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Free breathing (FB) positron emission tomography (PET) images are routinely used in radiotherapy for lung cancer patients. Respiration-induced artifacts in these images compromise treatment response assessment and obstruct clinical implementation of dose painting and PET-guided radiotherapy. The purpose of this study is to develop a blurry image decomposition (BID) method to correct motion-induced image-reconstruction errors in FB-PETs.
Materials and methods
Assuming a blurry PET is represented as an average of multi-phase PETs. A four-dimensional computed-tomography image is deformably registered from the end-inhalation (EI) phase to other phases. With the registration-derived deformation maps, PETs at other phases can be deformed from a PET at the EI phase. To reconstruct the EI-PET, the difference between the blurry PET and the average of the deformed EI-PETs is minimized using a maximum-likelihood expectation–maximization algorithm. The developed method was evaluated with computational and physical phantoms as well as PET/CT images acquired from three patients.
Results
The BID method increased the signal-to-noise ratio from 1.88 ± 1.05 to 10.5 ± 3.3 and universal-quality index from 0.72 ± 0.11 to 1.0 for the computational phantoms, and reduced the motion-induced error from 69.9% to 10.9% in the maximum of activity concentration and from 317.5% to 8.7% in the full width at half maximum of the physical PET-phantom. The BID-based corrections increased the maximum standardized-uptake values by 17.7 ± 15.4% and reduced tumor volumes by 12.5 ± 10.4% on average for the three patients.
Conclusions
The proposed image-decomposition method reduces respiration-induced errors in PET images and holds potential to improve the quality of radiotherapy for thoracic and abdominal cancer patients.
]. For example, the intensities of PET images in tumor regions need to be accurately determined in order to prescribe the target dose for dose painting; the location and spatial distribution of tumors in longitudinal PET images need to be identified and compared to facilitate adaptive treatment planning [
Utilization of a hybrid finite-element based registration method to quantify heterogeneous tumor response for adaptive treatment for lung cancer patients.
]. Quantitatively accurate PET images are fundamental to these applications. However, clinical PET images usually are acquired in a static free-breathing (FB) mode [
]. Respiratory motion could smear lesions and change standardized uptake values (SUVs), resulting in the maximum of SUVs (SUVmax) in tumor regions being mis-calculated [
]. Besides quantitative errors, target definition and contour delineation of small lesions in stereotactic body radiotherapy (SBRT) could be complicated by motion artifacts and reduced signal-to-noise ratios [
], gated PETs generally provide more accurate information on tumor location and uptake than 3D PETs. In the recent years, deformable model-based 4D reconstruction methods were proposed to reduce PET data acquisition time [
]. However, these techniques have not been widely used in clinical practice, and PET images acquired for lung cancer patients still suffer from motion induced artifacts [
]. For example, in a multi-institutional clinical trial for PET-guided adaptive radiotherapy, FB-PETs were acquired for treatment response assessment and four-dimensional computed-tomography images (4DCTs) acquired for plan adaptation [
Effect of Midtreatment PET/CT-adapted radiation therapy with concurrent chemotherapy in patients with locally advanced non-small-cell lung cancer: a phase 2 clinical trial.
]. Although some patients had tumor motion observed in their 4DCTs, there is a lack of an effective tool to correct motion-induced SUV errors in their FB-PETs [
In this study, we propose a novel blurry image decomposition (BID) method to convert a blurry image into a motion-frozen (MF) image. Specifically, we use 4DCT images to generate a set of deformation maps and then use these maps to decompose the blurry image into multiple phase images. The equations resulting from the decomposition are solved using a maximum-likelihood expectation–maximization (MLEM) algorithm. We will verify the BID method with both computational and physical phantoms and demonstrate its feasibility of reducing motion artifacts in clinical PET and CT images. The developed BID method has the potential to reduce respiration-induced artifacts in FB-PETs [
Kong FM, Machtay M, Bradley J, Ten Haken R, Xiao Y, Matuszak M, et al. RTOG 1106/ACRIN 6697: Randomized Phase II Trial of Individualized Adaptive Radiotherapy Using During-Treatment FDG-PET/CT and Modern Technology in Locally Advanced Non-Small Cell Lung Cancer (NSCLC). 2013. https://www.acr.org/-/media/ACR/NOINDEX/Research/ACRIN/Legacy-Trials/ACRIN-6697_RTOG1106.pdf.
Suppose B is a blurry FB-PET image that has been reconstructed from all projection data. To remove respiratory motion-induced artifacts in B, we decompose it into a set of phase images where K is the number of respiratory phases. Assuming X(k) is deformed from a MF image S with a deformation map fk, as illustrated in Fig. 1, we can use the following procedure to inversely reconstruct S from the blurry image B.
