1 INTRODUCTION

Growth and development play an important role in orthodontics because the jaw's growth and development in the apparatus used to treatment skeletal anomalies are associated with growth spurts and physiological facial growth. Previous studies aimed to achieve maximum success in the shortest time by performing the most appropriate treatment for an individual's developmental periods.1-3 The growth rate and the percentage of remaining facial growth are key for the success of the orthodontic treatment and thus should be accurately determined to prevent the relapse that may occur after treatment due to facial development.4

Various indicators of individual skeletal maturity have been proposed to determine the timing of treatment in orthodontics. Chronological age is one of the most used indicators5; however, circumpubertal growth is affected not only by the patient's age but also by gender, genetics, ethnic origin, nutrition and socioeconomic status.6-8 To determine the growth and development in practice, radiographic markers, especially hand-wrist radiographs, are frequently used.4, 9 However, the evaluation of cervical vertebrae by cephalometric radiographs has been considered a more practical method to determine the growth and development and to reduce radiation exposure.3, 10

Artificial neural network (ANN) have been developed by imitating the biological structure of the human brain.11-13 ANN are the systems that consist of several processing units connected to each other in a weighted manner. Neural computing is based on the concept of a distributed, non-linear process. They use neurons connected with synapses to send information like the human neural system. With repeated learning, each synapse connection can be reinforced or weakened. In each synapse, information of the input neurons is collected using a weighting technique. Weighted values are adjusted through iterative learning. Excessive iterative learning may increase the goodness-of-fit of the training set, but it may also increase the test set's errors, which is called overfitting. A validation matrix is required to prevent overfitting, stop the learning and build a generalized model.14

Radiographic evaluation software, widely used for dentistry diagnosis, has been rapidly improved with the advances in computer technology. Our study aimed to determine the growth-development periods and gender using ANN by generating models based on cervical vertebrae.

2 MATERIALS AND METHODS

The study population consisted of patients aged between 8 and 17 who were admitted to Necmettin Erbakan University, Faculty of Dentistry, Department of Orthodontics for examination, and whose hand-wrist and cephalometric radiographs were taken. Our retrospective study consisted of six groups (CVM 1-CVM 6), each of which was a group in the cervical vertebral maturation period (CVM). The study was planned for 420 patients, with 35 girls, 35 boys in each group. However, an individual in the third cervical vertebrae maturation stage was not included in the study group, and thus, the study was completed with 419 patients. The ethics committee approval was received from Necmettin Erbakan University.

The cephalometric radiographs were divided into six stages according to the maturation level,15 and the hand-wrist radiographs were divided into eleven stages according to the maturation indicators.9 These radiographic images were first compared with each other and then with the chronological age. These correlations also have been implemented to increase CVM labels' reliability too.

Twenty-seven vertebral reference points were marked on the cephalometric radiograph, and 32 linear measurements were taken at these points. The points and measurements were defined in Figures 1 and 2. The same researcher measured the measurements at two different times. The observer measurement consistency coefficients between the two different measurements were calculated.

A, Vertebral reference points. B, Horizontal measurements. C, Vertical measurements

Description of the Vertebral reference points, horizontal measurements and vertical measurements

Artificial Neural Network (ANN) formed by interrelated artificial neurons (nerve cells) is a mathematical model of the human nervous system in Figure 3. This learning-based system can work with incomplete knowledge and decide on new instances it has never encountered via establishing connections between the training examples. They can also learn and model non-linear and complex relationships, which is important because, in real-life, many of the relationships between inputs and outputs are non-linear as well as complicated. Because of these advantages, we preferred the ANN algorithm.

