Fig. 1.

Here we summarize the joint registration and biophysical inversion in SIBIA. (a) shows the segmented healthy brain (the atlas), (b) tumor-bearing atlas brain generated by biophysical simulation, (c) patient tumor registered to atlas (in atlas space), (d) tumor-bearing patient brain. The inputs are the images (a) and (d). The outputs are the tumor growth parameters, the registration parameters, and images (b) and (c). Here is $\tau$ the forward tumor map, which given image (a) grows a tumor and generates image (b). Similarly, $\mathcal{R}$ is the forward registration map, which given image (d) generates image (c). In SIBIA, we compute tumor-growth parameters and registration parameters so that images (b) and (c) are as similar as possible (in the L² norm). In this example, the biophysical tumor growth parameters are the initial conditions for a reaction–diffusion equation. The registration is parameterized using an Eulerian framework and a velocity field that is used to advect image (d) to image (c).