Sahar Ahmad^{1}, Zhengwang Wu^{1}, Gang Li^{1}, Li Wang^{1}, Weili Lin^{1}, Pew-Thian Yap^{1}, and Dinggang Shen^{1}

Spatial registration of infant brain images is challenging owing to significant changes in image appearance in association with rapid growth in the first year of life. In this abstract, we introduce a volumetric registration method that is constrained by cortical correspondences for consistent cortical and sub-cortical alignment.

The dataset comprised of T1-weighted and T2-weighted scans from $$$19$$$ healthy infant subjects (M: 14, F: 5) enrolled in the Multi-visit Advanced Pediatric (MAP) Brain Imaging Study. Each T1-weighted scan had $$$144$$$ sagittal slices with $$$1.0$$$ mm isotropic voxel size. And T2-weighted scans had 64 sagittal slices with $$$1.25\times1.25\times1.95$$$ $$$\mathrm{mm^{3}}$$$ voxel size. All the scans were processed by the UNC infant cortical surface pipeline^{1} to generate accurate tissue segmentation maps as well as inner and outer cortical surfaces. To deal with longitudinal appearance changes, we use tissue segmentation maps, instead of intensity images, for registration. We first established the cortical surface correspondence between the fixed and moving subjects using Spherical Demons^{2}. This vertex-wise transformation $$$\Phi(\vec{p_{s}})$$$ is used to constrain the subsequent volumetric registration step, which seeks an optimal transformation $$$\phi(\vec{p_{v}})$$$ such that $$$\phi(\vec{p_{s}})=\Phi(\vec{p_{s}})$$$, where $$$\vec{p_{v}}$$$ and $$$\vec{p_{s}}$$$ define the voxel coordinates and cortical surface vertices, respectively. The underlying large non-linear deformations are modeled using a dynamic elasticity model (DEM) with surface constraints imposed as follows: $$\frac{\partial^{2}{\phi\left(\vec{p_{v}}\right)}}{\partial{t^{2}}}=\alpha\big(\nabla^{2}\phi\left(\vec{p_{v}}\right)+\nabla(\nabla.\phi\left(\vec{p_{v}}\right))\big)+\beta f^{v}\!\left(\vec{p_{v}}\right)+\gamma f^{s}\!\left(\vec{p_{s}}\right),$$

where $$$f^{v}\!\left(\vec{p_{v}}\right)$$$ measures the discrepancy between the fixed and warped moving tissue segmentation maps and $$$f^{s}\!\left(\vec{p_{v}}\right)$$$ gives the error between $$$\Phi(\vec{p_{s}})$$$ and $$$\phi(\vec{p_{s}})$$$. $$$\alpha$$$, $$$\beta$$$ and $$$\gamma$$$ control the data irregularity, data mismatch and deformation error, respectively. We hereby denote our method as SC-DEM.

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4. Avants B, Epstein C, et al. Symmetric diffeomorphic image registration with cross-correlation: Evaluating automated labeling of elderly and neurodegenerative brain. Med Image Anal. 2008; 12(1): 26 - 41.