CorticalEvolve: Age-Conditioned Ordinary Differential Equation Model for Cortical Surface Reconstruction

Cortical surface reconstruction utilizing Neural Ordinary Differential Equation (NODE) stands as a prominent method, renowned for generating surfaces of accuracy and robustness. However, these methodologies, tailored predominantly for the adult brain, fall short in capturing the substantial morphological differences in the cortical surfaces arising from the rapid early development of the neonatal brain. Hence, post menstrual age (PMA) is an essential factor which should not be ignored. To address this, we propose the CorticalEvolve, a diffeomorphic transformation based progressive framework, for neonatal cortical surface reconstruction. We design a neonatal deformation block (DB) to preform deformation with developmental characteristics and a dynamic deformation block to refine the generated surface. Specifically, the proposed Neonatal DB firstly incorporates time-activated dynamic convolution to transform the stationary velocity field into a time-varying dynamic velocity field. Secondly, Age Conditioned ODE (Age-CDE) is proposed to depict the brain development nature, replacing the fixed step integration scheme in NODE with age-related one. Then, each discrete state of intermediate step represents the neonatal cortical surface at the corresponding PMA. The experimental results on the dHCP dataset effectively demonstrate the reconstruction capabilities of the proposed method, surpassing several state-of-the-art methods by a significant margin across various metrics. Visualization results underscore CorticalEvolve's ability to generate more robust cortical surfaces.