To date, artificial dental implants are the standard method for replacing damaged or missing teeth. More than a million implants are surgically placed in patients every year (le Guéhennec et al., 2007). This raises the problem of qualitative selection of the correct location of the implant, the proper diameter and length, as well as the material of the prosthesis to minimize the risk of rejection (Cobo-Vázquez et al., 2018). The percentage of biological complications that lead to implant rejection in the first year after implant placement is quite high and ranges from 2 to 5%. The mean 10-year survival rate for a single implant is 96.4% (Howe et al., 2019). In the subsequent period of functional load on the implant structure, technical complications come to the fore, which consist of a fracture of the superstructure or the implant itself. The percentage of technical complications reaches 15% in the first 3–5 years of operation of the structure (Roos-Jansåker et al., 2006). Up to 80% of all complications are associated with errors in diagnosis and treatment planning at the initial stage, which makes research on improving implant survival rates and prolonging the life of the prosthetic structure relevant for modern dentistry and maxillofacial surgery (den Hartog et al., 2008).

Today, medicine is considered one of the strategic and promising areas for the effective implementation of artificial intelligence (Alegre-Cortés et al., 2018). Neural network technologies have the potential to discover relationships and patterns in big data (Kim et al., 2018) and may allow computers to perform assisted disease diagnosis and prediction, as well as suggest further treatment options (Chan et al., 2018). The increase in the volume of information in the field of dental implantology, as well as the need to extract knowledge from this information, is the main reason for the development and use of data analysis systems based on artificial intelligence (Hashem et al., 2020; Alharbi and Almutiq, 2022). Artificial intelligence in dentistry is a method for generating an informed second opinion that is based on mathematical decision making and prediction (Bernauer et al., 2021; Choudhury et al., 2022). Machine learning is generally not intended to replace the dental professional (Carrillo-Perez et al., 2022). Neural network technologies are used in such areas as the analysis of dental radiographs (Lee et al., 2020), the prediction of the need for oral treatment in children (Wang et al., 2020), the classification of dental deposits and treatment planning for orthognathic surgery (Choi et al., 2019), and the auxiliary diagnosis of caries (Mansour et al., 2019).

Currently, the use of artificial intelligence technologies in clinical decision support systems in the field of dentistry is relevant (Khanna, 2010; Jiang et al., 2017). Expert systems based on neural networks can only be trained on clinical data and can be used in cases where “rule-based” decision making is not possible. This happens in many clinical situations, so intelligent systems can become an important decision-making tool in dentistry. The study Kim et al. (2009) proposed a toothache prediction model based on neural network algorithms. By analyzing patient statistics, the algorithm was trained to look for relationships between toothache and brushing frequency, brushing time (before meals or after meals), brushing learning experience, flossing, toothbrush replacement frequency, and other factors including diet. and exercise. A three-layer perceptron architecture with 131 input neurons, 6 hidden layers and an output layer was used as a neural network topology. As a result, a predictive model for the development of toothache was obtained with an accuracy of about 80%. The model identified proper nutrition, oral hygiene, and stress reduction as the most important factors in preventing toothache.

In Xie et al. (2010), an expert decision-making system based on artificial intelligence technologies was proposed to determine the need for extraction before orthodontic treatment. The proposed neural network topology had 23 neurons in the input layer and 1 neuron in the output layer. The training of the neural network system was carried out using the backpropagation algorithm. The simulation results showed that the proposed artificial neural network in this study can correctly judge the need for extraction before orthodontic treatment of patients with malocclusion aged 11–15 years with an accuracy of up to 80%.

In the study Miladinović et al. (2010), artificial intelligence technologies were used to analyze the indirect cause of tooth extraction based on the processing of a large volume of electronic medical records. As the topology of the neural network, a linear classifier consisting of two layers was proposed. The immediate reasons for extraction in 5,257 cases were dental caries (43.8%), periodontal disease (37.2%), fractures (6.8%), prostheses (4.3%), retention (3.1%), orthodontics (2.7%), milk teeth (0.3%). As a result of the data mining of electronic medical records of selected subjects using the proposed algorithm, it was confirmed that the number of extracted teeth was statistically influenced by gender, age and occupation. This algorithm made it possible to identify factors influencing the need for tooth extraction based on cause-and-effect relationships.

In Käkilehto et al. (2009), big data mining was performed to determine whether differences in materials during restoration are a determining factor in service life. As a result, it was found that the average service life of amalgam occlusal restorations was 16.8 years in the 1960 patient group, 13.6 years in the 1970 patient group, and 7.9 years in the 1980 patient group of glass ionomer and composite on the occlusal surface were 4.9 years in the 1970 patient group and 7.3 years in the 1980 patient group. The study clearly shows that undocumented information in large volumes over many years can be extracted and analyzed using data mining.

