Simultaneous imaging of multiple contrast agents

Simultaneous imaging of multiple contrast agents using full-spectrum micro-CT D. P. Clark1, M. Touch1,2, W. Barber3, C. T. Badea1,2,* Center for In Vivo Microscopy, Department of Radiology, 2 Medical Physics, Duke University, Durham, NC 27710 3 DxRay, Northridge, CA 91324

1

ABSTRACT One of the major challenges for in vivo, micro-computed tomography (CT) imaging is poor soft tissue contrast. To increase contrast, exogenous contrast agents can be used as imaging probes. Combining these probes with a photon counting x-ray detector (PCXD) allows energy-sensitive CT and probe material decomposition from a series of images associated with different x-ray energies. We have implemented full-spectrum micro-CT using a PCXD and 2 keV energy sampling. We then decomposed multiple k-edge contrast materials present in an object (iodine, barium, and gadolinium) from water. Since the energy bins were quite narrow, the projection data was very noisy. This noise and further spectral distortions amplify errors in post-reconstruction material decompositions. Here, we propose and demonstrate a novel post-reconstruction denoising scheme which jointly enforces local and global gradient sparsity constraints, improving the contrast-to-noise ratio in full-spectrum micro-CT data and resultant material decompositions. We performed experiments using both calibration phantoms and ex vivo mouse data. Denoising increased the material contrast-to-noise ratio by an average of 13 times relative to filtered backprojection reconstructions. The relative decomposition error after denoising was 21%. To further improve material decomposition accuracy in future work, we also developed a model of the spectral distortions caused by PCXD imaging using known spectra from radioactive isotopes (109Cd, 133Ba). In future work, we plan to combine this model with the proposed denoising algorithm, enabling material decomposition with higher sensitivity and accuracy. Keywords: spectral CT, micro-CT, split Bregman method, material decomposition, bilateral filtration *[email protected]; phone +1 919 684-7509; http://www.civm.duhs.duke.edu/

1. INTRODUCTION Spectral CT provides information about tissue composition by measuring the material-dependent attenuation of x-ray photons at different energies. The simplest implementation of spectral CT, namely dual-energy (DE) CT, scans the same subject with two different x-ray spectra, allowing separation of two materials. We have demonstrated preclinical, functional imaging applications of DE micro-CT involving the separation of iodine and calcium or iodine and gold, including classification of atherosclerotic plaque composition [1], non-invasive measurement of lung [2] and myocardial perfusion [3], and the classification of tumor aggressiveness and therapy response in the lungs [4] and in primary sarcoma tumors [5, 6]. Several factors limit further development and adoption of spectral CT imaging protocols. Chief among these are the radiation dose associated with scanning the same subject more than once and the relative insensitivity of polychromatic x-ray spectra to energy-localized, material-specific changes in x-ray attenuation (e.g. kedges). Photon-counting x-ray detectors (PCXD), currently under intensive development, show great potential for spectral CT imaging. These detectors bin incoming photons based on their energy, acquiring detailed spectral information and potentially enabling the decomposition of several k-edge materials from a single scan. We have developed a micro-CT system based on a PCXD and used it to acquire spectrally dense measurements. This technique, which sweeps the energy thresholds of the PCXD to sample the full energy spectrum for each detector element and projection angle, is called fullspectrum CT [7, 8]. As a technique, full-spectrum CT overcomes the hardware limitations of a fixed number of energy bins and allows for post-reconstruction rebinning of detected counts, at the expense of some increase in projection acquisition time. Reconstructed full-spectrum projection data from our imaging system provides high spectral resolution (~3 keV full width at half maximum, FWHM, at 30 keV); however, the data is generally very noisy due to low photon Medical Imaging 2015: Physics of Medical Imaging, edited by Christoph Hoeschen, Despina Kontos, Proc. of SPIE Vol. 9412, 941222 · © 2015 SPIE · CCC code: 1605-7422/15/$18 · doi: 10.1117/12.2081049

