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Soft-tissue differentiation and bone densitometry via energy-discriminating X-ray microCT

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Abstract

X-ray computed tomography (CT) is an important diagnostic tool in medicine as well as being an essential research technique for animal imaging and bioscience. The key aim of this study is to assess the effectiveness, in both simulation and experiment, of differentiating soft tissue from bone as well as bone densitometry, using energy-discriminating X-ray detection. Polychromatic sources, such as standard X-ray tubes, can produce similar CT numbers for materials with different compositions, making differentiation and quantification of tissue and bone extremely challenging. In addition, ‘beam-hardening’ which occurs due to the relative increase in the attenuation of low energy photons compared to high energy photons, can create significant CT artifacts. To improve material contrast and eliminate beam hardening, a number of different approaches have been developed. These include dual-energy CT using two different X-ray tube voltages, photon beam filtration, and post-processing of the data. Here we present an alternative approach using the photon counting PiXirad detector. Simulations are used to establish optimal parameters for data acquisition. This is followed by tomographic experiments performed on a phantom and a mouse embryo. The energy discriminating properties of the detector are exploited to avoid beam-hardening artefacts, to differentiate soft-tissue and bone within the mouse embryo, and to quantify bone density. Compared with polychromatic CT using an integrating detector this approach yields a number of significant advantages for materials specific imaging and quantification.

© 2017 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

1. Introduction

X-ray computed tomography is widely used for radiological and biomedical imaging applications due to its high-resolution and penetrating power, as well as its ability to provide 3D sample information. For over 30 years X-ray CT has undergone a process of continuous improvement in terms of data collection speed, spatial resolution, as well as significant advancements in detector technology. However, despite this, decomposition of samples, particularly weakly interacting biological samples, into their component elements in three dimensions remains an active area of research. Furthermore, obtaining quantitative absorption (and hence density) values using polychromatic X-rays can also be challenging due to the need for accurate knowledge of the spectrum and the issue of beam hardening. Beam hardening arises due to the increased attenuation of low energy X-rays in materials in comparison to high-energy X-rays. This modifies the detected signal transmitted through the sample in a non-trivial way, which normally requires additional correction of the data and often prevents accurate values for the sample attenuation from being determined. In terms of image artifacts, beam hardening produces visual distortion of the reconstructed slices in tomography, in the form of a brighter grey rim along the edge. These issues fundamentally arise due to the nonlinear relationship between the attenuation and the material thickness. Several protocols have been established for beam hardening correction [1] and image segmentation, including dual-energy CT [2], photon beam filtration or more filters during scanning [3], and post-processing of the data. For dual-energy CT a number of different experimental geometries have been demonstrated [4].

Dual-energy projection techniques [5] have been developed extensively for the measurement and separation of bone and soft tissue in vivo, a large variety of algorithms now exist specifically for dual-energy tomography. The three main configurations of dual-energy CT involve using a single source with and without beam filtration, rapidly switching the source voltage, or using a multilayered X-ray detector with a variable energy response. Whilst each configuration is based on the same underlying principle, each has its own unique set of disadvantages. These include poor image registration between data collected over different energy ranges, significant spectral overlap and a reduction in signal-to-noise [5,6].

In order to address the non-linearity of the attenuation coefficient due to beam-hardening using dual-energy CT, a polynomial correction can be applied in the post-data analysis. This involves first ‘calibrating’ the polynomial by measuring a range of different path lengths through a sample with known material-specific attenuation. Provided the spectrum is also known, a polynomial function can be fitted to the data points [2,7]. Using beam filtration, the source can also be ‘pre-hardened’ to leave only the higher energy X-rays, which are less prone to cause artifacts. Although both these approaches can provide an effective means of reducing beam hardening, they do not, in general, allow for a direct quantitative analysis of the data, for example to extract the material density [8].

Quantitative interpretation of polychromatic CT data is normally based on the measured CT values (or ‘grey level’) of a particular voxel. This is related to the linear attenuation coefficient for that voxel, integrated over all photon energies. To relate the grey level directly to a quantitative density value, samples of known density (usually denoted as ‘phantoms’ [9]) need to be scanned to provide a calibration scale [10]. In most cases, the unknown sample and the calibration phantom need to be scanned within the same field-of-view (FOV). This is because variations in the values obtained for the density can occur if the two objects are scanned separately, e.g. because of small fluctuations in the source intensity [8].