In the field of dental implantology, there is also an active introduction of decision support systems based on artificial neural networks. In Oliveira et al. (2005), the success of implant treatment was studied using several data mining algorithms. Algorithms based on neural networks, support vector machines and K-nearest neighbors have been proposed. The simulation showed that the accuracy of the proposed algorithms in diagnosing the success of implantation was 75.5, 75.9, and 75.9%, respectively. Statistical factors affecting implant survival in this study were age, gender, implant position, implant type, surgical technique, smoking, and previous illness. For a binary assessment of the probability of success or failure in the survival of a dental implant, a model based on artificial neural networks was proposed in Braga et al. (2012). As a result of training and testing various models, the largest value of the AUC estimation parameter was 0.789 and showed that in 78.9% of the prediction cases, the proposed model matches the test data. In the work (Sadighpour et al., 2014), based on artificial intelligence, a clinical decision support system for the installation of maxillary implants for a patient with a completely edentulous upper jaw is presented. Case histories of 47 patients were included in the study. An architecture consisting of one input layer, one hidden layer, and one output layer was used as the topology of the neural network. The accuracy of the decision support system network was 83.3%.

In all the works reviewed, it was proved that decision support systems based on artificial intelligence, which was trained on the data obtained as a result of dentists’ decisions, can be used as auxiliary tools. Studies show the relevance and prospects of using neural network technologies in modern dentistry for auxiliary diagnostics and prognosis by extracting meaningful information from a large number of medical records to create expert systems that will help dentists make decisions (Roongruangsilp and Khongkhunthian, 2021). Data mining and expert systems are based on a large amount of previous data regarding dental diagnosis, treatment and professional judgment, which is converted into text and numbers (Lee et al., 2012). The actual clinical evaluation and treatment are carried out by the dentist all the time and artificial intelligence can become an integral part of assisted diagnosis and further treatment (Pethani, 2021).

Despite significant progress in the implementation of artificial intelligence technologies in the field of dental implantology, the development of neural network systems for supporting medical decision-making of varying complexity is relevant for achieving higher accuracy in predicting the success of implant survival (Revilla-León et al., 2021). The main hypothesis of the article is a potential increase in the survival rate of dental implants due to the development and implementation of a system for predicting the success rate of single implants based on artificial intelligence as an additional auxiliary tool. The purpose of this study is to develop and model a neural network system for analyzing various statistical factors of patients to assess the success of single implant survival. The proposed neural network system makes it possible to achieve higher recognition accuracy than similar neural network systems by collecting and analyzing a large number of digitized statistical factors of patients and selecting the optimal neural network architecture for analyzing the obtained factors. The use of the proposed system based on artificial intelligence should help the implantologist to pay attention to the most significant factors affecting the quality of the installation and further survival of the implant, and reduce the percentage of complications at all stages of treatment.

The rest of the work is structured as follows. Section “Related work” is divided into several subsections. In subsection 3.1. A description of the collected and digitized case histories of patients who underwent surgical osseointegration is presented. In subsection 3.2. A pre-processing method by encoding the collected statistical factors is described. In subsection 3.3. A neural network architecture for the analysis of statistical factors based on a multilayer linear perceptron is presented. Section “Materials and methods” presents a practical simulation of the proposed system for analyzing patient statistical factors to assess the success of single implant survival based on artificial intelligence. Section “Results” discusses the obtained results and their comparison with known systems based on artificial intelligence for predicting the success rate of dental implants. In conclusion, the results of the work are summarized.

The paper proposes a system for predicting the survival rate of single implants based on artificial intelligence. The proposed neural network system analyzes the statistical data of patients represented by various factors influencing the success of single implants. The scheme of the proposed neural network system for classifying cases of implantation in surgical dental treatment is shown in Figure 1.

Patient statistics are pre-processed with coding to create a feature vector. The proposed neural network system consists of a linear multilayer perceptron. The resulting feature vector obtained after passing through all the layers of the perceptron is fed to the softmax output layer. The output signal of the proposed neural network system for predicting the success of single implant survival is the percentage for 2 diagnostic categories.

Artificial intelligence-based systems in the field of dental implantology are especially useful for processing and analyzing large amounts of data to classify results, as well as for handling repetitive workflows. AI algorithms enable evidence-based dental decision support, especially for less experienced practitioners, and facilitate the analysis of individual patient cases.

