CT Reconstruction Using Spectral and Morphological Prior Knowledge: Application to Imaging the Prosthetic Knee

CT Reconstruction Using Spectral and Morphological Prior Knowledge: Application to Imaging the Prosthetic Knee Wojciech Zbijewski, J. Webster Stayman, Abdullah Muhit, John Yorkston, John A. Carrino and Jeffrey H. Siewerdsen Abstract Imaging in the presence of prosthetic implants presents a notoriously difficult challenge to CT reconstrucion. Such hardware is made of alloys that are highly attenuating (e.g., Co-Cr-Mo) and impart severe degradation in image quality due to photon starvation, beam hardening, etc. An important clinical example is in the proliferation of total knee replacement, increasing the need for technologies capable of imaging in the presence of knee prostheses. The usefulness of CT in follow-up to knee replacement surgery is, however, extremely limited due to severe artifacts associated with the implant. Recent developments in likelihood-based CT reconstruction offer a potential solution to the problem. In particular, we exploit the fact that exact models of the shape and composition of prostheses are often available. A framework is proposed that extends earlier work [1,2] on known component reconstruction (KCR) to account for polyenergetic beam hardening and apply to the case of a large, highly attenuating object such as a knee implant. The proposed algorithm uses a polyenergetic object model to simultaneously estimate the unknown background density volume and the position and orientation of the known implant. We test the approach in studies emulating a recently developed, dedicated cone-beam CT scanner for extremities imaging. The results indicate substantial reduction of image artifacts and significant improvements in the visualization of areas adjacent to the implant. The KCR approach is found to outperform traditional filtered-backprojection and penalizedlikelihood methods that do not account for the implant model or polyenergetic object attenuation. The method suggests promising new capability to assess implant integrity, loosening, and tissue disease (osteolysis and soft-tissue derangement). Index Terms CT Reconstruction, Extremities Imaging, Implant Imaging, Metal Artifact Reduction, Penalized- Likelihood Estimation. I. INTRODUCTION The prevalence on knee replacement surgery is rapidly increasing, with some predictions suggesting over a million replacements per year by 2015 [3]. Consequently, there is a growing need for imaging technologies that enable follow- This work was supported in part by academic-industry partnership with Carestream Health (Rochester NY) and by NIH 2R01-CA-112163. W. Zbijewski, J. W. Stayman, A. Muhit and J. H. Siewerdsen are with the Department of Biomedical Engineering, Johns Hopkins University, Baltimore, MD 21212 USA (phone: 410-955-1305; fax: 410-955-1115; e- mail: wzbijewski@jhu.edu). J. Yorkston is with Carestream Health, Rochester, NY. J. A. Carrino is with Department of Radiology, Johns Hopkins University, Baltimore, MD up of knee prostheses, which requires reliable visualization in the direct vicinity of the implant. X-ray CT would be a compelling candidate thanks to its excellent spatial resolution and numerous existing applications in orthopedic radiology. However, its application to implant imaging remains a major and largely unsolved challenge due to severe artifacts caused primarily by beam hardening and photon starvation. An example knee implant is shown in Fig. 1(A), along with CT images of a prosthetic knee in (B) and (C), clearly demonstrating the magnitude of the associated artifacts. (CT images are courtesy of E. Fishman, MD, [4]). As illustrated in Fig. 1(D), typical alloys used in manufacturing knee prostheses (Co-Cr-Mo, consisting of ~60% Co, ~30% Cr and ~5% Mo) are significantly more attenuating to diagnostic x-rays than other common highly x-ray opaque materials, such as Ti or cortical bone. As a result, x-ray beams traversing even a short pathlength (~1-2 mm) in such alloys suffer not only from severe photon starvation but also significant beam hardening. This is shown in Fig. 1(E), where 110 kvp x-ray spectra are attenuated by 2 mm of cortical bone, Ti, and Co-Cr-Mo, with the spectrum attenuated by Co-Cr-Mo exhibiting the most significant shift to high energies. Fig. 1. (A) Example of a knee implant: DePuy Sigma [5]. Such prostheses present a large volume of highly x-ray attenuating alloy, often Cr-Co-Mo containing ~60% Cobalt, and thus pose a major challenge for x-ray CT. Artifacts associated with the presence of knee implants in CT scans are shown in (B) and (C) [4]. In (D), x-ray attenuation of Co-Cr-Mo (solid line) is compared to Titanium (dotted line) and cortical bone (dashed line). Significant loss of photon flux and substantial beam hardening are observed even for short path lengths through the alloy, as shown in (E), where x-ray spectra attenuated by 2 mm of Co-Cr-Mo (solid line), Ti (dotted line) and cortical bone (dashed line) are compared to the unattenuated 110 kvp beam. Page 434

