Abstract
Background:
Successful generation of biomechanical-model-based deformable image registration (BM-DIR) relies on user-defined parameters that dictate surface mesh quality. The trial-and-error process to determine the optimal parameters can be labor-intensive and hinder DIR efficiency and clinical workflow.
Purpose:
To identify optimal parameters in surface mesh generation as boundary conditions for a BM-DIR in longitudinal liver and lung CT images to facilitate streamlined image registration processes.
Methods:
Contrast-enhanced CT images of 29 colorectal liver cancer patients and end-exhale four-dimensional CT images of 26 locally advanced non-small cell lung cancer patients were collected. Different combinations of parameters that determine the triangle mesh quality (voxel side length and triangle edge length) were investigated. The quality of DIRs generated using these parameters was evaluated with metrics for geometric accuracy, robustness, and efficiency. Metrics for geometric accuracy included target registration error (TRE) of internal vessel bifurcations, dice similar coefficient (DSC), mean distance to agreement (MDA), Hausdorff distance (HD) for organ contours, and number of vertices in the triangle mesh. American Association of Physicists in Medicine Task Group 132 was used to ensure parameters met TRE, DSC, MDA recommendations before the comparison among the parameters. Robustness was evaluated as the success rate of DIR generation, and efficiency was evaluated as the total time to generate boundary conditions and compute finite element analysis.
Results:
Voxel side length of 0.2 cm and triangle edge length of 3 were found to be the optimal parameters for both liver and lung, with success rate of 1.00 and 0.98 and average DIR computation time of 100 and 143 s, respectively. For this combination, the average TRE, DSC, MDA, and HD were 0.38–0.40, 0.96–0.97, 0.09–0.12, and 0.87–1.17 mm, respectively.
Conclusion:
The optimal parameters were found for the analyzed patients. The decision-making process described in this study serves as a recommendation for BM-DIR algorithms to be used for liver and lung. These parameters can facilitate consistence in the evaluation of published studies and more widespread utilization of BM-DIR in clinical practice.
Keywords: biomechanical-model-based image registration, deformable image registration, optimization
1 |. INTRODUCTION
Biomechanical-model-based deformable image registrations (BM-DIRs) can aid image-guided radiation therapy in registering liver and lung anatomies, allowing contour propagation, tumor tracking, dose accumulation, and response assessment.1–4 They have been reported to provide improved accuracy and more realistic deformation compared to intensity-based DIRs.5–8 However, biomechanical models estimate a dense deformation vector field (DVF) by necessitating organ-specific boundary conditions applied on organ contours to estimate the finite element model (FEM) representing the patient anatomy before performing the finite element analysis (FEA),9 which can be more time-consuming than classical intensity-based DIR algorithms.10 Additionally, user-defined parameters such as boundary condition and mesh resolution dictate FEM quality and eventually affect the topology and success of the generated DVF. As a result, the current implementation of BM-DIR is limited by uncertainties in model parameters, which further increases registration time and vulnerability. From our clinical research experience, DIR failure can occur in ~15% cases. This disrupts the image registration workflow and especially hinders the efficiency of inter-fractional dose mapping where the DIRs sharing the same reference image would consistently fail. Therefore, identifying parameters that consistently produced accurate registrations is crucial toward a more comprehensive integration of BM-DIRs into clinical workflow, especially when longitudinal registrations are involved such as adaptive radiation therapy and image/dose deformations for response assessment.2,11–13
A BM-DIR algorithm (Morfeus) has been implemented in a commercial treatment planning system (TPS) (RayStation, RaySearch Laboratories, Stockholm, Sweden).14 In this study, we investigated the different parameters in surface mesh generation that influence the boundary conditions in the estimation of an FEM-based DVF for longitudinal liver and lung images. The robustness and efficiency of the DIR process using these parameters for liver and lung anatomies were compared to find the optimal parameters.