The proposed neural network system makes it possible to achieve higher recognition accuracy than similar neural network prediction systems by analyzing a large number of digitized statistical factors of patients. The use of the developed system based on artificial intelligence as an additional auxiliary tool will allow the dentist to pay attention to the factors that affect the quality of the installation and further survival of the implant and reduce the percentage of complications at all stages of treatment.

For the simulation, clinical cases of the experimental database of implant survival were used based on the description of the patient’s case histories. The database was collected using a multicenter retrospective and prospective study from patient records obtained according to a single protocol from dental implantation centers in such Russian cities as Stavropol, Moscow, Penza, Vladivostok, Grozny, Pyatigorsk, and Vologda. The collected and digitized database of implant treatment cases used for practical modeling is presented in LLC (2022). The collected and digitized database included 1,626 cases of dental implantation, which included 1,490 cases of successful implantation (91.64%) and 136 cases of implant rejection (8.36%). The dental database included digitized cases of implant treatment from 1998 to 2021. The average time of implant rejection was about 3 years. In most cases (87 patients out of 136), rejection occurred within the first year after implantation. The resulting base included 112 patient factors that affect the success of single implant survival, which could take 916 different values. Due to the fact that the collected database included 1,646 patient histories, training on a full experimental base is impossible due to the insufficient number of variations of all possible values of factors influencing implantation. Based on the recommendations received from specialists in the field of dental implantology, 55 factors were selected for modeling, divided into three groups (general somatic factors; the state of the dentoalveolar system; the state of the receptive bed). The factors used for neural network modeling and their cardinality are presented in Table 1.

The parameter of implant survival is represented by two possible values—“Successful survival,” “Rejection,” which are classes for neural network recognition of clinical cases. The parameter “Age at the time of implantation, years” was divided into three groups in accordance with the age classification adopted by the World Health Organization (WHO). The first group of “young age” is represented by patients under the age of 44 years. The second group of “middle age” is represented by patients aged 45–59 years. The third group of “elderly” is represented by patients aged 60 years and above. Also, in order to reduce the variability of the selected parameters, based on the recommendations, the available data were processed. Each factor was converted to one of three possible values - a positive effect (the variable value is “positive”), a neutral effect (the variable value is “neutral”), or a negative effect on implant success (the variable value is “negative”). Thus, it was possible to reduce the number of possible values that the selected 55 factors can take from 426 to 164. Table 2 presents the factors selected for neural network modeling and their cardinality after pre-treatment to reduce variance. An example of transformed variables is shown in Figure 5.

For modeling, 1,626 clinical cases were used, which were divided into data for training and testing in a percentage ratio of 80–20. The simulation was carried out using the high-level programming language Python 3.8.8. The Pytorch machine learning framework was used to model the neural network system. The NumPy, Pandas, and Scikit Learn libraries were used to process statistical data. The Matplotlib library was used to visualize the data. Each neural network system was trained for 100 epochs. When using a larger number of epochs, a pronounced retraining of each of the proposed neural network systems was observed. The batch size was 16. Adam was used as an optimizer with a standard learning rate of 0.001. CrossEntropyLoss function was used as an error function. All calculations were performed on a PC with an Intel^® Core™ i5-8500 processor at 3.00 GHz with 16 GB of RAM and a 64-bit Windows 10 operating system.

The simulation data was pre-processed using the one-hot encoding method in order to convert it into the vector format required for further analysis. Coding tables for each possible value of patient factors affecting implant survival are presented in Tables 3–5. An example of patient factor pre-processing using the one-hot encoding method is shown in Figure 6.

The main difficulty in choosing the optimal neural network architecture using evolutionary algorithms (Hamdia et al., 2021) is that they are time-consuming, computationally intensive, and demanding on user-defined parameters (Abbasi et al., 2015). In contrast, non-evolutionary algorithms and, in particular, trial-and-error method (Sun et al., 2008) require much less time for simulation and user parameters. Thus, in order to effectively select the optimal neural network topology for the system for predicting the risk of complications in implant treatment of the maxillofacial region, a number of experimental simulations of various neural network architectures were carried out using the trial-and-error method.

For the task of assessing the risk of complications in the implant treatment of pathologies of the maxillofacial region, the data for modeling include an expert assessment of the success of implant survival. Thus, a multilayer perceptron with direct connection was chosen as the type of neural network. The activation function used was the ReLU function, which is the most commonly used activation function in deep learning. The ReLU function has such advantages over the sigmoid and hyperbolic tangent as a quick and easy calculation of the derivative, as well as activation sparseness, which allows to reduce the number of neurons to turn on (Li and Yuan, 2017).

