Computational Intelligence in Metric Analysis of the Skull in the Context of Maxillofacial Surgery

Anthropometric studies focusing on facial metrics and their proportions form an important research area devoted to observations of the appearance of the human skull. Many different applications include the use of craniometry for maxillofacial reconstruction and surgery. This paper explores the possibility of using selected craniometric points and associated metric to observe spatial changes during the maxillofacial surgery treatment. The experimental dataset includes observations of 27 individuals. The proposed method is associated with the processing of measurements by selected methods of signal processing and computational intelligence. The statistical results point to changes of facial measures before and after the maxillofacial surgery. The proposed method conclusively demonstrates that the area of the mean upper law triangle after surgical treatment is decreased by 8.5%, at the 5% significance level of the two-sample t-test. The classification of selected measurements by a neural network model reached an accuracy of 84.9%.


I. INTRODUCTION
Anthropometric studies [1] form a research area devoted to observations of the appearance of the human skull. Facial measures, proportions, and symmetry [2], [3], [4] are very important in dentistry, orthodontics, plastic surgery, recognition of different diseases and their therapy, anthropological skull analysis [5], [6], and forensic identification [7]. An investigation of the mechanical properties of human skull bone and its geometry [8] form an associated research area. The dentofacial deformity, its early diagnosis [9], monitoring, and the following treatment are then closely related to the The associate editor coordinating the review of this manuscript and approving it for publication was Li He . maxillofacial surgery [10], appropriate computational strategies, and clinical validations.
Specific methods applied in forensic anthropology and forensic medicine allow the identification of an individual by their skull [11] on the basis of craniofacial comparison and subsequent superposition [12] using the relation between the skull and the soft tissues of the face [13]. Similar research is related to the measurement of skull sizes, shapes, and skull triangles [14] for the proposal of a systematic method in archaeology and in studies of evolutionary development. Specific methods are used for the correlation of external skull landmarks, the identification of regions of the brain, and intracranial measurements [15], [16].
Data processing methods are based on the values obtained by standard measurement techniques including VOLUME 10, 2022 This work is licensed under a Creative Commons Attribution 4.0 License. For more information, see https://creativecommons.org/licenses/by/4.0/ FIGURE 1. Main craniometric points on the skull for evaluation of their distances before and after the maxillofacial surgery and selected triangular areas used for their assessment.
three-dimensional scanning technology [17], and their analysis by specific imaging methods [18], [19] based on panoramic X-ray images [20], magnetic resonance data [21], and thermographic images. Skull registration [22] forms another important method in craniofacial reconstruction. Figure 1 presents the main craniometric points for the evaluation of the distances before and after the maxillofacial surgery. Selected triangular areas can then be used for the assessment of abnormalities in the shape of the skull and their classification [23].
Different mathematical methods include the use of selected computational algorithms, data preprocessing in the time and functional domains [24], [25], image processing methods [26], and machine learning methods for facial shape recognition. General computational intelligence tools [27], [28], [29] and deep learning methods [30] can be applied to extract features, classify them, and any associated statistical processing. These methods are also used for the analysis of the geometry required for surgical reconstruction [31] and for prediction of the postoperative results of orthognathic surgery [32].

II. METHODS
The experimental dataset includes 27 individuals (12 females and 15 males) with dentoaveolar deformities -hypoplasia of upper jaw, hypoplasia of lower jaw or both [33], [34]. The LeFort 1 osteotomy [35], [36] originally described by Rene LeFort in 1901, as a method used by maxillofacial surgeons to correct a wide range of dentofacial deformities (horizontal maxillary fracture, separating the teeth from the upper face) was used, monitored, and analyzed in Motol University Hospital for correction of those midface disorders. The reconstruction included the bilateral sagittal split osteotomy in the lower jaw. Monitoring of the treatment was done by facial measures before and after the surgery to analyze the result of the treatment and to allow the study of the long-term stability. For each individual, pre-treatment and post-treatment cone beam computed tomography data were acquired. The mean age of the patients prior to treatment was 18-44 years. The timespan between pre-and post-treatment imagery ranged from 1 to 40 months. This study was conducted according to the recommendations of the American Dental Association (ADA). In accordance with the Declaration of Helsinki, patients were requested to provide informed consent to the clinical examination by means of an informed consent form. The anonymity of the data obtained was strictly respected. Ethical approval for the study was obtained from the Ethics Committee (EK-973IGA 1.12/ 11) The Lefort 1 osteotomy allows for the movement in all three planes and its monitoring needs analysis of specific facial locations. The position of the craniometric landmarks [13], [37] in the 3D model of the skulls before and after therapy were determined by the Invivo Anatomage software. All cone beam computed tomography examinations were indicated for surgical and orthodontic treatment. The data processing goals are in the study of the effect of the maxillofacial surgery on selected measures. The observed measures have been processed by selected statistical methods, the two-sample t-test to detect the relation of specific datasets, and neural networks to test classification abilities for selected signal features.
The classification of selected features for the separation of measures before and after the maxillofacial surgery was performed by a two-layer neural network with sigmoidal and softmax transfer functions in the first and the second layer, respectively.

