Chapter 4 provided increased detail about the behavior of the poly-rigid transformation and the necessity for treatment of rotations in the Log domain in order to ensure both that poly-rigid transformations behave as intended and that the resulting transforma- tions remain invertible. The process for determining a weight function that, together with known rigid transformations for each bone, well approximates the deformation of tissue due to articulation of the pelvis and femurs was described. It was demon- strated that the proposed poly-rigid transformation accurately and rigidly aligns bone anatomy. The proposed poly-rigid transformation was used to register daily images of several patients to their template planning image. It was determined that performing a poly-rigid transformation along with a rigid transformation significantly decreases the image distance term when compared with using a rigid transformation alone. Proper alignment of the bones was demonstration by visual inspection. The poly-rigidly aligned and rigidly aligned images were then non-rigidly registered to their template images. After the non-rigid registration, the poly-rigidly aligned images retained a significantly
Figure 4.9: Distribution of the relative changes in SSD following a non-rigid registration which was initialized with rigidly aligned and poly-rigidly aligned images. Initializing the registration algorithm with a poly-rigidly aligned image significantly decreases the image match when compared with only rigid initialization.
(a) Rigid Transformation (b) Poly-rigid Transformation
(c) Rigid with Non-rigid (d) Poly-rigid with Non-rigid
Figure 4.10: Difference images between the fixed image and the images aligned by rigid transformation (a), poly-rigid transformation (b), rigid initialization to non-rigid registration (c), and poly-rigid initialization to non-rigid registration (a). Black regions are caused by padding in regions where image data is not defined. Bones do not remain well aligned in d when compared with b because they were not constrained to remain aligned. The constraint that bones remain aligned during non-rigid stages is used in this work and is further discussed in section 5.2.2
better image than the corresponding rigidly aligned images, indicating that performing a poly-rigid alignment prior to a non-rigid registration increases the quality of that registration.
The importance of the poly-rigid transformation in this work is three-fold.
First, the poly-rigid transformation allows (and, in this application, is forced to have) locally rigid regions. This enables the rigidity of bones to be preserved. If instead of accounting for articulated motion in this way, articulated motion were captured by the subsequent deformation models, the bony regions would almost never remain rigid, even if the non-rigid transformations from which the deformation model would be developed were rigid in bony regions (which is typically not the case unless the registration is constrained). Because bones have high contrast with their surrounding tissue, they have a tendency to overwhelm the signal from lower contrast soft-tissue boundaries. Bony anatomy that projects to the same region of the detector as soft tissue will entirely prevent the visualization of that soft tissue. Ensuring proper alignment of
bones in order that their contribution to detector signal is appropriately accounted for is critical to the success of this method.
Second, the poly-rigid transformation reduces the number of modes of variation in subsequent non-rigid deformation models. That is, articulated motion that is explained by the poly-rigid transformation does not appear in these subsequent deformation mod- els, meaning that fewer modes of variation are necessary to determine a sufficiently accurate deformation model. Deformation models in the male pelvis already need to explain a large amount of variation. There is sufficient variation in the male pelvis that a single PCA-based deformation model does not produce an effective shape space for registration from even as many as 16 daily images. In this work, the solution is to sep- arate the single deformation model into several independent models, thereby reducing the amount of variation to be explained by each model. The poly-rigid transformation serves to further reduce the amount of variation that needs to be explained by those models by removing the effects of articulation.
Third, because the poly-rigid transformation has removed deformation due to artic- ulation, the remaining deformation to be recovered by a succeeding non-rigid registra- tion is smaller, meaning the registration is better initialized. Registrations with better initializations typically result in more accurate transformations (as demonstrated by the reduction of image distance in figure 4.9). These more accurate transformations should produce a better shape space, resulting in a more accurate deformation model.
Chapter 5
Multi-Deformation Models for Tissue Deformation
5.1 Introduction
By this point in the document, the reader will have a good understanding of the method discussed in this work. A patient-specific deformation model is constructed which consists of the following:
1. An atlas image of the patient with consensus segmentations of bones, skin, and PBR
2. A poly-rigid transformation that accounts for articulated motion of the femurs and pelvis, as well as the motion of soft tissue and muscle near to that bony anatomy
3. A skin model that accounts for deformation of the skin and regions near to the skin
4. A prostate, bladder, and rectum model that accounts for deformation of that organ complex
5. A residual model that accounts for all other changes in the patient’s anatomy.
These parameters provide a transformation from the atlas image and any of the patient’s planning or daily images to treatment-time. This transformation provides both an approximate CT-like image that is suitable for dose accumulation and a segmentation of the patient’s prostate, bladder, rectum, skin, and bony anatomy (in terms of the deformed atlas). Chapter 4 provided details about the construction of the articulated poly-rigid transformation. This chapter provides further details about the construction of the non-rigid tissue deformation models and their application at treatment-time.