Dual source hybrid spectral micro-CT using an energy-integrating and a photon-counting detector

Abstract

Preclinical micro-CT provides a hotbed in which to develop new imaging technologies, including spectral CT using photon counting detector (PCD) technology. Spectral imaging using PCDs promises to expand x-ray CT as a functional imaging modality, capable of molecular imaging, while maintaining CT’s role as a powerful anatomical imaging modality. However, the utility of PCDs suffers due to distorted spectral measurements, affecting the accuracy of material decomposition. We attempt to improve material decomposition accuracy using our novel hybrid dual-source micro-CT system which combines a PCD and an energy integrating detector. Comparisons are made between PCD-only and hybrid CT results, both reconstructed with our iterative, multi-channel algorithm based on the split Bregman method and regularized with rank-sparse kernel regression. Multi-material decomposition is performed post-reconstruction for separation of iodine (I), gold (Au), gadolinium (Gd), and calcium (Ca). System performance is evaluated first in simulations, then in micro-CT phantoms, and finally in an in vivo experiment with a genetically modified p53^fl/fl mouse cancer model with Au, Gd, and I nanoparticle (NP)-based contrasts agents. Our results show that the PCD-only and hybrid CT reconstructions offered very similar spatial resolution at 10% MTF (PCD: 3.50 lp mm⁻¹; hybrid: 3.47 lp mm⁻¹) and noise characteristics given by the noise power spectrum. For material decomposition we note successful separation of the four basis materials. We found that hybrid reconstruction reduces RMSE by an average of 37% across all material maps when compared to PCD-only of similar dose but does not provide much difference in terms of concentration accuracy. The in vivo results show separation of targeted Au and accumulated Gd NPs in the tumor from intravascular iodine NPs and bone. Hybrid spectral micro-CT can benefit nanotechnology and cancer research by providing quantitative imaging to test and optimize various NPs for diagnostic and therapeutic applications.

1. Introduction

CT is a fast and powerful anatomical imaging method, but it is limited by its low contrast detectability. Contrast discrimination can be improved somewhat with dual-energy (DE) CT in which the same subject is scanned with two distinct polychromatic x-ray spectra (Johnson 2012). Unfortunately, DE CT methods are limited by standard energy integrating detectors (EIDs). EIDs record a signal proportional to the detected photon flux, weighted by the photon energy, and integrated across the entire x-ray energy spectrum. As a result, EIDs provide overlapping spectral responses which limits sensitivity (Yu et al 2009). Spectral CT using photon counting detectors (PCDs) has the potential to further improve CT image contrast and sensitivity (Iwanczyk et al 2009). PCDs compare incoming photons to adjustable energy thresholds, sorting photons into energy bins. Ideally, this yields non-overlapped spectral measurements and eliminates dark noise by rejecting all signals below the thresholds (Mccollough et al 2020). More importantly, spectral PCD-based CT is expected to provide better material separation compared to DE CT methods based on EIDs due to more flexibility in setting the energy thresholds, especially for K-edge contrast agents (Si-Mohamed et al 2019). Multi-energy PCD CT allows the measured data to be decomposed into material concentrations that, unlike CT numbers, are independent of the x-ray energy. Furthermore, relative to EID-based CT, PCD CT can provide additional benefits related to spatial resolution, radiation dose, and image noise (Willemink et al 2018).

The use of PCD CT is now being evaluated on some clinical research prototypes (Li et al 2016). Preclinical imaging represents an excellent development and testing environment for spectral PCD CT technologies with potential for clinical translation. Currently, there is one commercially available PCD-based micro-CT system, the Medipix All Resolution System (MARS Bioimaging Ltd.; Christchurch, New Zealand) (Getzin et al 2018). The MARS scanner uses the Medipix3 detector chip developed at CERN (Geneva, Switzerland) with charge-summing circuitry to compensate for charge sharing between neighboring detector pixels (Ballabriga et al 2006). Our group has also developed PCD-based micro-CT prototypes (Holbrook et al 2018, Clark et al 2019) for quantitative cancer imaging using nanoparticle (NP) based probes (Mukundan et al 2006, Moding et al 2013, Badea et al 2019). NPs tend to accumulate in tumors due to the enhanced permeability and retention (EPR) effect (Maeda et al 2000, Maeda 2001). Furthermore, NPs associated with various targeting strategies can facilitate even molecular imaging with spectral CT (Ashton et al 2018).

While the benefits of PCD CT are significant, the performance of current PCDs is limited by physical effects within the detector, such as K-escape, charge sharing, and pulse pileup (Taguchi and Iwanczyk 2013). These spectral distortions degrade the recorded spectral response of the detector and the accuracy of material decompositions. Several methods have been proposed to correct spectral distortions. For example, by modeling the imaging process, including sources of spectral distortion, maximum likelihood reconstruction (Schlomka et al 2008) or Monte Carlo methods (Maier et al 2018) can be employed to correct recorded spectra. Unfortunately, because PCD spectral distortion is non-linear, these corrections can be computationally expensive, numerically unstable, and sensitive to errors in the forward model. These drawbacks have motivated a number of data-driven approaches to compensate for spectral distortions including lookup table methods (Alvarez 2011) and methods based on artificial neural networks (Woo-Jin et al 2012, Zimmerman and Schmidt 2015, Touch et al 2016).

