Моделирование геометрической формы, слияния и распределения кислорода в тканевых сфероидах доброкачественной ткани (Geometrical Shape, Coalescence and Oxygen Distribution Modeling in Benign Tissue Spheroids) тема диссертации и автореферата по ВАК РФ 00.00.00, кандидат наук Вилински-Мазур Кэтрин Александровна

• Вилински-Мазур Кэтрин Александровна
• кандидат наук
• 2024

Оглавление диссертации кандидат наук Вилински-Мазур Кэтрин Александровна

CONTENT

INTRODUCTION

CHAPTER 1. BACKGROUND

1.1 CRUCIAL POINTS OF THE BIOCONSTRUCT MODELING

1.2 REVIEW OF SOFTWARE TOOLS FOR 3D BIOPRINTING

1.2.1 Brief description of the review

1.2.2 The research field description

1.2.3. Living cells printing

1.2.4 Scaffolds and bioimplants printing

1.2.5 Printer control software

1.2.6 Software for pre-processing

1.2.6.1 G-code operations

1.2.6.2 CAD-based software

1.2.7 Software for slicing

1.2.8 Software for scaffold generation (pre-processing)

1.2.8.1 Software for automatic scaffold generation

1.2.8.2 Software for post-processing issues

1.2.9 Approaches for future development

1.3 INDUSTRIAL PRACTICAL APPLICATION OF THE RESEARCH

1.3.1 The 3D bioprinting industry nowadays

1.3.2 3D bioprinting market

1.3.3 Tissue spheroids market

1.3.4 How Function Representation could help

CHAPTER 2. GEOMETRY MODELING: PROBLEM STATEMENT AND FUNCTION REPRESENTATIONS APPLICATION

2.1 INTRODUCTION

2.2 MATERIALS AND METHODS FOR THE GEOMETRY MODELING

2.2.1 Geometrical modeling with Function Representations

2.2.2 Blending and union operations for modeling the spheroid fusion

2.2.3 Scientific visualization of FRep geometry modeling

2.2.4 Hyperfun software for FRep modeling and visualization

2.2.5 An accelerated slicing algorithm for FRep models

2.3 RESULTS AND DISCUSSION FOR GEOMETRY MODELING WITH FUNCTION REPRESENTATION PARAMETRIC IMPLICIT FUNCTIONS

2.3.1 The flowchart of the scientific visualization of FRep geometry modeling

2.3.2 FRep geometry visualization with Hyperfun software

2.3.3 Hypothesis of spheroids fusion geometry testing with the simple analytical solution

2.3.4 FRep geometry visualization with C++

2.3.5 FRep geometry visualization with Java Script: spherical harmonics and tissue spheroids

CHAPTER 3. NUMERICAL SOLUTION FOR DISTRIBUTION, DIFFUSION AND CONSUMPTION OF OXYGEN WITH FINITE VOLUME METHOD VIA SPHEROIDS IN FUSION

3.1 INTRODUCTION

3.2 MATERIALS AND METHODS FOR NUMERICAL SOLUTION FOR DISTRIBUTION, DIFFUSION AND CONSUMPTION OF OXYGEN WITH FINITE VOLUME METHOD VIA SPHEROIDS IN FUSION

