In video-assisted thoracoscopic surgeries, successful procedures of nodule resection are highly dependent on the precise estimation of lung deformation between the inflated lung in the computed tomography (CT) images during preoperative planning and the deflated lung in the treatment views during surgery. Lungs in the pneumothorax state during surgery have a large volume change from normal lungs, making it difficult to build a mechanical model. The purpose of this study is to develop a deformation estimation method of the 3D surface of a deflated lung from a few partial observations. To estimate deformations for a largely deformed lung, a kernel regression-based solution was introduced. The proposed method used a few landmarks to capture the partial deformation between the 3D surface mesh obtained from preoperative CT and the intraoperative anatomical positions. The deformation for each vertex of the entire mesh model was estimated per-vertex as a relative position from the landmarks. The landmarks were placed in the anatomical position of the lung's outer contour. The method was applied on nine datasets of the left lungs of live Beagle dogs. Contrast-enhanced CT images of the lungs were acquired. The proposed method achieved a local positional error of vertices of 2.74 mm, Hausdorff distance of 6.11 mm, and Dice similarity coefficient of 0.94. Moreover, the proposed method could estimate lung deformations from a small number of training cases and a small observation area. This study contributes to the data-driven modeling of pneumothorax deformation of the lung.

翻译：在视频辅助的胸腔外科外科手术中,结核切除的成功程序高度取决于对手术前规划期间计算断层成像(CT)图像中肺膨胀和手术期间处理视图中肺减缩之间肺部畸形的准确估计。手术期间肺肺部肺部肺部与正常肺部有很大变化,因此很难建立机械模型。本研究的目的是从一些部分观测中,对肺部减缩后的肺部3D表面进行变形估计。为了估计肺部基本变形的肺部畸形,采用了一种基于心肺后退法的解决方案。拟议方法使用了几个地标来捕捉3D表面网形外科外科外科外科外科外科外科外科外科外科外科外科外科外科外科内科外科外科外科外科外科外科外科外科外科外科外科外科外科外科外科外科外科外科外科外科外科外科外科外科外科外科外科外科外科外科外科外科外科外科外科外科外科外科外科外科外科外科外科外科外科外科外科外科外科外科外科外科外科外科外科外科外科外科外科外科外科外科外科外科外科外科外科外科外科外科外科外科外科外科外科外科外科外科外科外科外科外科外科外科外科外科外科外科外科外科外科外科外科外科外科外科外科外科外科外科外科外科外科外科外科外科外科外科外科外科外科外科外科外科外科外科外科外科外科外科外科外科外科外科外科外科外科外科外科外科外科外科外科外科外科外科外科外科外科外科外科外科外科外科外科外科外科外科外科外科外科外科外科外科外科外科外科外科外科外科外科外科外科外科外科外科外科外科外