Impact of a novel exponential weighted 4DCT reconstruction algorithm

Abstract Purpose This work characterizes a novel exponential 4DCT reconstruction algorithm (EXPO), in phantom and patient, to determine its impact on image quality as compared to the standard cosine‐squared weighted 4DCT reconstruction. Methods A motion platform translated objects in the superior–inferior (S‐I) direction at varied breathing rates (8–20 bpm) and couch pitches (0.06–0.1) to evaluate interplay between parameters. Ten‐phase 4DCTs were acquired and data were reconstructed with cosine squared and EXPO weighting. To quantify the magnitude of image blur, objects were translated in the anterior–posterior (A‐P) and S‐I directions for full‐width half maximum (FWHM) analysis between both 4DCT algorithms and a static case. 4DCT sinogram data for 10 patients were retrospectively reconstructed using both weighting factors. Image subtractions elucidated intensity and boundary differences. Subjective image quality grading (presence of image artifacts, noise, spatial resolution (i.e., lung/liver boundary sharpness), and overall image quality) was conducted yielding 200 evaluations. Results After taking static object size into account, the FWHM of EXPO reconstructions in the A‐P direction was 3.3 ± 1.7 mm (range: 0–4.9) as compared to cosine squared 9.8 ± 4.0 mm (range: 2.6–14.4). The FWHM of objects translated in the S‐I direction reconstructed with EXPO agreed better with the static FWHM than the cosine‐squared reconstructions. Slower breathing periods, faster couch pitches, and intermediate 4DCT phases had the largest reductions of blurring with EXPO. 18 of 60 comparisons of artifacts were improved with EXPO reconstruction, whereas no appreciable changes were observed in image quality scores. In 18 of 20 cases, EXPO provided sharper images although the reduced projections also increased baseline noise. Conclusion Exponential weighted 4DCT offers potential for reducing image blur (i.e., improving image sharpness) in 4DCT with a tendency to reduce artifacts. Future work will involve evaluating the impact on treatment planning including delineation ability and dose calculation.

offers the ability to characterize tumor motion and therefore reconstruct its trajectory over a patient's breathing phase. 6 However, current 4DCT reconstruction approaches have some limitations.
Geometric inaccuracies may arise from the interplay between tumor and couch motion. This could cause instances during data acquisition where the gantry is rotating slower than a specific anatomical change, where the temporal resolution is no longer sufficient to represent patient anatomy. 7 It has been shown that as the temporal window is widened to collect more projection data, volumes will become more distorted, along with an increasing amount of image artifact. 8 Furthermore, including too much projection data has been shown to blur moving anatomy, 9 thus leading to poor definition at object boundaries. 7 In this study, we evaluate the impact of applying, in phantom and patient, an exponential weighting factor to the current standard of care (i.e., cosine-squared weighting factor) in order to generate an exponential 4DCT reconstruction algorithm ("EXPO"). Early work presented by Shen et al. suggested that using EXPO yielded improved volume estimation and reduced motion artifact in 4DCT. 10 Our work builds upon these preliminary results by presenting a detailed theoretical basis for the algorithm, evaluates its performance in controlled phantom experiments with a large variety of acquisition parameters, and then performs a quantitative and qualitative comparison between conventional and EXPO 4DCT reconstructions for a patient cohort, with the overarching goal of evaluating the potential of using EXPO reconstruction to sharpen the boundaries of moving targets for radiation therapy.

2.A | Exponential reconstruction
One of the main challenges in 4DCT is the ability of the scanner to capture an adequate amount of data during the entire respiratory cycle to accurately represent patient anatomy in each phase. When using a helical scan, it is imperative that the pitch factor be set low enough so that the entire scan volume, including the voxels at the edge of the field of view (FOV), are illuminated throughout the respiratory cycle. 11 Figure 1 (left) illustrates the distance (Z m ) along the axis of couch motion (z-axis) that is visible to the collimators at the edge of the FOV, which can be written as: where R S is the source to CT isocenter distance and COLL is the collimator width. Couch velocity can be expressed as where RT is the rotation time and PF is the pitch factor. Therefore, the transit time (TT) at which the voxel traversing the z-axis at the edge of the FOV remains within the FOV is determined by For the entire FOV to be illuminated throughout the breathing cycle, the TT for the voxel traversing along the line Z m must be greater than the breathing period (BP). This then specifies a condition for the BP: In terms of PF, this condition becomes when the PF is too large, this condition is violated, and the reconstruction software widens the temporal gate to ensure that the minimum criteria for the number of sinogram projections is met to accurately reconstruct the pixels at the edge of the FOV. The increase in the time window (T w ) for reconstruction can be derived using: where T w is temporal increase in seconds. A minimum of π (half-rotation) projections are required to accurately reconstruct a CT image.
When eq. (3) is satisfied, the reconstruction system can utilize π projections centered at each phase point and temporal resolution will be optimized. When the gating window is broadened because the pitch is not low enough, some pixels will be reconstructed from more than π projections. For these pixels, this represents redundant data, which may degrade temporal resolution as described in detail by Manzke et al. 12 To minimize this impact on the temporal window, a cosine-squared weighting factor is commonly used and, when applied to the ith projection, is given by 12 : where I t = total projections and I m = mid-phase point. However, using cosine-squared weighting employs a gradual downward slope that causes projections far from the reconstruction point (in a temporal sense) to contribute significantly to image reconstruction.
Thus, we propose to multiply the cosine-squared weighting factor with an exponential weighting function: This sharper slope ( Fig. 1, right) is expected to improve the magnitude of image blurring by minimizing the weighted contribution of outside projections. Thus, it is our hypothesis that by implementing the exponential weighting factor into the 4DCT reconstruction, image sharpening and edge enhancement will be achieved relative to the conventional cosine-squared reconstruction technique. Additionally, it is expected that the attenuation of redundant data will cause an increase in image noise.