3.2.1 Numerical modeling oxygen partial pressure, diffusion and consumption

3.2.2 Finite-volume approximation

3.2.3 Details of coefficients and data for diffusion simulation model

3.2.4 Meshes analysis and convergence

3.2.5 Linear models for analysis of surface irregularity influence on oxygen partial pressure

3.2.6 Using isotonic regression to find an inflection point of oxygen partial pressure function of spheroid diameter

3.3 RESULTS AND DISCUSSION OF NUMERICAL MODELING AND SIMULATIONS

3.3.1 Modeled configurations

3.3.2 Inclusion of surface irregularities into numerical simulation

3.3.3 Prediction the maximal necrosis-free spheroid size

3.3.4 Simulation results

3.3.4.1 Problem statement: geometries and parameters

3.3.4.2 Results of simulation: oxygen partial pressure by diameter for one spheroid and two spheroids in fusion

3.3.4.3. Results of simulation: mesh convergence

3.3.4.4 Results of simulation: surface irregularities impact to oxygen partial pressure rate

3.3.5 Discussion on modeling and simulation

CHAPTER 4. EXPERIMENTAL VALIDATION

4.1 INTRODUCTION

4.2 REAGENTS

4.3 CELL CULTURE

4.4 TISSUE SPHEROID FORMATION

4.5 TISSUE SPHEROID VIABILITY ASSAY

4.6 TISSUE SPHEROID GROWTH KINETICS

4.7 EXPERIMENTAL DATA ANALYSIS

4.8 DISCUSSION ON BENIGN TISSUE SPHEROIDS RESEARCH

CONCLUSIONS

REFERENCES

PUBLISHED PAPERS

ACKNOWLEDGMENTS

Введение диссертации (часть автореферата) на тему «Моделирование геометрической формы, слияния и распределения кислорода в тканевых сфероидах доброкачественной ткани (Geometrical Shape, Coalescence and Oxygen Distribution Modeling in Benign Tissue Spheroids)»

INTRODUCTION

The demand for donor organs was steadily increasing for the last twenty years due to several factors that include an increase in success rate of transplantation surgeries and the growing rates of vital organ failures [1] linked with changes in lifestyle, aging population and prevalence of chronic diseases [2]. That increase in demand lead to a dramatic shortage in supply of transplantable organs, with hundreds of thousands of patients on a waiting list and an average of seventeen people dying every day due to the inaccessibility of suitable transplants, for example in USA, according to Health Resources and Service Administration [3].

A three-dimensional cell culture called a spheroid serves as a foundational entity in a wide variety of modern tissue engineering applications, including 3D-bioprinting and preclinical drug testing [4, 5]. Lack of oxygen in the deep parts of tissue spheroids hinders the metabolism of cells which eventually leads to cell death. Prevention of necrosis within the tissue spheroids is crucial to the success of tissue engineering methods [5]. To prevent premature cell death, estimation of cell viability in the spheroid is needed. A novel approach for predictive modeling of diffusion in tissue spheroids during their fusion is proposed. The objectives of this thesis that are related to this approach formulation, are revealed below. The approach is based on numerical solutions for differential equations of diffusion and applying Functional Representations (FRep) framework for geometric modeling [6, 7]. A joint modeling of spheroids fusion and diffusion of oxygen, a method for selecting optimal spheroid size and several statistics for estimation of cellular viability are presented. The results are tested experimentally with cell viability assay. Obtained findings provide insights into oxygen diffusion in three-dimensional cell cultures thus improving the robustness of biotechnological methods that employ tissue spheroids.

Most currently implemented remedies [8] for organ shortage include merely a change of policies: switch from opt-in to opt-out system for donation, monetary supports for a family of deceased or living donor, educational programs to raise awareness and so

on. While undeniably important, these options do not provide an actionable solution of an underlying problem, lack of organs, and act rather as a form of support for the healthcare system.

From technological point of view, there exists several possible angles of attack for organ shortage, such as various organ preservation techniques [9, 10], fast transportation systems [11], organ-donor matching algorithms [12, 13] and artificial organs [14]. Note that while these technologies are well-conceptualized, most are still in the research stage and have years and years ahead before any kind of adoption. The current thesis is dedicated to a refinement for one of such technologies, 3D bioprinting.

While still in the developmental stage, 3D bioprinting holds promise for addressing the organ shortage by providing a means to fabricate organs on demand [15, 16]. Bioengineered organs [17], created by combining cells and scaffolds, have the potential to replace damaged or non-functional organs entirely.

Bioprinting is a research area that needs accurate and complex mathematical modeling, often transmitting biological and medical data. These models should meet some special requirements, and their creation demands high-specialized software. Several widespread nowadays software tools, focusing on using bioprinting technologies, are reviewed and analyzed in Chapter 1 of this thesis. Properties, advantages, and disadvantages of these software tools are considered applicable to issues of digital bioprinting, especially of the bioprinting of heterogeneous tissues and organs. A shortage of specialized suitable software tools is revealed with the classification as control tools, available CAD tools, tools to convert medical data to CAD formats, and a few highly specialized research project tools.

