Cone‐Beam CT image contrast and attenuation‐map linearity improvement (CALI) for brain stereotactic radiosurgery procedures

Abstract A Contrast and Attenuation‐map Linearity Improvement (CALI) framework is proposed for cone‐beam CT (CBCT) images used for brain stereotactic radiosurgery (SRS). The proposed framework is tailored to improve soft tissue contrast of a new point‐of‐care image‐guided SRS system that employs a challenging half cone beam geometry, but can be readily reproduced on any CBCT platform. CALI includes a pre‐ and post‐processing step. In pre‐processing we apply a shading and beam hardening artifact correction to the projections, and in post‐processing step we correct the dome/capping artifact on reconstructed images caused by the spatial variations in X‐ray energy generated by the bowtie‐filter. The shading reduction together with the beam hardening and dome artifact correction algorithms aim to improve the linearity and accuracy of the CT‐numbers (CT#). The CALI framework was evaluated using CatPhan to quantify linearity, contrast‐to‐noise (CNR), and CT# accuracy, as well as subjectively on patient images acquired on a clinical system. Linearity of the reconstructed attenuation‐map was improved from 0.80 to 0.95. The CT# mean absolute measurement error was reduced from 76.1 to 26.9 HU. The CNR of the acrylic insert in the sensitometry module was improved from 1.8 to 7.8. The resulting clinical brain images showed substantial improvements in soft tissue contrast visibility, revealing structures such as ventricles which were otherwise undetectable in the original clinical images obtained from the system. The proposed reconstruction framework also improved CT# accuracy compared to the original images acquired on the system. For frameless image‐guided SRS, improving soft tissue visibility can facilitate evaluation of MR to CBCT co‐registration. Moreover, more accurate CT# may enable the use of CBCT for daily dose delivery measurements.


| INTRODUCTION
The Leksell Gamma Knife Icon (Elekta AB, Stockholm, Sweden) integrates a cone-beam CT (CBCT) image guidance system 1 with an irradiation unit to enable frameless stereotactic radiosurgery (SRS). 2 The CBCT system provides the stereotactic reference, which together with co-registration of the planning image volume and the CBCT volume gives the transformation mapping of the planned isocenter positions to stereotactic coordinates. Since the X-ray beams cannot penetrate through the frame fixation on the treatment bed, a half cone geometry is used in the Icon system, which maximizes the field-of-view by aligning the X-ray tube parallel and close to the frame plane. 3 The half cone geometry results in more pronounced shading and cone-beam artifacts than the regular full cone geometries used in other commercial systems.
In the context of frameless SRS, improving CBCT image quality is highly motivated since stereotactic localization is based on MRI-to-CBCT co-registration. Although the commercial system uses a robust co-registration algorithm, the ability of the clinician to visualize soft tissue around the location of the brain lesions is crucial in order to verify target location. Additionally, if improvements in CT# accuracy could be made the CBCT images could also be used to calculate the daily delivered doses. Unlike in CT where a calibration phantom is commonly used to map the measured CT# to the electron density of the tissues, 4 in the native CBCT images this process is prohibited due to the resulting artifacts that are present. Improvement of the sources of artifacts in cone-beam CT has been an area of active research within the past few years, with dedicated frameworks being researched to correct for: shading artifact, 5 scatter, 6-8 and system blur. 3 A major area of focus of CBCT image quality improvement has been scatter reduction, 9 with several model-based approaches 7,8 including a dedicated cone-beam breast CT model. 7 For the Icon CBCT system, additional challenges such as a pronounced beam hardening, a bow-tie filter and the presence of metal (in the case of frame-based SRS) coupled with the half cone geometry, and limited acquisition span make it necessary to add to the robust model-based approaches such as by Zhao et al. 8 and propose a dedicated framework that works for the SRS system.
The purpose of the present study is to develop and evaluate a computationally efficient CBCT contrast improvement and attenuation-map correction framework for point-of-care Icon CBCT images without modifying the clinical workflow, i.e., no extra calibration measurements are required. The proposed framework is tested with CatPhan phantom and clinical brain images.