The recent availability of energy-discriminating photon counting detectors, offers the potential to provide a range of improvements for beam hardening correction [11] and quantitative image analysis. Energy-discriminating X-ray detectors use energy thresholds to provide spectral filtering of an incident polychromatic beam. As we demonstrate, this provides an extremely effective way to remove beam-hardening artefacts when using polychromatic X-rays. This open up a new capability for this type of the detector to produce quantitative results for measuring bone density. The ability to collect data simultaneously over different energy ranges, without any spectral overlap, also offers a wealth of new analysis options for decomposing materials into their constituent elements [12]. This is due to the ability of the detector to select a narrow bandwidth from the incident polychromatic X-rays providing a quasi-monochromatic source.

Energy-discriminating detectors based on chromatic photon counting detector technology have undergone extremely rapid advancement in recent years. A variety of such detectors are now on the market including the Medipix [11, 13], Pilatus [14], XPAD [15] and PiXirad [16] detectors. The opportunities for spectral computed tomography have been explored in a number of previous theoretical studies [17–19]. Some of these ideas have also been explored in some recent experimental work [20–22].

One particularly relevant experimental study using energy-resolved photon counting detectors, was the work carried out by Cajipe et al. [23]. In this work it was demonstrated that cadmium zinc tellutride (CZT) linear pixel arrays consisting of 2 x 16 pixels on a 1mm pitch could be used to generate four energy-binned radiographs of a phantom comprising six compositionally distinct materials. Similar research using a detector with the same geometry was conducted by Shikhaliev [21], this time using an X-ray fan-beam and 5 energy bins to separate out different elements within a phantom sample which included both iodine and CaCO3. Iwanczyk et al. [24] later used cadmium telluride (CdTe) and CZT arrays consisting of 16 x 16 pixels, also on a 1mm pitch to demonstrate the first patient CT scanning using photon counting, energy-dispersive X-ray detectors. In 2010, a high-resolution, photon counting detector (Medipix) was used to resolve the different characteristic photon energies produced by X-ray fluorescence of Mo, Pd, Ag and Sn [25]. Using microfocus X-ray CT, CdTe energy dispersive detectors were shown by Onishi et al. [20] to be effective at separating multiple elements within a phantom test sample. More recently in 2011, Wang et al. [26] used micro-CT and a photon counting detector with multiple energy thresholds, to separate out elements in a phantom sample. In the Wang et al. study, contrast agents containing K-absorption edges within the energy range of interest, were used to facilitate material separation.

In the present study, we use both simulation and experimental data to investigate high-resolution, energy-resolved CT imaging of both a phantom and a ‘real-world’ mouse embryo sample. The experiments utilize the recently developed, high-resolution, energy-resolving photon counting PiXirad detector and do not rely on the use of any contrast enhancing agents. The following key findings are made:

  • 1) Energy thresholding is an extremely effective means of eliminating all beam hardening artifacts. This is helped significantly by the sharp cut off (on the low energy side) of the bandwidth.
  • 2) Three-dimensional segmentation of soft-tissue from bone in X-ray micro-CT can be achieved using energy discriminating detectors, without any post processing of data.
  • 3) We provide the first demonstration that energy-discriminating detectors can be used to quantify bone density.

In simulation, the effectiveness of material differentiation was found to depend on the value of the energy threshold of the PiXirad detector that is used to eliminate beam-hardening. We explore the limitations on the effectiveness of the separation that can be achieved, based on the detector specifications. The demonstration of soft-tissue segmentation using energy-resolved photon counting detectors for ‘real-world’ sample imaging, confirms the significant potential these types of detectors have for biological and medical CT.

