Breast conserving surgery followed by radiotherapy is the standard of care for early-stage breast cancer patients. Deformable image registration (DIR) can in principle be of great value for accurate localization of the original tumor site to optimize breast irradiation after surgery. However, current state-of-the-art DIR methods are not very successful when tissue is present in one image but not in the other (i.e., in case of content mismatch). To tackle this challenge, we combined a multi-objective DIR approach with simulated tissue removal. Parameters defining the area to be removed as well as key DIR parameters (that are often tuned manually for each DIR case) are determined by a multi-objective optimization process. In multi-objective optimization, not one, but a set of solutions is found, that represent high-quality trade-offs between objectives of interest. We used three state-of-the-art multi-objective evolutionary algorithms as meta-optimizers to search for the optimal parameters, and tested our approach on four test cases of computed tomography (CT) images of breast cancer patients before and after surgery. Results show that using meta-optimization with simulated tissue removal improves the performance of DIR. This way, sets of high-quality solutions could be obtained with a mean target registration error of 2.4 mm over four test cases and an estimated excised volume that is within 20% from the measured volume of the surgical resection specimen.
Multiobjective optimization approaches for deformable image registration (DIR) remove the need for manual adjustment of key parameters and provide a set of solutions that represent high-quality trade-offs between objectives of interest. Choosing a desired outcome a posteriori is potentially far more insightful as differences between solutions can be immediately visualized. The purpose of this work is to investigate whether such an approach allows clinical experts to intuitively select their preferred DIR outcome. To this end, we developed a simplex-based tool for solution navigation and asked 10 clinical experts to use it to choose their preferred DIR outcome from sets of trade-off solutions obtained for 10 breast magnetic resonance DIR cases of low (prone-prone DIR; n = 5) and high (prone-supine DIR; n = 5) difficulty, of patients and volunteers, respectively. The usability of the software is subsequently evaluated by the observers using the system usability scale. Further, the quality of the selected DIR outcomes is evaluated using the mean target registration error. Results show that the users are able to identify and select high-quality DIR outcomes, and attested to high learnability and usability of our software, supporting the validity of the presumed added value of taking a multiobjective perspective on DIR in clinical practice.
KEYWORDS: Image registration, Evolutionary algorithms, Breast cancer, Optimization (mathematics), Breast, 3D image processing, 3D modeling, Visualization, Cancer, Magnetic resonance imaging
Deformable image registration is currently predominantly solved by optimizing a weighted linear combination of objectives. Successfully tuning the weights associated with these objectives is not trivial, leading to trial-and-error approaches. Such an approach assumes an intuitive interplay between weights, optimization objectives, and target registration errors. However, it is not known whether this always holds for existing registration methods. To investigate the interplay between weights, optimization objectives, and registration errors, we employ multi-objective optimization. Here, objectives of interest are optimized simultaneously, causing a set of multiple optimal solutions to exist, called the optimal Pareto front. Our medical application is in breast cancer and includes the challenging prone-supine registration problem. In total, we studied the interplay in three different ways. First, we ran many random linear combinations of objectives using the well-known registration software elastix. Second, since the optimization algorithms used in registration are typically of a local-search nature, final solutions may not always form a Pareto front. We therefore employed a multi-objective evolutionary algorithm that finds weights that correspond to registration outcomes that do form a Pareto front. Third, we examined how the interplay differs if a true multi-objective (i.e., weight-free) image registration method is used. Results indicate that a trial-and-error weight-adaptation approach can be successful for the easy prone to prone breast image registration case, due to the absence of many local optima. With increasing problem difficulty the use of more advanced approaches can be of value in finding and selecting the optimal registration outcomes.
The use of gradient information is well-known to be highly useful in single-objective optimization-based image registration methods. However, its usefulness has not yet been investigated for deformable image registration from a multi-objective optimization perspective. To this end, within a previously introduced multi-objective optimization framework, we use a smooth B-spline-based dual-dynamic transformation model that allows us to derive gradient information analytically, while still being able to account for large deformations. Within the multi-objective framework, we previously employed a powerful evolutionary algorithm (EA) that computes and advances multiple outcomes at once, resulting in a set of solutions (a so-called Pareto front) that represents efficient trade-offs between the objectives. With the addition of the B-spline-based transformation model, we studied the usefulness of gradient information in multiobjective deformable image registration using three different optimization algorithms: the (gradient-less) EA, a gradientonly algorithm, and a hybridization of these two. We evaluated the algorithms to register highly deformed images: 2D MRI slices of the breast in prone and supine positions. Results demonstrate that gradient-based multi-objective optimization significantly speeds up optimization in the initial stages of optimization. However, allowing sufficient computational resources, better results could still be obtained with the EA. Ultimately, the hybrid EA found the best overall approximation of the optimal Pareto front, further indicating that adding gradient-based optimization for multiobjective optimization-based deformable image registration can indeed be beneficial
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