Another strategy for alleviating some of the PCD spectral distortions is to supplement PCD data with that from an EID. Hybrid dual source CT data acquisitions have already been performed in a clinical prototype (Yu et al 2016). However, PCD and EID data are not routinely combined for hybrid reconstruction and material decomposition. To address this issue, we have previously proposed an iterative, hybrid reconstruction technique which combines the spectral properties of PCD data with the resolution and signal-to-noise characteristics of EID data (Clark and Badea 2017).

In this study we describe the implementation and evaluation of a new dual source hybrid (PCD + EID) micro-CT system and compare its performance with PCD-only micro-CT with similar radiation dose. We hypothesize that a hybrid spectral CT system can provide higher performance in simultaneously imaging a wide variety of NP probes constructed with different K-edge materials. We illustrate the use of hybrid spectral micro-CT in a cancer study in a mouse injected with theranostic-capable gold-based nanoparticles (AuNP) (Ashton et al 2018) together with iodine (I) and gadolinium (Gd) liposomal contrast agents (Badea et al 2019). These will be separated from calcium (Ca). Preclinically, our cancer imaging results show that hybrid spectral CT can benefit both nanotechnology and cancer research by providing quantitative imaging to test and optimize various NPs for theranostics i.e. combined therapy and diagnostics (Kelkar and Reineke 2011).

2. Materials and methods

First, we introduce our dual-source, hybrid micro-CT system setup along with our data acquisition, reconstruction, and image-domain material decomposition methods. Based on these parameters, realistic simulation experiments are conducted to provide understanding, establish limits on image quality, and expectations of accuracy for material decomposition. Finally, details are provided for phantom and in vivo preclinical CT experiments using a mouse model of soft tissue sarcoma injected with three NP contrast agents based on Au, I, and Gd.

2.1. Hybrid spectral micro-CT system

Our hybrid micro-CT system contains two imaging chains (see figure 1). Each chain uses a G-297 x-ray tube (Varian Medical Systems, Palo Alto, CA) with 0.3 mm focal spot size powered by an Epsilon high-frequency x-ray generator (EMD Technologies, Quebec, Canada). For one imaging chain, we use a Dexela 1512 flat-panel EID (PerkinElmer; CsI scintillator; 1944 × 1536 pixels, 75 μm pitch). For the second imaging, we use a SANTIS 0804 CdTe-based PCD prototype developed by Dectris, Ltd. (www.dectris.com). This prototype detector has 515 × 257 pixels, with 150 μm pixel size, and four energy thresholds with ~2 keV energy resolution at 22 keV. The maximum count rate of the PCD is given as 4 × 10⁸ photons s⁻¹ mm⁻². Compared to clinical CT systems, our EID has a much smaller pixel pitch (0.075 mm vs 1.5 mm) while the PCD pitch is smaller but more comparable to those seen in clinical prototypes (0.150 mm vs 0.275 mm) (Gutjahr et al 2016).

Figure 1.

Setup of the dual-source hybrid micro-CT system.

The scanner is set up so that the subject (e.g. a mouse) is mounted vertically in a cradle and rotated through all projection angles. The source-to-detector and source-to-object distances were 820 and 679 mm for the EID imaging chain and 831 and 680 mm for the PCD imaging chain, giving a magnification of approximately 1.2 for both chains. To extend the PCD field-of-view along the z-axis and to minimize ring artifacts in our reconstructions, the subject is placed on a translational stage, and scans are performed using a helical trajectory. The PCD and EID imaging acquisitions were run simultaneously to reduce subject motion and scanning time. We note that simultaneous acquisition can increase signal from scattered radiation. Currently, we do not correct for this. Due to the small size of the mouse (~3 cm diameter) scatter is less of an issue for preclinical imaging compared to clinical CT. Data acquisition is controlled by an in-house developed sequencing application written in LabVIEW (National Instruments).

Given that sampling is performed with an x-ray source using 125 kVp with Pb (0.1 mm) beam filtration, the PCD energy thresholds are set to 25, 34, 50 and 80 keV. The first threshold (25 keV) is selected to limit spectral distortions due to charge sharing and to remain well above the detector’s noise floor (<6 keV). The next two thresholds are chosen to capture the K-edges of I (33.2 keV) and Gd (50.2 keV). Finally, the last threshold at 80 keV is selected to match the K-edge of Au (80.7 keV).

For the PCD, the x-ray source operates in fluoroscopy mode with continuous exposure, and projections are integrated for 200 milliseconds. A total number of 900 views are acquired over 1070° of continuous rotation. The EID captures 720 projections with 12.5 millisecond pulsed exposures. Sampling for both chains requires 3 min. We have recently reported on both simulations and physical phantom experiments to validate the optimal scanning kVps for DE-CT preclinical imaging of the I and Gd-based contrast agents (Badea et al 2018). For the EID chain, maximum contrast discrimination for I was found at 50 kVp with Cu filtration (0.1 mm).