Various linear neural network architectures were used for modeling. The input of each neural network was a data vector of 164 characters after preprocessing by the one-hot encoding method of each clinical case from the database. As a result of a number of experimental simulations, 6 variants of the neural network topology were developed to predict the survival rate of single implants in the surgical treatment of pathologies of the maxillofacial region, which made it possible to obtain high results in the accuracy of recognizing the success of implant survival. The developed architectures of neural networks for predicting the success of implant survival are shown in Figure 7. The development of neural network architectures was carried out by trial and error. From the developed and trained neural network architectures, six most successful topologies were selected, which made it possible to obtain the best result in prediction accuracy. At the same time, in each of the neural network architectures, the number of neurons and the number of layers changed. It was found that a gradual decrease in the number of neurons makes it possible to obtain the highest results in the accuracy of predicting the survival rate of single implants.

For neural network architectures No. 1 and No. 4, a gradual decrease in the number of neurons on each new layer was carried out. For neural network architecture No. 2, the number of neurons was increased by two times and then the number of neurons was reduced by two times. For neural network architecture No. 3, a reduction and subsequent increase in the number of neurons was made. For neural network architecture No. 5, the number of neurons was constant and did not change throughout the layers. For neural network architecture No. 6, a slight reduction in the number of neurons was made and a further increase by two times.

Table 6 presents the results of evaluating the developed neural network systems for predicting the survival rate of single implants in the surgical treatment of pathologies of the maxillofacial region. The highest accuracy in predicting the survival rate of single implants was achieved using neural network architecture No. 4 and amounted to 94.48%. An increase in the number of neurons in the first layer and their gradual decrease in the subsequent ones in neural network architectures No. 1 and No. 4 made it possible to achieve the highest accuracy in predicting the success of implant survival. With an increase in the number of layers in neural network architectures, there was an increase in the time spent on training without a significant increase in the prediction accuracy index of the neural network. It was found that for the task of classifying statistical data of patients, the architecture consisting of four linear layers with a gradual decrease in the number of neurons is optimal in terms of accuracy and time costs.

The F1-score corresponds to the harmonic mean of the accuracy and recall of the neural network model and is used as one of the estimates of binary classification systems. The highest F1-score was obtained for high-precision neural network architectures No. 1 and No. 4 and amounted to 0.9657. The lowest F1-score was obtained when testing the neural network architecture No. 5, the distinctive feature of which is the constant number of neurons on each neural layer.

Recall is used as a statistical measure in cases where the cost of false negatives is high. In the field of medicine, and in particular, dental implantology, neural network false negative prediction is more dangerous due to potential risks to the health of patients. The best recall rate when testing the developed systems for predicting the survival of single implants was obtained with neural network architectures No. 1 and No. 4 and amounted to 0.9837.

Specificity is a statistical metric that is defined as the proportion of true negative neural network prediction results. For neural network systems in the field of medicine and, in particular, dental implantology, when the data are highly unbalanced toward positive cases (successful survival of implants), the specificity indicator is an important statistical measure of model evaluation. The highest specificity index was obtained for neural network models No. 1 and No. 4 and amounted to 0.9565.

As a result of the study, a neural network system was developed for predicting the success of single dental implants with a test accuracy of 94.48%. The developed neural network system analyzes 55 statistical factors of patients, which are the general somatic factors of the patient, the state of the dentoalveolar system, the state of the perceiving bed. The collection and digitization of a large number of case histories made it possible to create a unique training database for training artificial intelligence. Due to the multivariate analysis of statistical data of patients, the developed neural network system makes it possible to predict the success of single implants with high accuracy. Table 7 compares the accuracy of predicting the survival rate of single implants in similar neural network systems with the proposed neural network system.

The article Sadighpour et al. (2014) presents an AI-based system with a forward/backpropagation architecture for determining a plan for the surgical placement of dental implants. Modeling was carried out on digitized 47 clinical cases of osseointegration. Each clinical case included 9 possible variables. Recognition was made according to two possible categories, such as a general treatment plan or a detailed treatment plan. In the case of a detailed treatment plan, there was a high risk of dental implant rejection. The proposed neural network architecture included 9 input neurons, a hidden layer with 20 neurons, and an output layer with 2 neurons. The accuracy of the proposed neural network system from the study Sadighpour et al. (2014) was 83.30%, which is 11.18 percentage points lower than the proposed system for predicting the success of single implants. A significant difference in the accuracy of the considered systems may be due to the amount of training data as well as the optimality of the chosen neural network architecture. Modeling on an insufficient amount of data with a large number of various statistical factors affecting osseointegration can lead to unreliable obtaining of weight coefficients during training. At the same time, the number of possible combinations for 9 statistical factors is significantly higher than the amount of data used for training and testing. The absence of recurring combinations of statistical factors makes it impossible to determine the pattern between the possible rejection of a dental implant and the statistical information available in a particular case that affects osseointegration.

