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Purpose: To evaluate 2 deformable image registration (DIR) algorithms for the purpose of contour mapping to support image-guided adaptive radiation therapy with 4-dimensional cone-beam CT (4DCBCT)., Methods and Materials: One planning 4D fan-beam CT (4DFBCT) and 7 weekly 4DCBCT scans were acquired for 10 locally advanced non-small cell lung cancer patients. The gross tumor volume was delineated by a physician in all 4D images. End-of-inspiration phase planning 4DFBCT was registered to the corresponding phase in weekly 4DCBCT images for day-to-day registrations. For phase-to-phase registration, the end-of-inspiration phase from each 4D image was registered to the end-of-expiration phase. Two DIR algorithms-small deformation inverse consistent linear elastic (SICLE) and Insight Toolkit diffeomorphic demons (DEMONS)-were evaluated. Physician-delineated contours were compared with the warped contours by using the Dice similarity coefficient (DSC), average symmetric distance, and false-positive and false-negative indices. The DIR results are compared with rigid registration of tumor., Results: For day-to-day registrations, the mean DSC was 0.75 ± 0.09 with SICLE, 0.70 ± 0.12 with DEMONS, 0.66 ± 0.12 with rigid-tumor registration, and 0.60 ± 0.14 with rigid-bone registration. Results were comparable to intraobserver variability calculated from phase-to-phase registrations as well as measured interobserver variation for 1 patient. SICLE and DEMONS, when compared with rigid-bone (4.1 mm) and rigid-tumor (3.6 mm) registration, respectively reduced the average symmetric distance to 2.6 and 3.3 mm. On average, SICLE and DEMONS increased the DSC to 0.80 and 0.79, respectively, compared with rigid-tumor (0.78) registrations for 4DCBCT phase-to-phase registrations., Conclusions: Deformable image registration achieved comparable accuracy to reported interobserver delineation variability and higher accuracy than rigid-tumor registration. Deformable image registration performance varied with the algorithm and the patient., (Copyright © 2013 Elsevier Inc. All rights reserved.)

Purpose: To develop an algorithm for computing realistic digitally reconstructed radiographs (DRRs) that match real cone-beam CT (CBCT) projections with no artificial adjustments., Methods: The authors used measured attenuation data from cone-beam CT projection radiographs of different materials to obtain a function to convert CT number to linear attenuation coefficient (LAC). The effects of scatter, beam hardening, and veiling glare were first removed from the attenuation data. Using this conversion function the authors calculated the line integral of LAC through a CT along rays connecting the radiation source and detector pixels with a ray-tracing algorithm, producing raw DRRs. The effects of scatter, beam hardening, and veiling glare were then included in the DRRs through postprocessing., Results: The authors compared actual CBCT projections to DRRs produced with all corrections (scatter, beam hardening, and veiling glare) and to uncorrected DRRs. Algorithm accuracy was assessed through visual comparison of projections and DRRs, pixel intensity comparisons, intensity histogram comparisons, and correlation plots of DRR-to-projection pixel intensities. In general, the fully corrected algorithm provided a small but nontrivial improvement in accuracy over the uncorrected algorithm. The authors also investigated both measurement- and computation-based methods for determining the beam hardening correction, and found the computation-based method to be superior, as it accounted for nonuniform bowtie filter thickness. The authors benchmarked the algorithm for speed and found that it produced DRRs in about 0.35 s for full detector and CT resolution at a ray step-size of 0.5 mm., Conclusions: The authors have demonstrated a DRR algorithm calculated from first principles that accounts for scatter, beam hardening, and veiling glare in order to produce accurate DRRs. The algorithm is computationally efficient, making it a good candidate for iterative CT reconstruction techniques that require a data fidelity term based on the matching of DRRs and projections.

