Article
Mathematics, Applied
Darko Volkov, Yulong Jiang
Summary: This paper presents a Lipschitz stability result for a crack inverse problem in half space, focusing on the unknown geometry and location of the crack. By assuming certain conditions on the geometry, it is shown that the inverse problem is uniquely solvable, highlighting the stability of reconstructing the crack plane despite the unknown forcing term.
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
(2021)
Article
Mathematics
Marat Tleubergenov, Gulmira K. Vassilina
Summary: This study examines one of the inverse problems of dynamics in the presence of random perturbations, specifically the simultaneous construction of a set of first-order Ito stochastic differential equations with a given integral manifold and a set of comparison functions. The given manifold is stable in probability with respect to these comparison functions.
Article
Physics, Nuclear
N. A. Khokhlov
Summary: This study extends previous results on solving the inverse problem of quantum scattering theory, specifically focusing on the Marchenko theory with fixed -l inversion. By using isosceles triangular-pulse functions, the input kernel of the Marchenko equation is expanded in a separable form, allowing for a reduction of the equation to a system of linear equations. The linear expression of the input kernel is obtained in terms of Fourier series coefficients, which enables the determination of the potential function of the radial Schrodinger equation with high accuracy. A numerical algorithm is developed and implemented to analyze NN elastic scattering data.
Article
Physics, Nuclear
N. A. Khokhlov, L. Studenikina
Summary: A new algebraic method based on the Marchenko theory is introduced to solve the inverse problem of quantum scattering theory. By using a triangular wave set and a separable form, the method can reconstruct complex potentials from scattering data within a finite range, providing accurate descriptions of the scattering matrix below and above the threshold of inelasticity.
Article
Mathematics, Applied
Zineb Bouslah, Abdelhak Hadj, Hacene Saker
Summary: This paper addresses the Robin inverse problem for the biharmonic equation in a 2D simply connected domain. It proposes a method based on nonlinear boundary integral equation to reconstruct the shape of the boundary. By applying the Newton iterative technique and Frechet derivatives, the system can be linearized and the injectivity of the linearized system is established. Numerical examples are provided to illustrate the feasibility of the method.
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
(2023)
Article
Mathematics, Applied
Abdelhak Hadj, Hacene Saker
Summary: This study focuses on recovering Robin coefficients on a non-accessible part of the boundary in a planar domain from measured data using Tikhonov regularization method. The feasibility of this approach is demonstrated through numerical reconstructions of the missing Cauchy data on the known boundary curve.
APPLIED NUMERICAL MATHEMATICS
(2021)
Article
Mathematics, Applied
Mikhail Y. Medvedik, Yury G. Smirnov, Aleksei A. Tsupak
Summary: This article investigates the vector problem of reconstructing an unknown permittivity of an inhomogeneous body. The original problem of Maxwell's equations with an unknown permittivity and a given permeability is simplified into a system of integro-differential equations. The solution to the inverse problem is obtained through two steps. Firstly, a solution to the first-kind vector integro-differential equation is obtained from the given near-field data. The uniqueness of the solution to the first-kind integro-differential equation is proven in the class of piecewise constant functions. Secondly, the sought-for permittivity is calculated directly from the found solution and the total electric field. A series of test problems were solved using the two-step method, and procedures for refining approximate solutions were implemented. A comparison between the given permittivities and the found approximate solutions demonstrates the efficiency of the proposed method.
JOURNAL OF INVERSE AND ILL-POSED PROBLEMS
(2023)
Article
Mathematics, Applied
Valeria Martynova, Dmitry Valovik
Summary: The paper focuses on the problem of nonlinear electromagnetic wave propagation in a plane shielded waveguide filled with a nonlinear medium. The authors aim to find nonlinear eigenvalues corresponding to the propagation constants of the waveguide. They develop a nonlinear perturbation approach using a simpler nonlinear problem and prove the existence of nonlinearizable solutions to the main problem. Numerical results are also presented, and the electromagnetic background for the main problem is briefly discussed.
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
(2023)
Article
Mathematics, Applied
Alexandr Ovanesovich Vatulyan, Victor Olegovich Yurov
Summary: The study presents a scheme for solving the inverse problem of reconstructing the radial change in the Lame parameters and density in a cylindrical waveguide, using displacement fields corresponding to different loading types as additional information. An iterative process and regularization method are used to recover the functions, with a series of computational experiments conducted to discuss the role of initial approximation and frequency range.