These extremely strong attenuation characteristics of the Co-Cr-Mo alloy, combined with the large size of the implants [Fig. 1(A)] lead to large areas of missing data (zero or near-zero counts) and low signal-to-noise ratio in the projections. They are thus extremely challenging for conventional metal artifact reduction methods, such as those based on interpolation in the projection domain [6]. While the development of CT-compatible implants is an area of ongoing research, the ability to image heavy metallic prosthetics would be of significant immediate benefit to a growing population of patients. The ability to image the prosthetic knee could be especially beneficial in the context of recently introduced dedicated cone-beam CT (CBCT) systems for extremities, such as the prototype shown in Fig. 2 [7]. Providing novel capabilities (e.g., load-bearing imaging), these systems promise to significantly expand the scope and quality of CT applications in orthopedics. Increasing prevalence of knee replacement implies that the ability to image in the presence of implants will be an important aspect of broad utilization of such dedicated devices. Moreover, the open system architecture of the prototype in Fig. 2 provides an ideal platform for development of novel reconstruction algorithms. monoenergetic x-ray beam, which may be sufficient when polyenergetic effects in the object under consideration are relatively weak. However, as illustrated above, the heavy alloys used in knee implants exhibit significant beam hardening, and thus the KCR algorithm needs to be expanded to polyenergetic beams and energy-dependent attenuation. A number of approaches to include spectral effects in penalized-likelihood reconstruction have been proposed [8-10]. Here, we combine the algorithm of Elbakri et al. [9] with KCR and apply the resulting method to imaging in the presence of a knee prostheses. A. Forward Model II. METHODS We assume an energy-integrating x-ray detector with uniform detection efficiency and write the measured projection value for detector element i: (1) where is the total photon flux for pixel i, is the x-ray energy, is the spectral density of the x-ray beam, is the mass-attenuation coefficient of the object, is the object density, and x is the spatial dimension. We express the line integral in (1) for a voxelized object following Elbakri et al. [9], where we assume that the object consists of K materials (massattenuation of k-th material given by ) and that the fraction of k-th material in voxel j is known and denoted by. The mean signal at pixel i is then: Fig. 2. The recently developed flat-panel cone-beam CT system for extremities imaging. The scanner allows for scanning in both a weightbearing, standing (A) configuration and in a non-weight-bearing, sitting (B) configuration. Studies in cadaveric specimens indicate soft-tissue visibility comparable to conventional CT (C) and exquisite spatial resolution (D). Images in (C) and (D) were obtained from a single 80 kvp, 9 mgy acquisition using soft-tissue and bone reconstruction kernels, respectively. One of the unique features of implant imaging is that the knowledge of their shape and composition is often available (e.g., from CAD models). If properly leveraged in the reconstruction, such prior knowledge can be used to alleviate the effects of missing data and low signal-to-noise ratio. This is especially true if combined with a penalizedlikelihood (PL) approach, which properly accounts for projection noise, such as in the recently proposed Known Component Reconstruction (KCR) [1,2]. In KCR, the position of the known components is estimated jointly with the unknown background image (i.e., the underlying anatomy) using an alternating joint optimization method. This algorithm has been shown to yield excellent, near artifact-free reconstructions in imaging of pedicle screws under conditions of severe photon starvation. KCR has been previously developed under the assumption of a where is the system matrix. By assuming that the fraction is known throughout the volume, the formulation in (2) allows the likelihood-based objective function for image reconstruction to have only one unknown per voxel, namely the density (as opposed to a number of unknowns equal to the number of energy bins without this simplification). Elbakri et al. [9] assumed that the material fractions are known from segmentation of an initial FBP reconstruction. Analogous to KCR, we will now further parameterize the object as a superposition of an unknown background image, given by density distribution, and a known implant volume undergoing an arbitrary transformation (registration). The implant transformation is characterized by an unknown vector (e.g., rotation and translation). This leads to the following substitution in (2): where m is a mask representing the support of the implant. (2) (3) Page 435

