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MATHEMATICAL MODELING OF THE STRESS-STRAIN STATE OF BONE TISSUE USING INTRAOSSEOUS DENTAL IMPLANTS. (LITERATURE REVIEW)
Savransky Ph.
MD, professor, Department of General Dentistry, University of Jerusalem, Jerusalem, Israel
Grishin P.
Candidate of Medical Sciences, Associate Professor of the Department of Maxillofacial Surgery, GOU VPO
Kazan State Medical University, Kazan, Russia
Simakhov R.
Assistant of the Department of Maxillofacial Surgery, Omsk State Medical Academy of the Ministry of
Health, Omsk, Russia
Khaikin M.
Candidate of Medical Sciences, Assistant of the Department of Maxillofacial Surgery and Dentistry of the Samara State Medical University, Chief Medical Officer of the City Clinical Hospital of the Samara City Dental
Clinic No. 1, Samara, Russia Chigarina S.
Candidate of Medical Sciences, Associate Professor of the Department of Therapeutic Dentistry, Samara
State Medical University, Samara, Russia
Kalinnikova E.
student of the stomatological faculty, GOU VPO Kazan State Medical University, g. Kazan, Russia
Abstract
In this article, we give a brief review of the literature on the use of the method of mathematical modeling of stress-strain state and finite-element analysis during dental implantation. Based on the analysis, it was concluded that the application of this method in practice will make the implantation process and further prosthetics more reliable and predictable, especially in atypical clinical situations.
Keywords: implantation, mathematical modeling, stress-strain state, finite element analysis.
The biomechanical aspects of planning implantation and the functioning of intraosseous implants have not been adequately studied. This is due to the difficulty in measuring in vivo stresses in bone tissue when loading both the teeth and implants. Gnathodynamometric, strain-gauge, frequency-resonance measurements (RFA) give a relative and local view of the stress-strain state (VAT) in bone tissue with implant loads.
The most informative and promising experimental method for studying jaw biomechanics is three-dimensional mathematical modeling of the stress-strain state in various clinical situations during implantation [1, p.11; 2, p.103].
Work in this direction is based on mathematical models and calculations of different levels of complexity and compliance with clinical conditions give conflicting results on the magnitude and nature of stress in bone tissue [3, p.34; 4, p. 58; 5, p. 47].) In this case, it is rare in an identical model to compare the biomechan-ical parameters with the load of the intact dentition and in the presence of implants [6, p. 106]
Three-dimensional mathematical modeling of the stress-strain state of bone tissue around the implants is an informative tool for biomechanical planning of the number, size of implants, features of the surgical stage
and prosthetics based on the established values of maximum stresses (nomograms) depending on the volume of bone tissue (according to computed tomography) and the size of the implants [7, p.29].
In their work [8 ,p.34], data from the results of three-dimensional mathematical modeling of the state of the cortical bone around the dental implants in different parts of the dentition are cited. At the same time, the study demonstrated the possibilities of modern three-dimensional modeling of VAT in implantology using the example of implant biomechanics in different parts of the jaw in standard conditions. The authors came to the conclusion about the possibility of individual changes in jaw parameters and places of planned implant placement for predicting maximum stresses in bone tissue.
The majority of authors [9, p. 28; 10.20p; 11, p. 177] believe that the most informative and promising experimental method for studying biomechanics in dentistry and implantology is three-dimensional mathematical modeling of stress-strain state under various atypical clinical conditions.
The studies carried out in this direction on the creation of a mathematical model of stress-strain state did not always take into account the level of complexity of implantation in a particular clinical situation. This is
likely and explains the contradictory results of the main characteristics of the stresses surrounding the implant of bone tissue [12, 22 p.; 13, p. 307; 14, p. 127.]
In the opinion of [15, 197p.], experimental mathematical calculations of the stress-strain state in teeth, bone tissues and prosthetic structures should be carried out under the conditions of a single jaw model in connection with a significant effect on the magnitude of stresses in a separately researched area, the extent of their spread to other departments jaws. A mathematical model built on the basis of the individual characteristics of a particular patient makes it possible to simulate various situations and obtain data for subsequent analysis. At the same time, analysis of stress distribution in the finite element model for various types of load makes it possible to determine the optimal design of the dental intraosseous implant, the location of the supporting elements of the implant, the necessity of fixing them [16, p. 1412].
The effect of dental prostheses on the supporting implants and the alveolar ridge, determined using a mathematically finite element model, allow optimizing the process of selecting the type of implantation systems, which in turn will improve the patient's quality of life [17, p. 112; 18, p. 96].
A number of authors suggest using the method of mathematical modeling to assess the possibility of using teeth as a support, depending on the degree of their tilt. The use of this technique makes it possible to estimate the possibility of using teeth that incline under the support of non-removable structures on the basis of numeric indices [19, p.63].
At present, the search for the optimal implant design is carried out primarily in an analytical way. For this, computer programs of two- and three-dimensional mathematical modeling are used [20, p.20; 21.27p.; 22, 335p.]. Such studies, taking into account the biome-chanical characteristics of the bone, implant and prosthetic design, enable you to play different situations and obtain data for comparing stress levels, compression and adhesion forces inside and around the implant [23, p.34; 24, p. 50]
Using the finite elements method (FEM), it is possible to determine the problem areas of jaw sites with dental implants, characterized by a high concentration of stresses, which are expedient for use in temporary and permanent prosthetics. It is very important to determine the critical (permissible) loads on the newly created design [25, p.7].