Bioprinting based on usage of multicellular tissue spheroids as a component of bioink is a method for biofabrication of artificial tissues and bioconstructs that shows significant promise [18]. Tissue spheroids bioprinting is the most perspective for 3D tissues producing considering bioprinting with cells and bioprinting with biomolecules but difficult technology because of the necrosis risk in the depth of 3D cellular structure.

Spheroids are three-dimensional aggregates of cells that closely mimic the cellular organization and microenvironment of natural tissues. By utilizing spheroids as the starting material, 3D bioprinting can create more complex and functional tissue structures compared to using a one-dimensional cellular culture comprised of individual cells within a hydrogel matrix [19].

Typical pipeline of bioprinting with spheroids consists of four stages. During the first stage, the spheroids are produced in a laboratory setting using methods like "hanging drop" [20], forced aggregation [21] or microfluidics [22]. Then comes the stage of bioink preparation [23]. Bioink consists of cells in form of spheroids and a hydrogel that provides a structural function. Hydrogel allows for the spheroids to be precisely put at correct coordinates during the third stage, deposition of biological material, which involves the layered addition of spheroids and non-linked hydrogel followed by the initiation of gel crosslinking [24]. After bioprinting, the bioconstruct undergoes the fourth stage, maturation [25, 26]. Under the osmotic pressure, the spheroids start to fuse together and the cells placed in an incubator start to divide. Spheroids form functional tissue by merging with each other. The FRep approach represents a suitable method to solve the heterogeneous volume modeling for the digital bioprinting issue to reach progress in modeling methods. Hence, the possible solution to the crucial problems in bioprinting is to adapt the FRep approach to the bioprinting problems and develop a new application area such as computer science for bioprinting. Continuing the research in [4, 5], in Chapter 2, the research is focused on modeling the base of the robotic biofabrication process, the natural phenomenon of tissue spheroids fusion. During the lifecycle of a non-vascularized spheroid, there is little to no new oxygen present right before the last stage of the aforementioned pipeline. Lack of oxygen leads to the emergence of hypoxic region, followed by necrosis and then the degradation of a bioprinted construct [27, 28, 29]. Modeling the oxygen distribution can provide insights into the dynamics of the system and help estimate the time that is left for printing and maturation. With modeling, one could select the optimal size of a spheroid which would maximize the time of normal operation of bioprinted construct.

Most research of oxygen diffusion in spheroids was done on tumor tissues [30]. Tumor spheroids have many useful applications themselves, serving as an in vitro model for chemotherapy selection [31 - 34] and drug design [35 - 37], but this research is focused on their fusion and necrotic region formation in context of application for bioprinting.

Distribution of oxygen in multicellular spheroids is described by reaction-diffusion equations that model the diffusion of oxygen over the volume of the spheroid, inflow and outflow of oxygen through the boundaries and consumption of oxygen by the cells. There are analytical solutions for oxygen partial pressure for spherical, oblate and prolate shape [38] of spheroids but these solutions consider the boundary rather smooth, while in reality it consists of deformed cells that experience different amounts of pressure from their surroundings, which was never considered until the current work of ours, which constitutes the contents of Chapters 2 and 3.