| ME TH ODS
The proposed framework called CALI (Contrast and Attenuationmap Linearity Improvement) considers three important sources of the non-linearity in CBCT images, namely scattering, beam hardening, and blurriness. To improve the spatial resolution of the CBCT images, a high spatial resolution iterative reconstruction algorithm called simultaneous deblurring and iterative reconstruction (SDIR) was proposed, which estimates the blurriness in the image domain. 3 SDIR improves the spatial resolution, preserves edges, and improves the visibility of soft tissues in the brain. 3 For example, some brain folds and structures, such as ventricles, become clearly visible in the images reconstructed with SDIR. However, as is common in CBCT, SDIR reconstructed images still suffer from image inhomogeneity/ non-linearity, which is mainly caused by scatter contamination and beam hardening.
The CALI framework consists of pre-processing, iterative reconstruction, and post-processing phases. In the pre-processing phase, a low frequency artifact correction (LFAC) algorithm and a beam hardening correction (BHC) method are applied to the projection images.
The pre-processed projections are then reconstructed with SDIR. 3 In the post-processing phase, a dome artifact correction (DAC) is applied on the images reconstructed with SDIR. In the case of using fixed frames during the treatment, a metal artifact reduction (MAR) algorithm will be used with the LFAC algorithm. All of the acronyms used in the present manuscript are defined in Table 1. BHC plays a fundamental role in reducing CT# errors. In the CALI framework, LFAC algorithm not only improves the homogeneity of the images, but also, makes the application of the proposed BHC algorithm possible. The BHC uses an attenuation value mapping on the basis materials, which depends on the accuracy of the reconstructed attenuation values. The reconstructed attenuation-map in CBCT images usually contains large errors, mainly due to scatter contamination and flood image errors from detector saturation. The LFAC reduces the reconstruction error, enabling the BHC algorithm to effectively use the linear attenuation mapping. After reconstructing the pre-processed projections with SDIR, due to the application of a bowtie filter in the Icon, the images suffer from dome artifact, which should be corrected to achieve higher CT# linearity. This is done with the proposed DAC algorithm.
The only required a priori in the proposed framework is the X-ray spectrum. In this study we used a Monte-Carlo simulated T A B L E 1 Summary of abbreviations used in the manuscript. spectrum. However, the X-ray spectrum can also be estimated from the X-ray projections of a known object. 10,11

2.A | Low frequency artifact correction
The proposed LFAC algorithm, as shown in Fig. 1, includes segmentation of the brain images reconstructed with regular filtered back projection (i.e., Feldkamp method, 12 "FDK") into bony and soft tissue (brain white/gray matter) regions. A thresholding is used for this segmentation task, where the threshold values are estimated from the histogram of the images. 13 The segmentation information is fed into a polychromatic forward projector with the attenuation and mass density values of the soft tissue (brain) and bone calculated from the tables provided by NIST (https://www.nist.gov/pml/X-ray-mass-atte nuation-coefficients). The forward projector is a 3-D ray-driven method that uses bilinear interpolation and contains two loops over material and energy, respectively, to consider the energy dependent values of the X-ray attenuation. The X-ray spectrum is estimated by Monte Carlo simulation of the Icon X-ray source, using Elekta's proprietary Monte Carlo simulator (Pegasos) which uses PENELOPE at its core. 14 This can also be done by an iterative spectrum estimation algorithm. 10,11 The difference between the measured projections and the ideally calculated projections shows variations in different regions, caused by different factors including scattered photons and the saturation of the calibration gain/flood images used to normalize the measured projections. This difference is filtered with a smoothing total variation (TV) denoizing method, 15 to preserve the larger edges and to remove the remaining structures. The smoothed projection differences are then subtracted from the original measured projections. Reconstructing the corrected projections, it could be seen that the errors of the reconstructed attenuation map are highly reduced. As can be seen in Fig. 1, the cone-beam artifact increases the error at the top of the head. To determine the region affected by the cone artifact, we first set all the voxels in the entire image volume to one. We subsequently forward and back project the unity image volume and threshold voxels that differ from one by more than 30%. Those voxels define the coneartifact region that we subsequently interpolate. We used a TV inpainting algorithm for interpolation as it is robust to error and noise in neighboring pixels. 16 Since the LFAC involves forward projecting the image, the artifact propagates into the synthetic projections and would be back-projected into the image domain introducing additional streak artifacts. Therefore, in LFAC the removal and subsequent interpolation prevents propagation of that cone artifact error to the next step.

