Validation of biomechanical deformable image registration in the abdomen, thorax, and pelvis in a commercial radiotherapy treatment planning system

Validation of biomechanical deformable image registration in the abdomen, thorax, and pelvis in a commercial radiotherapy treatment planning system Michael Velec a) and Joanne L. Moseley Techna Institute and Princess Margaret Cancer Centre, University Health Network, Toronto M5G 2M9, Canada Stina Svensson and Bj orn Hardemark RaySearch Laboratories AB, Sveav agen 44, SE-103 65 Stockholm, Sweden David A. Jaffray Techna Institute and Princess Margaret Cancer Centre, University Health Network, Toronto M5G 2M9, Canada Department of Radiation Oncology, Medical Biophysics, and Institute of Biomaterials and Biomedical Engineering, University of Toronto, Toronto M5S 3E2, Canada Kristy K. Brock Department of Radiation Oncology, University of Michigan, Ann Arbor, MI 48109, USA (Received 25 October 2016; revised 20 March 2017; accepted for publication 20 April 2017; published 1 June 2017) Purpose: The accuracy of deformable image registration tools can vary widely between imaging modalities and specific implementations of the same algorithms. A biomechanical model-based algorithm initially developed in-house at an academic institution was translated into a commercial radiotherapy treatment planning system and validated for multiple imaging modalities and anatomic sites. Methods: Biomechanical deformable registration (MORFEUS) is a geometry-driven algorithm based on the finite element method. Boundary conditions are derived from the model-based segmentation of controlling structures in each image which establishes a point-to-point surface correspondence. For each controlling structure, material properties and fixed or sliding interfaces are assigned. The displacements of internal volumes for controlling structures and other structures implicitly deformed are solved with finite element analysis. Registration was performed for 74 patients with images (mean vector resolution) of thoracic and abdominal 4DCT (2.8 mm) and MR (5.3 mm), liver CT-MR (4.5 mm), and prostate MR (2.6 mm). Accuracy was quantified between deformed and actual target images using distance-to-agreement (DTA) for structure surfaces and the target registration error (TRE) for internal point landmarks. Results: The results of the commercial implementation were as follows. The mean DTA was 1.0 mm for controlling structures and 1.0 3.5 mm for implicitly deformed structures on average. TRE ranged from 2.0 mm on prostate MR to 5.1 mm on lung MR on average, within 0.1 mm or lower than the image voxel sizes. Accuracy was not overly sensitive to changes in the material properties or variability in structure segmentations, as changing these inputs affected DTA and TRE by 0.8 mm. Maximum DTA > 5 mm occurred for 88% of the structures evaluated although these were within the inherent segmentation uncertainty for 82% of structures. Differences in accuracy between the commercial and in-house research implementations were 0.5 mm for mean DTA and 0.7 mm for mean TRE. Conclusions: Accuracy of biomechanical deformable registration evaluated on a large cohort of images in the thorax, abdomen and prostate was similar to the image voxel resolution on average across multiple modalities. Validation of this treatment planning system implementation supports biomechanical deformable registration as a versatile clinical tool to enable accurate target delineation at planning and treatment adaptation. 2017 American Association of Physicists in Medicine [https://doi.org/10.1002/mp.12307] Key words: biomechanical models, deformable image registration, multimodality imaging 1. INTRODUCTION Deformable image registration (DIR) enables a wide range of research and clinical applications in radiation oncology. These include target delineation for planning, contour propagation and dose accumulation for treatment adaptation, correlative imaging-pathology studies, and therapy response assessment. 1 4 This has necessitated the development of numerous algorithms by academia and industry although relatively few implementations have been rigorously evaluated in multiple anatomic sites, modalities, and applications. 5 As DIR is increasingly incorporated into clinical processes, it is essential that the accuracy and behavior of these algorithms is well understood. The versatility of biomechanical model-based DIR, typically implemented with a linear elastic model using the finite 3407 Med. Phys. 44 (7), July 2017 0094-2405/2017/44(7)/3407/11 2017 American Association of Physicists in Medicine 3407

3408 Velec and Moseley: Biomechanical deformable registration 3408 element method, has been demonstrated in several of the above scenarios. Potential advantages over intensity-based algorithms are its ready applicability to many modalities and its improved accuracy in low contrast image regions. 6 9 A biomechanical DIR algorithm developed at an academic institution was shown to have an accuracy of 2 3 mm in the liver and lungs on patient images. 10,11 In studies using deformable dosimeters, it predicted 3D and 4D dose distributions with gamma indices > 90% for 4.7%/2 mm and 3%/3 mm criteria. 8,12 Reported computation times range from 1 min for single-organ to 25 min for multiorgan registrations, 11,13 excluding the time required for segmentation and certain preprocessing tasks such as surface mesh generation. The promising registration accuracy results however motivated the translation of this algorithm into a commercial treatment planning system (TPS) to facilitate its use in clinic. Previous DIR comparisons on common datasets revealed that registration accuracy varies even with different implementations or parameter settings for similar algorithms. 