To model such variable geometry, Functional Representations (FReps) is used [39] - a method for modeling geometry with noise. To describe the random deformations in solid geometry the Gardner Noise parametric implicit function was used [40]. This road leaves construction of analytical solution for the reaction-diffusion equations hard, maybe even impossible to obtain, so a numerical solution was opted, which is obtained using with Finite Volume Method [41, 42]. The application of FReps allows to model not only a single spheroid, but the fusion of two spheroids geometrically, so one could construct a mesh for a numerical method on any stage of spheroid fusion. The main contributions can be summarized as follows:

1. A new approach for modeling of oxygen diffusion in multicellular tissue spheroids is proposed;

2. A combination of geometrical modeling with Functional Representations and Finite Volume Method to solve reaction-diffusion equations which allows for introduction of aberrations from spherical shape and smooth surface into account is suggested;

3. For the first time, the combination of FReps and FVM to model the distribution of oxygen during the fusion of two spheroids is used;

4. A comprehensive computational study for influence of surface deformities on the oxygen diffusion and formulate several statistics for evaluation of cell viability is performed;

5. Using the method, the optimal (regarding the speed of necrotic region formation) size for a non-vascularized bovine chondrocyte spheroid is computed and results validate the modeling experimentally using Live/Dead viability assay [43].

The goal was to numerically describe the distribution of oxygen partial pressure in spheroids, considering their biorealistic shape and their oxygen consumption in the context of viability.

At the World Economic Forum in 2016, a report entitled "8 predictions for the world in 2030" was announced [44]. According to Melanie Walker, a physician and advisor to the World Bank, the technology will further destroy disease. The hospital is likely to become a thing of the past, due to fewer accidents caused by self-driving cars and major advances in preventative and personalized medicine. Scalpels and organ donors will be completely gone, and there will be tiny robotic tubes and bioprinted organs instead. This vision proves the relevance and sociological significance of 3D bioprinting research in general, and of this research work in particular. Thus, the motivation was to raise spheroids 3D bioprinting effectiveness. The relevance of this research work to practical application will be considered in details further. It resides the 3D bioprinting technology efficiency enhancement, which is critical for organ transplantation and tissue regeneration development.

The scientific novelty consists in the methodological tool development for the preprocessing stage of 3D bioprinting with tissue spheroids to enhance this technology effectiveness. It consists in the union of the geometric modelling of biological benign tissue spheroid shape and surface irregularities with FRep in benign tissue spheroids fusion with the numerical modelling of oxygen consumption, transport and distribution through a single benign tissue spheroid and tissue spheroids in fusion of different size and surface curvature, in order to numerically describe the oxygen partial pressure distribution in spheroids with consideration of the surface curvature and size of the spheroid in the

context of viability. While no one studied the viability of non-tumor spheroids, but exactly non-tumor spheroids are used for tissues and organs printing development, this research work has scientific novelty and practical value. The scientific value of this dissertation is the implementation of the new approach for tissue spheroids fusion modeling.

The relevance of this research work to practical application resides the 3D bioprinting technology efficiency enhancement focusing on the implementation of the new approach for tissue spheroids fusion modeling, which is critical for organ transplantation and tissue regeneration development. It will help to ensure cells survival in tissue spheroids bioprinting before practical experiment. A specialized solution for quality control of spheroids including cells survival, for their further use in bioprinting, is offered. Understanding the factors influencing cells survival and developing innovative strategies to improve it is a priority for 3D bioprinting research. Besides, the study results were commercialized and became a basis for the startup project "Spheroid Revolution" supported by the Skolkovo Foundation. The startup project focuses on the software and hardware development for 3D bioprinting. To implement the startup project, the company of the same name, LLC "Spheroid Revolution" (Skolkovo resident since 2021, ORN 1124277), headed by the author of the study, was established. In 2023, the startup project was granted funding from Skoltech Translational Research Innovation Program (STRIP), the funding was extended to 2024. The developed mathematical application became the basis for the created software product "Spheroid Revolution", protected by the certificate of software state registration for a program No. 2022664376, registered on July 28, 2022.

The general aim of this dissertation was to adapt Function Representation approach (FRep) to 3D bioprinting with tissue spheroids, to identify the field of its application and to explore how to improve the 3D bioprinting digital model development with parametric implicit functions.