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counts at hig gh and low en nergies relativee to the sourcee spectrum. Thhe projection ddata can also bbe affected by spectral distortions caaused by detecttor-side phenom mena such as charge c sharing and pulse pileeup [7]. In [8], a pen nalized weightted least squarres approach was w used to reeduce noise annd to produce reconstructionn results consistent with the expectted attenuation n curves of thee present mateerials (iodine, acrylic, waterr, and gold). H Here, we present a mu uch more generral post-reconsttruction denoissing scheme foor spectral CT ddata that can bbe applied regaardless of material com mposition, spectral distortionss, and differencces in noise leevel between ennergy bins, maaking it largelyy system and applicatiion independen nt. This approaach is an extenssion of our preeviously publisshed denoising scheme basedd on joint bilateral filtrration [9] with h additional prrovisions to preserve k-edgee contrast whhile enforcing spectral continnuity. In tandem with the developmeent of this gen neral denoising g tool, we are ddeveloping a sppectral model specific to ourr PCXD, with the ultim mate goal of combining c them m for model-baased, sparsity- constrained iteerative reconsttruction. We haave built our spectral model using experimental e data d acquired from 109Cd annd 133Ba radioaactive sources. To validate bboth our denoising sch heme and the fidelity f of our spectral s distorttion model, wee summarize thhe results of experiments usinng digital and physical material calibrration phantom ms, as well as exx vivo mouse ddata.

2. 2 METHOD DS CT system usess a CdTe-based d PCXD (DxR Ray Inc., Northhridge, CA) wiith 4 energy thhresholds. The detector Our micro-C has 4 rows of o 64 pixels, eaach with a 1.0 0 mm x 1.4 mm m pixel size. T The PCXD haas been integraated into our m micro-CT imaging set-u up with a polychromatic x-raay tube. The in ncoming beam is attenuated w with 5.6 cm off PMMA, 0.1 ccm of Al, and .01 cm of o Cu. In full-sspectrum CT sccanning mode,, the x-ray souurce exposes coontinuously annd the thresholdds of the PCXD are swept s during the exposure to separate the t x-ray phottons into mulltiple, contiguous energy bins. Our acquisitions used u 70 kVp, 0.6 0 mA, and 3.66 sec/exposu ure at each anggle, and 90 anggles over a 1800° arc. A full-sspectrum CT scan witth 90 projectio ons took appro oximately 330 seconds to aacquire (vs. ~223 seconds forr a single scann with 4 hardware-bassed energy bin ns). The projecttion data consiisted of 2 keV V bins from 0 too 120 keV. Duue to the large distance between the detector d and x--ray source (~7 70 cm), a paralllel beam approoximation was used for reconnstruction. Each energy bin was reco onstructed usin ng filtered bacck projection (FBP) with a R Ram-Lak frequuency filter. P Post-reconstrucction, we averaged thee 4 slices alon ng to z-axis to o create a sing gle axial CT sslice, a 2D im mage with 1x1 mm pixels. S Since the individual en nergy bins weree narrow, the projection p data was very noissy, resulting inn noisy reconstrructions (Fig. 11). Apart from noise, th he projections were also inacccurate due to the t spectral disstortion. In thee next sections,, we address booth noise (Section 2.1) and spectral distortion d (Secttion 2.2). 0.931

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Fig. 1: Full-sp pectrum CT data acquired for a physical p calibratiion phantom. (A A) System-calibraated and log-trannsformed sinogrrams from 22 keV to 52 2 keV acquired using a 70 kVp p spectrum. (B)) FBP reconstruuctions based oon sinogram datta. Note the noiise in the sinograms and d reconstructionss at the lowest an nd highest energies.


2.1 Denoising Post-reconstruction denoising was used to improve the regularity within and between the reconstructed data for each energy bin. The objective of the denoising algorithm is summarized by the following optimization problem: arg min ‖μ μ

μ

λΓ μ .

X‖

(1)

Given the input, reconstructed spectral CT data, , the aim is to find a denoised version of the data, , which best minimizes the cost specified by . for the CT data while preserving data fidelity. The data is organized in columns, with each column representing the reconstruction of a single energy bin. To compensate for the large differential in noise between energy bins, the data fidelity is weighted by one over the normalized variance of the noise measured in each bin, allowing proportionally stronger regularization for nosier energy bins (Fig. 2). A common choice for when working ‖ ‖ where is a finite difference operator. with piecewise constant signals is intensity gradient sparsity: Often, is chosen to be total variation. Here, we instead use bilateral total variation (BTV) which is reduced by applying bilateral filtration (BF) [10, 11]: ∑

BF: μ

,

Range kernel: R ,

(2)

,

exp

∑

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,

∑

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∑

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.

