Patient-specific finite element (FE) analysis is a promising technique to preoperatively estimate the mechanical behaviour of bone in response to loads, which can be advantageous for clinical treatment such as the evaluation of fracture risks or implant design. The material property assignment of a FE model of bone is not trivial due to the inhomogeneous and anisotropic character of bone [1, 2]. Many authors generate homogenized continuum-level models based on elasticity-density laws available in the literature [1–3] linking the material properties such as Young’s modulus to bone mineral density (BMD) [4–7], mostly derived from ash or apparent bone density measured ex situ [5, 6]. For clinical practice it would be beneficial to base material properties on the radiological BMD of the patient’s bone derived by in vivo quantitative computed tomography (qCT). However, radiological BMD is solely an indicator of bone mineral content. Investigating the bone density revealed a correlation between ash and apparent density . Ash density determined ex situ can be roughly assumed to be equal to in vivo radiological density . However, without analysing the impact of surrounding tissue on the in vivo BMD measurement the validity of the material mapping method remains questionable.
Common reconstruction algorithms, such as filtered backprojection, are based on the assumption of monochromatic X-rays and thus describe the intensity of the signal depending on the attenuation coefficient and the thickness of the absorber but neglect alternating effective beam energies along the path [10, 11]. Low-energy beams are in general more absorbed compared to high-energy beams, changing the X-ray spectrum and thereby the mean intensities. Clinical X-ray detectors solely measure an intensity integral and are not able to distinguish different X-ray energies. The attenuation coefficients of surrounding tissue, i.e. muscles, fat and adjacent bone, in in vivo condition, have diverse energy dependencies resulting in alternating effective beam energies along lines of response and therefore causing inconsistencies in the reconstruction process . Although CT numbers have been found to be related to mechanical properties in dissected bone [4, 7], the presence of surrounding tissue might degrade the quality of the material law approaches, since intensities and BMD may not be correctly determined in vivo. For qCT-based BMD determination, most authors use machined bone samples or dissected bones without soft tissue [7, 8]. In order to compensate for missing soft tissue, many authors scan their bone samples immersed in water [7, 8, 12].
The aim of this study was to investigate the accuracy of qCT determined patient-specific BMD results based on in situ and ex situ scans of body donors of variable stature. The influence of the surrounding tissue on the quantification of CT images was investigated at different anatomical locations of femora scanned in situ, in air and in water.
2 Material and methods
The right femora of three fresh human cadavers of obese, normal and slender stature were scanned in situ using a multislice CT scanner (Siemens SOMATOM Definition TM AS+, Erlangen, Germany) with the same scan protocol for all scans and the following baseline parameters: gantry rotation time 0.3 s, 120 kVp, 450 mAs, collimation 64 x 0.6 mm, pitch 0.5, slice thickness 1 mm, convolution kernel B31F. For the determination of BMD the femora were scanned with a five-chamber dipotassium phosphate phantom (Mindways, TX, USA) inside the field of view. In order to simulate common clinical procedures, no pre-processing calibrations, e.g. water calibration, or changes to the reconstruction process of the commercial CT-scanner were performed. Subsequently, the femora were extracted from the cadavers, cleaned of soft tissue and scanned under the same conditions. The phantom was covered with gel pads to reduce artifacts while the extracted femora were surrounded by air or immersed in a container filled with water.
An automatic grey value-based CT image registration was performed for all scans of one specific donor with AMIRA 5.3 (Visage Imaging, Inc., San Diego, USA), which allowed for a comparison between BMD in situ and ex situ . Regions of interest (ROIs) were drawn by a single observer at three different anatomical sites. In the centre of the femoral head, manual segmentation was performed by drawing a circle with a defined radius in order to investigate trabecular bone. A region-growing algorithm combined with morphological operations was applied for the segmentation of cortical bone within the diaphysis with a threshold of 500 Hounsfield Units (HU), whereas trabecular bone of the distal metaphysis was segmented using the same approach but lower thresholds (0-499 HU), as in Cheng et al. . BMD was determined by the following equation:(1)
where µROI describes the mean intensity in the segmented ROI, σCT defines the response of the CT scanner to dipotassium phosphate and βCT describes the characteristics of the CT number scale. σCT and βCT were derived from a least squares algorithm involving the mean intensities measured in all five calibrating rods of the investigated slices. Quantification of BMD was evaluated by comparing the BMDs of ex situ scans to the reference in situ scans of one specific donor at each anatomical location, in order to investigate the influence of different amount and type of surrounding tissue and surrounding medium, respectively. Deviations were further evaluated by observing the acquired mean intensities in the ROIs for in situ and ex situ scans. Additionally, the linear calibration equation was investigated for all scans, which had a major impact on the determination of BMD. In order to investigate potential changes in size of the ROI due to beam hardening, line profiles of the intensities were obtained at the location of the individual ROI. Additionally, changes in the area size of automatic segmented ROIs were measured.