A, Structure of a neuron. B, Structure of an artificial neuron. C, The structure of ANN-7 for the determination of growth-development periods

Determination of the growth-development periods was taken as a classification problem with six classes in this study. An artificial neural network that could be trained to classify inputs according to target classes was used for solving these problems. Our linear measurement types were basically horizontal, vertical and indent measurements. Combinations of the linear measurements were used to detect the most suitable model for our problems. Twenty-four different data sets were formed to train ANN, so 24 different ANN models for determining the growth-development periods were obtained. An ANN model was also done by all values (all measurements and age) to determine gender from the cervical vertebrae. All data sets were divided into three groups: 70% training set, 15% test set, 15% validation set. In training, it's unlikely to be memorized when validation and test data sets are randomly selected. Memorization is a more common problem when the size of the training set is small. While fewer test data set does not cause memorization, less training data set can cause memorization.16 According to the results, seven ANN models with a high success level and clinically applicable were selected. We aimed to report the highest success levels of each basic measurement type, so we shared ANN-2 and ANN-4 models' accuracy, which trained with horizontal measurements even if they had low accuracy. The details of the data sets and the graphical abstract of our study were given in Figure 4.

The graphical abstract of our study

A supervised learning algorithm called ‘Scaled conjugate gradient backpropagation’ and tan-sigmoid transfer function was used as an optimizer algorithm and activation function, respectively. The maximum number of epochs to train, minimum performance gradient, maximum validation failures, sigma (used for determining the change in weight for second derivative approximation) and lambda (parameter for regulating the indefiniteness of the Hessian) were set as 1000,1.0e-6, 6, 5.0e-5 and 5.0e-7, respectively. The learning rate and momentum were not used in the scaled conjugate gradient backpropagation algorithm. The number of neurons of each model is given in Table 1. Accuracy of the test data set given in Table 1 could be used to show the human and ANN models' consistency.

Table 1. The data sets details and structure parameters and accuracy information of the ANN models Data sets details Structure parameters and accuracy information of the Ann models

Data set No

Measurements No

(Table II&III)

Definition of The Measurements

(Also used as Inputs of ANN)

ANN Model No

Neuron Numbers of Input –Hidden-Output Layers, respectively

Training

Accuracy

Validation Accuracy Test Accuracy

All

Accuracy

DataSet1 23-26 All indents ANN-1 4-5-6 75% 79% 71.4% 75.1% DataSet2 1-10

Only horizontal

(excluding inclined measurements)

ANN-2 10-11-6 45.7% 46% 49.2% 46.3% DataSet3 14-22

Only vertical

(excluding inclined measurements)

ANN-3 9-12-6 73.7% 76.1% 76.1% 74.4% DataSet4 2, 5, 8, 11-13 Upper horizontal measurements with inclination ANN-4 6-2-6 45.7% 47.6% 50.7% 46.7% DataSet5 16, 19, 22-26 All anterior vertical measurements and indents ANN-5 7-6-6 71% 69.8% 69.8% 70.6% DataSet6 14-26 All vertical measurements and indents ANN-6 13-15-6 87.3% 90.4% 81% 86.8% DataSet7 1-32 All values ANN-7 33-34-6 95.2% 93.6% 90.4% 94.2% DataSet-Gender 1-32 All values ANN-Gender 33-35-2 88.7% 92% 90.5% 89.5% 2.1 Statistical analysis

Spearman's Rho rank-order correlation analysis was used to determine the relationship between the hand-wrist maturation level, cervical vertebral maturation level and age. The Kruskal-Wallis (KW) analysis and the paired comparison methods of the KW statistics were used in the comparisons based on the maturation levels. The vertical and horizontal measurements, age and gender information were used to create study models and analysed by the ANN method to determine the cervical vertebral maturation level. The accuracy, sensitivity and specificity values of the estimation model were calculated.

3 RESULTS

Correlations between hand-wrist data, cervical vertebral growth-development levels and age were calculated. Significantly positive correlations between hand-wrist data, cervical vertebral growth-development levels, and age were detected (P < .001). Observer measurement consistency coefficients between the measurements were calculated and ranged from 0.991 to 0.906.

The accuracy values of the ANN models were given in Table 2. The ANN-7 model (32 linear measurements and age) had the highest model accuracy with 0.9427. Considering the linear measurements' number, the best result was obtained at the ANN-6 model consisted of 13 linear measurements (with all vertical measurements and indents) with 0.8687. This result was the highest model accuracy with the least linear measurements among all our ANN models. Gender was also determined using ANN (0.8950) on cervical vertebrae data.