Purpose: To provide a proof of concept validation of a novel 4D cone-beam CT (4DCBCT) reconstruction algorithm and to determine the best methods to train and optimize the algorithm., Methods: The algorithm animates a patient fan-beam CT (FBCT) with a patient specific parametric motion model in order to generate a time series of deformed CTs (the reconstructed 4DCBCT) that track the motion of the patient anatomy on a voxel by voxel scale. The motion model is constrained by requiring that projections cast through the deformed CT time series match the projections of the raw patient 4DCBCT. The motion model uses a basis of eigenvectors that are generated via principal component analysis (PCA) of a training set of displacement vector fields (DVFs) that approximate patient motion. The eigenvectors are weighted by a parameterized function of the patient breathing trace recorded during 4DCBCT. The algorithm is demonstrated and tested via numerical simulation., Results: The algorithm is shown to produce accurate reconstruction results for the most complicated simulated motion, in which voxels move with a pseudo-periodic pattern and relative phase shifts exist between voxels. The tests show that principal component eigenvectors trained on DVFs from a novel 2D/3D registration method give substantially better results than eigenvectors trained on DVFs obtained by conventionally registering 4DCBCT phases reconstructed via filtered backprojection., Conclusions: Proof of concept testing has validated the 4DCBCT reconstruction approach for the types of simulated data considered. In addition, the authors found the 2D/3D registration approach to be our best choice for generating the DVF training set, and the Nelder-Mead simplex algorithm the most robust optimization routine.

Purpose: To evaluate the setup, interfraction, and intrafraction organ motion error distributions and simulate intrafraction intervention strategies for prostate radiotherapy., Methods and Materials: A total of 17 patients underwent treatment setup and were monitored using the Calypso system during radiotherapy. On average, the prostate tracking measurements were performed for 8 min/fraction for 28 fractions for each patient. For both patient couch shift data and intrafraction organ motion data, the systematic and random errors were obtained from the patient population. The planning target volume margins were calculated using the van Herk formula. Two intervention strategies were simulated using the tracking data: the deviation threshold and period. The related planning target volume margins, time costs, and prostate position "fluctuation" were presented., Results: The required treatment margin for the left-right, superoinferior, and anteroposterior axes was 8.4, 10.8, and 14.7 mm for skin mark-only setup and 1.3, 2.3, and 2.8 mm using the on-line setup correction, respectively. Prostate motion significantly correlated among the superoinferior and anteroposterior directions. Of the 17 patients, 14 had prostate motion within 5 mm of the initial setup position for ≥91.6% of the total tracking time. The treatment margin decreased to 1.1, 1.8, and 2.3 mm with a 3-mm threshold correction and to 0.5, 1.0, and 1.5 mm with an every-2-min correction in the left-right, superoinferior, and anteroposterior directions, respectively. The periodic corrections significantly increase the treatment time and increased the number of instances when the setup correction was made during transient excursions., Conclusions: The residual systematic and random error due to intrafraction prostate motion is small after on-line setup correction. Threshold-based and time-based intervention strategies both reduced the planning target volume margins. The time-based strategies increased the treatment time and the in-fraction position fluctuation., (Copyright © 2011 Elsevier Inc. All rights reserved.)

