We appreciate this valuable opportunity to discuss our study and hope this explanation will be helpful for evaluating patients with facial asymmetry.

In the beginning of this study, we questioned which cephalometric landmarks we should use for the midsagittal reference plane on the 3-dimensional (3D) skull images with 3D image software for evaluating facial asymmetry. Most orthodontists use and are familiar with 2-dimensional and 3D cephalometric landmarks for diagnosis and treatment planning. Yet, commercial 3D image programs still don’t give any information on the midsagittal reference plane in 3D images.

The purpose of this study was to determine, by statistical shape analysis of original and mirrored skeletal landmarks, the optimal landmark-based midsagittal reference plane for the evaluation of facial asymmetry. From the starting point of our study, we believed that using the symmetric midsagittal reference plane would be the best method for determining the individualized midsagittal reference plane. Several studies through landmark-based, surface model-based, and voxel-based superimpositions have been introduced to find the symmetric midsagittal reference plane. Unfortunately, however, these methods were not applicable to the commercial 3D image software. Therefore, we endeavored to find the cephalometric landmark-based midsagittal reference plane that could be conveniently applied for facial asymmetry evaluation.

In some cases with maxillary asymmetry or severe cranial base asymmetry, we agree that this landmark-based reference plane could produce some bias in assessing facial asymmetry. And at the soft tissue viewpoint, the perceptions of asymmetry could be affected by sex, direction of asymmetry, and observer groups. Therefore, we suggested that this method should be applied only in mild-to-moderate facial asymmetry.

We can adopt more cephalometric landmarks in the cranial base as the landmarks for midsagittal reference planes. However, we intended to use cephalometric landmarks that are already familiar to orthodontists and already available in commercial 3D image software. Therefore, they could be easily and reproducibly applied when evaluating patients with facial asymmetry. Unfortunately, there were not many suitable landmarks in the midline portion of the cranial base. A previous study’s cranial base landmarks as the midpoints of bilateral landmarks were difficult for clinicians to use without a specific 3D image module. We didn’t use them.

In the transition period from 2-dimensional to 3D cephalometric analysis, our study suggested well-known landmarks based on the midsagittal reference plane to evaluate facial asymmetry. The basic concept of our study and that of Damstra et al might be the same. The only difference was the landmarks or planes used in each study. We believe the best method may be the individualized symmetric midsagittal reference plane, which is produced from original and mirror configuration superimpositions. Further study is needed to identify which methods among the landmark-based, surface model-based, and voxel-based methods would be more appropriate for evaluating facial asymmetry.