The study is devoted to considering the effectiveness of modern approaches to the development of diagnostic technology for analyzing MRI images in neuro-oncology, based on artificial intelligence (AI) and computer vision. Such approaches are necessary for rapid and diagnostically effective analysis to implement the principle of individualized medicine. Material and methods. An analysis of the effectiveness of the choice of AI technologies for the formation of processes of segmentation and classification of neuro-oncological MRI images has been presented. AI was trained on its own annotated database (SBT Dataset), containing about 1000 clinical cases based on archival data from preoperative MRI studies at the Federal Neurosurgical Center (Novosibirsk, Russian Federation), in patients with astrocytoma, glioblastoma, meningioma, neuroma, and with metastases of somatic tumors, with histological and histochemical postoperative confirmation. Results and discussion. The effectiveness and efficiency of the developed technologies was tested during the international BraTS competition, in which it was proposed to segment and classify cases from a dataset of neuro-oncological patients prepared by the competition organizers. Conclusions. The methodological approaches proposed in the article in the development of diagnostic systems based on AI and the principles of computer vision have shown high efficiency at the level of dozens of world leaders and can be used to develop software and hardware systems for diagnostic neuroradiology with the functions of a “doctor’s assistant.”

A new cubic version of the least-squares collocation method based on adaptive grids is developed. Approximate values of the solution and its first derivatives at the vertices of quadrangular cells are the unknowns. This approach has made it possible to eliminate the matching conditions from the global overdetermined system of linear algebraic equations consisting of collocation equations and boundary conditions. The preconditioned system is solved using the SuiteSparse library by the orthogonal method with the CUDA parallel programming technology. We consider the Reissner–Mindlin plate problem in a mixed formulation. A higher accuracy of deflections and rotations of the transverse normal in comparison with the isogeometric collocation method as well as the uniform convergence of shear forces in the case of a thin plate are shown in the proposed method. Bending of an annular plate and round plates with an off-center hole is analyzed. An increase in the shear force gradient in the vicinity of the hole is shown both with a decrease in the plate thickness and with an increase in the eccentricity. The second order of convergence of the developed method is shown numerically. The results obtained using the Reissner–Mindlin theory are compared with the ones in the Kirchhoff–Love theory and three-dimensional finite element simulation.

The study is devoted to the application of the asymptotic splitting method for solving static problems of deformation of homogeneous isotropic and composite cylindrical shells. The problem of deformation of a composite cylindrical shell subjected to an internal axisymmetric load is considered. The solution is constructed by expanding the components of the stress tensor and the displacement vector in powers of differential operators acting along the cylinder axis. A small parameter is the ratio of the shell thickness to its length. A governing differential system of equations describing the deformation of a cylindrical shell is obtained. It is shown that the developed mathematical model allows to compute all components of the stress tensor for both thick-walled and thin -walled cylindrical shells. The obtained analytic and numerical solutions are compared with the finite element solution of the 2D axisymmetric problem.

A problem of restrained torsion of thin-walled beams under the action of an end torque is considered. The asymptotic splitting method is applied to obtain a system of resolving equations that describes combined torsion, tension-compression, and bending of the beam. The example of typical cross sections is used to compare the resulting model with a stress-strain state in the beam, determined in the calculation using the developed model and three-dimensional numerical calculation by the finite element method. The resulting mathematical model is analyzed and its advantages are revealed and compared to the widely used Vlasov theory. It is shown that the developed model does not contain the restrictions imposed by the Vlasov theory hypotheses, such as the nondeformability of the cross-sectional contour and the absence of shear strains on the middle surface. The resulting model makes it possible in many cases to more accurately determine the emerging stress-strain state. In particular, it is shown that the developed model accounts for the presence of a boundary layer near the clamped end, which arises during torsion of angle sections and makes a significant contribution to longitudinal stresses, while the Vlasov theory does not allow for the recovery of the arising longitudinal stresses.

