Accuracy of three-dimensional facial soft tissue simulation in post-traumatic zygoma reconstruction

Accuracy of three-dimensional facial soft tissue simulation in post-traumatic zygoma reconstruction

International Journal of Oral & Maxillofacial Surgery, 2016-12-01, Volume 45, Issue 12, Pages 1665-1670, Copyright © 2016

Abstract

The aim of this study was to evaluate the accuracy of novel software-CMF-preCADS-for the prediction of soft tissue changes following repositioning surgery for zygomatic fractures. Twenty patients who had sustained an isolated zygomatic fracture accompanied by facial deformity and who were treated with repositioning surgery participated in this study. Cone beam computed tomography (CBCT) scans and three-dimensional (3D) stereophotographs were acquired preoperatively and postoperatively. The 3D skeletal model from the preoperative CBCT data was matched with the postoperative one, and the fractured zygomatic fragments were segmented and aligned to the postoperative position for prediction. Then, the predicted model was matched with the postoperative 3D stereophotograph for quantification of the simulation error. The mean absolute error in the zygomatic soft tissue region between the predicted model and the real one was 1.42 ± 1.56 mm for all cases. The accuracy of the prediction (mean absolute error ≤2 mm) was 87%. In the subjective assessment it was found that the majority of evaluators considered the predicted model and the postoperative model to be ‘very similar’. CMF-preCADS software can provide a realistic, accurate prediction of the facial soft tissue appearance after repositioning surgery for zygomatic fractures. The reliability of this software for other types of repositioning surgery for maxillofacial fractures should be validated in the future.

In orthognathic surgery, facial deformities are corrected by repositioning the bone segments. Computerized prediction of the postoperative facial appearance could be valuable for guiding surgical plans and exploring different treatment options. It may also serve as a tool to allow members of the interdisciplinary team to communicate and provide the patient with the desired outcome. Many software packages have been designed for prediction in orthognathic surgery.

The aim of repositioning surgery for zygomatic fractures is not only the correction of dysfunction, such as limited mouth opening and malocclusion, but also for aesthetic improvement of the facial appearance. Because the final aesthetic result is indicated by the postoperative facial appearance, an accurate three-dimensional (3D) prediction of the soft tissue changes after bony tissue repositioning is essential in preoperative treatment planning. To date, no software package designed specifically for the virtual simulation of maxillofacial fracture repositioning surgeries has been developed, and no study on the corresponding soft tissue prediction has been published.

The novel software CMF-preCADS was recently developed for the computerized prediction of 3D facial appearance after maxillofacial repositioning surgeries. It is hypothesized that CMF-preCADS may be useful. However, before use in the clinical setting, its accuracy and reliability must be evaluated objectively based on clinical evidence and a large number of homogeneous patients.

Materials and methods

The sample consisted of 20 adult Chinese patients who had been referred to the department of oral and maxillofacial surgery of the study institution between January 2014 and March 2015. There were 14 men and six women, and their mean age was 34 years.

The inclusion criteria encompassed the following: patients diagnosed with isolated and old zygomatic fractures and a facial deformity, who agreed to the repositioning surgery involving a semicoronal scalp incision, and who required internal fixation. The exclusion criteria were as follows: patients with pre-traumatic or congenital deformities and facial soft tissue lacerated wounds, scars, swelling, or haematocele, and those requiring additional adjunctive surgical procedures.

This study did not influence the clinical treatment protocols and was approved by the university medical ethics committee. Full informed consent was obtained from all patients. Figure 1 shows a flow chart of the data processing procedure.

Flow chart of the data processing procedure.
Fig. 1
Flow chart of the data processing procedure.

Data acquisition and preparation

Cone beam computed tomography (CBCT) and 3D stereophotograph data were acquired preoperatively and at 3 months postoperatively for all patients. To minimize the effect of head position on the soft tissues, each patient was scanned while seated in natural head position looking at his or her image in a mirror, with lips and facial muscles relaxed.

The CBCT scans were performed using a standard protocol (field of view 16 cm diameter, 22 cm height, voxel size 0.4 mm, scan time 40 s, 120 kV) with the same machine (J Morita Mfg. Corp., Kyoto, Japan). CBCT data were stored in DICOM format (Digital Imaging and Communications in Medicine) and imported into CMF-preCADS installed on a personal computer (Lenovo, E540) for rendering of the head skeletal 3D models and facial surface models.

A 3D stereophotograph was captured with a commercial 3D camera system, FaceSCAN3D (3D-Shape, Erlangen, Germany), and stored in .obj format with facial texture information. Prior to use, the camera was calibrated to define a 3D coordinate system.