We perform scans with similar radiation dose using hybrid and PCD CT only acquisitions. For hybrid scans the x-ray current for each chain was PCD: 0.5 mA and EID: 80 mA. Radiation dose was measured using an ion chamber (RadCal Corporation, model 9015). Radiation dose using these settings is 38 mGy for the EID scan and 50 mGy for the PCD scan. Thus, the radiation dose for a hybrid scan is 88 mGy. To match the hybrid CT dose with PCD-only CT, the exposure current in the PCD-only CT is increased to 1.0 mA. This current gives the closest dose (100 mGy) to the hybrid scan our hardware would allow. The low tube currents used in this work were selected to minimize dose and avoid pulse pileup effects from negatively impacting the accuracy of the PCD-only scans.

2.2. Image reconstruction

The first steps of reconstruction involve projection corrections and geometric calibration for each chain independently followed by registration of the two imaging chains. These steps are described in detail in previous work (Johnston et al 2008, Clark and Badea 2017). Geometric calibration is the process of finding system parameters which describe the relationship of the x-ray source, object, and detector. These parameters were found using an iterative search comparing projections with their re-projections using given system parameters. The system projection matrix, R, for the PCD imaging chain includes a rigid affine transform. The transform is computed in MATLAB (The MathWorks, Inc.) using the imregister function and brings the PCD data into the image space of the EID data. The transform is computed using histogram-equalization to equate the contrast between the EID and PCD imaging chains and is optimized by minimizing a mean-square-error cost metric. This transform is applied to both hybrid and PCD-only CT reconstructions for easy comparisons between scans. Projections were air and log normalized, and gaps in the detectors were interpolated to reduce ring artifacts.

For both PCD-only and hybrid CT we use the same iterative spectral CT reconstruction framework we have previously described (Clark and Badea 2017, 2018). We apply the split Bregman method with the add-residual-back strategy (Gao et al 2011) to solve the following optimization problem:

$$\text{X}=\underset{\text{x}}{\mathrm{argmin}}\frac{1}{2}\sum _e{\Vert {\text{RX}}_e-{\text{Y}}_e\Vert }_2^2+\lambda \Vert \text{X}{\Vert }_{\text{BTV}}$$ (1)

This algebraic reconstruction problem solves for the vectorized, reconstructed data, the columns of X, for each sampled threshold (detector) simultaneously (indexed by e). The reconstruction for each threshold minimizes the reprojection error (R, system projection matrix for EID, PCD data) relative to the log-transformed projection data acquired at each threshold (the columns of Y). To reduce noise in the reconstructed results, the data fidelity term is minimized subject to the bilateral total variation (BTV) measured within and between thresholds. During iterative reconstruction, BTV is reduced by the application of joint bilateral filtering (BF). To maximize redundancy between the reconstructed thresholds and, therefore, minimize noise in the material decomposition results, we employ a specific extension of joint BF known as rank-sparse kernel regression (Clark and Badea 2017). PCD and hybrid CT phantom and mouse data were reconstructed with the same isotropic voxel size of 125 μm, facilitating comparisons.

2.3. Material decomposition

Spectral decomposition is performed by solving the following linear system at each voxel in the reconstructed images:

$$\text{x}=A^{-1}\text{b}.$$ (2)

Expanding the linear system:

$$\left[\begin{array}{c}{\text{x}}_{\text{I}}\\ {\text{x}}_{\text{Gd}}\\ {\text{x}}_{\text{Au}}\\ {\text{x}}_{\text{Ca}}\end{array}\right]={\left[\begin{array}{cccc}{\text{A}}_{\text{I},\text{E}1}& {\text{A}}_{\text{Gd},\text{E}1}& {\text{A}}_{\text{Au},\text{E}1}& {\text{A}}_{\text{Ca},\text{E}1}\\ ⋮& ⋮& ⋮& ⋮\\ {\text{A}}_{\text{I},\text{Ei}}& {\text{A}}_{\text{Gd},\text{Ei}}& {\text{A}}_{\text{Au},\text{Ei}}& {\text{A}}_{\text{Ca},\text{Ei}}\end{array}\right]}^{-1}\left[\begin{array}{c}{\text{b}}_{\text{E}1}\\ ⋮\\ {\text{b}}_{\text{Ei}}\end{array}\right]$$ (3)

In this formulation, x is the least-squares solution for the concentrations of I, Gd, Au, and Ca in mg/mL in the voxel under consideration. A is a sensitivity matrix measured for I, Gd, Au, and Ca in HU/mg/mL at each energy E_i, respectively. Finally, b is the intensity of the voxel under consideration at E_i with i = 1…4 for PCD-only and i = 1…5 for hybrid CT. In the hybrid case, an extra measurement b_E5 is added corresponding to the EID data set. Non-negativity of the resultant material concentrations was enforced by orthogonal subspace projection.

2.4. Simulations

The performance and limitations of our imaging methods are investigated first using simulations for both PCD-only and hybrid CT. A limitation of PCD-based imaging is the degradation of the energy response due to physical effects including charge sharing, pulse pileup, and K-escape x-rays. This imperfect energy response causes a distortion in the measured energy spectrum which deviates substantially from the incoming x-ray spectrum. To model the spectral response of the PCD, a nuclear source (Ba-133) was used to compare ideal and measured emission lines. These measurements were used to fit a distortion model as described by Schlomka et al (2008). This model uses Gaussian peaks to describe incident and K-escape photons but does not explicitly model charge sharing or pulse pileup. The measured spectra and fitted distortion model are shown in figure 2(a).

