Human-airway surface mesh smoothing based on graph convolutional neural networks

Background and Objective: A detailed representation of the airway geometry in the respiratory system is critical for predicting precise airflow and pressure behaviors in computed tomography (CT)-image-based computational fluid dynamics (CFD). The CT-image-based geometry often contains artifacts, noise, and discontinuities due to the so-called stair step effect. Hence, an advanced surface smoothing is necessary. The existing smoothing methods based on the Laplacian operator drastically shrink airway geometries, resulting in the loss of information related to smaller branches. This study aims to introduce an unsupervised airway-mesh-smoothing learning (AMSL) method that preserves the original geometry of the three-dimensional (3D) airway for accurate CT-image-based CFD simulations. Method: The AMSL method jointly trains two graph convolutional neural networks (GCNNs) defined on airway meshes to filter vertex positions and face normal vectors. In addition, it regularizes a combination of loss functions such as reproducibility, smoothness and consistency of vertex positions, and normal vectors. The AMSL adopts the concept of a deep mesh prior model, and it determines the self-similarity for mesh restoration without using a large dataset for training. Images of the airways of 20 subjects were smoothed by the AMSL method, and among them, the data of two subjects were used for the CFD simulations to assess the effect of airway smoothing on flow properties. Results: In 18 of 20 benchmark problems, the proposed smoothing method delivered better results compared with the conventional or state-of-the-art deep learning methods. Unlike the traditional smoothing, the AMSL successfully constructed 20 smoothed airways with airway diameters that were consistent with the original CT images. Besides, CFD simulations with the airways obtained by the AMSL method showed much smaller pressure drop and wall shear stress than the results obtained by the traditional method. Conclusions: The airway model constructed by the AMSL method reproduces branch diameters accurately without any shrinkage, especially in the case of smaller airways. The accurate estimation of airway geometry using a smoothing method is critical for estimating flow properties in CFD simulations.