B. Reconstruction algorithms Equation (2) with the line integral given by (3) provides a relationship between mean measurement at pixel i and the object volume. To estimate the background density and the parameters of the implant transformation, we invoke a Poisson noise model and write the loglikelihood: (4) The unknowns can be estimated by maximizing the penalized-likelihood estimator: (5) where is a regularization term to penalize noisy images (e.g., a pair-wise quadratic penalty). The estimator in (5) provides a general form that encompasses a variety of reconstruction object models (mono and polyenergetic, with and without the known components). Different iterative algorithms are used to solve (5), depending on the exact choice of the reconstruction object model. The simulated projection data in this study were obtained using the full spectral model. We consider the following cases: PL-Mono: if the x-ray spectrum is assumed to be monoenergetic ( and no implant is included in the reconstruction model, (5) becomes the familiar penalized-likelihood estimator for monoenergetic x-ray CT, which is solved iteratively as in [11]. KCR-Mono: in this case, the spectrum is still assumed monoenergetic, but the implant volume is included in the model, as in (3). Since polyenergetic effects are neglected, the implant attenuation is assumed equal to its attenuation at 90 kev, chosen to reflect the beam hardening effect of the Co alloy for the 110 kvp beam. The KCR algorithm of Stayman et al. [1,2] is used to solve this objective by an alternating minimization of and. PL-Poly: when the reconstruction uses a polyenergetic object model, but without knowledge of the implant volume, the segmentation-based polyenergetic PL algorithm of Elbakri et al. [9] is employed. Two cases are considered: PL-Poly-Single, where the segmentation ( in (2)) assumes that all the voxels are composed of soft-tissue (represented by of muscle) and PL-Poly-Full with oracle segmentation into soft tissue, bone, and implant. Obtaining such segmentation from the initial FBP corrupted by artifacts caused by the prosthesis may be difficult; thus, PL-Poly-Full provides an upper bound on the performance of PL-Poly for such data. KCR-Poly: the full model of (3) is assumed. We estimate the unknown background density volume and the position of the known implant using a polyenergetic model of x-ray transmission. The same update equation as in PL- Poly is employed, but with the terms depending on the forward projection computed using the separation of the volume into the density map and the registered implant volume, as in (3). This extension of the KCR methodology (aside from application to extremity imaging) is the main novel contribution of the current work. Similar to PL-Poly, segmentation needs to be provided to constrain the estimation of Note however that the segmentation of the implant is no longer required in KCR since the a priori knowledge of the implant is now part of the object model. Two approaches are tested: a simple segmentation assuming that all voxels consist of soft tissue (KCR-Poly- Single) and oracle segmentation into soft tissue and bone (KCR-Poly-Full, again providing the upper bound on algorithm performance). The initial studies were performed under the assumption that the implant transformation W is fixed - i.e., that the implant location is known. The minimization over in (5) is therefore omitted. While this is a simplification, the results presented in [1,2] indicate that the registration step is extremely robust for a wide range of conditions, including the presence of multiple known objects. We therefore expect that inclusion of this step in KCR-Poly (ongoing work) will not alter the conclusions. C. Phantoms, simulations, and reconstruction settings Fig. 3. (left) Phantoms used in the study. The knee implant (pink overlay) was simulated by replacing bone voxels with the Co-based alloy. Note the circular soft-tissue contrast inserts in the joint spaces