2 |. MATERIALS AND METHODS
2.1. Patient data
For liver registrations, pre- and posttreatment contrast-enhanced breath-hold CT images of 29 colorectal liver cancer patients were obtained under a retrospective institutional review board (IRB)-approved protocol. These patients were previously treated with microwave ablation to treat colorectal liver metastasis. The median image voxel size was 0.74 × 0.74 × 2.5 mm3 (minimum:0.56 × 0.56 × 2 mm3, maximum: 0.88 × 0.88 × 5 mm3). For each patient, the liver was manually contoured by a graduate student under the guidance and review of a board-certified interventional radiologist (BO).
For lung registrations, four-dimensional CT (4DCT) images of 26 locally advanced non-small cell lung cancer patients without major atelectasis or substantial tumor shrinkage were acquired under a retrospective IRB-approved protocol. These patients were previously treated with concurrent chemoradiotherapy on a prospective clinical trial. End-exhalation phases of the planning and mid-treatment 4DCT were used as the reference and target images, respectively. Image resolution across all images was 0.98 × 0.98 × 2.5 mm3. Both left and right lungs were contoured by a graduate student under the guidance and reviewed by a board-certified radiation oncologist (ZL).
To assess volumetric alignment, target registration error (TRE) was quantified using landmarks at vasculature branching points inside liver and lung anatomy. Liver landmarks were manually identified with an average of 4 per patient (0–29). The number of liver landmarks was limited by the number of vessels, varying contrast stages of the analyzed CTs, and underlying diseases. On the other hand, lung landmarks were identified using a validated, in-house, automatic landmark identification algorithm with an average of 191 per patient (111–343).15 The magnitude of deformation was assessed by computing the TRE immediately following rigid registration, which averaged 5.7 mm, with maximum TRE values per patient of 7.4–21.1 mm. Figure 1 shows renderings of landmarks within organs from sample patients in RayStation.
FIGURE 1.
3D rendering of landmarks in liver (left) and lungs (right)
2.1 |. Biomechanical-model-based registration algorithm in RayStation
The BM-DIR implementation in the commercial TPS (RayStation 10B, Stockholm, Sweden) consists of two steps: FEM generation and FEA. In the first step, organ and body drawn polygon-sliced contours in both reference and target images are converted into voxel masks of the same spacing (Figure 1 (left)). Triangular surface meshes are generated using a defined triangular length derived from the down-sampled voxel size of the voxel masks in the reference image, exerting a smoothing effect to the overall mesh surface reducing the number of sharp edges (Figure 2b). The reference triangle meshes are then rigidly transformed to the target image and adapted to the corresponding voxel mask. Distances from the edge of the voxel mask are used to drive the cost function in the adaptation process.
FIGURE 2.
(a) Voxel masks, (b) surface renderings, and (c) wireframe representations of the same lung using voxels with spacings of 0.1 cm (left) versus 0.25 cm (right)
In the second step, the reference triangular surface meshes are converted to tetrahedral volumetric meshes (i.e., FEM) using a finite element generator Netgen/NGSolve.16 Using the FEM representation of the reference patient anatomy and the point-to-point boundary conditions, an FEA is performed to estimate the displacements of the FEM nodes inside the organs, not constrained by the boundary conditions.
RayStation allows two types of relationship between organs within the FEM. The “fixed” interface attaches the surface points of the organ to the body nodes in the FEM, allowing a continuous deformation over the organ surface where the reference mesh vertices are mapped to the corresponding target mesh vertices—a point-to-point correspondence. In the case of a liver registration, the nodes outside the liver will follow the boundary condition direction.14 The “sliding” interface models a frictionless contact surface between the inner and external organ elements where the nodes directly outside the inner elements do not follow along. In the case of a lung registration where the sliding interface model is used, the FEM will allow discontinuity between the nodes at the interface of the lung and chest wall.17
The complexity of the triangular surface mesh, as determined by user-defined parameters, directly affects the generation of the FEM. If FEM generation fails, the user must recreate surface meshes using different parameters until the algorithm succeeds, hindering efficiency of the workflow. At the same time, the triangular surface mesh should retain the original organ shape. The following section therefore introduces the investigated parameters and the metrics that reflect the robustness and efficiency of the DIR process using these parameters.
2.2 |. Parameters for boundary conditions
In RayStation 10B, different combinations of two parameters: Voxel side length and triangle edge length were tested to generate the surface meshes and boundary conditions required for the biomechanical-model-based DIR. The voxel side length refers to the voxel size for the voxel masks. The triangle edge length is the approximate triangle edge length expressed in number of voxels in the voxel mask.