The tasks of this dissertation are subdivided as: •To apply the theory of parametric implicit functions modeling to 3D bioprinting of tissue spheroids;

•To describe the geometrical surface structure of tissue spheroid as a biological object with FRep;

•To develop of geometry similar to natural tissue spheroids models;

•To elucidate a tissue spheroids viability criterion and its implementation using FRep approach and numerical calculations;

•To develop a numerical model for oxygen diffusion on FRep models of tissue spheroids, including tissue spheroids in fusion;

•To validate of the numerical approach with practical laboratory experiments;

•To explore the new method for tissue spheroids 3D bioprinting digital modeling.

The object of research is 3D bioprinting with tissue spheroids, benign tissue spheroids, nutrient diffusion throughout the depth of the tissue spheroid, allowing the application of the methods proposed in this thesis for the purpose of modelling the viability of tissue spheroids.

The methodological basis of this work includes Functional Representation parametric implicit functions for geometry modeling, slicing and mesh generation for geometry adaptation, C++ and Java Script as programming languages. For numerical calculations, Finite Volume.

Regarding the validity and reliability of the results and conclusions, the model was validated with practical biological experiment in 3D Bioprinting Solutions Laboratory. Spheroids were grown, stained and analyzed considering its viability according to its diameter. The research work was presented and approbated at several conferences.

Regarding the personal contribution, all the results of the dissertation were obtained personally by the applicant or with her direct involvement. In particular, the applicant performed the search and analysis of the literature related to the research topic. The applicant together with scientific co-supervisor (passed away in 2022) Dr. Alexander A. Pasko, scientific ex-supervisor Dr. Iskander Sh. Akhatov (left Skoltech in 2022), and the scientific supervisor, Dr. Dmitry S. Kolomenskiy, participated in the formulation of aims and objectives of the dissertation and developed experimental methods.

The thesis statements to be defended can be summarized and associated with the research directions of the specialty 1.1.9. "Mechanics of liquids, gases and plasmas" as follows:

1. Based on the equations of continuum mechanics of fluid media, a new approach is proposed for numerical modeling of oxygen transport in multicellular tissue spheroids (directions 16 and 19);

2. A combination of geometrical modeling with Functional Representations and Finite Volume Method to solve reaction-diffusion equations which allows for introduction of aberrations from spherical shape and smooth surface into account is suggested (direction 19);

3. For the first time, the combination of FRep and FVM to model the distribution of oxygen during the fusion of two spheroids is used, whereas the shape of the connecting bridge is obtained considering the action of surface tension (directions 16, 19 and 25);

4. The effect of surface deformities on the oxygen transport and cell viability is quantified by means of a comprehensive computational study and statistical analyses (directions 9, 16 and 19);

5. Using the method, the optimal (regarding the speed of necrotic region formation) size for a non-vascularized bovine chondrocyte spheroid is computed and results validate the modeling experimentally using Live/Dead viability assay (directions 9 and 18);

Whereas the directions are defined as follows, in the order as they appear in the above: Direction 16: Heat and mass transfer in gaseous and liquid media; Direction 19: Exact, asymptotic, approximate analytical, numerical and combined methods for continuum and kinetic models of homogeneous and multiphase media; Direction 25: Effect of surface forces on the dynamics of liquids and gases; Direction 9: Physicochemical hydrodynamics (flows with chemical reactions, combustion, detonation, phase transition, radiation etc.)

Direction 18: Experimental methods to study dynamical processes in liquids and gases.

The structure and volume of the dissertation

The dissertation consists of an abstract, introduction, four chapters, conclusions, list of symbols and abbreviations, list of 175 references. The full volume of the dissertation is 142 pages, including 25 figures and 5 tables.

Заключение диссертации по теме «Другие cпециальности», Вилински-Мазур Кэтрин Александровна

CONCLUSIONS

The work focuses on tissue spheroid fusion and viability modeling in context of 3D bioprinting. The methodology of biological tissue spheroid fusion simulation was developed and implemented. For mathematical modeling of natural-like tissue spheroid geometry, Function Representation approach is used. Numerical simulation of oxygen distribution through benign tissue spheroids in fusion and its connection to tissue spheroid viability is produced. The modeling is validated by experiments in vitro with bovine chondrocyte tissue spheroid generation using Corning non-adhesive microplates. To assess viability, tissue spheroids were labeled with CellTox Green and Live/Dead assay.