2. Materials and methods

2.1 The PiXirad detector

The PiXirad detector system (PiXirad IC srl c/o INFN Pisa, Italy) consists of a CdTe solid state sensor in which “flip-chip” bonding technique connects the pixelated CdTe to the CMOS ASIC readout. The solid state sensor (CdTe) is a type of Schottky diode with a thickness of 650 µm. The CMOS ASIC has an array of 512 × 476 pixels that are arranged on a hexagonal pitch of 60 µm. Each pixel includes an electrode, connected to the charge amplifier, which provides two discriminators and two 15-bit counters per register. This enables each pixel to discriminate photons in terms of their energy [27]. As each pixel of the semiconductor sensor (CdTe) is connected to the corresponding channels of the ASIC, an analog and digital signal treatment can be provided. At the semiconductor, the X-ray photons are converted to electric charges which are collected on the pixels and transferred to the ASIC where the signal per each pixel is electronically treated. This technology has since been commercialized and forms the basis of the PiXirad detector for multi-colour imaging per single exposure. In the version of the detector used here, a maximum of 4 individual energy thresholds could be set resulting in 4 images. Each image corresponds to different energy ranges, all 4 images are produced simultaneously at each angular position of the tomographic scan. This capability opens up a wealth of possibilities for absorption edge enhanced contrast imaging (AECI) [12] as well as segmentation of the CT images on the basis of varying absorption coefficients between different materials.

2.2 Beam hardening correction and quantification

Quantitative imaging using standard polychromatic lab-based X-ray sources presents a range of challenges. One major issue that must often be corrected during post processing is beam hardening, which prevents accurate bone densitometry measurements and impacts the effectiveness of material discrimination. However, the flexibility of arbitrarily choosing a well-defined energy threshold using the PiXirad detector, means that beam-hardening artefacts can easily be avoided for a large variety of different materials and samples. It also means that a quantitative density distribution for the sample can be produced. This is possible due to the detector’s ability to mimic a quasi-monochromatic X-ray beam, by defining a narrow energy bandwidth at the detector.

To understand how a quantitative value for the sample density can be determined, let’s consider an object with a linear attenuation coefficient, µ(r,E) where r defines a specific location in the sample and E the incident X-ray energy. X-ray’s traversing point r, travel through the object along a straight line L(x,θ), parameterized by the path length, t, and uniquely defined by the rotation angle, θ, and the end-point, x, at the projection (detector) plane. Hence, µ(r,E) can be written as µ(r,E) = µ(x,θ,t,E); the polychromatic projected intensity (within the narrow bandwidth) after the object is then defined as

Iout(x,θ)=E0E1S(E).expL(x,θ)μ(x,θ,t,E) dtdE
Here, [E0, E1] is an interval determined by the detector energy threshold and the cut-off energy, and S(E) is the spectral density of the incident X-rays. The X-ray source spectrum S(E), in this case produced by a tungsten target at 40 kV tube voltage, is measured experimentally, and is shown in Fig. 1(a). The ability to arbitrarily set an energy threshold using the PiXirad detector means that the low end, E0, can be set to any value, whilst at the high end, E1, is fixed which defines the high-energy cut-off for the X-ray spectrum.

 figure: Fig. 1

Fig. 1 (a). The measured X-ray source spectrum for a tungsten target at 40 kV tube voltage, with the corresponding energy threshold (E0), up to the maximum x-ray energy spectra (E1). (b). Simulations of the value for ln(IoutIin), as a function of the projected thickness for various conditions.

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Using the PiXirad detector, the spectra forming the image contains signal from all photons whose energy is greater than E0 (set in the detector) up to the cut off X-ray energy, E1. A major advantage of energy-discriminating detectors is that the energy threshold cut-off is much sharper than beam filtration techniques. Moreover, in beam filtration, the value of the lowest X-ray energy cannot be precisely defined by the filter thickness. On the other hand, PiXirad only attenuates those X-rays below the energy threshold cut-off, leaving the remainder of the spectrum largely unaltered. In other words, the lowest energy is defined precisely by the value of the threshold energy set in the detector.

When both quantitative imaging and beam hardening correction are required, a narrow interval of energies needs to be defined. In this case the polychromatic absorption coefficient can be approximated by the monochromatic absorption coefficient specified at the average energy,E¯ , corresponding to the interval, [E0, E1]

μ(E)μ(E¯)      , E0EE1
where E¯ is defined as:
E¯=E0E1E.S(E).dEE0E1S(E).dE
Therefore, Eq. (1) can be written as:
Iout(x,θ)Iin.expL(x,θ)μ(x,θ,t,E¯) dtIin.exp(Rμ)(x,θ,E¯)
where Iin=E0E1S(E).dE is the intensity of the incident beam in between the energy interval [E0, E1], and  R is the Radon transform [28]. The CT reconstruction of the linear attenuation coefficient can then be calculated via an inverse Radon transform operation

