  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.
