Laboratory for the Mechanics of Biocompatible Materials

Scientific results:

• The Laboratory has developed methodologies for tooth tissue sample preparation for a subsequent research of their micromechanical properties. A research of the microstructure of oral cavity tissues has been conducted. For this purpose we used a scanning electron, an atomic force and an optical microscopes, a computer microtomography device, a medical X-ray device and other equipment. The structural elements of the tooth have been studied. We have compared our results with results published in literature, which allowed to evaluate the successfulness of sample preparation and the fitness of a sample for subsequent research using an indentometer. We have produced samples of healthy teeth and teeth with early-stage caries. A microscopic and microtomographic research of one of the tooth samples demonstrated the presence of a region of demineralization  («white» spot).
• Using the nanoindentation method, we have investigated the mechanical characteristics of different parts of the tooth — enamel, dentin, cement, the dentin-enamel junction. An experimental scheme has been developed that ensures  sample wetting in the course of the experiment that rules out the destruction of the tooth sample during a long-term research of a sample in an indentometer.
• The Laboratory has developed mathematical models describing the processes of indentation of samples of hard tissues of the oral cavity based on setting and solving contact problems of implantation of an indenter into homogeneous or inhomogeneous deformable media. We have set special problems of determining the elastic moduli of materials from the results of indentation and found solutions to those problems. Our researchers have compared the results of theoretical research with experimental data for samples whose properties are known a priori. It was found that the results are in good agreement, which allows to state that the produced mathematical models are efficient. A methodology has been developed for determining the properties of biological materials in the presence of an inhomogeneous near-surface structure and if the properties of the researched sample differ significantly from the properties of the substrate of the indenter.
• These results act as the basis for the development of methodologies for determining the properties of inhomogeneous poroelastic and fluid-saturated tissues.
• The research of the mechanical properties of the tooth was conducted in close cooperation  with the Department of Stomatology No. 2 of the Rostov State Medical University. The results of the research of the mechanical characteristic of a healthy and a demineralized region of a tooth have been used to study technologies of caries treatment and prevention..
• The Laboratory has conducted a research of the microstructure of soft biological tissues of the eyeball. For this purpose we used a computer microtomography device, a scanning electron microscope, an atomic force microscope and an  optical microscope. Our researchers were the first to study a human eye sample using a laboratory microtomography device. The results have been compared with previously published observations obtained using an optical microscope, including at the cell level with the use of histology methods. We have tasted a methodology  for preparing soft tissue samples for research in a computer microtomography device.
• We have developed a sample (phantom) for calibrating density relative to the level of gray on a 3D image (tomogram). Using this sample, it becomes possible to determine the distributions of density in the volume of the material of a sample researched using micro-CT in the range between 1,6 and 4,5 g/cm³, which matches solid biological tissues  and formations (bone tissue, enamel, cement and dentin). A device has also been developed for the positioning of the phantom relative to the researched micro-CT sample. Applications for patents for inventions and useful models have been submitted. The data on the distribution of the density in the volume of a material allowed to revise the distributions of the mechanical characteristics in tooth volume.
• Mathematical models have been developed that describe the processes of the indentation of soft fluid-saturated biological tissues on the basis of setting and solving contact problems of installation of an indenter into a porous medium within the scope of the consolidation theory. The set contact problems of the consolidation theory were solved analytically, asymptotically and numerically. We have also developed a methodology for the assessment of the poroelastic properties of biological materials based on results of nanoindentation.
• Our researchers have modeled destruction in layered biological tissues and identified and interlayer peeling. To perform this task, a theoretical model based on solving ill-posed problems of the elasticity theory in a flat and a 3D setting has been developed. We have reviewed a number of problems arising when modeling the destruction of artificial and living biological tissues under loads of a special type. It has been demonstrated that it is reasonable to rely on approaches that are used for layered media when describing the mechanical behavior and destruction of biological tissues. At the same time, the most relevant problems are detecting  interlayer peeling and determining the strains occurring in layers, i. e. ill-posed problems of the elasticity theory. The obtained results can be used for the development of a technology for peeling detection in biological tissues, for instance, in the retina.
• A database has been created that contains data on the properties of biological tissues and artificial materials for the purpose of their systematization and comparison with the results observed in the course of the implementation of the project. Relying on the database, we are developing a software product for selecting artificial materials for living tissue replacement.
• While conducting the planned work, we have produced a number of results that have no counterparts in the world. For example, we have conducted a research of a sample of the anterior chamber of the human eye by means of X-ray microtomography using a micro-CT device. We have found solutions of a number of new contact problems of indentation within the theories of  consolidation and poroelasticity.
• The Stomatological clinic of Rostov-on-Don and the Department of Ophthalmology of the Rostov State Medical University have shown interest in implementing the results of our research. The results of the research of the microstructure, porousness and mechanical properties of the human tooth will be used for the study of the efficiency of caries treatment and prevention technologies. It is suggested that the collected data on the microstructure of eyeball tissues will be used for modernizing the structures of implants.