μ(r,E¯)=R1[ln(Iout(x,θ)Iin)]

The linear attenuation coefficient at average energy, μ(E¯), can be directly related to the material density by using (in the case of bone) hydroxyapatite (HA) phantoms of known density as a calibration. It is important to note that this is not the same as the grey level calibration described earlier for dual-energy CT, since in the present case the quantitative linear attenuation coefficient μ(E¯) rather than the grey level is used to determine the material density. This means that the calibration of the experiment can be performed once separately, prior to any measurements, and is less sensitive then the grey levels to changes in the experimental parameters (e.g. the exposure time). Consequently, the measured sample does not need to be in the same FOV as the calibration phantom.

Figure 1(b) presents simulations of ln(IoutIin) as a function of the projected thickness for different energy settings. The monochromatic beam (dotted green line for 18 keV and dash-dot blue line for 26 keV) gives a linear profile, whilst the attenuation of the full range polychromatic spectrum (dashed black line) shows a curved, non-linear, profile that leads to beam hardening artefacts in computed tomography. The PiXirad detector can emulate a quasi-monochromatic beam, which gives a linear profile (solid red line) within the selected bandwidth of 21 to 40 keV.

2.3 Material separation using the PiXirad

A simulation study was first conducted using the measured incident polychromatic spectrum of the lab source. The simulation incorporated the specific characteristics of the PiXirad, e.g. the variation in energy threshold values [16] and its energy response [27]. In the simulation, a phantom was constructed which consisted of a 10 mm diameter cylinder of epoxy resin (density 1.13 g/cm3) with 5 inserts of the same resin enriched with varying amounts of HA, Ca10(PO4)6(OH)2. This is similar to other phantom studies in the literature and is representative of bone with densities of 1.19, 1.26, 1.39, 1.65 and 1.90 g/cm3, corresponding to the HA100, HA200, HA400, HA800 and HA1200 inserts respectively. The simulated phantom was identical to the one used for the later experimental studies (QRM-MicroCT-HA Phantom, QRM GmbH), enabling a direct comparison between the two results. The diameter of all the inserts was 2 mm. The absorption coefficient for the phantom elements as a function of X-ray energy were obtained from the NIST materials database [29].

The polychromatic intensity in the simulations was calculated via a summation of the monochromatic intensities over all incident wavelengths, weighted by their relative contribution to the measured incident X-ray spectrum, S(E) [30]. The detector was assumed to be operating in ‘two-colour’ imaging mode, where for a single exposure both a low-threshold energy and a high-threshold energy image were generated. The two corresponding energy ranges for the two images were, ΔE1 = 21 to 40 keV and ΔE2 = 27 to 40 keV, respectively. The energy threshold of 21 keV was sufficient to remove beam-hardening artifacts for all insert materials. The polychromatic projection intensity data for the phantom for ΔE1 and ΔE2, were generated for all 721 projections. Two example reconstructed slices calculated using Eq. (5), are shown in Figs. 2(a) and 2(b).

 figure: Fig. 2

Fig. 2 A reconstructed slice of the phantom model taken at low (ΔE1 = 21 to 40 keV) in (a) and high (ΔE2 = 27 to 40 keV) energy thresholds in (b) respectively. (c) Plot through the vertical middle line of both reconstructed slices across the HA200 and HA1200 insert materials (shown as green dotted line on Fig. 2(a)).

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Differentiation between soft tissue and bone was subsequently carried out by analyzing the differences between the high and low energy windowed images. Due to the differences in the gradient of the absorption coefficients between the epoxy resin and the ‘bone’ (HA inserts), bone exhibits a much greater variation in absorption between ΔE1 and ΔE2 compared to the epoxy resin, as shown in Fig. 2(c). These differences in the specific interaction of each of the materials tested with X-rays, within the two energy windows selected, enable their unambiguous separation using the PiXirad detector. The image absorption histogram also shows that there is much greater variation in the CT values for bone than for resin as a function of energy, shown in Fig. 3(a), with the signal from the resin essentially identical for the different energy windows. Figure 3(a) shows that the grey level peaks associated with each of the ‘bone’ inserts are clearly identifiable and that their relative separation (in terms of linear attenuation coefficient) changes dramatically depending on the choice of energy window. This is in contrast to the simulated results using the full spectrum, shown in Fig. 3(b), where broadening of the grey level peaks, predominantly due to beam-hardening, leads to convolution of the signals from the different bone densities. The figure shows that low density materials i.e. epoxy resin, HA100 and HA200, are not separable in the full spectrum image.