Figure 2.

Spectral modeling for PCD and EID CT. (a) Measured and fitted PCD detector spectra (Ba-133 source). (b) Modeled spectra created using 50 kVp for the EID and 125 kVp for the PCD, including a tungsten anode and copper and lead filtration, respectively. The distorted spectrum (dashed line) represents the PCD distortion model applied to the ideal PCD spectrum (solid line). (c) Material mass attenuation curves for water, I, Gd, Au, and Ca. PCD thresholds are given by grey dotted lines at 25, 34, 50, and 80 keV. Thresholds were chosen to capture the K-edges of iodine, gadolinium, and gold.

Ideal spectral responses are calculated for the EID and PCD imaging chains using a tungsten anode along with each chain’s filters and detector materials. Acquisition settings are adjusted to mimic the experimental setup. The EID chain is modeled with 50 kVp, 0.1 mm Cu filtration, and a CsI scintillator. The PCD chain uses 125 kVp, 0.1 Pb filtration, and the expected quantum efficiency of 1 mm CdTe (Radicci et al 2014). The spectral modeling was performed using the Spektr software package (Siewerdsen et al 2004) in MATLAB (The MathWorks, Inc.). These spectra along with the degraded PCD spectra are shown in figure 2(b). The energy-dependent attenuation of water, I, Gd, Au, and Ca are shown in figure 2(c). Note that PCD energy thresholds align with the K-edges of I (33.2 keV), Gd (50.2 keV) and Au (80 keV). The spectral responses and material attenuation curves were used to generate simulated projections of digital material phantoms using a forward model (Touch et al 2016).

We have previously introduced a digital contrast and resolution phantom constructed to assess the fidelity of hybrid spectral CT reconstruction (Clark and Badea 2017). As shown in figure 3, the phantom is composed of water and contains a series of structural disks. Each disk is dominated by a single contrast material we aim to separate in vivo: I (red), Gd (blue), Au (green) and Ca (white). The materials are present in realistic concentrations for small animal micro-CT—15 mg ml⁻¹ of I, 12 mg ml⁻¹ of Gd, 8 mg ml⁻¹ of Au, and 100 mg ml⁻¹ of Ca (maximum concentrations). To assess spatial resolution, each disk contains a set of line pairs which discretely represent spatial frequencies from 0.50 to 4.00 line pairs per mm (lp mm⁻¹). To assess the trade-offs in feature detection with feature size and material concentration, a grid of spheres is included within each disk. Along the horizontal axis, the diameters of these spheres vary from 0.5 mm to 2.0 mm in increments of 0.5 mm, with some truncation due to discretization. Along the vertical axis, the concentrations of each disk’s material take on the following fractions of the maximum concentration: 1.0, 0.5, 0.25, and 0.1.

Figure 3.

Description of the digital phantom. (a) The phantom used in simulations is comprised of water containing bar patterns and spherical lesions of varying sizes and material concentrations. The bar patterns range from 0.5 to 4.0 line pairs per mm (lp mm⁻¹ ). The sphere diameters are 2, 1.5, 1, and 0.5 mm. The background cylinder is composed of water. (b) There are four levels of these patterns, one for each aqueous material examined: iodine (red), gadolinium (blue), gold (green), and calcium (white). The iodine material map is shown here. Cylindrical inserts show the separation of materials in each slice. (c) A volumetric rendering shows the layout of the phantom for all four materials in water.

To better mimic experimental image quality, steps are taken to match simulated noise to experimental reconstructions. Poisson noise is added to simulated projections by sampling a Poisson distribution with a mean equal to the number of counts recorded for each detector pixel. The simulated input photon flux is adjusted such that filtered backprojection (FBP) reconstructions of a digital water phantom reproduced the noise standard deviations seen in experimental tests (figure 4). For the hybrid simulations, we match 167 HU of noise in the EID data with 1695 photons per line integral and 149, 176, 244, and 799 HU of noise for each threshold in the PCD data with 3256 photons per line integral. For PCD-only simulations, 106, 123, 172, and 555 HU of noise per threshold was attained with 6501 photons per line integral. For PCD sets the number of photons used is the mean of the first three thresholds; the fourth PCD threshold is not used since simulated and experimental noise measurements are less consistent.

Figure 4.

Simulated noise measurements for a given flux for EID and PCD reconstructions as measured in a cylindrical water phantom with a 3 cm diameter. These are compared to experimental noise measurements in water for hybrid and PCD-only filtered backprojection reconstructions, given respectively by star and square markers. The flux used in PCD simulated experiments is the mean value found for each threshold and is shown by dashed vertical lines. Only measurements from the first three PCD thresholds were used in calculating simulated flux.