The study of brain tumor structure and its type-dependent variations is one of the most important research areas in which medical imaging techniques are used. The structural and statistical analysis of these lesions raises various related problems and projects, such as the detection of the neuro oncology diseases, the shape and the segmentation of specific sub-regions (i.e. necrotic part, (non-)enhanced part, edema), the classification of the tumor occurrence and the subsequent treatment up-prognosis. Almost all of these problems are usually solved numerically, particularly with the tendency to use methods related to artificial intelligence (AI), often including deep learning (DL) networks. One of the most complicated, least researched and challenging tasks in this field is the classification of tumor types. This difficulty can be explained by several reasons, the most important of which is the severe limitation of existing open-source datasets that contain clinically confirmed tumor type designations based on radiological examination protocols. Magnetic resonance imaging (MRI) is the most common method for screening, primary detection and non-invasive diagnosis of brain diseases, as well as a source of recommendations for further treatment and observation. In this paper, we extend the previous research works on the robust multi-sequences segmentation and classification methods which allows to consider all available information from MRI scans by the composition of TI, TIC, T2 and T2-FLAIR sequences. It is based on the clinical radiology hypothesis and presents an efficient approach to combining and matching 3D methods to search for areas of comprised the GD-enhancing tumor in order to significantly improve the model's performance of the particular applied numerical problem of brain tumor classification and metastasis segmentation. All investigations performed and results presented are based on the private Siberian brain tumor dataset, including labeled volumetric MRI scans describing a wide variety of tumors and associated clinically relevant ground truth (GT) information.

BACKGROUND: The main reason for the development and implementation of artificial intelligence (AI) technologies in neuro-oncology is the high prevalence of brain tumors reaching up to 200 cases per 100,000 population. The incidence of a primary focus in the brain is 5%10%; however, 60%70% of those who die from malignant neoplasms have metastases in the brain. Magnetic resonance imaging (MRI) is the most common method for primary non-invasive diagnosis of brain tumors and monitoring disease progression. One of the challenges is the classification of tumor types and determination of clinical parameters (size and volume) for the conduct, diagnosis, and treatment procedures, including surgery. AIM: To develope a software module for the differential diagnosis of brain neoplasms on MRI images. METHODS: The software module is based on the developed Siberian Brain Tumor Dataset (SBT), which contains information on over 1000 neurosurgical patients with fully verified (histologically and immunohistochemically) postoperative diagnoses. The data for research and development was presented by the Federal Neurosurgical Center (Novosibirsk). The module uses two- and three-dimensional computer vision models with pre-processed MRI sequence data included in the following packages: pre-contrast T1-weighted image (WI), post-contrast T1-WI, T2-WI, and T2-WI with fluid-attenuated inversion-recovery technique. The models allow to detect and recognize with high accuracy 4 types of neoplasms, such as meningioma, neurinoma, glioblastoma, and astrocytoma, and segment and distinguish components and sizes: ET (tumor core absorbing Gd-containing contrast), TC (tumor core) = ET + Necr (necrosis) + NenTu, and WT (whole tumor) = TC + Ed (peritumoral edema). RESULTS: The developed software module shows high segmentation results on SBT by Dice metric for ET 0.846, TC 0.867, WT 0.9174, Sens 0.881, and Spec 1.000 areas. The testing and validation were done at the international BraTS Challenge 2021 competition. The test dataset yielded DiceET 0.86588, DiceTC 0.86932, and DiceWT 0.921 values, placing the developed software module in the top ten. According to the classification, the results demonstrate high accuracy rates of up to 92% in patient analysis (up to 89% in slice analysis), a very high potential, and a perspective for future research in this area. CONCLUSIONS: The developed software module may be used for training specialists and in clinical diagnostics.

Brain tumor segmentation is an important and time-consuming part of the usual clinical diagnosis process. Multi-class segmentation of different tumor types is a challenging task, due to the differences in shape, size, location and scanner parameters. Many 2D and 3D convolution neural network architectures have been proposed to address this problem achieving a significant success. It is well known that 2D approach is generally faster and more popular in the most of such problems. However, the usage of 3D models allows us to simultaneously improve the quality of segmentation. Accounting the context along the sagittal plane leads to the learning of 3-dimensional features that we used for computationally expensive 3D operations what in its turn increases the learning time as well as decreases the speed of operation.In this paper, we compare the 2D and 3D approaches on 2 datasets with MRI images: the one from the BraTS 2020 competition and a private Siberian Brain tumor dataset. In each dataset, any single scan is represented by 4 sequences T1, T1C, T2 and T2-Flair, annotated by two certified neuro-radiologist specialists. The datasets differ from each other in the dimension, grade set and tumor type. Numerical comparison was performed based on the Dice score index. We provide the case by case analysis for the samples that caused most difficulties for the models. The results obtained in our work demonstrate the significant over performing of 3D methods keeping robustness in a regard of data source and type that allow us to get a little closer to AI-assisted diagnosis.