14,15 In one study, the registration accuracy of liver 4DCT ranged from 2.3 4.8 mm for three Demons algorithms and 2.1 7.1 mm for three thin-plate spline algorithms. Parameter and material property optimization has been investigated for biomechanical DIR although different implementations have not yet been directly compared. The motivation for this work was to evaluate the accuracy of a commercial biomechanical DIR algorithm using clinical patient images with defined organ boundaries and landmarks across multiple anatomic sites and image modalities. Accuracy was compared to the results of the original implementation and an existing nonbiomechanical DIR in the TPS. A validated biomechanical algorithm integrated within the TPS would allow efficient clinical application of DIR for accurate target delineation at planning and plan adaptation during treatment. 2. METHODS AND MATERIALS 2.A. Algorithm implementations A biomechanical model-based DIR algorithm, MORFEUS, was previously developed at an academic institution. 10 In summary, single- or multiorgan tetrahedral mesh models are generated from region of interest (ROI) contours in the reference image and linear elastic material properties are assigned to different tissues represented by the tetrahedral meshes. For a subset of tissues, triangular surface meshes are additionally created from contours in the target image. These ROIs with meshes on both images, termed controlling ROIs, undergo individual deformations to align the surfaces and serve as boundary conditions. ROIs within the body ROI, such as the lungs, can interface with body elements with either a fixed or sliding method. Finite element analysis then solves the internal displacements of the tetrahedral model, including for all remaining organs and tumor ROIs that did not undergo individual surface deformations and are therefore implicitly deformed. Under a research collaboration, MORFEUS was recently implemented within a commercial TPS (MORFEUS v0.9, RayStation v4.5 4.6, RaySearch Laboratories, Stockholm, Sweden). Both the in-house and commercial implementations are based on the finite element method and compared in Table I. Major differences lie in the material properties and boundary conditions. The organ-specific material properties for the in-house DIR were optimized in previous studies. Poisson s ratio (m) ranges from 0.40 to 0.499 and Young s modulus (E) ranges from 1.5 to 500 kpa. 10 Preliminary testing of the commercial DIR was performed to optimize m, termed voxel compression ratio in the TPS. Commercial DIR results were not overly sensitive to the m applied, therefore the default value of 0.48 was applied to all organs except for the body, for which there was a sub-millimeter improvement with m = 0.40 (the same value used in-house). These values differ by < 10% compared to the in-house DIR, and therefore likely affect the results minimally. The current commercial implementation does not allow E to be varied in an effort to simplify the problem formulation. This is analogous to applying a uniform stiffness for all organs. The boundary conditions applied to the controlling ROIs for the in-house DIR are derived from guided-surface projections. In this manner, points along reference ROI surface meshes are projected onto target ROI surfaces without requiring an explicit point-to-point surface correspondence. The boundary conditions in the commercial DIR use the TPS s model-based segmentation to establish surface meshes with a point-to-point correspondence across the different geometries on the images. The model-based segmentation can be used to avoid the requirement for manually delineated contours. Alternatively for existing ROIs with manually delineated contours on both images, a common surface mesh can be adapted to the existing contours on each image. The impact of the boundary conditions was expected to be the largest source of difference between biomechanical DIR results. This was investigated for a subset of patients during initial testing by extracting the boundary conditions from the TPS and applying them to the in-house algorithm. Results for the in-house implementation were then compared between boundary conditions derived from the TPS s model-based segmentation or the regular guided-surface projections. Third party components used for mesh generation and the finite element analysis solver also differ between implementations although these function similarly. Prior experience with the in-house DIR development demonstrated virtually no difference in accuracy between different solvers. 2.B. Imaging data Registration accuracy was evaluated on data acquired for prior in-house studies (Table II). Approximately half of the cases in each anatomical category were randomly chosen, anonymized and transferred under a research ethics boardapproved data transfer agreement to the TPS vendor for initial algorithm development. Half of the cases were reserved for

3409 Velec and Moseley: Biomechanical deformable registration 3409 TABLE I. Comparison of the biomechanical DIR implementations (3rd party functions listed where applicable). DIR feature In-house biomechanical DIR Commercial TPS biomechanical DIR Environment ROI triangular surface meshing Volumetric/multiorgan tetrahedral meshing Linear elastic material properties MATLAB-based application, imports ROI binary masks or meshes exported from TPS Modified marching cubes on binary masks (IDL v6.3, Research Systems Inc., USA) a (HyperMesh, Altair HyperWorks v11.0, Altair Engineering Inc., Troy, USA) Ability to vary properties for any ROI in the reference image; m = 0.40 0.499; E = 1.5 500 kpa Boundary conditions Fixed interface Guided-surface projection of reference ROI surface mesh to target ROI surface (HyperMorph Altair HyperWorks v11.0, Altair Engineering Inc., Troy, USA) Sliding interface Frictionless contact surface where internal