Parameters for liver registrations were first investigated. Voxel side lengths of 0.15, 0.2, and 0.25 cm were each investigated in combination with triangle edge lengths of 1, 2, and 3. For lung, the tested parameters were narrowed down to four parameters that well performed for liver per the evaluation metrics mentioned in the following section: Voxel side lengths of 0.2 and 0.25 cm were each investigated in combination with triangle edge lengths of 2 and 3.
All tests were performed in a research version of RayStation (10B DTK, v10.1.110.138) running on Windows 2016 Server edition equipped with a 6-T T4 15-Gb GPU.
2.3 |. Evaluation
The resulting BM-DIR created from different parameter combinations were first evaluated based on a geometric accuracy of the registration, per recommendations of the American Association of Physicists in Medicine (AAPM) Task Group 132 (TG-132).18 The surface alignment was evaluated for each organ contour (i.e., liver, left lung, or right lung) using Dice similarity coefficient (DSC), mean distance to agreement (MDA),and Hausdorff distance (HD) between the deformed reference and the target organ representations. Achieving the TG-132 recommendations was identified as the most important goal.
Second, robustness was evaluated based on the average success rate (i.e., ability to create a DIR: pass/fail). Robustness was identified as the next highest priority as modest increases in time were deemed worth ensuring that the algorithm would complete the DIR. Third, efficiency was evaluated based on the total time to generate the DIR (from surface mesh to DVF generation). Together, these ensure minimum user intervention in a streamlined workflow (e.g., image-guided clinical workflow). Finally, FEM complexity was evaluated for each organ contour using the number of surface mesh vertices.
2.4 |. Statistical analysis
Performances of the different biomechanical-model-based DIRs were compared per set of parameters and evaluation metrics with paired comparisons using the paired student t-test, wherein a comparison was considered significant if the p value was strictly inferior to 0.05.
3 |. RESULTS
Tables 1 and 2 reported the mean (SD) performance of the BM-DIR using accuracy (mean and max TRE, DSC, MDA, and HD), robustness (success rate), efficiency (computation time), and FEM complexity for different boundary condition parameters for liver and lung images, respectively.
TABLE 1.
Biomechanical-model-based deformable image registration (BM-DIR) results for liver images
| Organ | Voxel side length (cm) | Triangle edge length | Success rate | Total time (s) | Mean TRE (cm) | Max TRE (cm) | DSC | MDA (cm) | HD (cm) | Number of vertices |
|---|---|---|---|---|---|---|---|---|---|---|
|
| ||||||||||
| Liver | 0.15 | 1 | 0.56 | 625 ± 98 | 0.35 ± 0.16 | 0.49 ± 0.32 | 0.98 ± 0.00 | 0.08 ± 0.01 | 0.93 ± 0.28 | 19529 ± 2750 |
| 2 | 0.93 | 277 ± 143 | 0.41 ± 0.28 | 0.53 ± 0.39 | 0.97 ± 0.00 | 0.08 ± 0.01 | 1.05 ± 0.35 | 8964 ± 1732 | ||
| 3 | 1.00 | 173 ± 78 | 0.39 ± 0.25 | 0.52 ± 0.35 | 0.97 ± 0.00 | 0.09 ± 0.01 | 1.06 ± 0.28 | 5254 ± 996 | ||
| 0.2 | 1 | 0.54 | 475 ± 136 | 0.48 ± 0.27 | 0.66 ± 0.37 | 0.97 ± 0.00 | 0.10 ± 0.01 | 0.96 ± 0.22 | 11496 ± 1741 | |
| 2 | 0.89 | 187 ± 134 | 0.40 ± 0.22 | 0.55 ± 0.34 | 0.97 ± 0.01 | 0.11 ± 0.01 | 1.10 ± 0.27 | 4938 ± 969 | ||
| 3 | 1.00 | 100 ± 53 | 0.38 ± 0.18 | 0.55 ± 0.35 | 0.97 ± 0.01 | 0.12 ± 0.02 | 1.17 ± 0.32 | 2936 ± 574 | ||
| 0.25 | 1 | 0.64 | 341 ± 192 | 0.50 ± 0.32 | 0.63 ± 0.39 | 0.97 ± 0.00 | 0.11 ± 0.01 | 0.99 ± 0.27 | 7431 ± 1643 | |
| 2 | 0.89 | 161 ± 157 | 0.46 ± 0.22 | 0.60 ± 0.31 | 0.96 ± 0.01 | 0.13 ± 0.01 | 1.12 ± 0.35 | 3098 ± 636 | ||
| 3 | 1.00 | 84 ± 46 | 0.42 ± 0.20 | 0.55 ± 0.29 | 0.96 ± 0.01 | 0.14 ± 0.02 | 1.18 ± 0.29 | 1850 ± 364 | ||
Note: Bold row represents the optimal parameters and their metrics for each function.