The study Braga et al. (2012) presents a binary neural network model for predicting the success of dental implant survival. Modeling was carried out on the basis of a database of 155 cases of implantation of patients. Moreover, each case included 57 variables that determine the possible risks of implant treatment. In addition to general somatic factors, as well as factors of the state of the dentition, data related to the genetic characteristics of patients, such as the presence of cytosine, thymine in local genes, etc., were used. As a result of testing five different neural network models, the highest accuracy result on the test set was 78.90% for neural network model No. 4. The results obtained are 15.58 percentage points lower than the test accuracy of the proposed neural network system for analyzing patient statistical factors for predicting the success of single dental implants. The low recognition accuracy of the considered model from Braga et al. (2012) can be explained by the insufficient number of training examples for 57 factors affecting osseointegration. With such insufficient data for modeling, it is almost impossible to repeat the combination of the 57 factors considered to find a pattern between the patient’s condition and implantation success.

The paper Oliveira et al. (2005) presents a comparative study of four machine learning methods for predicting the success rate of dental implants. Algorithms based on neural networks, support vector machines and K-nearest neighbors have been proposed. The modeling data set consisted of 157 patient statistics examples. Each training example included 7 statistical factors such as age, gender, implant position, implant type, surgical technique, smoking, and pre-existing medical conditions. All patient factors could take 17 possible values. At the same time, the classification of the analyzed data was carried out according to 7 possible categories. As a result of the simulation, the highest accuracy in predicting the successful survival of dental implants using the neural network algorithm was 75.90%, which is 18.58 percentage points lower than that of the proposed system based on artificial intelligence. A significant difference in prediction accuracy can be explained by a multivariate analysis of the statistical data of patients, as well as by training the proposed system on a large amount of digitized data with a more complete description of the factors affecting osseointegration.

In Liu et al. (2018) a model for predicting and early warning of potential implant rejection was developed. Modeling was carried out on the basis of clinical cases of 681 patients. Data were collected for each patient, including 20 factor variables. As a result of modeling using supervised learning methods, a neural network system was obtained with a prediction accuracy of 74.10%, which is 20.38 percentage points lower than the proposed neural network system for predicting the success of single dental implants. The difference in the results of the test prediction accuracy can be explained by the insufficient number of analyzed factors affecting osseointegration, as well as the insufficient amount of data for modeling.

The main limitation of using the proposed neural network system for analyzing patient statistical factors to predict the success of single dental implants is that dentists and specialists can only use the system as an additional diagnostic tool. The proposed system is not a medical device or program and cannot self-diagnose patients. At this stage, the developed neural network system is capable of predicting a positive or negative outcome of a single dental implant operation and cannot be used as a full-fledged tool for supporting medical decision-making. Since the majority of implant treatment cases describe successful engraftment of the implant during osseointegration, cases of false negative classification are possible.

The paper presents an artificial intelligence-based system for analyzing the statistical factors of patients in order to predict the success of dental implant survival. The collected and digitized database of clinical cases of osseointegration, as well as the neural network architecture optimally designed for the collected factors, made it possible to obtain a neural network system with a test accuracy of 94.48%. The proposed system based on artificial intelligence makes it possible to achieve higher prediction accuracy than similar neural network systems due to the analysis of a large number of statistical factors of patients, as well as deeper learning on a large amount of data. The use of the proposed system based on artificial intelligence as an additional auxiliary tool will allow the dentist to pay attention to minor factors that affect the quality of the installation and further survival of the implant, and reduce the percentage of complications at all stages of treatment.

The main limitation of using the proposed neural network system for predicting the survival rate of single dental implants is that specialists can use the system only as an additional diagnostic tool. The proposed system cannot be used as a full-fledged tool for supporting medical decision-making.

A promising direction for further research is the development of a medical decision support system based on the technology for generating recommendations to reduce the risk of complications, indicating certain factors that affect the clinical situation. It is also planned to develop of methods for minimizing false negative classification through the use of weighting factors. In further studies, it is planned to develop a detailed neural network study module to obtain the percentage of influence of each factor on the overall picture of the clinical case. Further development of a medical decision support system based on the proposed neural network system will make it possible to determine specific recommendations for the doctor and patient in order to identify the most potentially dangerous factors that negatively affect osseointegration to further minimize complications at all stages of implant treatment.

The raw data supporting the conclusions of this article will be made available by the authors, without undue reservation.

All authors listed have made a substantial, direct, and intellectual contribution to the work, and approved it for publication.