and inside the condyles. (center) FBP reconstruction of the phantom with no implant, illustrating the magnitude of beam hardening due to bone. (right) Beam hardening artifacts are efficiently removed with the polyenergetic PL algorithm of Elbakri et al. [10] This algorithm was combined with Known-Component Reconstruction (KCR) [1,2] to yield a polyenergetic algorithm robust to the presence of implants. Fig. 3 (left) demonstrates the phantoms used in this study. Two slices through segmented knee volumes from the Virtual Population dataset [12] were used. The base materials included four soft tissues (skin, fat, muscle, and cartilage), bone marrow, and cortical bone. Circular soft tissue contrast inserts (4 mm radius) were placed inside the joint space and inside the condyles; each insert was made from the same material as its background, but at a 1.2x higher density. The knee implant was simulated by replacing a region of bone voxels with a Co-Cr-Mo alloy, shown as pink overlay in Fig. 3. Following the basic geometry of such implants (Fig. 1), all bone voxels were replaced with the alloy in the distal region of the condyles (top row of Fig. 2); in the proximal region of the condyles (bottom row) only the inner and anterior bone surfaces were replaced with the alloy. The geometry of the extremities CBCT scanner (Fig. 2) was simulated. For simplicity, a single slice, fan-beam Page 436

acquisition was considered in this preliminary study. The SDD was 550 mm, and the SAD was 430 mm; there were 384 detector pixels at 0.776 mm pitch. A circular orbit with 360 projections at 1 o increment was assumed. The voxel size was 1 mm. Polyenergetic projections were simulated using Eq. (1) with 10 6 photons per detector element. The x- ray spectrum for a 110 kvp beam with 2 mm Al and 0.2 mm Cu filtration (as in the prototype scanner) was computed using SPEKTR [13]. Reconstruction by the PL and KCR methods above involved the same x-ray spectrum, pixel size, and voxel size as in the simulation. 200 iterations with 60 subsets were performed in each case. The regularization parameter β was varied to achieve similar resolution in all reconstructions. Matched forward- and back-projector based on separable footprints [14] were implemented in a CUDA-based library for nvidia GPUs. somewhat alleviated when a likelihood-based algorithm is used (PL-Mono). This demonstrates the value of including a noise model that penalizes low-count projections in the reconstruction. Nevertheless, the areas surrounding the implant are still plagued by artifacts. Including knowledge of the implant morphology (KCR-Mono) is not sufficient to reduce the artifacts because of the mismatch between the monoenergetic model of implant attenuation and the polyenergetic nature of the measured data. III. RESULTS Fig. 4. Monoenergetic reconstructions (from polyenergetic projection data) in the presence of a knee implant. (top) FBP, showing severe streaks due to photon starvation and beam-hardening in the presence of the implant. (center) PL-Mono reconstruction, demonstrating a degree of improvement in artifacts caused by poor photon statistics; however, significant streak artifacts are persistent. (bottom) KCR-Mono reconstruction, where the implant (pink overlay) was modeled using its attenuation at 90 kev. Neglecting spectral effects results in little or no improvement over PL- Mono. FBP and PL-Poly reconstructions of the two phantoms without the prostheses are shown Fig. 3 (center and right), demonstrating the strength of PL-Poly in addressing beam hardening from common materials such as cortical bone. In Fig. 4, reconstructions of polyenergetic projections of the phantoms with the implant included are compared for monoenergetic algorithms. The FBP images are severely compromised by streak artifacts. These artifacts are Fig. 5. Polyenergetic PL and KCR reconstructions. (top) PL-Poly reconstruction of the implanted knee, where object segmentation consisted of only soft tissue. The single-component model is not sufficient to suppress streak artifacts. (second row) PL-Poly with oracle segmentation that included soft tissue, bone, and the implant. While significantly improved from either PL-Mono or PL-Poly-Single, the image still suffers from artifacts. Such artifacts are largely removed with KCR-Poly-Single (third row), which applies knowledge of the material and morphological characteristics of the implant and estimates the unknown underlying anatomy simultaneously with the position of the known implant. (bottom) KCR-Poly-Full gives further improvement by including segmentation of bone and soft tissue. In Fig. 5, reconstruction algorithms that employ a polyenergetic object model are compared for the same projection data. A simple model of object attenuation used in PL-Poly-Single (all voxels consisting of soft-tissue) fails to produce significant reduction in artifacts. Even when the implant is included in the initial segmentation (PL-Poly- Full), artifacts persist in the vicinity of the prosthesis. They are significantly reduced with KCR-Poly-Single (third row in Fig. 5), as evident by the improved visualization of the Page 437