• We have produced models of the indentation of poroelastic and fluid-saturated artificial biocompatible materials and biological tissues on the basis of solutions of contact problems of the elasticity theory, the consolidation theory, and the poroelasticity theory. A finite-element modeling of the process of indentation of soft biological tissues has been conducted. The stress-strain state and the features of the process of the indentation of fluid-saturated tissues has been investigated.
• Our researchers have produced a mathematical model of the strained state in the vicinity of the  natural indentation of the occlusal surface of the tooth for the optimization of the profile of artificial materials (crowns and prosthetics). We have conducted a comparison of our computations with experimental data – mineralization density fields in human teeth with fissure caries at various stages.
• We have created a mathematical model of the interaction of the tip of a lensotom (a tool for removing a damaged eye lens) with  piezoelectric supply and biological tissue. Models of various structures of intraocular lenses for the replacement of damaged eye lenses have been produced and researched. On the basis of the results of the modeling we have developed an optimized structure of intraocular lenses that can be installed in the capsular bag of the lens. Our researchers have produced and studied mathematical models of various structures  of keratoprostheses for the replacement of damaged regions of the cornea.
• The Laboratory has produced models describing the deformation of the outer layer of the eye (sclera) and the changing of the intraocular pressure (IOP) after administering a certain volume of injections into the vitreous body. We gave assessed changes of the tonometric IOP observed in mathematical models of several types of tonometers. Our researchers have evaluated the impact of the geometric parameters and the       orthotropy of the plate, the spherical or sloping coat on the value of the critical load. Our researchers have built mathematical models describing elastotonometty after hypermetropia correction surgery using the LASIK and FemtoLASIK methods. We have conducted an analysis of the impact of the inhomogeneity of the cornea caused by hypermetropia correction surgery in the behavior of the elastic curve.
• We have collected data on the microstructure and physical and mechanical properties  of artificial biocompatible materials and coatings manufactured using various methods. We have compared the properties of natural human tooth tissues in the norm and in pathology with the properties of orthodontic materials. The impact of various methodologies of treatment on the change in density of adjacent human dental tissue  has been assessed.
• Our researchers have performed a mathematical modeling of the process of indentation of fluid-saturated poroelastic material imitating soft elastic biological tissues of the eyeball  and the oral cavity. We have mathematically defined contact problems of indentation of liquid-saturated poroelastic media factoring in two unknown functions in the region of contact characterizing the elastic and fluid properties of the indented medium in the 2D and 3D cases that can be reduced to a system of two two-dimensional integral equations with two-dimensional nuclei on the difference of the variables in terms of the coordinate and time. Analytical methods have been proposed for solving the produced system of two two-dimensional integral equations. We have built a solution of the problem and analyzed it. Finite-element solutions of contact problems of indentation of a liquid-saturated poroelastic material have been found, including an anisotropic layered material with variable degree of porousness accounting for various boundary conditions on the surface.
• Equipment has been developed for conducting in situ microindentation in a microtomograph, a methodology has been created for processing and interpreting results, and protocols for  researching the process of indentation in a microtomograph equipped with a micro- or nanoindentometer have been described. The protocols allow to measure the geometric and physical parameters of indentation, such as the region of contact, the value of immersion of the surface of the sample outside the contact region etc. Protocols for the processing of visual information obtained using a microtomograph on the basis of projection images and reconstructed 3D images have also been proposed.
• We have conducted several experiments involving biological and biocompatible  materials. The mechanical properties of biocompatible structures have been determined (polymer scaffolds) depending on their structure, data on the mechanical properties of artificial poroelastic fluid-saturated materials from the results of indentation, the size of the contact region, the form of the immersion of the surface outside the region of contact measured experimentally from the results of in situ testing in a microtomograph to refine methodologies for determining the elastic moduli according to the results of indentation.
• A number of practically important applied problems have been solved using the developed theoretical apparatus. Mathematical models of the occlusal surface of the tooth have been built on the basis of solving problems of the stress-strain state of the enamel in the top of the fissure  (in the presence of a crack and without it), modeled by an inverted wedge. Mathematical models     of interaction of keratoprotheses of various structures with the eyeball have been proposed that allow to select the safest designs in terms of the shape and the elastic properties of haptics from the viewpoint of initial rejection of the prosthetic. Mathematical models have been developed for determining changes of the intraocular pressure (IOP) after intracranial injections have been proposed, as well as models of measurement of the IOP after eyesight correction surgeries accounting for the nonlinear properties of the material.
• The Laboratory has developed a number of refined models of elasticity and poroelasticity. We have solved several model initial-boundary value problems in the case of  small and finite deformations within the generalized models of poroelasticity. Mathematical models of an elastic  soft coat accounting for finite deformation and liquid filtration have been produced for the purpose of modeling biological layers (eye sclera and others). Mathematical models  describing   indentation and destruction in piecewise-homogeneous layered poroelastic media have been proposed that are based on methods of integral equations. A mathematical model has been developed describing the contact of a soft layer with a solid body factoring in friction in the presence of large-scale deformations of the shell to assess the impact of friction in contacts of thin-wall structures made of high elasticity materials, including biological membranes.
• Our researchers have generalized the results of the research of biological and biocompatible materials, optimized structures of biocompatible materials and products. 