 figure: Fig. 3

Fig. 3 Absorption histogram of the reconstructed image taken at (a) low (ΔE1 = 21 to 40 keV) and high (ΔE2 = 27 to 40 keV) energy thresholds and (b) using the full spectrum (minimum energy = 5 keV).

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Another key point to consider is the possible effect of the energy bandwidth on the broadening of the absorption histogram peaks. Due the comparatively low density of biological materials such as the soft tissue and bone studied here, the position of the higher end energy and hence the effective energy bandwidth has relatively little influence on the FWHM (full width at half maximum) of the absorption peaks. For example, in simulations, the change in the HA1200 absorption peak FWHM just due to the 6 keV decrease in bandwidth moving from 21 - 40 keV to 21 - 34 keV was 6.8%. This is much less than the corresponding change due to beam hardening when moving from 21- 34 keV to 8 - 21 keV say, where simulations show beam hardening causes a massive ~3500% increase in the HA1200 peak FWHM.

The following conclusions can be drawn from the simulations of the phantom sample and subsequent analysis of the absorption histogram:

  • 1) The separation of the peaks in the absorption histogram depends strongly on the choice of energy threshold, with higher energies producing less contrast, this is illustrated by the fact that the peaks move closer together.
  • 2) The FWHM of the peaks becomes narrower as the threshold energy moves to higher values. This indicates more effective beam hardening correction, since beam-hardening artefacts are characterized by a broadening of the peaks in the absorption histogram.
  • 3) For relatively low density biological materials (e.g. soft tissue and bone) the effect of the position of the low end energy, in relation to beam hardening, dominates over the bandwidth in determining the FWHM of the absorption histogram peaks.

From this, we conclude that for each sample there is an optimum balance between choosing higher energy thresholds, which have narrower peaks for the CT values, and maximizing image contrast, which can be achieved by moving to lower energy thresholds. We also note that there is a minimum energy that needs to be maintained to avoid beam-hardening, this is particularly critical for dense materials. This minimum energy can be estimated, by checking the linearity of ln(IoutIin) as a function of the projected sample thickness. Thus, the correct choice of energy threshold for the PiXirad detector depends critically on the density of the materials being separated.

If only a simple, qualitative, separation of soft tissue (e.g. epoxy) from bone (e.g. HA) is required, a straightforward image subtraction, with a suitable weighting to account for the differences in photon numbers can be performed between the low and high energy threshold images. Subtraction of the high energy data from the low energy data for example, will remove the epoxy matrix, with the result representing the difference in absorption between the 5 different bone inserts. Although this can yield separate images of the bone and soft tissue, the resulting data cannot be used for quantitative analysis of the absorption coefficient. In addition, it does not allow for further differentiation for materials of different density. In order to separately image and quantitatively analyze bone of different density, in three dimensions, the absorption histogram was used to segment out each of the five different inserts.

3. Experimental results

A number of previous studies have been performed using simulations to investigate the applications of energy-sensitive photon counting detectors for medical and biological X-ray CT. This includes a recent 2017 review of the topic by Taguchi [31]. However, there are to date, few experimental demonstrations of micro X-ray CT, which exploit energy discriminating X-ray detectors. It is thus important that the simulation results presented in the previous section are verified using actual experimental data; these results may then be used as a basis for applying these methods to ‘real-world’ samples (here we use the example of a head of a mouse embryo). It is well known that the bones of embryos have a reduced level of calcium compared to adults of the same species [32]. Thus, this particular choice of sample, allows us to explore the limits and potential sensitivity of our technique to relatively small changes in density where segmentation is more challenging than in an adult specimen.