ROI elements slide against fixed external elements (RADIOSS, Altair HyperWorks v11.0, Altair Engineering Inc., Troy, USA) Finite element analysis solver (RADIOSS, Altair HyperWorks v11.0, Altair Engineering Inc., Troy, USA) Deformation resolution after Equivalent to reference image b resampling to cubic grid Module within TPS Model-based segmentation module adapts model mesh to contours by minimizing binarized edge distance (NETGEN, open-source: http://www.hpfem.jku.at/ne tgen) Ability to vary m only for controlling ROIs used as boundary conditions; 0.40 for body, 0.48 for all other organs Point-to-point ROI surface mesh correspondence via model-based segmentation Mixed Dirichlet/Neumann conditions where external ROI elements slide against fixed internal elements (FEniCS, 26,27 open-source) (FEniCS, 26,27 open-source) 2.5 9 2.5 9 2.5 mm 3 (default) a TPS meshes from model-based segmentation used for current study. b 4DCT data were down-sampled to 256 9 256 voxels in-plane due to computer memory limitations. subsequent validation. This approved retrospective study reports the accuracy from the combined development and validation data cohorts for 74 patients in total. Data contained manually delineated ROIs and points of interest (POI) representing anatomy and landmarks in both reference and target images. Images include the abdomen and thorax with 4DCT or exhale and inhale breath-hold MR, the liver with exhale CT and MR, and the prostate MR with and without the adjacent rectum distended by an endorectal coil (n = 19) or severe gas (n = 1). TPS-generated meshes were also exported for use with the in-house DIR, and hence not a source of difference in the results. Using the same surface meshes was necessary to allow accurate alignment of the deformation vector fields to directly compare the in-house and commercial DIR results. Note that these meshes are used differently within the boundary conditions for each DIR implementation as described above. The accuracy of the in-house implementation was previously shown to be insensitive to variations in surface and volumetric mesh resolution and magnitude of smoothing applied. 13 2.B.1. ROI preprocessing For the commercial DIR, controlling ROI surface meshes based on the manually delineated contours shown in Fig. 1 was generated within the TPS using default parameters. Meshes were visually inspected to ensure they preserve the topology and volume of the ROI. For the current study, these 2.C. Evaluation 2.C.1. Accuracy metrics Evaluations were computed via scriptable functions inside a research version of the TPS (v4.6) which allowed importing TABLE II. Imaging, delineations, and setup conditions for DIR. Site, imaging [prior study] N Mean 3D voxel resolution (mm) Initial DIR conditions: Rigid pre registration Evaluation delineations Reference image, target image ROIs ( used during DIR as a controlling ROI) POIs, median (range) Abdominal 4DCT [ 28 ] 10 2.7 Spine Exhale, inhale Liver, spleen, body, stomach, kidney(s) Liver vessels, 9 (5 25) Thoracic 4DCT [ 18 ] 16 2.9 Spine Inhale, exhale Lung(s), body, tumor(s), heart, bronchus, bone Lung vessels 51.5 (18 71) Liver CT-MR [ 29 ] 18 4.5 Liver CT, MR Liver Liver vessels, 5 (4 7) Abdominal MR-MR [ 10 ] 5 5.2 Spine Exhale, inhale Liver, spleen, body, stomach, kidney(s) Liver vessels, 10 (8 14) Thoracic MR-MR [ 10 ] 5 5.4 Spine Inhale, exhale Lung(s), body, breast tissue(s) Lung vessels, 20 (17 27) Prostate MR-MR [ 30 ] 20 2.6 Implanted fiducials Empty rectum, distended rectum Prostate Fiducials, 3 (2 3)

3410 Velec and Moseley: Biomechanical deformable registration 3410 FIG. 1. Reference (blue) and target (orange) images with the corresponding controlling ROIs used as inputs for biomechanical DIR (solid and dashed green lines for each image respectively). [Color figure can be viewed at wileyonlinelibrary.com] of the external deformation vector field from the in-house DIR. Deformed reference images were compared to target images as follows. For ROI and POI structures manually delineated on both the reference and target images, deformed reference structures (i.e., manually delineated on the reference image and deformed via DIR) are compared to manually delineated target structures. The geometric differences of these structures represent the registration accuracy. Results for all metrics were averaged over the patient datasets per anatomical category. ROIs were first assessed using the Dice similarity coefficient (DSC) volume overlap measure. DSC ranges between 0 and 1 indicating no overlap and perfect overlap respectively, and is given by: DSC ¼ 2ð½deformed reference volume \ ½target volume Þ ð½deformed reference volume þ ½target volume Þ (1) The residual surface distances for ROIs were also assessed using the distance-to-agreement (DTA) metric. The distances between points along deformed reference ROI surfaces were measured to the nearest point along target ROI surfaces and the mean/maximum DTA values are reported. POIs were assessed by computing the 3D distances for landmarks in the deformed reference and target images, and the mean values per-patient are reported as the target registration error (TRE). Two image similarity metrics, the correlation coefficient (CC), and mutual information (MI), were computed between registered images to assess if there is a correlation with the geometry-based accuracy metrics above. The impact of contour variability was assessed by re-contouring ROIs for five patients each for thoracic and abdominal 4DCT and prostate MR. The original contours were created during previous investigations (Table II). For this study, a single clinician experienced in each anatomic site, and blinded to the original contours, re-contoured the organs. Accuracy metrics were applied between the original and repeat contours to assess the baseline variability. New controlling ROI meshes were then generated from the new contours and DIR was re-performed. DIR accuracy between registrations driven by the original and repeat controlling ROI meshes were compared to assess sensitivity to contour variability. 2.C.2. Comparison to hybrid DIR For all patients, commercial biomechanical DIR results are additionally compared to the TPS s existing hybrid DIR to identify specific data for which the application of biomechanical DIR may improve registration accuracy. The hybrid intensity-geometry-based algorithm (ANACONDA v2.0) has been previously developed primarily for CT, 4DCT and conebeam CT registration.16 Briefly, this DIR uses a CC image similarity metric, a Chamfer matching approach to minimize contour surface distances for controlling ROIs and grid regularization to ensure a smooth, invertible deformation. Hybrid