Purpose: To present a novel method for reconstructing the 3D pose (position and orientation) of radio-opaque applicators of known but arbitrary shape from a small set of 2D x-ray projections in support of intraoperative brachytherapy planning., Methods: The generalized iterative forward projection matching (gIFPM) algorithm finds the six degree-of-freedom pose of an arbitrary rigid object by minimizing the sum-of-squared-intensity differences (SSQD) between the computed and experimentally acquired autosegmented projection of the objects. Starting with an initial estimate of the object's pose, gIFPM iteratively refines the pose parameters (3D position and three Euler angles) until the SSQD converges. The object, here specialized to a Fletcher-Weeks intracavitary brachytherapy (ICB) applicator, is represented by a fine mesh of discrete points derived from complex combinatorial geometric models of the actual applicators. Three pairs of computed and measured projection images with known imaging geometry are used. Projection images of an intrauterine tandem and colpostats were acquired from an ACUITY cone-beam CT digital simulator. An image postprocessing step was performed to create blurred binary applicators only images. To quantify gIFPM accuracy, the reconstructed 3D pose of the applicator model was forward projected and overlaid with the measured images and empirically calculated the nearest-neighbor applicator positional difference for each image pair., Results: In the numerical simulations, the tandem and colpostats positions (x,y,z) and orientations (alpha, beta, gamma) were estimated with accuracies of 0.6 mm and 2 degrees, respectively. For experimentally acquired images of actual applicators, the residual 2D registration error was less than 1.8 mm for each image pair, corresponding to about 1 mm positioning accuracy at isocenter, with a total computation time of less than 1.5 min on a 1 GHz processor., Conclusions: This work describes a novel, accurate, fast, and completely automatic method to localize radio-opaque applicators of arbitrary shape from measured 2D x-ray projections. The results demonstrate approximately 1 mm accuracy while compared against the measured applicator projections. No lateral film is needed. By localizing the applicator internal structure as well as radioactive sources, the effect of intra-applicator and interapplicator attenuation can be included in the resultant dose calculations. Further validation tests using clinically acquired tandem and colpostats images will be performed for the accurate and robust applicator/sources localization in ICB patients.

Purpose: To generalize and experimentally validate a novel algorithm for reconstructing the 3D pose (position and orientation) of implanted brachytherapy seeds from a set of a few measured 2D cone-beam CT (CBCT) x-ray projections., Methods: The iterative forward projection matching (IFPM) algorithm was generalized to reconstruct the 3D pose, as well as the centroid, of brachytherapy seeds from three to ten measured 2D projections. The gIFPM algorithm finds the set of seed poses that minimizes the sum-of-squared-difference of the pixel-by-pixel intensities between computed and measured autosegmented radiographic projections of the implant. Numerical simulations of clinically realistic brachytherapy seed configurations were performed to demonstrate the proof of principle. An in-house machined brachytherapy phantom, which supports precise specification of seed position and orientation at known values for simulated implant geometries, was used to experimentally validate this algorithm. The phantom was scanned on an ACUITY CBCT digital simulator over a full 660 sinogram projections. Three to ten x-ray images were selected from the full set of CBCT sinogram projections and postprocessed to create binary seed-only images., Results: In the numerical simulations, seed reconstruction position and orientation errors were approximately 0.6 mm and 5 degrees, respectively. The physical phantom measurements demonstrated an absolute positional accuracy of (0.78 +/- 0.57) mm or less. The theta and phi angle errors were found to be (5.7 +/- 4.9) degrees and (6.0 +/- 4.1) degrees, respectively, or less when using three projections; with six projections, results were slightly better. The mean registration error was better than 1 mm/6 degrees compared to the measured seed projections. Each test trial converged in 10-20 iterations with computation time of 12-18 min/iteration on a 1 GHz processor., Conclusions: This work describes a novel, accurate, and completely automatic method for reconstructing seed orientations, as well as centroids, from a small number of radiographic projections, in support of intraoperative planning and adaptive replanning. Unlike standard back-projection methods, gIFPM avoids the need to match corresponding seed images on the projections. This algorithm also successfully reconstructs overlapping clustered and highly migrated seeds in the implant. The accuracy of better than 1 mm and 6 degrees demonstrates that gIFPM has the potential to support 2D Task Group 43 calculations in clinical practice.