Prediction of facial soft tissue appearance

Preoperative and postoperative skeletal 3D models were superimposed in CMF-preCADS using surface-based registration on unchanged sub-regions, such as the cranial base, forehead, and normal side, in order to eliminate discrepancies between the planned skeletal displacement and the actual movement. Virtual repositioning surgery was then performed on the preoperative 3D model. The fractured zygomatic fragments were segmented according to the actual osteotomies and aligned to their respective postoperative positions (postoperative skeletal 3D model).

Before simulating the facial appearance, the preoperative 3D stereophotograph was aligned to the CBCT facial surface model for more realistic visualization with a previously validated superimposition method, the iterative closest point (ICP) algorithm.

CMF-preCADS computed the soft tissue deformation caused by the simulated skeletal movements using a finite element method (FEM) algorithm, which has been published previously. The graphical interface in CMF-preCADS makes it possible to preview the patient’s new facial appearance.

Analysis of the soft tissue simulation

The predicted 3D facial model and postoperative 3D stereophotograph model were superimposed in Geomagic Studio 11.0 (Raindrop Geomagic, Rock Hill, SC, USA) using surface-based registration on unchanged sub-regions (the forehead and the normal side). To quantify the simulation error, the zygomatic soft tissue region was defined and other regions were omitted ( Fig. 2 ). The mean absolute error, standard deviation, maximum absolute error, and 95th percentile for the comparison of the predicted model and the actual postoperative model for each case were calculated using an inter-surface distance algorithm. A distance colour map for the zygomatic soft tissue region was generated to depict the prediction error graphically. The relative ratio of the number of simulations with a high degree of accuracy (absolute error ≤2 mm) was calculated and defined as the ability to predict facial appearance correctly. This threshold value was based on a previous study that showed a distance of 2 mm to be clinically significant in facial change.

Definition of the zygomatic soft tissue region. (A) The reference frame was established. (B) These planes were used to define the borders of the zygomatic soft tissue region (the blue area). Plane a: parallel to the horizontal plane running through the stomion. Plane b: parallel to the horizontal plane running through the lateral canthus. Plane c: parallel to the median sagittal plane running through the stomion. Plane d: parallel to the coronal plane running through the tragus. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
Fig. 2
Definition of the zygomatic soft tissue region. (A) The reference frame was established. (B) These planes were used to define the borders of the zygomatic soft tissue region (the blue area). Plane a: parallel to the horizontal plane running through the stomion. Plane b: parallel to the horizontal plane running through the lateral canthus. Plane c: parallel to the median sagittal plane running through the stomion. Plane d: parallel to the coronal plane running through the tragus. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

Subjective assessment of the similarity

The method described by Giangreco et al. was used for subjective assessment of the similarity of the predicted facial model to the postoperative 3D stereophotograph. For each case, 10 calibrated evaluators (maxillofacial and plastic surgeons) graded the similarity as either ‘very similar’, ‘similar’, ‘moderately similar’, ‘somewhat different’, or ‘different’.

Results

After 3 months of follow-up, all patients showed considerable improvements in aesthetic facial appearance and were satisfied with the surgical outcomes. The mean absolute error, standard deviation, maximum absolute error, and 95th percentile for the comparison of the prediction model and actual postoperative model, and the relative ratio (absolute error ≤2 mm) for each patient are shown in Table 1 . Figure 3 shows the distance colour maps of the zygomatic soft tissue region for 10 cases.

Table 1
Absolute error descriptive statistics for the 20 study patients (data in millimetres).
Patient Mean absolute error SD Maximum absolute error 95th percentile Percentage ≤2 mm
1 1.25 1.62 3.73 2.71 88.1%
2 0.97 1.05 2.38 1.64 93.6%
3 1.58 1.39 2.94 1.83 92.4%
4 1.43 1.78 3.85 2.90 85.2%
5 1.39 1.72 2.86 2.83 86.3%
6 1.38 1.44 2.69 2.20 90.7%
7 1.72 1.85 3.17 2.97 88.4%
8 1.04 1.49 3.50 3.14 82.6%
9 1.31 1.62 3.54 3.12 86.0%
10 1.23 1.31 3.20 2.84 88.9%
11 1.09 1.15 3.31 3.02 83.7%
12 1.18 1.50 3.56 2.99 86.5%
13 1.72 2.37 3.92 3.60 84.8%
14 1.59 1.26 3.47 3.17 87.2%
15 1.92 1.57 4.86 3.87 76.4%
16 1.86 2.43 3.88 1.96 92.1%
17 1.17 1.38 3.59 2.50 87.4%
18 1.48 1.57 3.22 2.48 90.5%
19 1.20 1.06 3.29 2.62 87.8%
20 1.83 1.64 3.70 2.83 85.1%
Total 1.42 1.56 3.43 2.76 87.2%
SD, standard deviation.
Colour maps for the zygomatic soft tissue regions of 10 cases, showing the accuracy of the 3D soft tissue facial prediction.
Fig. 3
Colour maps for the zygomatic soft tissue regions of 10 cases, showing the accuracy of the 3D soft tissue facial prediction.

