Incorporating a-priori information in deep learning models for quantitative susceptibility mapping via adaptive convolution

Quantitative susceptibility mapping (QSM) has attracted considerable interest for tissue characterization (e.g., iron and calcium accumulation, myelination, venous vasculature) in the human brain and relies on extensive data processing of gradient-echo MRI phase images. While deep learning-based field-to-susceptibility inversion has shown great potential, the acquisition parameters applied in clinical settings such as image resolution or image orientation with respect to the magnetic field have not been fully accounted for. Furthermore, the lack of comprehensive training data covering a wide range of acquisition parameters further limits the current QSM deep learning approaches. Here, we propose the integration of a priori information of imaging parameters into convolutional neural networks with our approach, adaptive convolution, that learns the mapping between the additional presented information (acquisition parameters) and the changes in the phase images associated with these varying acquisition parameters. By associating a-priori information with the network parameters itself, the optimal set of convolution weights is selected based on data-specific attributes, leading to generalizability towards changes in acquisition parameters. Moreover, we demonstrate the feasibility of pre-training on synthetic data and transfer learning to clinical brain data to achieve substantial improvements in the computation of susceptibility maps. The adaptive convolution 3D U-Net demonstrated generalizability in acquisition parameters on synthetic and in-vivo data and outperformed models lacking adaptive convolution or transfer learning. Further experiments demonstrate the impact of the side information on the adaptive model and assessed susceptibility map computation on simulated pathologic data sets and measured phase data.