The mathematical model of "removable prosthesis - implant-bone" with variable parameters of bone size and density has been developed, which allows studying the biomechanical bases of interaction of the mandibular bone structure with complete removable prostheses of various designs and fixing them with dental in-traosseous implants [26, 45p].
In the opinion of [27, p. 49], mathematical modeling and finite element analysis are the most promising and affordable for solving the problems of the biome-chanical substantiation of the construction of plate prostheses that overlap intraosseous implants. An individual approach that ensures biomechanical
compatibility of the implant system and bone, an increase in the reliability of fixation and the durable functioning of the prosthesis cannot be carried out without revealing the patterns of the stress-strain state of the tissues surrounding the dental implant and the elements of the removable prosthesis, a safe load level for bone remodulation [28, 270p.; 29 p.49 ].
In studies on the evaluation of bone stress in implant placement, the simplest models are found that simplify the bone to some cylindrical pocket framing the tooth [30, p. 32] sections of bone and crown in the form of a cube [31, p.37]), and models that take into account the real geometry of the jaw [32. p. 102].
Including the analysis of the stressed-deformed state of the human jaw in the Minics program. The undoubted advantage of this program is the ability to discretely specify the modulus of elasticity of tissues depending on the characteristics of images of computed tomography, which allows to take into account the porous structure of the spongy bone and the Young's modulus variation depending on the density [30, p.32]
The method of mathematical modeling of the stress-strain state with finite elements [3, p.34] was used to study the mechanism of the orthodontic movement of the teeth. The authors found that the orthodontic movement of the teeth is achieved by modeling the processes of the alveolar bone, which are caused by changes in the distribution of stress (deformation) in the periodontitis of the teeth during orthodontic treatment.
On the three-dimensional mathematical model the stress-deformed state of the system "dental implant -bone tissue of the jaw" was studied by the finite element analysis for various sizes of the intraosseous part of the implant. At the same time, data were obtained on the patterns of stress distribution in the dental implant system-the jaw bone [33, 24p.].
Using three-dimensional mathematical modeling (FEM) [7, 157p.] calculated the level of functional stresses in cortical and spongy bone tissue around the intraosseous implant with different volumes and thicknesses in the neck area of the implant. Comparison of the maximum stresses with the limits of bone strength, biomechanics, the indications for bone implantation in the implant zone are substantiated.
In his work [34, p. 148] we considered a mathematical model for assessing the effect of implants on bone tissue by the finite element method and applying mathematical modeling in dental implantology. It was concluded that due to the use of such methods, dental im-plantology and prosthetics achieve high accuracy in the installation and choice of the prosthesis design and help to establish the chosen structures knowingly correctly.
With the help of mathematical modeling and finite element analysis [35, 27p.] he theoretically substantiated the possibility of using temporary non-removable dentures with support for temporary implants.
As a result of scientific research, the stress-strain state (VAT), strength and rigidity of the temporal design of the dental prosthesis on the temporary dental implant "MINI" was made.
Of particular interest is the work on the study of the stress-strain state of bone tissue around the in-traosseous part of cylindrical implants using a two-
bearing bridge structure at different load angles [36, p.3; 37, p. 85]. According to the authors, the study of the impact of the intra-osseous part of the implant on the cortical layer of bone tissue with its various geometric parameters and angles of transfer of the load is necessary for developing practical recommendations for planning treatment with dental implants.
In the conditions of three-dimensional mathematical modeling [9, 28p.] Received the characteristics of VAT in the transdental implant of titanium nickelide with the effect of tooth molding and the underlying bone tissue under vertical and horizontal load, stress concentration zones in the tooth-alveolar complex and implant were determined.
According to [38, p.14], the influence of biome-chanical factors revealed during mathematical modeling of the stressed-deformed state of ceramic crowns is confirmed by unsatisfactory remote clinical results of crown functioning in the absence of disianiserization of patients and under unfavorable conditions of their load.
In the opinion of several authors, the three-dimensional mathematical modeling of the stress-strain state in bone tissue around dental implants, including taking into account individual biomechanical characteristics from computed tomography, improves the accuracy of predicting implantation efficiency and justifies the optimal plan for implant treatment [39, 148p .; 40, p.140; 41, p.85]
Particular attention should be paid to the recent publications on the qualitative and quantitative assessment of the mechanism of the osseointegration process in the tissue-engineering "implant-bone" system from the standpoint of systemic biology and biological cybernetics [42, p.18]).
Thus, a brief review of available literature shows that in recent years, more and more attention of researchers has been attracted by the method of mathematical modeling when introducing new implantation systems into practice. The finite element analysis of the stress-strain state in the implant itself, in the surrounding bone tissues, as well as in the place of abutment connection with the implant reveals high stress zones or comparable to the destruction threshold of structural materials and bone. At the same time, we did not find a publication with examples of individual scheduling of implant system selection and appropriate suprastruc-tures, as well as implantation methods based on situa-tional mathematical modeling.
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