The differences in BMD of femora scanned ex situ with reference to the in situ results are illustrated in Figure 1 and Figure 2. In general, trends in the deviation of BMD with respect to stature could be observed for the diaphysis and the distal metaphysis in air as well as for the femoral head and the distal metaphysis in water. A universal trend was not observed for the different locations or types of bone. The highest deviation was found in the distal metaphysis of the obese donor scanned in air (17.5%). Deviations were lowest for the subject with normal stature. Scans in air showed higher deviations for trabecular bone regions and slightly lower deviations for cortical bone compared to water.
The scans in air resulted in higher HU compared to the cadaveric scan, which was counteracted by a decrease of the calibration slope. In this context, the data suggests that these effects are related to the stature. In water scans HU values and calibration slopes were closer to the reference. Typical linear BMD calibration equations for different media are shown in Figure 3. The slope and ordinate intercept changed in all measurements but water calibration equations were closer to the reference.
The projection of the image showed consistent deviations in different media as well, which is exemplarily illustrated in the line profile of the femoral head of the obese donor (see Figure 4). The projection drawn in red (air) is consistently narrower compared to the other projections. The projection values of water scans were in general closer to the projection values of cadaveric scans. The size of the automatic segmented ROI changed by up to 3%.
The study showed deviations between BMD measured in situ and ex situ, depending on anatomical site, stature, structure of the bone and the surrounding media. It is challenging to isolate the impact of each influence on the outcome in water and air, respectively. BMD of trabecular bone was considerably underestimated in literature when scanned in air , which was confirmed by this study investigating trabecular bone in the femoral head and the distal metaphysis. Chen and Lam used dissected, dry bone and linked the difference to missing water inside the intraosseous space . In the present study fresh bone was used and the intraosseous space was in a physiological condition indicating that the surrounding medium has an impact on the determination of BMD as well. Deviations were lower in water, suggesting that water is able to act as a surrogate of soft tissue to a certain extent. In the case of cortical bone, water could not improve results.
Although no universal trend could be observed, the results indicate a locally varying influence of stature on the BMD results. Differences in the type and amount of tissue surrounding the femora caused variations in the quantification of BMD, which have to be considered when assigning material properties with elasticity-density laws. In general, specific attenuation coefficients lead to beam hardening, occurring with different effects induced by different tissue types, which cannot be simultaneously corrected . Hence, beam hardening is inevitable in clinical CT scanners with commercial reconstruction algorithms. Conclusions can be drawn that the specific attenuation coefficient of different adjacent tissues is a limiting factor for the radiological determination of BMD.
Mathematically, BMD is a result of the mean intensity in the ROI and the calibration equation. Alterations in the projection could be an indication of the presence of beam hardening, leading to a change in spectrum and altered mean intensities. This study showed that missing tissue affects the intensity in the ROI but also the intensity of the rods of the calibration phantom, thereby influencing the calibration equation. Conclusively, deviations in BMD are mutually dependent on the individual impact of the surrounding tissue on intensity measured in the body and in the rods of the phantom. Since beam hardening is different for varying anatomical locations due to the amount and type of tissue, deviations in intensity and calibration depend on anatomical location as well. Furthermore, the altered calibration equation might have a different impact on the determination of BMD in tissue with significantly different intensities, i.e. cortical or trabecular bone. Diverging intensities inside the ROI were lower in water and the calibration line was closer to the reference compared to air but the resulting impact on BMD was minor.
Keyak et al. investigated the influence of femoral image data obtained in situ and ex situ on the results of FE analysis. They found substantial differences in predicted fracture load . This study showed that distorted projections alter automatically segmented geometries, which might further reduce the accuracy of FE models. In order to compensate for energy-dependent attenuation, the use of dual energy CT systems, i.e. scanning the patient at different voltages , might be beneficial.
One limitation of this study is the possible errors introduced by interpolation used during image registration, which could have distorted the results. Another limitation is the small number of investigated body donors and, on the technical side, quantum noise, which might have an effect on all results. Pre-filters integrated into the X-ray tube, as well as different reconstruction algorithms incorporating convolution kernels can be optimized to compensate for beam hardening [10, 11, 15]. In this case, only a commonly used medium smooth body convolution kernel was used, which is known to provide a better peak signal-to-noise ratio as well as lower root mean square errors and mean absolute errors compared to other kernels .
The authors would like to thank the Institute of Anatomy, University of Lübeck, for the supply and dissection of cadaveric material. We further thank Jörg Barkhausen and Attila Kovàcs from the Department of Radiology, University Medical Center Schleswig-Holstein, Lübeck, for the provision of technical equipment.
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About the article
Published Online: 2015-09-12
Published in Print: 2015-09-01
Conflict of interest: Authors state no conflict of interest. Material and Methods: Informed consent: Informed consent is not applicable. Ethical approval: The research related to human use has been complied with all the relevant national regulations and institutional policies. The human cadavers in this examination were used and dissected under permission of the „Gesetz über das Leichen-, Bestattungs- und Friedhofswesen (Bestattungsgesetz) des Landes Schleswig- Holstein vom 04.02.2005, Abschnitt II, § 9 (Leichenöffnung, anatomisch)“. In this case, it is allowed to dissect the bodies of donors (Körperspender/in) for scientific and/or educational purposes.