3411 Velec and Moseley: Biomechanical deformable registration 3411 DIR has not yet been validated for use on MR, and its application to CT-MR registration is specifically not recommended by the vendor because of the mono-modality similarity metric (i.e., CC). CT-MR and MR-MR results were included to study the impact of applying DIR relying on image intensity to data for which it was not initially developed, and compare these results to the modality-independent biomechanical DIR. Manual contours from which surface meshes were generated for use as controlling ROIs in biomechanical DIR, were input as controlling ROIs in hybrid DIR. Default TPS parameters were used for hybrid DIR, except for the MR-MR data where the tri-resolution optimization range was changed from 5.0 2.5 mm to 7.5 2.5 mm in order to account for the slice thickness > 5 mm. Hybrid DIR was tested in its initial hybrid mode (i.e., using both image intensity and ROIs) and the optional ROI-only mode which discards intensity information. Testing the ROI-only mode allowed an additional comparison of two purely geometrybased DIRs: biomechanical DIR and hybrid DIR using only ROI information. 2.C.3. Evaluation of clinical system The TPS version intended for clinical use (v4.5) has two main differences from the research build (v4.6). First, external deformation vector fields cannot be imported into the clinical version. Second, minor difference exists in the surface meshing, with the research version generating finer meshes intended to improve visualization, although the results also affect DIR. Biomechanical DIR is otherwise identical. Accuracy was verified by re-generating meshes, and re-performing DIR for 30 patients in v4.5. Computation time was also recorded for the clinical version which is accessed via Citrix virtual desktop from workstations with dual Intel â Xeon TM x560 processors (3.46 GHz, 48 GB RAM). 3. RESULTS 3.A. ROI surface and volume overlap accuracy The mean DTA for the commercial biomechanical DIR was 1.0 mm for controlling ROIs and ranged from 1.0 2.0 mm on 4DCT and 1.9 3.5 mm on MR for implicitly deformed soft-tissue ROIs (Fig. 2). These are reduced by a factor of 1.4 to 7.4 compared to rigid registration and within the image voxel resolution. The GTV on thoracic 4DCT which was deformed implicitly had a mean DTA of 1.3 mm vs. 2.2 mm with rigid registration (P = 0.004). When sliding interfaces were applied to the lungs, the mean DTA for the ribs on the thoracic 4DCT was 1.0 mm with biomechanical DIR vs. 0.6 mm with rigid registration (P < 0.001). With fixed interfaces, however the ribs mean DTA worsened to 1.6 mm with biomechanical DIR (Fig. 3). On average maximum DTA errors 5 mm were observed in 88% of ROIs evaluated, ranging from 4.6 21.0 mm on MR and CT-MR to 3.7 10.9 on 4DCT. The sensitivity of this metric to variability in the manual ROI delineations is discussed later. Mean DSC ranged from 0.93 to 0.99 for controlling ROIs and 0.78 0.93 for implicitly deformed ROIs. DSC < 0.80 occurred for the GTV (0.78) and bronchus (0.79) on thoracic 4DCT both of which had relatively small volumes (< 25 cc on average). FIG. 2. Surface ROI accuracy ( denotes structures used as controlling ROIs). [Color figure can be viewed at wileyonlinelibrary.com]

3412 Velec and Moseley: Biomechanical deformable registration 3412 Differences in mean DTA between the commercial and inhouse biomechanical DIR were all 0.5 mm despite the different boundary conditions used. Max DTA errors were similar in magnitude between implementations and differences in DSC were < 0.3. 3.B. Internal ROI accuracy The TRE for the commercial biomechanical DIR varied across the organs and datasets (Fig. 4) ranging from 2.0 mm for prostate MR to 5.1 mm for lung MR. These were within 0.1 mm or lower than the corresponding image voxel resolutions. Biomechanical DIR reduced the TRE by a factor of 1.6 to 6.4 compared to rigid registration. The prostate MR data, initially rigidly registered using fiducial markers, was one exception with a TRE of 2.1 mm before and after DIR although the prostate surface s mean DTA was concurrently reduced by half (Fig. 5) after DIR from 1.6 to 0.8 mm. Each organ s TRE was noted to be approximately 2 to 3 times larger than the corresponding mean DTA. Maximum errors at individual POIs > 5 mm were observed with the commercial and in-house biomechanical DIR for all data except for the prostate MR with a max error of 4.4 mm. These were largest in the lungs with maximum (95th percentile) errors of 10.2 (9.0) and 17.8 (6.9) mm for MR and 4DCT, respectively. Individual POI errors of any magnitude from DIR correlated poorly with motion magnitude (i.e., baseline errors with rigid registration), with R 2 ranging from < 0.0001 on abdominal 4DCT to 0.2373 on abdominal MR. No trends were observed for the locations of errors > 5 mm, for example proximity to the controlling ROI surfaces. Mean TRE differences between the commercial and inhouse DIR ranged