LDW-RS Loss: Label Density-Weighted Loss with Ranking Similarity Regularization for Imbalanced Deep Fetal Brain Age Regression

Estimation of fetal brain age based on sulci by magnetic resonance imaging (MRI) is crucial in determining the normal development of the fetal brain. Deep learning provides a possible way for fetal brain age estimation using MRI. However, real-world MRI datasets often present imbalanced label distribution, resulting in the model tending to show undesirable bias towards the majority of labels. Thus, many methods have been designed for imbalanced regression. Nevertheless, most of them on handling imbalanced data focus on targets with discrete categorical indices, without considering the continuous and ordered nature of target values. To fill the research gap of fetal brain age estimation with imbalanced data, we propose a novel label density-weighted loss with a ranking similarity regularization (LDW-RS) for deep imbalanced regression of the fetal brain age. Label density-weighted loss is designed to capture information about the similarity between neighboring samples in the label space. Ranking similarity regularization is developed to establish a global constraint for calibrating the biased feature representations learned by the network. A total of 1327 MRI images from 157 healthy fetuses between 22 and 34 weeks were used in our experiments for the fetal brain age estimation regression task. In the random experiments, our LDW-RS achieved promising results with an average mean absolute error of 0.760 ± 0.066 weeks and an R-square ( \({\mathrm{R}}^{2}\) ) coefficient of 0.914 ± 0.020. Our fetal brain age estimation algorithm might be useful for identifying abnormalities in brain development and reducing the risk of adverse development in clinical practice.