contrast inserts. The artifacts are further diminished when bone is also included in segmentation (KCR-Poly-Full, bottom row on Fig. 5). While traditional algorithms attempt to extract information from data with very few or zero counts (in effect a data null-space), KCR uses a priori implant knowledge to better condition the problem and select solutions from within potential null-spaces. Note also that KCR-Poly-Single achieves excellent artifact reduction while not requiring a complete segmentation of the object, which is likely difficult to obtain in the presence of artifacts caused by the prosthesis. IV. DISCUSSION A novel reconstruction algorithm (KCR-Poly) that combines the knowledge of the material and morphological characteristics of the prosthesis with a polyenergetic model of x-ray propagation was introduced. The algorithm was shown to yield excellent results in reduction of severe image artifacts around such implants in conventional reconstructions. The success of KCR-Poly owes to both the use of a priori knowledge of the implant and the account of the polyenergetic nature of object attenuation, as indicated by the persistence of artifacts for the monoenergetic version of KCR. Ongoing work includes inclusion of the implant registration step as part of the joint optimization [1,2] in KCR, extension to segmentation-free polyenergetic reconstruction [10], and testing in real data, including an analysis of the effects of scatter [15]. The algorithm will be tested on the prototype extremities scanner in realistic scenarios and extended to other applications involving large metallic implants. REFERENCES [1] Stayman J. W., Otake Y., Prince J. L., Siewerdsen J. H., "Likelihoodbased CT Reconstruction of Objects Containing Known Components," Int l Mtg. Fully 3D Image Recon., (2011). [2] Stayman J. W., Otake Y., Prince J. L., Siewerdsen J. H., "Model- Based Tomographic Reconstruction of Objects Containing Known Components", IEEE Trans. Med. Im., in press (2012). [3] Kim, S., "Changes in Surgical Loads and Economic Burden of Hip and Knee Replacements in the US: 1997 2004," Arthritis & Rheumatism (Arthritis Care & Research), 59(4):481 488 (2008). [4] Fishman E. K., "Case 3563: Total Knee Replacement," www.ctisus.com. [5] DePuy Companies, "Sigma Rotating Platform Knee," www.depuy.com. [6] Kalender W. A., Hebel R., Ebersberger J., "Reduction of CT artifacts caused by metallic implants," Radiology, 164:576 577 (1987). [7] Zbijewski, W., De Jean P., Prakash P., Ding Y., Stayman J. W., Packard N., Senn R., Yang D., Yorkston J., Machado A., Carrino J. A., Siewerdsen J. H., "A dedicated cone-beam CT system for musculoskeletal extremities imaging: Design, optimization, and initial performance characterization," Med. Phys. 38(8):4700-4713 (2011) [8] De Man, B., Nuyts, J., Dupont, P., Marchal, G., Suetens, P., "An iterative maximum-likelihood polychromatic algorithm for CT," IEEE Trans. Med. Im., 20(10):999-1008 (2001). [9] Elbakri, I. A., Fessler, J. A., "Statistical image reconstruction for polyenergetic X-ray computed tomography," IEEE Trans. Med. Im. 21(2):89-99 (2002). [10] Elbakri, I. A., Fessler, J. A., " Segmentation-free statistical image reconstruction for polyenergetic X-ray computed tomography with experimental validation, Phys. Med. Biol., 48(15):2543-78 (2003) [11] Erdogan, H., Fessler, J. A., "Ordered subsets algorithms for transmission tomography," Phys. Med. Biol. 44:2835-51 (1999). [12] IT'IS Foundation, "The Virtual Population," www.itis.ethz.ch. [13] Siewerdsen, J. H., Waese, A. M., Moseley, D. J., Richard, S., Jaffray, D. A., " Spektr: A computational tool for x-ray spectral analysis and imaging system optimization," Med. Phys., 31:3057 (2004). [14] Long, Y., Fessler, J. A., Balter, J. M., "3D forward and backprojection or X-ray CT using separable footprints," IEEE Trans. Med. Im., 29:1839-50 (2010). [15] Zbijewski, W., Sisniega, A., Vaquero, J. J., Packard, N., Senn, R., Yang, D., J. Yorkston, Carrino, J. A., Siewerdsen, J. H., Dose and Scatter Characteristics of a Novel Cone Beam CT system for Musculoskeletal Extremities, Proc. of SPIE Medical Imaging (2011). Page 438