This work is aimed at the numerical analysis of the stationary non-isothermal flows of an incompressible viscoelastic polymer fluid in the channels with elliptical cross-sections. The description of such flows is done on the basis of the mesoscopic approach, and the resolving equations are derived. For solving them three algorithms, which use different techniques of constructing the approximate solutions, are designed: the least-squares collocation method based on the piecewise polynomial approximations, which lead to the overdetermined systems of linear algebraic equations; the finite element method, which uses weak formulations; and the non-local method without saturation, which operates with the global approximations in the elliptical coordinate system and with the matrix Sylvester equations. The proposed algorithms are verified by solving the test problem with the known analytical solution. Further we use them for the numerical analysis of the polymer fluid flows with its parameters varying in wide ranges. Comparison of the results obtained by the different algorithms shows their high performance and confirms that the solution of the considered non-linear problem exists and that it was computed accurately. The singularities of the obtained stationary solutions are analyzed. Taking them into account within the proposed algorithms enables us to increase the accuracy and the speed of simulations.

The research was aimed at analyzing current approaches to the organization and design methodology of visualization database built on the basis of computer vision . Such approaches are necessary for effective development of diagnostic systems using artificial intelligence (AI). A training data set of high quality is a mandatory prerequisite for that . Material and methods . The paper presents the technology for designing an annotated database (SBT Dataset ) that contains about 1000 clinical cases based on the archived data acquired by the Federal Neurosurgical Center, Novosibirsk , Russia including data on patients with astrocytoma , glioblastoma , meningioma , neurinoma , and patients with metastases of somatic tumors . Each case is represented by a preoperative MRI. The Results and discussion . The dataset was built (SBT Dataset ) containing segmented 3D MRI images of 5 types of brain tumors with 991 verified observations . Each case is represented by four MRI sequences T1-WI, T1C ( with Gd-contrast ), T2-WI and T2-FLAIR with histological and histochemical postoperative confirmation . Tumors segmentation with verification of the tumor core elements boundaries and perifocal edema was approved by two certified experienced neuroradiologists . Conclusion . The database built during the research is comparable in its volume and quality ( verification level ) with the state-of-the-art databases . The methodological approaches proposed in this paper were focused on designing the high-quality medical computer vision systems . The database was used to create artificial intelligence systems with the “ physician assistant ” functions for preoperative MRI diagnostics in neurosurgery.

New h-, p-, and hp-versions of the least-squares collocation method are proposed and implemented. They yield approximate solutions of boundary value problems for an inhomogeneous biharmonic equation in irregular and multiply-connected domains. Formulas for the extension operation in the transition from coarse to finer grids on a multigrid complex are given in the case of applying various spaces of polynomials. It is experimentally shown that numerical solutions of boundary value problems produced by the developed versions of the method have a higher order of convergence to analytical solutions with no singularities. The results are compared with those of other authors produced by applying finite difference, finite element, and other methods based on Chebyshev polynomials. Examples of problems with singularities are considered. The developed versions of the method are used to simulate the bending of an elastic isotropic plate of irregular shape subjected to transverse loading.

In this paper, we extend the previous research works on the robust multi-sequences segmentation methods which allows to consider all available information from MRI scans by the composition of T1, T1C, T2 and T2-FLAIR sequences. It is based on the clinical radiology hypothesis and presents an efficient approach to combining and matching 3D methods to search for areas of comprised the GD-enhancing tumor in order to significantly improve the model's performance of the particular applied numerical problem of brain tumor segmentation. Proposed in this paper method also demonstrates strong improvement on the segmentation problem. This conclusion was done with respect to Dice and Hausdorff metric, Sensitivity and Specificity compare to identical training/test procedure based only on any single sequence and regardless of the chosen neural network architecture. We achieved on the test set of 0.866, 0.921 and 0.869 for ET, WT, and TC Dice scores. Obtained results demonstrate significant performance improvement while combining several 3D approaches for considered tasks of brain tumor segmentation. In this work we provide the comparison of various 3D and 2D approaches, pre-processing to self-supervised clean data, post-processing optimization methods and the different backbone architectures.