For the evaluation of similarity by subjective assessment, the data were transformed into percentages. Most of the evaluators assessed the predicted model as ‘very similar’ or ‘similar’ to the postoperative 3D stereophotograph. Of the 200 evaluations (20 patients assessed by 10 examiners), eight (4%) were graded as ‘somewhat different’ or ‘different’. Figure 4 shows two cases of accurate 3D prediction of the appearance of the soft tissues of the face after repositioning surgery for zygomatic fractures using CMF-preCADS.

Two cases of accurate 3D prediction with CMF-preCADS of the facial soft tissue appearance after repositioning surgery for zygomatic fractures. Case 1: (A) preoperative, (B) predicted, and (C) postoperative 3D stereophotographs. Case 2: (D) preoperative, (E) predicted, and (F) postoperative 3D stereophotographs.
Fig. 4
Two cases of accurate 3D prediction with CMF-preCADS of the facial soft tissue appearance after repositioning surgery for zygomatic fractures. Case 1: (A) preoperative, (B) predicted, and (C) postoperative 3D stereophotographs. Case 2: (D) preoperative, (E) predicted, and (F) postoperative 3D stereophotographs.

Discussion

At present there are several software packages designed for facial prediction after orthognathic surgery. Many two-dimensional (2D) programmes, including Dolphin (Dolphin Imaging, Chatsworth, CA, USA), Dentofacial Planner (Dentofacial Software, Toronto, Ontario, Canada), Quick Ceph (Quick Ceph Systems Inc., San Diego, CA, USA), and TIOPS (Total Interactive Orthodontic Planning System, http://www.tiops.com ), are based on the lateral linear ratios of soft tissue to hard tissue movement for predicting the facial profile in the anteroposterior and vertical views. Their main shortcomings are the inaccuracy of the prediction algorithms and inability to predict the transverse changes. 3D systems are now becoming more popular. It is feasible to generate facial models by colour texture mapping with actual 2D photos. Maxilim (Medicim, Sint-Niklaas, Belgium), SurgiCase (Materialize, Leuven, Belgium), and 3dMDvultus (3dMD, Atlanta, GA, USA) simulate the deformation of the soft tissues based on a biomechanical model. They are specially designed for orthognathic surgery, not for the repositioning of facial fractures, and there is no version available for patients of Asian ancestry. Wirthlin et al. reported that different populations and ethnicities have different facial features and averages, and that these should be considered in treatment planning. All of these factors greatly inspired the current work and the development of the programme described herein.

The accuracy of the computerized prediction of postoperative facial changes depends on the computer algorithms used. Currently, the most widely used are the mass spring model (MSM), the finite element model (FEM), and the mass tensor model (MTM), which are more biomechanically accurate than others and have been adopted by several commercial software developers. The MSM can produce the effect of real-time, but lacks sufficient accuracy for the precise modelling of physiological behaviour. The more accurate simulations are based on the FEM. Keeve et al. first proposed an anatomy-based FEM that can forecast the soft tissue deformations resulting from movement of the underlying hard tissue. Gladilin et al. showed soft tissues as an isotropic homogeneous and linear elastic continuum based on FEM. Mollemans et al. compared four computational strategies and concluded that MTM reduced the calculation time considerably. Therefore, considering the significant time saving, MTM appears more favourable for clinical use than the other methods.

CMF-preCADS software is based on a co-rotational linear elasticity FEM. The OpenGL library was used for visualization. Considering the computational complexity, the facial model built using 3D photographs is extracted to form an intermediate mesh model. A tetrahedral volumetric model is then built. Moreover, an algorithm was designed and implemented to generate a high-quality tetrahedral mesh from the intermediate mesh. The algorithm establishes tetrahedron elements on the strength of the surface mesh along the reverse direction of the face normal and point normal. In computer graphics, the direction of a triangle can be represented by its normal vector, and the direction of one point can be represented by the mean of several directions of triangles around this point. A new algorithm is suggested here to generate tetrahedral elements in a continuous grid. Along the inverse normal direction of the grid points, this algorithm creates new points in the certain position. In the same way, new points can be generated from the centre of the triangle surface along the inverse normal direction of the triangle. After FEM discretization, the motion of deformable tissue can be described using the Euler–Lagrange equation, which is a second order system of an ordinary differential equation. It is one of the key advantages of this software.