Implemented results of research: 

The following inventions and computer software are based on the results of the implementation of the project:

1. Alexander N. Yepikhin“s combined keratoprosthesis: patent for an invention   No. 2707646 Russian Federation / Alexander N. Yepikhin; applicant and copyright holder: Don State Technical University. – application No 2018146759 of 27 December 2018, registered on 28 November 2019.
2. A device for fixing and dissecting biological tissues for the production and implantation of a combined keratoprosthesis: a patent for an invention No. 2704565 Russian Federation / Alexander N. Yepikhin; applicant and copyright holder: Don State Technical University –  application. No. 2018146782 of 27 December 2018, registered on 29 October 2019.
3. A device for the 3D imaging of the deformed state of the surface of a material in the region of elastic deformations: a patent for an invention No. 2714515 Russian Federation /Andrey L. Nikolayev, Alexandr G. Sukiyazov, Vladimir B. Zelentsov, Yevgeniy V. Sadyrin, Sergey M. Aizekovich; applicant and copyright holder: Don State Technical University. – application No. 2019126330 of 21 August 2019, registered on 18 February 2020.
4. A device for the positioning of a calibration phantom in the research of microstructure of biological objects: a patent for an invention No. 2731412 Russian Federation /Yevgeniy V. Sadyrin, Alexandr G. Sukiyazov, Andrey L. Nikolayev, Boris I. Mitrin, A. S. Vasultyev; applicant and copyright holder: Don State Technical University . – application No. 2020101530 of 16 January 2020, registered on 02 September 2020.
5. A method for the fixation of a whole cadaver  eyeball and its sectional fragments during X-ray computer micro- and nanotomography and a device for its implementation: a patent for an invention № 2715926 Russian Federation /Alexander N. Yepikhin, Boris I. Mitrin, Yevgeniy V. Sadyrin, I. A. Toporkova; applicant and copyright holder: Don State Technical University. – application No. 2019129833 of 23 September 2019, registered on 04 March 2020.
6. A method of measurement of the region of contact of an indenter with the surface of a sample: a patent for an invention No. 2771063 Russian Federation /Andrey L. Nikolayev, Yevgeniy V. Sadyrin, Vladimir B. Zelentsov, Ivan Yu. Golushko, M. Ye. Kutepov; applicant and copyright holder: Don State Technical university. – application No. 2021116397 of 07 June 2021, registered on 25 April 2022.
7. A  computation of the displacement of the free surface of a coating lying on an elastic substrate during indentation: certificate of state registration of a computer program No. 2021667825 Russian Federation / S. S. Volkov, Andrey S. Vasiliyev, Andrey L. Nikolayev; applicant and copyright holder: Don State Technical University . – application No. 2021666873 of 27 October 2021., registered on 03 November 2021.
8. A method of the morphological assessment of pathological states of the retina and  the choroid by means of scanning optical coherence tomography of the eye: patent for an application No. 2021124660 Russian Federation // Alexander N. Yepikhin, Yuriy F. Bondarenko, Vasiliy V. Dolgov, V. A. Filipenko; applicant and copyright holder: Don State Technical University. – application No. 2021124660 of 19 August 2021.
9. A database of materials medicine and the industry: certificate of state registration of a database No. 2019621772 / A. N. Litvinenko, Sergey M. Aizekovich, Boris I. Mitrin;  applicant and copyright holder: Don State Technical University. – application No.  2019621660 of 24 September 2019, registered on 14 October 2019.
10. A calculation of the displacements of the free surface of a coating lying on an elastic substrate during indentation: certificate of state registration of a computer program No. 2021667825 Russian Federation / S. S. Volkov, Andrey S. Vasiliyev, Andrey L. Nikolayev; applicant and copyright holder: Don State Technical University. – application No. 2021666873 of 27 November .2021, registered on 03 November 2021.

