones show that cortical bones are thicker in abnormal than normal aging mice. In specific, the inner radius is reduced by 6.14%, while the outer radius remains similar to that of normal aging mice. The shrinkage of inner radius in abnormal aging mice suggested that the cortical bones at mid-diaphysis grow and expand toward the interior space of medullary cavity. As a consequence, the volume of medullary cavity is projected to be less space in abnormal aging mice than normal aging mice. Our further calculations confirm that the space of medullary cavity is indeed reduced by 37.59% in abnormal aging mice. In addition, the medullary cavity is further occupied by the densely populated trabecular bones as shown in Fig. 3B. In the femoral bone, diaphysis is composed mainly with exterior cortical bones and interior bone marrow (Bilezikian et al., 2008). Red blood cells are produced in the bone marrow space by the hematopoiesis process. As a consequence, the total number of red blood cells is projected to be affected by the volume of medullary cavity. A decrease in the number of red blood cells may result in an anemia disorder. Previous literature showed a positive correlation between osteopetrosis and anemia disorder (Fischer et al., 1991; Gamsu et al., 1961; Lees and Sautter, 1979; Saluja et al., 2009; Sreehari et al., 2011). Our quantitative study of abnormal aging mice suggests that the anemia disorder may be directly linked to the internal expansion of cortical bones at diaphysis. Bones are organs of supporting body frame and quality of cortical bones is critical to the performance of biomechanical functions. Our imaging assessment of cortical bones shows high BMD and BMC in abnormal aging mice; therefore, quality of mobility may be affected. In addition to BMD and BMC, biomechanical strength is an essential factor of cortical bone quality (Bouxsein et al., 2010). Cortical bones in nature are grown to minimize the fracture risk induced by the stress or strain from external forces of different directions. In particular, parameter of cross-sectional area is a geometry quantity of breaking resistance to an external force of axial compression; cross-sectional moment of inertia is a mechanical quantity for resistance to external tensile force; rotational moment of inertia for resistance to angular rotation and angular distortion; sectional modulus is a quantity for breaking risk assessment when suffered by a two-point bending force (Hartog, 1987; Young et al., 2011b). Our technical assessment of cortical bones for biomechanical strength shows that fracture risk by external forces to femur cortical bones may be lower in abnormal aging mice than normal aging mice at both mid-diaphysis and femur neck. Nevertheless, assessment of
bone fracture risk is a complex subject and some essential variables remain critical. They include total body weight, BMD, BMC, number of cortical pore, cortical porosity, and the placement of an external force (Mayhew et al., 2005). Our further works on the assessment of biomechanical strength for femoral bones include experimental measurements of different force models with an instrument such as a material testing system (Hsu et al., 2012). 5. Conclusions We used an imaging approach of micro CT to perform a quantitative study of bone quality in aging mice with osteopetrotic disorder. Bone quality was determined by parameters of BMD, geometric structure, and biomechanical strength. New parameters for bone characterization were developed. We presented radiographic images, micro CT images of different viewing planes, and 3D images for complete visual comparisons. The calculations of inner and outer radius of cortical bones at mid-diaphysis suggested that cortical bones grew thicker and expanded toward the direction of bone center. Parameters of biomechanical strength were used to evaluate bone fracture risk. Conceivably, our micro CT study may be extended to quantitative evaluation for other similar bone-related diseases. Acknowledgements This work was supported by research grants from Ministry of Science and Technology of Taiwan, Department of Research and Development at Chang Gung Memorial Hospital of Taiwan (CMRPD1C0671, CMRPD1C0672), and the Healthy Aging Research Center at Chang Gung University. References Barbour, K.E., Zmuda, J.M., Strotmeyer, E.S., Horwitz, M.J., Boudreau, R., Evans, R.W., Ensrud, K.E., Petit, M.A., Gordon, C.L., Cauley, J.A., 2010. Correlates of trabecular and cortical volumetric bone mineral density of the radius and tibia in older men: the osteoporotic fractures in men study. J. Bone Miner. Res. 25, 1017–1028. Bilezikian, J.P., Raisz, L.G., Martin, T.J., 2008. Principles of Bone Biology, third ed. Academic Press, Waltham, MA, USA. Blake, G.M., McKeeney, D.B., Chhaya, S.C., Ryan, P.J., Fogelman, I., 1992. Dual energy X-ray absorptiometry: the effects of beam hardening on bone density measurements. Med. Phys. 