2.B | Beam hardening correction
The output of LFAC is fed into a BHC algorithm. This BHC algorithm is similar to previously described work, 17  : where f(x) is the reconstructed attenuation map. Note that since the pixel values larger than basis material attenuation values are not possible using the basis materials, we try to choose materials with larger attenuation as any one of the basis materials and the larger values are capped. This would be corrected in subsequent iterations. Three materials are used in this paper, namely bone, soft tissue, and air.
Then, the measured projections will be corrected by iteratively adding the difference between the simulated monochromatic (i.e., g n;i and g n;i ¼ PT i f n for i th basis material n th iteration with P being the forward cone beam X-ray projection) and polychromatic projections calculated from the mapped basis materials is the normalized spectrum of the Icon X-ray tube. Using these notations the updated projections at the (n+1) th iteration would be: where I C is the output of the shading correction. The results of preliminary experiments indicated that three iterations are enough to achieve adequate BHC results, after which the difference between , becomes sufficiently small.

2.C | Dome artifact correction
Because of the use of bowtie filter in Icon's CBCT system, the Xray spectrum has different energy distribution across the detector, which affects the attenuation values at each pixel of the image.
Therefore, after the BHC step, the attenuation value of the reconstructed images are larger at the center of the image than the pixels with the same material content but away from the center.

2.D | Metal artifact correction
Although the main goal of Icon CBCT system is the application of frameless planning and treatments, some of the patients are still treated using the fixed frames. This causes the familiar metal artifacts in the images. To reduce the metal artifacts in these cases the following algorithms are proposed. The projections are first processed with a method similar to "MAR" to remove the effect of metal. 18 In this step the images are reconstructed with FDK and a threshold is applied to identify the metals in the image. 13 The metal images are forward projected and used to mask the projections affected by metal. The masked projections are replaced with data interpolated from its neighbor's values using the aforementioned inpainting algorithm. 16 The proposed CALI framework is then applied on the processed projections. Then, to add the metal information, a The workflow of this correction is depicted in Fig. 2. the present study was the same source as the study described in previous SDIR work. 3 To accelerate the reconstruction, all methods are implemented in-house with CUDA to run on an NVIDIA GPU (GTX970, CUDA7.5),

2.E | Experimental studies
and are compiled with Matlab as MEX files. The natively reconstructed images from the Icon system were generated using filtered backprojection (FBP) with a standard FDK approach 12 and are denoted as "FDK" throughout the Results section. For more details on the reconstruction implementation, the readers are referred to previous SDIR work. 3      Improving image quality of CBCT continues to be an area of active development, in particular for intraoperative imaging in imageguided interventions. [19][20][21] Improved image quality could increase utility of such systems by facilitating soft tissue surgeries, or enabling repeat imaging at sufficiently low dose, and extending applications to minimally invasive pediatric surgery. 19 In the present manuscript, we have demonstrated that the proposed CALI framework adds to the line of CBCT image quality improvement methods currently available. Additionally, CALI may be useful in situations requiring the use of injected contrast agent in order to improve the visibility of soft tissue structures such vessels and ventricles.