Purpose: To experimentally validate a new algorithm for reconstructing the 3D positions of implanted brachytherapy seeds from postoperatively acquired 2D conebeam-CT (CBCT) projection images., Methods: The iterative forward projection matching (IFPM) algorithm finds the 3D seed geometry that minimizes the sum of the squared intensity differences between computed projections of an initial estimate of the seed configuration and radiographic projections of the implant. In-house machined phantoms, containing arrays of 12 and 72 seeds, respectively, are used to validate this method. Also, four 103Pd postimplant patients are scanned using an ACUITY digital simulator. Three to ten x-ray images are selected from the CBCT projection set and processed to create binary seed-only images. To quantify IFPM accuracy, the reconstructed seed positions are forward projected and overlaid on the measured seed images to find the nearest-neighbor distance between measured and computed seed positions for each image pair. Also, the estimated 3D seed coordinates are compared to known seed positions in the phantom and clinically obtained VariSeed planning coordinates for the patient data., Results: For the phantom study, seed localization error is (0.58 +/- 0.33) mm. For all four patient cases, the mean registration error is better than 1 mm while compared against the measured seed projections. IFPM converges in 20-28 iterations, with a computation time of about 1.9-2.8 min/ iteration on a 1 GHz processor., Conclusions: The IFPM algorithm avoids the need to match corresponding seeds in each projection as required by standard back-projection methods. The authors' results demonstrate approximately 1 mm accuracy in reconstructing the 3D positions of brachytherapy seeds from the measured 2D projections. This algorithm also successfully localizes overlapping clustered and highly migrated seeds in the implant.

Purpose: To assess the precision and robustness of patient setup corrections computed from 3D/3D rigid registration methods using image intensity, when no ground truth validation is possible., Methods: Fifteen pairs of male pelvic CTs were rigidly registered using four different in-house registration methods. Registration results were compared for different resolutions and image content by varying the image down-sampling ratio and by thresholding out soft tissue to isolate bony landmarks. Intrinsic registration precision was investigated by comparing the different methods and by reversing the source and the target roles of the two images being registered., Results: The translational reversibility errors for successful registrations ranged from 0.0 to 1.69 mm. Rotations were less than 1 degrees. Mutual information failed in most registrations that used only bony landmarks. The magnitude of the reversibility error was strongly correlated with the success/ failure of each algorithm to find the global minimum., Conclusions: Rigid image registrations have an intrinsic uncertainty and robustness that depends on the imaging modality, the registration algorithm, the image resolution, and the image content. In the absence of an absolute ground truth, the variation in the shifts calculated by several different methods provides a useful estimate of that uncertainty. The difference observed by reversing the source and target images can be used as an indication of robust convergence.

Purpose: To develop a population-based model of surface segmentation uncertainties for uncertainty-weighted surface-based deformable registrations., Methods: The contours of the prostate, the bladder, and the rectum were manually delineated by five observers on fan beam CT images of four prostate cancer patients. First, patient-specific representations of structure segmentation uncertainties were derived by determining the interobserver variability (i.e., standard deviation) of the structure boundary delineation. This was achieved by (1) generating an average structure surface mesh from the structure contours drawn by different observers, and (2) calculating three-dimensional standard deviation surface meshes (SDSMs) based on the perpendicular distances from the individual boundary surface meshes to the average surface mesh computed above. Then an average structure surface mesh was constructed to be the reference mesh for the population-based model. The average structure meshes of the other patients were deformably registered to the reference mesh. The calculated deformable vector fields were used to map the patient-specific SDSMs to the reference mesh to obtain the registered SDSMs. Finally, the population-based SDSM was derived by taking the average of the registered SDSMs in quadrature., Results: Population-based structure surface statistical models of the prostate, the bladder, and the rectum were created by mapping the patient-specific SDSMs to the population surface model. Graphical visualization indicates that the boundary uncertainties are dependent on anatomical location., Conclusions: The authors have developed and demonstrated a general method for objectively constructing surface maps of uncertainties derived from topologically complex structure boundary segmentations from multiple observers. The computed boundary uncertainties have significant spatial variations. They can be used as weighting factors for surface-based probabilistic deformable registration.