2.5. Physical phantoms

To assess the real performance of the hybrid and PCD-only CT imaging, we use the micro-CT phantom kit commercially available from Pure Imaging Phantoms (www.pureimagingphantoms.com/product/micro-ct/). Using the scanning parameters described, we scanned and reconstructed a 25 μm tungsten wire phantom designed to assess the MTF, as well as a water phantom to measure the noise power spectrum (NPS). To assess material decompositions, we scanned a 3D printed phantom containing solutions of Au (2 and 8 mg ml⁻¹), I (15, 12, 5.3 mg ml⁻¹), Gd (15 and 7.5 mg ml⁻¹), and Ca (20 mg ml⁻¹) in water. The vials are measured and linear regression, constrained to pass through the origin, is used to obtain the sensitivity matrix for the decomposition which we use in all our animal experiments. Material map measurements assessed the accuracy of the decomposition for the PCD-only and hybrid CT cases.

2.6. In vivo experiments

The in vivo animal work was conducted under a protocol approved by the Duke University Institutional Animal Care and Use Committee (IACUC). The study was performed in a carcinogen-induced and genetically engineered primary model of soft tissue sarcoma developed in p53^fl/fl mice (Kirsch et al 2007). Primary sarcomas (p53/MCA model) are generated by intramuscular delivery into the gastrocnemius of adenovirus expressing Cre recombinase (Adeno-Cre; Gene Transfer Vector Core, University of Iowa) into p53^fl/fl mice followed by intramuscular injection of 0.3 mg 3-methylcholanthrene (MCA; Sigma-Aldrich, Saint Louis, MO) at the same site (Lee et al 2019). Tumors develop approximately 8–12 weeks after induction. The imaging study was initiated after the tumor became palpable (>100 mm³).

The mouse, weighting 24.4 g, was first administered with vascular targeted NPs at day 0: RGD-AuNPs injected through the tail vein (0.125 ml, 160 mg Au ml⁻¹ in PBS). These NPs were made in-house and have been characterized in a previous study (Ashton et al 2018). When the targeted RGD-AuNPs pass through the tumor blood vessels, they bind strongly to the endothelial cells, which may prevent them from passing out of the bloodstream into the tumor tissue. Our previous study has also reported intestinal targeting (Ashton et al 2018). The same mouse was injected with liposomal gadolinium on day 1 (Lip-Gd dose: 0.4 mg Gd kg⁻¹ body weight) and with liposomal iodine on day 2 (Lip-I dose 1.32 mg I kg⁻¹ body weight) (Badea et al 2019). The I concentration in the Lip-I formulation was 110 ± 4 mg ml⁻¹, and the Gd concentration in the Lip-Gd formulation was 20 ± 3 mg ml⁻¹. This timing allowed the Lip-Gd to accumulate within tumor tissue via the EPR effect, while the Lip-I remained largely intravascular. We performed PCD-only and hybrid CT imaging immediately after the injection of Lip-I.

2.7. Quantitative evaluation

Several metrics were used to quantitatively evaluate the results of PCD-only and hybrid CT. This includes separate analysis of the EID component of hybrid CT to better understand performance-limiting factors. The EID data was iteratively reconstructed separately prior to evaluation. Measurements were made in each energy channel and then averaged across energy channels.

• 1
  Root-mean-square error (RMSE) was computed to assess the accuracy of the material decomposition maps:

  $$\mathrm{RMSE}=\sqrt{\frac{1}{\mathrm{n}}{\sum }_{\mathrm{y}=1}^{\mathrm{n}}{\left({[\mathrm{C}]}_{\mathrm{y}}-{[\text{C}]}_{{\text{y}}_0}\right)}^2},$$ (4)

  where y indexed the voxels, n was the total number of voxels, [C]_y was the measured concentration of I, Gd, Au, or Ca in voxel y, and ${[\text{C}]}_{{\text{y}}_0}$ was the expected concentration of the same material in voxel y.

• 2
  Modulation transfer function (MTF) was measured to assess spatial resolution in the reconstructed results. In simulation we computed the modulation transfer (MT) at each spatial frequency sampled by the bar patterns in the digital phantom:

  $$\mathrm{MT}(\mathrm{a},\mathrm{b})=\frac{|\mathrm{a}-\mathrm{b}|}{\mathrm{a}+\mathrm{b}}.$$ (5)

The variables a and b correspond with average attenuation measurements taken from the expected locations of a set of contrast-enhanced lines and from the corresponding, expected gaps between the lines, respectively. Prior to the MT calculation, the expected attenuation of water was subtracted from each measurement. Any negative values of MT were set to zero. Given a vector of 32 independent MT measurements per energy taken in the digital phantom (n_l = 32; 8 sets of line pairs, 4 disks; figure 3), a Gaussian modulation transfer function (MTF) was fitted to match the observed measurements under a least-squares penalty:

$$\mathrm{MTF}\left({\text{l}}_i,\sigma \right)=\exp \left(-\frac{{\text{l}}_i{}^2}{2{\sigma }^2}\right),$$ (6)

$$\sigma =\underset{\sigma }{\arg \min }{\sum }_{i=1}^{{\text{n}}_l}{\left(\mathrm{MTF}\left(1_i,\sigma \right)-{\text{n}}_i\right)}^2.$$ (7)

The standard deviation of the MTF, σ, is the only free parameter. The vector l contains the spatial frequencies in lp/mm for each corresponding measurement.

