Multi-dimensional topological loss for cortical plate segmentation in fetal brain MRI

The fetal cortical plate (CP) undergoes drastic morphological changes during the in utero development. Therefore, CP growth and folding patterns are key indicator in the assessment of the brain development and maturation. Magnetic resonance imaging (MRI) offers specific insights for the analysis of quantitative imaging biomarkers. Nonetheless, accurate and, more importantly, topologically correct MR image segmentation remains the key baseline to such analysis. In this study, we propose a deep learning segmentation framework for automatic and morphologically consistent segmentation of the CP in fetal brain MRI. Our contribution is two fold. First, we generalized a multi-dimensional topological loss function in order to enhance the topological accuracy. Second, we introduced hole ratio, a new topology-based validation measure that quantifies the size of the topological defects taking into account the size of the structure of interest. Using two publicly available datasets, we quantitatively evaluated our proposed method based on three complementary metrics which are overlap-, distance- and topology-based on 27 fetal brains. Our results evidence that our topology-integrative framework outperforms state-of-the-art training loss functions on super-resolution reconstructed clinical MRI, not only in shape correctness but also in the classical evaluation metrics. Furthermore, results on additional 31 out-of-domain SR reconstructions from clinical acquisitions were qualitatively assessed by three experts. The experts' consensus ranked our TopoCP method as the best segmentation in 100\% of the cases with a high inter-expert agreement. Overall, both quantitative and qualitative results, on a wide range of gestational ages and number of cases, support the generalizability and added value of our topology-guided framework for fetal CP segmentation.