There are at present many types of prediction software that have been validated qualitatively and quantitatively, but the results of these processes are not comparable with each other because they have evaluated different types of maxillofacial surgery. Marchetti et al. reported a reliability of 91% using SurgiCase-CMF software in a clinical study. Khambay and Ullah evaluated the accuracy of soft tissue simulation of Le Fort I osteotomy using 3dMDvultus software. The mean simulation error for the whole face was 0.8 mm, which was much lower than that reported by Shafi et al., who used Maxilim, but for isolated Le Fort I advancements. The results also did not match those reported by Bianchi et al. and Marchetti et al., who found an average absolute error of 0.94 mm and 0.75 mm, respectively. Both studies used the volumetric FEM-based SurgiCase-CMF software. In another study, Liebregts et al. concluded that the simulation is more accurate for the whole face than for the regions of interest. With the inclusion of facial areas that were not affected by surgery, the reported error tended to be an underestimation of the actual error caused by the surgery. It is crucial to understand these errors and develop a protocol for conducting soft tissue facial prediction. In this study, the zygomatic soft tissue region was defined and other regions were omitted. The use of specific anatomical regions is more clinically meaningful than the full face.

With regard to the present study, the following issues must be considered. Firstly, CBCT data rather than spiral CT data were used to reconstruct the soft and hard tissues of the face because CBCT exposes the patient to much less radiation. Most importantly, the position of the face during a CBCT scan is identical to that during 3D stereophotography. In this way, the effects of gravity on the facial morphology can be eliminated. It is concluded that CBCT should be used as a reference standard for conducting facial soft tissue predictions.

Second, postoperative image data were acquired 3 months after surgery. Based on clinical observations, facial swelling disappears completely during the 3 months after surgery. However, in the authors’ previous experience, some patients show great changes in postoperative weight and also skeletal relapse at follow-up appointments, and these factors may lead to a great change in the facial contour.

Third, registration is a crucial element of objective evaluation. This involves three registration procedures, in which the ICP algorithm is used. The preoperative and postoperative skeletal 3D models were first registered together. Next, the preoperative 3D stereophotograph was registered to the CBCT facial surface model. Following this, the prediction facial model and postoperative 3D stereophotograph were registered together. The major strength of this ICP algorithm is that registration does not depend on the precision of single user-placed specific landmarks, but rather works semi-automatically on the 3D surface models.

Fourth, several methods of measuring the mean absolute error have been reported, including differences between all of the 3D points of the predefined anatomical regions in two facial surface models. These 3D models can simply be thought of as numerous 3D points in space, joined together to form a triangular surface mesh. In this method, the over-prediction (positive values) and the under-prediction (negative values) were treated equally to prevent them from cancelling each other out. This approach was also adopted in the present study to achieve more accurate data.

Fifth, due to the accurate and reproducible data provided, with high resolution, 3D stereophotography was introduced several years ago for the quantitative measurement of soft tissue changes after orthognathic surgery, similar to photogrammetry. The 3D stereophotograph can be rotated, translated, and zoomed. It is likely that 3D stereophotography will revolutionize preoperative planning, simulation, and the assessment of postoperative outcomes. For CMF-preCADS, soft tissue predictions directly on the preoperative 3D stereophotograph may provide clearer and more realistic images, with textured information of the human face. This is another key advantage of this software.

It is worth noting that this study only validated the accuracy of facial prediction after repositioning surgery for zygomatic fractures. However, the purpose of this newly developed CMF-preCADS software is to develop an accurate facial prediction model that can be used universally for patients requiring the repositioning of maxillofacial fractures and for orthodontic patients, regardless of the surgical area. Therefore, to optimize the computer algorithm, a comprehensive multicenter database for surgical repositioning of maxillofacial fractures must be established. Furthermore, because age can influence the elasticity of the soft tissues, distribution of fat, and orofacial muscle tone, the computing parameters of the prediction model may be adjusted slightly to provide more accurate simulations for elderly patients. However, in this work, Young’s modulus was set to 1 MP and the Poisson ratio was set to 0.46 during all simulations.

In conclusion this study evaluated the accuracy of the novel software CMF-preCADS based on the FEM algorithm for the computerized prediction of soft tissue changes after the surgical repositioning of zygomatic fractures in 20 patients. The results indicated that the accuracy of the prediction (mean absolute error ≤2 mm) was 87%. In the subjective assessment, the majority of evaluators assessed the predicted and the postoperative models to be ‘very similar’. The CMF-preCADS software can provide a realistic, accurate prediction of the facial soft tissue appearance after repositioning surgery for zygomatic fractures. In the future, it may be possible to improve the accuracy and reliability of the CMF-preCADS prediction by modifying the algorithm. Additional clinical validation studies with larger sample sizes should be carried out to provide more evidence regarding the accuracy of facial prediction by the CMF-preCADS software package.

Funding

This study was funded by the Chinese National 863 Program ( 2013AA040804 ).

Competing interests

The authors declare that they have no competing interests.