For the experimental characterization, we have scanned and reconstructed a 25 μm tungsten wire phantom designed to assess MTF as defined in (Kayugawa et al 2013), where the MTF is defined as the Fourier Transform of the integrated in-plane image around the wire. We note that the experimental MTF describes more than the imaging system due to the non-linear reconstruction method employed. Thus, it is used for comparing similarly reconstructed images rather than as an absolute measure of system resolution.

• 3Noise power spectrum (NPS) was acquired for PCD-only and hybrid CT data of either a simulated or real water cylinder (3 cm diameter) using the data acquisition parameters described above.

  Post-reconstruction, 64 × 64 × 64 voxel volumes of interest were extracted from the periphery of the water phantom and at three different z positions. These are used to measure the NPS for each PCD threshold and the EID data (Siewerdsen et al 2014). A total of 96 blocks were analyzed and averaged per threshold.

• 4
  Detectability index, D, was computed to assess the visibility of the spherical lesions within the digital phantom under a non-prewhitening observer model (Gang et al 2017):

  $$\text{D}=\sqrt{\frac{{\left({\sum }_{\mathbf{j}}{\left({\text{MTF}}_{3\text{D}}(\mathbf{j},\sigma )\text{W}(\mathbf{j})\right)}^2\right)}^2}{{\sum }_{\mathbf{j}}\text{NPS}(\mathbf{j}){\left({\text{MTF}}_{3\text{D}}(\mathbf{j},\sigma )\text{W}(\mathbf{j})\right)}^2}}.$$ (8)

  Specifically, the detectability index was computed over a cubic region of interest defined around each spherical lesion (side length: 32 voxels; no overlap between regions) in the material maps post decomposition. All voxels within each cubic region were indexed by the Cartesian offset vector j. Specific to our implementation of the detectability index calculation, MTF_3D denotes the 1D MTF extrapolated to 3D in an isotropic fashion based on the Euclidean distance of each voxel center from the origin of each region of interest. We defined the task function, W, as the discrete Fourier transform of the same cubic region of interest in the expected phantom. The local NPS was approximated as the power spectral density of the residuals computed between the experimental results and the expected results within each cubic region of interest. Detectability was computed in the material decomposition domain.

3. Results

The simulation reconstructions for our digital phantom are shown in figure 5. We compare the hybrid and PCD-only reconstructions at similar dose, each matching experimental dose. Note that the added EID image shows visibly higher enhancement for the iodine line pairs and spheres than the PCD images. Following iterative reconstruction, the noise standard deviation measured near the center of the phantom (HU, lower left corner) is similar for PCD-only and hybrid CT (~30 HU). Our multi-channel iterative reconstruction algorithm significantly reduces the noise at the highest energy thresholds (compared to an analytical FBP reconstruction the noise is reduced by ~95%), while preserving spectral contrast.

Figure 5.

Simulated phantoms reconstructed using PCD with EID data (hybrid) and PCD-only data for filtered backprojection (a) and iterative reconstructions (b). Noise is markedly reduced after iterative reconstruction, particularly for high PCD thresholds. Of the four material sections, a 2D axial slice through the iodine disk is shown here. Noise was measured as the standard deviation of the CT numbers in the water between material sections and is shown in yellow. The EID reconstruction shows higher contrast for iodine and gold than the PCD images.

Image quality metrics for the simulated PCD-only and hybrid CT iterative reconstructions are shown in figure 6. The quantities shown are measured in each energy channel and averaged. The EID data from the hybrid set has been independently reconstructed and analyzed to demonstrate performance of each component of the hybrid system. The resolution of the PCD-only and hybrid reconstructions, given by the MTF, have been estimated by the line pair patterns. The MTF plots demonstrate that spatial resolution in the PCD data is nearly identical between the PCD-only and hybrid CT reconstructions (3.9 lp mm⁻¹ at 10% MTF), while being slightly lower for the hybrid EID reconstruction (3.6 lp mm⁻¹ at 10% MTF). The lower resolution measured for the EID chain is likely the result of undersampling (720 EID projections angles compared to 900 for PCD) and stronger regularization when the EID data is reconstructed alone. Regularization strength is scaled automatically based on noise estimates within our reconstruction framework. The noise properties of the PCD and hybrid sets are also very similar.

Figure 6.

Image quality metrics from simulated reconstructions. (a) The MTF demonstrates that resolution between the PCD and hybrid sets is nearly identical at 10% (EID: 3.62 lp mm⁻¹, PCD: 3.90 lp mm⁻¹, and hybrid: 3.92 lp mm−1 ). (b) The noise properties of PCD and hybrid sets are also very similar.

In figure 7 we focus first on reconstructed voxel values for the four materials of interest (I, Gd, Au, Ca) measured in the material inserts (see figure 3(b)). Plots of mean values which provide the sensitivity in HU/mg/mL are shown in figures 7(b) and (c). Each material follows an expected enhancement trend with peaks for I in the 34 keV energy bin, for Gd at 50 keV, and for Au at 80 keV, matching their K-edges. The associated sensitivity values are very similar for the PCD-only and the PCD component of the hybrid cases. EID values in the hybrid set show the highest sensitivity for I and Au compared to PCD reconstructions. The condition number of the PCD-only material sensitivity matrix, following unit normalization of the material sensitivity vectors, is 34. This increases to 47 for the hybrid case, indicating the expected redundancy between the EID and PCD measurements when the number of spectral channels increases relative to the number of materials. The results of post-reconstruction decomposition using the measured sensitivity values are shown in figure 7(d). Axial slices through different sections of the phantom are shown, corresponding with each target material. Material maps from the hybrid data show less contamination between materials, particularly for calcium at the phantom’s periphery and for gold in the phantom’s center.