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
(2021)
Article
Mathematics, Applied
V. G. Romanov
Summary: The paper focuses on the inverse problem of recovering two variable coefficients from phaseless information in electrodynamic equations related to non-conducting dispersible medium. The inverse problem is reduced to two subproblems: the inverse kinematic problem and the integral geometry problem. The uniqueness theorem has been stated for the first problem, but the second problem remains open. The paper proposes some natural assumptions, analyzes the weight function, and suggests numerical algorithms.
APPLICABLE ANALYSIS
(2022)
Article
Mathematics
Asselkhan Imanbetova, Abdissalam Sarsenbi, Bolat Seilbekov
Summary: This paper investigates the existence and uniqueness of the classical solution to inverse problems for a fourth-order hyperbolic equation with a complex-valued coefficient. By using the separation of variables method, formal solutions are obtained in the form of a Fourier series with eigenfunctions of a non-self-adjoint fourth-order ordinary differential operator. The proofs of the uniform convergence of the Fourier series rely on estimates of the derivatives' norms of the eigenfunctions and the uniform boundedness of the Riesz bases.
Article
Mathematics
Abdallah El Hamidi, Mokhtar Kirane, Ali Tfayli
Summary: This paper investigates the inverse problem of finding the solution of a generalized time-space fractional equation and the source term. The existence and continuity of the solution for both the direct and inverse problem are proven using Fourier's method and the Schauder fixed-point theorem. The paper points out the incorrect use of estimates in the generalized Mittag-Leffler functions in previous studies, which results in false proofs of Fourier series' convergence. The paper establishes the correct framework to recover the decay of fractional Fourier coefficients and accurately recover the initial data, boundary conditions, and partial differential equations in the space-time domain.
Article
Mathematics
Suzan Cival Buranay, Mehmet Ali Ozarslan, Sara Safarzadeh Falahhesar
Summary: This paper aims to numerically solve first kind linear Fredholm and Volterra integral equations using Modified Bernstein-Kantorovich operators. Through discretization, the equations are transformed into systems of algebraic linear equations. By introducing regularization features, stability of the solutions and accuracy of results are improved, especially when high order approximations are used with the operators.
Article
Engineering, Electrical & Electronic
Anna I. Repina, Alina O. Oktyabrskaya, Alexander O. Spiridonov, Ilya V. Ketov, Evgenii M. Karchevskii
Summary: This article discusses how to achieve a trade-off between the high directionality of emissions and low threshold gain in active eccentric microring cavities, highlighting that the size and location of the air hole control the emission directivities and gain threshold values of working modes. The developed code allows for elementary optimization of the considered cavity, promising to be an engineering tool in the design of microring lasers.
IET MICROWAVES ANTENNAS & PROPAGATION
(2021)
Article
Mathematics, Applied
Jaan Janno, Yavar Kian
Summary: In this article, we study the inverse source problems for time-fractional diffusion equations using a posteriori boundary measurement. We solve these inverse problems for different space- or time-dependent source terms by utilizing the memory effect of these equations. Furthermore, we prove the unique determination of a general class of space-time-dependent separated variables source terms from such measurement. Our approach is based on the analysis of singularities in the Laplace transform of boundary traces of solutions of time-fractional diffusion equations.
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
(2023)
Article
Biophysics
Reijer Leijsen, Cornelis van den Berg, Andrew Webb, Rob Remis, Stefano Mandija
Summary: Magnetic resonance electrical properties tomography (MR-EPT) is a technique used to estimate the conductivity and permittivity of tissues from MR measurements. Different reconstruction methods have limitations. In this study, we explore the feasibility of a hybrid approach by using MR-EPT or DL-EPT as initialization guesses for standard 3D CSI-EPT.
NMR IN BIOMEDICINE
(2022)
Article
Radiology, Nuclear Medicine & Medical Imaging
Thomas O'Reilly, Andrew G. Webb
Summary: Low-field MRI at 50 mT provides shorter T-1 relaxation times for tissues compared to higher field strengths, except for cerebrospinal fluid. T-2 relaxation times are similar to those at typical clinical field strengths. Segmentation of white and gray matter based purely on T-1 or T-2 is challenging at low field strengths due to small differences in relaxation times.