from 0 to 0.7 mm (P > 0.05) and maximum errors to any POI were similar in magnitude between implementations. The magnitudes of POI-specific errors between implementations were well correlated with r 2 ranging from 0.5339 on prostate MR to 0.8681 on thoracic MR. Maximum differences in POI error were < 4 mm for all datasets. Although TRE differences described above were submillimeter on average, during initial testing of the liver datasets 6 of 33 cases were observed to have individual POI differences > 2 mm (CT-MR n = 4, MR-MR n = 1). The source of the internal POI differences was investigated in further detail as follows. The surface mesh displacements from the commercial DIR from the TPS were extracted and applied to the in-house biomechanical FIG. 3. Impact of three different registrations on rib alignment between inhale (blue image) and exhale (orange image) thoracic 4DCT datasets: biomechanical DIR with either fixed (left) or sliding lung interfaces (middle), or baseline rigid registration (right). [Color figure can be viewed at wileyonlinelibrary.com] FIG. 4. Internal ROI accuracy (all organs were used as controlling ROIs during DIR). [Color figure can be viewed at wileyonlinelibrary.com]

3413 Velec and Moseley: Biomechanical deformable registration 3413 FIG. 5. Example of biomechanical DIR improving prostate surface alignment (solid surface = reference, mesh = target) vs. rigid registration. Fiducial alignment is similar for both registrations (solid spheres = reference, dashed spheres = target). [Color figure can be viewed at wileyonlinelibrary.com] model, allowing the impact of different boundary conditions (i.e., model-based segmentation vs. guided-surface projections) to be tested. The correlation of the magnitude of individual POI errors between implementations improved from r 2 0.51 to 0.92 when the TPS boundary conditions were used in both models. In two of the six patients, the TRE differed by 1.7 mm and 2.3 mm between implementation and these differences were reduced to 0.1 mm when the TPS boundary conditions were used in both models. These results indicate any differences between biomechanical DIR implementations are largely due to the boundary conditions. 3.C. Image similarity metrics As with the DTA and TRE metrics, there were trends for improved (i.e., higher) CC and MI across the datasets with biomechanical DIR vs. rigid registration on average. Patientspecific TRE magnitude and image similarity metrics were poorly correlated (not shown), although the sample size for any one anatomical category was small (range 5 20). 3.D. Impact of contour variability ROI contours on thoracic/abdominal 4DCT and prostate MR were repeated and compared to the original contours using the average surface accuracy metrics. DSC was 0.90 for all ROIs except for the lung GTV and bronchus with DSC = 0.85. Mean DTA was 1.0 mm for all ROIs except for the heart and each lung (range 1.5 1.7 mm). Max DTA was < 5 mm for the prostate, spleen, lung GTV, bronchus, 8.0 9.4 mm for the kidneys, liver and stomach, 11.1 mm for the heart and 13.9 mm for the lungs. The max DTA between original and repeat contours are compared to the max DTA errors from biomechanical DIR. The magnitude of max DTA was similar for the prostate and spleen with differences < 1 mm. For the kidneys, liver, heart, and lungs, the max DTA between contours were 1.2 7.7 mm larger than the errors from DIR. The max DTA between contours was smaller than the results from DIR by 2.1 mm for the lung GTV, 3.0 mm for the bronchus, and 5.7 mm for the stomach. Therefore on average, for the majority of ROIs (82%) the max DTA error from DIR is within the contouring uncertainty. Biomechanical DIR was repeated using new controlling ROI meshes generated from repeat contours. Mean changes in accuracy, initial DIR repeat DIR, to the original contours for the implicitly deformed ROIs and POIs were measured. Changes in TRE (maximum POI error) were 0.1 (2.8), 0.3 (4.7) and 0.8 (3.4) mm for the liver, lung and prostate respectively. All ROI surface changes were DSC 0.05, mean DTA 0.2 mm and max DTA 0.6 mm

3414 Velec and Moseley: Biomechanical deformable registration 3414 (except for the heart with a change of 2.2 mm). On average, the sensitivity of biomechanical DIR results to contour variability is sub-millimeter as in shown in the example in Fig. 6. 3.E. Comparison to hybrid DIR For hybrid DIR using both intensity and ROI information, or ROI-only, the mean DTA was within the image voxel resolution for all ROIs across all datasets, including for images for which hybrid DIR was not yet validated (i.e., MR only) or recommended by the vendor (i.e., CT-MR). The mean DTA for hybrid DIR using both intensity and ROIs was generally lower than biomechanical DIR although differences were 0.7 mm, except for the lungs on MR which was 1.4 mm lower (Fig. 2). For hybrid DIR using both intensity and ROIs, the mean TRE varied more widely across the datasets compared to biomechanical DIR which performed consistently similar to or lower than the image resolutions (Fig. 4). As expected, the residual errors were lowest on the mono-modality, featurerich 4DCT data with a lung TRE of 2.7 mm (vs. biomechanical DIR 2.9 mm, P = 0.15) and liver TRE of 3.3 mm (vs. 2.7 mm, P = 0.09). The same ROIs on MR data had a lung TRE of 4.5 mm (vs. biomechanical DIR 4.4 mm, P=0.87) and liver TRE of 3.9 mm (vs. 2.8 mm, P = 0.13). The TRE was 8.2 mm for liver CT-MR (vs. 4.4 mm for biomechanical DIR, P=0.0008) and 3.9 mm for prostate MR data (vs. 2.0 mm, P=0.0001), larger than the baseline rigid registrations despite aligning the organ surfaces with sub-millimeter accuracy. Using ROI-only information for hybrid DIR, effectively behaving as a pure geometry-based algorithm, reduced the TRE for liver CT-MR by 3.2 mm and for prostate MR by 1.7 mm compared to