| RESULTS
It is worth noting that our LFAC workflow (Fig. 1) follows a similar workflow to that present by Zhao et al., who developed a robust scatter correction model. 8 It should also be noted that the idea of the proposed LFAC algorithm is similar to a shading reduction method proposed by Wu et al. although their shading reduction is applied on the reconstructed images whereas we apply corrections on the projections. 5 Due to the particulars of the Icon CBCT system's geometry and construction (compact, half cone, half-scan, pronounced bow-tie filter) the output of the LFAC must subsequently undergo further beam hardening correct (BHC) and our so-called dome-artifact correction (DAC) in order to truly realize improved image homogeneity. As noted in the Methods, our BHC is similar to the method proposed by van Gompel et al., 17 so it worth noting that the overall CALI framework assembles elements individually similar to published methods, but with modifications and tailoring to our point-of-care system. The half cone geometry used for the Icon system has previously been used in breast 3-D X-ray imaging but is a new geometry for this application with a larger field of view.
Despite the unfavorable geometry the proposed method showed substantial improvement in visibility of low contrast details and the homogeneity of the images. For instance, the visibility of the ventricles in the brain images and the low contrast acrylic inserts in Cat-Phan phantom were improved. Our measured CNR values for the acrylic insert were comparable to those found in the literature for modern and advanced CBCT systems. For example, Stankovic et al 22 report that the native CNR for the acrylic insert on a commercial system is approximately two compared to 1.8 (for Icon FDK), which can be improved by a factor of up to five compared to our factor of four using a combination of software and hardware corrections proposed by the authors. Similarly, the CT# linearity and CT# accuracy were improved in the sensitometry module of the CatPhan phantom and were comparable to CT# linearity and integrity for head and neck sized phantoms. 22 The attenuation-map of the images reconstructed from shading corrected projections (i.e., processed with LFAC) were very similar to the image processed with LFAC, BHC, and DAC all together. This is due to the fact that the bowtie filter reduces the effect of the beam hardening. 23 As a result, the LFAC phantom. The shading and BHC algorithms require the X-ray spectrum. Although we have used Monte-Carlo in the present work, the spectrum can also be estimated from phantom measurements using spectrum-based algorithms. 10,11 Although the CALI component is relatively fast, the SDIR algorithm is computationally expensive, as we discuss in our previous work. 3 We have implemented SDIR on GPU to reduce calculation time of this component. Regarding image artifacts, although the SDIR+CALI corrected images include residual dome and beam hardening artficats, the main point is that the inclusion of CALI reduces these artifacts with respect to FDK or SDIR-only, as shown in Fig. 4 with respect to linearity. With respect to registration with MRI, the accuracy of mutual information (used in Gamma Knife) is unaffected by the window-level used for either modality. The key issue is in how a clinician assesses the resulting co-registration and there are two broad approaches for this: (a) using a bone window for CBCT or (b) using a narrower soft tissue window. If we use a bone window for our CBCT images the skull width is well-visualized and co-registration assessment involves aligning skull edges between the two modalities. If using a soft tissue window, the bone and adjacent tissue become saturated and appears thicker (even though it is not), but the evaluation of the co-registration would focus on soft tissue areas such as the ventricles. We have ongoing work investigating the co-registration of MRI with various CBCT algorithms. Although outside the scope of the present manuscript to comment on, the production of CBCT images with improved soft tissue CNR and uniformity will only benefit clinicians in their ability to assess co-registration quality.

| CONCLUSION
Despite the challenging CBCT geometry of the Icon commercial system, we have demonstrated that the proposed CALI method improves image quality and CT# accuracy. The CALI framework can readily be adopted to other CBCT systems, which is the scope of future work by our group. In the context of frameless SRS, the image quality improvements afforded by CALI can facilitate evaluation of MRI-to-CBCT image co-registration, as well as dose calculations using daily CBCT.

ACKNOWLEDG MENTS
The authors are grateful to Dr. Jean Régis and Antoine Dorenlot from University Hospital La Timone, Marseille, France, for their assistance in providing raw data in advance of us getting our system.