Abbreviations: DSC: dice similarity coefficient; DTA: distance to agreement; HD: Hausdorff distance;TRE: target registration error.
TABLE 2.
Biomechanical-model-based deformable image registration (BM-DIR) results for lung images
| Organ | Voxel side length (cm) | Triangle edge length | Success rate | Total time (s) | Mean TRE (cm) | Max TRE (cm) | DSC |
MDA (cm) |
HD (cm) |
Number of vertices |
||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Left lung | Right lung | Left lung | Right lung | Left lung | Right lung | Left lung | Right lung | |||||||
|
| ||||||||||||||
| Lung | 0.2 | 2 | 0.92 | 249 ± 136 | 0.41 ± 0.09 | 1.09 ± 0.28 | 0.97 ± 0.01 | 0.97 ± 0.01 | 0.09 ± 0.01 | 0.09 ± 0.01 | 0.84 ± 0.38 | 0.87 ± 0.40 | 5222 ± 996 | 5402 ± 965 |
| 3 | 0.96 | 143 ± 100 | 0.40 ± 0.09 | 1.07 ± 0.26 | 0.96 ± 0.01 | 0.97 ± 0.01 | 0.09 ± 0.01 | 0.09 ± 0.01 | 0.87 ± 0.39 | 0.88 ± 0.45 | 2995 ± 600 | 3218 ± 629 | ||
| 0.25 | 2 | 0.96 | 159 ± 102 | 0.41 ± 0.09 | 1.08 ± 0.27 | 0.95 ± 0.01 | 0.96 ± 0.01 | 0.12 ± 0.01 | 0.11 ± 0.01 | 0.94 ± 0.45 | 0.91 ± 0.44 | 3224 ± 742 | 3372 ± 616 | |
| 3 | 0.88 | 155 ± 166 | 0.40 ± 0.07 | 1.02 ± 0.23 | 0.95 ± 0.01 | 0.96 ± 0.01 | 0.12 ± 0.01 | 0.11 ± 0.01 | 1.02 ± 0.50 | 0.94 ± 0.40 | 1930 ± 337 | 1975 ± 409 | ||
Note: Bold row represents the optimal parameters and their metrics. Mean and max TRE were calculated for both lungs combined. For DSC, mean DTA, HD, and number of vertices, results of each left and right lung were shown in the left and right half cells, respectively.
Abbreviations: DSC: dice similarity coefficient; DTA: distance to agreement; HD: Hausdorff distance;TRE: target registration error.
3.1 |. Accuracy
AAPM TG-132 recommends that TRE and MDA be within the maximum image voxel dimension.18 The diagonal dimension (longest vertex–vertex distance) of liver and lung image voxel was 2.71 (2.15–5.15) and 2.86 mm, respectively. The parameters for liver and lung both returned mean TREs exceeding the respective tolerance but were comparable to the mean TRE of original publication of the DIR algorithm using inhale–exhale liver and lung CT images as the benchmark of 4.4 ± 2.0 mm. The three parameters with the lowest TRE were recommended for further consideration based on this test, which achieved a TRE of less than 4.0 mm. The largest MDA among liver parameters was 1.4 mm, and the largest MDA among lung parameters was 1.2 (left lung) and 1.1 mm (right lung).