Fig. 1A blurry image B is decomposed into multiple phase images X(k) which will be used to reconstruct a motion-frozen image S.
Let the FB-PET image B be defined by , and the phase image X(k) defined by , k = 1, …, K, where K is the number of the respiratory phases, and N is the total number of voxels in the image B. Without loss of generality, the MF image S is assumed to be x(1)defined by . Suppose a 4DCT dataset is acquired and binned into K phases. A three-dimensional (3D) deformable image registration (DIR) can be performed from phase 1 to phase k, k = 1, …, K, with the resultant deformation map denoted by fk. Then the image or S can be reconstructed by minimizing the following objective function
(1)
where is a set of weighting factors associated with the duration of individual phases. As illustrated in Fig. 1, the mapping function maps voxel in image X(1) to voxel i in image X(k). Let denote the index function of the inverse deformation map , then and consequently
(2)
where . The derivatives of the objective function with respect to can be set to zero to generate a set of linear equations
(3)
where , and A is defined by
(4)
Here A is an asymmetric matrix, consisting of N×(NK) elements with N denoting the total number of voxels in the PET image. corresponds to the position (i, j+(k-1) × N) in the matrix A. The element of A at this position is wk when and zero otherwise. Therefore, there are N variables , in equation (3) that need to be determined.
2.2 Implementation of the BID method
In this study, a maximum likelihood expectation–maximization (MLEM) method [
] was implemented to solve equation (3). To improve computational efficiency, the matrix A was reformatted with zero entries suppressed, and the resultant matrix was represented as a linked list of those non-zero entries. For a phase-based 4DCT, each respiratory cycle is equally divided into K phases, so the weighting factor for each phase is 1/K. For an amplitude-based 4DCT, the duration of each phase could be slightly different from 1/K. To address this issue, a random function is defined by
(5)
where is a simulated amplitude and rand () is a function in the C library that returns a pseudo-random integral number. The weighting factor can be calculated from . We may take W = as the starting point to find an optimal set and MF image such that reaches its minimum at the position ). 4DCT image registrations were performed using an intensity-based, free-form deformable registration algorithm in the MIM software (MIM Software Inc., Cleveland, OH), where the sum of squared differences was used as similarity metric and a modified gradient descent method was used for optimization [
2.3 Computational and physical phantoms for verification of the BID method
Two computational phantoms and one physical phantom were developed to verify the BID method. Details of the computational phantoms were described in the Supplementary Materials (Section S1). The physical phantom used in the experiment was modified from a motion phantom (Anzai medical system, Tokyo) which has a control panel and a cylindrical container connected by a metal rod. A motor was used to drive the container to move sinusoidally in the superior and inferior direction. A capillary tube measuring 40 mm in length and 0.5 mm in inner diameter was affixed to the top of the container, containing approximately 0.2 μCi of fluorine-18 fluorodeoxyglucose (18F-FDG) and orientated perpendicular to the direction of motion. A 4DCT scan of the moving phantom was acquired on a Siemens SOMATOM CT scanner (Siemens Medical Solutions, USA) and sorted into 10 phases at a slice thickness of 2 mm to derive the motion trajectory of the capillary tube.
The quality of the reconstructed phantom images was evaluated with signal-to-noise ratio (SNR) and universal quality index (UQI). Suppose R and X represent the reference and reconstructed images for the computational phantoms. SNR is defined by , where is the mean value of the image X and is the standard deviation of the difference image between R and X [
where is the joined correlation between the images R and X. The value of UQI is in a range from 0 to 1 and indicates the highest consistency between X and R. For the capillary tube phantom, its static, and moving and BID-reconstructed PET images were evaluated using the maximum of activity concentration (ACmax) and the full width at half maximum (FWHM) of activity profiles along a line in the moving direction, respectively.
2.4 Acquisition of 4DCT and PET images from patients
Three lung cancer patients were enrolled in this study under a retrospective protocol approved by the Institutional Review Board of Medical College of Wisconsin (PRO00036446). 4DCT and FB-PET/CT images were acquired from these patients on a SOMATOM CT scanner and a GE Discovery PET/CT scanner (GE Healthcare, Waukesha, WI), respectively. The acquired 4DCT has an in-plane voxel resolution of 1.1 × 1.1 mm2/pixel and a slice thickness of 3.0 mm. The FB-PET images have an in-plane voxel spacing between 2.7 and 5.2 mm and a slice thickness between 3.2 and 4.0 mm. To improve computational efficiency, regions outside patient contours were cropped out from all PET and CT images. The 4DCT images were deformably registered from either the end-of-inhalation (EI) or end-of-exhalation (EE) phase to other phases. The resultant deformation vector fields were assigned to the domain of PET images using a trilinear interpolation method and then employed in the BID method to convert FB-PET images to MF images.