Education and career development:

The following textbooks have been created:

1. Yevgeniy V. Sadyrin, Sergey M. Aizekovich, Vladimir B. Zelentsov, Boris I. Mitrin The use of spherical indenters and the multiple point analysis of results of nanoindentation  for the experimental determination of the local characteristics of the surface: a case study for master’s degree students / Yevgeniy V. Sadyrin, Sergey M. Aizekovich, Vladimir B. Zelentsov, Boris I. Mitrin; Don State Technical University. – Rostov-on-Don: Don State Technical University, 2018. – 30 p. Publishing center of the Don State Technical University, 2017. – 29 p.
2. Yevgeniy V. Sadyrin, Michael V. Swain., Sergey M. Aizekovich, Arkadiy N. Soloviyov. The preparation of samples of frontal cross-sections of a human tooth for the study of  of the local mechanical properties of enamel and dentin: case study for master’s degree students / Yevgeniy V. Sadyrin, Michael V. Swain, Sergey M. Aizekovich, Arkadiy N. Soloviyov – Rostov-on-Don: Publishing center of the Don State Technical Univeristy, 2019. – 16 p.
3. Yevgeniy V. Sadyrin, Michael V. Swain, Sergey M. Aizekovich, Arkadiy N. Soloviyov Determining the mechanical properties. The calibration of the density scale in X-ray computer microtomography: case study for master’s degree students / Yevgeniy V. Sadyrin, Michael V. Swain,, Sergey M. Aizekovich, Arkadiy N. Soloviyov – Rostov-on-Don: Publishing center of the Don State Technical University, 2020. – 25 p.
4. Yevgeniy V. Sadyrin, Michael V. Swain,, Sergey M. Aizekovich, Arkadiy N. Soloviyov. Determining the mechanical properties. Calibrating the density scale in X-ray computer microtomography: case study / Yevgeniy V. Sadyrin, Michael V. Swain,,  Sergey M. Aizekovich, Arkadiy N. Soloviyov. – Rostov-on-Don: Publishing center of the Don State Technical University, 2021. – 24 p. 

Organizational and structural changes:

Unique equipment of the Laboratory purchased in 2018 – the submicron resolution computer tomography scanner – will be introduced to the collective utilization center of the Don State Technical University.

Other results:

• Facilitators of the project have conducted several meetings with employees of medical education institutions and medical organization of Rostov-on-Don and Stavropol.
• We have conducted research of microstructure of human teeth at industrial tomography laboratories of General Electric and Carl Zeiss Microscopy GmbH in Germany.

Collaborations:

• Institute for Heat and Mass Transfer named after A. V. Lykov of the Belarus Academy of Sciences (Belarus), 

• National Cheng Kung University (Taiwan), 

• University of São Paulo  (Brazil), 

• Institute of Biodiversity and Ecosystem Research at the Bulgarian Academy of Sciences (Bulgaria), 

• I. M. Sechenov First Moscow State Medical University of the Ministry of Health of the Russian Federation, 

• Institute of Living Systems of the North-Caucasus Federal University, 

• Rostov State Medical University of the Ministry of Health of the Russian Federation, 

• Southern  Federal University (Russia): joint research.