## 4 Discussion and Conclusions  
In this paper, we proposed a quantification method for evaluating surgical effects on regional cranial bones by comparing preoperative and postoperative skull shapes. The contributions of the proposed method are threefold. First, we quantified the effects of surgery according to the shape deformation of each cranial bone in the preoperative and postoperative skull shapes from head CT images. Most previous studies used preoperative and postoperative 3D scan datasets to quantify morphological changes of the head surface. However, quantification of morphological changes using 3D scan data is limited when quantifying the shape deformation of each cranial bone. Second, we analyzed the effect of surgery on patients with craniosynostosis of the regional cranial bones using an age-matched mean-normal skull surface model generated from normal skulls consisting of five cranial bones based on open sutures. Third, to compare the skull shape before and after surgery, we quantified the degree of regional expansion and reduction caused by correction of skull deformities via surgery. Here, expansion means that the reduced regional bone due to the restricted growth of the preoperative skull is expanded similarly to a normal skull after surgery, and reduction means that the expanded regional bone due to the compensatory growth of the preoperative skull shape is reduced similarly to a normal skull after surgery. Most previous studies suggest that the CI and the CVAI are the most common measure for evaluating the surgical effects in cases of craniosynostosis. The CI is used as a severity index for sagittal and bilateral coronal cases characterized by a symmetric shape, while the CVAI is used as a severity index for unilateral coronal and unilateral lambdoid cases characterized by an asymmetric shape. Table 2 shows the average value of the CI and CVAI for the preoperative and postoperative skulls for all subjects with representative synostoses of craniosynostosis. It showed that the CI in severe sagittal synostosis case increased similarly to a normal skull after surgery, while the CI in severe bilateral coronal synostosis case decreased similarly to a normal skull after surgery. Additionally, it showed that the CVAI in unilateral lambdoid case significantly decreased after surgery, but the CVAI of the preoperative skull in unilateral coronal case was mostly a mild deformity and slightly decreased after surgery. Thus, it can be confirmed that the two indices represent the effect of overall skull correction before and after surgery, but it is difficult to quantify regional morphological changes such as expansion or reduction of the five regional bones divided by sutures. In this study, we analyzed the effects of surgery on patients with craniosynostosis of regional cranial bones using proposed reduction and expansion indices considering the distance and area ratio. In cases involving sagittal synostosis with a long and narrow shape, the frontal and occipital bones showed a large reduction index, and the parietal bones showed a large expansion index. In cases of bicoronal synostosis with short and high features, the frontal and parietal bones showed a large reduction index, and the parietal and occipital bones showed a large expansion index. In cases of unilateral bicoronal synostosis