The experimental data presented here were collected using the Xradia© micro XCT200 (Carl Zeiss X-ray Microscopy, Inc., Pleasanton, CA, USA) polychromatic X-ray laboratory source with an additional connection to the PiXirad detector system for data collection. The source was a closed X-ray tube (Hamamatsu) consisting of a tungsten target and operated at a tube voltage of 40 kV and with a power of 10 W. The PiXirad detector, which contained 512 × 476 pixels, in a hexagonal arrangement with a pitch of 60 μm (equivalent to 55 μm in a square arrangement) was cooled down to an operating temperature of −20°C using a combination of water cooling and nitrogen gas. The spatial resolution of the experiment was determined by the ‘effective’ pixel size in the image, defined as the actual detector pixel size divided by the geometric magnification factor, M, where  M=R1+R2R1. Here, R1 is the source-to-sample distance, and R2 is the sample-to-detector distance. In this experiment M = 1.9, giving an effective pixel size of 30 μm. In each projection, images were simultaneously collected with two energy thresholds of 21 keV and 27 keV with an exposure time of 6s. We collected 721 projected images by rotating the sample in 0.25 degree steps between −90° and + 90°. Both a phantom model sample (QRM-MicroCT-HA Phantom, QRM GmbH) and a mouse embryo were measured. The embryo sample was provided by Dr. Stephen J. Goldie (Monash University, Department of Medicine) [33]. It was stored in formalin and for X-ray tomography was removed from solution and sealed inside a plastic container to prevent dehydration.

In Figs. 4(a)-4(c), we present the reconstructed slice of the phantom sample taken with a low (ΔE1 = 21 to 40 keV) and high energy threshold (ΔE2 = 27 to 40 keV) as well as using the full spectrum. Note that the full spectrum data was collected in a separate CT scan, since the exposure time per projection needed to be reduced to 0.6s to avoid detector saturation. The 3D image reconstruction and segmentation processing was carried out using the Matlab (MathWorks®) programming language. During the reconstruction process, we applied a ring artefact correction before applying the inverse Radon transform. A possible explanation for the origin of the initial ring artefacts, is the presence of small inter-pixel variations in the detector response, due to slight variations in the sensitivity of each pixel as a function of X-ray energy. The absorption histogram for the experimental data is shown in Fig. 4(d). In this figure, all the peaks are broader than in the corresponding simulation result, shown in Fig. 3(a). We suggest that this broadening of the peaks was caused by charge sharing between adjacent pixels in PiXirad detector, which is proportional to the photoelectron range and charge diffusion, both of which depend on the absorbed photon energy [27]. The practical consequences of charge sharing are that the signal from individual photons is spread over several pixels and produces multiple counts with reduced apparent energy. An additional factor, characterized by symmetric broadening of the energy threshold, is caused by slight differences in the pixel amplifier gain and the residual pixel-to-pixel DC offset spread. Charge sharing is expected to lead to a higher number of low-energy photon counts being measured. The broadening effect caused by charge sharing, in conjunction with beam hardening artefacts, can be seen in the absorption histogram of the experimentally reconstructed slices taken with the full polychromatic spectrum, shown in Fig. 4(e). We also observe that there are a larger number of negative values for the linear attenuation coefficient in Fig. 4(e). These negative values are physically meaningless and we attribute their presence to the beam hardening artifacts which are more apparent when using the full spectrum, shown in Fig. 4(c), than when using energy thresholds, shown in Figs. 4(a) and 4(b).

 figure: Fig. 4

Fig. 4 The reconstructed slice of the experimental data from the phantom sample taken at low (ΔE1 = 21 to 40 keV) in (a) and high (ΔE2 = 27 to 40 keV) energy threshold in (b) respectively, and using the full spectrum in (c). (d). Absorption histogram of the reconstructed image of (a) in blue color and (b) in red color respectively. (e). The corresponding absorption histogram for the phantom for the full spectrum (minimum energy = 5 keV).

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In the calibration step presented in this section, we use only three different materials (HA100, HA400 and HA1200) as a reference. Their corresponding measured linear attenuation coefficient values at an energy bandwidth of 21- 40 keV are presented in Table 1. This same energy bandwidth is later also used for experiments conducted on a mouse embryo (results presented in the second half of this paper). The average energy,E¯ , is calculated using Eq. (3). For the energy bandwidth of 21 – 40 keV, the average energy is 27.3 keV. The relationship between the measured linear attenuation coefficient and the corresponding density is presented in Fig. 5. This calibration data was then used to determine the density of the remaining materials epoxy, HA200 and HA800 in order to verify the accuracy of this technique. The results are also shown in Table 1. The density values obtained using our method are in good agreement with the values given by the manufacturer. The experimental bone density measurements conducted on the mouse embryo are also determined using the same calibration plot shown in Fig. 5.