Purpose: To determine the optimal configuration and performance of an adaptive feed forward neural network filter to predict breathing in respiratory motion compensation systems for external beam radiation therapy., Method and Materials: A two-layer feed forward neural network was trained to predict future breathing amplitudes for 27 recorded breathing histories. The prediction intervals ranged from 100 to 500 ms. The optimal sampling frequency, number of input samples, training rate, and number of training epochs were determined for each breathing history and prediction interval. The overall optimal filter configuration was determined from this parameter survey, and its accuracy for each breathing example was compared to the individually optimal filter setups. Prediction accuracy was also compared to breathing stability as measured by the autocorrelation of the breathing signal., Results: The survey of filter configurations converged on a standard setup for all examples of breathing. For 24 of the 27 breathing histories the accuracy of the standard filter for a 300 ms prediction interval was within a few percent of the individually optimized filter setups; for the remaining three histories the standard filter was 5%-15% less accurate., Conclusions: A standard adaptive neural network filter setup can provide approximately optimal breathing prediction for a wide range of breathing patterns. The filter accuracy has a clear correlation with the stability of breathing.

Real-time tumor targeting involves the continuous realignment of the radiation beam with the tumor. Real-time tumor targeting offers several advantages such as improved accuracy of tumor treatment and reduced dose to surrounding tissue. Current limitations to this technique include mechanical motion constraints. The purpose of this study was to investigate an alternative treatment scenario using a moving average algorithm. The algorithm, using a suitable averaging period, accounts for variations in the average tumor position, but respiratory induced target position variations about this average are ignored during delivery and can be treated as a random error during planning. In order to test the method a comparison between five different treatment techniques was performed: (1) moving average algorithm, (2) real-time motion tracking, (3) respiration motion gating (at both inhale and exhale), (4) moving average gating (at both inhale and exhale) and (5) static beam delivery. Two data sets were used for the purpose of this analysis: (a) external respiratory-motion traces using different coaching techniques included 331 respiration motion traces from 24 lung-cancer patients acquired using three different breathing types [free breathing (FB), audio coaching (A) and audio-visual biofeedback (AV)]; (b) 3D tumor motion included implanted fiducial motion data for over 160 treatment fractions for 46 thoracic and abdominal cancer patients obtained from the Cyberknife Synchrony. The metrics used for comparison were the group systematic error (M), the standard deviation (SD) of the systematic error (sigma) and the root mean square of the random error (sigma). Margins were calculated using the formula by Stroom et al. [Int. J. Radiat. Oncol., Biol., Phys. 43(4), 905-919 (1999)]: 2sigma + 0.7sigma. The resultant calculations for implanted fiducial motion traces (all values in cm) show that M and sigma are negligible for moving average algorithm, moving average gating, and real-time tracking (i.e., M and sigma = 0 cm) compared to static beam (M = 0.02 cm and sigma = 0.16 cm) or gated beam delivery (M = -0.05 and 0.16 cm at both exhale and inhale, respectively, and sigma = 0.17 and 0.26 cm at both exhale and inhale, respectively). Moving average algorithm sigma = 0.22 cm has a slightly lower random error than static beam delivery sigma = 0.24 cm, though gating, moving average gating, and real-time tracking have much lower random error values for implanted fiducial motion. Similar trends were also observed for the results using the external respiratory motion data. Moving average algorithm delivery significantly reduces M and sigma compared with static beam delivery. The moving average algorithm removes the nonstationary part of the respiration motion which is also achieved by AV, and thus the addition of the moving average algorithm shows little improvement with AV. Overall, a moving average algorithm shows margin reduction compared with gating and static beam delivery, and may have some mechanical advantages over real-time tracking when the beam is aligned with the target and patient compliance advantages over real-time tracking when the target is aligned to the beam.