Ethical approval

The study was approved by the Institutional Review and Ethics Board of Sichuan University (WCCSIRB-D-2013-027).

Patient consent

Full informed consent was obtained from each patient.

3 These authors contributed equally to this work.

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Accuracy of three-dimensional facial soft tissue simulation in post-traumatic zygoma reconstruction P. Li , Z.W. Zhou , J.Y. Ren , Y. Zhang , W.D. Tian and W. Tang International Journal of Oral & Maxillofacial Surgery, 2016-12-01, Volume 45, Issue 12, Pages 1665-1670, Copyright © 2016 Abstract The aim of this study was to evaluate the accuracy of novel software-CMF-preCADS-for the prediction of soft tissue changes following repositioning surgery for zygomatic fractures. Twenty patients who had sustained an isolated zygomatic fracture accompanied by facial deformity and who were treated with repositioning surgery participated in this study. Cone beam computed tomography (CBCT) scans and three-dimensional (3D) stereophotographs were acquired preoperatively and postoperatively. The 3D skeletal model from the preoperative CBCT data was matched with the postoperative one, and the fractured zygomatic fragments were segmented and aligned to the postoperative position for prediction. Then, the predicted model was matched with the postoperative 3D stereophotograph for quantification of the simulation error. The mean absolute error in the zygomatic soft tissue region between the predicted model and the real one was 1.42 ± 1.56 mm for all cases. The accuracy of the prediction (mean absolute error ≤2 mm) was 87%. In the subjective assessment it was found that the majority of evaluators considered the predicted model and the postoperative model to be ‘very similar’. CMF-preCADS software can provide a realistic, accurate prediction of the facial soft tissue appearance after repositioning surgery for zygomatic fractures. The reliability of this software for other types of repositioning surgery for maxillofacial fractures should be validated in the future. In orthognathic surgery, facial deformities are corrected by repositioning the bone segments. Computerized prediction of the postoperative facial appearance could be valuable for guiding surgical plans and exploring different treatment options. It may also serve as a tool to allow members of the interdisciplinary team to communicate and provide the patient with the desired outcome. Many software packages have been designed for prediction in orthognathic surgery. The aim of repositioning surgery for zygomatic fractures is not only the correction of dysfunction, such as limited mouth opening and malocclusion, but also for aesthetic improvement of the facial appearance. Because the final aesthetic result is indicated by the postoperative facial appearance, an accurate three-dimensional (3D) prediction of the soft tissue changes after bony tissue repositioning is essential in preoperative treatment planning. To date, no software package designed specifically for the virtual simulation of maxillofacial fracture repositioning surgeries has been developed, and no study on the corresponding soft tissue prediction has been published. The novel software CMF-preCADS was recently developed for the computerized prediction of 3D facial appearance after maxillofacial repositioning surgeries. It is hypothesized that CMF-preCADS may be useful. However, before use in the clinical setting, its accuracy and reliability must be evaluated objectively based on clinical evidence and a large number of homogeneous patients. Materials and methods The sample consisted of 20 adult Chinese patients who had been referred to the department of oral and maxillofacial surgery of the study institution between January 2014 and March 2015. There were 14 men and six women, and their mean age was 34 years. The inclusion criteria encompassed the following: patients diagnosed with isolated and old zygomatic fractures and a facial deformity, who agreed to the repositioning surgery involving a semicoronal scalp incision, and who required internal fixation. The exclusion criteria were as follows: patients with pre-traumatic or congenital deformities and facial soft tissue lacerated wounds, scars, swelling, or haematocele, and those requiring additional adjunctive surgical procedures. This study did not influence the clinical treatment protocols and was approved by the university medical ethics committee. Full informed consent was obtained from all patients. Figure 1 shows a flow chart of the data processing procedure. Fig. 1 Flow chart of the data processing procedure. Data acquisition and preparation Cone beam computed tomography (CBCT) and 3D stereophotograph data were acquired preoperatively and at 3 months postoperatively for all patients. To minimize the effect of head position on the soft tissues, each patient was scanned while seated in natural head position looking at his or her image in a mirror, with lips and facial muscles relaxed. The CBCT scans were performed using a standard protocol (field of view 16 cm diameter, 22 cm height, voxel size 0.4 mm, scan time 40 s, 120 kV) with the same machine (J Morita Mfg. Corp., Kyoto, Japan). CBCT data were stored in DICOM format (Digital Imaging and Communications in Medicine) and imported into CMF-preCADS installed on a personal computer (Lenovo, E540) for rendering of the head skeletal 3D models and facial surface models. A 3D stereophotograph was captured with a commercial 3D camera system, FaceSCAN3D (3D-Shape, Erlangen, Germany), and stored in .obj format with facial texture information. Prior to use, the camera was calibrated to define a 3D coordinate system. Prediction of facial soft tissue appearance Preoperative and postoperative skeletal 3D models were superimposed in CMF-preCADS using surface-based registration on unchanged sub-regions, such as the cranial base, forehead, and normal side, in order to eliminate discrepancies between the planned skeletal displacement and the actual movement. Virtual repositioning surgery was then performed on the preoperative 3D model. The fractured zygomatic fragments were segmented according to the actual osteotomies and aligned to their respective postoperative positions (postoperative skeletal 3D model). Before simulating the facial appearance, the preoperative 3D stereophotograph was aligned to the CBCT facial surface model for more realistic visualization with a previously validated superimposition method, the iterative closest point (ICP) algorithm. CMF-preCADS computed the soft tissue deformation caused by the simulated skeletal movements using a finite element method (FEM) algorithm, which has been published previously. The graphical interface in CMF-preCADS makes it possible to preview the patient's new facial appearance. Analysis of the soft tissue simulation The predicted 3D facial model and postoperative 3D stereophotograph model were superimposed in Geomagic Studio 11.0 (Raindrop Geomagic, Rock Hill, SC, USA) using surface-based registration on unchanged sub-regions (the forehead and the normal side). To quantify the simulation error, the zygomatic soft tissue region was defined and other regions were omitted ( Fig. 2 ). The mean absolute error, standard deviation, maximum absolute error, and 95th percentile for the comparison of the predicted model and the actual postoperative model for each case were calculated using an inter-surface distance algorithm. A distance colour map for the zygomatic soft tissue region was generated to depict the prediction error graphically. The relative ratio of the number of simulations with a high degree of accuracy (absolute error ≤2 mm) was calculated and defined as the ability to predict facial appearance correctly. This threshold value was based on a previous study that showed a distance of 2 mm to be clinically significant in facial change. Fig. 2 Definition of the zygomatic soft tissue region. (A) The reference frame was established. (B) These planes were used to define the borders of the zygomatic soft tissue region (the blue area). Plane a: parallel to the horizontal plane running through the stomion. Plane b: parallel to the horizontal plane running through the lateral canthus. Plane c: parallel to the median sagittal plane running through the stomion. Plane d: parallel to the coronal plane running through the tragus. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.) Subjective assessment of the similarity The method described by Giangreco et al. was used for subjective assessment of the similarity of the predicted facial model to the postoperative 3D stereophotograph. For each case, 10 calibrated evaluators (maxillofacial and plastic surgeons) graded the similarity as either ‘very similar’, ‘similar’, ‘moderately similar’, ‘somewhat different’, or ‘different’. Results After 3 months of follow-up, all patients showed considerable improvements in aesthetic facial appearance and were satisfied with the surgical outcomes. The mean absolute error, standard deviation, maximum absolute error, and 95th percentile for the comparison of the prediction model and actual postoperative model, and the relative ratio (absolute error ≤2 mm) for each patient are shown in Table 1 . Figure 3 shows the distance colour maps of the zygomatic soft tissue region for 10 cases. Table 1 Absolute error descriptive statistics for the 20 study patients (data in millimetres). Patient Mean absolute error SD Maximum absolute error 95th percentile Percentage ≤2 mm 1 1.25 1.62 3.73 2.71 88.1% 2 0.97 1.05 2.38 1.64 93.6% 3 1.58 1.39 2.94 1.83 92.4% 4 1.43 1.78 3.85 2.90 85.2% 5 1.39 1.72 2.86 2.83 86.3% 6 1.38 1.44 2.69 2.20 90.7% 7 1.72 1.85 3.17 2.97 88.4% 8 1.04 1.49 3.50 3.14 82.6% 9 1.31 1.62 3.54 3.12 86.0% 10 1.23 1.31 3.20 2.84 88.9% 11 1.09 1.15 3.31 3.02 83.7% 12 1.18 1.50 3.56 2.99 86.5% 13 1.72 2.37 3.92 3.60 84.8% 14 1.59 1.26 3.47 3.17 87.2% 15 1.92 1.57 4.86 3.87 76.4% 16 1.86 2.43 3.88 1.96 92.1% 17 1.17 1.38 3.59 2.50 87.4% 18 1.48 1.57 3.22 2.48 90.5% 19 1.20 1.06 3.29 2.62 87.8% 20 1.83 1.64 3.70 2.83 85.1% Total 1.42 1.56 3.43 2.76 87.2% SD, standard deviation. Fig. 3 Colour maps for the zygomatic soft tissue regions of 10 cases, showing the accuracy of the 3D soft tissue facial prediction. For the evaluation of similarity by subjective assessment, the data were transformed into percentages. Most of the evaluators assessed the predicted model as ‘very similar’ or ‘similar’ to the postoperative 3D stereophotograph. Of the 200 evaluations (20 patients assessed by 10 examiners), eight (4%) were graded as ‘somewhat different’ or ‘different’. Figure 4 shows two cases of accurate 3D prediction of the appearance of the soft tissues of the face after repositioning surgery for zygomatic fractures using CMF-preCADS. Fig. 4 Two cases of accurate 3D prediction with CMF-preCADS of the facial soft tissue appearance after repositioning surgery for zygomatic fractures. Case 1: (A) preoperative, (B) predicted, and (C) postoperative 3D stereophotographs. Case 2: (D) preoperative, (E) predicted, and (F) postoperative 3D stereophotographs. Discussion At present there are several software packages designed for facial prediction after orthognathic surgery. Many two-dimensional (2D) programmes, including Dolphin (Dolphin Imaging, Chatsworth, CA, USA), Dentofacial Planner (Dentofacial Software, Toronto, Ontario, Canada), Quick Ceph (Quick Ceph Systems Inc., San Diego, CA, USA), and TIOPS (Total Interactive Orthodontic Planning System, http://www.tiops.com ), are based on the lateral linear ratios of soft tissue to hard tissue movement for predicting the facial profile in the anteroposterior and vertical views. Their main shortcomings are the inaccuracy of the prediction algorithms and inability to predict the transverse changes. 