3. Results
3.1 Verification of the BID method with the computational phantoms
The two computational phantoms were used to validate the BID method. The blurred, BID-reconstructed and referenced images were shown in Fig. 2 (a, b, c) and Fig. 2(d–f) for phantoms 1 and 2, respectively. The BID reconstructions were performed with 104 iterations. The difference between the reference and BID-reconstructed images is in the order of O(10−4), as shown in Fig. 2i. The BID reconstructions increased the UQI from 0.72 ± 0.11 to 1.0 and the SNR from 1.88 ± 1.05 to 10.5 ± 3.3 on average for the two computational phantoms.
Fig. 2Two computational phantoms: (a-c) the blurry input, BID-reconstructed and reference image for phantom 1; (d-f) the corresponding images for phantom 2; (g) the blurry image imposed with noise (B1N); (h) the image reconstructed from B1N; (i) the image reconstructed from B1 subtracted by R1.
To test the stability of the BID method, the blurred image of phantom 1 in Fig. 2a was multiplied by the random function with μ = 10%, and up to 4 mm random errors were added to the deformation maps of this phantom. The modified blurry image and deformation maps were substituted into the BID method to convert the noisy image to an MF image with the result shown in Fig. 2h. Although compromised by the imaging and displacement errors, the BID reconstruction still increased the SNR from 2.62 to 4.13 and the UQI from 0.79 to 0.92 for this phantom. The pattern of residuals in Fig. 2(i) is related to the MLEM optimization algorithm. Since the phantom’s motion was simulated in one direction, the residuals of the BID correction are observable only in the moving direction. The convergence of this algorithm is illustrated in Table 3 in the supplementary materials (Section S1).
3.2 Verification of the BID method with the physical motion phantom
The physical motion phantom with the FDG source tube is shown in Fig. 3 (a1). The 4DCT images of the phantom were rigidly registered within the MIM software to calculate displacements between different phases. The maximum of the calculated displacements between the EI and EE phases is 19.5 mm which is close to the 20 mm motion amplitude preconfigured in the Anzai phantom. Fig. 3 (b1-c1) shows the coronal and sagittal slices of the PET scan acquired from the moving phantom. The capillary tube was blurred in the phantom’s moving direction and the tube at two extreme positions showed higher activity concentration (AC) than at other transitional positions. The AC difference is due to the fact that the phantom traveled shorter distances in EI or EE phases than in any middle or transitional phase. With moving distances measured from the 4DCT phase images, the BID method was used to decompose the blurred PET. The resultant BID image is shown in Fig. 3(b2–c2) that is highly consistent to the static PET image shown in Fig. 3(b3–c3).
Fig. 3(a1) the physical motion phantom; (b1) and (c1) coronal and sagittal slices of the moving PET; (b2) and (c2) coronal and sagittal slices of the BID reconstructed PET; (b3) and (c3) coronal and sagittal slices of the static PET; (a2) profiles of activity concentration in the static, moving and BID-reconstructed PETs along the line of x = 30 (voxels) in the phantom’s moving direction.
The AC profiles in the moving, static and BID reconstructed PET images along a superior-inferior line that passes through the middle point (x = 30) of the tube were illustrated in Fig. 3(a2). ACmax was reduced from 4.02 × 104 Bq/ml in the static PET to 1.33 × 104 Bq/ml in the moving PET. After the BID correction, the ACmax increased to 4.46 × 104 Bq/ml. The FWHM of the profiles in the moving, static and BID-reconstructed images are 23.47 ± 0.49, 5.61 ± 1.14 and 6.1 ± 0.91 mm, respectively. The BID reconstruction reduced the motion-induced error from 69.9% to 10.9% in the ACmax and from 317.5% to 8.7% in the FWHM of the FDG source tube.
3.3 MF-PET images reconstructed for the three lung cancer patients
The average 4DCTs of the three patients were fused to their PET-CTs and consequently aligned to their FB-PETs within the MIM software. The average 4DCT and FB-PET with the target contour for the first patient were shown in Fig. 4a and b. The contour was copied to the BID-reconstructed image (Fig. 4c). The tumor in the reconstructed image is lower than the contour, showing that the BID reconstruction corrected the respiration induced error. Due to DIR and setup uncertainties, there are artifacts in the BID-reconstructed image (Fig. 4c). To address this issue, the FB-PET was down-sampled to the resolution of 0.8 × 0.8 × 0.8 cm3/voxel (Fig. 4e) and overlaid with the average 4DCT in Fig. 4d. The BID method was applied to the down-sampled PET to generate a reconstructed image (Fig. 4f) which shows less artifacts than in Fig. 4c. The location of SUVmax in the BID reconstructed PET was found about 0.62 cm lower than that in the blurry PET as shown in Fig. 4(e, f). This number is consistent with the difference of the tumor position between the EI-4DCT and average 4DCT as shown in the Supplementary materials (Section S2). In addition to the location change, SUVmax increased from 18.9 to 24.3 after the BID reconstruction.