Figure 7.

Material sensitivity measurements and material decomposition maps. (a) Measurements were made inside the material inserts (yellow box) at each slice of the phantom and averaged. (b) Values measured in the PCD reconstruction show peaks in value around expected K-edges (I: 34 keV, Gd: 50 keV, and Au: 80 keV). (c) The hybrid data shows a similar trend with the addition of high sensitivity iodine and gold imaging with the EID channel. (d) Material decompositions of I, Gd, Au, and Ca for hybrid and PCD-only reconstructions.

A quantitative assessment of the decompositions is given via the distribution of measured concentrations for each material vial (figure 8(a)) and by the RMSE of the entire material maps relative to the expected material maps (figure 8(b)). Hybrid reconstruction reduces RMSE values by an average of 37% across all material maps compared to PCD-only. We note that the recovered concentration values in the material inserts are very similar, but over the whole phantom, hybrid CT appears to be more accurate (lowest RMSE) for all materials.

Figure 8.

Evaluation of material decompositions for the simulated phantom. (a) The distribution of voxels within the material inserts (figure 7(a): yellow box). Box boundaries and whiskers indicate quartiles of the data; outliers are not shown. Calcium is plotted with a separate axis to allow all measurements to be shown. (b) RMSE values as measured against the expected material maps. Values were computed globally within each material map, i.e. inside and outside the material patterns. (c) Detectability index for each material in hybrid and PCD-only reconstructions. The index was calculated in the decomposed material maps using the spherical lesions marked in figure 3(a).

The detectability indices are shown in figure 8(c). The indices have been zero-centered by subtracting the mean value of the combined hybrid and PCD data. Blue values are lower than the mean whereas yellow and red are higher. The highest indices for all cases are found by the largest and highest concentration spheres. The hybrid data provides higher on average values for I, Au, and Ca, while Gd has better detectability without the addition of EID data. High detectability values for I and Ca are sometimes shown for smaller diameter spheres. This is attributed to an artifact or cross-contamination.

Figure 9 presents image quality measures taken in physical image quality phantoms for each imaging case. As in the simulated data, the metrics shown are measured for each energy channel and averaged. Both hybrid and PCD-only reconstructions yield nearly identical 10% MTF values (PCD: 3.50 lp mm⁻¹; hybrid: 3.47 lp mm⁻¹) as well as similar NPS profiles. The EID data presents lower resolution with a 10% MTF value of 3.34 lp mm⁻¹. The lower EID resolution is attributed to undersampling vs the PCD chain and scintillator blur at the detector. The EID data also presents higher NPS profiles than either PCD or hybrid reconstructions.

Figure 9.

Image quality metrics for PCD, EID, and hybrid reconstructions. The PCD and hybrid data are shown as an average across all energies. (a) The MTF was measured using a wire phantom. It shows that the hybrid and PCD transfer functions are very similar. (b) The NPS was measured in a water phantom and demonstrates similarly that the PCD and hybrid reconstructions have similar noise properties.

Figure 10 displays reconstructions and material decompositions for the vial phantom containing water, I, Gd, Au, and Ca. The condition number of the hybrid material sensitivity matrix is 82. For PCD-only data this increases to 761. The higher condition number in the PCD-only case is due to the loss of a distinct I K-edge in the PCD measurements, which is supplemented by high sensitivity EID measurements in the hybrid case seen in figure 10(c). The iodine K-edge was distinct in our simulations (figures 7(b) and (c)), highlighting deficiencies in our PCD spectral model with regard to physical phenomena such as K-escape and charge sharing. We note successful separation of our four basis materials in both PCD-only and hybrid reconstructions. PCD-only material maps demonstrate higher material map contamination compared to hybrid maps, particularly for I and Ca maps (yellow arrows). The mean values of recovered concentrations are, however, very similar (figure 10(d)). Lower than expected attenuation values for the highest concentration of Au (8 mg ml⁻¹) are due to precipitation out of the field of view during imaging.

Figure 10.

Reconstruction and material decomposition of the vial phantom. (a) Reconstruction (EID) of the phantom shows the distribution and concentrations of material vials. (b) Decomposed material maps for PCD and hybrid reconstructions. (c) Material measurements in the tomographic images show sensitivity to each K-edge material. (d) Box plots showing material values within each vial compared to the known concentration of each vial. Inaccuracies in the vial marked ‘Gold 8’ may be due to the precipitation of gold within the vial, pulling precipitate out of the field of view.