Table 2. ANN analysis results of the models OUTPUT Sensitivity Specificity F1 All indents ANN-1 CVM 1 0.9142 0.9541 0.8533 CVM 2 0.7 0.9570 0.7313 CVM 3 0.8695 0.9628 0.8450 CVM 4 0.7428 0.9627 0.7703 CVM 5 0.6571 0.9140 0.6301 CVM 6 0.6285 0.9512 0.6717 Only horizontal (excluding inclined measurements) ANN-2 CVM 1 0.4285 0.8968 0.4411 CVM 2 0.3 0.9140 0.3471 CVM 3 0.4347 0.8771 0.4225 CVM 4 0.3857 0.8710 0.3802 CVM 5 0.5714 0.8825 0.5298 CVM 6 0.6571 0.9140 0.6301 Only vertical (excluding inclined measurements) ANN-3 CVM 1 0.7285 0.9484 0.7338 CVM 2 0.6285 0.9197 0.6197 CVM 3 0.6086 0.96 0.672 CVM 4 0.8571 0.9426 0.8 CVM 5 0.7571 0.9455 0.7464 CVM 6 0.8857 0.9770 0.8857 Upper horizontal measurements with inclination ANN-4 CVM 1 0.6285 0.8538 0.5333 CVM 2 0.3 0.9398 0.375 CVM 3 0.5072 0.8885 0.4895 CVM 4 0.1428 0.9770 0.2272 CVM 5 0.4714 0.8911 0.4680 CVM 6 0.7571 0.8108 0.5608 All anterior vertical measurements and indents ANN-5 CVM 1 0.5857 0.9627 0.6612 CVM 2 0.7571 0.8911 0.6583 CVM 3 0.6376 0.9428 0.6616 CVM 4 0.7142 0.9455 0.7194 CVM 5 0.7428 0.9541 0.7536 CVM 6 0.8 0.9512 0.7832 All vertical measurements and indents ANN-6 CVM 1 0.9142 0.9742 0.8951 CVM 2 0.8142 0.9627 0.8142 CVM 3 0.8260 0.9914 0.8837 CVM 4 0.9857 0.9713 0.9261 CVM 5 0.8428 0.9627 0.8309 CVM 6 0.8285 0.9799 0.8592 All values ANN-7 CVM 1 0.9428 0.9885 0.9428 CVM 2 0.8857 0.9856 0.9051 CVM 3 0.8985 0.9828 0.9051 CVM 4 0.9714 0.9770 0.9315 CVM 5 0.9571 0.9971 0.9710 CVM 6 1.0 1.0 1.0 ANN-Gender Male 0.8852 0.9048 0.8937 Female 0.9048 0.8852 0.8962 4 DISCUSSION

Among many radiological methods developed to evaluate skeletal age, hand-wrist radiography has been considered the gold standard. However, cephalometric radiographs are preferred for their clinical applicability and reduced radiation exposure levels to determine growth-development periods.17-19 Uysal et al20 were reported that the Spearman correlation coefficient between hand-wrist and cervical vertebral maturation was 0.86 (P < .001). Our study group included individuals who had cephalometric and hand-wrist radiographs simultaneously. We used hand-wrist radiographs because we aimed to test the cervical vertebrae and hand-wrist methods’ consistency for our study group obtained from our population. Also, the precision of class labels of the data set used for ANN training was fortified by hand-wrist radiographs usage. We found that the maturation periods in hand-wrist radiography and cervical vertebrae were strongly correlated (P < .001).

