Another idea to circumvent the problem of a missing correspondence between the atlas image of healthy individuals and the pathological patient image is to seed the atlas with a tumor before applying the non-rigid registration. Most of the underlying approaches make use of a bio-mechanical tumor-growth model that simulates patient-specific tumor growth in the atlas image, and they finally apply a standard non-rigid registration method to the modified atlas image.

Kyriacou et al. (1999), the first ones to suggest this type of approach, assumed a uniform strain of the tumor and non-linear elastic behavior of the surrounding tissues. In a first step, they shrank the tumor in the patient image to obtain a simulated healthy patient image. Then, the tumor shrinkage process was inverted by performing tumor growth on the registered atlas using a regression method. This allowed them to obtain a patient-adapted atlas including pathology in a final step. Mohamed et al. (2006) grew the tumor in the atlas according to the pathological patient image, instead of shrinking the tumor first. The final adaptation of the modified atlas to the patient image was achieved with a non-rigid registration method. To handle the significant computational cost of the tumor growth modeling in 3D, they employed an approach based on a statistical model using principal component analysis (PCA). For each available case, they estimated the most likely parameters and applied the deformation using the pre-built statistical model. Zacharaki et al. (2008) improved this approach by implementing a multi-resolution framework for registration of brain tumor images. In their so-called ORBIT method, they also used a statistical model of tumor-induced deformation, but they embedded it into a hierarchical framework for parameter optimization. Local information was incorporated into the tumor growth model and the registration methodology was improved. In a further step, the same group improved their tumor growth model compared to the previous method (Zacharaki et al. 2009). They dropped the need for a simplified PCA-based tumor growth model while still achieving computational efficiency. To this end, they employed a piecewise Eulerian tumor mass-effect simulator with a uniform outward-pushing pressure model for the bulk tumor. Parameter optimization was parallelized for further speed improvements.

Recently, researchers from the same group built upon the previous methods by making improvements to the tumor growth model. Instead of considering only bio-mechanical mass effects with a simplified pressure model, they proposed a more sophisticated coupled physio-mechanical model. In GLISTR, Gooya et al. (2011a), employed a diffusion–reaction model for tumor growth, which was coupled with an Eulerian finite element method (FEM) for simulating the mass effect. They operated on multi-sequence images to obtain a probability map of the different tissue classes using classification techniques. In the atlas, a patient-specific tumor was grown and a Demons-like algorithm was finally used for the atlas-to-patient transformation. For this, the tissue probability map output from the classifier was used in the cost function. The process was formulated as an EM problem, which jointly estimated tumor growth parameters and the spatial transformations to adapt the atlas to the patient image. This resulted in a large optimization problem, which had to be solved. In a next step, Gooya et al. (2011b) dropped the requirement for pre-classification and proposed a joint segmentation and registration model, which also included tumor growth. This was again formulated in an EM framework for joint estimation of tumor growth parameters and the deformation field for registration. The posterior tissue probabilities, which had been derived from the deformed atlas, yielded the segmentation of the patient image.

Our own research was inspired by methods which suggested combining tumor-growth modeling for the tumor mass effect and the establishment of initial correspondence between atlas and patient image with advanced non-rigid registration. In our method for atlas-based segmentation of tumor-bearing brain images, we explored two different lines of research: On the one hand, we worked on a simplistic but fast method for atlas-based segmentation, and on the other hand, we explored a more sophisticated but computationally more demanding approach.

For the simplistic but fast approach, in Bauer et al. (2011a), we developed a method, that segmented the healthy tissues surrounding the tumor in a brain image by atlas-based segmentation. These tissues included cerebrospinal fluid (CSF), gray matter (GM) and white matter (WM). The method used a simplistic but computationally fast bio-mechanical tumor growth method to first grow a patient-specific tumor in the atlas and then deform the modified atlas to match the patient image using a non-rigid Demons registration method. We relied on a pre-segmentation of the tumor as an input and performed automatic skull-stripping in a pre-processing step. Then, we aligned the atlas to the patient image using an affine transformation model. From there, we defined a tumor seed in the atlas which was located in the center of mass of the patient tumor. Subsequently, a mesh-free method based on Markov Random Fields (MRF) was used for modeling the tumor-mass effect. We chose a radial expansion model which was propagated by an MRF on the deformation field and which was bio-mechanically justified because it considered the Young’s modulus of different brain tissues during tumor expansion. Tumor expansion was formulated as an energy minimization problem in an MRF context which was solved using the iterated conditional modes (ICM) algorithm. The ICM algorithm had the advantage that it could be parallelized very easily and it was implemented on a massively parallel graphics processing unit (GPU); this led to significant speed improvements. After tumor growth modeling, the final adaptation of the modified atlas to the patient image was done using an ITK implementation (Ibanez et al. 2005) of the Diffeomorphic Demons non-rigid registration method (Vercauteren et al. 2009). Figure 14.2 illustrates the pipeline. A tumor seed was automatically selected in the center of mass of the patient tumor and the tumor was grown in the atlas, deforming the surrounding tissues, before the final non-rigid registration was applied. The results were analyzed on four T₁-weighted images from the ContraCancrum database (Marias et al. 2011) and four synthetically generated brain tumor images with a well-defined ground truth (Prastawa et al. 2009). Quantitative evaluation was performed using the Dice similarity coefficient, which measures the overlap with the ground-truth segmentation. The Dice coefficient can range from 0 to 1, with 0 indicating no overlap and 1 indicating perfect overlap. The algorithm achieved Dice coefficients between 0.7 and 0.82 for the relevant tissue CSF, GM and WM within a total computation time of less than 30 min on a GPU.

For the biophysically more realistic approach, in Bauer et al. (2012), we explored a computationally more demanding method for multi-scale tumor growth modeling in atlas-based segmentation of tumor-bearing brain images. We chose the same pipeline as in the previous method that included automatic skull-stripping of the patient image, affine registration of the atlas, seeding the atlas with a physically realistic tumor seed in the center of mass of the patient tumor, tumor growth simulation to model the tumor mass effect, and final non-rigid registration. The difference was that, in this case, we replaced the simplified purely bio-mechanical tumor growth model with a more sophisticated tumor growth model which considered multiple scales ranging from the microscopic cellular level up to the macroscopic bio-mechanical level. To this end, a discrete-entity, discrete-event cellular-level based oncosimulator (Stamatakos et al. 2010) focusing on biological phenomena like cell-cycling and apoptosis was coupled with a bio-mechanical stress/strain simulation (May et al. 2011) which could provide pressure gradient information. Since the limit of applicability of the standard Lagrangian formulation of structural mechanics was reached under large tumor-induced deformations, the linear-elastic model was solved in an Eulerian implementation of FEM. Thus, the calculation was performed on a fixed geometrical mesh and material properties were advected to neighboring elements upon deformation. Furthermore, this allowed for operating directly on the voxel mesh obtained from the image, eliminating the need for complex mesh generation procedures. The cell simulator required information on the direction into which new tumor cells would spread. This direction could be decided based on the pressure of the surrounding tissues. The pressure was obtained from the mechanical simulator which in turn required information about the expansion of each geometrical cell. This was calculated from the cellular proliferation model. The direction of least pressure was calculated based on the negative gradient