Tables Icon

Table 1. Calibration and measured density values for the phantom and corresponding linear attenuation coefficient values.

 figure: Fig. 5

Fig. 5 The relationship between the linear attenuation coefficients as a function of the material density. Both the data used for calibration (filled red squares) and the measured density data (hollow squares) is shown.

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In order to separate materials of different densities, an automated segmentation utilizing Gaussian fitting of the absorption histogram peaks was applied. This created a range of local thresholds for the grey levels, corresponding to each of the different materials comprising the sample [34]. Utilizing the energy thresholding capabilities of the PiXirad, effective segmentation of the HA200, HA400, HA800 and HA1200 inserts could be achieved, the results are presented in Fig. 6. For the HA100 (density = 1.19 ± 0.02 g/cm3) insert however, only partial segmentation from the surrounding epoxy (density = 1.13 ± 0.02 g/cm3) is achieved. This is at the limit of what we are currently able to differentiate in terms of densities using our approach, in addition it is close to the error limits quoted by the manufacturer on the density values which could further impact the quality of segmentation. This is reflected in the fact that the peaks for the epoxy and HA100 overlap in the absorption histogram presented in Fig. 4(d) due to the similarity of their linear attenuation coefficients. We note that no differentiation of these two materials was possible using the full spectrum .

 figure: Fig. 6

Fig. 6 Material segmentation of the components of the phantom sample, via fitting of the absorption spectra peaks presented in Fig. 4(d). A single reconstructed slice through the 3D object is shown.

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In the final part of this study, we used a mouse embryo to demonstrate 3D soft tissue and bone segmentation using energy-discriminating micro-CT on a ‘real-world’ biological sample. After segmentation, the density of the bone within the embryo was quantified using the method outlined above. The energy bandwidth used was 21 – 40 keV. The bone density within the mouse embryo was determined from the reconstructed linear attenuation coefficient and the calibration plot shown in Fig. 5. After segmentation, based on the Fig. 7(a) absorption histogram with Gaussian fitting (as described above), the linear attenuation coefficient for the bone was determined to be 108.2 ± 21.5 m−1, corresponding to a density of 1.31 ± 0.06 g/cm3 using Fig. 5. The result of the reconstruction and segmentation is presented in Fig. (8). The plastic container surrounding the mouse embryo, along with the soft tissue and bone, could be readily segmented in 3D. However, we note that due to the limited photon statistics after segmentation the signal-to-noise for the reconstructed soft-tissue images is poorer than for the phantom sample. This could be improved via longer exposures or by summing more exposures per angle. In this current data, no summation per angle has been applied. In the full-spectrum absorption histogram for the mouse embryo, shown in Fig. 7(b), the absorption peaks are very broad and have significant overlap, this prevented the differentiation of soft tissue from bone in the analysis. For the energy-thresholded (21-40 keV) result, shown in Fig. 7(a), the FWHM of the peaks is significantly reduced, enabling effective segmentation of bone from the soft-tissue in 3D.

 figure: Fig. 7

Fig. 7 (a). Absorption histogram with Gaussian fitting corresponding to the reconstructions shown in Fig. 8 (21-40 keV). (b). The absorption histogram corresponding to the full spectrum (5-40 keV) for the mouse embryo sample.

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 figure: Fig. 8

Fig. 8 The reconstructed and the segmentation result of the mouse embryo experiment taken at (ΔE = 21 to 40 keV).

