Phase Aberration Correction for in vivo Ultrasound Localization Microscopy Using a Spatiotemporal Complex-Valued Neural Network

Ultrasound Localization Microscopy (ULM) can map microvessels at a resolution of a few micrometers ({\mu}m). Transcranial ULM remains challenging in presence of aberrations caused by the skull, which lead to localization errors. Herein, we propose a deep learning approach based on recently introduced complex-valued convolutional neural networks (CV-CNNs) to retrieve the aberration function, which can then be used to form enhanced images using standard delay-and-sum beamforming. Complex-valued convolutional networks were selected as they can apply time delays through multiplication with in-phase quadrature input data. Predicting the aberration function rather than corrected images also confers enhanced explainability to the network. In addition, 3D spatiotemporal convolutions were used for the network to leverage entire microbubble tracks. For training and validation, we used an anatomically and hemodynamically realistic mouse brain microvascular network model to simulate the flow of microbubbles in presence of aberration. We then confirmed the capability of our network to generalize to transcranial in vivo data in the mouse brain (n=2). Qualitatively, vascular reconstructions using a pixel-wise predicted aberration function included additional and sharper vessels. The spatial resolution was evaluated by using the Fourier ring correlation (FRC). After correction, we measured a resolution of 16.7 {\mu}m in vivo, representing an improvement of up to 27.5 %. This work leads to different applications for complex-valued convolutions in biomedical imaging and strategies to perform transcranial ULM.