The main conclusions of the work are the following:

1. There exist a variety of software tools and approaches used now for 3D bioprinting. Function Representation method is found to be well appropriate because, with the help of parametric implicit functions, it allows to model complex geometry that is critical for natural-like surfaces with curvature and deformation.

2. The objective of geometric modeling was to model single tissue spheroid and tissue spheroids in fusion with precise natural- like geometry using FRep approach. Tissue spheroid fusion geometrical modeling with FRep implicit functions using parametric Union Blending (UN) and Bounding Blending (BB) functions was performed. The optimal dimensionless parameters for GN with the scaling factor equal to 100 mm per 1 dimensionless unit are the following:

• For small deformities, the scaled amplitude is equal to 0.13, the scaled frequency is 16.1, the scaled phase is 5.8;

• For medium deformities, the scaled amplitude is 0.19, the scaled frequency is 19.1, the scaled phase is 6.8;

• For large deformities, the scaled amplitude is 0.17, the scaled frequency is 22.1, the scaled phase is 5.8.

Optimal dimensionless parameters with the same scaling factor for UN and BN functions are: a0 = 0.043, a1 = 0.07, a2 = 0.1, a3 = 0.9 was found. Thus, the union of GN, UB and BB FRep implicit functions with the mentioned above parameters enables precise modeling of natural-like tissue spheroid geometry in fusion.

3. The oxygen partial pressure level was analyzed as the main viability criteria. Numerical modeling of oxygen diffusion and consumption using an implicit-explicit finite volume method and Dirichlet boundary conditions on the geometrical domains modeled with FRep functions has been performed. Geometrical domains were single tissue spheroids of various diameters and two equal-sized tissue spheroids in fusion of various diameters and various surface curvatures. Initial partial pressure of oxygen in DMEM was taken equal to 140 mmHg.

The main conclusions from the numerical simulations are the following:

• The maximum diameter without any necrotic processes equals to 288 ¡dm for single spheroids and 200 ¡im for two equal-sized tissue spheroids in fusion.

• The size threshold equal to 288 ¡im for a single spheroid and 200 ¡im for two equal-sized tissue spheroids in fusion corresponds to the oxygen partial pressure inflection point equal to 104.5 mmHg. The inflection point was obtained from the dependency of minimal oxygen partial pressure from the spheroid diameter using isotonic regression and classical formula for inflection points.

• The optimum mesh convergence was obtained on meshes of 300000 polygons.

• While tissue spheroid size impacts the oxygen partial pressure, the natural- like surface curvature has marginal impact. Of the three Gardner Noise parameters discussed in this work, only the amplitude has an impact on two equal- sized tissue spheroids in fusion. Note that

when the amplitude is too large (>0.2 dimensionless amplitude parameter) the geometry is no longer natural-like.

4. An experiment with tissue spheroids in vitro with the same conditions as in the model was conducted. Tissue spheroids of bovine chondrocytes were grown on non-adhesive Corning microplates, seeded in DMEM and then labeled with Live/Dead and CellTox Green assay to assess viability. Spheroids were analyzed on the third day after seeding measuring the intensity of fluorescence that directly correlates with the number of dead cells. Imaging was performed using a Nikon A1R laser scanning confocal microscope. The threshold for maximum tissue spheroid diameter without necrotic areas in its depth was measured equal to 285 jum. This is close to the value of288 jum found from numerical simulation. Thus, the model is validated with biological experiments in vitro.

