Diffusion tensor transformation for personalizing target volumes in radiation therapy

Abstract

Diffusion tensor imaging (DTI) is used in tumor growth models to provide information on the infiltration pathways of tumor cells into the surrounding brain tissue. When a patient-specific DTI is not available, a template image such as a DTI atlas can be transformed to the patient anatomy using image registration. This study investigates a model, the invariance under coordinate transform (ICT), that transforms diffusion tensors from a template image to the patient image, based on the principle that the tumor growth process can be mapped, at any point in time, between the images using the same transformation function that we use to map the anatomy. The ICT model allows the mapping of tumor cell densities and tumor fronts (as iso-levels of tumor cell density) from the template image to the patient image for inclusion in radiotherapy treatment planning. The proposed approach transforms the diffusion tensors to simulate tumor growth in locally deformed anatomy and outputs the tumor cell density distribution over time. The ICT model is validated in a cohort of ten brain tumor patients. Comparative analysis with the tumor cell density in the original template image shows that the ICT model accurately simulates tumor cell densities in the deformed image space. By creating radiotherapy target volumes as tumor fronts, this study provides a framework for more personalized radiotherapy treatment planning, without the use of additional imaging.

Keywords: Brain; DTI; Oncology.

Fig. 1:

Illustration of the experimental setup. $𝒯$ describes the spatial transformation to deform the template image (= atlas) to match the fixed image (= patient), and ${𝒯}^{-1}$ its inverse. The solutions of the equations at time $t$ are compared in the deformed image space by mapping the 3D density distributions from the original template image space and superimposing the resulting tumor fronts defined as isodensity contours.

Fig. 2:

Visualization of the original and transformed tumor diffusion tensors in the template and patient image of the toy example, where the images are related by a linear transformation (non-uniform scaling and horizontal shearing). The tensors are represented by ellipses, where the size of the ellipse axes is given by the tensor coefficients. The hypothetical GTV, in green, is defined in the patient image and gets inversely mapped to the template image, whereas the original diffusion tensors are defined in the template image (in gray) and get transformed to the patient image. According to the ICT model, the diffusion tensors transform covariantly with the mapping of the template image to the patient image. Hence, the shape of the diffusion tensors will follow the same transformation; the tensors become elongated for horizontal scaling, while the tensors appear more slanted for horizontal shearing. In contrast, in both the FS and PPD models, the tensors are invariantly transformed and remain unchanged after the transformation.

Fig. 3:

Comparison of the solutions of the diffusion equation in the patient image at time points 0 and 100 days according to invariance under coordinate transform (ICT), finite strain (FS) and preservation of principle direction (PPD) models. As indicated, the different panels compare mapped template solution to the solution that applies either a non-uniform scaling or horizontal shearing in a diffusion only or reaction-diffusion system. The vertical lines indicate the predicted 1%-isodensity fronts.

Fig. 4:

Results of the tumor cell density simulations shown in the patient image at $t=400\mathrm{d}\mathrm{a}\mathrm{y}\mathrm{s}$ in the (a) diffusion-only, and (b) reaction-diffusion systems. (Left) reference tumor cell density distribution. The magenta and white contours show the Gross Target Volume (GTV) and 1%-isodensity fronts respectively. The volume encompassed by the 1%-isodensity front could represent the patient-specific Clinical Target Volume (CTV) in radiotherapy treatment planning. (Middle) comparison of the model-generated CTVs with the reference CTV; the CTV generated with the ICT model overlaps with the reference CTV (CTV Ref.) with near perfect agreement. (Right) line profile comparison.

Fig. 5:

Boxplots for the diffusion only and reaction-diffusion simulations. Dice similarity coefficients (DSC) and Hausdorff 95% percentile index (HD95) in mm, comparing the reference 1%-isodensity volume to the model 1%-isodensity volume in the patient image, at 200, and 400 days. The mean absolute error (MAE) is reported for the voxel-wise difference of cell density within the 1%-isodensity volume.