2.B | Phantom research methods
Phantom experiments were carried out using a commercially avail- All raw 4DCT data were reconstructed using both the standard cosine squared and experimental (exponential) weighting factors.
Image subtraction images for each phase were then generated to elucidate intensity and boundary differences. Maximum intensity projection images (MIPs), minimum intensity projections (minIPs) and average CTs (AVG-CTs) were generated using in-house MATLAB (version R2014b) software previously described. 14      The pneumatic belt is placed around the anterior to posterior excursion surrogate, whereas the objects of varied densities, shapes, and sizes were placed on the platform moving in the superiorinferior direction using a sinusoidal waveform. Right: Difference maps of phantom experiment between cosine squared and exponential (EXPO) reconstruction algorithm for several acquisition parameters. Difference maps were calculated using cosine squared less EXPO. F I G . 5. Retrospective reconstructions using the standard of care (cosine squared) and experimental (exponential, or EXPO) reconstruction algorithms for four different lung cancer patient 4DCTs for the endinhale breathing phase (0%). Difference maps were calculated using cosine-squared less EXPO and boxes indicate the location of the tumor regions treated. The largest improvement was observed for Patient 4, where EXPO significantly decreased the use of incorrect projections in the phase reconstruction and increased lesion conspicuity substantially.

3.B | Results for human subject studies
F I G . 6. Qualitative consensus grading (3 observers) for the presence of liver dome artifacts using the following image grading scale: 1. negligible impact, 2. minor impact without relevance for clinical evaluation, 3. major impact causing clinical evaluation to be difficult, and 4. significant impact rendering image not suitable for clinical use. Abbreviations: EI = end-inhale, EE = end-exhale, MIP = maximum intensity projection, minIP = minimum intensity projection. every case and had regular/periodic waveforms). Figure 6 also highlights that image artifact scores were equivalent between images reconstructed with cosine squared and EXPO for 70% (42 of 60) of the datasets. As expected, patients with high-quality, cosine-squared 4DCT reconstructions did not yield artifact improvement with the use of EXPO, with scores of 1 (negligible impact) observed in 28/60 matched pairs across phases. In rare cases with severe artifacts with a consensus score of 4 (significant impact rendering image not suitable for clinical use), using EXPO did not reduce the artifacts. This is likely because the window of image projections used could not be narrowed enough for significant artifact improvement while still maintaining an adequate signal to noise ratio in the image. Nevertheless, Patient 4 did show a reduction in major artifacts that improved tumor visibility when EXPO was employed (Fig. 5).  the underlying image quality shown in Fig. 7. This case can be considered the worst-case scenario due to large body habitus secondary to the patient's body mass index and treatment position (one arm up for breast treatment).

| DISCUSSION
This study sought to introduce a novel exponential weighting factor for 4DCT reconstruction and evaluate its performance against the current clinically implemented cosine-squared reconstruction algorithm. The phantom evaluation revealed that the impact of the exponential weighting factor increased during transitional 4DCT phases, between EXPO and cosine-squared reconstructions were less apparent with rapid breathers such as patients 5, 6, and 8 shown in Fig. 6, with mean breathing rates of 20-27 bpm. For both the phantom and patient evaluations, when the breathing rate increased, the impact of EXPO was less prominent. With higher breathing rates, the reconstruction algorithm utilizes the temporal window constrained to its minimum of π projections and thus, a weighting scheme is not employed. This suggests that patients with the slowest breathing rates will be most impacted by EXPO, which is also confirmed by the phantom reconstructions where the slowest breathing rates (8-10 bpm) yielded the largest differences, particularly near object boundaries.  17 Nevertheless, appreciable differences in image sharpness were observed in 85% of the images reviewed with a substantial reduction in 4DCT artifact through the inclusion of fewer projections. Important next steps of this work are to include physician delineation analysis to determine if the tradeoff in image sharpness and reduction of 4DCT artifacts with the slightly increased image noise render the images suitable for contouring, although this will largely depend on disease site. However, delineations have been shown to be prone to a great deal of interand intraobserver variability, 17 and thus it may be difficult to decouple the source of contouring differences. Thus, the work conducted here was an important first step toward clinical implementation.
Our work revealed that 4DCT phases with little to no motion, such as end-exhalation, are least affected by the reconstruction algorithm. This suggests that clinics using the end-exhalation phase for respiratory-gated deliveries may not benefit from EXPO reconstructions. 18,19 In a similar manner, derivative images such as the MIP and AVG-CT were not as sensitive to EXPO, likely due to the redundancy of data among the 10 different breathing phases offsetting any impact on individual 4DCT phases. This work included only phase-based 4DCT sorting. It is possible that amplitude-based sorting may produce different results which can be explored in future work.
Overall, our analysis of both phantom and patient data showed that the EXPO reconstruction algorithm improved image sharpness while decreasing image artifacts. A potential clinical implementation may be to reconstruct raw data using both reconstruction techniques and building hybrid patient models to take advantage of the increased sharpness provided in high motion areas, whereas preserving signal in the noise-starved conditions typically present in the abdominal and liver regions.

Henry Ford Health System holds research agreements with Philips
Healthcare. Paul Klahr is a clinical scientist employed at Philips Healthcare.