using both intensity and ROI information. However, the TRE increased slightly in the remaining datasets by 0.7 1.2 mm compared to using both intensity and ROI-only information. The two algorithms driven purely by contours were compared in more detail. Compared to biomechanical DIR, the TRE from hybrid DIR using ROI-only information was higher by 1.2 (P = 0.01), 1.5 (P = 0.003), 1.6 (P < 0.0001), 1.9 (P = 0.002), and 1.3 mm (P = 0.02) for the liver CT- MR, liver 4DCT, lung 4DCT, liver MR and lung MR data respectively. Differences were 0.1 mm for the prostate MR (P = 0.79) data. The overall trend is a significant improvement in the internal ROI accuracy for structures used as controlling ROIs for five of six datasets with biomechanical DIR. Among structures not used as controlling ROIs (Fig. 2), and which lack internal landmarks to quantify the TRE, the mean DTA was lower (P 0.03) in the GTV on lung 4DCT and the kidneys on liver 4DCT with biomechanical DIR, although the improvement was sub-millimeter. To further investigate how much biomechanical modeling impacts the registration over the hybrid DIR using ROI-only information, the deformation vector fields were extracted from the TPS and compared voxel-by-voxel. Averaged over all the datasets, the mean standard deviation (95th percentile) of 3D differences in the deformation vector field are 1.8 0.7 mm (5.9 mm) in the prostate, 3.8 1.8 mm (7.1 mm) in the liver, and 3.6 2.4 mm (8.3 mm) in the lung. Figure 7 shows individual examples of the distribution (a) (b) FIG. 6. Impact of contouring variability on accuracy metrics: (a). Manual original contours vs. manual repeat contours on inhale 4DCT; (b). Accuracy of rigid registration (manual exhale contours vs. manual inhale contours), and biomechanical DIR (manual exhale contours deformed to inhale vs. actual inhale contours) using two different sets of contours (yellow or green). DIR reduces the mean DTA for the liver and stomach to values similar to the baseline variations, irrespective of contours used for DIR. [Color figure can be viewed at wileyonlinelibrary.com]

3415 Velec and Moseley: Biomechanical deformable registration 3415 of vector differences for each dataset. It should be noted that these plot relative differences and the ground-truth deformation on patient images are not known voxel-by-voxel. However, the relative differences in the deformation maps combined with the differences in absolute accuracy described above demonstrate that both DIR approaches relying only on contours behave substantially different. 3.F. Performance of clinical system Accuracy of commercial biomechanical DIR was compared between TPS versions, v4.5 v4.6. On average, the differences in TRE were 0.1 mm for the liver and lung and 0.4 mm for the prostate, and differences in mean DTA and DSC were 0.1 mm and 0.01 respectively. DIR computation time for the commercial implementation excluding contouring and mesh generation ranged from 24 s for the prostate to 162 s for the lung data on average. 4. DISCUSSION A biomechanical DIR algorithm developed in-house was translated into the first commercial TPS implementation. In this study, DIR was evaluated on over 70 patients with thoracic and abdominal 4DCT and MR, and prostate MR imaging. Accuracy measured at ROI surfaces and internally at anatomic POI landmarks was on average within the image voxel resolutions, and differences compared to the previously validated in-house implementation were sub-millimeter. In the commercial TPS, biomechanical DIR had favorable internal ROI accuracy overall compared to hybrid DIR using either contours and image intensities, or contours alone. Although in vivo material properties may not be accurately known, studies have reported varying material property parameters in finite element models does not substantially impact registration accuracy. Chi et al. estimated that a 30% material uncertainty in the prostate results in maximum subvolume registration errors of 1.3 mm on average, with most sub-volume errors being much smaller. 17 In general, boundary conditions have a larger impact on registration accuracy than material properties (including linear vs. nonlinear elasticity), element type and size, and analysis technique (linear vs. nonlinear geometry). 13,18 20 The commercial TPS implementation uses meshes from a model-based segmentation module as boundary conditions. Therefore future modifications to this feature require verification of DIR accuracy. It should be noted that boundary conditions for small irregularly shaped ROIs often failed to be created in the current TPS (v4.5) when surfaces failed to adapt to contours. This specifically prevented using the rectum as a controlling ROI and limited the prostate MR data to single-organ registration. Future TPS versions are expected to improve the ability to generate meshes for these ROIs. Other studies of biomechanical DIR including the in-house implementation have successfully registered rectum ROIs using different boundary conditions. 21,22 Hybrid DIR uses contours directly without the need of a surface mesh correspondence and has previously resulted in DSC > 0.90 for rectum Voxels, % Liver GTV Spleen R Kidney L Kidney Stomach Lungs GTV Heart Bone Bronchus Liver GTV Abdominal 4DCT Thoracic 4DCT Liver CT-MR Voxels, % Liver Spleen R Kidney L Kidney Stomach Lungs R Breast L Breast Prostate Abdominal MR Thoracic MR Prostate MR Difference, mm Difference, mm Difference, mm FIG. 7. Cumulative histogram of the 3D differences in the deformation vector fields between biomechanical DIR and hybrid DIR using ROI-only information. Representative cases for each dataset are shown. [Color figure can be viewed at wileyonlinelibrary.com]