By monitoring brachytherapy seed placement and determining the actual configuration of the seeds in vivo, one can optimize the treatment plan during the process of implantation. Two or more radiographic images from different viewpoints can in principle allow one to reconstruct the configuration of implanted seeds uniquely. However, the reconstruction problem is complicated by several factors: (1) the seeds can overlap and cluster in the images; (2) the images can have distortion that varies with viewpoint when a C-arm fluoroscope is used; (3) there can be uncertainty in the imaging viewpoints; (4) the angular separation of the imaging viewpoints can be small owing to physical space constraints; (5) there can be inconsistency in the number of seeds detected in the images; and (6) the patient can move while being imaged. We propose and conceptually demonstrate a novel reconstruction method that handles all of these complications and uncertainties in a unified process. The method represents the three-dimensional seed and camera configurations as parametrized models that are adjusted iteratively to conform to the observed radiographic images. The morphed model seed configuration that best reproduces the appearance of the seeds in the radiographs is the best estimate of the actual seed configuration. All of the information needed to establish both the seed configuration and the camera model is derived from the seed images without resort to external calibration fixtures. Furthermore, by comparing overall image content rather than individual seed coordinates, the process avoids the need to establish correspondence between seed identities in the several images. The method has been shown to work robustly in simulation tests that simultaneously allow for unknown individual seed positions, uncertainties in the imaging viewpoints and variable image distortion.

Purpose: To develop an automatic knot placement algorithm to enable the use of NonUniform Rational B-Splines (NURBS) in deformable image registration.Methods: The authors developed a two-step approach to fit a known displacement vector field (DVF). An initial fit was made with uniform knot spacing. The error generated by this fit was then assigned as an attractive force pulling on the knots, acting against a resistive spring force in an iterative equilibration scheme. To demonstrate the accuracy gain of knot optimization over uniform knot placement, we compared the sum of the squared errors and the frequency of large errors.Results: Fits were made to a one-dimensional DVF using 1-20 free knots. Given the same number of free knots, the optimized, nonuniform B-spline fit produced a smaller error than the uniform B-spline fit. The accuracy was improved by a mean factor of 4.02. The optimized B-spline was found to greatly reduce the number of errors more than 1 standard deviation from the mean error of the uniform fit. The uniform B-spline had 15 such errors, while the optimized B-spline had only two. The algorithm was extended to fit a two-dimensional DVF using control point grid sizes ranging from 8 × 8 to 15 × 15. Compared with uniform fits, the optimized B-spline fits were again found to reduce the sum of squared errors (mean ratio = 2.61) and number of large errors (mean ratio = 4.50).Conclusions: Nonuniform B-splines offer an attractive alternative to uniform B-splines in modeling the DVF. They carry forward the mathematical compactness of B-splines while simultaneously introducing new degrees of freedom. The increased adaptability of knot placement gained from the generalization to NURBS offers increased local control as well as the ability to explicitly represent topological discontinuities. [ABSTRACT FROM AUTHOR]

Purpose: To assess the precision and robustness of patient setup corrections computed from 3D/3D rigid registration methods using image intensity, when no ground truth validation is possible. Methods: Fifteen pairs of male pelvic CTs were rigidly registered using four different in-house registration methods. Registration results were compared for different resolutions and image content by varying the image down-sampling ratio and by thresholding out soft tissue to isolate bony landmarks. Intrinsic registration precision was investigated by comparing the different methods and by reversing the source and the target roles of the two images being registered. Results: The translational reversibility errors for successful registrations ranged from 0.0 to 1.69 mm. Rotations were less than 1°. Mutual information failed in most registrations that used only bony landmarks. The magnitude of the reversibility error was strongly correlated with the success/failure of each algorithm to find the global minimum. Conclusions: Rigid image registrations have an intrinsic uncertainty and robustness that depends on the imaging modality, the registration algorithm, the image resolution, and the image content. In the absence of an absolute ground truth, the variation in the shifts calculated by several different methods provides a useful estimate of that uncertainty. The difference observed by reversing the source and target images can be used as an indication of robust convergence. [ABSTRACT FROM AUTHOR]