Mathematical Modeling and Numerical Optimization of Composite Structures

This chapter is devoted to modeling the properties of composite materials and structures. Mathematical relations describing the nonlinear elastic three-point bending of isotropic and reinforced beams with account of different strength and stiffness behavior in tension and compression are obtained. An algorithm for numerical solution of corresponding boundary-value problems is proposed and implemented. Results of numerical modeling were compared to acquired data for polymer matrix and structural carbon fiber reinforced plastics. A computational technology for analysis and optimization of composite pressure vessels was developed and presented

Specific features of designing a database for neuro-oncological 3D MRI images to be used in training artificial intelligence

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

Analytic solutions for free vibration analysis of laminated beams in three-dimensional statement

In this research we consider free vibrations of laminated beams in terms of three-dimensional linear theory of elasticity. Analytic solutions for natural frequencies of laminated beams are obtained by using an asymptotic splitting method. The results were compared with classical Euler“Bernoulli beam theory and Timoshenko beam theory

Analytic solutions for free vibration analysis of laminated beams in three-dimensional statement

In this research we consider free vibrations of laminated beams in terms of three-dimensional linear theory of elasticity. Analytic solutions for natural frequencies of laminated beams are obtained by using an asymptotic splitting method. The results were compared with classical Euler“Bernoulli beam theory and Timoshenko beam theory

New Possibilities and Applications of the Least Squares Collocation Method

Least squares collocation method (LSC) is a versatile numerical method for solving boundary value problems for PDE. The present article demonstrates the abilities of LSC to solve various problems – in particular, calculations of bending of isotropic irregular shaped plates and multi-layered anisotropic plates. In order to achieve higher accuracy, new versions of the method utilize high-degree polynomial spaces. The numerical experiments demonstrate high accuracy of the solutions

New Possibilities and Applications of the Least Squares Collocation Method

Least squares collocation method (LSC) is a versatile numerical method for solving boundary value problems for PDE. The present article demonstrates the abilities of LSC to solve various problems – in particular, calculations of bending of isotropic irregular shaped plates and multi-layered anisotropic plates. In order to achieve higher accuracy, new versions of the method utilize high-degree polynomial spaces. The numerical experiments demonstrate high accuracy of the solutions

Software for brain tumor diagnosis on magnetic resonance imaging

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