The task group recommends a DSC of 0.80–0.90, which is the typical inter- and intra-observer variability in contouring.18 The lowest DSC was 0.96 for liver and 0.95 and 0.96 for left and right lungs, respectively. Both MDA and DSC results were based on comparing the target contour with the mapped reference contour. All liver and lung parameters satisfied MDA and DSC recommendations.
3.2 |. Robustness, efficiency, and complexity
Triangle edge length of 1 resulted in 54%–64% success rate and was therefore not considered a clinically robust solution. Overall, 100% success was found in three parameter combinations: voxel side lengths of 0.15, 0.2, and 0.25 cm each combined with a triangle edge length of 3. However, 0.15-cm side length on average required more than double the time to compute FEA for the remaining two (both p < 0.001), thereby not clinically advantageous. In addition, compared to a voxel side length of 0.25 cm, a voxel side length of 0.2 cm resulted in no significant difference for MDA, HD, or DSC, a decrease in efficiency (longer FEA computation time, p < 0.05), but an improvement in TRE (p < 0.05). As a result, the optimal parameter combination was determined to be a side length of 0.2 cm and an edge length of 3 cm.
For lung, all parameter combinations experienced failures from the Netgen FEA generator, the third-party software component implemented for volumetric tetrahedral generation. However, voxel side length of 0.25 cm + triangle edge length of 3 succeeded in less than 90% of total cases and was therefore not considered ideal for a clinically robust solution. Subsequently, DIR computation time was evaluated for the remaining parameters, and voxel side length of 0.2 cm + triangle edge length of 2 on average required more than 1 min that is more than that of the remaining parameters, thereby not clinically advantageous. Comparing the remaining two parameter combinations: voxel side length of 0.2 cm + triangle edge length of 3 versus voxel side length of 0.25 cm + triangle edge length of 2, the former on average yielded insignificantly superior TRE metrics and HD but significantly superior DSC and MDA (p < 0.01), despite not clinically significant. However, the former yielded coarser meshes (number of vertices) indicating inferior FEM complexity (p < 0.05). Despite the similar quality of FEM and DIR between these two parameters, the optimal parameter was determined to be a voxel side length of 0.2 cm with a triangle edge length of 3 due to its slightly outperforming surface alignment. However, a voxel side length of 0.25 cm with a triangle edge length of 2 is recommended as a viable option.
4 |. DISCUSSION
This study investigated different parameter combinations used to generate the surface mesh for the BM-DIR implemented in a commercial TPS, using pre- and post-ablation liver contrast-enhanced CT and planning and mid-treatment radiotherapy lung 4DCT images. The success rate, efficiency, and accuracy of the generated DIR using these parameters were evaluated, and the optimal parameters for each organ were found. The decision-making process described in this study serves as a recommendation for the RayStation biomechanical-model-based DIR algorithm and a potential reference for other biomechanical DIR systems. These parameters were subsequently verified on 16 head-and-neck cancer patients and 16 prostate cancer patients randomly selected from an existing IRB protocol. All cases had biomechanical DIR successfully completed using the optimized parameters for the parotid glands19 and prostate.20
First and foremost, the DIR should strive to meet volumetric and surface accuracy tolerances recommended by AAPM TG-132.18 Volumetrically, the optimal parameters yielded comparable TRE results compared to the original Morfeus publication14 but did not meet the TG-132 tolerance, with the TRE exceeding the voxel dimension by 1.1 mm. However, TG-132 did note that these metrics were a target goal and may not be met with current DIR algorithms, and when not met, the uncertainty should be included in the clinical process. Research into adding additional boundary conditions at internal vasculatures to the standard Morfeus DVF demonstrated a significant reduction in TRE for both lung and liver longitudinal CTs.5,6 For surface alignment, DSC and MDA were met by all remaining parameters. These metrics would naturally be satisfactory as boundary conditions required matching organ mesh surfaces between the reference and target images.