19, 459–465. Bouxsein, M.L., Boyd, S.K., Christiansen, B.A., Guldberg, R.E., Jepsen, K.J., Müller, R., 2010. Guidelines for assessment of bone microstructure in rodents using microcomputed tomography. J. Bone Miner. Res. 25, 1468–1486. Bushberg, J., Seibert, J., Leidholdt, E., Boone, J., 2011. The Essential Physics of Medical Imaging, third ed. Lippincott Williams & Wilkins, Philadelphia, PA, USA. Feldkamp, I.A., Davis, L.C., Kress, J.W., 1984. Practical cone-beam algorithm. J. Opt. Soc. Am. A: Opt. Image Sci. Vis. 1, 612–619. Fischer, A., Friedrich, W., Fasth, A., Blanche, S., Le Deist, F., Girault, D., Veber, F., Vossen, J., Lopez, M., Griscelli, C., Hirn, M., 1991. Reduction of graft failure by a monoclonal antibody (anti-LFA-1 CD11a) after HLA nonidentical bone marrow transplantation in children with immunodeficiencies, osteopetrosis, and Fanconi’s anemia: a European Group for Immunodeficiency/European Group for Bone Marrow Transplantation Report. Blood 77, 249–256. Gamsu, H., Lorber, J., Rendle-Short, J., 1961. Haemolytic anaemia in osteopetrosis. A report of two cases. Arch. Dis. Child. 36, 494–499. Glatt, V., Canalis, E., Stadmeyer, L., Bouxsein, M.L., 2007. Age-related changes in trabecular architecture differ in female and male C57BL/6J mice. J. Bone Miner. Res. 22, 1197–1207. Greenspan, A., 1991. Sclerosing bone dysplasias – a target-site approach. Skelet. Radiol. 20, 561–583. Hartog, J.P., 1987. Advanced strength of materials. Dover Publications, Mineola, NY, USA. Holdsworth, D.W., Thornton, M.M., 2002. Micro-CT in small animal and specimen imaging. Trends Biotechnol. 20, S34–S39. Hsu, J.T., Chen, Y.J., Tsai, M.T., Lan, H.H.C., Cheng, F.C., Chen, M.Y.C., Wang, S.P., 2012. Predicting cortical bone strength from DXA and dental cone-beam CT. PLoS ONE 7. Kalender, W., 2011. Computed Tomography: Fundamentals, System Technology, Image Quality, Applications, third ed. Publicis Corporate Publishing, Erlangen. Kalender, W.A., 2006. X-ray computed tomography. Phys. Med. Biol. 51, R29–R43. Laskey, M.A., 1996. Dual-energy X-ray absorptiometry and body composition. Nutrition 12, 45–51.
S.-J. Tu et al. / Micron 71 (2015) 14–21 Lees, G.E., Sautter, J.H., 1979. Anemia and osteopetrosis in a dog. J. Am. Vet. Med. Assoc. 175, 820–824. Malluche, H.H., Porter, D.S., Pienkowski, D., 2013. Evaluating bone quality in patients with chronic kidney disease. Nat. Rev. Nephrol. 9, 671–680. Marxen, M., Thornton, M.M., Chiarot, C.B., Klement, G., Koprivnikar, J., Sled, J.G., Henkelman, R.M., 2004. MicroCT scanner performance and considerations for vascular specimen imaging. Med. Phys. 31, 305–313. Mayhew, P.M., Thomas, C.D., Clement, J.G., Loveridge, N., Beck, T.J., Bonfield, W., Burgoyne, C.J., Reeve, J., 2005. Relation between age, femoral neck cortical stability, and hip fracture risk. Lancet 366, 129–135. Qiu, S., Rao, D.S., Palnitkar, S., Parfitt, A.M., 2010. Dependence of bone yield (volume of bone formed per unit of cement surface area) on resorption cavity size during osteonal remodeling in human rib: implications for osteoblast function and the pathogenesis of age-related bone loss. J. Bone Miner. Res. 25, 423–430. Ritman, E.L., 2011. Current status of developments and applications of micro-CT. Annu. Rev. Biomed. Eng. 13, 531–552. Rosenberg, G., Ramus, J., 1984. Uptake of inorganic nitrogen and seaweed surface area: volume ratios. Aquat. Bot. 19, 65–72. Rubin, G.D., Dake, M.D., Napel, S., Jeffrey Jr., R.B., McDonnell, C.H., Sommer, F.G., Wexler, L., Williams, D.M., 1994. Spiral CT of renal artery stenosis: comparison of three-dimensional rendering techniques. Radiology 190, 181–189.
21
Saluja, S., Bhandari, S., Aggarwal, S., Kapoor, S., 2009. Osteopetrosis: a rare cause of anemia – review of literature. Indian J. Pathol. Microbiol. 52, 363– 367. Sreehari, S., Naik, D.R., Eapen, M., 2011. Osteopetrosis: a rare cause of anemia. Hematol. Rev. 3, 1–2. Tu, S.J., Shaw, C.C., Chen, L., 2006. Noise simulation in cone beam CT imaging with parallel computing. Phys. Med. Biol. 51, 1283–1297. Vos, F.M., Van Gelder, R.E., Serlie, I.W.O., Florie, J., Nio, C.Y., Glas, A.S., Post, F.H., Truyen, R., Gerritsen, F.A., Stoker, J., 2003. Three-dimensional display modes for CT colonography: conventional 3D virtual colonoscopy versus unfolded cube projection. Radiology 228, 878–885. Yin, Z., Sadok, A., Sailem, H., McCarthy, A., Xia, X., Li, F., Garcia, M.A., Evans, L., Barr, A.R., Perrimon, N., Marshall, C.J., Wong, S.T.C., Bakal, C., 2013. A screen for morphological complexity identifies regulators of switch-like transitions between discrete cell shapes. Nat. Cell Biol. 15, 860–871. Young, H.D., Freedman, R.A., Ford, A.L., 2011a. University Physics with Modern Physics, 13th ed. Addison-Wesley Publishing Company, Reading, MA, USA. Young, W., Budynas, R., Sadegh, A., 2011b. Roark’s Formulas for Stress and Strain, eighth ed. McGraw-Hill Professional, New York, NY, USA.