III. RESULTS
The visual monitoring of the treatment progress was combined with the application of computational intelligence for the assessment of data recorded by computed tomography. The correction of the facial profile presenting the situation  before and after the treatment of a selected individual is presented in Fig. 2.
Repeated observations of D1:ZyDx-ZySin, D2:MxDx-MxSin, D3:GoDx-GoSin, and D4:Subsp-Pog on the skull were analysed at first. Table 1 presents statistics of these measures before and after the maxillofacial surgery for a selected individual and 10 experiments with their mean values, standard deviations, and their differences. Figure 3 presents the distributions of these observations with their mean values during the dental, orthodontic and maxillofacial treatment.
Mean distances acquired before and after the surgery for the set of 15 males and 12 females were studied in the following step. Figure 4 presents the fundamental evaluations of the results including the distances D1:ZyDx-ZySin and D2:MxDx-MxSin after the surgery vs. these distances before the treatment.
The pair comparison of selected distances with their mean values and c multiples of standard deviation for c = 0.5, 1, 2 before and after the maxillofacial surgery is presented in Figure 5.  The two-sample t-test was evaluated to test the decision for the null hypothesis that the data of the triangle area for males and females comes from independent random samples with equal means. This hypothesis was accepted for triangles A2 and A3 and rejected for triangle A1 at the 5% significance level both for the initial and final area.
Selected measures between craniometric landmarks before and after the maxillofacial surgery for 27 individuals are presented in Table 2 together with their mean values and standard deviations.  Table 3 presents the area S and standard deviation of three main triangles in the facial region for 15 males and 12 females before and after maxillofacial surgery for triangles A1:ZyDx-ZySin-Subsp, A2:MxDx-MxSin-Subsp, and A3:GoDx-GoSin-Pog. Figure 7 presents the changes in the areas of these triangles in the facial region before and after  maxillofacial surgery, not taking gender into account. The two-sample t-test was evaluated to test the decision for the null hypothesis that the data of the areas of the triangles before and after maxillofacial surgery comes from independent random samples with equal means. This hypothesis is accepted only for triangle A2, at the 5% significance level.
The areas of the second and the third triangles were used as features for the classification of skull measures before and after maxillofacial surgery. The results of the classification by the support vector machine (SVM) and the two-layer neural network neural network with 10 neurons in the first layer are presented in Fig. 8 together with the class boundaries. Table 4 presents the classification results of selected methods with the highest accuracy of 84.9% (in bold) and the 10-fold cross-validation error of 0.17 achieved by the neural network method.
The complete dataset is stored at the IEEE Dat-aPort (https://dx.doi.org/10.21227/n78r-xd27) for further investigation. This repository includes also the Matlab 2022b (MathWorks, Massachusetts, USA) source code for data analysis before and after the treatment.

IV. DISCUSSION
Facial appearance and facial features are traditionally employed in orthodontic, maxillofacial treatment plans, and  spatial therapy image tasks. The results can establish a person's new appearance based on an examination of craniofacial traits. The proposed therapy must be based on sound scientific principles to yield accurate and reliable results.
This paper investigates the influence of maxillofacial surgery on specific anthropological skull measures for 27 patients with dentoaveolar deformities: hypoplasia of the upper jaw, hypoplasia of the lower jaw, or both. LeFort 1 osteotomy (horizontal maxillary fracture, separating the teeth from the upper face) was used for correction of those midface deformities.
Evaluation of computed tomography and analysis of measures between craniometric landmarks include the following results for the given set of patients: • The distribution of observation measurement errors presented in Fig. 3 that occur during repeated measurements of a single individual, • Changes of mean skull measures before and after the surgery presented in Table 1) that point to: (i) a reduction of D1:ZyDx-ZySin measure by 0.3 mm, (ii) a reduction of D2:MxDx-MxSin measure by 0.1 mm, (iii) an increase of D3:GoDx-GoSin measure by 0.3 mm. The trend of these changes is confirmed by 27 individuals as presented in Table 2, • Standard deviations of selected measures presented in Table 1 that point to a reduction of their mean values evaluated before and after the surgery by 0.2 mm in average, • The effect of the maxillofacial surgery on the main triangular areas in the skull presented in Fig. 1 with similar results of the treatment both for the set of males and females showing that (i) area A1 is slightly enlarged, (ii) area A2 is reduced, (iii) area A3 is enlarged (as presented in Fig. 6 and Table 3), • The comparison of areas A3 vs. A2 showing that mean values for females are lower than for males both before and after the treatment as presented in Fig. 6, • The possibility of classification of skull measures affected by maxillofacial surgery using machine learning tools as presented in Fig. 8. While distances between craniometric landmarks are studied in different papers [38], [39], the present study includes the analysis of additional features estimated as selected triangular facial areas. Results point to differences of these measures for males and females during the treatment. The most significant difference was observed for triangle A2:MxDx-MxSin-Subsp in the given set of patients.
The classification of skull measures before and after maxillofacial surgery by the two-layer neural network model was achieved with an accuracy of 84.9%. A slightly lower classification accuracy was achieved by the support vector machine (81.1%), the 3-nearest neighbours method (77.4%), and a Bayesian classification method (71.7%).

V. CONCLUSION
The paper forms a contribution to the increasing role of the computational intelligence and visualization tools in surgery. The direct consequence of the very fast technological progress is the more extensive use of the three-dimensional treatment planning with 3D reconstruction, especially in connection with 3D printing and experimental robotic-assisted surgery [40], [41].
It is expected that further research will be devoted to the evaluation of facial measures for more extensive datasets, different types of maxillofacial surgery, and to the use of deep learning methods for more complex analysis of skull shapes to contribute to the multidisciplinary area of biomedical engineering.