3D systems are now becoming more popular. It is feasible to generate facial models by colour texture mapping with actual 2D photos. Maxilim (Medicim, Sint-Niklaas, Belgium), SurgiCase (Materialize, Leuven, Belgium), and 3dMDvultus (3dMD, Atlanta, GA, USA) simulate the deformation of the soft tissues based on a biomechanical model. They are specially designed for orthognathic surgery, not for the repositioning of facial fractures, and there is no version available for patients of Asian ancestry. Wirthlin et al. reported that different populations and ethnicities have different facial features and averages, and that these should be considered in treatment planning. All of these factors greatly inspired the current work and the development of the programme described herein. The accuracy of the computerized prediction of postoperative facial changes depends on the computer algorithms used. Currently, the most widely used are the mass spring model (MSM), the finite element model (FEM), and the mass tensor model (MTM), which are more biomechanically accurate than others and have been adopted by several commercial software developers. The MSM can produce the effect of real-time, but lacks sufficient accuracy for the precise modelling of physiological behaviour. The more accurate simulations are based on the FEM. Keeve et al. first proposed an anatomy-based FEM that can forecast the soft tissue deformations resulting from movement of the underlying hard tissue. Gladilin et al. showed soft tissues as an isotropic homogeneous and linear elastic continuum based on FEM. Mollemans et al. compared four computational strategies and concluded that MTM reduced the calculation time considerably. Therefore, considering the significant time saving, MTM appears more favourable for clinical use than the other methods. CMF-preCADS software is based on a co-rotational linear elasticity FEM. The OpenGL library was used for visualization. Considering the computational complexity, the facial model built using 3D photographs is extracted to form an intermediate mesh model. A tetrahedral volumetric model is then built. Moreover, an algorithm was designed and implemented to generate a high-quality tetrahedral mesh from the intermediate mesh. The algorithm establishes tetrahedron elements on the strength of the surface mesh along the reverse direction of the face normal and point normal. In computer graphics, the direction of a triangle can be represented by its normal vector, and the direction of one point can be represented by the mean of several directions of triangles around this point. A new algorithm is suggested here to generate tetrahedral elements in a continuous grid. Along the inverse normal direction of the grid points, this algorithm creates new points in the certain position. In the same way, new points can be generated from the centre of the triangle surface along the inverse normal direction of the triangle. After FEM discretization, the motion of deformable tissue can be described using the Euler–Lagrange equation, which is a second order system of an ordinary differential equation. It is one of the key advantages of this software. There are at present many types of prediction software that have been validated qualitatively and quantitatively, but the results of these processes are not comparable with each other because they have evaluated different types of maxillofacial surgery. Marchetti et al. reported a reliability of 91% using SurgiCase-CMF software in a clinical study. Khambay and Ullah evaluated the accuracy of soft tissue simulation of Le Fort I osteotomy using 3dMDvultus software. The mean simulation error for the whole face was 0.8 mm, which was much lower than that reported by Shafi et al., who used Maxilim, but for isolated Le Fort I advancements. The results also did not match those reported by Bianchi et al. and Marchetti et al., who found an average absolute error of 0.94 mm and 0.75 mm, respectively. Both studies used the volumetric FEM-based SurgiCase-CMF software. In another study, Liebregts et al. concluded that the simulation is more accurate for the whole face than for the regions of interest. With the inclusion of facial areas that were not affected by surgery, the reported error tended to be an underestimation of the actual error caused by the surgery. It is crucial to understand these errors and develop a protocol for conducting soft tissue facial prediction. In this study, the zygomatic soft tissue region was defined and other regions were omitted. The use of specific anatomical regions is more clinically meaningful than the full face. With regard to the present study, the following issues must be considered. Firstly, CBCT data rather than spiral CT data were used to