Finally, in figures 11 and 12, we present results of our cancer imaging experiment. As shown in figure 11(a), after iterative reconstruction, the reconstructed images for both PCD-only and hybrid CT cases show similar image quality with different contrasts depending on their energy. The images show the presence of contrast agents and bone (Ca), however enhancement values can be ambiguous in any of the single energy bins. The material decomposition results shown in figure 11(b) provide clear separation of the target materials. As confirmed by the calibration vials present in the images, we can separate I (red), Gd (blue), Au (green), and Ca (white). In the PCD-only case the Ca vial appears to be contaminated with iodine. The hybrid CT data shows less contamination present than the PCD-only data, particularly in the I and Ca maps. The RGD-AuNPs show uptake in the intestines, and the cradle, made of PLA plastic, decomposes mostly into the Gd map (hybrid) or the Gd and Au maps (PCD-only).

Figure 11.

Results of in vivo cancer imaging study with I, Gd, and Au NP contrast agents. (a) Iterative reconstruction of the PCD-only and hybrid data for each energy sample of a tumor-bearing mouse. Enhancement is show in the tumor and intestines where gold and gadolinium have accumulated. Vascular enhancement is accomplished via iodine. This slice shows enhancement in the tumor, intestine, and blood vessels (yellow labels). (b) Material maps of the same mouse and axial slice. Individual material maps are shown for I, Gd, Au, and Ca; maps are also shown overlaid to better view spatial relationships between maps. Material map contamination is evident, particularly in the PCD-only data, in the calibration vials (yellow arrows). Bone appears in the hybrid Ca map with greater clarity than in the PCD-only case (red arrows).

Figure 12.

2D coronal slices comparing the CT image (hybrid scan, PCD: 25 keV threshold) with the PCD and hybrid material decompositions. In this orientation the tumor is clearly visible as contrast has accumulated along the tumor boundary. The hybrid material maps show clear improvements in reducing material contamination between channels. Maximum intensity projections (MIPs) show increased contrast and vasculature within the tumor.

In figure 12, we present the same data but in a coronal orientation both for a single slice and using maximum intensity projection over 40 slices. As expected, the three contrast agents and Ca are separated in the decomposition, indicating an accumulation of Gd (blue) and Au (green) in the tumor due to the EPR effect (Maeda et al 2000, Maeda 2001). Vasculature is enhanced due to I (red) in the blood pool. The hybrid images are much less contaminated than in the PCD-only case. The result is striking particularly in the MIP images.

4. Discussion and conclusions

We have implemented a hybrid dual-source micro-CT system and compared its performance to PCD-only CT for the similar dose both in simulation and real experiments. The results confirm that our hybrid CT system provides similar spatial resolution and NPS characteristics compared to PCD-only CT. By adding the EID data and co-reconstructing it with the PCD data, we have achieved less contamination in material decomposition maps. We attribute this improvement to the high sensitivity of our EID chain to photons above the K-edge of iodine, since it uses a CsI scintillator. By contrast, our CdTe-based PCD has relatively poor sensitivity to iodine due to overlapping signals recorded from low-energy source photons, Cd and Te K-escape photons, and charge sharing between neighboring pixels. Combining this PCD and EID data with a hybrid reconstruction and decomposition approach, as demonstrated in this work, already allows visually better iodine and calcium separation (figures 10–12). Practically, however, we acknowledge that to perform spectral CT imaging with higher fidelity, our hybrid approach will need to be combined with explicit methods to improve against spectral distortions and to numerically constrain our solution based on the EID data. We believe that the recent generation of ‘one-step’ reconstruction methods, which are well suited to combining data with different underlying spectral models when jointly reconstructing material maps, will be the next logical extension of our hybrid reconstruction methods (Mory et al 2018). Here, we have established a baseline for the combined reconstruction of PCD and EID data at similar dose, which we intend to build upon in this future work.

In concluding this work, we further acknowledge a practical limitation of our current approach and provide additional context for the future applications. First, a notable limitation of our approach is unmitigated cross-scatter of x-rays between the EID (pulsed exposure) and PCD (continuous exposure) imaging chains during the hybrid data acquisition. For in vivo, preclinical imaging, where data acquisition times are commonly on the order of a minute or more, temporal coherence and registration between the EID and PCD data recommends acquiring both data sets simultaneously. However, the spatial resolution and dose constraints on preclinical imaging make the use of anti-scatter grids infeasible, while hardware and software constraints on our data acquisition make it difficult to perform staggered, pulsed exposures for both imaging chains. Therefore, with our current system, we were unable to avoid cross-scatter during imaging. Regarding future applications, we believe research into hybrid CT data acquisition and reconstruction methods is crucial, as combined EID and PCD CT systems will likely provide the smoothest path to clinical translation: systems capable of performing EID imaging protocols clinicians are familiar with, while slowly introducing fundamentally new data acquisition and reconstruction modes based on PCDs into clinical workflows.

Preclinically, our cancer imaging results prove that spectral micro-CT can benefit both nanotechnology and cancer research by providing an imaging method that can help test and optimize the development of various NP-based contrast agents. As shown here, we are able to separate three NP-based contrast agents simultaneously used in the same experiments. One of these contrast agents is molecularly targeted (RGD-AuNP), while the other two (Lip-I and Lip-Gd) are blood pool. We have recently shown that using RGD-AuNP targeting of the vasculature also locally enhances radiation therapy dose and can improve local delivery of liposomal chemotherapeutics (Ashton et al 2018). Such approaches using combination therapies are of high interest in cancer research. Future theranostics studies will undoubtedly benefit from improved spectral CT imaging.