Registration of brain images to atlases is critical to label regions in the patient’s brain for group analysis. Registration assisted labeling could also help improve planning for radiation therapy[1-4] and surgical resection of tumors[5]. Large pathologies can adversely affect image registration due to absence of corresponding structures in the atlas. There are two main classes of tumors: (a) intra-axial tumors (such as gliomas) which generally exhibit infiltrative growth and (b) extra-axial tumors (such as meningiomas) which grow and push the surrounding tissue leading to brain tissue compression and change in morphology of the surrounding tissue. Here, we present a complete framework to tackle both types of tumors for registration to atlas, incorporating a tumor shrinking method for extrinsic tumors.

A detailed flowchart describing our framework is presented Figure 1a. The inputs to our system include a ED image, tumor masks, and classification of the specific tumor type. As infiltrating tumors penetrate surrounding tissues without altering the structure, we mask out the tumor region and follow that by accurate deformable registration. Large extrinsic tumors alter surrounding structures significantly; hence it is necessary to reverse the effects of tumor growth before registration. Past efforts model tumor growth using elastic bio-mechanical models[2] or incorporate diffusion models[4]. Additionally, most efforts address the problem of registering the atlas to the subject data, where the goal is to model the growth of the lesion on the atlas and register. In the proposed work, we address the problem of registering subject scans to atlases to facilitate population studies. We mathematically model the tumor growth process similar to [1] and infer the motion-vector fields capturing the tumor growth from a single seed-point. By inverting this forward deformation field, large tumors are shrunk and compression in the adjoining structures is also reversed, which is followed by the registration algorithm. Figure 1b explains the tumor shrinking algorithm. We assume a radially uniform tumor-growth model and use signed-distance transform (D) computed from the tumor origin point (P) to encapsulate the lesion growth (1). 3D gradient operators on D are used to calculate the forward deformation field at every voxel (2).

$$D=Distance Transform(P) \space\space\space\space\space\space\space\space\space\space(1)$$

$${D_{x},D_{y},D_{z}}=gradient(D)\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space(2)$$

To reverse the compression effects outside the tumor, we hypothesize uniform and exponential compression in the surrounding tissue. We filter the tumor mask (M) by an isotropic 3D Gaussian function (F) controlled by the filter-size parameter (w) (3). We also flatten the filtered output to a constant value (C) inside the tumor mask (4). This ensures that all the voxels (x) inside tumor collapse to the origin point while the surrounding compressed tissues relax exponentially and fill the tumor region.

$$M=Mask \circledcirc F(w)\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space(3)$$

$$M(x)=\frac{C}{sum(M)} \forall x \in Mask\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space(4)$$

$$M(x)=\frac{M(x)*C}{sum(M)} \forall x \notin Mask\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space (5)$$

Finally the forward deformation fields (FDF) are obtained by multiplying M with the gradient fields as shown in equation (6). Inversion of the FDF provides us the deformation fields (IDF) to shrink the tumor to the seed-point equation (7).

$${FD_{x},FD_{y},FD_{z}}={D_{x},D_{y},D_{z}}*M\space\space\space\space\space\space\space\space(6)$$

$$({FD_{x},FD_{y},FD_{z}})=inv({D_{x},D_{y},D_{z}})\space\space\space\space\space(7)$$

Data was acquired after obtaining informed consent on three patients with metastatic brain tumors. Scans included post gadolinium 3D T1-weighted images used in this work. T2 and FLAIR images were used for tumor delineation. Tumor mask and tumor origin point was manually segmented and selected.

To verify our framework, we performed a simulation experiment by artificially growing a circular tumor and shrinking it back to the seed point. Figure 2a shows MRI scan of a healthy patient. Figure 2b shows the simulated tumor and Fig 2c shows the result of our tumor shrinking algorithm proving the efficacy of our approach. Figure 3a shows an axial slice of subject MR scan with a large meningioma which is subjected to the tumor shrink algorithm resulting in Figure 3b. Firstly, the large tumor has been shrunk to a single point and the contrast in the region that contained the tumor is similar to the region surrounding the tumor. Secondly, streaking artifacts are observed in the proximity of the seed-point. This could be attributed to the difficult interpolation problem of filling a large region. Finally, we show the effect of tumor shrinking algorithm on the registration result in Fig 4. Figure 4a-b contain the registration result to the brain atlas without and with tumor shrinking respectively. It is visibly apparent that tumor shrinking algorithm has improved the registration around the tumor region, highlighted in the difference image shown in 4c.This framework provides an accurate method to localize atlas brain labels in patients with large pathologies which may improve the understanding and treatment of brain tumor patients.