Список литературы диссертационного исследования кандидат наук Вилински-Мазур Кэтрин Александровна, 2024 год

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PUBLISHED PAPERS Journal articles:

1. Q2: Pakhomova, Catherine, Alexander Pasko, and Iskander Akhatov. "Modeling and Simulation of Tissue Spheroids Fusion Based on the Function Representation Approach. Materials Science Forum, Trans Tech Publications Ltd, 2021. Vol. 1046, P. 119-123. https://doi.org/10.4028/www.scientific.net/MSR1046.119 [1]

2. Q1: Pakhomova, Catherine, Dmitry Popov, Eugenii Maltsev, Iskander Akhatov, and Alexander Pasko. "Software for bioprinting." International Journal of Bioprinting 6, Vol. 3, P. 114-125. https://doi.org/10.18063/ijb.v6i3.279. PMID: 33088988; PMCID: PMC7557344. [2]

Conference presentations:

1. Pakhomova. C. FRep for tissue spheroids fusion, International scientific conference «Falling Walls Moscow Lab», Moscow, October 1, 2020.

2. Pakhomova. E.A. Adaptation of the functional presentation method (FRep) for 3D bioprinting: modeling the fusion of tissue spheroids considering accuracy (fidelity) as a criterion for the quality of the bioprinting process. International scientific conference of students, graduate students and young scientists "Lomonosov-2020" Moscow, November 10-27, 2020.

3. Pakhomova. E.A. Modeling the fusion of tissue spheroids for 3D bioprinting using the functional representation method. XXVII International Conference "Mathematics. Computer. Education." Dubna, January 27 - February 1, 2020.

4. Pakhomova. C., Pasko A. Modeling and simulation of tissue spheroids fusion using function representation (FREP) approach. The 5-th

International Symposium and International School for Young Scientists on "Physics, Engineering and Technologies for BioMedicine" Moscow, November 21-25, 2020.

5. Pakhomova, E.A. Modeling heterogeneous structures in 3D- and bioprinting: protocols and software, International Scientific Conference of Students, Graduate Students and Young Scientists "Lomonosov-2021" Moscow, April 12-23, 2021.

6. Pakhomova, E.A. Modeling and simulation of the fusion of tissue spheroids using the functional presentation All-Russian scientific conference with international participation "Regenerative Biology and medicine" Moscow, April 15-16, 2021.

7. Catherine, A. Pakhomova, Alexander A. Pasko, Iskander Sh. Akhatov; Function Representation (FRep) for basic processes modeling in 3D bioprinting. BTLA-2021.

8. Katheirne, Vilinski-Mazur. Spheroid Revolution, 3D bioprinting and women in science. SPIEF-2022.

9. Vilinski-Mazur K., Kirillov B., Annikov M. Spheroid Revolution project presentation. Startup Village - 2022, three pitch sessions.

10.Kirillov, B., Vilinski-Mazur K., Pasko A., Akhatov, I. Finite element modeling of physical processes in multilayer spheroids based on Functional Representations. BGRS-2022.

11. Vilinski-Mazur, K. Presentation about SW and HW for bioprinting (Spheroid Revolution project) at the Projects Fair, IW-2022, Skoltech.

12.K.A.Vilinski-Mazur, B.A.Kirillov, O.A.Rogozin, D.S.Kolomenskiy; Modelling of oxygen diffusion during tissue spheroids fusion; XIII All- Russian Congress On Theoretical And Applied Mechanics, 2023.

13.K.A.Vilinski-Mazur, B.A.Kirillov, O.A.Rogozin, D.S.Kolomenskiy; Geometrical shape, coalescence, and oxygen distribution modeling in

benign tissue spheroids; The 4th International Workshop of Advanced Manufacturing Technologies, 2024.

IP and patents:

1. Patent for invention, number 2797494 Method of three-dimensional modelling of personalized maxillofacial implants for chin shape modelling, registered June 06, 2023. Authors: Maltsev E., Popov D., Pasko A., Akhatov I., Pakhomova E., Guryanov R., Kamal W., Guryanov A.

2. The certificate of software state registration, number 2022664376, Spheroid Revolution, registered July 28, 2022. Authors: Vilinski- Mazur K., Kirillov B., Pasko A., Popov D., Maltsev E.

Startups based on PhD research:

1. Spheroid Revolution LLC, Skolkovo Resident since 2021, ORN 1124277. The startup, founded by applicant and colleagues, is about software and hardware development for 3D bioprinting. At 2023, the STRIP financing granted for the startup.