Once a consistent accuracy was ensured, robustness (success rate) was the next criteria for the selection process as it ensures minimum user input needed, which is critical for automated clinical workflows. Even for parameters achieving superior accuracy, a lower success rate would indicate a higher chance for potential failure, necessitating user manual interventions to optimize parameter settings (e.g., a voxel side length of 0.2 cm with a triangle edge length of 3 for lung) or create the boundary conditions in the user interface on a patient-specific base. This would be especially burdensome for heavy offline dose accumulation workflows to monitor delivered dose during online adaptive radiotherapy or image-guided ablation that relies on robust DIRs.7,21 In addition, parameters that are accurate and robust alone would not guarantee a clinically feasible solution unless they are reasonably efficient. Therefore, for parameters with similar accuracy and robustness, those that require substantially longer computational time were excluded to ensure robust and fast DIRs. Even though the results from this study showed a potential positive relationship between efficiency and robustness, parameters with exceptional accuracy but a long computational time would not be recommended.
The last criteria, mesh complexity was subsequently considered because a coarse mesh would not provide enough vertices to maintain a low surface accuracy (MDA and HD), whereas a substantially complex mesh might be burdensome to solve the finite element problem, which negatively impacts efficiency and even robustness. This can be seen from the liver result where decreasing the triangle edge length from 3 to 1 for the same voxel side length drastically increased the number of vertices but required significantly longer processing time. Therefore, finding the balance of accuracy, robustness, efficiency, and complexity is the essence of parameter optimization. The parameter selection process can be automated by configuring a scoring system where different metrics are weighted to find the highest scoring parameter sets. It is important to note that users can adapt the ordering of the metrics according to their own clinical needs: Online adaptive radiotherapy may require robustness and efficiency weighed highest, whereas hypo-fractionated treatments may require accuracy weighed highest.
In this study, there were two primary sources of failure in the tested biomechanical-model-based DIR algorithm: mesh generation failure and DIR generation failure. Mesh generation failure can be due to a lower number of smoothing iterations to achieve the desired fine mesh structures. Note that these failures are not due to the magnitude of deformation between the reference and target images but the complexity of structures being modeled and the quality of the generated mesh as determined by the parameters. DIR generation failure can be due to intersecting triangles in the meshes that rendered solving the FEA impossible. As observed in the study, DIR generation failure can also come from Netgen failing to convert the reference triangular meshes to tetrahedral volumetric meshes, for which the failure is not reproduceable and the source is currently under investigation by RaySearch. Further work is required to seek parameters that achieve potential 100% success rate. For the one case that failed for a voxel side length of 0.2 cm and a triangle edge length of 3, the remaining three parameter combinations completed without failing, which encouraged the selection of an alternative parameter combination (a voxel side length of 0.25 cm and a triangle edge length of 2) as a temporary solution when the optimal parameter fails. Rerunning with the same parameters could also resolve the failure but it is a less optimal solution.
5 |. CONCLUSION
In this study, several parameter settings for boundary condition generation of the biomechanical-model-based DIR algorithm in a commercial TPS have been evaluated based on accuracy, robustness, and efficiency. The optimal parameters were found for liver CT and lung CT DIR to be a voxel side length of 0.2 cm and a triangle edge length of 3. Improved robustness and efficiency may encourage more widespread usage of biomechanical-model-based DIR algorithms in clinical practice, such as adaptive radiotherapy workflows and retrospective dose accumulation studies. The consistent use of the same reported optimal parameter by users across institutions can also facilitate standardized evaluation of published studies.
ACKNOWLEDGMENTS
This work was funded in-part by NIH Grant no. 1P01CA261669, by the Helen Black Image Guided Fund, and by RaySearch Laboratories AB and the University of Texas MD Anderson Cancer Center through a co-development and collaboration agreement. This work was supported by the CPRIT-CURE Summer Undergraduate Research Program and the Image Guided Cancer Therapy Research Program at the University of Texas MD Anderson Cancer Center.
Funding information
NIH, Grant/Award Number: 1P01CA261669
Footnotes
CONFLICTS OF INTEREST
Stina Svensson is an employee of Research Laboratories (Stockholm, Sweden). Kristy K. Brock reports research funding and a Licensing Agreement with RaySearch Laboratories for deformable image registration.
DATA AVAILABILITY STATEMENT
The data that support the findings of this study are available upon reasonable request from the corresponding author (YH).
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Associated Data
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Data Availability Statement
The data that support the findings of this study are available upon reasonable request from the corresponding author (YH).