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4. Conclusion

The results of both simulations and experiments exploiting the energy thresholding capabilities of a photon-counting (PiXirad) detector for analyzing biological samples, have been presented. In both cases three-dimensional tomographic imaging with material differentiation and bone densitometry was readily achievable. This was due to the ability of the PiXirad to arbitrarily set multiple energy-thresholds. We observed that a higher energy threshold produced narrower absorption peaks, but at the cost of smaller peak separation (lower contrast). Hence segmentation of different materials could be optimized by varying the energy thresholds. This was demonstrated in both the simulations and experiments conducted on the phantom sample. Via energy thresholding, we demonstrated that it is possible to eliminate beam hardening in X-ray micro-CT. Compared to dual-energy CT, energy thresholding provides a variable, sharp cut-off on the low-energy side of the bandwidth which is both simpler and more efficient than either filters or multilayer detectors. The variable energy windows allow for maximum differentiation for biological materials, based on analysis of the absorption histogram. A single independent calibration of density versus linear attenuation, then allows for quantitative density measurements to be performed, provided beam-hardening has been effectively removed. Since the linear attenuation coefficient is a physical property of the material (unlike the ‘grey level’), this is a more robust route to quantifying material density via X-ray CT, with only a single calibration measurement required. Moreover, these benefits have been demonstrated both on a phantom and on a ‘real-world’ biological sample. These results further demonstrate that energy-thresholding detectors offer significant advantages for materials separation and analysis in 3D X-ray imaging. Based on this study we are confident that this approach will find a number of useful applications in both the materials and life sciences and in particular medical imaging.

Funding

The Australian Research Council through the Centre of Excellence in Advanced Molecular Imaging. (CE140100011) (http://imagingcoe.org/).

Acknowledgments

The authors would like to thank Dr. Stephen J. Goldie at Monash University, Department of Medicine for providing the mouse embryo sample.

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Figures (8)

Fig. 1
Fig. 1 (a). The measured X-ray source spectrum for a tungsten target at 40 kV tube voltage, with the corresponding energy threshold (E0), up to the maximum x-ray energy spectra (E1). (b). Simulations of the value for ln( I out I in ), as a function of the projected thickness for various conditions.
Fig. 2
Fig. 2 A reconstructed slice of the phantom model taken at low (ΔE1 = 21 to 40 keV) in (a) and high (ΔE2 = 27 to 40 keV) energy thresholds in (b) respectively. (c) Plot through the vertical middle line of both reconstructed slices across the HA200 and HA1200 insert materials (shown as green dotted line on Fig. 2(a)).
Fig. 3
Fig. 3 Absorption histogram of the reconstructed image taken at (a) low (ΔE1 = 21 to 40 keV) and high (ΔE2 = 27 to 40 keV) energy thresholds and (b) using the full spectrum (minimum energy = 5 keV).
Fig. 4
Fig. 4 The reconstructed slice of the experimental data from the phantom sample taken at low (ΔE1 = 21 to 40 keV) in (a) and high (ΔE2 = 27 to 40 keV) energy threshold in (b) respectively, and using the full spectrum in (c). (d). Absorption histogram of the reconstructed image of (a) in blue color and (b) in red color respectively. (e). The corresponding absorption histogram for the phantom for the full spectrum (minimum energy = 5 keV).
Fig. 5
Fig. 5 The relationship between the linear attenuation coefficients as a function of the material density. Both the data used for calibration (filled red squares) and the measured density data (hollow squares) is shown.
Fig. 6
Fig. 6 Material segmentation of the components of the phantom sample, via fitting of the absorption spectra peaks presented in Fig. 4(d). A single reconstructed slice through the 3D object is shown.
Fig. 7
Fig. 7 (a). Absorption histogram with Gaussian fitting corresponding to the reconstructions shown in Fig. 8 (21-40 keV). (b). The absorption histogram corresponding to the full spectrum (5-40 keV) for the mouse embryo sample.
Fig. 8
Fig. 8 The reconstructed and the segmentation result of the mouse embryo experiment taken at (ΔE = 21 to 40 keV).

Tables (1)

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Table 1 Calibration and measured density values for the phantom and corresponding linear attenuation coefficient values.

Equations (5)

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I out (x,θ)= E 0 E 1 S(E).ex p L(x,θ)μ( x,θ,t,E ) dt dE
μ( E )μ( E ¯ )      ,  E 0 E E 1
E ¯ = E 0 E 1 E.S( E ).dE E 0 E 1 S( E ).dE
I out (x,θ) I in .exp L( x,θ ) μ( x,θ,t, E ¯ ) dt I in .ex p (Rμ)(x,θ, E ¯ )
μ( r, E ¯ )= R 1 [ ln( I out (x,θ) I in ) ]
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