reconstruct the soft and hard tissues of the face because CBCT exposes the patient to much less radiation. Most importantly, the position of the face during a CBCT scan is identical to that during 3D stereophotography. In this way, the effects of gravity on the facial morphology can be eliminated. It is concluded that CBCT should be used as a reference standard for conducting facial soft tissue predictions. Second, postoperative image data were acquired 3 months after surgery. Based on clinical observations, facial swelling disappears completely during the 3 months after surgery. However, in the authors’ previous experience, some patients show great changes in postoperative weight and also skeletal relapse at follow-up appointments, and these factors may lead to a great change in the facial contour. Third, registration is a crucial element of objective evaluation. This involves three registration procedures, in which the ICP algorithm is used. The preoperative and postoperative skeletal 3D models were first registered together. Next, the preoperative 3D stereophotograph was registered to the CBCT facial surface model. Following this, the prediction facial model and postoperative 3D stereophotograph were registered together. The major strength of this ICP algorithm is that registration does not depend on the precision of single user-placed specific landmarks, but rather works semi-automatically on the 3D surface models. Fourth, several methods of measuring the mean absolute error have been reported, including differences between all of the 3D points of the predefined anatomical regions in two facial surface models. These 3D models can simply be thought of as numerous 3D points in space, joined together to form a triangular surface mesh. In this method, the over-prediction (positive values) and the under-prediction (negative values) were treated equally to prevent them from cancelling each other out. This approach was also adopted in the present study to achieve more accurate data. Fifth, due to the accurate and reproducible data provided, with high resolution, 3D stereophotography was introduced several years ago for the quantitative measurement of soft tissue changes after orthognathic surgery, similar to photogrammetry. The 3D stereophotograph can be rotated, translated, and zoomed. It is likely that 3D stereophotography will revolutionize preoperative planning, simulation, and the assessment of postoperative outcomes. For CMF-preCADS, soft tissue predictions directly on the preoperative 3D stereophotograph may provide clearer and more realistic images, with textured information of the human face. This is another key advantage of this software. It is worth noting that this study only validated the accuracy of facial prediction after repositioning surgery for zygomatic fractures. However, the purpose of this newly developed CMF-preCADS software is to develop an accurate facial prediction model that can be used universally for patients requiring the repositioning of maxillofacial fractures and for orthodontic patients, regardless of the surgical area. Therefore, to optimize the computer algorithm, a comprehensive multicenter database for surgical repositioning of maxillofacial fractures must be established. Furthermore, because age can influence the elasticity of the soft tissues, distribution of fat, and orofacial muscle tone, the computing parameters of the prediction model may be adjusted slightly to provide more accurate simulations for elderly patients. However, in this work, Young's modulus was set to 1 MP and the Poisson ratio was set to 0.46 during all simulations. In conclusion this study evaluated the accuracy of the novel software CMF-preCADS based on the FEM algorithm for the computerized prediction of soft tissue changes after the surgical repositioning of zygomatic fractures in 20 patients. The results indicated that the accuracy of the prediction (mean absolute error ≤2 mm) was 87%. In the subjective assessment, the majority of evaluators assessed the predicted and the postoperative models to be ‘very similar’. The CMF-preCADS software can provide a realistic, accurate prediction of the facial soft tissue appearance after repositioning surgery for zygomatic fractures. In the future, it may be possible to improve the accuracy and reliability of the CMF-preCADS prediction by modifying the algorithm. Additional clinical validation studies with larger sample sizes should be carried out to provide more evidence regarding the accuracy of facial prediction by the CMF-preCADS software package. Funding This study was funded by the Chinese National 863 Program ( 2013AA040804 ). Competing interests The authors declare that they have no competing interests. Ethical approval The study was approved by the Institutional Review and Ethics Board of Sichuan University (WCCSIRB-D-2013-027). Patient consent Full informed consent was obtained from each patient. 3 These authors contributed equally to this work. References 1. Bianchi A., Muyldermans L., Di Martino M., Lancellotti L., Amadori S., Sarti A., et. al.: Facial soft tissue esthetic predictions: validation in craniomaxillofacial surgery with cone beam computed tomography data. J Oral Maxillofac Surg 2010; 68: pp. 1471-1479. 2. Nadjmi N., Tehranchi A., Azami N., Saedi B., Mollemans W.: Comparison of soft-tissue profiles in Le Fort I osteotomy patients with Dolphin and Maxilim softwares. Am J Orthod Dentofacial Orthop 2013; 144: pp. 654-662. 3. 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