Computer-aided systems have been developed to minimize the interobserver differences that may arise in determining growth and development and inconsistencies in the evaluations of observers at different times. The literature review performed in this study revealed no fully automated computer-aided systems that determine the growth-development stages from the cervical vertebrae data using the algorithms. The success of the algorithms can vary according to the problem types. For that reason, we first focused on the ANN algorithm's evaluation for our problems, which determined the growth-development periods and gender from the cervical vertebrae. Previous studies on semi-automatic determination systems performed regression analyses on cervical vertebrae data. Mito et al21 performed an evaluation using regression analysis with eight linear measurements on 176 Japanese girls aged between 7 and 14.9 years, Beit et al6 with ten linear measurements on 730 individuals (352 girls and 378 boys) aged between 6 and 18 years, and Alhadlaq and Al-Maflehi22 with eight linear measurements on 122 Saudi men. With our study, we wanted to contribute to the studies in this area. Based on the observation of horizontal, vertical changes and indentation formation in vertebrae with growth development, ANN-1 model was trained with only indents, ANN-2 model was trained only horizontal measurements (excluding inclined measurements), and ANN-3 models were trained with only vertical measurements (excluding inclined measurements). While ANN-1 model was a model that contains only four indents measurements, its accuracy was 0.7517. Nevertheless, ANN-3 model consisted of only nine vertical measurements; its accuracy was 0.7446. In ANN-2 model, although more measurements were made (10 measurements), it was determined that the accuracy was quite low 0.4630. The ANN-7 model (32 linear measurements and age) accuracy value was found 0.9427. The accuracy of the ANN-6 model (13 linear measurements) was obtained 0.8687. This was the highest model accuracy of the least linear measurements by drawing 13 linear measurements using vertical measurements and indents.

Although machine learning has been used for classification problems in many studies,23-27 research on the accurate determination of the growth-development levels was limited. In this study, models were created using 32 points in different variations to determine the classification. All values (32 measurements and age) were used for the ANN-7 model and the ANN-gender model. Data were divided into three sets: training, validation and test sets. The validation set was used to minimize over memorization. Similar success ratios of the training, validation and test sets indicate that the models are well generalized.

The accuracy was 0.4677 at the ANN-4 model because the trapezoidal shape in the vertebrae changes over time. When only vertical measurements (ANN-5 model) were evaluated, the accuracy was 0.7064. High sensitivity and specificity values were achieved at the fourth, fifth and sixth growth-development levels, which can be explained by the vertical changes in the vertebrae with the growth spurt.

Hassel and Farman15 and Bacetti et al28 reported that the fundamental change was in the vertical height and indents. The accuracy of the anterior measurements and indents (ANN-5 model) observed as fundamental changes in C3, C4 and C5 was 0.7064. When all vertical measurements and indents (ANN-6 model) were evaluated together, the accuracy was 0.8687. The changes in vertebral shapes (trapezoid, horizontal rectangle, square and vertical rectangle) are the reason for the increase in accuracy. High sensitivity and specificity values at the third, fourth and fifth growth-development levels can be attributed to the formal changes that are more obvious at these stages. When all the values (all measurements and age) were evaluated, the accuracy increased (0.9427).

The studies on the use of artificial intelligence in hand-wrist age determination are much more advanced in automation.29-33 However, according to our knowledge, studies on cephalometry and cervical vertebra are very limited. The different algorithm's success was compared previously.34, 35 Kök et al34 trained the ANN model with the data set they created with 20 measurements. In our study, 24 different ANN models trained with 24 different combinations of the 32 measurements were evaluated. As a result, we noticed that increasing the number of measurements does not increase the ANN model accuracy. Increasing the number of measurements allows us to identify the best combinations of model inputs for the classification problem. We have concluded that the determination of qualified measurements carrying more information for CVM detection is more important than the measurement quantity increase.

Gender determination is an important parameter used in forensic medicine. Teke et al36 performed gender determination using the computer tomography (CT) images of the maxillary sinus and reported an accuracy of 69.4% in women and 69.3% in men. In the multi-parameter cranium study carried out by Fernandes et al,37 the accuracy of gender determination using maxillary sinus was 79.2%. In our study, the accuracy of gender determination using ANN was 0.8950. Gender determination can also be performed using the cephalometric radiograph images of the vertebrae. The high ratio in gender determination is caused by reflecting the mean height differences between boys and girls on the vertebrae.

We foresee that using the other information in the cephalometric radiograph (the features from the skull base, the features from other parts of cervical vertebrae, the pixel intensity values or even the features from soft tissue) in addition to linear measurements for a fully automated feature extraction system will positively affect the system's success.

5 CONCLUSIONS

The growth-development periods and gender were determined from the cervical vertebrae by using ANN. The success of the ANN algorithm has been satisfactory. Further studies are needed for a fully automatic decision support system.

CONFLICT OF INTEREST

None of the authors declare any conflicts of interest.

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