MAGNETIC RESONANCE IN MEDICINE
(2022)
Article
Pharmacology & Pharmacy
Frank M. P. van Haren, Lex M. van Loon, Anne Steins, Thomas L. Smoot, Caitlin Sas, Sabrina Staas, Alicia B. Vilaseca, Ruben A. Barbera, Gustavo Vidmar, Hugo Beccari, Frida Popilevsky, Eleonora Daribayeva, Bhuvaneshwari Venkatesan, Susan Mozes, Rachel Postel, Natalie Popilevski, Andrew Webb, Quentin Nunes, John G. Laffey, Antonio Artigas, Roger Smith, Barry Dixon, Alice Richardson, Hwan-Jin Yoon, Clive Page
Summary: This study retrospectively evaluated the safety and efficacy potential of inhaled nebulised UFH in hospitalised patients with COVID-19. The results showed improvement in oxygenation levels with inhaled UFH, but no clinically significant increase in APTT. Patients receiving therapeutic anticoagulation had a higher risk of adverse events.
BRITISH JOURNAL OF CLINICAL PHARMACOLOGY
(2022)
Editorial Material
Engineering, Electrical & Electronic
Marine A. C. Moussu, Redha Abdeddaim, Marc Dubois, Elodie Georget, Andrew G. Webb, Elizaveta Nenasheva, Pavel Belov, Stanislav Glybosvski, Luisa Ciobanu, Stefan Enoch
Summary: This article is a reply to the comments on a previous article about the use of high-permittivity dielectric ring resonators as microscopy magnetic resonance probes.
IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION
(2022)
Article
Biophysics
Chloe Najac, Vincent O. Boer, Hermien E. Kan, Andrew G. Webb, Itamar Ronen
Summary: This study proposes an improved method using J-sLASER sequence to quantify J-coupled metabolites at ultrahigh field (UHF). Compared with the traditional sLASER sequence, J-sLASER sequence can reduce the quantification error of J-coupled metabolites and achieve satisfactory results in experiments.
NMR IN BIOMEDICINE
(2022)
Article
Multidisciplinary Sciences
Amir Seginer, Rita Schmidt
Summary: Magnetic resonance imaging (MRI) is a powerful technique that provides a range of measurements. This study presents a new approach to achieve high-resolution T-2 mapping in ultra-high field MRI, addressing the challenges associated with it. The method allows fast 3D whole brain imaging without requiring special hardware, making it highly valuable in clinical practice.
SCIENTIFIC REPORTS
(2022)
Review
Pharmacology & Pharmacy
Joshua Koslover, Deborah Bruce, Shivani Patel, Andrew J. Webb
Summary: We reviewed the pharmacological and prescribing principles of metformin using the mnemonic framework 'BRAINS & AIMS' (Benefits, Risks, Adverse Effects, Interactions, Necessary prophylaxis, Susceptibilities, Administering, Informing, Monitoring, and Stopping). Metformin is used for the treatment of type 2 diabetes mellitus (T2DM) and in reducing the risk or delaying the onset of the disease. However, there is no clear evidence that metformin influences patient-important outcomes. The drug is inexpensive and considered essential by WHO, but contraindicated or not tolerated in 15% of patients, such as those with renal impairment and a risk of lactic acidosis. Common adverse effects include gastrointestinal side effects and vitamin B-12 deficiency. Interactions may occur with drugs impairing renal function and those inhibiting specific transporters. It is necessary to detect and treat vitamin B-12 deficiency and consider the susceptibility of certain patient groups. The administration of metformin should start with a low dose and be titrated slowly. Renal function, HbA1c, and vitamin B-12 levels need to be monitored regularly. Stopping metformin is not associated with harm and should be considered in patients with worsening renal or liver function.
BRITISH JOURNAL OF CLINICAL PHARMACOLOGY
(2023)
Editorial Material
Pharmacology & Pharmacy
Andrew J. J. Webb
BRITISH JOURNAL OF CLINICAL PHARMACOLOGY
(2023)
Article
Radiology, Nuclear Medicine & Medical Imaging
Wyger M. Brink, Rob F. Remis, Andrew G. Webb
Summary: This study evaluates the impact of insulation material between high permittivity dielectric pads and the body using RF simulations and phantom experiments. The results show that removing the insulation material increases RF heating, indicating the importance of considering insulation properties for RF safety assessment.