3416 Velec and Moseley: Biomechanical deformable registration 3416 ROIs. 16 In the current study, ROIs were also re-contoured and the variations were found to have minimal impact on the TRE and mean DTA indicating biomechanical DIR is not sensitive to delineation-scale variations on average. In general, maximum DTA errors > 5 mm following DIR were similar in magnitude to the inherent uncertainty in the delineations. Intraobserver variability in POI identification was previously quantified to be 0.7 mm. 11 Data from one patient for each of 4DCT, CT-MR, and prostate MR were used in a previous multi-institution DIR accuracy study allowing for a comparison to other algorithms. 14 Compared to the best-performing, nonbiomechanical DIR algorithm which differed between datasets, the TRE for the current commercial biomechanical DIR is within 1.8 mm for lung and liver 4DCT, 1.1 mm lower for liver CT- MR, and 2.2 mm lower for prostate MR. In the previous work, 16 institutions submitted results for 4DCT and only two for the CT-MR and prostate MR highlighting limited options for multimodality registration. This is notable as more non-ct images are being relied on for radiotherapy planning, guidance, and response assessment. Hybrid DIR had in general the lowest mean DTA including for structures not used as controlling ROIs and on MR. It was likely aided by the relatively high contrast along ROI surfaces for CT and MR data, though it should be noted that hybrid DIR was not developed for use on MR or CT-MR. This was included in the current study to highlight the effect of applying intensity-based or hybrid algorithms to data for which it was not intended. Hybrid DIR had a TRE exceeding the resolutions for the liver CT-MR and prostate MR, although this TRE was reduced when the algorithm used ROI information only on this data. The fact that surface alignment does not guarantee accurate internal registration is particularly challenging for DIR that fully or partially relies on image intensities, as validation on one modality should not be assumed to hold for another without verification. An additional complication arises when it is not be possible to verify TRE in particular scenarios (e.g., using liver anatomic landmarks on cone-beam CT). Other intensity-based DIR algorithms have had success with MR images. Rohlfing et al. registered liver MR within the image resolution using a B- spline algorithm driven by a mutual information similarity metric. 23 For biomechanical DIR, the TRE was similar or lower than the resolution for all datasets and this can be reasonably assumed to hold for any modality provided the controlling ROIs can be delineated consistently. Two variations of geometry-based DIRs were also compared in the current work with results showing a significantly more accurate registration with the biomechanical model, indicating not all purely contour-driven algorithms are equal. There is no consensus method to verify DIR accuracy in routine clinical application. Motion magnitude and image similarity metrics that could be rapidly computed had no clear relationship with respect to residual geometric DIR errors at the magnitude found here. Manually delineating anatomy to quantify TRE and DTA is time consuming and POI landmarks are not always visible on noncontrast imaging. Even with automated segmentation or visual inspection of organ boundary alignment, discrepancies between internal accuracy (i.e., TRE) and surface accuracy (i.e., DTA) were observed. This underscores importance of upfront DIR validation to establish baseline accuracy and this work will supplement the commissioning tests based on phantom data outlined in the AAPM Task Group 132 report when released. 24 This study focused on registration of thorax, abdomen, and prostate only and separate evaluations of other regions are recommended prior to clinical use, as accuracy differs somewhat by anatomic site. Potential clinical applications of the commercial biomechanical DIR supported by this work include 4D dose accumulation in the thorax or abdomen (i.e., based on exhale and inhale images) and MR-guided targeting of intraprostatic lesions with brachytherapy, currently performed using the in-house implementation. 25 Although beyond the scope of this study, interfraction dose accumulation based on daily cone-beam CT is under development for these anatomic sites and requires additional DIR validation. Planned efforts include investigating the effect of contour variability on cone-beam CT and the need for additional ROIs to resolve motion not observed on the images use in the current study (e.g., organ filling, tumor regression). 5. CONCLUSIONS In summary, a biomechanical model-based DIR algorithm initially developed in-house was translated to a commercial TPS and its accuracy was validated over a large cohort of clinical data in the abdomen, thorax, and prostate. Registration accuracy of the TPS was on average within the image voxel resolution for 4DCT, CT-MR, and MR data, and differences compared to the in-house implementation were submillimeter. The TPS implementation facilitates the routine clinical application of biomechanical DIR to enable accurate image registration across multiple modalities. ACKNOWLEDGMENTS This research is supported by the Canadian Institutes of Health Research (Fellowship 140905) and RaySearch Laboratories. Prior in-house algorithm development was supported by the U.S. National Institutes of Health (5RO1CA124714). From the Princess Margaret Cancer Centre, the authors thank A. McPartlin and B. Lofgren for their help with this study, L.A. Dawson, C. Menard and A.J. Bezjak for providing the clinical data, and the patients for their research participation. CONFLICT OF INTEREST K.K. Brock, J.L. Moseley, and D.A. Jaffray have a licensing agreement with RaySearch Laboratories for the deformable registration technology in this study. S. Svensson and B. Hardemark are employees of RaySearch Laboratories.