Investigation of brain tumor structure and its type-dependent variations are among the list of most important research directions where the medical imaging methods are used. Structural and statistical analysis of these lesions originates various associated problems and projects such as detection of the tumors, shape and specific sub-regions segmentation (i.e. necrotic part, (non-)enhanced part, edema), classification of the tumor presence and treatment follow up prognosis. Almost all of these problems are usually solved numerically, specifically with the tendency to use the Artificial Intelligence (AI) related methods often including Deep Learning (DL) networks. One of the most complicated, weakly explored and challenging tasks in this domain is the classification of the tumor types. This difficulty is explained by several reason where the most principle one is the strong limitation of the existing open-sourced datasets that include clinically confirmed tumor type labels based on the radiological examination protocols. In this work we present current results of the brain tumor classification problem, where we consider and operate with four different lesion types such as meningioma, neurinoma, glioblastoma and astrocytoma. All the conducted research and presented results are obtained on the newly introduced dataset including 255 labeled volume MRI scans describing wide variety of the tumors and its clinically associated ground truth (GT) information. Obtained in this work results demonstrate not only inspiring and strong Accuracy performance of 0.925 on patient level (and accordingly 0.894 slice-wise) but also very high potential and perspective for the future research in this field.

This paper describes new versions of the least-squares collocation method for solving differential and integral equations. A p-version of the method has been proposed and implemented to solve nonlinear systems of partial differential equations. The stationary Navier-Stokes equations are used as an example. A hp-version of the method has been implemented for the numerical solution of the Fredholm integral equations of the second kind in the one-and two-dimensional cases. This paper shows that approximate solutions obtained by various versions of the least-squares collocation method converge with a high order and agree with analytical solutions of test problems with a high degree of accuracy.

Neuro-oncological MRI imaging is a complex, expensive procedure that is responsible for all further treatment tactics. The following issues must be unambiguously resolved: (1) to detect a volumetric process in the brain (e.g., tumor); (2) to outline the exact boundaries of the tumor (to delimit the edematous zone and healthy brain tissue); (3) to determine the level of tumor malignancy as accurately as possible. Artificial intelligence technologies make it possible to speed up the process of MRI diagnostics via 3D visualization and increase its accuracy and specificity. This paper presents pipeline and approaches to the creation of a dataset, which can serve as a basis for solving the problems mentioned above. The description of the dataset which is formed in our research project is presented. The methods and algorithms that were used to solve the problem of multiclass segmentation of the tumor are also described.

A new mathematical model for the four-point bending of reinforced concrete beams is developed and investigated. The model takes into account multi-modulus concrete behavior, nonlinear stress-strain relationships, and damage evolution. An algorithm for a numerical implementation of the model is proposed. The corresponding boundary value problem is solved by the hp-version of the least-squares collocation method in combination with an acceleration of an iterative process based on Krylov subspaces and parallelizing. Special attention is given to the influence of mathematical model parameters on the results of numerical simulation. The results are compared with experimental data and three-dimensional simulation. A satisfactory agreement is shown

The paper is devoted to the application of the least-squares collocation method for solving the two- and one-dimensional problems in the mechanics of deformable solids. Calculation results of the deflections of isotropic and orthotropic elastic plates within the framework of various theories are presented. This paper shows that approximate solutions obtained by the hp-version of the least-squares collocation method converge with a high order and agree with analytical solutions of test problems with a high degree of accuracy. Numerical and mathematical modeling of three-point bending of composite beams was carried out taking into account nonlinear stress-strain relationships, multi-modulus behavior, and incipient fracture. It was found that the simulation results are in good agreement with the results of mechanical tests of three-point bending of composite beams.

The brain tumor segmentation is one of the crucial tasks nowadays among other directions and domains where daily clinical workflow requires to put a lot of efforts while studying computer tomography (CT) or structural magnetic resonance imaging (MRI) scans of patients with various pathologies. MRI is the most common method of primary detection, non-invasive diagnostics and a source of recommendations for further treatment of brain diseases. The brain is a complex structure, different areas of which have different functional significance. In this paper, we extend the previous research work on the robust pre-processing methods which allow to consider all available information from MRI scans by the composition of T1, T1C, T2 and T2-Flair sequences in the unique input. Such approach enriches the input data for the segmentation process and helps to improve the accuracy of the segmentation and associated uncertainty evaluation performance. Proposed in this paper method also demonstrates strong improvement on the segmentation problem. This conclusion was done with respect to Dice metric, Sensitivity and Specificity compare to identical training/validation procedure based only on any single sequence and regardless of the chosen neural network architecture. Obtained results demonstrate significant performance improvement while combining three MRI sequences in the 3-channel RGB like image for considered tasks of brain tumor segmentation. In this work we provide the comparison of various gradient descent optimization methods and of the different backbone architectures.

A number of statements of inverse problems of rational and optimal design of composite structures are considered. The problem of maintenance of a momentless state of a composite shell with respect to parameters’ choice of reinforcement is solved. The problem of optimum design of composite pressure vessels is investigated.