(4)

Equation 2 describes BF as a locally adaptive convolution operation, replacing the attenuation at coordinate x with a weighted average of neighboring voxels indexed by y. The weights are based on geometric distance in space (domain weights, D(y)) and photometric distance in intensity (range weights, R(x,y)) from the pixel being filtered. The range kernel (Equation 3) is modeled as Gaussian, with the filtration strength determined by the noise level measured in the image, σ, and a constant scaling factor, m. BTV is then defined as the product of the BF weights and the image gradients (Equation 4). Consistent with the objective of BF (“edge-preserving, smoothing,” [12]), BTV assigns near-zero weights to small image gradients (constant intensity) and to large image gradients (edges), penalizing gradients of intermediate magnitude (noise). Because BF abstracts image intensities to probabilistic weights, range weights computed using several images representing the same image structure can be multiplied at each spatial location, constructing a joint range kernel: R ,

R

,

…R

,

exp

∑

,

(5)

The resulting joint kernel is then used to filter each component image (images c = 1 to c = N, the total number of images). We have previously described and illustrated the application of joint BF in great detail [9]. For denoising fullspectrum CT data (Fig. 2), we use two forms of filtration in tandem: d d

,

,

BF BF

μ

μ μ

(6)

:μ :μ

(7)

where denotes the component image being filtered and the corresponding column of in which the filtered result is stored. Global filtration (Equation 6) jointly filters each component image, , with an additional reconstructed image , which is presumed to have low noise. Global filtration exploits the fact produced from all available projection data, that all spectral CT images represent the same underlying image structure, and, therefore, must adhere to the same gradient sparsity pattern. Local filtration (Equation 7) extends the filtration domain to include g phases before and after the target phase (with mirroring at the edges of the spectrum). Resampling along the spectral dimension (see [5]) combined with the action of BF results in smoothing along the spectral dimension. The edge-preserving nature of bilateral filtration prevents oversmoothing of k-edge features which are adequately differentiated from noise. Fig. 2 outlines the proposed denoising algorithm which combines noise weighting for the data fidelity term (Steps 1, 8) with global and local filtration (Steps 3-6). Iteratively solving for the minimum residual intersection of the global and local sparsity constraints subject to weighted data fidelity finds a denoised solution that is spectrally contiguous up to the


k-edge featurres with match hing image strructure across all componentt spectral reconnstructions, roobustly precondditioning the data for material m decom mposition (Step p 9). The algorithm solves thee original cost function (Equuation 1) using the split Bregman fram mework and th he add-residuall-back strategy [13, 14]. Fig 2: IIterative denoisinng of full-spectrrum CT data with joint bilaterall filtration andd the split Breegman method. (1) A diagonall covariance m matrix is construucted by measurring the noise levvel of each inpuut data set (assum mes noise indepeendence betweenn energy bins). (2) Initializationn of the input ddata, µ0, and thee data regulariization residualls, v. (3-4) Ennforcing gradientt sparsity with gglobal and local bilateral filtratioon. (5-6) Regulari rization residuall updates. (7) Data fidelity residual update w with relaxation cconstant δ. (8) Soolution update sttep with regularizzation constantss λ1 and λ2. I dennotes the identityy matrix. Converggence of the alggorithm is declarred when the chhange in magnituude of the residdual updates fa falls below a sppecified thresholld (~5 iterationns). (9) Post-rreconstruction m material material decompoosition with nonn-negativity connstraint on the m concentrrations, C. M is a system calibraated material sennsitivity matrix ((Section 2.3).

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2.2 Detectorr distortion modeling m A limitation of PCXD-baseed imaging usiing CdTe can be b the degradaation of the eneergy response due to physicaal effects like charge sharing s between detector elem ments, pulse piileup, and enerrgy loss due too K-escape [7]. This energy rresponse degradation causes c a distorrtion in the meeasured energy y spectrum whiich deviates froom the incomiing x-ray specttrum. To compensate for f this distortion, a detectorr response funcction (DRF) w was experimenttally determineed following thhe model first describeed in [15]. The DRF model in ncludes two Gaussian peaks: one at the inccident photon’ss energy and one at the K-escape eneergy of CdTe.. An additionaal background term models a lower-energgy tail. Hence, the DRF, , , at energy U resu ulting from inccident photons of energy E in nteracting with the detector caan be modeledd as: R U, E

c E

√

exp

√

eexp

B U, E

(8)

and d represent the energy sprread of the inccident photon ppeak and the K K-escape peak,, respectively. Ee is the where average escaape photon eneergy of the deteector material (~25 keV for CdTe). The baackground term m, B(U,E), deppends on both the meaasured and inccident photon energy. B(U,E E) is modeled as the producct of the measuured energy, U U, and a constant c3(E E) for U

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