Fig. 4(a) the average 4DCT image; (b) the 4-mm FB-PET; (c) the BID-reconstructed PET; (d) the average 4DCT overlaid with the down-sampled 8-mm FB-PET; (e) 8-mm FB-PET; (f) the BID-reconstructed 8-mm PET.
Fig. 5(a, b) shows a tumor in the right lung for patient 2 and the center of the tumor moves about 2.1 cm between the EE and EI phases. After the BID reconstruction, motion artifacts in the FB-PET (Fig. 5c) are corrected, and the tumor position in the BID-reconstructed PET (Fig. 5d) is consistent to that in the EE-4DCT (Fig. 5a). The BID reconstruction increased SUVmax from 17.1 to 21.3 and reduced the tumor volume from 89.6 cm3 to 68.7 cm3. In contrast to patient 2, patient 3 does not show noticeable tumor motion or deformation between the EE and EI 4DCT images in Fig. 5(e, f), and the BID reconstruction reduces the tumor volume slightly from 36.6 cm3 to 35.7 cm3. On average, the BID reconstruction increased SUVmax by 17.7 ± 15.4% and decreased tumor volume by 12.5 ± 10.4% for the three patients.
Fig. 5Images from patients 2 and 3 were illustrated in the upper and lower rows, respectively: (a) EE 4DCT, (b) EI 4DCT, (c) FB-PET overlaid on the EE 4DCT, (d) BID-reconstructed PET overlaid on the EE 4DCT; the correspondent images for patient 3 were shown in (e–h).
Image reconstruction programs such as Software for Tomographic Image Reconstruction (STIR) and Customizable and Advanced Software for Tomographic Reconstruction (CASToR) allow list mode data to be combined with a motion model to reconstruct motion-frozen PETs [
Utilization of a hybrid finite-element based registration method to quantify heterogeneous tumor response for adaptive treatment for lung cancer patients.
Effect of Midtreatment PET/CT-adapted radiation therapy with concurrent chemotherapy in patients with locally advanced non-small-cell lung cancer: a phase 2 clinical trial.
]. We found that motion artifacts in these images compromise voxel-based response assessments. In this study, we proposed an image decomposition method that employs a deformable model to transform a blurry PET into a motion-frozen one, eliminating the need for list-mode data [
There are multiple strategies proposed to remove motion artifacts in FB-PETs. For example, a patient-specific deconvolution kernels was developed to remove rigid motion induced artifacts in a local region [
]. However, this method is not applicable to largely deformed structures as the kernel is invariant in the local region. The BID method, on the other hand, can be considered as a generalized deconvolution method that uses a different kernel at each voxel and therefore can be applied to deformed anatomies. Different from deconvolution techniques, a straightforward method was proposed by registering an average 4DCT to each of its phase images to build a deformable model [
]. This model was then applied to a blurred 3D PET to create a virtual 4D PET. However, it was reported that this method may reduce motion-induced blurs but cannot restore the maximum of the SUVs [
]. In this study, we proposed a voxel-based motion correction method that uses a blurry PET and a 4DCT-based deformable model as input to reconstruct a motion-frozen PET. The developed method can help reduce motion-induced artifacts in PET scans and improve the accuracy of SUV measurements. As 4DCTs are routinely acquired in radiation therapy for treatment planning, the use of the BID method to reduce motion-induced SUV errors in PETs does not add any additional cost to radiotherapy patients.
Declaration of Competing Interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
Acknowledgement
This project was funded in part by the grants R01-EB028324 and R01-EB032680 from National Institute of Biomedical Imaging and Bioengineering, NIH, USA.
Appendix A. Supplementary data
The following are the Supplementary data to this article:
Utilization of a hybrid finite-element based registration method to quantify heterogeneous tumor response for adaptive treatment for lung cancer patients.
Effect of Midtreatment PET/CT-adapted radiation therapy with concurrent chemotherapy in patients with locally advanced non-small-cell lung cancer: a phase 2 clinical trial.
Kong FM, Machtay M, Bradley J, Ten Haken R, Xiao Y, Matuszak M, et al. RTOG 1106/ACRIN 6697: Randomized Phase II Trial of Individualized Adaptive Radiotherapy Using During-Treatment FDG-PET/CT and Modern Technology in Locally Advanced Non-Small Cell Lung Cancer (NSCLC). 2013. https://www.acr.org/-/media/ACR/NOINDEX/Research/ACRIN/Legacy-Trials/ACRIN-6697_RTOG1106.pdf.
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