3417 Velec and Moseley: Biomechanical deformable registration 3417 a) Author to whom correspondence should be addressed. Electronic mail: michael.velec@rmp.uhn.ca. REFERENCES 1. Kumarasiri A, Siddiqui F, Liu C, et al. Deformable image registration based automatic CT-to-CT contour propagation for head and neck adaptive radiotherapy in the routine clinical setting. Med Phys. 2014;41:121712. 2. Mazaheri Y, Bokacheva L, Kroon DJ, et al. Semi-automatic deformable registration of prostate MR images to pathological slices. J Magn Reson Imaging. 2010;32:1149 1157. 3. Speight R, Sykes J, Lindsay R, Franks K, Thwaites D. The evaluation of a deformable image registration segmentation technique for semi-automating internal target volume (ITV) production from 4DCT images of lung stereotactic body radiotherapy (SBRT) patients. Radiother Oncol. 2011;98:277 283. 4. Swaminath A, Massey C, Brierley JD, et al. Accumulated delivered dose response of stereotactic body radiation therapy for liver metastases. Int J Radiat Oncol Biol Phys. 2015;93:639 648. 5. Brock KK, Velec M, Lee JHM. Validation of image registration. In: Brock KK, ed. Image Processing in Radiation Therapy. Boca Raton: CRC Press; 2013:41 62. 6. Brock KK, Dawson LA, Sharpe MB, Moseley DJ, Jaffray DA. Feasibility of a novel deformable image registration technique to facilitate classification, targeting, and monitoring of tumor and normal tissue. Int J Radiat Oncol Biol Phys. 2006;64:1245 1254. 7. Juang T, Das S, Adamovics J, Benning R, Oldham M. On the need for comprehensive validation of deformable image registration, investigated with a novel 3-dimensional deformable dosimeter. Int J Radiat Oncol Biol Phys. 2013;87:414 421. 8. Velec M, Juang T, Moseley JL, Oldham M, Brock KK. Utility and validation of biomechanical deformable image registration in low-contrast images. Pract Radiat Oncol. 2015;5:e401 e408. 9. Zhong H, Kim J, Li H, Nurushev T, Movsas B, Chetty IJ. A finite element method to correct deformable image registration errors in low-contrast regions. Phys Med Biol. 2012;57:3499 3515. 10. Brock KK, Sharpe MB, Dawson LA, Kim SM, Jaffray DA. Accuracy of finite element model-based multi-organ deformable image registration. Med Phys. 2005;32:1647 1659. 11. Samavati N, Velec M, Brock K. A hybrid biomechanical intensity based deformable image registration of lung 4DCT. Phys Med Biol. 2015;60:3359 3373. 12. Niu CJ, Foltz WD, Velec M, Moseley JL, Al-Mayah A, Brock KK. A novel technique to enable experimental validation of deformable dose accumulation. Med Phys. 2012;39:765 776. 13. Brock KK, Nichol AM, Menard C, et al. Accuracy and sensitivity of finite element model-based deformable registration of the prostate. Med Phys. 2008;35:4019 4025. 14. Brock KK. Results of a multi-institution deformable registration accuracy study (MIDRAS). Int J Radiat Oncol Biol Phys. 2010;76:583 596. 15. Kashani R, Hub M, Balter JM, et al. Objective assessment of deformable image registration in radiotherapy: a multi-institution study. Med Phys. 2008;35:5944 5953. 16. Weistrand O, Svensson S. The ANACONDA algorithm for deformable image registration in radiotherapy. Med Phys. 2015;42:40 53. 17. Chi Y, Liang J, Yan D. A material sensitivity study on the accuracy of deformable organ registration using linear biomechanical models. Med Phys. 2006;33:421 433. 18. Al-Mayah A, Moseley J, Velec M, Brock K. Toward efficient biomechanical-based deformable image registration of lungs for image-guided radiotherapy. Phys Med Biol. 2011;56:4701 4713. 19. Al-Mayah A, Moseley J, Velec M, Brock KK. Sliding characteristic and material compressibility of human lung: parametric study and verification. Med Phys. 2009;36:4625 4633. 20. Tanner C, Schnabel JA, Hill DL, Hawkes DJ, Leach MO, Hose DR. Factors influencing the accuracy of biomechanical breast models. Med Phys. 2006;33:1758 1769. 21. Boubaker MB, Haboussi M, Ganghoffer JF, Aletti P. Finite element simulation of interactions between pelvic organs: predictive model of the prostate motion in the context of radiotherapy. J Biomech. 2009;42:1862 1868. 22. Brierley JD, Dawson LA, Sampson E, et al. Rectal motion in patients receiving preoperative radiotherapy for carcinoma of the rectum. Int J Radiat Oncol Biol Phys. 2011;80:97 102. 23. Rohlfing T, Maurer CR Jr, O Dell WG, Zhong J. Modeling liver motion and deformation during the respiratory cycle using intensity-based nonrigid registration of gated MR images. Med Phys. 2004;31:427 432. 24. Brock KK, Mutic S, McNutt TR, Li H, Kessler ML. Use of image registration and fusion algorithms and techniques in radiotherapy: report of the AAPM radiation therapy committee task group no. 132. Med Phys. Accepted Author Manuscript. https://doi.org/10.1002/mp.12256 25. Hosni A, Carlone M, Rink A, Menard C, Chung P, Berlin A. Dosimetric feasibility of ablative dose escalated focal monotherapy with MRIguided high-dose-rate (HDR) brachytherapy for prostate cancer. Radiother Oncol. 2017;122:103 108. 26. Logg A, Mardal KA, Wells GN. Automated Solution of Differential Equations by the Finite Element Method, 1st edn. Berlin, Heidelberg: Springer-Verlag; 2012. 27. Logg A, Wells GN. DOLFIN: automated finite element computing. ACM Trans Math Softw (TOMS) 2010; 37, 20. 28. Al-Mayah A, Moseley J, Velec M, Brock KK. Deformable modeling of human liver with contact surface. In: Science and Technology for Humanity (TIC-STH), 2009 IEEE Toronto International Conference. Vol. 7261. Toronto, ON: IEEE; 2009:137 140. 29. Voroney JP, Brock KK, Eccles C, Haider M, Dawson LA. Prospective comparison of computed tomography and magnetic resonance imaging for liver cancer delineation using deformable image registration. Int J Radiat Oncol Biol Phys. 2006;66:780 791. 30. Hensel JM, Menard C, Chung PW, et al. Development of multiorgan finite element-based prostate deformation model enabling registration of endorectal coil magnetic resonance imaging for radiotherapy planning. Int J Radiat Oncol Biol Phys. 2007;68:1522 1528.