MAGNETIC RESONANCE IN MEDICINE
(2023)
Article
Chemistry, Multidisciplinary
Rishabh Sharma, Panagiotis Tsiamyrtzis, Andrew G. Webb, Ioannis Seimenis, Constantinos Loukas, Ernst Leiss, Nikolaos Tsekos
Summary: The article introduces a method to improve low-quality MRI images using deep learning techniques (UNets) and conducts experimental evaluation. The results indicate that these UNets perform similarly in image upscaling. The study supports the potential of deep learning as an integral part of holistic approaches in MRI acquisitions, but emphasizes the importance of the actual data collection step.
APPLIED SCIENCES-BASEL
(2022)
Article
Radiology, Nuclear Medicine & Medical Imaging
Aashley S. D. Sardjoe Mishre, Borja Martinez-Tellez, Maaike E. Straat, Mariette R. Boon, Oleh Dzyubachyk, Andrew G. Webb, Patrick C. N. Rensen, Hermien E. Kan
Summary: This study demonstrates that coregistration and mutual thresholding can improve the variability in measuring fat fraction, and enhance the assessment stability of fat fraction changes in supraclavicular brown adipose tissue following cold exposure.
MAGNETIC RESONANCE IN MEDICINE
(2023)
Review
Radiology, Nuclear Medicine & Medical Imaging
Adrienne E. Campbell-Washburn, Kathryn E. Keenan, Peng Hu, John P. Mugler, Krishna S. Nayak, Andrew G. Webb, Johnes Obungoloch, Kevin N. Sheth, Juergen Hennig, Matthew S. Rosen, Najat Salameh, Daniel K. Sodickson, Joel M. Stein, Jose P. Marques, Orlando P. Simonetti
Summary: The first ISMRM Workshop on Low-Field MRI was held virtually in March 2022, discussing recent advancements in low field MRI technology and its clinical applications. With 368 registrants from 24 countries, the workshop included invited talks, abstract presentations, panel discussions, and live scanner demonstrations. The workshop emphasized the potential of low-field MRI in expanding MRI usage through cost reduction, portability, and ease of installation, as well as the challenges in overcoming SNR limitations and establishing clinical value.
MAGNETIC RESONANCE IN MEDICINE
(2023)
Review
Radiology, Nuclear Medicine & Medical Imaging
Andrew Webb, Thomas O'Reilly
Summary: This study aims to review the major hardware components of low-field point-of-care MRI systems that affect the overall sensitivity. The designs of magnet, RF coils, transmit/receive switches, preamplifiers, data acquisition system, and methods for grounding and mitigating electromagnetic interference are reviewed and analyzed. The results show that high homogeneity magnets can be produced in various designs and using Litz wire for RF coil designs enables high Q values. Different schemes are available to address the low coil bandwidth issue. Good RF shielding, proper electrical grounding, and effective electromagnetic interference reduction can lead to substantial increases in image signal-to-noise ratio. It is suggested that a standardized set of sensitivity measures should be determined for meaningful comparisons and optimizations.
MAGNETIC RESONANCE MATERIALS IN PHYSICS BIOLOGY AND MEDICINE
(2023)
Article
Radiology, Nuclear Medicine & Medical Imaging
Javad Parsa, Andrew Webb
Summary: The study aims to simulate the magnetic and electric fields produced by commonly used RF coil geometries at low field, and to derive the specific absorption rate (SAR) efficiency based on these simulations. The results showed that SAR efficiency needs to be carefully considered only when using TSE sequences with 180 degrees refocusing pulses of duration similar to 10 ms.
MAGNETIC RESONANCE MATERIALS IN PHYSICS BIOLOGY AND MEDICINE
(2023)
Review
Radiology, Nuclear Medicine & Medical Imaging
Andrew Webb, Alena Shchelokova, Alexey Slobozhanyuk, Irena Zivkovic, Rita Schmidt
Summary: This article reviews recent developments in designing and testing new types of materials for MRI scans, which can improve the image quality for both in vivo and magnetic resonance microscopy applications. The article discusses the basic operation and design of different types of materials, as well as their applications in various imaging scenarios. However, practical issues have hindered the widespread use of these new materials in clinical applications.
MAGNETIC RESONANCE MATERIALS IN PHYSICS BIOLOGY AND MEDICINE
(2022)
